| Perspective | Method | Characteristic | Representative Work |
| Action-Environment Interactions | Incorporating Feedback | Use environment feedback to filter trajectories | Ni et al. (2024); Xin et al. (2024b) |
| Training External Models | Train models (e.g., to critic) from the interaction | Wu et al. (2024c) |
| Search with Verifiers | Use verifiers to identify better reasoning trajectories | Wan et al. (2024c) |
| Distillation from Teacher | Distill capability from frontier reasoning model | Gou et al. (2024); Ma et al. (2024a) |
| Training from Trajectories | Supervised Fine-Tuning | Collected offline trajectories + learn via SFT | Dou et al. (2024b); Yin et al. (2024) |
| Reinforcement Learning | Learning directly on questions and their rewards | Shao et al. (2024) |
| Learning with Refiner | Train refiner model to iteratively improve the last-round solution. | Xiong et al. (2025) |
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| Designing Communication | Centralized communication | Use a centralized controller for information aggregation | Canese et al. (2021); Matta et al. (2019) |
| Conditioned information sharing | Share information based on relevancy and privacy | Hong et al. (2023); Qiu et al. (2024) |
| Coordinating Actions | Leverage knowledge | Utilize expert knowledge as constraints | Lau et al. (2012) |
| Graph-based methods | Use graphs as structured frameworks | Ruan et al. (2022); Li et al. (2020) |
| Hierarchical approach | Divide policies to strategy and execution | Xu et al. (2023) |
| Training from Trajectories | Training data from interactions | Obtain high-quality trajectories from interactions | Li et al. (2024c); Estornell et al. (2024) |
| Gradient modification | Modify gradients towards optimal points | Li et al. (2024f) |
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+ "content": "Challenges in reward modeling Early studies have investigated the feasibility of process supervision (Lightman et al., 2024) and its effectiveness in inference-time scaling (Snell et al., 2025). However, its high annotation costs and ambiguous definition—particularly in long CoT scenarios where self-reflection is encouraged—have limited its adoption in large-scale reinforcement learning. Despite these challenges, the key advantage of accurate process supervision is its ability to reduce hallucinations, making it essential for automated reasoning and knowledge discovery. Additionally, as discussed in Section 4.2, the training paradigm for reward models is closely tied to that of reasoning models. This raises concerns about whether allocating the same annotation budget directly to reasoning models could lead to more stable and general improvements, potentially limiting the gains achievable through inference-time scaling."
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+ "content": "In this work, we provide a timely and comprehensive survey on LLM reasoning. We first formalize the goal of LLM reasoning and consolidate past research by categorizing reasoning techniques along two dimensions: regimes and architectures. Within each of these dimensions, we review both input and output perspectives in detail. Our review highlights emerging trends, including the shift from inference-time scaling to learning-to-reason regimes, and the transition from standalone models to agentic systems. We also review and compare a wide range of learning algorithms, including supervised fine-tuning and reinforcement learning, as well as the training of reasoners and training of verifiers. Despite these advancements, challenges remain in evaluating reasoning and understanding real reasoning mechanisms as well as addressing data challenges in advancing reasoning capabilities. We encourage future research to further explore these trends, such as inference-aware learning-to-reason and automated multi-agent design, to enhance LLM reasoning."
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+ "content": "Jingming Zhuo, Songyang Zhang, Xinyu Fang, Haodong Duan, Dahua Lin, and Kai Chen. ProSA: Assessing and understanding the prompt sensitivity of LLMs. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen (eds.), Findings of the Association for Computational Linguistics: EMNLP 2024, pp. 1950-1976, Miami, Florida, USA, November 2024. Association for Computational Linguistics. doi: 10.18653/v1/2024.findings-emnlp.108. URL https://aclanthology.org/2024 findings-emnlp.108/."
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+ {
+ "type": "text",
+ "text": "VisuoThink: Empowering LVLM Reasoning with Multimodal Tree Search",
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+ "text": "Yikun Wang $^{12}$ , Siyin Wang $^{12}$ , Qinyuan Cheng $^{1}$ , Zhaoye Fei $^{1}$ , Liang Ding $^{3}$ , Qipeng Guo $^{24}$ , Dacheng Tao $^{5}$ , Xipeng Qiu $^{\\dagger 12}$",
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+ "text": "$^{1}$ Fudan University $^{2}$ Shanghai Innovation Institute",
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+ {
+ "type": "text",
+ "text": "| References | Focus |
| [19] | A review of cybersecurity threats, countermeasures, and research gaps in UAV networks, with a focus on emerging attack surfaces and commercial UAV applications |
| [20] | A survey of security threats, vulnerabilities, and countermeasures in UAV swarm networks, with a focus on classifying attack types and reviewing emerging defense technologies |
| [21] | A review of security threats, vulnerabilities, and countermeasures in UAVs and Flying Ad Hoc Networks with attack surface analysis with simulation-based evaluation |
| [22] | A survey of vulnerabilities across software, hardware, and communication layers in UAV systems, and an exploration of emerging defense technologies |
| [23] | A survey of security challenges in drone communication and a review of emerging technologies used to enhance the speed, reliability, and security of UAV networks |
| [24] | A review of UAV security challenges, existing controls, and future research directions, with an emphasis on the transformative role of AI in enabling secure UAV systems |
| [25] | A review of security threats classified from a cyberspace security perspective and countermeasures in UAV systems |
| [26] | A survey of security threats, requirements, and counter-measures in UAV-aided Internet of Things (IoT) applications |
| [27] | A survey of cybersecurity vulnerabilities and countermeasures in UAV systems, integrating threat classification, communication protocols, and emerging techniques |
| [28] | A survey of PLS in UAV communications, focusing on key challenges, methodologies, and recent advancements for both static and mobile UAV deployment scenarios |
| [29] | A review of security challenges, practical deployment aspects, and standardization progress associated with integrating UAVs into cellular networks |
| [30] | A survey of layer-wise cybersecurity threats and AI-enabled countermeasures in UAV-assisted IoT applications |
",
+ "bbox": [
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "systems. The authors in [21] provide a detailed examination of security challenges in UAVs and FANETs, covering various attack vectors including communication, identity-based, resource, routing, data, and machine learning attacks. The study in [22] examines security and privacy vulnerabilities in UAV systems across hardware, software, and communication layers. It discusses various threats such as eavesdropping and jamming attacks, and presents defense mechanisms including blockchain, machine learning-based intrusion detection, and secure communication protocols.",
+ "bbox": [
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+ "page_idx": 2
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+ "type": "text",
+ "text": "Some studies emphasize cyber security challenges within UAV networks. The study in [23] comprehensively reviews security issues in drone communication, including Denial of Service (DoS), GPS spoofing, and man-in-the-middle attacks. It examines vulnerabilities across different drone applications and presents countermeasures using blockchain, software-defined networks, machine learning, and fog computing. The authors of [24] provide a comprehensive survey of security challenges in UAV systems, including various types of attacks, privacy concerns, and trust issues. It identifies current research trends and gaps while establishing a future roadmap with a focus on artificial intelligence (AI)'s potential to enhance UAV security. The authors in [25] provide a comprehensive review of security issues in UAV networks, examining various potential attacks such as spoofing, replay, jamming, and",
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+ "type": "text",
+ "text": "TABLE II",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "CHALLENGES AND SOLUTIONS",
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+ "text": "RED CIRCLES DESCRIBE THE SECURITY ISSUES; GREEN CIRCLES REPRESENT THE OVERALL COUNTERMEASURES FOR THE SECURITY ISSUES; GREEN CHECK MARKERS INDICATE DIFFERENT TYPES OF SOLUTIONS UNDER EACH COUNTERMEASURE",
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+ "table_body": "| Section III, Challenge 1: Communication confidentiality |
| Issues | ● Eavesdropping attack [46], [50]● Unauthorized access [31], [51], [52] |
| Solutions | ● Anti-eavesdropping strategies√ Convex optimization-based strategies [53]–[59]√ Reinforcement learning-based strategies [60]–[65]√ Deep learning-based strategies [66]–[71]● Communication authentication√ PUFs-based authentication [72]–[74]√ Channel based-authentication [75]–[77] |
| Section IV, Challenge 2: Communication availability |
| Issues | ● Jamming attack [48], [78], [79]● Spoofing attack [49], [50], [52], [78] |
| Solutions | ● Anti-jamming strategies√ Convex optimization [80]–[82]√ Single-agent RL [83]–[86]√ Multi-agent RL [87]–[89]● Spoofing defense√ PLA [77], [90], [91]√ GNSS spoofing detection [92]–[94] |
| Section V, Challenge 3: Communication Integrity |
| Issues | ● Anomalous behaviors [61], [95], [96]● Injection attacks [28], [46], [97] |
| Solutions | ● Anomaly detection√ Jamming anomaly detection [98]–[101]√ Abnormal power detection [102]√ Eavesdropping anomaly detection [103]● Injection defense√ Jamming signal injection defense [98], [101], [104]● Spoofing signal injection defense [105]–[107] |
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+ {
+ "type": "text",
+ "text": "eavesdropping attacks. It categorizes these threats and presents corresponding security technologies and countermeasures. The study in [26] provides a comprehensive review of security issues in UAV-aided IoT applications and presents corresponding security technologies and countermeasures. The work in [27] reviews cybersecurity threats affecting UAV systems and evaluates existing countermeasures in enhancing UAV security.",
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+ "text": "In addition, some surveys analyze the challenges faced by UAV systems from a layered perspective (e.g., physical layer, link layer, network layer, application layer). The work in [28] deeply reviews the current state of physical layer security (PLS) in UAV communications, examining unique air-to-ground channel characteristics, static and mobile UAV deployment scenarios, and various security enhancement techniques. The work in [29] presents a comprehensive overview of UAV cellular communications, covering the classification of consumer drones, the concept and potential of UAV-mounted flying base stations. It explores the integration of UAVs into cellular networks as novel user equipment and addresses key challenges related to interference, regulatory compliance, and security. The authors of [30] review the cybersecurity landscape of UAV-assisted IoT applications, examining layer-wise security threats from physical to application layers. It explores how AI, ML, deep learning (DL), and reinforcement learning (RL) techniques have been employed to address authentication, data privacy, and attack prevention challenges.",
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+ "TABLE III",
+ "LIST OF ABBREVIATIONS"
+ ],
+ "table_footnote": [],
+ "table_body": "| Abbreviation | Description | Abbreviation | Description |
| A2G | Air-to-ground | ABS | Aerial Base Station |
| AN | Artificial Noise | AI | Artificial Intelligence |
| BCD | Block Coordinate Descent | BS | Base Station |
| CNN | Convolutional Neural Network | CSI | Channel State Information |
| DDPG | Deep Deterministic Policy Gradient | DDQN | Double-deep Q-Learning |
| DL | Deep Learning | DNN | Deep Neural Network |
| DQN | Deep Q-Network | eVTOL | Electric Vertical Take-off and Landing |
| DRL | Deep Reinforcement Learning | FAR | False Alarm Rate |
| G2A | Ground-to-air | G2U | Ground-to-UAV |
| GAN | Generative Adversarial Network | GNSS | Global Navigation Satellite System |
| GPS | Global Positioning System | GS | Ground Station |
| IoT | Internet of Things | LAENet | Low-Altitude Economy Networking |
| LSTM | Long Short-Term Memory | LoS | Line-of-sight |
| MARL | Multi-agent Reinforcement Learning | MDP | Markov Decision Process |
| MDR | Miss Detection Rate | MEC | Mobile Edge Computing |
| ML | Machine Learning | MSE | Mean Square Error |
| NOMA | Non-orthogonal Multiple Access | PLA | Physical-layer Authentication |
| PLS | Physical Layer Security | PUF | Physical Unclonable Function |
| QoE | Quality of Experience | RF | Radio Frequency |
| RIS | Reconfigurable Intelligent Surfaces | RL | Reinforcement Learning |
| RNN | Recurrent Neural Network | RSS | Received Signal Strength |
| SCA | Successive Convex Approximation | SDNR | Signal-to-disturbance-plus-noise Ratio |
| SNR | Signal-to-noise Ratio | SOC | Second-Order Cone |
| TDMA | Time-division Multiple Access | THz | Terahertz |
| U2G | UAV-to-ground Communication | UAV | Unmanned Aerial Vehicle |
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+ "text": "B. Contributions of Our Survey",
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+ "text": "The related surveys and tutorials primarily focus on the classification of overall security threats and corresponding countermeasures in UAV networks or UAV-assisted applications, with relatively little attention given to security issues of communication in the physical layer. Different from existing studies, our survey uniquely concentrates on the security challenges specific to physical layer communications in the LAENet, as summarized in Table II. It fills a critical gap in the literature by conducting an in-depth analysis of threats in physical layer communications that were previously underexplored or only briefly mentioned in prior studies. By offering a comprehensive and systematic analysis of these underexplored issues, our work brings new insights to seek effective solutions to enhance physical layer security in communications of the LAENet. The key contributions of this paper are summarized as follows:",
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+ "text": "The key contributions of this paper are summarized as follows:",
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+ "- A thorough discussion of the six main security issues in the physical layer communication of the LAENet is presented, namely, eavesdropping attack, unauthorized access, jamming attack, spoofing attack, anomalous behaviors, and injection attack. We analyze these attacks in the context of their potential occurrence throughout the entire operation of LAENet, providing essential references for ensuring the security of physical layer communication in the future LAENet deployments.",
+ "- We review countermeasures against various attacks in detail and offer a comprehensive tutorial on achieving communication confidentiality, communication availability, and communication integrity in LAENet. In addition,"
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+ "text": "the lessons learned for each security issue are presented to emphasize the limitations of existing works and provide high-level insights for improvements.",
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+ "text": "- Several potential future research directions for secure physical layer communication in LAENet are proposed, including energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. These diverse perspectives offer new guidance for future research on secure physical layer communication in LAENet.",
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+ "text": "The remainder of this paper is given as follows. Section II introduces the background of the LAENet and security issues in physical layer communication of the LAENet. In Section III, a comprehensive exploration of achieving communication confidentiality for the LAENet is presented. Section IV reviews the solutions for communication availability in the LAENet. In Section V, countermeasures on communication integrity for the LAENet are discussed. Section VI provides future research directions, and Section VII concludes this paper. Additionally, Table III lists the abbreviations commonly employed throughout this survey.",
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+ "text": "In this section, we introduce the background of the LAENet, including its definition and application scenarios. Subsequently, the concept of physical layer communication in the LAENet and its security threats are elaborated in detail.",
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+ "Fig. 2. Background knowledge of the LAENet and security issues in its physical layer communication. Describe the definition of the LAENet and its communication application scenarios. Elaborate on three key metrics for secure physical layer communication: communication confidentiality, which combats eavesdropping attacks and unauthorized access; anti-jamming strategies and spoofing defense for ensuring communication availability; and anomaly detection and injection defense to prevent adversaries from compromising communication integrity."
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+ "text": "able seamless communication, coordination, and management of diverse aerial operations within low-altitude airspace [1], [108]. The LAENet includes numerous different types of constituents, such as flight equipment, base stations, and other communication platforms. Specifically, the LAENet connects various aerial vehicles, including general aviation aircraft for passenger transport and emergency rescue, drones for surveillance and logistics, and eVTOL designed for urban air mobility and last-mile cargo delivery [109], [110]. These aerial vehicles can incorporate ground and aerial base stations, further high-altitude platforms, such as weather balloons and satellites, to receive environmental information and precise navigation [13].",
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+ "text": "Different from traditional aviation networks that rely on centralized air traffic control, the LAENet can independently construct communication and networking by seamlessly interconnecting a variety of aerial and ground-based systems, which enables continuous information exchange, flight path optimization, and autonomous operations [8], [111]. Therefore, the LAENet has opened opportunities for various application scenarios and plays key roles from the perspective of communication coverage and relay [112]–[114]. Specifically, the LAENet can extend the communication coverage by deploying aircraft as ABSs in areas lacking communication infrastructure [115]–[117]. For instance, these ABSs deployed at optimal altitudes can provide connectivity and network services in remote or disaster-stricken areas [118], [119]. Moreover, if the direct communication links between ground base stations and user equipment are unreliable, such as in",
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+ "text": "mountainous regions and densely populated areas, the aircraft can act as mobile relays to improve connectivity by capturing, amplifying, and transmitting communication signals [120]–[122]. It also can be regarded as a surveillance unit to monitor airspace dynamics while simultaneously functioning as a low-altitude network orchestrator to optimize communication and computing resources [118], [123], [124].",
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+ "text": "To integrate and evolve these capabilities, the LAENet needs to establish effective communication infrastructure to ensure reliable connectivity and efficient interaction across various environments [31], [125]. Physical layer communication, as the bottom layer in the network architecture, may directly influence the communication performance of the LAENet across aerial and terrestrial networks [43], [46]. For example, it governs how signals are generated, transmitted, and received between aircraft and base stations [31]. Building on this, it manages the channel and spectrum resources to enhance signal transmission quality and maintain stable connectivity [43]. Therefore, ensuring the security of physical layer communication in the LAENet is crucial for supporting a wide range of applications in low-altitude domains.",
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+ "text": "Based on previous studies [126], [127], we discuss the security issues in the physical layer communication of the LAENet from three aspects: confidentiality, availability, and",
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+ "text": "integrity of communications. The details of each measurement are described as follows.",
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+ "- The confidentiality of physical layer communications in the LAENet can be compromised by security threats such as eavesdropping and unauthorized access [128]. Eavesdropping arises primarily from the broadcast nature of wireless signals and LoS link, making transmissions highly susceptible to interception [46]. An eavesdropper silently capturing or intercepting signals can lead to the exposure of confidential information. Meanwhile, unauthorized access threats exploit the open and broadcast nature of UAV communications [31]. Attackers may gain illegal access to the LAENet by disguising themselves as legitimate UAVs or ground stations, thereby deceiving or interfering with the normal operation of UAVs [51].",
+ "- Similarly, the open nature of wireless channels and LoS propagation bring jamming and spoofing security issues for communication availability [78]. Specifically, jammers can continuously transmit interference signals to disrupt communication, where a jammer can be a drone or a base station [48]. The spoofing attack can not only achieve identity spoofing by forging legitimate transmission identities but also launch signal deception attacks to disrupt UAV communications and positioning [49]. Therefore, jamming and spoofing lead to unauthorized access and signal disruptions or errors, making communication unavailable in the LAENet.",
+ "- Integrity as a microscopic metric measures the deviations of signals, channels, and spectrum in communication under adversaries' influence [129]. The communication integrity of the LAENet can be affected by anomalous behaviors and injection attacks. Anomalous behaviors often use dynamic spectrum access and the open wireless medium, including abnormal jamming, abnormal transmission power, and covert eavesdropping [95]. These anomalous behaviors can introduce harmful interference, violate spectrum policies, and expose sensitive information to eavesdroppers [61], [96]. Moreover, the injection attack exploits the open nature of wireless channels to alter signals or inject illegal signals, such as spoofing signals or malicious GNSS signals, to deceive receivers and interfere with communication, thereby leading to degraded signal quality, false navigation, and network congestion [28], [46], [97]."
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+ "type": "text",
+ "text": "Overall, as illustrated in Fig. 2, this survey reviews existing research on achieving communication confidentiality, availability, and integrity for the LAENet. Specifically, the investigation of anti-jamming strategies and communication authentication schemes aims to enhance communication confidentiality. Studies on anti-jamming techniques and spoofing defense mechanisms have been explored to ensure communication availability. Furthermore, research on communication integrity has focused on anomaly detection and injection attack mitigation approaches.",
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+ "text": "III. COMMUNICATION CONFIDENTIALITY FOR LAENET",
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+ "text": "The LAENet faces significant eavesdropping threats due to the inherent vulnerabilities of UAV-enabled wireless communications. The openness of wireless channels, especially the LoS links in air-to-ground (A2G) and ground-to-air (G2A) communications, increases susceptibility to interception by eavesdroppers that disrupt legitimate communications compared to traditional terrestrial channels [50]. Traditional cryptographic methods, while effective in many scenarios, are less suitable for UAV communications due to their computational complexity and the dynamic mobility of UAVs [130]. This highlights the critical need for robust security measures to ensure the confidentiality and reliability of the LAENet communications. To address these limitations, leveraging PLS techniques to counter eavesdropping threats effectively has emerged as a promising solution [131]-[134].",
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+ "text": "In the LAENet, anti-eavesdropping solutions can leverage the controllable mobility of low-altitude aircraft to enhance physical layer security. By dynamically optimizing their trajectories, low-altitude aircraft can actively adapt their flight paths to shape the communication environment [135]. This approach allows them to fly closer to legitimate ground nodes, strengthening communication links and improving channel conditions for intended receivers, while simultaneously distancing themselves from potential eavesdroppers. In this subsection, we present a critical role of UAV trajectory in forming the communication environment, and how PLS can be enhanced through trajectory optimization and resource allocation to mitigate eavesdropping risks. Our analysis focuses on three prominent methodologies in this domain: convex optimization, deep learning, and reinforcement learning.",
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+ "text": "Convex optimization plays a crucial role in addressing anti-eavesdropping challenges in UAV-enabled communication networks, particularly for solving the joint optimization of trajectory and resource allocation [137]. Due to the inherent non-convex nature of these problems, advanced convex optimization techniques such as Successive Convex Approximation (SCA) and Block Coordinate Descent (BCD) are widely utilized [135]. These methods enable UAVs to enhance physical layer security by optimizing flight paths and resource utilization, minimizing the risk of eavesdropping while ensuring secure and efficient communication. Additionally, the decision variables may be discrete, which requires the application of various relaxation methods to transform the complex optimization problem into a more tractable form to obtain efficient solutions [138].",
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+ "text": "The study in [53] explores physical-layer security in UAV-assisted Mobile Edge Computing (MEC) systems in the presence of multiple ground-based eavesdroppers. The proposed system utilizes dual UAVs for task execution and anti-eavesdropping measures. One UAV operates as a mobile MEC server, while the other emits jamming signals to disrupt eavesdroppers, as shown in Fig. 3. The time-division multiple access (TDMA) scheme and non-orthogonal multiple access (NOMA) scheme are proposed to maximize the minimum secure computing capacity by jointly optimizing communica",
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+ "TABLE IV SUMMARY OF CONVEX OPTIMIZATION FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
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+ "| Ref | Optimization Objectives | Eavesdropper and Jammer Type | OptimizationConstraints | Pros & Cons |
| [53] | Secure calculation capacity1 | UAV jammer and fixed ground eavesdropper | Transmit power, time allocation, and computation capacity | BCD and P-BCD for secure calculation capacity maximization\n✓ Secure capacity of NOMA and TDMA has been significantly improved\nX High complexity for NOMA due to dual-loop iterations |
| [54] | Secure calculation capacity | Base station jammer and fixed ground eavesdropper | Transmission power, time allocation, and CPU processing frequency | JDPB algorithm with SCA and BCD for secure task offloading\n✓ Reduce complexity via region division\nX Fixed UAV altitude limits 3D trajectory optimization |
| [55] | Average secrecy rate2 | Antenna jammer and fixed aerial eavesdropper | Transmit power and jamming power | BCD and SCA optimization with hybrid FSO/RF links\n✓ Enhance communication security via hybrid FSO/RF links and AN\nX Rely on simplified channel models (e.g., free-space path loss) |
| [56] | Worst-case secrecy rate | UAV jammer and fixed ground eavesdropper | UAV speed, collision avoidance, positioning error, and energy harvesting | Robust 3D trajectory and time switching optimization\n✓ Full mobility of UAVs in 3D for improving secrecy rate\nX The performance may degrade with flying eavesdroppers |
| [57] | Average secrecy rate | None and flying eavesdropper | Transmit power control and user scheduling | Joint trajectory and communication design against mobile eavesdroppers\n✓ Initial trajectory design for keeping away from eavesdroppers\nX Security performance relies on the initial trajectory design |
| [58] | Secure calculation capacity | Ground jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | Integrate a dual-UAV system with a ground jammer in MEC\n✓ Incorporate the UAV server and UAV eavesdropper with a ground jammer\n✓ Allow a UAV server to hover near ground users for secure offloading\nX Numerous flight constraints may require extensive tuning |
| [59] | Secrecy rate | Coastal jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | A secure communication for UAV-relay-assisted maritime MEC\n✓ Simultaneously optimize multiple parameters for improved secrecy rate\nX Iterative decomposition increases the computational burden\nX Assume prior knowledge of Channel State Information (CSI) of devices |
",
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+ "type": "text",
+ "text": "tion resources, computation resources, and UAV trajectories. To address the non-convexity of the optimization problem, the problem is transformed into tractable forms via auxiliary variables and decomposition. Specifically, for the TDMA scheme, the problem is decoupled into two sub-problems using BCD. The communication and computation resources are optimized via second-order cone (SOC) constraints and SCA, while UAV trajectories are iteratively updated via first-order Taylor approximations to handle non-convex terms. For the NOMA scheme, a penalized BCD (P-BCD) algorithm is proposed to tackle binary constraints. The problem is split into three blocks that are penalty parameter adjustment, resource allocation via SOC and SCA, and trajectory optimization with convex relaxations. The experimental results demonstrate that the proposed algorithms significantly enhance secure computing capacity, with the NOMA scheme achieving up to about 4.3 Mbps and the TDMA scheme reaching about 4.2 Mbps under optimal conditions. Compared to baselines including the straight flight design and no power control, the proposed strategies improve secure computing capacity by about $20\\%$ to $30\\%$ , particularly in scenarios with lower power budgets (e.g., 0.2 W) and higher required computing bits (e.g., 1 Mbps). The convergence of the algorithms is achieved within 20 iterations, which indicates the efficiency in optimizing UAV trajectories and resource allocation for anti-eavesdropping.",
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+ "text": "The study in [53] mainly focuses on a dual-UAV-assisted secure MEC system. In some cases, multi-UAV systems hold great promise for collaboratively executing complex tasks while enhancing the secure communications [49], [54]. In the",
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+ "text": "work [54], the joint optimization of task offloading, trajectory planning, and resource allocation for secure communications in multi-UAV MEC systems is studied. Firstly, a base station emits jamming signals to protect against fixed-location ground eavesdroppers. Then, it investigated the joint optimization of task offloading, trajectory planning, and resource allocation for secure communications in multi-UAV MEC systems. The problem is decomposed into two sub-problems: (1) resource allocation and trajectory planning, addressed via SCA and BCD algorithms; (2) offloading decisions, solved through Joint Dynamic Programming and Bidding (JDPB) method. For the first sub-problem, non-convex constraints related to transmission power and UAV trajectory are transformed into convex forms using first-order Taylor expansion and relaxation techniques. Specifically, the transmission power optimization sub-problem is approximated via SCA, while the trajectory planning sub-problem is iteratively solved by introducing auxiliary variables and convex approximations. For the second sub-problem, a bidding mechanism is integrated with dynamic programming to reduce computational complexity by grouping dynamic users into sub-regions. The experimental results demonstrate that the proposed JDPB algorithm achieves a sum average secure calculation capacity of 10.1 Mbps in the first time slot. Additionally, under different settings of time slot sizes, transmission power, and flying speed, the sum average secure calculation capacity achieved by JDPB consistently outperforms baseline schemes such as the Greedy Strategy and the Random Strategy.",
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+ "text": "Unlike the above studies that deal with ground eavesdrop-",
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+ "image_caption": [
+ "Fig. 3. The overall architecture of the anti-eavesdropping strategy. Part A illustrates the system model against fixed ground eavesdroppers. In this setup, one UAV operates as a mobile server, while another UAV serves as a jammer to emit jamming signals to disrupt the eavesdroppers' interception capabilities. Part B presents the system model for flying eavesdroppers, where one UAV acts as the server, and another UAV functions as a mobile eavesdropper. To mitigate eavesdropping risks, a ground-based jammer actively emits interference signals to secure communications."
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+ "text": "pers, the work in [55] targets threats from aerial eavesdroppers and explores secure communication in a hybrid Free Space Optical (FSO) and Radio Frequency (RF) system. The UAV acts as both a relay and a jammer, emitting artificial noise (AN) during RF transmission to confuse a fixed-position aerial eavesdropper. The work introduces a novel perspective on protecting space-air-ground networks from eavesdropping by leveraging FSO for its inherent resistance to interception and jointly optimizing trajectory design and power allocation to maximize the secrecy rate with two transmission schemes. The first scheme is the slot-based scheme for delay-sensitive data. The trajectory sub-problem is convexified using first-order Taylor expansion to approximate elevation angle and channel gain constraints, while the power allocation sub-problem is transformed into a convex form by introducing a lower bound on transmit power to ensure convexity. The second scheme is the period-based scheme for delay-insensitive data, in which the relaxed constraints on sum secrecy rates over the entire flight period are adopted. A similar SCA method [54] is applied to convexly approximate the non-convex terms in the constraints. Compared to benchmark schemes without jamming power optimization, both methods achieve approximately 0.4 Mbps higher secrecy rates by integrating AN transmission",
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+ "text": "It is worth noting that most existing studies consider optimizing UAV trajectories on a 2D plane. However, optimizing UAV 3D trajectories may be more practical [139]. The study in [56] considers the UAV's 3D flight trajectory and imperfect knowledge of eavesdroppers' locations, while formulating an optimization approach to maximize the worst-case secrecy rate under various practical constraints, including maximum UAV speed, UAV collision avoidance, UAV positioning error, and UAV energy harvesting. To address the non-convexity of the optimization problem, the original problem is decomposed into multiple sub-problems using BCD and SCA techniques similar to studies in [54] and [55]. By incorporating the additional degree of freedom in the vertical dimension, the proposed approach improves the ability to avoid fixed eavesdropping zones, outperforming 2D trajectory models in maintaining secure communication links under dynamic conditions. Simulation results show that the average secrecy rate of the proposed 3D optimization scheme outperforms that of the fixed-height 2D benchmarks (set at $100\\mathrm{m}$ ) by over $20\\%$ .",
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+ "text": "Unlike the above studies that focus on fixed ground eavesdroppers, mobile eavesdroppers, such as hostile UAVs, introduce more complex threats due to their ability to maneuver, track, and position for intercept communications [22], [57]. For example, the authors in [57] address the challenges caused by a flying eavesdropper that exploits UAV LOS communication. This work focuses on jointly optimizing the UAV's trajectory, transmit power control, and user scheduling to maximize the minimum average secrecy rate, which enables dynamic adjustments to ensure secure communication even against an mobile eavesdropper.",
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+ "text": "Compared to the anti-eavesdropping strategies in [57] that rely heavily on accurate trajectory optimization and resource allocation, the studies in [58], [59] propose using a jammer to actively emit jamming signals, effectively reducing the interception capability of flying eavesdroppers during the computational offloading process of relay UAVs, as shown in Fig. 3. Meanwhile, with the support of SCA and BCD methods similar to [56], the joint optimization problem of UAV trajectories, resource allocation (including transmit power, time slot allocation, and computation capacity), and jamming strategies can be solved while ensuring practical constraints such as flight speed and anti-collision requirements. Importantly, compared to systems targeting fixed ground eavesdroppers, the works in [58], [59] enhance secure calculation capacity or secrecy rate by modeling the trajectories of both the relay UAV and the mobile eavesdropper as dynamic variables optimized over discrete time slots. Specifically, simulation results in [58] demonstrate that the secure calculation capacity of the proposed scheme converges to approximately 2.78 Mbps within 4 iterations, which is significantly higher than the baseline strategy (where only the location of the relay UAV, transmit power, and jamming power are optimized) by approximately 1.6 Mbps.",
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+ "type": "text",
+ "text": "Lesson Learned. Convex optimization has emerged as a fundamental tool for developing anti-eavesdropping strategies in UAV-enabled communication systems, particularly for addressing the inherent non-convexity of joint trajectory and",
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+ "img_path": "images/45d7c87df94084b85e80ffec3b31f41bc270ce4f3ed9cdb12fa2a0d42e0bd614.jpg",
+ "image_caption": [
+ "Part A. DDQN-based Scheme"
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+ "Part B. DDPG-based Scheme"
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+ "Part D. MAPPO-LSTM-based Scheme"
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+ "image_caption": [
+ "Part C. MADDPG-based Scheme",
+ "Fig. 4. The overall architecture of the RL for anti-eavesdropping. Part A describes the DDQN-based scheme, where the system state is used to generate actions through the DDQN network, followed by action execution and obtaining the next state and reward. An experience replay mechanism is employed to store and randomly sample training data. Part B presents the DDPG-based scheme, where actions are generated through Actor and Critic networks, interacting with the environment to obtain rewards. An experience replay buffer is used to store and sample mini-batches. Part C describes the MADDPG-based scheme, involving multiple UAV agents, each with its own Actor and Critic networks, interacting with the environment and sharing rewards. Part D showcases the MAPPO-LSTM-based scheme, where Actor and Critic networks with LSTM layers process time-series data and train through an experience replay buffer."
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+ "text": "resource allocation problems. For fixed eavesdroppers, simpler optimization models with fewer dynamic variables (e.g., 2D trajectory optimization) can achieve secure communication effectively. However, mobile eavesdroppers require more sophisticated formulations, including 3D trajectory optimization and robust constraints to account for uncertainties in eavesdropper positions. Another important insight is the adaptability of convex optimization when combined with complementary methods like artificial noise jamming and resource allocation strategies. By leveraging convex optimization, systems can balance secrecy performance with energy efficiency, ensuring practical applicability in real-world UAV operations. Techniques such as SCA and BCD have proven highly effective in decoupling complex optimization problems into solvable subproblems, allowing iterative refinement toward locally optimal solutions. Overall, convex optimization offers a flexible and mathematically rigorous approach to securing UAV-enabled communication systems for anti-eavesdropping.",
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+ "text": "As the number of ground devices increases, along with UAV flight time and the number of optimization variables, the computational complexity of conventional algorithms grows exponentially, leading to infeasibility or suboptimal solutions [140], [141]. Moreover, these methods struggle to adapt to real-time scenarios where UAVs must communicate with mobile users and operate in environments with uncertain or partial information [140], [142]. RL enables UAVs to interact with the environment and autonomously learn optimal policies based on real-time observations [143], as shown in Fig. 4. By leveraging Deep RL (DRL), UAVs can efficiently",
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+ "type": "text",
+ "text": "adapt to changing eavesdropping conditions, optimize secure trajectories, and dynamically allocate resources [144], [145]. This learning-driven approach significantly enhances PLS by ensuring adaptive, scalable, and intelligent anti-eavesdropping strategies in UAV communication networks.",
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+ "text": "The study in [60] proposes a Deep Q-Network (DQN)-based approach to address the challenge of securing UAV-assisted multi-user wireless communications against passive eavesdropping attacks. The UAV trajectory optimization is formulated as a Markov Decision Process (MDP), where the state space includes the UAV's 3D coordinates and the positions of users. The action space consists of discrete movements in the $x$ , $y$ , and $z$ directions, with each action representing a step change in position. The reward function is designed to maximize the legitimate users' rates, defined as the sum of the channel capacities of users served by the UAV. Unlike many prior works that assume perfect knowledge of eavesdropper CSI [53], [59], this study focuses on optimizing legitimate user rates and using the DQN-based approach without requiring full knowledge of the eavesdropping channels. The DQN iteratively optimizes the UAV's trajectory, beamforming matrix, and transmit power allocation, ensuring the UAV dynamically adjusts its position to maximize secrecy capacity. Numerical results show that the secrecy capacity improves with the number of users. The proposed method converges an order of magnitude faster than the Q-learning method and achieves around $35\\%$ higher secrecy capacity than Q-learning after 20,000 episodes.",
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+ "text": "However, the DQN method may face the issue of Q-",
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+ "table_caption": [
+ "TABLE V SUMMARY OF RL FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Techniques | Reference | Algorithm | Pros & Cons |
| Value-based RL | [60] | DQN | ○ DQN algorithm for UAV trajectory optimization to maximize the secrecy capacity\n✓ Low computational complexity, making it easy to train\n× Q-value overestimation, leading to suboptimal action selection |
| [61] | DDQN | ○ DDQN-based joint trajectory, time allocation, and offloading optimization\n✓ Accelerated convergence via action space pruning\n✓ Real-time optimization of trajectory and resources\n× DDQN is restricted to discrete action spaces\n× DDQN is not suitable for continuous action control |
| Policy Gradient-based RL | [62] | CAA-MADDPG | ○ Multi-Agent DRL with attention mechanisms (CAA-MADDPG) for secrecy rate maximization\n✓ Handle complex multi-agent with the attention mechanism\n× Assume prior knowledge of eavesdropper locations\n× Assume ground devices are static |
| [63] | DDPG | ○ DDPG-based RL for enhancing bi-directional UAV communication security\n✓ Support mobile devices and ensure bi-directional secureit\n× Computational overhead increases with device density\n× performance may be sensitive to hyperparameter selection |
| [64] | PPO+DCCN | ○ Hybrid DCCN and PPO for secrecy rate maximization\n✓ The PPO optimizes the UAV trajectory based on the results from DCCN\n× The performance is sensitive to the choice of clipping factor in PPO |
| [65] | MAPPO+LSTM | ○ MAPPO for multi-agent cooperative anti-eavesdropping and LSTM-enhanced sequential learning\n✓ The MAPPO+LSTM improves the learning capability of sequential sample data\n× Assume perfect knowledge of CSI may be challenging in real-world scenarios |
",
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+ "type": "text",
+ "text": "value overestimation, leading to suboptimal action selection [146]. The authors in [61] propose a double-deep Q-learning (DDQN)-based scheme to jointly optimize the UAV trajectory, time allocation, and offloading decision strategy, aiming to maximize the average secure computing capacity for antieavesdropping in UAV-aided MEC. The system model involves one legitimate UAV server, one illegitimate UAV eavesdropper, one ground jammer, and ground users. The proposed DDQN-based scheme models the optimization problem as an MDP with states, actions, and rewards. The states include the coordinates of the UAVs, while the actions involve offloading decisions, time allocation, and trajectory adjustments. The reward function maximizes secure computing capacity. The DDQN model includes a deep Q-network (QN) and a deep target network (TN) to generate actions and evaluate their values. The parameters of the QN are updated by minimizing the loss function, and the parameters of the TN are periodically updated. The proposed scheme reduces the action space size by deleting illegal actions, such as those that violate time allocation constraints or result in resource waste. Unlike prior works [57], [60] that rely on conventional optimization or DQN with limited consideration of task queues, this approach integrates real-time resource allocation and trajectory optimization while ensuring dynamic constraints. The proposed DDQN scheme converges in 2000 episodes, half the episodes required by DQN (4000 episodes), and achieves a 0.02 Mbits higher average secure computing capacity.",
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+ "text": "The value-based RL method (e.g., DQN) mainly focuses on dealing with discrete action spaces that may lead to the loss of optimal solutions [147]. The policy gradient-based RL method (e.g., Deep Deterministic Policy Gradient (DDPG)) can handle continuous action spaces [148], which are more suitable for UAV trajectory and transmit power optimization problems.",
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+ "text": "The authors in [62] propose a multi-agent DRL framework to address the challenge of secure UAV communications in",
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+ "text": "the presence of eavesdroppers. The system model is similar to Part A of Fig. 3, where the UAV server sends confidential information to ground users, and UAV jammers send AN signals to ground eavesdroppers using 3D beamforming. This study designs the Multi-Agent Deep Deterministic Policy Gradient with a continuous action attention mechanism (CAA-MADDPG) to maximize the system's secrecy rate. The attention mechanism dynamically prioritizes relevant agents' observations (e.g., jammers focusing on eavesdroppers) to reduce the exploration space and accelerate convergence, thereby enhancing the system's ability to counteract eavesdropping attempts. The simulation results show that CAA-MADDPG achieves a secure rate of $4.5\\mathrm{bps / Hz}$ and converges in 1000 episodes with three UAV jammers, outperforming MADDPG (around $4\\mathrm{bps / Hz}$ and 1400 episodes) and DDPG schemes.",
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+ "text": "However, the study in [62] just considers UAV-to-ground communication (U2G) and assumed the ground devices are static. The work in [63] addresses the challenge of securing bi-directional ground-UAV communications in a dynamic environment with mobile ground devices and eavesdroppers. Different from prior works that assume static ground eavesdroppers [54], [56], this study considers mobile ground eavesdroppers for more practical real-world scenarios. The communication in U2G and ground-to-UAV (G2U) cases is modeled, considering factors such as channel gains and distances. The problem of maximizing the worst-case average secrecy rate is formulated as a constrained MDP (CMDP) under the constraints of UAV flight space, flight speed, energy capacity, anti-collision, and peak transmit power. To solve the CMDP, the authors design a DDPG-based RL algorithm. The algorithm includes three key components: the primary network (actor and critic networks), the target network, and the replay buffer. They also adopt state normalization and exploration noise to speed up the training convergence of the DDPG. The proposed joint optimization scheme achieves a secrecy rate",
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+ "text": "10",
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+ "text": "over $40\\%$ higher compared to baselines that optimize only trajectory or only power. In addition, DDPG outperforms DQN by approximately $15\\%$ in secrecy rate due to its ability to handle continuous actions.",
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+ "text": "The DDPGG methods form a fixed mapping from states to actions, which is not suitable for large state spaces that require more exploration and uncertainty [149]. The PPO alleviates this limitation by introducing proximal policy optimization, which allows for more exploration in the large action space.",
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+ "text": "The study in [64] proposes a hybrid framework (Double Cascade Correlation Network (DCCN) + PPO) to maximize the secrecy capacity. DCCN bypasses the need for labeled training data by cascading two neural networks to maximize the secrecy channel rate. The PPO dynamically adjusts the UAV's position by using clipped surrogate objectives to stabilize policy updates and advantage estimation to prioritize high-reward actions. Simulation results show that the proposed scheme (DCCN + PPO) achieves an average secrecy rate of 0.73 bps/Hz, outperforming the benchmarks DCCN + DDPG (0.67 bps/Hz) and Random RIS + PPO (0.13 bps/Hz). However, the average secrecy continues to decline when the transmit power is higher than 2 W, since the jamming signals transmitted by the secondary source against the eavesdropper will also affect the primary users.",
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+ "text": "The study in [64] considered only the use of one UAV to assist in secure communication. However, in low-altitude economic networks, it may be more important for multiple UAVs to collaborate to implement anti-eavesdropping strategies. The study in [65] considers a system model treats all secondary transmitters and multiple UAV jammers as multi-agents. A Multi-Agent PPO algorithm combined with Long Short-Term Memory (LSTM) networks, named MAPPO-LSTM, is proposed to maximize the secure communication rate by jointly optimizing the UAV trajectory, transmission power, and energy harvesting coefficients. The problem is formulated as a nonconvex MDP consisting of an action space, state space, observation, and reward (which consists of the sum of the secure communication rate, SINR information, and battery capacity). The MAPPO algorithm introduces counterfactual baselines to address the credit assignment problem in centralized learning and combines with the LSTM network to enhance the learning capability of sequential sample data. Compared to benchmark schemes MAPPO and MADDPG, the proposed MAPPO-LSTM method achieved around $17\\% - 20\\%$ higher average secrecy rate in large-scale scenarios, with convergence speeds 1.37 times and 1.93 times faster, respectively. In addition, the reward is sensitive to the discount factor, where setting factor to 0.99 enables faster and more stable convergence. Deviations from this value result in more pronounced fluctuations in the reward and secrecy rate.",
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+ "text": "Lesson Learned. The RL has emerged as a powerful yet challenging tool for anti-eavesdropping in UAV-assisted secure communications. A key lesson is that multi-agent cooperation significantly enhances security compared to single-agent approaches, enabling adaptive trajectory control, power allocation, and jamming coordination in dynamic environments. However, scalability and convergence efficiency remain critical bottlenecks, especially in high-dimensional, time-",
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+ "type": "text",
+ "text": "varying settings, as many studies unrealistically assume perfect channel information, and deep RL's convergence time leaves the system vulnerable before optimization completes. Furthermore, key limitations demand further attention, such as RL's computational complexity, which restricts its use in resource-limited settings requiring real-time security, and its sensitivity to hyperparameter tuning that requires meticulous configuration to ensure optimal performance. Future advancements should focus on developing generalizable and robust learning architectures that can dynamically adapt to evolving threats while maintaining computational feasibility, addressing practical deployment challenges, exploring hybrid approaches, prioritizing security in system design, and balancing security performance with energy consumption.",
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+ "text": "Deep learning, with its strong learning capabilities, parallel processing, and comprehensive reasoning [150]–[152], has huge potential to enhance anti-eavesdropping strategies in UAV communications, especially in environments with rapidly changing conditions and complex interactions [153]. Given the intricate problem of UAV trajectory variation and its nonlinear characteristics in time and space [154], [155], deep learning networks, such as neural networks and generative models, are emerging as potential solutions to improve the security and performance of UAV communication systems.",
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+ "text": "The study in [66] explores the use of deep learning to optimize UAV deployment and jamming strategies against eavesdroppers to maximize the secrecy rate in the complete CSI scenario. The optimization problem is decomposed into two layers: the inner layer optimizes jamming power for a fixed UAV location, and the outer layer optimizes UAV deployment. The inner problem is solved using a bi-section search algorithm, while the outer problem is addressed using a deep neural network (DNN) to approximate the optimal UAV deployment. The DNN is designed as a fully connected structure, which includes an input layer, two hidden layers, and an output layer, as shown in part A of Fig. 5. The DNN is trained using a dataset generated by simulating different UAV deployments and corresponding secrecy rates. The final optimal deployment of the UAV can be approximated when the mean square error of weights between neurons is minimized. The DNN model achieves an average distance error of 2.2 meters compared to the optimal deployment found by the exhaustive search baseline.",
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+ "text": "The fully connected neural network used in [66] is suited for problems where inputs and outputs are fixed-dimensional vectors without inherent spatial or sequential relationships [150]. Moreover, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) can also contribute to antieavesdropping. In contrast to fully connected networks, CNNs are particularly effective for exploring spatial features from images or spatial maps [156]. RNNs, on the other hand, focus on handling sequential data by maintaining a memory of previous inputs through recurrent connections [150]. The authors in [67] propose a CNN-LSTM-based secure efficiency map (SEM) framework, which is constructed by calculating each subarea's security-efficiency index using a weighted exponential coefficient to combine normalized secure spectrum efficiency (secrecy rate per unit bandwidth) and secure energy",
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+ "img_path": "images/fce984a856adf58da26013e00ddd120d464b283587d49890dccfd1c7c26d073d.jpg",
+ "table_caption": [
+ "TABLE VI SUMMARY OF DEEP LEARNING FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Techniques | Reference | Algorithm | Pros & Cons |
| Neural network model | [66] | DNN | ● Use DNN to optimize UAV deployment and jamming strategies for secure communication\n● The DNN model reduces the complexity of exhaustive searches\n● Rely on complete statistical channel knowledge\n● require intensive resources to generate a large amount of training data |
| [67] | CNN-LSTM | ● CNN-LSTM-based SEM prediction for dynamic secure UAV trajectory optimization\n● Efficient spatiotemporal feature extraction via CNN-LSTM\n● Assume fixed UAV height and passive eavesdropper\n● Training CNN-LSTM network requires a substantial amount of data |
| [68] | FL-DNN | ● FL-DNN-RL integration (FairLearn) for maximizing fairness in secrecy rates\n● Collaborative learning via FL improves generalization in anti-eavesdropping strategies\n● Involving multiple learning mechanisms requires significant computational resources\n● Assuming perfect CSI and eavesdropper localization may be impractical |
| Generative AI model | [69] | MD-GAN | ● MD-GAN with unknown CSI as model weights\n● Adapt to dynamic environments via gradient-based training\n● Do not require knowledge of the eavesdropper's detection threshold\n● Training a GAN can be computationally intensive |
| [70] | DD-GAN | ● DD-GAN uses genetic algorithm-generated datasets for GAN training\n● Achieve an effective trade-off between covert rate and detection probability\n● Training relies on the quality and quantity of the genetic algorithm-generated data |
| [71] | GDMTD3 | ● GDMTD3 integrates generative diffusion models into TD3\n● Handle high-dimensional action spaces to adapt mobile eavesdroppers\n● Computational complexity from diffusion denoising steps |
",
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+ "text": "efficiency (secrecy rate per unit power). Historical SEMs are fed into a CNN-LSTM network to predict future SEMs by leveraging spatial-temporal feature extraction and time-series correlation. Based on predicted SEMs, a trajectory planning algorithm dynamically guides the UAV to subareas with the highest security-efficiency indices. The proposed SEM-enabled trajectory planning achieves an average security-efficiency index of 0.81, outperforming baseline schemes (e.g., static trajectory [142] or non-predictive methods [62], [157]) by over $30\\%$ .",
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+ "text": "Previous deep learning-based architectures [66], [67] are centralized, lacking collaboration and knowledge sharing among UAVs, while also facing challenges in privacy preservation and scalability. To address these limitations and optimize secrecy rate maximization under constraints such as UAV mobility, power budgets, and scheduling fairness, the authors in [68] propose a federated learning (FL)-based framework (FairLearn). As shown in part B of Fig. 5, the FairLearn employs three learning modules: (1) Module-D uses RL to dynamically generate training datasets by exploring UAV trajectories, power allocation, and scheduling policies; (2) Module-P employs a DNN trained on these datasets to predict optimal 3D trajectory, transmit power, and user scheduling, maximizing proportional fairness in secrecy rates (defined as the difference between legitimate UAV-user rates and eavesdropper rates); (3) Module-C applies FL to aggregate DNN models across UAVs, enabling collaborative learning while preserving data privacy. Simulation results show that FairLearn's secrecy rate is $26.6\\%$ higher than BCD at 1.4W transmit power. After 100s of execution, FairLearn achieves $14.34\\%$ , $24.56\\%$ , and $108\\%$ higher secrecy rates than BCD, MAQ, and QCQP baselines, respectively.",
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+ "type": "text",
+ "text": "It is worth noting that UAVs can only obtain limited prior environmental information without knowing perfect channel information and the eavesdropper's detection threshold or ex",
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+ "type": "text",
+ "text": "act location. Some previous methods [59], [65], [68] may find it difficult to solve the optimization problem in such scenarios. In contrast, the generative adversarial network (GAN) has emerged as a new model for solving optimization problems with limited prior information [158], [159]. GAN can effectively model and approximate unknown distributions (such as channel coefficients, detection thresholds, and environmental parameters) through adversarial learning, where the generator continuously improves its strategy by learning from the feedback from the discriminator [158].",
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+ "text": "The work in [69] addresses challenges related to partial channel distribution information and unknown eavesdropper detection thresholds by proposing a model-driven GAN (MDGAN) framework. The unknown channel coefficients and detection thresholds are treated as trainable weights in the MD-GAN. The MD-GAN transforms the joint trajectory and power optimization problem into a dynamic game between a generator (UAV) and a discriminator (eavesdropper), where the UAV acts as a jammer to protect secondary users from eavesdroppers. The generator optimizes the UAV's 3D trajectory and jamming power, while the discriminator evaluates detection errors. Then, a GAN-based joint trajectory and power optimization (GAN-JTP) algorithm is developed to achieve Nash equilibrium (i.e., maximizing the covert rate and the probability of detection errors). As shown in part C of Fig. 5, the GAN-JTP algorithm consists of two stages: network learning and network training. In the network learning stage, the generator optimizes the UAV's trajectory and transmit power based on the current state and environment. In the network training stage, the generator and discriminator are alternately trained using gradient backpropagation to update their weights. Simulation results show that increasing the training of the discriminator accelerates the convergence of the generator (e.g., when the training step is 10, convergence is achieved within 30 iterations, compared to 89 iterations when",
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+ "img_path": "images/44334917753d0735f58e494eaeb14ab8b73c2c003ece0c5817ff07e552328506.jpg",
+ "image_caption": [
+ "Part A. DNN-based Architecture"
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+ "Part B. FL-DNN-based Architecture"
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+ "Part C. MD-GAN-based Architecture"
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+ "Part D. DD-GAN-based Architecture"
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+ "image_caption": [
+ "Part E. GDMTD3-based Architecture",
+ "Fig. 5. The overall architecture illustrates various deep learning-based architectures designed to enhance anti-eavesdropping capabilities in UAV deployment scenarios. Part A presents a DNN-based architecture that processes air-ground and ground-ground channel states to determine UAV deployment. Part B shows an FL-DNN-based architecture, incorporating modules for reinforcement learning, DNN-based feature mapping, and FL. Part C depicts an MD-GAN-based architecture, where a generator produces trajectories and power outputs based on location and environment status, while a discriminator evaluates the decisions. Part D introduces a DD-GAN-based architecture, focusing on generating jamming solutions to maximize covert rates, with a discriminator distinguishing between jamming and non-jamming solutions. Part E illustrates a GDMTD3-based architecture, utilizing an experience replay buffer and diffusion reverse process to optimize UAV deployment strategies."
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+ "text": "the training step is 1). For a flight period of 100 seconds, the GAN-JTP algorithm achieves a $0.47\\%$ increase in covert rate with a $0.15\\%$ reduction in detection error probability compared to the BCD-based scheme [160].",
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+ "text": "The MD-GAN [69] relies on model-driven methods where the unknown channel information and detection threshold are treated as trained weights. Differently, the authors in [70] propose a data-driven GAN (DD-GAN) framework that focuses on generating data consisting of environmental parameters and optimal solutions to train the GAN. Specifically, the DD-GAN transforms the optimization process into an interactive game between the UAV and eavesdropper, where the UAV aims to maximize the covert rate, and the eavesdropper aims to detect the presence of covert communication. To address the non-convexity and lack of eavesdropper detection threshold information in the optimization process, the DD-GAN trains a generator (UAV) and discriminator (eavesdropper) adversarially, using genetic algorithm-generated samples as prior data, as shown in part D of Fig. 5. The generator produces power and trajectory solutions, while the discriminator evaluates the detectability. The loss function of the discriminator is designed to maximize the probability of correctly identifying real data and minimize the probability of being fooled by generated data. The generator's loss function aims to maximize the probability that the generated data is mistaken for real data by the discriminator.",
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+ "type": "text",
+ "text": "Besides GANs [69], [70], another generative model, the diffusion model, has advanced the effective representation",
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+ "type": "text",
+ "text": "of multi-dimensional data distributions [161]. The diffusion model can better capture the complex dynamics and the tradeoff in the multi-objective optimization problem concerning secure communication [112]. For example, The diffusion model captures complex state-action distributions, enabling adaptive beamforming and UAV repositioning under eavesdropper mobility. To tackle dynamic environments and high-dimensional action spaces in secure communication and energy efficiency multi-objective optimization problem, the authors in [71] propose GDMTD3, a Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm enhanced with generative diffusion models. Key innovations include integrating diffusion-based reverse processes into the actor network for robust policy generation and addressing continuous action spaces, as shown in part E in Fig. 5. The training process of GDMTD3 involves initializing the online critic and actor networks, interacting with the environment, and updating the network parameters based on the collected experiences. The actor network uses a generative diffusion model to sample actions, while the critic networks evaluate the actions using twin critic networks to reduce overestimation bias. Simulation results show that GDMTD3 outperforms DRL-based benchmarks (including PPO, TD3, and DDPG), achieving about $50\\%$ higher cumulative rewards and around $21\\%$ higher average secrecy rate than TD3. In addition, when the number of UAVs increases from 4 to 8, the average secrecy rate increases accordingly. However, increasing the number of UAVs from 8 to 16 raises",
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+ "table_caption": [
+ "TABLE VII SUMMARY OF AUTHENTICATION FOR COMMUNICATION CONFIDENTIALITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [
+ "Physical Unclonable Functions (PUFs) are hardware-based security primitives that exploit inherent and unique physical variations in devices to generate unclonable and unpredictable responses for communication authentication.",
+ "2Authentication Distance (AD) is a metric proposed in [77] to distinguish legitimate and illegitimate signals for communication authentication."
+ ],
+ "table_body": "| Techniques | Reference | Algorithm | Pros & Cons |
| PUFs-based authentication | [72] | PUF\\(s^1\\) | PUF-based dynamic session key generation and mutual authentication protocol\n✓ Lightweight design with no stored secrets\n✗ Potential overhead during temporary identity updates |
| [73] | PUF-fuzzy extractor | PUF-fuzzy extractor mutual authentication with TS-based dynamic session adaptation\n✓ Dynamic session time adaptation minimizes idle periods and enhancing security\n✗ Higher computational cost due to fuzzy extractors |
| [74] | PUFs-fuzzy extractor-AEGIS | Integration of PUFs, fuzzy extractors, and AEGIS for mutual authentication\n✓ The proposed password/biometric update mechanism reduces server dependency\n✗ Multiple cryptographic operations and protocols may be cause delay in the implementation |
| Channel based authentication | [75] | Rician channel | Physical-layer fingerprinting authentication based on Rician channel characteristics\n✓ Optimal power allocation balances data, AN, and authentication tag transmission\n✗ Reliance on encrypted tags requires high demand on UAV processing capabilities |
| [76] | Rayleigh channel | SNR difference-based PLA scheme\n✓ The SNR-based design can be implemented without additional hardware infrastructure\n✗ The simplified Rayleigh channel model may limit to real-world propagation environments |
| [77] | Rayleigh/Rician channels | AD metric2for authentication under Rayleigh/Rician channels\n✓ AD metric-based method improves the detection accuracy of authentication\n✓ Detailed analysis of authentication performance under different propagation conditions\n✗ Computational complexity in Rician channels due to hypergeometric functions |
",
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+ "text": "energy consumption but only marginally improves secrecy rates, highlighting a performance-energy trade-off.",
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+ "text": "Lesson Learned A key lesson learned is that deep learning, particularly through advanced architectures such as GANs [69], [70] and diffusion models [71], can address complex, dynamic environments with partial channel state information and unknown eavesdropper locations, while demonstrating superior performance over traditional methods [59], [65], [66]. These approaches demonstrate that deep learning not only strengthens the resilience of secure communications but also enables autonomous, real-time decision-making to counteract evolving eavesdropping threats in UAV networks.",
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+ "text": "B. Communication Authentication",
+ "text_level": 1,
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+ "text": "In the LAENet, as UAVs operate in open environments and rely on wireless communication, they are highly vulnerable to security threats such as node capture and man-in-the-middle attacks [46]. Ensuring secure and reliable authentication between UAVs and ground stations/users or among UAVs is critical to preventing unauthorized access [52], [162]. Traditional cryptographic authentication schemes often impose significant computational and memory overheads and incur considerable lantency, making them unsuitable for resource-constrained UAVs [163]. Recently, advancements such as PUFs and Physical-layer Authentication (PLA) mechanisms have opened new possibilities for lightweight and effective authentication in the LAENet.",
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+ "text": "PUFs are a class of hardware security primitives that leverage the inherent manufacturing variations (such as variations in circuit delay or RF properties) in semiconductor devices to generate unique and unpredictable responses [164]. When a specific input is applied to a PUF, the device generates a corresponding response, forming a challenge-response pair that is unique to this device [164]. Such uniqueness and unpredictability make PUFs highly resistant to cloning and",
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+ "type": "text",
+ "text": "tampering, making them as a secure means for device authentication and key generation [165]. In addition, employing a PUF in a UAV allows for secure authentication without the need for complex cryptographic operations, making it an efficient solution for resource-constrained scenarios [166].",
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+ "text": "The work in [72] proposes a lightweight mutual authentication protocol, named SecAuthUAV, for securing UAV-ground station and UAV-UAV communications. SecAuthUAV employs PUFs in each UAV to generate a unique, unclonable session key that functions as a non-reproducible fingerprint. The protocol consists of three phases, as shown in Fig. 6. During UAV registration, a challenge-response pair from the UAV's PUF is stored, and a temporary identity is generated. In the UAV-ground station authentication phase, the UAV and ground station authenticate each other using challenge-response pairs and nonces, establish a session key, and update their identities. Lastly, in the UAV-UAV authentication phase, the GS facilitates secure communication by authenticating a second UAV and generates a session key for both UAVs.",
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+ "text": "However, the work in [72] ignores the fact that the noise in PUFs can result in significant deviation in the output for the same input at different time points. In addition, [72] does not adjust the session time after establishing an authenticated session between two parties, which may lead to the active session remaining idle for a long time and thus give an opportunity for an adversary to interfere with the communication link. In light of this, the authors in [73] propose an UAV Authentication with Adaptive Session (UAAS) framework to address these challenges. Firstly, they combine PUFs and fuzzy extractors to address PUF noise. The fuzzy extractors consist of two phases: the $Gen(.)$ phase creates a key and non-sensitive helper data, and the $Rep(.)$ phase reconstructs the key from a noisy PUF response using the helper data while tolerating minor deviations. Then, the Thompson Sampling (TS)-based scheme is proposed to dynamically adapt the session time.",
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+ "img_path": "images/1a454107197f0583fff2fc6224b7c4e7b0c3d8f3354f603056d3b238606f5780.jpg",
+ "image_caption": [
+ "Fig. 6. The overall architecture of the PUF-based authentication schemes for UAV-GS and UAV-UAV communication in [72]. Part A illustrates the PUF-based authentication process between a UAV and a ground station (GS). The UAV sends its ID and a nonce to the GS, which responds with a hash value based on the PUF, UAV ID, and nonce. The UAV then sends a value derived from the PUF and another nonce, and the GS verifies the authentication by comparing hash values. Part B shows the PUF-based authentication between two UAVs (U1 and U2) through the GS. After establishing a session key with the GS, U1 requests a connection to U2. The GS facilitates the authentication by generating a new session key, which is securely shared between U1 and U2."
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+ "text": "TS is a probabilistic approach that balances exploration and exploitation, determining the session time based on the fraction of busy time to minimize idle periods and reduce the risk of adversarial interference. Although the security analysis demonstrates that UAAS improves the security level in the mutual authentication mechanism, its throughput is $20.38\\%$ lower and computational cost is 126 ms higher than the baseline [72] due to security overhead.",
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+ "text": "In the LAENet, while establishing mutual authentication between UAVs and ground stations is critical, it is also important to incorporate role-specific access controls for users to ensure communication confidentiality and preventing unauthorized access [167]. The work in [74] proposes an authentication framework PUF-enabled authentication framework for Internet of Drones (PAF-IoD) to establish mutual authentication among users, UAVs, and ground stations. Users need to authenticate with stations to access the stored data or communicate directly with UAVs, where the users' authentication mechanism includes three factors (identity, password, and biometric data). Similar to [73], PAF-IoD uses PUFs and a fuzzy extractor in the authentication process to generate a unique and tamper-proof session key while tolerating the noise in PUFs. Furthermore, the designed authenticated encryption with associative data (AEAD)-based encryption algorithm is utilized for encrypting and decrypting messages exchanged between the user, ground station server, and UAVs.",
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+ "text": "In addition to leveraging intrinsic physical properties of hardware for authentication design through PUFs [72]–[74], the characteristics of communication channels can be used for authentication. The PLA mechanism authenticates devices by exploiting the unique physical characteristics of wireless communication channels, such as CSI, received signal strength (RSS), and signal-to-noise ratio (SNR) [168]. The main reason is that the wireless channel between two communicating entities exhibits location-specific and time-varying properties",
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+ "text": "due to multipath propagation, fading, and environmental factors [169]. These diverse physical channel conditions, which provide a robust set of features for authentication, have been investigated in terrestrial communication networks [168]–[170]. Furthermore, the source of received signals can be accurately and promptly detected [170], making PLA particularly advantageous in the dynamic and complex communication environments of the LAENet.",
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+ "text": "The authors in [75] leverage the unique properties of the physical layer channel, Rician channel, to develop a PLA for UAV-ground station communication. Given that UAVs receive signals subject to the Rician fading model, the ground station integrates authentication directly into the transmission process. It employs a one-way collision-resistant function (e.g. cryptographic hash function) that combines data symbols with a shared secret key to generate a low-power authentication tag for UAV and seamlessly embeds it into the transmitted signal. The authentication tag is validated by the correlation shaped by the Rician statistical characteristics of the fading channel, i.e., the correlation between the estimated tag (derived from the received signal) and the expected tag (generated using the secret key and decoded data symbols).",
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+ "text": "However, the work in [75] still partially relies on cryptographic tag generation for authentication, which may not be suitable for UAVs with limited processing capabilities. The study in [76] leverages channel characteristics and geographical locations for PLA design, where the SNR differences between consecutive transmissions are utilized as the authentication metric. Specifically, a legitimate transmitter and a jammer have distinct channel variations due to differences in their geographical locations. The UAV authenticates the legitimate transmitter or jammer by formulating a binary hypothesis test based on the SNR difference between two successive transmissions. If the difference falls within a predefined threshold, the transmission is authenticated as from the legitimate",
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+ "text": "15",
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+ "img_path": "images/f2a0eafa0a8185bc1fc9742760bf005b8217a9d36dcaad8f6cc2e5c56af12ae0.jpg",
+ "image_caption": [
+ "Part A. Channel-based authentication in urban"
+ ],
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+ "img_path": "images/967f281427d80e32166ad3daced3cb08fb45a53cc42cab57a86b73497c509e23.jpg",
+ "image_caption": [
+ "Part B. Channel-based authentication in suburban",
+ "Fig. 7. The overall architecture of the channel-based authentication in urban and suburban environments in [77]. Part A depicts the authentication process in an urban environment under Rayleigh channel conditions. The UAV receiver calculates the SNR, computes the AD, and compares it with a detection threshold to distinguish between legitimate and malicious sensors. Part B illustrates the authentication process in a suburban environment, where the UAV receiver performs similar steps to authenticate legitimate sensors and detect malicious ones under Rayleigh channel conditions."
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+ "text": "transmitter; otherwise, it is classified as a jammer. The closed-form expressions for the probability density function of SNR differences, false alarm rate (FAR), and miss detection rate (MDR) are derived under Rayleigh fading channels in single-UAV and dual-UAV scenarios. The non-convex optimization problem of minimizing MDR under FAR constraints is solved using an SCA algorithm, which outperforms the RSS-based baseline [90] by about $40\\%$ .",
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+ "text": "It is worth noting that study [75] may lack a comprehensive analysis of the UAV-PLA performance under different propagation conditions. Additionally, the detection performance may be further improved with other indicators. As shown in Fig. 7, the work in [77] proposes a novel PLA framework under different propagation conditions, including dense urban and suburban environments modeled by Rayleigh and Rician channels, respectively. A new metric, Authentication Distance",
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+ "text": "(AD), is proposed as the normalized difference in received SNR between adjacent transmissions. For Rayleigh channels, closed-form expressions for FAR and MDR are derived using convolution and integration-by-parts, while Rician channels employ doubly non-central $F$ distributions to model AD statistics. Similar to study [76], this authentication framework minimizes MDR under FAR constraints. In dense urban settings, MDR depends on path loss and transmitter-UAV geometry. For suburban environments, it incorporates elevation angle-dependent Rician factors and path loss exponents to improve discriminability between legitimate and illegitimate signals. The proposed AD-based method outperforms the SNR-difference baseline [171], achieving 40–60% lower MDR.",
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+ "text": "Lesson Learned. Leveraging physical-layer characteristics, such as PUFs and channel properties, in conjunction with communication models and optimization algorithms, has proven effective in enhancing authentication accuracy and reducing detection errors. However, some methods also reveal limitations. For instance, the assumptions of ideal channel conditions and the neglect of practical implementation constraints may limit the applicability of the proposed solutions [76], [77]. Future research should focus on addressing these limitations by exploring more practical channel models and considering the trade-offs between security and system complexity.",
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+ "type": "text",
+ "text": "IV. COMMUNICATION AVAILABILITY FOR LAENET",
+ "text_level": 1,
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+ "text": "A. Anti-Jamming Strategy",
+ "text_level": 1,
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+ "text": "Jamming attacks pose significant challenges to communication availability in the LAENet by disrupting legitimate communication links and degrading the performance of aircraft communication networks [79], [172]. As shown in Fig. 10, these attacks can exploit the openness and broadcasting nature of UAV networks, making them particularly vulnerable to interference [79]. Malicious jammers can transmit strong signals that weaken signal strength, degrade signal quality, and increase communication delays, leading to unreliable coverage and potential paralysis of the entire network [172], [173]. This vulnerability underscores the urgent need for effective anti-jamming technologies to ensure reliable communication in the LAENet.",
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+ "text": "Various anti-jamming strategies have been explored to safeguard the LAENet against malicious jamming, mainly focusing on trajectory adjustment, as well as channel and power control. Overall, by adjusting the trajectory in the spatial domain, an UAV can evade jamming signals while maintaining reliable communication with legitimate devices [80], [173]. Besides the spatial-domain anti-jamming strategy, the UAV can implement a frequency-domain-based anti-jamming scheme. The UAV can select legitimate channels while avoiding jamming signals and control transmit power to minimize energy consumption and latency under jamming attacks [83], [84].",
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+ "type": "text",
+ "text": "Convex optimization methods can be used to adjust the UAV's trajectory to achieve anti-jamming by strategically guiding its movement to reduce interference and enhance communication reliability [80], [173]. It provides a systematic and efficient approach to handle the complex, non-convex",
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+ "type": "page_number",
+ "text": "16",
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+ {
+ "type": "table",
+ "img_path": "images/ac755b49caad673c5969aa85578ccfc3367cd5587e9664d857f416a9905f81b7.jpg",
+ "table_caption": [
+ "TABLE VIII SUMMARY OF ANTI-JAMMING STRATEGY FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Techniques | Reference | Algorithm | Pros & Cons |
| Convex optimization | [80] | BCD, SCA | BCD and SCA for UAV 3D trajectory optimization for anti-jamming\n✓ Probabilistic LoS performs well in real-world scenarios such as urban environments\nX High computational complexity may be challenging in resource-constrained environments |
| [81] | SCA, Dinkelbach | SCA and Dinkelbach algorithm for energy-efficient trajectory optimization under malicious jammers\n✓ Balance between throughput and energy consumption in anti-jamming\nX Assume static and LoS-dominated channels |
| [82] | BCD, SCA | BCD and SCA for joint UAV trajectory and transmit power optimization under jamming\n✓ Improve throughput by considering transmit power optimization against jammers\nX Assume a fixed UAV altitude and a static channel environment |
| Multi-agent RL | [87] | MALQL | Collaborative MALQL algorithm for anti-jamming with channel and power allocation\n✓ Accelerate convergence compared to single-agent Q-learning\nX Assume predefined UAV trajectories limits to adaptability |
| [88] | MARL | MARL with adversarial pre-training for dynamic and generalized jamming\n✓ Generalize to various jamming patterns via adversarial populations for pre-training\nX Pre-training for generalized jamming may require significant offline resources |
| [89] | MATD3 | MATD3 algorithm with PER for dynamic resource management under jamming attacks\n✓ Handle high-dimensional continuous action spaces\nX The integration of PER and spectrum sensing may increase the computational complexity |
",
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+ {
+ "type": "text",
+ "text": "problems that arise when optimizing UAV trajectories and various constraints under malicious jamming conditions [131]. The work in [80] investigates anti-jamming 3D trajectory design for UAV-enabled wireless sensor networks under a probabilistic LoS channel model. The probabilistic LoS model accounts for elevation angle-dependent shadowing effects in urban environments compared with simplified LoS models. The BCD and SCA algorithms are employed to optimize the UAV's horizontal and vertical trajectory, allowing the UAV to move closer to the ground station for improved transmission rates while dynamically adjusting its elevation angle relative to the jammer to mitigate interference.",
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+ "text": "However, the anti-jamming trajectory optimization in [80] under the probabilistic LoS model does not consider the energy consumption issue. The study in [81] utilizes SCA and Dinkelbach's algorithm to adjust the UAV's trajectory to avoid areas with jammers while maximizing energy efficiency, which is defined as the ratio of total throughput to propulsion energy consumption during flight. Compared to hovering-centric benchmarks, the optimized trajectory reduced energy consumption by $82\\%$ while maintaining $73.16\\%$ of the sum throughput. It is worth noting that the transmit power of the UAV and station is fixed in [81], whereas power optimization is also an important factor for energy efficiency. The authors in [82] use the SCA and BCD algorithms to maximize throughput by iteratively optimizing power allocation (via convex reformulation of throughput bounds) and UAV trajectory (via slack variables for distance constraints and jamming mitigation) to avoid jamming signals. The proposed scheme achieves $40\\%$ higher throughput compared to the \"Line trajectory with fixed power\" baseline.",
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+ "text": "While convex optimization methods [80]–[82] work well for fixed jamming patterns, they may struggle to handle dynamic, intelligent jamming [174] in real-time due to their reliance on global information and the challenges inherent in solving nonconvex problems with increased optimized variables [142]. In contrast, RL and DRL offer significant advantages by enabling autonomous, adaptive decision-making [143], [147]. These",
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+ {
+ "type": "text",
+ "text": "approaches can continuously adjust to environmental changes, learn from past interactions, and optimize performance in real-time [144], [175]. The RL-based anti-jamming methods have emerged as a promising solution due to their ability to operate without excessive prior information (such as unknown environment, CSI, and jamming mode) [147]. Single-agent RL algorithms have been used in previous works to develop anti-jamming strategies in communication networks by regarding jammers and other legitimate users as part of the environment, including independent anti-jamming channel selection methods [83]–[86]. However, these single-agent approaches may fail to converge when dealing with a large number of agents or a high-dimensional action-state space [87], making them impractical for complex, multi-agent scenarios in the LAENet. To address these limitations, multi-agent RL (MARL) methods have been proposed to allow each agent to make decisions based on local information and exchange data with others (such as observations or model parameters).",
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+ "text": "The study in [87] proposes a collaborative multiagent layered Q-learning (MALQL) algorithm for anti-jamming communication in UAV networks by jointly optimizing channel and power allocation to maximize system Quality of Experience (QoE). The problem is modeled as a local interaction Markov game based on the constructed interference graph. The MALQL divides the problem into two subgames of channel selection (Layer 1) and power allocation (Layer 2), as shown in part B of Fig. 10. The channel layer uses a graph-based interference model to capture mutual interference among UAVs. Each UAV is represented as a node, and edges are formed between UAVs that are within a predefined interference distance. This model allows UAVs to identify and avoid channels that are being used by neighboring UAVs or jammed by external attackers, thereby reducing the jamming likelihood. The power layer optimizes transmit power to meet rate thresholds. Theoretical analysis confirms that MALQL can converge to a pure strategy Nash equilibrium.",
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+ "text": "Nevertheless, there are still some issues with the anti-jamming mechanism in [87]. Considering that the rapid mo",
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+ "image_caption": [
+ "Part A. Overall system model under jamming"
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+ "Part B. MALQL-based anti-jamming scheme"
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+ "Part C. Population update of pre-training for generalized anti-jamming scheme"
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+ "Part D. PER-MATD3-based anti-jamming scheme"
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+ "image_caption": [
+ "Actor-Critic network for agent k",
+ "Fig. 8. The overall architecture illustrates various reinforcement learning-based anti-jamming schemes designed to enhance communication reliability in UAV-assisted MEC systems under jamming attacks. Part A presents the overall system model, depicting UAVs and jammers interacting within a dynamic environment. Part B shows the MALQL-based anti-jamming scheme, where agents use layered Q-learning to determine actions based on local observations and rewards. Part C depicts the population update mechanism for pre-training a generalized anti-jamming scheme, involving a jammer population, trajectory encoder, and decoder network to optimize jamming policies. Part D introduces the PER-MATD3-based anti-jamming scheme, incorporating a priority experience replay buffer and actor-critic networks to dynamically allocate resources and optimize UAV deployment strategies."
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+ "text": "bility of UAVs may expose them to various and unknown jamming patterns due to frequent transitions to new scenarios, the anti-jamming methods need to be generalized [176], especially in the LAENet. The work [87] randomly initializes strategies and learns from scratch for a particular deployment environment with no pretraining, which may lead to a reduction in the generalization ability of the anti-jamming strategy. In light of this, the authors in [88] introduce an adversarial pre-training stage in the proposed two-stage MARL with a decentralized partially observable Markov decision process. Specifically, the adversarial pre-training stage uses a quality-diverse jammer population (e.g., fixed, random, sweeping, statistic, and RL-based jamming) to bootstrap generalized anti-jamming strategies instead of directly initializing the agents with random anti-jamming policies, as shwon in part C of Fig. 10. This pre-training ensures that UAVs are not overfitted to specific jamming patterns and can generalize to new jamming attacks in real-world deployments. The pre-trained policies are deployed in the fine-tuning stage, where a graph convolutional-based MARL algorithm is proposed to jointly optimize channel selection and power allocation for anti-jamming similar to [87]. Simulation results show that the proposed solution achieves $20 - 30\\%$ higher cumulative rewards than collaborative multi-agent Q-learning [177] and independent Q-learning [83] under fixed and sweeping jamming.",
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+ "text": "Note that previous RL-based anti-jamming strategies [87], [88] mainly rely on the Q-learning method, which is suitable for discrete action spaces but may be limited in dealing with high-dimensional continuous spaces [147], [148]. The authors in [89] propose a PER-MATD3 algorithm against jamming",
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+ {
+ "type": "text",
+ "text": "by integrating spectrum-aware channel selection and prioritized experience replay (PER) into an MADRL framework, as shown in part D of Fig. 10. The proposed spectrum-aware intelligent channel selection uses energy detection-based spectrum sensing, enabling UAVs to identify and avoid jammed channels. The TD3 is specifically designed to handle continuous-valued states and actions, where two critic networks, target policy smoothing, and delayed policy updates are used to further stabilize DRL training. By leveraging PER, the agents can learn from high-error experiences, thereby accelerating adaptation to time-varying CSI, imperfect jamming detection, and co-channel interference. By jointly optimizing CPU frequency, bandwidth allocation, and channel selection to minimize the impact of jamming, PER-MATD3 reduces system cost (a linear combination of latency and energy consumption) by approximately $16.7\\%$ , $9.1\\%$ , and $1.2\\%$ compared to the baselines of Q-learning, MATD3-JSC (without PER), and PER-MATD3 (without channel selection), respectively.",
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+ "text": "Lesson Learned. Recent advancements in anti-jamming strategies show that intelligent decision-making for trajectory control, channel selection, and power control is essential for effective jamming mitigation. A key takeaway is the successful integration of MARL to develop dynamic and adaptive anti-jamming solutions [75]. By employing intelligent algorithms such as adversarial pre-training and decentralized decision-making, UAV networks can generalize anti-jamming strategies across diverse environments [76], [77]. However, challenges persist in the generalization of these strategies across various jamming types and environmental conditions, as well as balancing the trade-offs between energy consumption,",
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+ "text": "18",
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+ "img_path": "images/c26ca86189ba5e15945340467e93f9446f6ab0e20c20d86854d84170b44e6d6a.jpg",
+ "image_caption": [
+ "Part A. ML-based spoofing detection"
+ ],
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+ "image_caption": [
+ "Part B. Rule and ML-based spoofing detection",
+ "Fig. 9. The overall framework of ML and rule-based spoofing detection for GPS spoofing detection in the LAENet. Part A depicts an ML-based spoofing detection mechanism in [93], where multiple CNN classifiers are trained with updated sample weights to form an integrated classification model. Each CNN transfers its optimized parameters to subsequent classifiers, enhancing the model's robustness. Part B presents a hybrid rule and ML-based approach in [94], where statistical analysis of path losses between UAVs and multiple base stations (BSs) is performed by edge servers. The analyzed data is processed through MLPs to generate individual predictions, which are aggregated to produce a final spoofing detection decision."
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+ "text": "latency, and throughput. Future research could delve into the integration of more adaptive learning frameworks (such as deep learning) into the LAENet for anti-jamming, enabling it to better manage partial or imperfect environmental observations for low-latency, real-time decision-making in multi-UAV systems.",
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+ "text": "B. Spoofing Defense",
+ "text_level": 1,
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+ "text": "In the LAENet, the openness of A2G transmission channels and the dynamic nature of low-altitude aircraft networks make them particularly susceptible to identity-based spoofing attacks [50]. In such attacks, a malicious entity impersonates a legitimate transmitter using falsified identity information, such as a spoofed media access control address, to gain unauthorized access to the network [52]. Once authenticated, the spoofer can disrupt communications among aircraft by launching more severe attacks, such as rogue access point infiltration and denial-of-service attacks, ultimately leading to network congestion and service outages [75]. Given the limitations of conventional authentication methods that rely on complex cryptographic protocols [52], PLA offers a promising alternative by leveraging the inherent and unique physical characteristics of wireless transmissions for the LAENet, which is introduced in Section III-B. Overall, this type of PLA can defend against spoofing",
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+ {
+ "type": "text",
+ "text": "attacks in the LAENet by exploiting the unique characteristics of the wireless channel (such as RSS, Rayleigh channel, and Rician channel) to identify and separate between legitimate devices and spoofers.",
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+ "text": "The work in [90] proposes a PLA framework to detect spoofing attacks by exploiting spatial correlations of RSS in A2G channels. The key idea is that the RSS from a legitimate transmitter will remain relatively consistent due to its fixed location, while the RSS from a spoofer will vary significantly because of its different position and channel conditions. Thus, the UAV receiver can perform a hypothesis test to authenticate incoming signals. if the RSS distance between the current signal and a previously authenticated signal is below a predefined threshold, the signal is accepted as legitimate. Otherwise, it is flagged as a spoofing attempt. However, the work [90] is considered under an ideal transmission scenario, where the propagation environment is perfectly exempted from external interference. To address this limitation, the authors in [91] develop a PLA framework that accounts for channel randomness and interference uncertainty. First, they model the G2A link as a Rayleigh fading channel. Then, they introduce jamming signals as external interference. By modeling the jamming power statistically and incorporating it into the analysis of detected power differences, if the difference in power exceeds a predefined threshold, it is identified as a spoofing attempt. Thus, even in real-world scenarios with interference, the proposed framework can better differentiate between natural channel fading and anomalies caused by spoofing attacks.",
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+ "text": "In addition to using the statistical properties of the Rayleigh channel to design PLA against spoofing in environments with multipath fading (such as urban areas), the channel characteristics in suburban environments should also be considered. To address this, the work [77] proposes a PLA framework to counter spoofing attacks in both urban (Rayleigh channel) and suburban (Rician channel) environments. As mentioned earlier (in Section III-B), a new metric AD is devised to distinguish between legitimate signals and spoofing signals based on differences in channel randomness and geographical factors, such as elevation angles and distances. Adopting the unique fading characteristics of Rayleigh and Rician channels makes it statistically difficult for a spoofer to accurately mimic a legitimate signal. By considering elevation angles and distances in channel modeling, it ensures that a spoofer cannot easily replicate a legitimate signal even if the spoofer knows the legitimate transmitter's location. Simulation results show that the probability of a successful spoofing attack is significantly reduced compared to the baseline [171], where the spoofing miss detection probability drops to 0.014 in suburban environments and 0.371 in dense urban areas.",
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+ "type": "text",
+ "text": "In the LAENet, in addition to being vulnerable to identity-based spoofing attacks, aircrafts are also susceptible to signal spoofing attacks from the Global Navigation Satellite System (GNSS), particularly GPS spoofing, which poses a significant security threat by generating and transmitting counterfeit satellite signals resulting in severe positioning deviations [25]. By interfering with or suppressing legitimate GNSS signals, attackers can manipulate UAV locations in an imperceptible manner to mislead UAVs, causing deviations from intended",
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+ "type": "page_number",
+ "text": "19",
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+ "type": "table",
+ "img_path": "images/35f27e74f7c34c861495fa1c76195ab51abea9e536ca4fcaa9d1d7ca44689523.jpg",
+ "table_caption": [
+ "TABLE IX SUMMARY OF SPOOFING DEFENSE FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Techniques | Reference | Algorithm | Pros & Cons |
| PLA | [90] | RSS | Spatial correlations of RSS distances in PLA against spoofing attacksUse RSS-based channel characteristics to reduce PLA computational complexityAssume an ideal transmission scenario without external interference |
| [91] | Rayleigh channel | Defend against spoofing attacks by considering channel randomness and jammingSimultaneously address spoofing and jamming attacks via PLAAssume static UAVs and a known jamming distribution |
| [77] | Rayleigh and Rician channels | AD-based PLA for spoofing defense under Rayleigh and Rician channelsProvide a thorough analysis of spoofer identification in urban and suburban environmentsAssume perfect CSI in channel modeling |
| GNSS spoofing detection | [92] | Rule-based detection | Combine cooperative localization mechanism with Stackelberg game against spoofing attacksSpoofing detection is based on neighboring UAV signal sources without predefined thresholdsExtending to larger UAV groups may require complex adjustments |
| [93] | ML-based detection | Improved AdaBoost-CNN for multi-modal spoofing attack identificationHigh accuracy in identifying spoofing attacks with limited data samplesDependence on predefined signal features may lead to model overfitting |
| [94] | Rule & ML-based detection | MLP and statistical feature extraction on path-loss data for detecting GPS spoofingNo additional hardware/energy burden on UAVsRobust performance under sparse base station coverageSpoofing detection performance degrades in areas with unstable cellular signals |
",
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+ "type": "text",
+ "text": "flight paths, violations of no-fly zone regulations, or increased collision risks [46]. Given a critical role of GNSS in UAV operations, effective detection and mitigation strategies for spoofing attacks are essential to ensure flight safety and prevent security breaches in the LAENet. Currently, studies on signal spoofing attack recognition in the LAENet mostly focuses on recognizing GNSS spoofing attack detection, which primarily falls into two categories with respect on rule-based and ML-based methods [19], [25]. Rule-based detection methods typically assess the relative distance and positional deviations of UAVs to determine if they are under GNSS spoofing attack. On the other hand, the ML-based methods pay attention to recognize different spoofing types by learning the characteristics of received signals.",
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+ "text": "Generally, the simplified rule-based methods determine whether a UAV has encountered spoofing attacks based on whether its trajectory follows a predictable path [178], [179], since a UAV may exhibit deviations from this path due to the false signals imposed by the spoofer. If the measured deviations exceed predefined thresholds, it indicates a potential spoofing attack. However, relying on predefined thresholds for detecting deviations may not dynamically adapt to the spoofing attacks. The study in [92] proposes a defense mechanism based on cooperative localization, where each UAV uses the relative distances and real locations of neighboring UAVs to detect spoofing attacks. Specifically, each UAV measures its relative distances based on alternative signal sources of neighboring UAVs and compares these results with its own GPS-derived location. If inconsistencies are detected (e.g., the GPS-derived location does not match the majority of the calculated locations), the UAV identifies itself or a neighboring UAV as being under attack. To optimize defense deployment, an equilibrium of a dynamic Stackelberg game is derived between the drone operator (leader) and the spoofer (follower). Simulation results show that the proposed scheme can effectively prevent spoofer's capture, while random/deterministic baselines suffer from attackers capturing one to two UAVs.",
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+ "text": "Recent ML-based methods for spoofing defense primarily focus on binary classification concerning normal GPS signals and spoofing signals [180], [181]. However, they fail to recognize specific types of spoofing attack necessary for countermeasures in complex environments. Hence, there is an urgent need to recognize diverse GPS spoofing attack patterns for effective countermeasures for the LAENet. The authors in [93] propose an improved AdaBoost-CNN algorithm to address the challenge of recognizing diverse GPS spoofing attack patterns for UAVs, as shown in part A of Fig. 9. Three categorized spoofing attack patterns are considered including static and dynamic spoofing based on the UAV's motion state, power-matched and overpowered spoofing based on signal power, and position and time spoofing based on the spoofing targets. The authors select key GPS spoofing signal features such as signal quality monitoring, carrier-to-noise ratio, Doppler shift, and clock error to train the classification model. The improved AdaBoost-CNN algorithm integrates multiple weak CNN classifiers into a strong classification model. Each CNN base classifier uses the updated network parameters from the previous CNN as initial values, enabling iterative refinement of network weights to enhance feature extraction and generalization. With 800 simulated samples, the improved AdaBoost-CNN achieves $100\\%$ accuracy, outperforming original AdaBoost-CNN $(94.38\\%)$ , CNN $(74.38\\%)$ , DNN $(60.94\\%)$ , SVM $(40.63\\%)$ , and KNN $(53.13\\%)$ .",
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+ {
+ "type": "text",
+ "text": "Furthermore, integrating rule-based approaches with machine learning-based methods provides an effective and robust defense against spoofing attacks. The work in [94] leverages statistical features of path losses between UAVs and terrestrial base stations to detect a UAV's trajectory deviation due to GPS spoofing, as shown in part B of Fig. 9. The spoofing detection is formulated as a nonlinear optimization problem that aims to minimize hypothesis test errors by adjusting thresholds, statistical feature weights, and the number of base stations. To further accurately analyze path loss's statistical features for final decisions on predicting GPS spoofing probabilities,",
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+ "page_idx": 19
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+ {
+ "type": "page_number",
+ "text": "20",
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+ "type": "table",
+ "img_path": "images/b18000f7aeb2c577b647d747d82e6d530210f92f8540c1ae3fe4804b6814cb6a.jpg",
+ "table_caption": [
+ "TABLE X SUMMARY OF ANOMALY DETECTION FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Anomaly type | Reference | Algorithm | Pros & Cons |
| Jamming | [98] | HDBN | SA module based on HDBN for detecting jamming anomalies\n✓ UAccurately characterize and detect jamming anomalies via KLD/DB metrics\n✗ Unstable initialization in unsupervised learning affects the performance of the HDBN |
| [99] | GDBN | GDBN to model the radio environment and detect and classify jamming anomalies\n✓ Unsupervised learning eliminates dependency on labeled data in classification of anomalies\n✗ Computational complexity increases with the number of jamming categories |
| [100] | Active-GDBN | Active-GDBN used to model UAV-jammer interactions for anomaly detection\n✓ Actively incorporate UAV's actions for faster adaptation and jamming detection\n✗ M-MJPF requires significant computational resources |
| [101] | Blind channel estimation & ACS | Blind channel estimation based on ACS properties to detect jammer signals\n✓ Does not rely on prior knowledge of the jammer's behavior\n✗ Assumes a specific structure of the multicarrier modulation format |
| Abnormal Power | [102] | Spectrum surveillance | Local and cooperative detection of abnormal power emission\n✓ Handle both aggressive and passive power misuse\n✓ Cloud-based framework enables real-time closed-loop surveillance\n✗ Computational complexity increases with the number of SN |
| Eavesdropping | [103] | SVM & K-means | One-class SVM and K-means clustering for detecting eavesdropping anomalies\n✓ One-class SVM and K-means are stable under varying eavesdropper power\n✗ Detection performance mainly depends on the quality and quantity of the ATD |
",
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+ "page_idx": 20
+ },
+ {
+ "type": "text",
+ "text": "multilayer perceptron (MLP) neural networks are deployed on edge cloud servers, where individual MLP models at each BS are used to analyze statistical features of path losses. Simulation results show that the proposed method achieves $97\\%$ accuracy with two base stations and $83\\%$ accuracy with a single base station, outperforming baseline approaches such as adaptive trustable residence area (ATRA), which necessitates three base stations for triangulation [182].",
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+ "type": "text",
+ "text": "Lesson Learned. For identity spoofing in the LAENet, leveraging signal features such as received signal strength and channel randomness in PLA design is an effective approach [77], [90], [91]. On the other hand, employing rule-based or ML-based techniques can detect and mitigate GNSS signal spoofing [92]–[94]. While ML-based methods show promising performance, they are limited by factors such as computational complexity and dependency on large datasets. Rule-based methods are simpler but may struggle in dynamic or uncertain environments. Future research could explore the application of RL to develop adaptive and robust spoofing defense mechanisms in the LAENet, which has not yet been extensively studied. Different from the abovementioned approaches, RL dynamically learns from interactions with the environment, and its sequential decision-making ability enables UAVs and ground stations to optimize spoofing defense strategies based on continuous feedback [147], make it a promising direction for enhancing spoofing defense in the LAENet",
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+ {
+ "type": "text",
+ "text": "V. COMMUNICATION INTEGRITY FOR LAENET",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "A. Anomaly Detection",
+ "text_level": 1,
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+ "text": "Due to the open nature of wireless channels and the dominant LoS links in the LAENet, communication becomes particularly vulnerable to a diverse range of anomalous behaviors such as abnormal jamming, abnormal transmission power, and covert eavesdropping [46], [49]. Specifically, malicious jammers sense spectrum activity and dynamically adapt their interference patterns to mislead the UAV into taking suboptimal or harmful actions [81], [95]. In parallel, abnormal",
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+ {
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+ "text": "power emissions, either due to device faults, selfish behavior, or malicious intent, can violate spectrum policies, introduce harmful interference, and disrupt cooperative spectrum sharing [96]. Additionally, the pervasive risk of eavesdropping is that adversaries exploit the UAV's uplink or downlink transmissions to intercept sensitive data [61], [67]. Thus, it is essential to detect and mitigate these abnormal activities in the LAENet. Different from previously reviewed approaches such as anti-eavesdropping (Section III-A) and anti-jamming (Section IV-A), anomaly detection is a method used to identify and mitigate unexpected deviations from or irregularities in normal operational patterns by monitoring communication channels in the LAENet [127], [183].",
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+ "text": "Jamming anomalies generally aim to disrupt the normal operation of UAV communication links, such as by injecting disruptive signals to interfere with the legitimate communication process. The study in [98] proposes a novel Self-Awareness (SA) module to leverage the radio to detect abnormal behaviors caused by jamming attacks for Cognitive UAV communications. The SA module unsupervisedly learns a generative model using a Hierarchical Dynamic Bayesian Network (HDBN) [184] to represent the joint distribution of random variables characterizing the radio environment at different levels of abstraction and across time, where the Modified Bayesian Filtering [185] is used to integrate multilevel abnormality measurements for online predictions of radio environmental states at different levels. Since jamming can disrupt and shift the distributions of the radio environment, the abnormalities can be detected by calculating the Kullback-Leibler Divergence (KLD) and Dhattacharyya distance (DB) [186] between predictive messages and diagnostic messages. The predictive messages are generated by the HDBN to capture the expected patterns of normal signals, and diagnostic messages reflect the actual state of the signal. The jammer's impact is characterized by calculating generalized errors based on shifts in amplitude, phase, and frequency of signals, allowing the radio to predict future activities of the jammer. The SA",
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+ {
+ "type": "page_number",
+ "text": "21",
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+ {
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+ "img_path": "images/77a3923ca021fd3efb360f7086344f55ac8a6517a1d3d497b159cd347884c6bc.jpg",
+ "image_caption": [
+ "Part A. HDBN-based Scheme"
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ },
+ {
+ "type": "image",
+ "img_path": "images/90cd29842c633091f87cc0f88b31ff42f3aa3d723ca41aa33e5bffc52b6ea94e.jpg",
+ "image_caption": [
+ "Part B. GDBN-based Scheme"
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "image",
+ "img_path": "images/57804c0b57ed072e72c64d0c713f6844a0ec91912cdd542854e4d53830070bae.jpg",
+ "image_caption": [
+ "Part C. Active-GDBN-based Scheme",
+ "Fig. 10. The overall architecture illustrates jamming anomaly detection to enhance communication integrity in the LAEnet. Part A presents an HDBN-based scheme focusing on hierarchical dynamic models to predict and detect abnormal signals caused by jammers. It details the transition probabilities between model states and the prediction of continuous states based on discrete superstates. Part B introduces a GDBN-based scheme, extending the HDBN approach by incorporating generalized states and observations, allowing for more nuanced predictions and error calculations. Part C depicts an Active-GDBN-based scheme, integrating UAV actions into the model to actively infer and adapt to the environment, thereby optimizing resource allocation and anti-jamming measures."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 21
+ },
+ {
+ "type": "text",
+ "text": "module achieves a near $100\\%$ abnormality detection accuracy, approximately $12\\%$ higher than the traditional energy detector-based scheme.",
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+ "page_idx": 21
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+ {
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+ "text": "Different from the previous work [98], which introduced the SA module using HDBN for anomaly detection, the authors in [99] propose a Generalized Dynamic Bayesian Network (GDBN)-based framework to enhance the SA module by further classifying the detected anomalies caused by multiple jammers. A generalized state-space model [184] is used to represent the evolving radio environment as a GDBN model learned in an unsupervised manner. Different from the KLD/DB metric in [1], Kullback-Leibler divergence and Bhattacharyya distance are used as abnormality measurements between predicted and observed signals to detect jamming. Once an abnormality indicative of jamming is detected, the UAV extracts the interfering signal and compares it with prelearned GDBN models (each representing a different jamming modulation scheme). By evaluating which pre-learned model best explains the extracted jamming signal, the UAV can not only detect the presence of a jammer but also classify its modulation type. Simulation results show that the GDBN-based method achieves an overall classification accuracy of $98\\%$ at $\\mathrm{SNR} = 10$ dB, outperforming LSTM $(88\\%)$ , CNN $(67\\%)$ , and SAE $(90\\%)$ .",
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+ "text": "Based on the study [99], the authors in [100] propose an Active-GDBN to model the dynamic interaction between the UAV and jammer for anomaly detection. Similar to [99], the generalized state-space model [184] is used to capture the features and dynamic evolution of UAV signals to represent the radio environment. Differently from passive detection and classification of jamming signals in [99], the Active-GDBN achieves active anomaly detection by incorporating the UAV's actions into the inference process. Specifically, the UAV employs a Modified Markov Jump Particle Filter (M-MJPF) [187] to link the UAV's actions to environmental",
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+ },
+ {
+ "type": "text",
+ "text": "states and observations. Meanwhile, the UAV dynamically adjusts physical resource block selections to evade jamming by encoding jammer behavior and updating beliefs. The Active-GDBN achieves about $25\\%$ to $37.5\\%$ faster convergence on anomaly detection probability than the Q-learning-based baseline under various jamming types.",
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+ {
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+ "text": "Different from previous works [98]–[100] that detect jamming anomalies based on the statistical distribution divergence of the signal, study [101] focuses on detecting anomalies by exploiting the time delays, shifts, and modulation of the signal characteristics. Firstly, achieving blind channel estimation involves constructing cyclic correlation matrices to identify distinct Doppler shifts and time delays associated with transmissions by exploiting the inherent almost-cyclostationary (ACS) properties of UAV and jammer signals (e.g., periodic statistics from OFDM modulation). Then, this blind estimation process is combined with a widely linear minimum mean square error (WL-MMSE) filter to provide an initial estimate of the symbol vector by leveraging the non-circular statistics of the received signal, where the initial estimate includes contributions from both the UAV and the jammer. Finally, a post-sorting algorithm (PSA) is employed to iteratively decode and cancel the jammer's contribution by ranking and removing symbols with the highest signal-to-disturbance-plus-noise ratio (SDNR). Simulation results demonstrate that the proposed scheme can effectively detect and separate the jamming signals from UAV signals without requiring prior knowledge of the jammer's characteristics, even when the jammer's power is twice as strong as the UAV's power.",
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+ {
+ "type": "text",
+ "text": "In addition to jamming anomalies, which cause interference and security threats in the LAENet, abnormal power emissions in UAV communication networks also represent a critical type of anomaly, potentially leading to severe disruption of communication quality and violation of spectrum policies. The work in [102] proposes a cloud-based surveillance framework",
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+ {
+ "type": "page_number",
+ "text": "22",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/aefb9e00909efa991b8f89e18e40ebc9e14f812ef0f371b6668cba7d6f813151.jpg",
+ "table_caption": [
+ "TABLE XI SUMMARY OF INJECTION DEFENSE FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ ],
+ "table_footnote": [],
+ "table_body": "| Injection type | Reference | Algorithm | Pros & Cons |
| Jamming signal | [98] | HDBN | HDBN-based jamming signal extraction and suppression\n✓ Autonomous learning from raw I/Q data enables adaptability to dynamic jamming patterns\nX Assume the jammer's output power remains constant during attacks |
| [101] | SIC | SIC with blind channel estimation for detecting and eliminating jamming signals\n✓ Eliminate jamming signals regardless of the mobility patterns of jammers\nX Rely on sufficient cyclostationary features in the received signal |
| [104] | DBF | DBF algorithm for nullifying jamming signals\n✓ Effective suppression of jamming signals while maintaining carrier phase integrity\nX May be limited to specific GNSS frequency bands |
| Spoofing signal | [105], [106] | API & LSR | SIC combined with API and LSR to recover legitimate signals from spoofing attacks\n✓ SemperFi with a single antenna does not require additional hardware\nX Limited to attackers with a power advantage lower than 15 dB |
| [107] | Subspace projection | Subspace projection for nullifying spoofing signals\n✓ Low parameter dependency, requiring only code delays and carrier frequencies\nX Suppression performance declines if spoofing and legitimate signals have similar code delays |
",
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+ "page_idx": 22
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+ {
+ "type": "text",
+ "text": "to address the detection of abnormal power emissions, where the cloud server assigns spectrum resources to the UAVs and shares UAVs' spectrum usage information with the surveillance center. The surveillance center assigns the detection task to $K$ surveillance nodes (SNs) for local detection of abnormal power emission, where the detection rule is based on the Lagrange multiplier method and the generalized likelihood ratio test. After local decisions, $K$ SNs report results to the surveillance center, where cooperative detection of abnormal power emission is performed using the decision rule that declares an abnormal event when at least $L$ out of $K$ nodes detect an abnormality, where the optimal global threshold of $L$ is determined by solving the constraints on the global false-alarm probabilities. Simulation results show that the global detection probability exceeds 90% when transmit power deviation exceeds 0.02W (allocated power is 0.01W).",
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+ "text": "Besides the threats of jamming and abnormal power emission, another critical anomaly that requires detection is eavesdropping in the LAENet, where malicious devices covertly intercept sensitive information during UAV-to-ground and UAV-to-UAV transmissions [66], [67]. Note that most previous works on anti-eavesdropping focused on measuring secure performance through secrecy rate and/or secrecy outage probability (such as [71], [76]) rather than emphasizing the detection of eavesdropping attacks. The work in [103] explores anomaly detection for eavesdropping attacks in UAV-aided wireless systems using unsupervised learning. Two datasets are prepared: artificial training data (ATD), simulated without eavesdropping based on CSI (all labeled normal), and a practical dataset extracted from received signal features (mean and variance of amplitude). Two types of unsupervised learning methods are designed for anomaly detection. One-class SVM maps data to a high-dimensional space, defining a normal region where outliers are detected. K-means clustering classifies test data into two clusters, labeling the one nearest to the ATD center as normal.",
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+ },
+ {
+ "type": "text",
+ "text": "Lesson Learned For jamming anomalies, the statistical distribution divergence detection and signal structural feature-based detection, such as HDBN, GDBN, and ACS, are used to model the dynamic environment and detect deviations from",
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+ {
+ "type": "text",
+ "text": "learned normal patterns. For abnormal transmission power detection, a cloud-based surveillance framework supports a statistical distribution detection approach to monitor and identify power emission outliers. Leveraging its high computing power, the cloud enables cooperative analysis through multi-source data aggregation, dynamically optimizes detection thresholds using global information, and maintains a feedback loop for adaptive anomaly detection. For eavesdropping detection, unsupervised learning techniques, including One-Class SVM and K-means clustering, achieve the identification of anomalies in received signals. These approaches effectively achieve anomaly detection and demonstrate excellent performance. However, challenges remain, including the reliance on high-quality training data and the complexity of maintaining real-time adaptability in dynamic spectrum environments. Currently, Generative AI such as GANs and generative diffusion models presents a promising research direction for anomaly detection, as demonstrated in the use of generalized models in HDBN and the artificial data generation for training ML and clustering models in [188], [189]. Generative AI could further enrich training datasets and provide a high-level generative model to enhance anomaly detection in the dynamic and uncertain LAENet.",
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+ {
+ "type": "text",
+ "text": "B. Injection Defense",
+ "text_level": 1,
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+ "text": "The low-altitude economy is highly dependent on open communication and network architecture with dense communication links, which brings injection attacks as a significant threat to UAV communication integrity [28], [46]. These attacks involve the deliberate injection of malicious signals, such as jamming and spoofing signals, to disrupt or manipulate legitimate communications [97], [190]. Jamming signal injection can make legitimate signals unrecognizable by emitting high-power electromagnetic interference to degrade signal reception [98]. Additionally, spoofing signal injection can transmit high-power signals to overshadow legitimate GNSS signals. Therefore, eliminating injection signals or separating them from legitimate signals is crucial for ensuring communication integrity in the LAENet.",
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+ "img_path": "images/0a2b881bbb436b377c3415cb335afd7cf07d689d5c423c459fd8a5651c2607af.jpg",
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+ "Part A. SNDR-based SIC for jamming injection defense"
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+ "Part B. SIC with API and LSR for spoofing injection defense"
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+ "Part C. Subspace projection for spoofing injection defense",
+ "Fig. 11. The overall architecture of injection defense mechanisms for UAVs in smart city applications. Part A presents the SIC architecture that processes channel state information to defend against jamming injection attacks [101]. Part B shows an SIC architecture integrated with API and LSR modules, which subtracts injection signals from the received signal to recover normal signals [105], [106]. Part C depicts a subspace projection-based architecture for spoofing injection defense, where the received signal is projected onto the orthogonal null space of the spoofing signals to eliminate them [107]."
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+ "text": "The UAV's communication can be severely disrupted by jammers that exploit LoS propagation to inject jamming signals into the transmission channel, which may effectively mask legitimate signals and render them unrecognizable [101]. The work in [98] proposes an HDBN-based injection defense scheme to extract and remove the jammer's signal. This work first utilizes the HDBN to detect abnormal behaviors caused by jamming attacks, as mentioned earlier in Section V-A. Once the jammer's presence is confirmed, its signal characteristics are analyzed across multiple levels of continuous in-phase (I) and quadrature (Q) components and observation-level state vectors [191]. The extracted jammer signal is then separated from the received observation using frequency-domain subtraction [192], component-wise I/Q processing, and adaptive filtering [191]. The corrected signal is subsequently demodulated and decoded using techniques and error correction coding to restore the original signal. To maintain resilience against evolving jamming tactics, the system continuously updates the HDBN model to improve suppression commands. Simulation results show that the mean square error (MSE) of suppression commands decreases as the JSR increases, meaning that jammers attacking with higher power can be better estimated than jammers attacking with lower power.",
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+ "text": "Different from the work in [98], which separates the jamming signal by analyzing its I/Q characteristics, the study in [101] proposes a Serial Interference Cancellation (SIC) scheme based on SDNR to eliminate injected anomalous signals in UAV communications, as shown in part A of Fig. 11. First, blind channel estimation and a WL-MMSE filter are used to identify UAV and jammer signals (as detailed in Section V-A). Then, the PSA ranks detected symbols based on SDNR, where the jamming signals rank higher in SDNR due to their higher emitted power. The SIC [193],",
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+ "text": "[194] is subsequently designed for progressively eliminating jamming signals. Specifically, the high-rank jamming symbol is decoded, reconstructed using estimated channel parameters, and subtracted from the received signal. The process continues iteratively to eliminate previously detected jamming signals until all UAV symbols are successfully recovered, with the receiver dynamically updating channel estimation to adapt to jammer mobility and environmental changes. Simulation results demonstrate that the UAV signal can be recovered with low bit error rates $(< 10^{-4})$ even when the power of the jammer is double that of the UAV.",
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+ "text": "Jamming attacks not only affect U2G and UAV-to-UAV communications but also cause RF interference, leading to UAVs failing to track GNSS signals in the LAENet. In light of this, the work in [104] proposes a self-calibrating digital beamforming (DBF) algorithm to effectively nullify jamming signals while preserving high-precision carrier phase measurements. It calibrates the antenna array's steering vectors and RF channel characteristics. Once calibration is complete, the system performs jamming detection and direction estimation by analyzing interference patterns across the antenna array. Then, the minimum power distortionless response (MPDR) optimization rule is used to calculate optimal beamforming weights, which aim to create nulls in the beam pattern corresponding to the directions of jamming signals, effectively suppressing them. The calculated beamforming weights are applied to the received signals to produce the beamformer output, which effectively suppresses jamming signals while preserving the carrier phase integrity of the desired signals. The proposed scheme achieves up to 80 dB Jammer-to-Signal Ratio (JSR) suppression, significantly outperforming the conventional Power Inversion (PI) scheme.",
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+ "text": "In addition to jamming signals, spoofing attacks can easily",
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+ {
+ "type": "text",
+ "text": "transmit fake signals to manipulate GNSS signals due to their open signal structure and weak signal strength [195]. One type of method is based on signal encryption or data encryption to prevent malicious spoofers from injecting illegitimate signals [196]–[198]. However, they may not be suitable for resource-constrained UAVs in the LAENet. Therefore, defending against spoofing signal injection based on different signal characteristics is a promising solution. The authors in [105], [106] propose an anti-spoofing system, called SemperFi, to autonomously recover legitimate signals during active spoofing for UAVs. The system employs two core modules: the Adversarial Peak Identifier (API) and the Legitimate Signal Retriever (LSR), as shown in part B of Fig. 11. The API detects spoofed signals by correlating inertial measurement unit (IMU) data with calculated position-velocity-time (PVT) solutions [199]. The LSR module replicates the spoofing signal once it is identified. Then, similar to the study in [101], the SIC is applied to subtract the replica from the composite received signal that contains legitimate and spoofing signals. SemperFi enters an iterative refinement process if spoofing signals persist after initial cancellation, where replication, subtraction, and reassessment are performed until the spoofing detector no longer triggers an alarm, indicating sufficient attenuation or elimination of spoofing.",
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+ "text": "Besides recovering legitimate signals by subtracting spoofing signals from the received signal [101], [105], [106], projecting the signal is also a viable injection defense strategy. In the study [107], the GNSS receiver's spoofing mitigation algorithm employs a subspace projection-based interference cancellation method to effectively eliminate spoofing signals, as shown in part C of Fig. 11. Specifically, the receiver on UAVs acquires and tracks incoming signals, identifying potential spoofing signals and reconstructing them based on their power levels, pseudo-random noise (PRN) code delays, and carrier frequencies. Then, the receiver uses these reconstructed spoofing signals to construct a spoofing subspace, which represents all possible linear combinations of spoofing signal characteristics. To effectively remove spoofing signals from the received signal, the receiver performs orthogonal projection to obtain a cleaned signal by mapping the received signal onto a complementary null space that is mathematically orthogonal to the spoofing subspace. Simulation results show that shorter projection lengths suppress spoofing signals more effectively than longer projections, achieving a $20\\mathrm{dB}$ gain in Signal-to-Interference Ratio (SIR).",
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+ "text": "Lesson Learned The above-mentioned studies have demonstrated the effectiveness for mitigating injection signals, such as jamming and spoofing attacks, thereby enhancing UAV communication reliability and security. These advancements leverage techniques that not only detect malicious signal interference but also enable autonomous recovery. One key advantage is that non-cooperative detection techniques, such as blind estimation [101] and self-awareness models [98], allow for efficient attack identification without requiring prior knowledge of the attacker's signal characteristics to adapt to dynamic and adversarial environments. However, several challenges remain in that beamforming-based or spatial filtering techniques rely on multi-antenna configurations [101],",
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+ "type": "text",
+ "text": "[104], limiting their applicability in cost-sensitive or small UAV systems. Future work should explore lightweight and energy-efficient implementations of injection defense to support stable UAV signal integrity protection. Additionally, more intelligent injection defense strategies combining optimization methods, RL, and ML could enhance resilience against more sophisticated adversaries.",
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+ "text": "VI. FUTURE RESEARCH DIRECTIONS",
+ "text_level": 1,
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+ "text": "A. Energy-efficient Physical Layer Security",
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+ "text": "Future work can focus on exploring more unique physical characteristics of wireless communication, such as exploiting channel characteristics and implementing simple coding schemes, to develop secure and low-energy protocols. Meanwhile, drones in the LAENet need to develop adaptive power control strategies that dynamically adjust transmission power based on channel conditions and security requirements to minimize unnecessary energy consumption [200]. Moreover, dynamic trajectory optimization is equally important for energy efficiency [201]. Future research can explore enabling UAVs to learn attack patterns in real time, share secure trajectory models across swarms, and dynamically adjust flight paths based on real-time security and power consumption feedback.",
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+ "text": "B. Multi-drone Collaboration for Secure Communication",
+ "text_level": 1,
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+ "text": "Future research on secure physical layer communication in the LAENet should move beyond existing dual-UAV collaboration models and explore distributed multi-UAV coordination (or UAV swarms) for enhanced resilience against jamming, spoofing, and unauthorized access [202]. For example, UAV swarms can collaboratively emit interference signals to obscure unauthorized receivers, thereby enhancing the confidentiality of communications [20]. Additionally, the integration of adaptive trust-based mutual authentication protocols among UAVs is essential [26]. Multiple UAVs with mutually verified identities can enable dynamic and secure spectrum-sharing mechanisms to optimize resource utilization in the LAENet.",
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+ "type": "text",
+ "text": "C. AI-driven Security Defense Strategy",
+ "text_level": 1,
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+ "text": "Existing AI-based security strategies mainly focus on training AI models to identify anomalous signals while having some limitations. The resource-constrained drones are unable to train high-quality AI models, making the integration of edge computing a promising approach for model training [200]. Note that AI models may be difficult to generalize in recognizing various anomalous signals because they are pre-trained on previously collected datasets of fixed size. Future work can explore leveraging GAN or diffusion models to generate datasets based on real-time captured anomalous signals [203]. Furthermore, emerging generative AI technologies, such as the diffusion model for secure network topology generation in low-altitude domains [189], [204], AI agents for human-aerial vehicle secure interaction [205], and mixture of experts for robust wireless communications [2], [206], can be explored to achieve a more autonomous and intelligent LAENet.",
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+ {
+ "type": "page_number",
+ "text": "25",
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+ "type": "text",
+ "text": "D. Space-Air-Ground Integrated Security Architecture",
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+ "text": "Future research can explore establishing a multi-domain physical layer security framework for LAENet to connect space, air, and ground layers, providing seamless communication coverage and cost-effective network access [55], [207]. A potential key research direction is the development of a coordinated multi-tier security mechanism, where satellites, UAVs, and terrestrial base stations collaboratively enhance physical layer security through dynamic resource allocation and interference management based on real-time CSI and environmental conditions, such as UAV mobility, channel fading, and spectrum constraints.",
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+ "text": "E. 6G-Enabled Secure UAV Communication",
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+ "text": "The advent of 6G networks presents new opportunities for LAENet. Terahertz (THz) communication can offer ultrahigh-speed data transmission capabilities for LAENet [208]. Future research can explore the integration of THz with advanced beamforming techniques to focus signals on legitimate users, thereby enhancing security and reducing the risk of interception. Furthermore, Reconfigurable Intelligent Surfaces (RIS) play a crucial role in strengthening physical layer security by intelligently controlling wireless signal propagation [209], [210]. Future work can investigate RIS-based secure beamforming strategies to mitigate adversary interception, and leverage optimization techniques and DRL to adaptively adjust beamforming against eavesdropping or jamming attacks.",
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+ "text": "VII. CONCLUSION",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "This paper has presented a comprehensive survey on secure physical layer communications in the LAENet, emphasizing the importance of safeguarding confidentiality, availability, and integrity in communications. It introduced the concept and architecture of the LAENet and outlined the associated security issues in physical layer communication. Then, the survey provided in-depth reviews of countermeasures for anti-eavesdropping strategies, authentication schemes, anti-jamming strategies, spoofing defenses, anomaly detection, and injection defense. Finally, the paper proposed a set of forward-looking future research directions. These discussions highlighted the critical role of secure physical layer communication in supporting the development of the LAENet and offered valuable insights for ongoing advancements in this emerging domain.",
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+ "text": "REFERENCES",
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+ "content": "arXiv:2504.09153v1 [cs.CR] 12 Apr 2025"
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+ "type": "title",
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+ "content": "Secure Physical Layer Communications for Low-Altitude Economy Networking: A Survey"
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+ "content": "Lingyi Cai, Jiacheng Wang, Ruichen Zhang, Yu Zhang, Tao Jiang, Fellow, IEEE, Dusit Niyato, Fellow, IEEE, Xianbin Wang, Fellow, IEEE, Abbas Jamalipour, Fellow, IEEE, and Xuemin Shen, Fellow, IEEE"
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+ "content": "Abstract—The Low-Altitude Economy Networking (LAENet) is emerging as a transformative paradigm that enables an integrated and sophisticated communication infrastructure to support aerial vehicles in carrying out a wide range of economic activities within low-altitude airspace. However, the physical layer communications in the LAENet face growing security threats due to inherent characteristics of aerial communication environments, such as signal broadcast nature and channel openness. These challenges highlight the urgent need for safeguarding communication confidentiality, availability, and integrity. In view of the above, this survey comprehensively reviews existing secure countermeasures for physical layer communication in the LAENet. We explore core methods focusing on anti-eavesdropping and authentication for ensuring communication confidentiality. Subsequently, availability-enhancing techniques are thoroughly discussed for anti-jamming and spoofing defense. Then, we review approaches for safeguarding integrity through anomaly detection and injection protection. Furthermore, we discuss future research directions, emphasizing energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. This survey may provide valuable references and new insights for researchers in the field of secure physical layer communication for the LAENet."
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+ "content": "Index Terms—Low-altitude economy networking, secure physical layer communications, communication confidentiality, communication availability, communication integrity."
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+ "type": "title",
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+ "content": "I. INTRODUCTION"
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+ "content": "WITH the rapid development of aerial vehicle technologies and communication networks, the concept of Low-Altitude Economic Networking (LAENet) has emerged to enable more comprehensive, large-scale, and intelligent"
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+ "content": "Lingyi Cai is with the Research Center of 6G Mobile Communications, School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China, and also with the College of Computing and Data Science, Nanyang Technological University, Singapore (e-mail: lingyicai@hust.edu.cn)."
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+ "content": "Jiacheng Wang, Ruichen Zhang, and Dusit Niyato are with the College of Computing and Data Science, Nanyang Technological University, Singapore (e-mails: jiacheng.wang@ntu.edu.sg; ruichen.zhang@ntu.edu.sg; dniyato@ntu.edu.sg)."
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+ "content": "Yu Zhang and Tao Jiang are with the Research Center of 6G Mobile Communications, School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China (e-mail: yuzhang123@hust.edu.cn; tao.jiang@ieee.org)."
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+ "content": "Xianbin Wang is with the Department of Electrical and Computer Engineering, Western University, London, ON, N6A 5B9, Canada (e-mail: xianbin.wang@uwo.ca)."
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+ "content": "Abbas Jamalipour is with the School of Electrical and Computer Engineering, University of Sydney, Australia (e-mail: a.jamalipour@ieee.org)."
+ },
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+ "content": "Xuemin Shen is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: sshen@uwaterloo.ca)."
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+ "type": "text",
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+ "content": "connectivity to support various low-altitude activities [1]–[4], such as intelligent transportation, logistics delivery, communication enhancement, disaster monitoring, and emergency response [5]–[8], as shown in Fig. 1. The LAENet is built upon earlier frameworks of single Unmanned Aerial Vehicle (UAV) operation and multi-UAV networks. A single UAV typically maintains a direct link to a ground station or base station, operating with simple control procedures and delivering cost-effective services but with limited range and scalability [9]. The UAV network focuses on formation control and multi-UAV collaboration, enabling broader mission areas and stronger fault tolerance [9]–[11]. Advancing from these foundations, the LAENet integrates various aerial vehicles into a high-density communication network, connecting them not only to ground stations but also to other platforms such as base stations, access points, and even satellites [12], [13]. Thus, the LAENet can enable ubiquitous coverage, high reliability, robust fault tolerance, greater autonomy, and intelligence."
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+ "content": "Specifically, the LAENet refers to an integrated network system that connects various low-altitude flight operations, including general aviation, drones, electric vertical take-off and landing (eVTOL) aircraft, and other aerial platforms, within the designated low-altitude airspace (typically below 1,000 meters, and in some cases extending up to 3,000 meters) [1], [13]. The LAENet serves as a vital bridge between ground-based economies and airspace resources, which will drive technological innovation and unlock substantial social and economic benefits [14], [15]. The Civil Aviation Administration of China estimates that the country's low-altitude market will soar from 500 billion Chinese yuan (about 70 billion US dollars) in 2023 to 1.5 trillion Chinese yuan (about 200 billion US dollars) in 2025 and as much as 3.5 trillion Chinese yuan (about 480 billion US dollars) in 2035 [16]. Currently, research institutions and enterprises across multiple regions in China are continuously advancing and expanding innovative research and commercial applications of UAVs and eVTOLs in low-altitude activities [17]. Meanwhile, in the United States, the Federal Aviation Administration has confirmed its commitment to actively promoting the development of electric air taxis and integrating this type of aircraft into the national airspace [18]."
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+ "content": "In the LAENet, physical layer communication serves as a critical foundation for wireless communication between aerial vehicles and between aerial vehicles and communication infrastructure [10], [28], [31]. The physical layer converts digital data from higher protocol layers into signals suitable for transmission over aerial communication channels [32]–[34]."
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+ "content": "Fig. 1. The overall architecture of the LAENet covers the main application scenarios, including emergency monitoring and response, temporary communication relay, communication coverage expansion, low-altitude smart logistics, and urban air mobility. The table compares the similarities and differences between the LAENet, single UAV, and UAV networks, representing the evolution of the LAENet."
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+ "content": "This process encompasses encoding data into bit sequences, modulating them onto carrier waves, and ensuring reliable signal propagation through the wireless medium [32], [35], [36]. At the receiver side, the physical layer performs inverse operations, including demodulating the incoming signals, decoding the bit sequences, and passing the data to upper layers for further processing [37]–[39]. Therefore, the physical layer supports the core communication mechanisms in the LAENet and plays a crucial role in its aerial deployment. For example, aerial vehicles deployed as aerial base stations (ABSs) or aerial relays can overcome interference, signal distortion, and environmental variations inherent in communication links by using physical layer functionalities such as channel access, multiplexing, and channel equalization [33], [40], [41]."
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+ "content": "However, physical layer communication in the LAENet is exposed to a variety of security threats due to the inherent characteristics of aerial communication environments [42]. The broadcast nature of wireless signals and the prevalence of line-of-sight (LoS) propagation make aerial links particularly vulnerable to eavesdropping, jamming, and spoofing attacks [1], [43]. These attacks can compromise communication confidentiality, disrupt communication, or deceive aerial vehicles by impersonating legitimate transmitters [44], [45]. Furthermore, the openness of wireless channels and weak authentication mechanisms increase the risk of unauthorized access and injection attacks, allowing adversaries to infiltrate the network or inject malicious signals [46], [47]. Additionally, the open medium and dynamic spectrum access may cause anomalous behaviors to disrupt normal communication operations in the LAENet [48], [49]."
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+ "content": "Confronted with these substantial security challenges, this paper conducts a comprehensive analysis on physical layer communications of the LAENet and provides a thorough survey of technologies and solutions to address communication confidentiality, availability, and integrity. Table II gives a clear structure for showing existing efforts on secure physical layer communications for the LAENet."
+ },
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+ "angle": 0,
+ "content": "A. Related Surveys"
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+ "content": "Recently, a number of excellent survey and tutorial papers have overviewed security issues in UAV networks and communications and have summarized corresponding countermeasures and solutions, as shown in Table I. Some works consider security issues at the system level including intrusion, privacy, and trust issues. The work in [19] provides a comprehensive review of security threats facing UAVs and UAV networks, including communication vulnerabilities, sensor spoofing, jamming, and malware attacks. It examines various countermeasures such as encryption, global positioning system (GPS) spoofing mitigation, and firmware signing. A gap analysis is performed to identify remaining security vulnerabilities and provide recommendations for future UAV development. The study in [20] conducts a comprehensive review of security issues in UAV swarm networks, examining various potential attacks such as communication attacks, identity-based attacks, resource attacks, routing attacks, data attacks, and machine learning (ML) attacks. It categorizes these threats and presents corresponding security technologies and countermeasures, including cryptography, physical layer security techniques, blockchain, machine learning, and intrusion detection"
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+ "content": "TABLEI SUMMARY OF RELATED SURVEYS"
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+ "angle": 0,
+ "content": "| References | Focus |
| [19] | A review of cybersecurity threats, countermeasures, and research gaps in UAV networks, with a focus on emerging attack surfaces and commercial UAV applications |
| [20] | A survey of security threats, vulnerabilities, and countermeasures in UAV swarm networks, with a focus on classifying attack types and reviewing emerging defense technologies |
| [21] | A review of security threats, vulnerabilities, and countermeasures in UAVs and Flying Ad Hoc Networks with attack surface analysis with simulation-based evaluation |
| [22] | A survey of vulnerabilities across software, hardware, and communication layers in UAV systems, and an exploration of emerging defense technologies |
| [23] | A survey of security challenges in drone communication and a review of emerging technologies used to enhance the speed, reliability, and security of UAV networks |
| [24] | A review of UAV security challenges, existing controls, and future research directions, with an emphasis on the transformative role of AI in enabling secure UAV systems |
| [25] | A review of security threats classified from a cyberspace security perspective and countermeasures in UAV systems |
| [26] | A survey of security threats, requirements, and counter-measures in UAV-aided Internet of Things (IoT) applications |
| [27] | A survey of cybersecurity vulnerabilities and countermeasures in UAV systems, integrating threat classification, communication protocols, and emerging techniques |
| [28] | A survey of PLS in UAV communications, focusing on key challenges, methodologies, and recent advancements for both static and mobile UAV deployment scenarios |
| [29] | A review of security challenges, practical deployment aspects, and standardization progress associated with integrating UAVs into cellular networks |
| [30] | A survey of layer-wise cybersecurity threats and AI-enabled countermeasures in UAV-assisted IoT applications |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "systems. The authors in [21] provide a detailed examination of security challenges in UAVs and FANETs, covering various attack vectors including communication, identity-based, resource, routing, data, and machine learning attacks. The study in [22] examines security and privacy vulnerabilities in UAV systems across hardware, software, and communication layers. It discusses various threats such as eavesdropping and jamming attacks, and presents defense mechanisms including blockchain, machine learning-based intrusion detection, and secure communication protocols."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Some studies emphasize cyber security challenges within UAV networks. The study in [23] comprehensively reviews security issues in drone communication, including Denial of Service (DoS), GPS spoofing, and man-in-the-middle attacks. It examines vulnerabilities across different drone applications and presents countermeasures using blockchain, software-defined networks, machine learning, and fog computing. The authors of [24] provide a comprehensive survey of security challenges in UAV systems, including various types of attacks, privacy concerns, and trust issues. It identifies current research trends and gaps while establishing a future roadmap with a focus on artificial intelligence (AI)'s potential to enhance UAV security. The authors in [25] provide a comprehensive review of security issues in UAV networks, examining various potential attacks such as spoofing, replay, jamming, and"
+ },
+ {
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+ "content": "TABLE II"
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+ "angle": 0,
+ "content": "CHALLENGES AND SOLUTIONS"
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+ "content": "RED CIRCLES DESCRIBE THE SECURITY ISSUES; GREEN CIRCLES REPRESENT THE OVERALL COUNTERMEASURES FOR THE SECURITY ISSUES; GREEN CHECK MARKERS INDICATE DIFFERENT TYPES OF SOLUTIONS UNDER EACH COUNTERMEASURE"
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+ "content": "| Section III, Challenge 1: Communication confidentiality |
| Issues | ● Eavesdropping attack [46], [50]● Unauthorized access [31], [51], [52] |
| Solutions | ● Anti-eavesdropping strategies√ Convex optimization-based strategies [53]–[59]√ Reinforcement learning-based strategies [60]–[65]√ Deep learning-based strategies [66]–[71]● Communication authentication√ PUFs-based authentication [72]–[74]√ Channel based-authentication [75]–[77] |
| Section IV, Challenge 2: Communication availability |
| Issues | ● Jamming attack [48], [78], [79]● Spoofing attack [49], [50], [52], [78] |
| Solutions | ● Anti-jamming strategies√ Convex optimization [80]–[82]√ Single-agent RL [83]–[86]√ Multi-agent RL [87]–[89]● Spoofing defense√ PLA [77], [90], [91]√ GNSS spoofing detection [92]–[94] |
| Section V, Challenge 3: Communication Integrity |
| Issues | ● Anomalous behaviors [61], [95], [96]● Injection attacks [28], [46], [97] |
| Solutions | ● Anomaly detection√ Jamming anomaly detection [98]–[101]√ Abnormal power detection [102]√ Eavesdropping anomaly detection [103]● Injection defense√ Jamming signal injection defense [98], [101], [104]● Spoofing signal injection defense [105]–[107] |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "eavesdropping attacks. It categorizes these threats and presents corresponding security technologies and countermeasures. The study in [26] provides a comprehensive review of security issues in UAV-aided IoT applications and presents corresponding security technologies and countermeasures. The work in [27] reviews cybersecurity threats affecting UAV systems and evaluates existing countermeasures in enhancing UAV security."
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+ "angle": 0,
+ "content": "In addition, some surveys analyze the challenges faced by UAV systems from a layered perspective (e.g., physical layer, link layer, network layer, application layer). The work in [28] deeply reviews the current state of physical layer security (PLS) in UAV communications, examining unique air-to-ground channel characteristics, static and mobile UAV deployment scenarios, and various security enhancement techniques. The work in [29] presents a comprehensive overview of UAV cellular communications, covering the classification of consumer drones, the concept and potential of UAV-mounted flying base stations. It explores the integration of UAVs into cellular networks as novel user equipment and addresses key challenges related to interference, regulatory compliance, and security. The authors of [30] review the cybersecurity landscape of UAV-assisted IoT applications, examining layer-wise security threats from physical to application layers. It explores how AI, ML, deep learning (DL), and reinforcement learning (RL) techniques have been employed to address authentication, data privacy, and attack prevention challenges."
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+ "content": "4"
+ },
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+ "content": "TABLE III"
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+ "angle": 0,
+ "content": "LIST OF ABBREVIATIONS"
+ },
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+ "angle": 0,
+ "content": "| Abbreviation | Description | Abbreviation | Description |
| A2G | Air-to-ground | ABS | Aerial Base Station |
| AN | Artificial Noise | AI | Artificial Intelligence |
| BCD | Block Coordinate Descent | BS | Base Station |
| CNN | Convolutional Neural Network | CSI | Channel State Information |
| DDPG | Deep Deterministic Policy Gradient | DDQN | Double-deep Q-Learning |
| DL | Deep Learning | DNN | Deep Neural Network |
| DQN | Deep Q-Network | eVTOL | Electric Vertical Take-off and Landing |
| DRL | Deep Reinforcement Learning | FAR | False Alarm Rate |
| G2A | Ground-to-air | G2U | Ground-to-UAV |
| GAN | Generative Adversarial Network | GNSS | Global Navigation Satellite System |
| GPS | Global Positioning System | GS | Ground Station |
| IoT | Internet of Things | LAENet | Low-Altitude Economy Networking |
| LSTM | Long Short-Term Memory | LoS | Line-of-sight |
| MARL | Multi-agent Reinforcement Learning | MDP | Markov Decision Process |
| MDR | Miss Detection Rate | MEC | Mobile Edge Computing |
| ML | Machine Learning | MSE | Mean Square Error |
| NOMA | Non-orthogonal Multiple Access | PLA | Physical-layer Authentication |
| PLS | Physical Layer Security | PUF | Physical Unclonable Function |
| QoE | Quality of Experience | RF | Radio Frequency |
| RIS | Reconfigurable Intelligent Surfaces | RL | Reinforcement Learning |
| RNN | Recurrent Neural Network | RSS | Received Signal Strength |
| SCA | Successive Convex Approximation | SDNR | Signal-to-disturbance-plus-noise Ratio |
| SNR | Signal-to-noise Ratio | SOC | Second-Order Cone |
| TDMA | Time-division Multiple Access | THz | Terahertz |
| U2G | UAV-to-ground Communication | UAV | Unmanned Aerial Vehicle |
"
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+ "angle": 0,
+ "content": "B. Contributions of Our Survey"
+ },
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+ "angle": 0,
+ "content": "The related surveys and tutorials primarily focus on the classification of overall security threats and corresponding countermeasures in UAV networks or UAV-assisted applications, with relatively little attention given to security issues of communication in the physical layer. Different from existing studies, our survey uniquely concentrates on the security challenges specific to physical layer communications in the LAENet, as summarized in Table II. It fills a critical gap in the literature by conducting an in-depth analysis of threats in physical layer communications that were previously underexplored or only briefly mentioned in prior studies. By offering a comprehensive and systematic analysis of these underexplored issues, our work brings new insights to seek effective solutions to enhance physical layer security in communications of the LAENet. The key contributions of this paper are summarized as follows:"
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+ "angle": 0,
+ "content": "The key contributions of this paper are summarized as follows:"
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+ "bbox": [
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+ "angle": 0,
+ "content": "- A thorough discussion of the six main security issues in the physical layer communication of the LAENet is presented, namely, eavesdropping attack, unauthorized access, jamming attack, spoofing attack, anomalous behaviors, and injection attack. We analyze these attacks in the context of their potential occurrence throughout the entire operation of LAENet, providing essential references for ensuring the security of physical layer communication in the future LAENet deployments."
+ },
+ {
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+ "angle": 0,
+ "content": "- We review countermeasures against various attacks in detail and offer a comprehensive tutorial on achieving communication confidentiality, communication availability, and communication integrity in LAENet. In addition,"
+ },
+ {
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+ "angle": 0,
+ "content": "the lessons learned for each security issue are presented to emphasize the limitations of existing works and provide high-level insights for improvements."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "- Several potential future research directions for secure physical layer communication in LAENet are proposed, including energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. These diverse perspectives offer new guidance for future research on secure physical layer communication in LAENet."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The remainder of this paper is given as follows. Section II introduces the background of the LAENet and security issues in physical layer communication of the LAENet. In Section III, a comprehensive exploration of achieving communication confidentiality for the LAENet is presented. Section IV reviews the solutions for communication availability in the LAENet. In Section V, countermeasures on communication integrity for the LAENet are discussed. Section VI provides future research directions, and Section VII concludes this paper. Additionally, Table III lists the abbreviations commonly employed throughout this survey."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "II. BACKGROUND KNOWLEDGE"
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+ "angle": 0,
+ "content": "In this section, we introduce the background of the LAENet, including its definition and application scenarios. Subsequently, the concept of physical layer communication in the LAENet and its security threats are elaborated in detail."
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+ "angle": 0,
+ "content": "A. Background of LAENet"
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+ "angle": 0,
+ "content": "The LAENet is a sophisticated and dynamic system that integrates various aerial and terrestrial technologies to en"
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+ "angle": 0,
+ "content": "Fig. 2. Background knowledge of the LAENet and security issues in its physical layer communication. Describe the definition of the LAENet and its communication application scenarios. Elaborate on three key metrics for secure physical layer communication: communication confidentiality, which combats eavesdropping attacks and unauthorized access; anti-jamming strategies and spoofing defense for ensuring communication availability; and anomaly detection and injection defense to prevent adversaries from compromising communication integrity."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "able seamless communication, coordination, and management of diverse aerial operations within low-altitude airspace [1], [108]. The LAENet includes numerous different types of constituents, such as flight equipment, base stations, and other communication platforms. Specifically, the LAENet connects various aerial vehicles, including general aviation aircraft for passenger transport and emergency rescue, drones for surveillance and logistics, and eVTOL designed for urban air mobility and last-mile cargo delivery [109], [110]. These aerial vehicles can incorporate ground and aerial base stations, further high-altitude platforms, such as weather balloons and satellites, to receive environmental information and precise navigation [13]."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Different from traditional aviation networks that rely on centralized air traffic control, the LAENet can independently construct communication and networking by seamlessly interconnecting a variety of aerial and ground-based systems, which enables continuous information exchange, flight path optimization, and autonomous operations [8], [111]. Therefore, the LAENet has opened opportunities for various application scenarios and plays key roles from the perspective of communication coverage and relay [112]–[114]. Specifically, the LAENet can extend the communication coverage by deploying aircraft as ABSs in areas lacking communication infrastructure [115]–[117]. For instance, these ABSs deployed at optimal altitudes can provide connectivity and network services in remote or disaster-stricken areas [118], [119]. Moreover, if the direct communication links between ground base stations and user equipment are unreliable, such as in"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "mountainous regions and densely populated areas, the aircraft can act as mobile relays to improve connectivity by capturing, amplifying, and transmitting communication signals [120]–[122]. It also can be regarded as a surveillance unit to monitor airspace dynamics while simultaneously functioning as a low-altitude network orchestrator to optimize communication and computing resources [118], [123], [124]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To integrate and evolve these capabilities, the LAENet needs to establish effective communication infrastructure to ensure reliable connectivity and efficient interaction across various environments [31], [125]. Physical layer communication, as the bottom layer in the network architecture, may directly influence the communication performance of the LAENet across aerial and terrestrial networks [43], [46]. For example, it governs how signals are generated, transmitted, and received between aircraft and base stations [31]. Building on this, it manages the channel and spectrum resources to enhance signal transmission quality and maintain stable connectivity [43]. Therefore, ensuring the security of physical layer communication in the LAENet is crucial for supporting a wide range of applications in low-altitude domains."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "B. Security Issues in Physical Layer Communication of LAENet"
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+ "angle": 0,
+ "content": "Based on previous studies [126], [127], we discuss the security issues in the physical layer communication of the LAENet from three aspects: confidentiality, availability, and"
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+ "angle": 0,
+ "content": "integrity of communications. The details of each measurement are described as follows."
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+ "content": "- The confidentiality of physical layer communications in the LAENet can be compromised by security threats such as eavesdropping and unauthorized access [128]. Eavesdropping arises primarily from the broadcast nature of wireless signals and LoS link, making transmissions highly susceptible to interception [46]. An eavesdropper silently capturing or intercepting signals can lead to the exposure of confidential information. Meanwhile, unauthorized access threats exploit the open and broadcast nature of UAV communications [31]. Attackers may gain illegal access to the LAENet by disguising themselves as legitimate UAVs or ground stations, thereby deceiving or interfering with the normal operation of UAVs [51]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Similarly, the open nature of wireless channels and LoS propagation bring jamming and spoofing security issues for communication availability [78]. Specifically, jammers can continuously transmit interference signals to disrupt communication, where a jammer can be a drone or a base station [48]. The spoofing attack can not only achieve identity spoofing by forging legitimate transmission identities but also launch signal deception attacks to disrupt UAV communications and positioning [49]. Therefore, jamming and spoofing lead to unauthorized access and signal disruptions or errors, making communication unavailable in the LAENet."
+ },
+ {
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+ "bbox": [
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+ "content": "- Integrity as a microscopic metric measures the deviations of signals, channels, and spectrum in communication under adversaries' influence [129]. The communication integrity of the LAENet can be affected by anomalous behaviors and injection attacks. Anomalous behaviors often use dynamic spectrum access and the open wireless medium, including abnormal jamming, abnormal transmission power, and covert eavesdropping [95]. These anomalous behaviors can introduce harmful interference, violate spectrum policies, and expose sensitive information to eavesdroppers [61], [96]. Moreover, the injection attack exploits the open nature of wireless channels to alter signals or inject illegal signals, such as spoofing signals or malicious GNSS signals, to deceive receivers and interfere with communication, thereby leading to degraded signal quality, false navigation, and network congestion [28], [46], [97]."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ "content": "Overall, as illustrated in Fig. 2, this survey reviews existing research on achieving communication confidentiality, availability, and integrity for the LAENet. Specifically, the investigation of anti-jamming strategies and communication authentication schemes aims to enhance communication confidentiality. Studies on anti-jamming techniques and spoofing defense mechanisms have been explored to ensure communication availability. Furthermore, research on communication integrity has focused on anomaly detection and injection attack mitigation approaches."
+ },
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+ "type": "title",
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+ "content": "III. COMMUNICATION CONFIDENTIALITY FOR LAENET"
+ },
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+ "content": "A. Anti-eavesdropping Strategy"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "The LAENet faces significant eavesdropping threats due to the inherent vulnerabilities of UAV-enabled wireless communications. The openness of wireless channels, especially the LoS links in air-to-ground (A2G) and ground-to-air (G2A) communications, increases susceptibility to interception by eavesdroppers that disrupt legitimate communications compared to traditional terrestrial channels [50]. Traditional cryptographic methods, while effective in many scenarios, are less suitable for UAV communications due to their computational complexity and the dynamic mobility of UAVs [130]. This highlights the critical need for robust security measures to ensure the confidentiality and reliability of the LAENet communications. To address these limitations, leveraging PLS techniques to counter eavesdropping threats effectively has emerged as a promising solution [131]-[134]."
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+ "content": "In the LAENet, anti-eavesdropping solutions can leverage the controllable mobility of low-altitude aircraft to enhance physical layer security. By dynamically optimizing their trajectories, low-altitude aircraft can actively adapt their flight paths to shape the communication environment [135]. This approach allows them to fly closer to legitimate ground nodes, strengthening communication links and improving channel conditions for intended receivers, while simultaneously distancing themselves from potential eavesdroppers. In this subsection, we present a critical role of UAV trajectory in forming the communication environment, and how PLS can be enhanced through trajectory optimization and resource allocation to mitigate eavesdropping risks. Our analysis focuses on three prominent methodologies in this domain: convex optimization, deep learning, and reinforcement learning."
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+ "type": "text",
+ "bbox": [
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+ "content": "Convex optimization plays a crucial role in addressing anti-eavesdropping challenges in UAV-enabled communication networks, particularly for solving the joint optimization of trajectory and resource allocation [137]. Due to the inherent non-convex nature of these problems, advanced convex optimization techniques such as Successive Convex Approximation (SCA) and Block Coordinate Descent (BCD) are widely utilized [135]. These methods enable UAVs to enhance physical layer security by optimizing flight paths and resource utilization, minimizing the risk of eavesdropping while ensuring secure and efficient communication. Additionally, the decision variables may be discrete, which requires the application of various relaxation methods to transform the complex optimization problem into a more tractable form to obtain efficient solutions [138]."
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+ "content": "The study in [53] explores physical-layer security in UAV-assisted Mobile Edge Computing (MEC) systems in the presence of multiple ground-based eavesdroppers. The proposed system utilizes dual UAVs for task execution and anti-eavesdropping measures. One UAV operates as a mobile MEC server, while the other emits jamming signals to disrupt eavesdroppers, as shown in Fig. 3. The time-division multiple access (TDMA) scheme and non-orthogonal multiple access (NOMA) scheme are proposed to maximize the minimum secure computing capacity by jointly optimizing communica"
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+ "bbox": [
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+ "angle": 0,
+ "content": "TABLE IV SUMMARY OF CONVEX OPTIMIZATION FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
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+ "angle": 0,
+ "content": "| Ref | Optimization Objectives | Eavesdropper and Jammer Type | OptimizationConstraints | Pros & Cons |
| [53] | Secure calculation capacity1 | UAV jammer and fixed ground eavesdropper | Transmit power, time allocation, and computation capacity | BCD and P-BCD for secure calculation capacity maximization\n✓ Secure capacity of NOMA and TDMA has been significantly improved\nX High complexity for NOMA due to dual-loop iterations |
| [54] | Secure calculation capacity | Base station jammer and fixed ground eavesdropper | Transmission power, time allocation, and CPU processing frequency | JDPB algorithm with SCA and BCD for secure task offloading\n✓ Reduce complexity via region division\nX Fixed UAV altitude limits 3D trajectory optimization |
| [55] | Average secrecy rate2 | Antenna jammer and fixed aerial eavesdropper | Transmit power and jamming power | BCD and SCA optimization with hybrid FSO/RF links\n✓ Enhance communication security via hybrid FSO/RF links and AN\nX Rely on simplified channel models (e.g., free-space path loss) |
| [56] | Worst-case secrecy rate | UAV jammer and fixed ground eavesdropper | UAV speed, collision avoidance, positioning error, and energy harvesting | Robust 3D trajectory and time switching optimization\n✓ Full mobility of UAVs in 3D for improving secrecy rate\nX The performance may degrade with flying eavesdroppers |
| [57] | Average secrecy rate | None and flying eavesdropper | Transmit power control and user scheduling | Joint trajectory and communication design against mobile eavesdroppers\n✓ Initial trajectory design for keeping away from eavesdroppers\nX Security performance relies on the initial trajectory design |
| [58] | Secure calculation capacity | Ground jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | Integrate a dual-UAV system with a ground jammer in MEC\n✓ Incorporate the UAV server and UAV eavesdropper with a ground jammer\n✓ Allow a UAV server to hover near ground users for secure offloading\nX Numerous flight constraints may require extensive tuning |
| [59] | Secrecy rate | Coastal jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | A secure communication for UAV-relay-assisted maritime MEC\n✓ Simultaneously optimize multiple parameters for improved secrecy rate\nX Iterative decomposition increases the computational burden\nX Assume prior knowledge of Channel State Information (CSI) of devices |
"
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+ "type": "table_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Techniques | Reference | Algorithm | Pros & Cons |
| Value-based RL | [60] | DQN | ○ DQN algorithm for UAV trajectory optimization to maximize the secrecy capacity\n✓ Low computational complexity, making it easy to train\n× Q-value overestimation, leading to suboptimal action selection |
| [61] | DDQN | ○ DDQN-based joint trajectory, time allocation, and offloading optimization\n✓ Accelerated convergence via action space pruning\n✓ Real-time optimization of trajectory and resources\n× DDQN is restricted to discrete action spaces\n× DDQN is not suitable for continuous action control |
| Policy Gradient-based RL | [62] | CAA-MADDPG | ○ Multi-Agent DRL with attention mechanisms (CAA-MADDPG) for secrecy rate maximization\n✓ Handle complex multi-agent with the attention mechanism\n× Assume prior knowledge of eavesdropper locations\n× Assume ground devices are static |
| [63] | DDPG | ○ DDPG-based RL for enhancing bi-directional UAV communication security\n✓ Support mobile devices and ensure bi-directional secureit\n× Computational overhead increases with device density\n× performance may be sensitive to hyperparameter selection |
| [64] | PPO+DCCN | ○ Hybrid DCCN and PPO for secrecy rate maximization\n✓ The PPO optimizes the UAV trajectory based on the results from DCCN\n× The performance is sensitive to the choice of clipping factor in PPO |
| [65] | MAPPO+LSTM | ○ MAPPO for multi-agent cooperative anti-eavesdropping and LSTM-enhanced sequential learning\n✓ The MAPPO+LSTM improves the learning capability of sequential sample data\n× Assume perfect knowledge of CSI may be challenging in real-world scenarios |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "value overestimation, leading to suboptimal action selection [146]. The authors in [61] propose a double-deep Q-learning (DDQN)-based scheme to jointly optimize the UAV trajectory, time allocation, and offloading decision strategy, aiming to maximize the average secure computing capacity for antieavesdropping in UAV-aided MEC. The system model involves one legitimate UAV server, one illegitimate UAV eavesdropper, one ground jammer, and ground users. The proposed DDQN-based scheme models the optimization problem as an MDP with states, actions, and rewards. The states include the coordinates of the UAVs, while the actions involve offloading decisions, time allocation, and trajectory adjustments. The reward function maximizes secure computing capacity. The DDQN model includes a deep Q-network (QN) and a deep target network (TN) to generate actions and evaluate their values. The parameters of the QN are updated by minimizing the loss function, and the parameters of the TN are periodically updated. The proposed scheme reduces the action space size by deleting illegal actions, such as those that violate time allocation constraints or result in resource waste. Unlike prior works [57], [60] that rely on conventional optimization or DQN with limited consideration of task queues, this approach integrates real-time resource allocation and trajectory optimization while ensuring dynamic constraints. The proposed DDQN scheme converges in 2000 episodes, half the episodes required by DQN (4000 episodes), and achieves a 0.02 Mbits higher average secure computing capacity."
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+ "bbox": [
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+ "angle": 0,
+ "content": "The value-based RL method (e.g., DQN) mainly focuses on dealing with discrete action spaces that may lead to the loss of optimal solutions [147]. The policy gradient-based RL method (e.g., Deep Deterministic Policy Gradient (DDPG)) can handle continuous action spaces [148], which are more suitable for UAV trajectory and transmit power optimization problems."
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+ "bbox": [
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+ "angle": 0,
+ "content": "The authors in [62] propose a multi-agent DRL framework to address the challenge of secure UAV communications in"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "the presence of eavesdroppers. The system model is similar to Part A of Fig. 3, where the UAV server sends confidential information to ground users, and UAV jammers send AN signals to ground eavesdroppers using 3D beamforming. This study designs the Multi-Agent Deep Deterministic Policy Gradient with a continuous action attention mechanism (CAA-MADDPG) to maximize the system's secrecy rate. The attention mechanism dynamically prioritizes relevant agents' observations (e.g., jammers focusing on eavesdroppers) to reduce the exploration space and accelerate convergence, thereby enhancing the system's ability to counteract eavesdropping attempts. The simulation results show that CAA-MADDPG achieves a secure rate of \\(4.5\\mathrm{bps / Hz}\\) and converges in 1000 episodes with three UAV jammers, outperforming MADDPG (around \\(4\\mathrm{bps / Hz}\\) and 1400 episodes) and DDPG schemes."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, the study in [62] just considers UAV-to-ground communication (U2G) and assumed the ground devices are static. The work in [63] addresses the challenge of securing bi-directional ground-UAV communications in a dynamic environment with mobile ground devices and eavesdroppers. Different from prior works that assume static ground eavesdroppers [54], [56], this study considers mobile ground eavesdroppers for more practical real-world scenarios. The communication in U2G and ground-to-UAV (G2U) cases is modeled, considering factors such as channel gains and distances. The problem of maximizing the worst-case average secrecy rate is formulated as a constrained MDP (CMDP) under the constraints of UAV flight space, flight speed, energy capacity, anti-collision, and peak transmit power. To solve the CMDP, the authors design a DDPG-based RL algorithm. The algorithm includes three key components: the primary network (actor and critic networks), the target network, and the replay buffer. They also adopt state normalization and exploration noise to speed up the training convergence of the DDPG. The proposed joint optimization scheme achieves a secrecy rate"
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+ "bbox": [
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+ "content": "11"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "over \\(40\\%\\) higher compared to baselines that optimize only trajectory or only power. In addition, DDPG outperforms DQN by approximately \\(15\\%\\) in secrecy rate due to its ability to handle continuous actions."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "The DDPGG methods form a fixed mapping from states to actions, which is not suitable for large state spaces that require more exploration and uncertainty [149]. The PPO alleviates this limitation by introducing proximal policy optimization, which allows for more exploration in the large action space."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "The study in [64] proposes a hybrid framework (Double Cascade Correlation Network (DCCN) + PPO) to maximize the secrecy capacity. DCCN bypasses the need for labeled training data by cascading two neural networks to maximize the secrecy channel rate. The PPO dynamically adjusts the UAV's position by using clipped surrogate objectives to stabilize policy updates and advantage estimation to prioritize high-reward actions. Simulation results show that the proposed scheme (DCCN + PPO) achieves an average secrecy rate of 0.73 bps/Hz, outperforming the benchmarks DCCN + DDPG (0.67 bps/Hz) and Random RIS + PPO (0.13 bps/Hz). However, the average secrecy continues to decline when the transmit power is higher than 2 W, since the jamming signals transmitted by the secondary source against the eavesdropper will also affect the primary users."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The study in [64] considered only the use of one UAV to assist in secure communication. However, in low-altitude economic networks, it may be more important for multiple UAVs to collaborate to implement anti-eavesdropping strategies. The study in [65] considers a system model treats all secondary transmitters and multiple UAV jammers as multi-agents. A Multi-Agent PPO algorithm combined with Long Short-Term Memory (LSTM) networks, named MAPPO-LSTM, is proposed to maximize the secure communication rate by jointly optimizing the UAV trajectory, transmission power, and energy harvesting coefficients. The problem is formulated as a nonconvex MDP consisting of an action space, state space, observation, and reward (which consists of the sum of the secure communication rate, SINR information, and battery capacity). The MAPPO algorithm introduces counterfactual baselines to address the credit assignment problem in centralized learning and combines with the LSTM network to enhance the learning capability of sequential sample data. Compared to benchmark schemes MAPPO and MADDPG, the proposed MAPPO-LSTM method achieved around \\(17\\% - 20\\%\\) higher average secrecy rate in large-scale scenarios, with convergence speeds 1.37 times and 1.93 times faster, respectively. In addition, the reward is sensitive to the discount factor, where setting factor to 0.99 enables faster and more stable convergence. Deviations from this value result in more pronounced fluctuations in the reward and secrecy rate."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Lesson Learned. The RL has emerged as a powerful yet challenging tool for anti-eavesdropping in UAV-assisted secure communications. A key lesson is that multi-agent cooperation significantly enhances security compared to single-agent approaches, enabling adaptive trajectory control, power allocation, and jamming coordination in dynamic environments. However, scalability and convergence efficiency remain critical bottlenecks, especially in high-dimensional, time-"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "varying settings, as many studies unrealistically assume perfect channel information, and deep RL's convergence time leaves the system vulnerable before optimization completes. Furthermore, key limitations demand further attention, such as RL's computational complexity, which restricts its use in resource-limited settings requiring real-time security, and its sensitivity to hyperparameter tuning that requires meticulous configuration to ensure optimal performance. Future advancements should focus on developing generalizable and robust learning architectures that can dynamically adapt to evolving threats while maintaining computational feasibility, addressing practical deployment challenges, exploring hybrid approaches, prioritizing security in system design, and balancing security performance with energy consumption."
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+ "angle": 0,
+ "content": "Deep learning, with its strong learning capabilities, parallel processing, and comprehensive reasoning [150]–[152], has huge potential to enhance anti-eavesdropping strategies in UAV communications, especially in environments with rapidly changing conditions and complex interactions [153]. Given the intricate problem of UAV trajectory variation and its nonlinear characteristics in time and space [154], [155], deep learning networks, such as neural networks and generative models, are emerging as potential solutions to improve the security and performance of UAV communication systems."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The study in [66] explores the use of deep learning to optimize UAV deployment and jamming strategies against eavesdroppers to maximize the secrecy rate in the complete CSI scenario. The optimization problem is decomposed into two layers: the inner layer optimizes jamming power for a fixed UAV location, and the outer layer optimizes UAV deployment. The inner problem is solved using a bi-section search algorithm, while the outer problem is addressed using a deep neural network (DNN) to approximate the optimal UAV deployment. The DNN is designed as a fully connected structure, which includes an input layer, two hidden layers, and an output layer, as shown in part A of Fig. 5. The DNN is trained using a dataset generated by simulating different UAV deployments and corresponding secrecy rates. The final optimal deployment of the UAV can be approximated when the mean square error of weights between neurons is minimized. The DNN model achieves an average distance error of 2.2 meters compared to the optimal deployment found by the exhaustive search baseline."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The fully connected neural network used in [66] is suited for problems where inputs and outputs are fixed-dimensional vectors without inherent spatial or sequential relationships [150]. Moreover, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) can also contribute to antieavesdropping. In contrast to fully connected networks, CNNs are particularly effective for exploring spatial features from images or spatial maps [156]. RNNs, on the other hand, focus on handling sequential data by maintaining a memory of previous inputs through recurrent connections [150]. The authors in [67] propose a CNN-LSTM-based secure efficiency map (SEM) framework, which is constructed by calculating each subarea's security-efficiency index using a weighted exponential coefficient to combine normalized secure spectrum efficiency (secrecy rate per unit bandwidth) and secure energy"
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+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "TABLE VI SUMMARY OF DEEP LEARNING FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Techniques | Reference | Algorithm | Pros & Cons |
| Neural network model | [66] | DNN | ● Use DNN to optimize UAV deployment and jamming strategies for secure communication\n● The DNN model reduces the complexity of exhaustive searches\n● Rely on complete statistical channel knowledge\n● require intensive resources to generate a large amount of training data |
| [67] | CNN-LSTM | ● CNN-LSTM-based SEM prediction for dynamic secure UAV trajectory optimization\n● Efficient spatiotemporal feature extraction via CNN-LSTM\n● Assume fixed UAV height and passive eavesdropper\n● Training CNN-LSTM network requires a substantial amount of data |
| [68] | FL-DNN | ● FL-DNN-RL integration (FairLearn) for maximizing fairness in secrecy rates\n● Collaborative learning via FL improves generalization in anti-eavesdropping strategies\n● Involving multiple learning mechanisms requires significant computational resources\n● Assuming perfect CSI and eavesdropper localization may be impractical |
| Generative AI model | [69] | MD-GAN | ● MD-GAN with unknown CSI as model weights\n● Adapt to dynamic environments via gradient-based training\n● Do not require knowledge of the eavesdropper's detection threshold\n● Training a GAN can be computationally intensive |
| [70] | DD-GAN | ● DD-GAN uses genetic algorithm-generated datasets for GAN training\n● Achieve an effective trade-off between covert rate and detection probability\n● Training relies on the quality and quantity of the genetic algorithm-generated data |
| [71] | GDMTD3 | ● GDMTD3 integrates generative diffusion models into TD3\n● Handle high-dimensional action spaces to adapt mobile eavesdroppers\n● Computational complexity from diffusion denoising steps |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "efficiency (secrecy rate per unit power). Historical SEMs are fed into a CNN-LSTM network to predict future SEMs by leveraging spatial-temporal feature extraction and time-series correlation. Based on predicted SEMs, a trajectory planning algorithm dynamically guides the UAV to subareas with the highest security-efficiency indices. The proposed SEM-enabled trajectory planning achieves an average security-efficiency index of 0.81, outperforming baseline schemes (e.g., static trajectory [142] or non-predictive methods [62], [157]) by over \\(30\\%\\)."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Previous deep learning-based architectures [66], [67] are centralized, lacking collaboration and knowledge sharing among UAVs, while also facing challenges in privacy preservation and scalability. To address these limitations and optimize secrecy rate maximization under constraints such as UAV mobility, power budgets, and scheduling fairness, the authors in [68] propose a federated learning (FL)-based framework (FairLearn). As shown in part B of Fig. 5, the FairLearn employs three learning modules: (1) Module-D uses RL to dynamically generate training datasets by exploring UAV trajectories, power allocation, and scheduling policies; (2) Module-P employs a DNN trained on these datasets to predict optimal 3D trajectory, transmit power, and user scheduling, maximizing proportional fairness in secrecy rates (defined as the difference between legitimate UAV-user rates and eavesdropper rates); (3) Module-C applies FL to aggregate DNN models across UAVs, enabling collaborative learning while preserving data privacy. Simulation results show that FairLearn's secrecy rate is \\(26.6\\%\\) higher than BCD at 1.4W transmit power. After 100s of execution, FairLearn achieves \\(14.34\\%\\), \\(24.56\\%\\), and \\(108\\%\\) higher secrecy rates than BCD, MAQ, and QCQP baselines, respectively."
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+ "angle": 0,
+ "content": "It is worth noting that UAVs can only obtain limited prior environmental information without knowing perfect channel information and the eavesdropper's detection threshold or ex"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "act location. Some previous methods [59], [65], [68] may find it difficult to solve the optimization problem in such scenarios. In contrast, the generative adversarial network (GAN) has emerged as a new model for solving optimization problems with limited prior information [158], [159]. GAN can effectively model and approximate unknown distributions (such as channel coefficients, detection thresholds, and environmental parameters) through adversarial learning, where the generator continuously improves its strategy by learning from the feedback from the discriminator [158]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The work in [69] addresses challenges related to partial channel distribution information and unknown eavesdropper detection thresholds by proposing a model-driven GAN (MDGAN) framework. The unknown channel coefficients and detection thresholds are treated as trainable weights in the MD-GAN. The MD-GAN transforms the joint trajectory and power optimization problem into a dynamic game between a generator (UAV) and a discriminator (eavesdropper), where the UAV acts as a jammer to protect secondary users from eavesdroppers. The generator optimizes the UAV's 3D trajectory and jamming power, while the discriminator evaluates detection errors. Then, a GAN-based joint trajectory and power optimization (GAN-JTP) algorithm is developed to achieve Nash equilibrium (i.e., maximizing the covert rate and the probability of detection errors). As shown in part C of Fig. 5, the GAN-JTP algorithm consists of two stages: network learning and network training. In the network learning stage, the generator optimizes the UAV's trajectory and transmit power based on the current state and environment. In the network training stage, the generator and discriminator are alternately trained using gradient backpropagation to update their weights. Simulation results show that increasing the training of the discriminator accelerates the convergence of the generator (e.g., when the training step is 10, convergence is achieved within 30 iterations, compared to 89 iterations when"
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+ "content": "Part A. DNN-based Architecture"
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+ "angle": 0,
+ "content": "Part B. FL-DNN-based Architecture"
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+ "content": "Part C. MD-GAN-based Architecture"
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+ "content": "Part D. DD-GAN-based Architecture"
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+ "content": "Part E. GDMTD3-based Architecture"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Fig. 5. The overall architecture illustrates various deep learning-based architectures designed to enhance anti-eavesdropping capabilities in UAV deployment scenarios. Part A presents a DNN-based architecture that processes air-ground and ground-ground channel states to determine UAV deployment. Part B shows an FL-DNN-based architecture, incorporating modules for reinforcement learning, DNN-based feature mapping, and FL. Part C depicts an MD-GAN-based architecture, where a generator produces trajectories and power outputs based on location and environment status, while a discriminator evaluates the decisions. Part D introduces a DD-GAN-based architecture, focusing on generating jamming solutions to maximize covert rates, with a discriminator distinguishing between jamming and non-jamming solutions. Part E illustrates a GDMTD3-based architecture, utilizing an experience replay buffer and diffusion reverse process to optimize UAV deployment strategies."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.523,
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+ ],
+ "angle": 0,
+ "content": "the training step is 1). For a flight period of 100 seconds, the GAN-JTP algorithm achieves a \\(0.47\\%\\) increase in covert rate with a \\(0.15\\%\\) reduction in detection error probability compared to the BCD-based scheme [160]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.583,
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+ 0.914
+ ],
+ "angle": 0,
+ "content": "The MD-GAN [69] relies on model-driven methods where the unknown channel information and detection threshold are treated as trained weights. Differently, the authors in [70] propose a data-driven GAN (DD-GAN) framework that focuses on generating data consisting of environmental parameters and optimal solutions to train the GAN. Specifically, the DD-GAN transforms the optimization process into an interactive game between the UAV and eavesdropper, where the UAV aims to maximize the covert rate, and the eavesdropper aims to detect the presence of covert communication. To address the non-convexity and lack of eavesdropper detection threshold information in the optimization process, the DD-GAN trains a generator (UAV) and discriminator (eavesdropper) adversarially, using genetic algorithm-generated samples as prior data, as shown in part D of Fig. 5. The generator produces power and trajectory solutions, while the discriminator evaluates the detectability. The loss function of the discriminator is designed to maximize the probability of correctly identifying real data and minimize the probability of being fooled by generated data. The generator's loss function aims to maximize the probability that the generated data is mistaken for real data by the discriminator."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Besides GANs [69], [70], another generative model, the diffusion model, has advanced the effective representation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.523,
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+ "angle": 0,
+ "content": "of multi-dimensional data distributions [161]. The diffusion model can better capture the complex dynamics and the tradeoff in the multi-objective optimization problem concerning secure communication [112]. For example, The diffusion model captures complex state-action distributions, enabling adaptive beamforming and UAV repositioning under eavesdropper mobility. To tackle dynamic environments and high-dimensional action spaces in secure communication and energy efficiency multi-objective optimization problem, the authors in [71] propose GDMTD3, a Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm enhanced with generative diffusion models. Key innovations include integrating diffusion-based reverse processes into the actor network for robust policy generation and addressing continuous action spaces, as shown in part E in Fig. 5. The training process of GDMTD3 involves initializing the online critic and actor networks, interacting with the environment, and updating the network parameters based on the collected experiences. The actor network uses a generative diffusion model to sample actions, while the critic networks evaluate the actions using twin critic networks to reduce overestimation bias. Simulation results show that GDMTD3 outperforms DRL-based benchmarks (including PPO, TD3, and DDPG), achieving about \\(50\\%\\) higher cumulative rewards and around \\(21\\%\\) higher average secrecy rate than TD3. In addition, when the number of UAVs increases from 4 to 8, the average secrecy rate increases accordingly. However, increasing the number of UAVs from 8 to 16 raises"
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "14"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "TABLE VII SUMMARY OF AUTHENTICATION FOR COMMUNICATION CONFIDENTIALITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Techniques | Reference | Algorithm | Pros & Cons |
| PUFs-based authentication | [72] | PUF\\(s^1\\) | PUF-based dynamic session key generation and mutual authentication protocol\n✓ Lightweight design with no stored secrets\n✗ Potential overhead during temporary identity updates |
| [73] | PUF-fuzzy extractor | PUF-fuzzy extractor mutual authentication with TS-based dynamic session adaptation\n✓ Dynamic session time adaptation minimizes idle periods and enhancing security\n✗ Higher computational cost due to fuzzy extractors |
| [74] | PUFs-fuzzy extractor-AEGIS | Integration of PUFs, fuzzy extractors, and AEGIS for mutual authentication\n✓ The proposed password/biometric update mechanism reduces server dependency\n✗ Multiple cryptographic operations and protocols may be cause delay in the implementation |
| Channel based authentication | [75] | Rician channel | Physical-layer fingerprinting authentication based on Rician channel characteristics\n✓ Optimal power allocation balances data, AN, and authentication tag transmission\n✗ Reliance on encrypted tags requires high demand on UAV processing capabilities |
| [76] | Rayleigh channel | SNR difference-based PLA scheme\n✓ The SNR-based design can be implemented without additional hardware infrastructure\n✗ The simplified Rayleigh channel model may limit to real-world propagation environments |
| [77] | Rayleigh/Rician channels | AD metric2for authentication under Rayleigh/Rician channels\n✓ AD metric-based method improves the detection accuracy of authentication\n✓ Detailed analysis of authentication performance under different propagation conditions\n✗ Computational complexity in Rician channels due to hypergeometric functions |
"
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Physical Unclonable Functions (PUFs) are hardware-based security primitives that exploit inherent and unique physical variations in devices to generate unclonable and unpredictable responses for communication authentication."
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "2Authentication Distance (AD) is a metric proposed in [77] to distinguish legitimate and illegitimate signals for communication authentication."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "energy consumption but only marginally improves secrecy rates, highlighting a performance-energy trade-off."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Lesson Learned A key lesson learned is that deep learning, particularly through advanced architectures such as GANs [69], [70] and diffusion models [71], can address complex, dynamic environments with partial channel state information and unknown eavesdropper locations, while demonstrating superior performance over traditional methods [59], [65], [66]. These approaches demonstrate that deep learning not only strengthens the resilience of secure communications but also enables autonomous, real-time decision-making to counteract evolving eavesdropping threats in UAV networks."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "B. Communication Authentication"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "In the LAENet, as UAVs operate in open environments and rely on wireless communication, they are highly vulnerable to security threats such as node capture and man-in-the-middle attacks [46]. Ensuring secure and reliable authentication between UAVs and ground stations/users or among UAVs is critical to preventing unauthorized access [52], [162]. Traditional cryptographic authentication schemes often impose significant computational and memory overheads and incur considerable lantency, making them unsuitable for resource-constrained UAVs [163]. Recently, advancements such as PUFs and Physical-layer Authentication (PLA) mechanisms have opened new possibilities for lightweight and effective authentication in the LAENet."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "PUFs are a class of hardware security primitives that leverage the inherent manufacturing variations (such as variations in circuit delay or RF properties) in semiconductor devices to generate unique and unpredictable responses [164]. When a specific input is applied to a PUF, the device generates a corresponding response, forming a challenge-response pair that is unique to this device [164]. Such uniqueness and unpredictability make PUFs highly resistant to cloning and"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "tampering, making them as a secure means for device authentication and key generation [165]. In addition, employing a PUF in a UAV allows for secure authentication without the need for complex cryptographic operations, making it an efficient solution for resource-constrained scenarios [166]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The work in [72] proposes a lightweight mutual authentication protocol, named SecAuthUAV, for securing UAV-ground station and UAV-UAV communications. SecAuthUAV employs PUFs in each UAV to generate a unique, unclonable session key that functions as a non-reproducible fingerprint. The protocol consists of three phases, as shown in Fig. 6. During UAV registration, a challenge-response pair from the UAV's PUF is stored, and a temporary identity is generated. In the UAV-ground station authentication phase, the UAV and ground station authenticate each other using challenge-response pairs and nonces, establish a session key, and update their identities. Lastly, in the UAV-UAV authentication phase, the GS facilitates secure communication by authenticating a second UAV and generates a session key for both UAVs."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, the work in [72] ignores the fact that the noise in PUFs can result in significant deviation in the output for the same input at different time points. In addition, [72] does not adjust the session time after establishing an authenticated session between two parties, which may lead to the active session remaining idle for a long time and thus give an opportunity for an adversary to interfere with the communication link. In light of this, the authors in [73] propose an UAV Authentication with Adaptive Session (UAAS) framework to address these challenges. Firstly, they combine PUFs and fuzzy extractors to address PUF noise. The fuzzy extractors consist of two phases: the \\( Gen(.) \\) phase creates a key and non-sensitive helper data, and the \\( Rep(.) \\) phase reconstructs the key from a noisy PUF response using the helper data while tolerating minor deviations. Then, the Thompson Sampling (TS)-based scheme is proposed to dynamically adapt the session time."
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "15"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.081,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.074,
+ 0.32,
+ 0.925,
+ 0.381
+ ],
+ "angle": 0,
+ "content": "Fig. 6. The overall architecture of the PUF-based authentication schemes for UAV-GS and UAV-UAV communication in [72]. Part A illustrates the PUF-based authentication process between a UAV and a ground station (GS). The UAV sends its ID and a nonce to the GS, which responds with a hash value based on the PUF, UAV ID, and nonce. The UAV then sends a value derived from the PUF and another nonce, and the GS verifies the authentication by comparing hash values. Part B shows the PUF-based authentication between two UAVs (U1 and U2) through the GS. After establishing a session key with the GS, U1 requests a connection to U2. The GS facilitates the authentication by generating a new session key, which is securely shared between U1 and U2."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "TS is a probabilistic approach that balances exploration and exploitation, determining the session time based on the fraction of busy time to minimize idle periods and reduce the risk of adversarial interference. Although the security analysis demonstrates that UAAS improves the security level in the mutual authentication mechanism, its throughput is \\(20.38\\%\\) lower and computational cost is 126 ms higher than the baseline [72] due to security overhead."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the LAENet, while establishing mutual authentication between UAVs and ground stations is critical, it is also important to incorporate role-specific access controls for users to ensure communication confidentiality and preventing unauthorized access [167]. The work in [74] proposes an authentication framework PUF-enabled authentication framework for Internet of Drones (PAF-IoD) to establish mutual authentication among users, UAVs, and ground stations. Users need to authenticate with stations to access the stored data or communicate directly with UAVs, where the users' authentication mechanism includes three factors (identity, password, and biometric data). Similar to [73], PAF-IoD uses PUFs and a fuzzy extractor in the authentication process to generate a unique and tamper-proof session key while tolerating the noise in PUFs. Furthermore, the designed authenticated encryption with associative data (AEAD)-based encryption algorithm is utilized for encrypting and decrypting messages exchanged between the user, ground station server, and UAVs."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In addition to leveraging intrinsic physical properties of hardware for authentication design through PUFs [72]–[74], the characteristics of communication channels can be used for authentication. The PLA mechanism authenticates devices by exploiting the unique physical characteristics of wireless communication channels, such as CSI, received signal strength (RSS), and signal-to-noise ratio (SNR) [168]. The main reason is that the wireless channel between two communicating entities exhibits location-specific and time-varying properties"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "due to multipath propagation, fading, and environmental factors [169]. These diverse physical channel conditions, which provide a robust set of features for authentication, have been investigated in terrestrial communication networks [168]–[170]. Furthermore, the source of received signals can be accurately and promptly detected [170], making PLA particularly advantageous in the dynamic and complex communication environments of the LAENet."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The authors in [75] leverage the unique properties of the physical layer channel, Rician channel, to develop a PLA for UAV-ground station communication. Given that UAVs receive signals subject to the Rician fading model, the ground station integrates authentication directly into the transmission process. It employs a one-way collision-resistant function (e.g. cryptographic hash function) that combines data symbols with a shared secret key to generate a low-power authentication tag for UAV and seamlessly embeds it into the transmitted signal. The authentication tag is validated by the correlation shaped by the Rician statistical characteristics of the fading channel, i.e., the correlation between the estimated tag (derived from the received signal) and the expected tag (generated using the secret key and decoded data symbols)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, the work in [75] still partially relies on cryptographic tag generation for authentication, which may not be suitable for UAVs with limited processing capabilities. The study in [76] leverages channel characteristics and geographical locations for PLA design, where the SNR differences between consecutive transmissions are utilized as the authentication metric. Specifically, a legitimate transmitter and a jammer have distinct channel variations due to differences in their geographical locations. The UAV authenticates the legitimate transmitter or jammer by formulating a binary hypothesis test based on the SNR difference between two successive transmissions. If the difference falls within a predefined threshold, the transmission is authenticated as from the legitimate"
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "16"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Part A. Channel-based authentication in urban"
+ },
+ {
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+ "bbox": [
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+ 0.445,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Part B. Channel-based authentication in suburban"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.116,
+ 0.354,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.075,
+ 0.578,
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+ ],
+ "angle": 0,
+ "content": "Fig. 7. The overall architecture of the channel-based authentication in urban and suburban environments in [77]. Part A depicts the authentication process in an urban environment under Rayleigh channel conditions. The UAV receiver calculates the SNR, computes the AD, and compares it with a detection threshold to distinguish between legitimate and malicious sensors. Part B illustrates the authentication process in a suburban environment, where the UAV receiver performs similar steps to authenticate legitimate sensors and detect malicious ones under Rayleigh channel conditions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
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+ ],
+ "angle": 0,
+ "content": "transmitter; otherwise, it is classified as a jammer. The closed-form expressions for the probability density function of SNR differences, false alarm rate (FAR), and miss detection rate (MDR) are derived under Rayleigh fading channels in single-UAV and dual-UAV scenarios. The non-convex optimization problem of minimizing MDR under FAR constraints is solved using an SCA algorithm, which outperforms the RSS-based baseline [90] by about \\(40\\%\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "It is worth noting that study [75] may lack a comprehensive analysis of the UAV-PLA performance under different propagation conditions. Additionally, the detection performance may be further improved with other indicators. As shown in Fig. 7, the work in [77] proposes a novel PLA framework under different propagation conditions, including dense urban and suburban environments modeled by Rayleigh and Rician channels, respectively. A new metric, Authentication Distance"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(AD), is proposed as the normalized difference in received SNR between adjacent transmissions. For Rayleigh channels, closed-form expressions for FAR and MDR are derived using convolution and integration-by-parts, while Rician channels employ doubly non-central \\( F \\) distributions to model AD statistics. Similar to study [76], this authentication framework minimizes MDR under FAR constraints. In dense urban settings, MDR depends on path loss and transmitter-UAV geometry. For suburban environments, it incorporates elevation angle-dependent Rician factors and path loss exponents to improve discriminability between legitimate and illegitimate signals. The proposed AD-based method outperforms the SNR-difference baseline [171], achieving 40–60% lower MDR."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
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+ 0.432
+ ],
+ "angle": 0,
+ "content": "Lesson Learned. Leveraging physical-layer characteristics, such as PUFs and channel properties, in conjunction with communication models and optimization algorithms, has proven effective in enhancing authentication accuracy and reducing detection errors. However, some methods also reveal limitations. For instance, the assumptions of ideal channel conditions and the neglect of practical implementation constraints may limit the applicability of the proposed solutions [76], [77]. Future research should focus on addressing these limitations by exploring more practical channel models and considering the trade-offs between security and system complexity."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "IV. COMMUNICATION AVAILABILITY FOR LAENET"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "A. Anti-Jamming Strategy"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Jamming attacks pose significant challenges to communication availability in the LAENet by disrupting legitimate communication links and degrading the performance of aircraft communication networks [79], [172]. As shown in Fig. 10, these attacks can exploit the openness and broadcasting nature of UAV networks, making them particularly vulnerable to interference [79]. Malicious jammers can transmit strong signals that weaken signal strength, degrade signal quality, and increase communication delays, leading to unreliable coverage and potential paralysis of the entire network [172], [173]. This vulnerability underscores the urgent need for effective anti-jamming technologies to ensure reliable communication in the LAENet."
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+ "content": "Various anti-jamming strategies have been explored to safeguard the LAENet against malicious jamming, mainly focusing on trajectory adjustment, as well as channel and power control. Overall, by adjusting the trajectory in the spatial domain, an UAV can evade jamming signals while maintaining reliable communication with legitimate devices [80], [173]. Besides the spatial-domain anti-jamming strategy, the UAV can implement a frequency-domain-based anti-jamming scheme. The UAV can select legitimate channels while avoiding jamming signals and control transmit power to minimize energy consumption and latency under jamming attacks [83], [84]."
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+ "content": "Convex optimization methods can be used to adjust the UAV's trajectory to achieve anti-jamming by strategically guiding its movement to reduce interference and enhance communication reliability [80], [173]. It provides a systematic and efficient approach to handle the complex, non-convex"
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+ "content": "TABLE VIII SUMMARY OF ANTI-JAMMING STRATEGY FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
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+ "type": "table",
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+ "content": "| Techniques | Reference | Algorithm | Pros & Cons |
| Convex optimization | [80] | BCD, SCA | BCD and SCA for UAV 3D trajectory optimization for anti-jamming\n✓ Probabilistic LoS performs well in real-world scenarios such as urban environments\nX High computational complexity may be challenging in resource-constrained environments |
| [81] | SCA, Dinkelbach | SCA and Dinkelbach algorithm for energy-efficient trajectory optimization under malicious jammers\n✓ Balance between throughput and energy consumption in anti-jamming\nX Assume static and LoS-dominated channels |
| [82] | BCD, SCA | BCD and SCA for joint UAV trajectory and transmit power optimization under jamming\n✓ Improve throughput by considering transmit power optimization against jammers\nX Assume a fixed UAV altitude and a static channel environment |
| Multi-agent RL | [87] | MALQL | Collaborative MALQL algorithm for anti-jamming with channel and power allocation\n✓ Accelerate convergence compared to single-agent Q-learning\nX Assume predefined UAV trajectories limits to adaptability |
| [88] | MARL | MARL with adversarial pre-training for dynamic and generalized jamming\n✓ Generalize to various jamming patterns via adversarial populations for pre-training\nX Pre-training for generalized jamming may require significant offline resources |
| [89] | MATD3 | MATD3 algorithm with PER for dynamic resource management under jamming attacks\n✓ Handle high-dimensional continuous action spaces\nX The integration of PER and spectrum sensing may increase the computational complexity |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "problems that arise when optimizing UAV trajectories and various constraints under malicious jamming conditions [131]. The work in [80] investigates anti-jamming 3D trajectory design for UAV-enabled wireless sensor networks under a probabilistic LoS channel model. The probabilistic LoS model accounts for elevation angle-dependent shadowing effects in urban environments compared with simplified LoS models. The BCD and SCA algorithms are employed to optimize the UAV's horizontal and vertical trajectory, allowing the UAV to move closer to the ground station for improved transmission rates while dynamically adjusting its elevation angle relative to the jammer to mitigate interference."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "However, the anti-jamming trajectory optimization in [80] under the probabilistic LoS model does not consider the energy consumption issue. The study in [81] utilizes SCA and Dinkelbach's algorithm to adjust the UAV's trajectory to avoid areas with jammers while maximizing energy efficiency, which is defined as the ratio of total throughput to propulsion energy consumption during flight. Compared to hovering-centric benchmarks, the optimized trajectory reduced energy consumption by \\(82\\%\\) while maintaining \\(73.16\\%\\) of the sum throughput. It is worth noting that the transmit power of the UAV and station is fixed in [81], whereas power optimization is also an important factor for energy efficiency. The authors in [82] use the SCA and BCD algorithms to maximize throughput by iteratively optimizing power allocation (via convex reformulation of throughput bounds) and UAV trajectory (via slack variables for distance constraints and jamming mitigation) to avoid jamming signals. The proposed scheme achieves \\(40\\%\\) higher throughput compared to the \"Line trajectory with fixed power\" baseline."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "While convex optimization methods [80]–[82] work well for fixed jamming patterns, they may struggle to handle dynamic, intelligent jamming [174] in real-time due to their reliance on global information and the challenges inherent in solving nonconvex problems with increased optimized variables [142]. In contrast, RL and DRL offer significant advantages by enabling autonomous, adaptive decision-making [143], [147]. These"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "approaches can continuously adjust to environmental changes, learn from past interactions, and optimize performance in real-time [144], [175]. The RL-based anti-jamming methods have emerged as a promising solution due to their ability to operate without excessive prior information (such as unknown environment, CSI, and jamming mode) [147]. Single-agent RL algorithms have been used in previous works to develop anti-jamming strategies in communication networks by regarding jammers and other legitimate users as part of the environment, including independent anti-jamming channel selection methods [83]–[86]. However, these single-agent approaches may fail to converge when dealing with a large number of agents or a high-dimensional action-state space [87], making them impractical for complex, multi-agent scenarios in the LAENet. To address these limitations, multi-agent RL (MARL) methods have been proposed to allow each agent to make decisions based on local information and exchange data with others (such as observations or model parameters)."
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+ "bbox": [
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+ "content": "The study in [87] proposes a collaborative multiagent layered Q-learning (MALQL) algorithm for anti-jamming communication in UAV networks by jointly optimizing channel and power allocation to maximize system Quality of Experience (QoE). The problem is modeled as a local interaction Markov game based on the constructed interference graph. The MALQL divides the problem into two subgames of channel selection (Layer 1) and power allocation (Layer 2), as shown in part B of Fig. 10. The channel layer uses a graph-based interference model to capture mutual interference among UAVs. Each UAV is represented as a node, and edges are formed between UAVs that are within a predefined interference distance. This model allows UAVs to identify and avoid channels that are being used by neighboring UAVs or jammed by external attackers, thereby reducing the jamming likelihood. The power layer optimizes transmit power to meet rate thresholds. Theoretical analysis confirms that MALQL can converge to a pure strategy Nash equilibrium."
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+ "content": "Nevertheless, there are still some issues with the anti-jamming mechanism in [87]. Considering that the rapid mo"
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+ "content": "Part A. Overall system model under jamming"
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+ "content": "Part B. MALQL-based anti-jamming scheme"
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+ "content": "Part C. Population update of pre-training for generalized anti-jamming scheme"
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+ "content": "Part D. PER-MATD3-based anti-jamming scheme"
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+ "content": "Actor-Critic network for agent k"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "Fig. 8. The overall architecture illustrates various reinforcement learning-based anti-jamming schemes designed to enhance communication reliability in UAV-assisted MEC systems under jamming attacks. Part A presents the overall system model, depicting UAVs and jammers interacting within a dynamic environment. Part B shows the MALQL-based anti-jamming scheme, where agents use layered Q-learning to determine actions based on local observations and rewards. Part C depicts the population update mechanism for pre-training a generalized anti-jamming scheme, involving a jammer population, trajectory encoder, and decoder network to optimize jamming policies. Part D introduces the PER-MATD3-based anti-jamming scheme, incorporating a priority experience replay buffer and actor-critic networks to dynamically allocate resources and optimize UAV deployment strategies."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.491,
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+ 0.868
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+ "angle": 0,
+ "content": "bility of UAVs may expose them to various and unknown jamming patterns due to frequent transitions to new scenarios, the anti-jamming methods need to be generalized [176], especially in the LAENet. The work [87] randomly initializes strategies and learns from scratch for a particular deployment environment with no pretraining, which may lead to a reduction in the generalization ability of the anti-jamming strategy. In light of this, the authors in [88] introduce an adversarial pre-training stage in the proposed two-stage MARL with a decentralized partially observable Markov decision process. Specifically, the adversarial pre-training stage uses a quality-diverse jammer population (e.g., fixed, random, sweeping, statistic, and RL-based jamming) to bootstrap generalized anti-jamming strategies instead of directly initializing the agents with random anti-jamming policies, as shwon in part C of Fig. 10. This pre-training ensures that UAVs are not overfitted to specific jamming patterns and can generalize to new jamming attacks in real-world deployments. The pre-trained policies are deployed in the fine-tuning stage, where a graph convolutional-based MARL algorithm is proposed to jointly optimize channel selection and power allocation for anti-jamming similar to [87]. Simulation results show that the proposed solution achieves \\(20 - 30\\%\\) higher cumulative rewards than collaborative multi-agent Q-learning [177] and independent Q-learning [83] under fixed and sweeping jamming."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Note that previous RL-based anti-jamming strategies [87], [88] mainly rely on the Q-learning method, which is suitable for discrete action spaces but may be limited in dealing with high-dimensional continuous spaces [147], [148]. The authors in [89] propose a PER-MATD3 algorithm against jamming"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "by integrating spectrum-aware channel selection and prioritized experience replay (PER) into an MADRL framework, as shown in part D of Fig. 10. The proposed spectrum-aware intelligent channel selection uses energy detection-based spectrum sensing, enabling UAVs to identify and avoid jammed channels. The TD3 is specifically designed to handle continuous-valued states and actions, where two critic networks, target policy smoothing, and delayed policy updates are used to further stabilize DRL training. By leveraging PER, the agents can learn from high-error experiences, thereby accelerating adaptation to time-varying CSI, imperfect jamming detection, and co-channel interference. By jointly optimizing CPU frequency, bandwidth allocation, and channel selection to minimize the impact of jamming, PER-MATD3 reduces system cost (a linear combination of latency and energy consumption) by approximately \\(16.7\\%\\), \\(9.1\\%\\), and \\(1.2\\%\\) compared to the baselines of Q-learning, MATD3-JSC (without PER), and PER-MATD3 (without channel selection), respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Lesson Learned. Recent advancements in anti-jamming strategies show that intelligent decision-making for trajectory control, channel selection, and power control is essential for effective jamming mitigation. A key takeaway is the successful integration of MARL to develop dynamic and adaptive anti-jamming solutions [75]. By employing intelligent algorithms such as adversarial pre-training and decentralized decision-making, UAV networks can generalize anti-jamming strategies across diverse environments [76], [77]. However, challenges persist in the generalization of these strategies across various jamming types and environmental conditions, as well as balancing the trade-offs between energy consumption,"
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+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Part A. ML-based spoofing detection"
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Part B. Rule and ML-based spoofing detection"
+ },
+ {
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+ "bbox": [
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+ "bbox": [
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+ "angle": 0,
+ "content": "Fig. 9. The overall framework of ML and rule-based spoofing detection for GPS spoofing detection in the LAENet. Part A depicts an ML-based spoofing detection mechanism in [93], where multiple CNN classifiers are trained with updated sample weights to form an integrated classification model. Each CNN transfers its optimized parameters to subsequent classifiers, enhancing the model's robustness. Part B presents a hybrid rule and ML-based approach in [94], where statistical analysis of path losses between UAVs and multiple base stations (BSs) is performed by edge servers. The analyzed data is processed through MLPs to generate individual predictions, which are aggregated to produce a final spoofing detection decision."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "latency, and throughput. Future research could delve into the integration of more adaptive learning frameworks (such as deep learning) into the LAENet for anti-jamming, enabling it to better manage partial or imperfect environmental observations for low-latency, real-time decision-making in multi-UAV systems."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "B. Spoofing Defense"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the LAENet, the openness of A2G transmission channels and the dynamic nature of low-altitude aircraft networks make them particularly susceptible to identity-based spoofing attacks [50]. In such attacks, a malicious entity impersonates a legitimate transmitter using falsified identity information, such as a spoofed media access control address, to gain unauthorized access to the network [52]. Once authenticated, the spoofer can disrupt communications among aircraft by launching more severe attacks, such as rogue access point infiltration and denial-of-service attacks, ultimately leading to network congestion and service outages [75]. Given the limitations of conventional authentication methods that rely on complex cryptographic protocols [52], PLA offers a promising alternative by leveraging the inherent and unique physical characteristics of wireless transmissions for the LAENet, which is introduced in Section III-B. Overall, this type of PLA can defend against spoofing"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "attacks in the LAENet by exploiting the unique characteristics of the wireless channel (such as RSS, Rayleigh channel, and Rician channel) to identify and separate between legitimate devices and spoofers."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The work in [90] proposes a PLA framework to detect spoofing attacks by exploiting spatial correlations of RSS in A2G channels. The key idea is that the RSS from a legitimate transmitter will remain relatively consistent due to its fixed location, while the RSS from a spoofer will vary significantly because of its different position and channel conditions. Thus, the UAV receiver can perform a hypothesis test to authenticate incoming signals. if the RSS distance between the current signal and a previously authenticated signal is below a predefined threshold, the signal is accepted as legitimate. Otherwise, it is flagged as a spoofing attempt. However, the work [90] is considered under an ideal transmission scenario, where the propagation environment is perfectly exempted from external interference. To address this limitation, the authors in [91] develop a PLA framework that accounts for channel randomness and interference uncertainty. First, they model the G2A link as a Rayleigh fading channel. Then, they introduce jamming signals as external interference. By modeling the jamming power statistically and incorporating it into the analysis of detected power differences, if the difference in power exceeds a predefined threshold, it is identified as a spoofing attempt. Thus, even in real-world scenarios with interference, the proposed framework can better differentiate between natural channel fading and anomalies caused by spoofing attacks."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In addition to using the statistical properties of the Rayleigh channel to design PLA against spoofing in environments with multipath fading (such as urban areas), the channel characteristics in suburban environments should also be considered. To address this, the work [77] proposes a PLA framework to counter spoofing attacks in both urban (Rayleigh channel) and suburban (Rician channel) environments. As mentioned earlier (in Section III-B), a new metric AD is devised to distinguish between legitimate signals and spoofing signals based on differences in channel randomness and geographical factors, such as elevation angles and distances. Adopting the unique fading characteristics of Rayleigh and Rician channels makes it statistically difficult for a spoofer to accurately mimic a legitimate signal. By considering elevation angles and distances in channel modeling, it ensures that a spoofer cannot easily replicate a legitimate signal even if the spoofer knows the legitimate transmitter's location. Simulation results show that the probability of a successful spoofing attack is significantly reduced compared to the baseline [171], where the spoofing miss detection probability drops to 0.014 in suburban environments and 0.371 in dense urban areas."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the LAENet, in addition to being vulnerable to identity-based spoofing attacks, aircrafts are also susceptible to signal spoofing attacks from the Global Navigation Satellite System (GNSS), particularly GPS spoofing, which poses a significant security threat by generating and transmitting counterfeit satellite signals resulting in severe positioning deviations [25]. By interfering with or suppressing legitimate GNSS signals, attackers can manipulate UAV locations in an imperceptible manner to mislead UAVs, causing deviations from intended"
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+ ],
+ [
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+ "bbox": [
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+ "angle": 0,
+ "content": "20"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "TABLE IX SUMMARY OF SPOOFING DEFENSE FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Techniques | Reference | Algorithm | Pros & Cons |
| PLA | [90] | RSS | Spatial correlations of RSS distances in PLA against spoofing attacksUse RSS-based channel characteristics to reduce PLA computational complexityAssume an ideal transmission scenario without external interference |
| [91] | Rayleigh channel | Defend against spoofing attacks by considering channel randomness and jammingSimultaneously address spoofing and jamming attacks via PLAAssume static UAVs and a known jamming distribution |
| [77] | Rayleigh and Rician channels | AD-based PLA for spoofing defense under Rayleigh and Rician channelsProvide a thorough analysis of spoofer identification in urban and suburban environmentsAssume perfect CSI in channel modeling |
| GNSS spoofing detection | [92] | Rule-based detection | Combine cooperative localization mechanism with Stackelberg game against spoofing attacksSpoofing detection is based on neighboring UAV signal sources without predefined thresholdsExtending to larger UAV groups may require complex adjustments |
| [93] | ML-based detection | Improved AdaBoost-CNN for multi-modal spoofing attack identificationHigh accuracy in identifying spoofing attacks with limited data samplesDependence on predefined signal features may lead to model overfitting |
| [94] | Rule & ML-based detection | MLP and statistical feature extraction on path-loss data for detecting GPS spoofingNo additional hardware/energy burden on UAVsRobust performance under sparse base station coverageSpoofing detection performance degrades in areas with unstable cellular signals |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "flight paths, violations of no-fly zone regulations, or increased collision risks [46]. Given a critical role of GNSS in UAV operations, effective detection and mitigation strategies for spoofing attacks are essential to ensure flight safety and prevent security breaches in the LAENet. Currently, studies on signal spoofing attack recognition in the LAENet mostly focuses on recognizing GNSS spoofing attack detection, which primarily falls into two categories with respect on rule-based and ML-based methods [19], [25]. Rule-based detection methods typically assess the relative distance and positional deviations of UAVs to determine if they are under GNSS spoofing attack. On the other hand, the ML-based methods pay attention to recognize different spoofing types by learning the characteristics of received signals."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Generally, the simplified rule-based methods determine whether a UAV has encountered spoofing attacks based on whether its trajectory follows a predictable path [178], [179], since a UAV may exhibit deviations from this path due to the false signals imposed by the spoofer. If the measured deviations exceed predefined thresholds, it indicates a potential spoofing attack. However, relying on predefined thresholds for detecting deviations may not dynamically adapt to the spoofing attacks. The study in [92] proposes a defense mechanism based on cooperative localization, where each UAV uses the relative distances and real locations of neighboring UAVs to detect spoofing attacks. Specifically, each UAV measures its relative distances based on alternative signal sources of neighboring UAVs and compares these results with its own GPS-derived location. If inconsistencies are detected (e.g., the GPS-derived location does not match the majority of the calculated locations), the UAV identifies itself or a neighboring UAV as being under attack. To optimize defense deployment, an equilibrium of a dynamic Stackelberg game is derived between the drone operator (leader) and the spoofer (follower). Simulation results show that the proposed scheme can effectively prevent spoofer's capture, while random/deterministic baselines suffer from attackers capturing one to two UAVs."
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+ "content": "Recent ML-based methods for spoofing defense primarily focus on binary classification concerning normal GPS signals and spoofing signals [180], [181]. However, they fail to recognize specific types of spoofing attack necessary for countermeasures in complex environments. Hence, there is an urgent need to recognize diverse GPS spoofing attack patterns for effective countermeasures for the LAENet. The authors in [93] propose an improved AdaBoost-CNN algorithm to address the challenge of recognizing diverse GPS spoofing attack patterns for UAVs, as shown in part A of Fig. 9. Three categorized spoofing attack patterns are considered including static and dynamic spoofing based on the UAV's motion state, power-matched and overpowered spoofing based on signal power, and position and time spoofing based on the spoofing targets. The authors select key GPS spoofing signal features such as signal quality monitoring, carrier-to-noise ratio, Doppler shift, and clock error to train the classification model. The improved AdaBoost-CNN algorithm integrates multiple weak CNN classifiers into a strong classification model. Each CNN base classifier uses the updated network parameters from the previous CNN as initial values, enabling iterative refinement of network weights to enhance feature extraction and generalization. With 800 simulated samples, the improved AdaBoost-CNN achieves \\(100\\%\\) accuracy, outperforming original AdaBoost-CNN \\((94.38\\%)\\), CNN \\((74.38\\%)\\), DNN \\((60.94\\%)\\), SVM \\((40.63\\%)\\), and KNN \\((53.13\\%)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.779,
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+ ],
+ "angle": 0,
+ "content": "Furthermore, integrating rule-based approaches with machine learning-based methods provides an effective and robust defense against spoofing attacks. The work in [94] leverages statistical features of path losses between UAVs and terrestrial base stations to detect a UAV's trajectory deviation due to GPS spoofing, as shown in part B of Fig. 9. The spoofing detection is formulated as a nonlinear optimization problem that aims to minimize hypothesis test errors by adjusting thresholds, statistical feature weights, and the number of base stations. To further accurately analyze path loss's statistical features for final decisions on predicting GPS spoofing probabilities,"
+ }
+ ],
+ [
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+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "21"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "TABLE X SUMMARY OF ANOMALY DETECTION FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.898,
+ 0.348
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+ "angle": 0,
+ "content": "| Anomaly type | Reference | Algorithm | Pros & Cons |
| Jamming | [98] | HDBN | SA module based on HDBN for detecting jamming anomalies\n✓ UAccurately characterize and detect jamming anomalies via KLD/DB metrics\n✗ Unstable initialization in unsupervised learning affects the performance of the HDBN |
| [99] | GDBN | GDBN to model the radio environment and detect and classify jamming anomalies\n✓ Unsupervised learning eliminates dependency on labeled data in classification of anomalies\n✗ Computational complexity increases with the number of jamming categories |
| [100] | Active-GDBN | Active-GDBN used to model UAV-jammer interactions for anomaly detection\n✓ Actively incorporate UAV's actions for faster adaptation and jamming detection\n✗ M-MJPF requires significant computational resources |
| [101] | Blind channel estimation & ACS | Blind channel estimation based on ACS properties to detect jammer signals\n✓ Does not rely on prior knowledge of the jammer's behavior\n✗ Assumes a specific structure of the multicarrier modulation format |
| Abnormal Power | [102] | Spectrum surveillance | Local and cooperative detection of abnormal power emission\n✓ Handle both aggressive and passive power misuse\n✓ Cloud-based framework enables real-time closed-loop surveillance\n✗ Computational complexity increases with the number of SN |
| Eavesdropping | [103] | SVM & K-means | One-class SVM and K-means clustering for detecting eavesdropping anomalies\n✓ One-class SVM and K-means are stable under varying eavesdropper power\n✗ Detection performance mainly depends on the quality and quantity of the ATD |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.374,
+ 0.492,
+ 0.496
+ ],
+ "angle": 0,
+ "content": "multilayer perceptron (MLP) neural networks are deployed on edge cloud servers, where individual MLP models at each BS are used to analyze statistical features of path losses. Simulation results show that the proposed method achieves \\(97\\%\\) accuracy with two base stations and \\(83\\%\\) accuracy with a single base station, outperforming baseline approaches such as adaptive trustable residence area (ATRA), which necessitates three base stations for triangulation [182]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.495,
+ 0.493,
+ 0.768
+ ],
+ "angle": 0,
+ "content": "Lesson Learned. For identity spoofing in the LAENet, leveraging signal features such as received signal strength and channel randomness in PLA design is an effective approach [77], [90], [91]. On the other hand, employing rule-based or ML-based techniques can detect and mitigate GNSS signal spoofing [92]–[94]. While ML-based methods show promising performance, they are limited by factors such as computational complexity and dependency on large datasets. Rule-based methods are simpler but may struggle in dynamic or uncertain environments. Future research could explore the application of RL to develop adaptive and robust spoofing defense mechanisms in the LAENet, which has not yet been extensively studied. Different from the abovementioned approaches, RL dynamically learns from interactions with the environment, and its sequential decision-making ability enables UAVs and ground stations to optimize spoofing defense strategies based on continuous feedback [147], make it a promising direction for enhancing spoofing defense in the LAENet"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "V. COMMUNICATION INTEGRITY FOR LAENET"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "A. Anomaly Detection"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.824,
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+ ],
+ "angle": 0,
+ "content": "Due to the open nature of wireless channels and the dominant LoS links in the LAENet, communication becomes particularly vulnerable to a diverse range of anomalous behaviors such as abnormal jamming, abnormal transmission power, and covert eavesdropping [46], [49]. Specifically, malicious jammers sense spectrum activity and dynamically adapt their interference patterns to mislead the UAV into taking suboptimal or harmful actions [81], [95]. In parallel, abnormal"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.374,
+ 0.923,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "power emissions, either due to device faults, selfish behavior, or malicious intent, can violate spectrum policies, introduce harmful interference, and disrupt cooperative spectrum sharing [96]. Additionally, the pervasive risk of eavesdropping is that adversaries exploit the UAV's uplink or downlink transmissions to intercept sensitive data [61], [67]. Thus, it is essential to detect and mitigate these abnormal activities in the LAENet. Different from previously reviewed approaches such as anti-eavesdropping (Section III-A) and anti-jamming (Section IV-A), anomaly detection is a method used to identify and mitigate unexpected deviations from or irregularities in normal operational patterns by monitoring communication channels in the LAENet [127], [183]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Jamming anomalies generally aim to disrupt the normal operation of UAV communication links, such as by injecting disruptive signals to interfere with the legitimate communication process. The study in [98] proposes a novel Self-Awareness (SA) module to leverage the radio to detect abnormal behaviors caused by jamming attacks for Cognitive UAV communications. The SA module unsupervisedly learns a generative model using a Hierarchical Dynamic Bayesian Network (HDBN) [184] to represent the joint distribution of random variables characterizing the radio environment at different levels of abstraction and across time, where the Modified Bayesian Filtering [185] is used to integrate multilevel abnormality measurements for online predictions of radio environmental states at different levels. Since jamming can disrupt and shift the distributions of the radio environment, the abnormalities can be detected by calculating the Kullback-Leibler Divergence (KLD) and Dhattacharyya distance (DB) [186] between predictive messages and diagnostic messages. The predictive messages are generated by the HDBN to capture the expected patterns of normal signals, and diagnostic messages reflect the actual state of the signal. The jammer's impact is characterized by calculating generalized errors based on shifts in amplitude, phase, and frequency of signals, allowing the radio to predict future activities of the jammer. The SA"
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+ ],
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+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "22"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.084,
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+ ],
+ "angle": 0,
+ "content": "Part A. HDBN-based Scheme"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.084,
+ 0.092,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Part B. GDBN-based Scheme"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Part C. Active-GDBN-based Scheme"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.527,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.074,
+ 0.318,
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+ ],
+ "angle": 0,
+ "content": "Fig. 10. The overall architecture illustrates jamming anomaly detection to enhance communication integrity in the LAEnet. Part A presents an HDBN-based scheme focusing on hierarchical dynamic models to predict and detect abnormal signals caused by jammers. It details the transition probabilities between model states and the prediction of continuous states based on discrete superstates. Part B introduces a GDBN-based scheme, extending the HDBN approach by incorporating generalized states and observations, allowing for more nuanced predictions and error calculations. Part C depicts an Active-GDBN-based scheme, integrating UAV actions into the model to actively infer and adapt to the environment, thereby optimizing resource allocation and anti-jamming measures."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.412,
+ 0.492,
+ 0.456
+ ],
+ "angle": 0,
+ "content": "module achieves a near \\(100\\%\\) abnormality detection accuracy, approximately \\(12\\%\\) higher than the traditional energy detector-based scheme."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.076,
+ 0.459,
+ 0.493,
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+ ],
+ "angle": 0,
+ "content": "Different from the previous work [98], which introduced the SA module using HDBN for anomaly detection, the authors in [99] propose a Generalized Dynamic Bayesian Network (GDBN)-based framework to enhance the SA module by further classifying the detected anomalies caused by multiple jammers. A generalized state-space model [184] is used to represent the evolving radio environment as a GDBN model learned in an unsupervised manner. Different from the KLD/DB metric in [1], Kullback-Leibler divergence and Bhattacharyya distance are used as abnormality measurements between predicted and observed signals to detect jamming. Once an abnormality indicative of jamming is detected, the UAV extracts the interfering signal and compares it with prelearned GDBN models (each representing a different jamming modulation scheme). By evaluating which pre-learned model best explains the extracted jamming signal, the UAV can not only detect the presence of a jammer but also classify its modulation type. Simulation results show that the GDBN-based method achieves an overall classification accuracy of \\(98\\%\\) at \\(\\mathrm{SNR} = 10\\) dB, outperforming LSTM \\((88\\%)\\), CNN \\((67\\%)\\), and SAE \\((90\\%)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.779,
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+ ],
+ "angle": 0,
+ "content": "Based on the study [99], the authors in [100] propose an Active-GDBN to model the dynamic interaction between the UAV and jammer for anomaly detection. Similar to [99], the generalized state-space model [184] is used to capture the features and dynamic evolution of UAV signals to represent the radio environment. Differently from passive detection and classification of jamming signals in [99], the Active-GDBN achieves active anomaly detection by incorporating the UAV's actions into the inference process. Specifically, the UAV employs a Modified Markov Jump Particle Filter (M-MJPF) [187] to link the UAV's actions to environmental"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.411,
+ 0.921,
+ 0.503
+ ],
+ "angle": 0,
+ "content": "states and observations. Meanwhile, the UAV dynamically adjusts physical resource block selections to evade jamming by encoding jammer behavior and updating beliefs. The Active-GDBN achieves about \\(25\\%\\) to \\(37.5\\%\\) faster convergence on anomaly detection probability than the Q-learning-based baseline under various jamming types."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.505,
+ 0.922,
+ 0.852
+ ],
+ "angle": 0,
+ "content": "Different from previous works [98]–[100] that detect jamming anomalies based on the statistical distribution divergence of the signal, study [101] focuses on detecting anomalies by exploiting the time delays, shifts, and modulation of the signal characteristics. Firstly, achieving blind channel estimation involves constructing cyclic correlation matrices to identify distinct Doppler shifts and time delays associated with transmissions by exploiting the inherent almost-cyclostationary (ACS) properties of UAV and jammer signals (e.g., periodic statistics from OFDM modulation). Then, this blind estimation process is combined with a widely linear minimum mean square error (WL-MMSE) filter to provide an initial estimate of the symbol vector by leveraging the non-circular statistics of the received signal, where the initial estimate includes contributions from both the UAV and the jammer. Finally, a post-sorting algorithm (PSA) is employed to iteratively decode and cancel the jammer's contribution by ranking and removing symbols with the highest signal-to-disturbance-plus-noise ratio (SDNR). Simulation results demonstrate that the proposed scheme can effectively detect and separate the jamming signals from UAV signals without requiring prior knowledge of the jammer's characteristics, even when the jammer's power is twice as strong as the UAV's power."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.855,
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+ ],
+ "angle": 0,
+ "content": "In addition to jamming anomalies, which cause interference and security threats in the LAENet, abnormal power emissions in UAV communication networks also represent a critical type of anomaly, potentially leading to severe disruption of communication quality and violation of spectrum policies. The work in [102] proposes a cloud-based surveillance framework"
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.906,
+ 0.031,
+ 0.921,
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+ ],
+ "angle": 0,
+ "content": "23"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.082,
+ 0.071,
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+ ],
+ "angle": 0,
+ "content": "TABLE XI SUMMARY OF INJECTION DEFENSE FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.097,
+ 0.117,
+ 0.903,
+ 0.303
+ ],
+ "angle": 0,
+ "content": "| Injection type | Reference | Algorithm | Pros & Cons |
| Jamming signal | [98] | HDBN | HDBN-based jamming signal extraction and suppression\n✓ Autonomous learning from raw I/Q data enables adaptability to dynamic jamming patterns\nX Assume the jammer's output power remains constant during attacks |
| [101] | SIC | SIC with blind channel estimation for detecting and eliminating jamming signals\n✓ Eliminate jamming signals regardless of the mobility patterns of jammers\nX Rely on sufficient cyclostationary features in the received signal |
| [104] | DBF | DBF algorithm for nullifying jamming signals\n✓ Effective suppression of jamming signals while maintaining carrier phase integrity\nX May be limited to specific GNSS frequency bands |
| Spoofing signal | [105], [106] | API & LSR | SIC combined with API and LSR to recover legitimate signals from spoofing attacks\n✓ SemperFi with a single antenna does not require additional hardware\nX Limited to attackers with a power advantage lower than 15 dB |
| [107] | Subspace projection | Subspace projection for nullifying spoofing signals\n✓ Low parameter dependency, requiring only code delays and carrier frequencies\nX Suppression performance declines if spoofing and legitimate signals have similar code delays |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.329,
+ 0.493,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "to address the detection of abnormal power emissions, where the cloud server assigns spectrum resources to the UAVs and shares UAVs' spectrum usage information with the surveillance center. The surveillance center assigns the detection task to \\( K \\) surveillance nodes (SNs) for local detection of abnormal power emission, where the detection rule is based on the Lagrange multiplier method and the generalized likelihood ratio test. After local decisions, \\( K \\) SNs report results to the surveillance center, where cooperative detection of abnormal power emission is performed using the decision rule that declares an abnormal event when at least \\( L \\) out of \\( K \\) nodes detect an abnormality, where the optimal global threshold of \\( L \\) is determined by solving the constraints on the global false-alarm probabilities. Simulation results show that the global detection probability exceeds 90% when transmit power deviation exceeds 0.02W (allocated power is 0.01W)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.576,
+ 0.493,
+ 0.879
+ ],
+ "angle": 0,
+ "content": "Besides the threats of jamming and abnormal power emission, another critical anomaly that requires detection is eavesdropping in the LAENet, where malicious devices covertly intercept sensitive information during UAV-to-ground and UAV-to-UAV transmissions [66], [67]. Note that most previous works on anti-eavesdropping focused on measuring secure performance through secrecy rate and/or secrecy outage probability (such as [71], [76]) rather than emphasizing the detection of eavesdropping attacks. The work in [103] explores anomaly detection for eavesdropping attacks in UAV-aided wireless systems using unsupervised learning. Two datasets are prepared: artificial training data (ATD), simulated without eavesdropping based on CSI (all labeled normal), and a practical dataset extracted from received signal features (mean and variance of amplitude). Two types of unsupervised learning methods are designed for anomaly detection. One-class SVM maps data to a high-dimensional space, defining a normal region where outliers are detected. K-means clustering classifies test data into two clusters, labeling the one nearest to the ATD center as normal."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.074,
+ 0.884,
+ 0.492,
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+ ],
+ "angle": 0,
+ "content": "Lesson Learned For jamming anomalies, the statistical distribution divergence detection and signal structural feature-based detection, such as HDBN, GDBN, and ACS, are used to model the dynamic environment and detect deviations from"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
+ 0.329,
+ 0.923,
+ 0.676
+ ],
+ "angle": 0,
+ "content": "learned normal patterns. For abnormal transmission power detection, a cloud-based surveillance framework supports a statistical distribution detection approach to monitor and identify power emission outliers. Leveraging its high computing power, the cloud enables cooperative analysis through multi-source data aggregation, dynamically optimizes detection thresholds using global information, and maintains a feedback loop for adaptive anomaly detection. For eavesdropping detection, unsupervised learning techniques, including One-Class SVM and K-means clustering, achieve the identification of anomalies in received signals. These approaches effectively achieve anomaly detection and demonstrate excellent performance. However, challenges remain, including the reliance on high-quality training data and the complexity of maintaining real-time adaptability in dynamic spectrum environments. Currently, Generative AI such as GANs and generative diffusion models presents a promising research direction for anomaly detection, as demonstrated in the use of generalized models in HDBN and the artificial data generation for training ML and clustering models in [188], [189]. Generative AI could further enrich training datasets and provide a high-level generative model to enhance anomaly detection in the dynamic and uncertain LAENet."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "B. Injection Defense"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.503,
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+ ],
+ "angle": 0,
+ "content": "The low-altitude economy is highly dependent on open communication and network architecture with dense communication links, which brings injection attacks as a significant threat to UAV communication integrity [28], [46]. These attacks involve the deliberate injection of malicious signals, such as jamming and spoofing signals, to disrupt or manipulate legitimate communications [97], [190]. Jamming signal injection can make legitimate signals unrecognizable by emitting high-power electromagnetic interference to degrade signal reception [98]. Additionally, spoofing signal injection can transmit high-power signals to overshadow legitimate GNSS signals. Therefore, eliminating injection signals or separating them from legitimate signals is crucial for ensuring communication integrity in the LAENet."
+ }
+ ],
+ [
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+ "type": "page_number",
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+ "angle": 0,
+ "content": "24"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Part A. SNDR-based SIC for jamming injection defense"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Part B. SIC with API and LSR for spoofing injection defense"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.495,
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+ "angle": 0,
+ "content": null
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+ {
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+ "angle": 0,
+ "content": "Part C. Subspace projection for spoofing injection defense"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.074,
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+ ],
+ "angle": 0,
+ "content": "Fig. 11. The overall architecture of injection defense mechanisms for UAVs in smart city applications. Part A presents the SIC architecture that processes channel state information to defend against jamming injection attacks [101]. Part B shows an SIC architecture integrated with API and LSR modules, which subtracts injection signals from the received signal to recover normal signals [105], [106]. Part C depicts a subspace projection-based architecture for spoofing injection defense, where the received signal is projected onto the orthogonal null space of the spoofing signals to eliminate them [107]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The UAV's communication can be severely disrupted by jammers that exploit LoS propagation to inject jamming signals into the transmission channel, which may effectively mask legitimate signals and render them unrecognizable [101]. The work in [98] proposes an HDBN-based injection defense scheme to extract and remove the jammer's signal. This work first utilizes the HDBN to detect abnormal behaviors caused by jamming attacks, as mentioned earlier in Section V-A. Once the jammer's presence is confirmed, its signal characteristics are analyzed across multiple levels of continuous in-phase (I) and quadrature (Q) components and observation-level state vectors [191]. The extracted jammer signal is then separated from the received observation using frequency-domain subtraction [192], component-wise I/Q processing, and adaptive filtering [191]. The corrected signal is subsequently demodulated and decoded using techniques and error correction coding to restore the original signal. To maintain resilience against evolving jamming tactics, the system continuously updates the HDBN model to improve suppression commands. Simulation results show that the mean square error (MSE) of suppression commands decreases as the JSR increases, meaning that jammers attacking with higher power can be better estimated than jammers attacking with lower power."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.075,
+ 0.794,
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+ "angle": 0,
+ "content": "Different from the work in [98], which separates the jamming signal by analyzing its I/Q characteristics, the study in [101] proposes a Serial Interference Cancellation (SIC) scheme based on SDNR to eliminate injected anomalous signals in UAV communications, as shown in part A of Fig. 11. First, blind channel estimation and a WL-MMSE filter are used to identify UAV and jammer signals (as detailed in Section V-A). Then, the PSA ranks detected symbols based on SDNR, where the jamming signals rank higher in SDNR due to their higher emitted power. The SIC [193],"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.603
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+ "angle": 0,
+ "content": "[194] is subsequently designed for progressively eliminating jamming signals. Specifically, the high-rank jamming symbol is decoded, reconstructed using estimated channel parameters, and subtracted from the received signal. The process continues iteratively to eliminate previously detected jamming signals until all UAV symbols are successfully recovered, with the receiver dynamically updating channel estimation to adapt to jammer mobility and environmental changes. Simulation results demonstrate that the UAV signal can be recovered with low bit error rates \\((< 10^{-4})\\) even when the power of the jammer is double that of the UAV."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Jamming attacks not only affect U2G and UAV-to-UAV communications but also cause RF interference, leading to UAVs failing to track GNSS signals in the LAENet. In light of this, the work in [104] proposes a self-calibrating digital beamforming (DBF) algorithm to effectively nullify jamming signals while preserving high-precision carrier phase measurements. It calibrates the antenna array's steering vectors and RF channel characteristics. Once calibration is complete, the system performs jamming detection and direction estimation by analyzing interference patterns across the antenna array. Then, the minimum power distortionless response (MPDR) optimization rule is used to calculate optimal beamforming weights, which aim to create nulls in the beam pattern corresponding to the directions of jamming signals, effectively suppressing them. The calculated beamforming weights are applied to the received signals to produce the beamformer output, which effectively suppresses jamming signals while preserving the carrier phase integrity of the desired signals. The proposed scheme achieves up to 80 dB Jammer-to-Signal Ratio (JSR) suppression, significantly outperforming the conventional Power Inversion (PI) scheme."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In addition to jamming signals, spoofing attacks can easily"
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "25"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.079,
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+ "angle": 0,
+ "content": "transmit fake signals to manipulate GNSS signals due to their open signal structure and weak signal strength [195]. One type of method is based on signal encryption or data encryption to prevent malicious spoofers from injecting illegitimate signals [196]–[198]. However, they may not be suitable for resource-constrained UAVs in the LAENet. Therefore, defending against spoofing signal injection based on different signal characteristics is a promising solution. The authors in [105], [106] propose an anti-spoofing system, called SemperFi, to autonomously recover legitimate signals during active spoofing for UAVs. The system employs two core modules: the Adversarial Peak Identifier (API) and the Legitimate Signal Retriever (LSR), as shown in part B of Fig. 11. The API detects spoofed signals by correlating inertial measurement unit (IMU) data with calculated position-velocity-time (PVT) solutions [199]. The LSR module replicates the spoofing signal once it is identified. Then, similar to the study in [101], the SIC is applied to subtract the replica from the composite received signal that contains legitimate and spoofing signals. SemperFi enters an iterative refinement process if spoofing signals persist after initial cancellation, where replication, subtraction, and reassessment are performed until the spoofing detector no longer triggers an alarm, indicating sufficient attenuation or elimination of spoofing."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Besides recovering legitimate signals by subtracting spoofing signals from the received signal [101], [105], [106], projecting the signal is also a viable injection defense strategy. In the study [107], the GNSS receiver's spoofing mitigation algorithm employs a subspace projection-based interference cancellation method to effectively eliminate spoofing signals, as shown in part C of Fig. 11. Specifically, the receiver on UAVs acquires and tracks incoming signals, identifying potential spoofing signals and reconstructing them based on their power levels, pseudo-random noise (PRN) code delays, and carrier frequencies. Then, the receiver uses these reconstructed spoofing signals to construct a spoofing subspace, which represents all possible linear combinations of spoofing signal characteristics. To effectively remove spoofing signals from the received signal, the receiver performs orthogonal projection to obtain a cleaned signal by mapping the received signal onto a complementary null space that is mathematically orthogonal to the spoofing subspace. Simulation results show that shorter projection lengths suppress spoofing signals more effectively than longer projections, achieving a \\(20\\mathrm{dB}\\) gain in Signal-to-Interference Ratio (SIR)."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Lesson Learned The above-mentioned studies have demonstrated the effectiveness for mitigating injection signals, such as jamming and spoofing attacks, thereby enhancing UAV communication reliability and security. These advancements leverage techniques that not only detect malicious signal interference but also enable autonomous recovery. One key advantage is that non-cooperative detection techniques, such as blind estimation [101] and self-awareness models [98], allow for efficient attack identification without requiring prior knowledge of the attacker's signal characteristics to adapt to dynamic and adversarial environments. However, several challenges remain in that beamforming-based or spatial filtering techniques rely on multi-antenna configurations [101],"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "[104], limiting their applicability in cost-sensitive or small UAV systems. Future work should explore lightweight and energy-efficient implementations of injection defense to support stable UAV signal integrity protection. Additionally, more intelligent injection defense strategies combining optimization methods, RL, and ML could enhance resilience against more sophisticated adversaries."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "VI. FUTURE RESEARCH DIRECTIONS"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "A. Energy-efficient Physical Layer Security"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Future work can focus on exploring more unique physical characteristics of wireless communication, such as exploiting channel characteristics and implementing simple coding schemes, to develop secure and low-energy protocols. Meanwhile, drones in the LAENet need to develop adaptive power control strategies that dynamically adjust transmission power based on channel conditions and security requirements to minimize unnecessary energy consumption [200]. Moreover, dynamic trajectory optimization is equally important for energy efficiency [201]. Future research can explore enabling UAVs to learn attack patterns in real time, share secure trajectory models across swarms, and dynamically adjust flight paths based on real-time security and power consumption feedback."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "B. Multi-drone Collaboration for Secure Communication"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Future research on secure physical layer communication in the LAENet should move beyond existing dual-UAV collaboration models and explore distributed multi-UAV coordination (or UAV swarms) for enhanced resilience against jamming, spoofing, and unauthorized access [202]. For example, UAV swarms can collaboratively emit interference signals to obscure unauthorized receivers, thereby enhancing the confidentiality of communications [20]. Additionally, the integration of adaptive trust-based mutual authentication protocols among UAVs is essential [26]. Multiple UAVs with mutually verified identities can enable dynamic and secure spectrum-sharing mechanisms to optimize resource utilization in the LAENet."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "C. AI-driven Security Defense Strategy"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Existing AI-based security strategies mainly focus on training AI models to identify anomalous signals while having some limitations. The resource-constrained drones are unable to train high-quality AI models, making the integration of edge computing a promising approach for model training [200]. Note that AI models may be difficult to generalize in recognizing various anomalous signals because they are pre-trained on previously collected datasets of fixed size. Future work can explore leveraging GAN or diffusion models to generate datasets based on real-time captured anomalous signals [203]. Furthermore, emerging generative AI technologies, such as the diffusion model for secure network topology generation in low-altitude domains [189], [204], AI agents for human-aerial vehicle secure interaction [205], and mixture of experts for robust wireless communications [2], [206], can be explored to achieve a more autonomous and intelligent LAENet."
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "26"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.076,
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+ ],
+ "angle": 0,
+ "content": "D. Space-Air-Ground Integrated Security Architecture"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Future research can explore establishing a multi-domain physical layer security framework for LAENet to connect space, air, and ground layers, providing seamless communication coverage and cost-effective network access [55], [207]. A potential key research direction is the development of a coordinated multi-tier security mechanism, where satellites, UAVs, and terrestrial base stations collaboratively enhance physical layer security through dynamic resource allocation and interference management based on real-time CSI and environmental conditions, such as UAV mobility, channel fading, and spectrum constraints."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "E. 6G-Enabled Secure UAV Communication"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The advent of 6G networks presents new opportunities for LAENet. Terahertz (THz) communication can offer ultrahigh-speed data transmission capabilities for LAENet [208]. Future research can explore the integration of THz with advanced beamforming techniques to focus signals on legitimate users, thereby enhancing security and reducing the risk of interception. Furthermore, Reconfigurable Intelligent Surfaces (RIS) play a crucial role in strengthening physical layer security by intelligently controlling wireless signal propagation [209], [210]. Future work can investigate RIS-based secure beamforming strategies to mitigate adversary interception, and leverage optimization techniques and DRL to adaptively adjust beamforming against eavesdropping or jamming attacks."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "VII. CONCLUSION"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This paper has presented a comprehensive survey on secure physical layer communications in the LAENet, emphasizing the importance of safeguarding confidentiality, availability, and integrity in communications. It introduced the concept and architecture of the LAENet and outlined the associated security issues in physical layer communication. Then, the survey provided in-depth reviews of countermeasures for anti-eavesdropping strategies, authentication schemes, anti-jamming strategies, spoofing defenses, anomaly detection, and injection defense. Finally, the paper proposed a set of forward-looking future research directions. These discussions highlighted the critical role of secure physical layer communication in supporting the development of the LAENet and offered valuable insights for ongoing advancements in this emerging domain."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
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+# Secure Physical Layer Communications for Low-Altitude Economy Networking: A Survey
+
+Lingyi Cai, Jiacheng Wang, Ruichen Zhang, Yu Zhang, Tao Jiang, Fellow, IEEE, Dusit Niyato, Fellow, IEEE, Xianbin Wang, Fellow, IEEE, Abbas Jamalipour, Fellow, IEEE, and Xuemin Shen, Fellow, IEEE
+
+Abstract—The Low-Altitude Economy Networking (LAENet) is emerging as a transformative paradigm that enables an integrated and sophisticated communication infrastructure to support aerial vehicles in carrying out a wide range of economic activities within low-altitude airspace. However, the physical layer communications in the LAENet face growing security threats due to inherent characteristics of aerial communication environments, such as signal broadcast nature and channel openness. These challenges highlight the urgent need for safeguarding communication confidentiality, availability, and integrity. In view of the above, this survey comprehensively reviews existing secure countermeasures for physical layer communication in the LAENet. We explore core methods focusing on anti-eavesdropping and authentication for ensuring communication confidentiality. Subsequently, availability-enhancing techniques are thoroughly discussed for anti-jamming and spoofing defense. Then, we review approaches for safeguarding integrity through anomaly detection and injection protection. Furthermore, we discuss future research directions, emphasizing energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. This survey may provide valuable references and new insights for researchers in the field of secure physical layer communication for the LAENet.
+
+Index Terms—Low-altitude economy networking, secure physical layer communications, communication confidentiality, communication availability, communication integrity.
+
+# I. INTRODUCTION
+
+WITH the rapid development of aerial vehicle technologies and communication networks, the concept of Low-Altitude Economic Networking (LAENet) has emerged to enable more comprehensive, large-scale, and intelligent
+
+Lingyi Cai is with the Research Center of 6G Mobile Communications, School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China, and also with the College of Computing and Data Science, Nanyang Technological University, Singapore (e-mail: lingyicai@hust.edu.cn).
+
+Jiacheng Wang, Ruichen Zhang, and Dusit Niyato are with the College of Computing and Data Science, Nanyang Technological University, Singapore (e-mails: jiacheng.wang@ntu.edu.sg; ruichen.zhang@ntu.edu.sg; dniyato@ntu.edu.sg).
+
+Yu Zhang and Tao Jiang are with the Research Center of 6G Mobile Communications, School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China (e-mail: yuzhang123@hust.edu.cn; tao.jiang@ieee.org).
+
+Xianbin Wang is with the Department of Electrical and Computer Engineering, Western University, London, ON, N6A 5B9, Canada (e-mail: xianbin.wang@uwo.ca).
+
+Abbas Jamalipour is with the School of Electrical and Computer Engineering, University of Sydney, Australia (e-mail: a.jamalipour@ieee.org).
+
+Xuemin Shen is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: sshen@uwaterloo.ca).
+
+connectivity to support various low-altitude activities [1]–[4], such as intelligent transportation, logistics delivery, communication enhancement, disaster monitoring, and emergency response [5]–[8], as shown in Fig. 1. The LAENet is built upon earlier frameworks of single Unmanned Aerial Vehicle (UAV) operation and multi-UAV networks. A single UAV typically maintains a direct link to a ground station or base station, operating with simple control procedures and delivering cost-effective services but with limited range and scalability [9]. The UAV network focuses on formation control and multi-UAV collaboration, enabling broader mission areas and stronger fault tolerance [9]–[11]. Advancing from these foundations, the LAENet integrates various aerial vehicles into a high-density communication network, connecting them not only to ground stations but also to other platforms such as base stations, access points, and even satellites [12], [13]. Thus, the LAENet can enable ubiquitous coverage, high reliability, robust fault tolerance, greater autonomy, and intelligence.
+
+Specifically, the LAENet refers to an integrated network system that connects various low-altitude flight operations, including general aviation, drones, electric vertical take-off and landing (eVTOL) aircraft, and other aerial platforms, within the designated low-altitude airspace (typically below 1,000 meters, and in some cases extending up to 3,000 meters) [1], [13]. The LAENet serves as a vital bridge between ground-based economies and airspace resources, which will drive technological innovation and unlock substantial social and economic benefits [14], [15]. The Civil Aviation Administration of China estimates that the country's low-altitude market will soar from 500 billion Chinese yuan (about 70 billion US dollars) in 2023 to 1.5 trillion Chinese yuan (about 200 billion US dollars) in 2025 and as much as 3.5 trillion Chinese yuan (about 480 billion US dollars) in 2035 [16]. Currently, research institutions and enterprises across multiple regions in China are continuously advancing and expanding innovative research and commercial applications of UAVs and eVTOLs in low-altitude activities [17]. Meanwhile, in the United States, the Federal Aviation Administration has confirmed its commitment to actively promoting the development of electric air taxis and integrating this type of aircraft into the national airspace [18].
+
+In the LAENet, physical layer communication serves as a critical foundation for wireless communication between aerial vehicles and between aerial vehicles and communication infrastructure [10], [28], [31]. The physical layer converts digital data from higher protocol layers into signals suitable for transmission over aerial communication channels [32]–[34].
+
+
+Fig. 1. The overall architecture of the LAENet covers the main application scenarios, including emergency monitoring and response, temporary communication relay, communication coverage expansion, low-altitude smart logistics, and urban air mobility. The table compares the similarities and differences between the LAENet, single UAV, and UAV networks, representing the evolution of the LAENet.
+
+This process encompasses encoding data into bit sequences, modulating them onto carrier waves, and ensuring reliable signal propagation through the wireless medium [32], [35], [36]. At the receiver side, the physical layer performs inverse operations, including demodulating the incoming signals, decoding the bit sequences, and passing the data to upper layers for further processing [37]–[39]. Therefore, the physical layer supports the core communication mechanisms in the LAENet and plays a crucial role in its aerial deployment. For example, aerial vehicles deployed as aerial base stations (ABSs) or aerial relays can overcome interference, signal distortion, and environmental variations inherent in communication links by using physical layer functionalities such as channel access, multiplexing, and channel equalization [33], [40], [41].
+
+However, physical layer communication in the LAENet is exposed to a variety of security threats due to the inherent characteristics of aerial communication environments [42]. The broadcast nature of wireless signals and the prevalence of line-of-sight (LoS) propagation make aerial links particularly vulnerable to eavesdropping, jamming, and spoofing attacks [1], [43]. These attacks can compromise communication confidentiality, disrupt communication, or deceive aerial vehicles by impersonating legitimate transmitters [44], [45]. Furthermore, the openness of wireless channels and weak authentication mechanisms increase the risk of unauthorized access and injection attacks, allowing adversaries to infiltrate the network or inject malicious signals [46], [47]. Additionally, the open medium and dynamic spectrum access may cause anomalous behaviors to disrupt normal communication operations in the LAENet [48], [49].
+
+Confronted with these substantial security challenges, this paper conducts a comprehensive analysis on physical layer communications of the LAENet and provides a thorough survey of technologies and solutions to address communication confidentiality, availability, and integrity. Table II gives a clear structure for showing existing efforts on secure physical layer communications for the LAENet.
+
+# A. Related Surveys
+
+Recently, a number of excellent survey and tutorial papers have overviewed security issues in UAV networks and communications and have summarized corresponding countermeasures and solutions, as shown in Table I. Some works consider security issues at the system level including intrusion, privacy, and trust issues. The work in [19] provides a comprehensive review of security threats facing UAVs and UAV networks, including communication vulnerabilities, sensor spoofing, jamming, and malware attacks. It examines various countermeasures such as encryption, global positioning system (GPS) spoofing mitigation, and firmware signing. A gap analysis is performed to identify remaining security vulnerabilities and provide recommendations for future UAV development. The study in [20] conducts a comprehensive review of security issues in UAV swarm networks, examining various potential attacks such as communication attacks, identity-based attacks, resource attacks, routing attacks, data attacks, and machine learning (ML) attacks. It categorizes these threats and presents corresponding security technologies and countermeasures, including cryptography, physical layer security techniques, blockchain, machine learning, and intrusion detection
+
+TABLEI SUMMARY OF RELATED SURVEYS
+
+| References | Focus |
| [19] | A review of cybersecurity threats, countermeasures, and research gaps in UAV networks, with a focus on emerging attack surfaces and commercial UAV applications |
| [20] | A survey of security threats, vulnerabilities, and countermeasures in UAV swarm networks, with a focus on classifying attack types and reviewing emerging defense technologies |
| [21] | A review of security threats, vulnerabilities, and countermeasures in UAVs and Flying Ad Hoc Networks with attack surface analysis with simulation-based evaluation |
| [22] | A survey of vulnerabilities across software, hardware, and communication layers in UAV systems, and an exploration of emerging defense technologies |
| [23] | A survey of security challenges in drone communication and a review of emerging technologies used to enhance the speed, reliability, and security of UAV networks |
| [24] | A review of UAV security challenges, existing controls, and future research directions, with an emphasis on the transformative role of AI in enabling secure UAV systems |
| [25] | A review of security threats classified from a cyberspace security perspective and countermeasures in UAV systems |
| [26] | A survey of security threats, requirements, and counter-measures in UAV-aided Internet of Things (IoT) applications |
| [27] | A survey of cybersecurity vulnerabilities and countermeasures in UAV systems, integrating threat classification, communication protocols, and emerging techniques |
| [28] | A survey of PLS in UAV communications, focusing on key challenges, methodologies, and recent advancements for both static and mobile UAV deployment scenarios |
| [29] | A review of security challenges, practical deployment aspects, and standardization progress associated with integrating UAVs into cellular networks |
| [30] | A survey of layer-wise cybersecurity threats and AI-enabled countermeasures in UAV-assisted IoT applications |
+
+systems. The authors in [21] provide a detailed examination of security challenges in UAVs and FANETs, covering various attack vectors including communication, identity-based, resource, routing, data, and machine learning attacks. The study in [22] examines security and privacy vulnerabilities in UAV systems across hardware, software, and communication layers. It discusses various threats such as eavesdropping and jamming attacks, and presents defense mechanisms including blockchain, machine learning-based intrusion detection, and secure communication protocols.
+
+Some studies emphasize cyber security challenges within UAV networks. The study in [23] comprehensively reviews security issues in drone communication, including Denial of Service (DoS), GPS spoofing, and man-in-the-middle attacks. It examines vulnerabilities across different drone applications and presents countermeasures using blockchain, software-defined networks, machine learning, and fog computing. The authors of [24] provide a comprehensive survey of security challenges in UAV systems, including various types of attacks, privacy concerns, and trust issues. It identifies current research trends and gaps while establishing a future roadmap with a focus on artificial intelligence (AI)'s potential to enhance UAV security. The authors in [25] provide a comprehensive review of security issues in UAV networks, examining various potential attacks such as spoofing, replay, jamming, and
+
+# TABLE II
+
+# CHALLENGES AND SOLUTIONS
+
+RED CIRCLES DESCRIBE THE SECURITY ISSUES; GREEN CIRCLES REPRESENT THE OVERALL COUNTERMEASURES FOR THE SECURITY ISSUES; GREEN CHECK MARKERS INDICATE DIFFERENT TYPES OF SOLUTIONS UNDER EACH COUNTERMEASURE
+
+| Section III, Challenge 1: Communication confidentiality |
| Issues | ● Eavesdropping attack [46], [50]● Unauthorized access [31], [51], [52] |
| Solutions | ● Anti-eavesdropping strategies√ Convex optimization-based strategies [53]–[59]√ Reinforcement learning-based strategies [60]–[65]√ Deep learning-based strategies [66]–[71]● Communication authentication√ PUFs-based authentication [72]–[74]√ Channel based-authentication [75]–[77] |
| Section IV, Challenge 2: Communication availability |
| Issues | ● Jamming attack [48], [78], [79]● Spoofing attack [49], [50], [52], [78] |
| Solutions | ● Anti-jamming strategies√ Convex optimization [80]–[82]√ Single-agent RL [83]–[86]√ Multi-agent RL [87]–[89]● Spoofing defense√ PLA [77], [90], [91]√ GNSS spoofing detection [92]–[94] |
| Section V, Challenge 3: Communication Integrity |
| Issues | ● Anomalous behaviors [61], [95], [96]● Injection attacks [28], [46], [97] |
| Solutions | ● Anomaly detection√ Jamming anomaly detection [98]–[101]√ Abnormal power detection [102]√ Eavesdropping anomaly detection [103]● Injection defense√ Jamming signal injection defense [98], [101], [104]● Spoofing signal injection defense [105]–[107] |
+
+eavesdropping attacks. It categorizes these threats and presents corresponding security technologies and countermeasures. The study in [26] provides a comprehensive review of security issues in UAV-aided IoT applications and presents corresponding security technologies and countermeasures. The work in [27] reviews cybersecurity threats affecting UAV systems and evaluates existing countermeasures in enhancing UAV security.
+
+In addition, some surveys analyze the challenges faced by UAV systems from a layered perspective (e.g., physical layer, link layer, network layer, application layer). The work in [28] deeply reviews the current state of physical layer security (PLS) in UAV communications, examining unique air-to-ground channel characteristics, static and mobile UAV deployment scenarios, and various security enhancement techniques. The work in [29] presents a comprehensive overview of UAV cellular communications, covering the classification of consumer drones, the concept and potential of UAV-mounted flying base stations. It explores the integration of UAVs into cellular networks as novel user equipment and addresses key challenges related to interference, regulatory compliance, and security. The authors of [30] review the cybersecurity landscape of UAV-assisted IoT applications, examining layer-wise security threats from physical to application layers. It explores how AI, ML, deep learning (DL), and reinforcement learning (RL) techniques have been employed to address authentication, data privacy, and attack prevention challenges.
+
+TABLE III
+LIST OF ABBREVIATIONS
+
+| Abbreviation | Description | Abbreviation | Description |
| A2G | Air-to-ground | ABS | Aerial Base Station |
| AN | Artificial Noise | AI | Artificial Intelligence |
| BCD | Block Coordinate Descent | BS | Base Station |
| CNN | Convolutional Neural Network | CSI | Channel State Information |
| DDPG | Deep Deterministic Policy Gradient | DDQN | Double-deep Q-Learning |
| DL | Deep Learning | DNN | Deep Neural Network |
| DQN | Deep Q-Network | eVTOL | Electric Vertical Take-off and Landing |
| DRL | Deep Reinforcement Learning | FAR | False Alarm Rate |
| G2A | Ground-to-air | G2U | Ground-to-UAV |
| GAN | Generative Adversarial Network | GNSS | Global Navigation Satellite System |
| GPS | Global Positioning System | GS | Ground Station |
| IoT | Internet of Things | LAENet | Low-Altitude Economy Networking |
| LSTM | Long Short-Term Memory | LoS | Line-of-sight |
| MARL | Multi-agent Reinforcement Learning | MDP | Markov Decision Process |
| MDR | Miss Detection Rate | MEC | Mobile Edge Computing |
| ML | Machine Learning | MSE | Mean Square Error |
| NOMA | Non-orthogonal Multiple Access | PLA | Physical-layer Authentication |
| PLS | Physical Layer Security | PUF | Physical Unclonable Function |
| QoE | Quality of Experience | RF | Radio Frequency |
| RIS | Reconfigurable Intelligent Surfaces | RL | Reinforcement Learning |
| RNN | Recurrent Neural Network | RSS | Received Signal Strength |
| SCA | Successive Convex Approximation | SDNR | Signal-to-disturbance-plus-noise Ratio |
| SNR | Signal-to-noise Ratio | SOC | Second-Order Cone |
| TDMA | Time-division Multiple Access | THz | Terahertz |
| U2G | UAV-to-ground Communication | UAV | Unmanned Aerial Vehicle |
+
+# B. Contributions of Our Survey
+
+The related surveys and tutorials primarily focus on the classification of overall security threats and corresponding countermeasures in UAV networks or UAV-assisted applications, with relatively little attention given to security issues of communication in the physical layer. Different from existing studies, our survey uniquely concentrates on the security challenges specific to physical layer communications in the LAENet, as summarized in Table II. It fills a critical gap in the literature by conducting an in-depth analysis of threats in physical layer communications that were previously underexplored or only briefly mentioned in prior studies. By offering a comprehensive and systematic analysis of these underexplored issues, our work brings new insights to seek effective solutions to enhance physical layer security in communications of the LAENet. The key contributions of this paper are summarized as follows:
+
+The key contributions of this paper are summarized as follows:
+
+- A thorough discussion of the six main security issues in the physical layer communication of the LAENet is presented, namely, eavesdropping attack, unauthorized access, jamming attack, spoofing attack, anomalous behaviors, and injection attack. We analyze these attacks in the context of their potential occurrence throughout the entire operation of LAENet, providing essential references for ensuring the security of physical layer communication in the future LAENet deployments.
+- We review countermeasures against various attacks in detail and offer a comprehensive tutorial on achieving communication confidentiality, communication availability, and communication integrity in LAENet. In addition,
+
+the lessons learned for each security issue are presented to emphasize the limitations of existing works and provide high-level insights for improvements.
+
+- Several potential future research directions for secure physical layer communication in LAENet are proposed, including energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. These diverse perspectives offer new guidance for future research on secure physical layer communication in LAENet.
+
+The remainder of this paper is given as follows. Section II introduces the background of the LAENet and security issues in physical layer communication of the LAENet. In Section III, a comprehensive exploration of achieving communication confidentiality for the LAENet is presented. Section IV reviews the solutions for communication availability in the LAENet. In Section V, countermeasures on communication integrity for the LAENet are discussed. Section VI provides future research directions, and Section VII concludes this paper. Additionally, Table III lists the abbreviations commonly employed throughout this survey.
+
+# II. BACKGROUND KNOWLEDGE
+
+In this section, we introduce the background of the LAENet, including its definition and application scenarios. Subsequently, the concept of physical layer communication in the LAENet and its security threats are elaborated in detail.
+
+# A. Background of LAENet
+
+The LAENet is a sophisticated and dynamic system that integrates various aerial and terrestrial technologies to en
+
+
+Fig. 2. Background knowledge of the LAENet and security issues in its physical layer communication. Describe the definition of the LAENet and its communication application scenarios. Elaborate on three key metrics for secure physical layer communication: communication confidentiality, which combats eavesdropping attacks and unauthorized access; anti-jamming strategies and spoofing defense for ensuring communication availability; and anomaly detection and injection defense to prevent adversaries from compromising communication integrity.
+
+able seamless communication, coordination, and management of diverse aerial operations within low-altitude airspace [1], [108]. The LAENet includes numerous different types of constituents, such as flight equipment, base stations, and other communication platforms. Specifically, the LAENet connects various aerial vehicles, including general aviation aircraft for passenger transport and emergency rescue, drones for surveillance and logistics, and eVTOL designed for urban air mobility and last-mile cargo delivery [109], [110]. These aerial vehicles can incorporate ground and aerial base stations, further high-altitude platforms, such as weather balloons and satellites, to receive environmental information and precise navigation [13].
+
+Different from traditional aviation networks that rely on centralized air traffic control, the LAENet can independently construct communication and networking by seamlessly interconnecting a variety of aerial and ground-based systems, which enables continuous information exchange, flight path optimization, and autonomous operations [8], [111]. Therefore, the LAENet has opened opportunities for various application scenarios and plays key roles from the perspective of communication coverage and relay [112]–[114]. Specifically, the LAENet can extend the communication coverage by deploying aircraft as ABSs in areas lacking communication infrastructure [115]–[117]. For instance, these ABSs deployed at optimal altitudes can provide connectivity and network services in remote or disaster-stricken areas [118], [119]. Moreover, if the direct communication links between ground base stations and user equipment are unreliable, such as in
+
+mountainous regions and densely populated areas, the aircraft can act as mobile relays to improve connectivity by capturing, amplifying, and transmitting communication signals [120]–[122]. It also can be regarded as a surveillance unit to monitor airspace dynamics while simultaneously functioning as a low-altitude network orchestrator to optimize communication and computing resources [118], [123], [124].
+
+To integrate and evolve these capabilities, the LAENet needs to establish effective communication infrastructure to ensure reliable connectivity and efficient interaction across various environments [31], [125]. Physical layer communication, as the bottom layer in the network architecture, may directly influence the communication performance of the LAENet across aerial and terrestrial networks [43], [46]. For example, it governs how signals are generated, transmitted, and received between aircraft and base stations [31]. Building on this, it manages the channel and spectrum resources to enhance signal transmission quality and maintain stable connectivity [43]. Therefore, ensuring the security of physical layer communication in the LAENet is crucial for supporting a wide range of applications in low-altitude domains.
+
+# B. Security Issues in Physical Layer Communication of LAENet
+
+Based on previous studies [126], [127], we discuss the security issues in the physical layer communication of the LAENet from three aspects: confidentiality, availability, and
+
+integrity of communications. The details of each measurement are described as follows.
+
+- The confidentiality of physical layer communications in the LAENet can be compromised by security threats such as eavesdropping and unauthorized access [128]. Eavesdropping arises primarily from the broadcast nature of wireless signals and LoS link, making transmissions highly susceptible to interception [46]. An eavesdropper silently capturing or intercepting signals can lead to the exposure of confidential information. Meanwhile, unauthorized access threats exploit the open and broadcast nature of UAV communications [31]. Attackers may gain illegal access to the LAENet by disguising themselves as legitimate UAVs or ground stations, thereby deceiving or interfering with the normal operation of UAVs [51].
+- Similarly, the open nature of wireless channels and LoS propagation bring jamming and spoofing security issues for communication availability [78]. Specifically, jammers can continuously transmit interference signals to disrupt communication, where a jammer can be a drone or a base station [48]. The spoofing attack can not only achieve identity spoofing by forging legitimate transmission identities but also launch signal deception attacks to disrupt UAV communications and positioning [49]. Therefore, jamming and spoofing lead to unauthorized access and signal disruptions or errors, making communication unavailable in the LAENet.
+- Integrity as a microscopic metric measures the deviations of signals, channels, and spectrum in communication under adversaries' influence [129]. The communication integrity of the LAENet can be affected by anomalous behaviors and injection attacks. Anomalous behaviors often use dynamic spectrum access and the open wireless medium, including abnormal jamming, abnormal transmission power, and covert eavesdropping [95]. These anomalous behaviors can introduce harmful interference, violate spectrum policies, and expose sensitive information to eavesdroppers [61], [96]. Moreover, the injection attack exploits the open nature of wireless channels to alter signals or inject illegal signals, such as spoofing signals or malicious GNSS signals, to deceive receivers and interfere with communication, thereby leading to degraded signal quality, false navigation, and network congestion [28], [46], [97].
+
+Overall, as illustrated in Fig. 2, this survey reviews existing research on achieving communication confidentiality, availability, and integrity for the LAENet. Specifically, the investigation of anti-jamming strategies and communication authentication schemes aims to enhance communication confidentiality. Studies on anti-jamming techniques and spoofing defense mechanisms have been explored to ensure communication availability. Furthermore, research on communication integrity has focused on anomaly detection and injection attack mitigation approaches.
+
+# III. COMMUNICATION CONFIDENTIALITY FOR LAENET
+
+# A. Anti-eavesdropping Strategy
+
+The LAENet faces significant eavesdropping threats due to the inherent vulnerabilities of UAV-enabled wireless communications. The openness of wireless channels, especially the LoS links in air-to-ground (A2G) and ground-to-air (G2A) communications, increases susceptibility to interception by eavesdroppers that disrupt legitimate communications compared to traditional terrestrial channels [50]. Traditional cryptographic methods, while effective in many scenarios, are less suitable for UAV communications due to their computational complexity and the dynamic mobility of UAVs [130]. This highlights the critical need for robust security measures to ensure the confidentiality and reliability of the LAENet communications. To address these limitations, leveraging PLS techniques to counter eavesdropping threats effectively has emerged as a promising solution [131]-[134].
+
+In the LAENet, anti-eavesdropping solutions can leverage the controllable mobility of low-altitude aircraft to enhance physical layer security. By dynamically optimizing their trajectories, low-altitude aircraft can actively adapt their flight paths to shape the communication environment [135]. This approach allows them to fly closer to legitimate ground nodes, strengthening communication links and improving channel conditions for intended receivers, while simultaneously distancing themselves from potential eavesdroppers. In this subsection, we present a critical role of UAV trajectory in forming the communication environment, and how PLS can be enhanced through trajectory optimization and resource allocation to mitigate eavesdropping risks. Our analysis focuses on three prominent methodologies in this domain: convex optimization, deep learning, and reinforcement learning.
+
+Convex optimization plays a crucial role in addressing anti-eavesdropping challenges in UAV-enabled communication networks, particularly for solving the joint optimization of trajectory and resource allocation [137]. Due to the inherent non-convex nature of these problems, advanced convex optimization techniques such as Successive Convex Approximation (SCA) and Block Coordinate Descent (BCD) are widely utilized [135]. These methods enable UAVs to enhance physical layer security by optimizing flight paths and resource utilization, minimizing the risk of eavesdropping while ensuring secure and efficient communication. Additionally, the decision variables may be discrete, which requires the application of various relaxation methods to transform the complex optimization problem into a more tractable form to obtain efficient solutions [138].
+
+The study in [53] explores physical-layer security in UAV-assisted Mobile Edge Computing (MEC) systems in the presence of multiple ground-based eavesdroppers. The proposed system utilizes dual UAVs for task execution and anti-eavesdropping measures. One UAV operates as a mobile MEC server, while the other emits jamming signals to disrupt eavesdroppers, as shown in Fig. 3. The time-division multiple access (TDMA) scheme and non-orthogonal multiple access (NOMA) scheme are proposed to maximize the minimum secure computing capacity by jointly optimizing communica
+
+TABLE IV SUMMARY OF CONVEX OPTIMIZATION FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Ref | Optimization Objectives | Eavesdropper and Jammer Type | OptimizationConstraints | Pros & Cons |
| [53] | Secure calculation capacity1 | UAV jammer and fixed ground eavesdropper | Transmit power, time allocation, and computation capacity | BCD and P-BCD for secure calculation capacity maximization
+✓ Secure capacity of NOMA and TDMA has been significantly improved
+X High complexity for NOMA due to dual-loop iterations |
| [54] | Secure calculation capacity | Base station jammer and fixed ground eavesdropper | Transmission power, time allocation, and CPU processing frequency | JDPB algorithm with SCA and BCD for secure task offloading
+✓ Reduce complexity via region division
+X Fixed UAV altitude limits 3D trajectory optimization |
| [55] | Average secrecy rate2 | Antenna jammer and fixed aerial eavesdropper | Transmit power and jamming power | BCD and SCA optimization with hybrid FSO/RF links
+✓ Enhance communication security via hybrid FSO/RF links and AN
+X Rely on simplified channel models (e.g., free-space path loss) |
| [56] | Worst-case secrecy rate | UAV jammer and fixed ground eavesdropper | UAV speed, collision avoidance, positioning error, and energy harvesting | Robust 3D trajectory and time switching optimization
+✓ Full mobility of UAVs in 3D for improving secrecy rate
+X The performance may degrade with flying eavesdroppers |
| [57] | Average secrecy rate | None and flying eavesdropper | Transmit power control and user scheduling | Joint trajectory and communication design against mobile eavesdroppers
+✓ Initial trajectory design for keeping away from eavesdroppers
+X Security performance relies on the initial trajectory design |
| [58] | Secure calculation capacity | Ground jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | Integrate a dual-UAV system with a ground jammer in MEC
+✓ Incorporate the UAV server and UAV eavesdropper with a ground jammer
+✓ Allow a UAV server to hover near ground users for secure offloading
+X Numerous flight constraints may require extensive tuning |
| [59] | Secrecy rate | Coastal jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | A secure communication for UAV-relay-assisted maritime MEC
+✓ Simultaneously optimize multiple parameters for improved secrecy rate
+X Iterative decomposition increases the computational burden
+X Assume prior knowledge of Channel State Information (CSI) of devices |
+
+| Techniques | Reference | Algorithm | Pros & Cons |
| Value-based RL | [60] | DQN | ○ DQN algorithm for UAV trajectory optimization to maximize the secrecy capacity
+✓ Low computational complexity, making it easy to train
+× Q-value overestimation, leading to suboptimal action selection |
| [61] | DDQN | ○ DDQN-based joint trajectory, time allocation, and offloading optimization
+✓ Accelerated convergence via action space pruning
+✓ Real-time optimization of trajectory and resources
+× DDQN is restricted to discrete action spaces
+× DDQN is not suitable for continuous action control |
| Policy Gradient-based RL | [62] | CAA-MADDPG | ○ Multi-Agent DRL with attention mechanisms (CAA-MADDPG) for secrecy rate maximization
+✓ Handle complex multi-agent with the attention mechanism
+× Assume prior knowledge of eavesdropper locations
+× Assume ground devices are static |
| [63] | DDPG | ○ DDPG-based RL for enhancing bi-directional UAV communication security
+✓ Support mobile devices and ensure bi-directional secureit
+× Computational overhead increases with device density
+× performance may be sensitive to hyperparameter selection |
| [64] | PPO+DCCN | ○ Hybrid DCCN and PPO for secrecy rate maximization
+✓ The PPO optimizes the UAV trajectory based on the results from DCCN
+× The performance is sensitive to the choice of clipping factor in PPO |
| [65] | MAPPO+LSTM | ○ MAPPO for multi-agent cooperative anti-eavesdropping and LSTM-enhanced sequential learning
+✓ The MAPPO+LSTM improves the learning capability of sequential sample data
+× Assume perfect knowledge of CSI may be challenging in real-world scenarios |
+
+value overestimation, leading to suboptimal action selection [146]. The authors in [61] propose a double-deep Q-learning (DDQN)-based scheme to jointly optimize the UAV trajectory, time allocation, and offloading decision strategy, aiming to maximize the average secure computing capacity for antieavesdropping in UAV-aided MEC. The system model involves one legitimate UAV server, one illegitimate UAV eavesdropper, one ground jammer, and ground users. The proposed DDQN-based scheme models the optimization problem as an MDP with states, actions, and rewards. The states include the coordinates of the UAVs, while the actions involve offloading decisions, time allocation, and trajectory adjustments. The reward function maximizes secure computing capacity. The DDQN model includes a deep Q-network (QN) and a deep target network (TN) to generate actions and evaluate their values. The parameters of the QN are updated by minimizing the loss function, and the parameters of the TN are periodically updated. The proposed scheme reduces the action space size by deleting illegal actions, such as those that violate time allocation constraints or result in resource waste. Unlike prior works [57], [60] that rely on conventional optimization or DQN with limited consideration of task queues, this approach integrates real-time resource allocation and trajectory optimization while ensuring dynamic constraints. The proposed DDQN scheme converges in 2000 episodes, half the episodes required by DQN (4000 episodes), and achieves a 0.02 Mbits higher average secure computing capacity.
+
+The value-based RL method (e.g., DQN) mainly focuses on dealing with discrete action spaces that may lead to the loss of optimal solutions [147]. The policy gradient-based RL method (e.g., Deep Deterministic Policy Gradient (DDPG)) can handle continuous action spaces [148], which are more suitable for UAV trajectory and transmit power optimization problems.
+
+The authors in [62] propose a multi-agent DRL framework to address the challenge of secure UAV communications in
+
+the presence of eavesdroppers. The system model is similar to Part A of Fig. 3, where the UAV server sends confidential information to ground users, and UAV jammers send AN signals to ground eavesdroppers using 3D beamforming. This study designs the Multi-Agent Deep Deterministic Policy Gradient with a continuous action attention mechanism (CAA-MADDPG) to maximize the system's secrecy rate. The attention mechanism dynamically prioritizes relevant agents' observations (e.g., jammers focusing on eavesdroppers) to reduce the exploration space and accelerate convergence, thereby enhancing the system's ability to counteract eavesdropping attempts. The simulation results show that CAA-MADDPG achieves a secure rate of $4.5\mathrm{bps / Hz}$ and converges in 1000 episodes with three UAV jammers, outperforming MADDPG (around $4\mathrm{bps / Hz}$ and 1400 episodes) and DDPG schemes.
+
+However, the study in [62] just considers UAV-to-ground communication (U2G) and assumed the ground devices are static. The work in [63] addresses the challenge of securing bi-directional ground-UAV communications in a dynamic environment with mobile ground devices and eavesdroppers. Different from prior works that assume static ground eavesdroppers [54], [56], this study considers mobile ground eavesdroppers for more practical real-world scenarios. The communication in U2G and ground-to-UAV (G2U) cases is modeled, considering factors such as channel gains and distances. The problem of maximizing the worst-case average secrecy rate is formulated as a constrained MDP (CMDP) under the constraints of UAV flight space, flight speed, energy capacity, anti-collision, and peak transmit power. To solve the CMDP, the authors design a DDPG-based RL algorithm. The algorithm includes three key components: the primary network (actor and critic networks), the target network, and the replay buffer. They also adopt state normalization and exploration noise to speed up the training convergence of the DDPG. The proposed joint optimization scheme achieves a secrecy rate
+
+over $40\%$ higher compared to baselines that optimize only trajectory or only power. In addition, DDPG outperforms DQN by approximately $15\%$ in secrecy rate due to its ability to handle continuous actions.
+
+The DDPGG methods form a fixed mapping from states to actions, which is not suitable for large state spaces that require more exploration and uncertainty [149]. The PPO alleviates this limitation by introducing proximal policy optimization, which allows for more exploration in the large action space.
+
+The study in [64] proposes a hybrid framework (Double Cascade Correlation Network (DCCN) + PPO) to maximize the secrecy capacity. DCCN bypasses the need for labeled training data by cascading two neural networks to maximize the secrecy channel rate. The PPO dynamically adjusts the UAV's position by using clipped surrogate objectives to stabilize policy updates and advantage estimation to prioritize high-reward actions. Simulation results show that the proposed scheme (DCCN + PPO) achieves an average secrecy rate of 0.73 bps/Hz, outperforming the benchmarks DCCN + DDPG (0.67 bps/Hz) and Random RIS + PPO (0.13 bps/Hz). However, the average secrecy continues to decline when the transmit power is higher than 2 W, since the jamming signals transmitted by the secondary source against the eavesdropper will also affect the primary users.
+
+The study in [64] considered only the use of one UAV to assist in secure communication. However, in low-altitude economic networks, it may be more important for multiple UAVs to collaborate to implement anti-eavesdropping strategies. The study in [65] considers a system model treats all secondary transmitters and multiple UAV jammers as multi-agents. A Multi-Agent PPO algorithm combined with Long Short-Term Memory (LSTM) networks, named MAPPO-LSTM, is proposed to maximize the secure communication rate by jointly optimizing the UAV trajectory, transmission power, and energy harvesting coefficients. The problem is formulated as a nonconvex MDP consisting of an action space, state space, observation, and reward (which consists of the sum of the secure communication rate, SINR information, and battery capacity). The MAPPO algorithm introduces counterfactual baselines to address the credit assignment problem in centralized learning and combines with the LSTM network to enhance the learning capability of sequential sample data. Compared to benchmark schemes MAPPO and MADDPG, the proposed MAPPO-LSTM method achieved around $17\% - 20\%$ higher average secrecy rate in large-scale scenarios, with convergence speeds 1.37 times and 1.93 times faster, respectively. In addition, the reward is sensitive to the discount factor, where setting factor to 0.99 enables faster and more stable convergence. Deviations from this value result in more pronounced fluctuations in the reward and secrecy rate.
+
+Lesson Learned. The RL has emerged as a powerful yet challenging tool for anti-eavesdropping in UAV-assisted secure communications. A key lesson is that multi-agent cooperation significantly enhances security compared to single-agent approaches, enabling adaptive trajectory control, power allocation, and jamming coordination in dynamic environments. However, scalability and convergence efficiency remain critical bottlenecks, especially in high-dimensional, time-
+
+varying settings, as many studies unrealistically assume perfect channel information, and deep RL's convergence time leaves the system vulnerable before optimization completes. Furthermore, key limitations demand further attention, such as RL's computational complexity, which restricts its use in resource-limited settings requiring real-time security, and its sensitivity to hyperparameter tuning that requires meticulous configuration to ensure optimal performance. Future advancements should focus on developing generalizable and robust learning architectures that can dynamically adapt to evolving threats while maintaining computational feasibility, addressing practical deployment challenges, exploring hybrid approaches, prioritizing security in system design, and balancing security performance with energy consumption.
+
+Deep learning, with its strong learning capabilities, parallel processing, and comprehensive reasoning [150]–[152], has huge potential to enhance anti-eavesdropping strategies in UAV communications, especially in environments with rapidly changing conditions and complex interactions [153]. Given the intricate problem of UAV trajectory variation and its nonlinear characteristics in time and space [154], [155], deep learning networks, such as neural networks and generative models, are emerging as potential solutions to improve the security and performance of UAV communication systems.
+
+The study in [66] explores the use of deep learning to optimize UAV deployment and jamming strategies against eavesdroppers to maximize the secrecy rate in the complete CSI scenario. The optimization problem is decomposed into two layers: the inner layer optimizes jamming power for a fixed UAV location, and the outer layer optimizes UAV deployment. The inner problem is solved using a bi-section search algorithm, while the outer problem is addressed using a deep neural network (DNN) to approximate the optimal UAV deployment. The DNN is designed as a fully connected structure, which includes an input layer, two hidden layers, and an output layer, as shown in part A of Fig. 5. The DNN is trained using a dataset generated by simulating different UAV deployments and corresponding secrecy rates. The final optimal deployment of the UAV can be approximated when the mean square error of weights between neurons is minimized. The DNN model achieves an average distance error of 2.2 meters compared to the optimal deployment found by the exhaustive search baseline.
+
+The fully connected neural network used in [66] is suited for problems where inputs and outputs are fixed-dimensional vectors without inherent spatial or sequential relationships [150]. Moreover, convolutional neural networks (CNNs) and recurrent neural networks (RNNs) can also contribute to antieavesdropping. In contrast to fully connected networks, CNNs are particularly effective for exploring spatial features from images or spatial maps [156]. RNNs, on the other hand, focus on handling sequential data by maintaining a memory of previous inputs through recurrent connections [150]. The authors in [67] propose a CNN-LSTM-based secure efficiency map (SEM) framework, which is constructed by calculating each subarea's security-efficiency index using a weighted exponential coefficient to combine normalized secure spectrum efficiency (secrecy rate per unit bandwidth) and secure energy
+
+TABLE VI SUMMARY OF DEEP LEARNING FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Techniques | Reference | Algorithm | Pros & Cons |
| Neural network model | [66] | DNN | ● Use DNN to optimize UAV deployment and jamming strategies for secure communication
+● The DNN model reduces the complexity of exhaustive searches
+● Rely on complete statistical channel knowledge
+● require intensive resources to generate a large amount of training data |
| [67] | CNN-LSTM | ● CNN-LSTM-based SEM prediction for dynamic secure UAV trajectory optimization
+● Efficient spatiotemporal feature extraction via CNN-LSTM
+● Assume fixed UAV height and passive eavesdropper
+● Training CNN-LSTM network requires a substantial amount of data |
| [68] | FL-DNN | ● FL-DNN-RL integration (FairLearn) for maximizing fairness in secrecy rates
+● Collaborative learning via FL improves generalization in anti-eavesdropping strategies
+● Involving multiple learning mechanisms requires significant computational resources
+● Assuming perfect CSI and eavesdropper localization may be impractical |
| Generative AI model | [69] | MD-GAN | ● MD-GAN with unknown CSI as model weights
+● Adapt to dynamic environments via gradient-based training
+● Do not require knowledge of the eavesdropper's detection threshold
+● Training a GAN can be computationally intensive |
| [70] | DD-GAN | ● DD-GAN uses genetic algorithm-generated datasets for GAN training
+● Achieve an effective trade-off between covert rate and detection probability
+● Training relies on the quality and quantity of the genetic algorithm-generated data |
| [71] | GDMTD3 | ● GDMTD3 integrates generative diffusion models into TD3
+● Handle high-dimensional action spaces to adapt mobile eavesdroppers
+● Computational complexity from diffusion denoising steps |
+
+efficiency (secrecy rate per unit power). Historical SEMs are fed into a CNN-LSTM network to predict future SEMs by leveraging spatial-temporal feature extraction and time-series correlation. Based on predicted SEMs, a trajectory planning algorithm dynamically guides the UAV to subareas with the highest security-efficiency indices. The proposed SEM-enabled trajectory planning achieves an average security-efficiency index of 0.81, outperforming baseline schemes (e.g., static trajectory [142] or non-predictive methods [62], [157]) by over $30\%$ .
+
+Previous deep learning-based architectures [66], [67] are centralized, lacking collaboration and knowledge sharing among UAVs, while also facing challenges in privacy preservation and scalability. To address these limitations and optimize secrecy rate maximization under constraints such as UAV mobility, power budgets, and scheduling fairness, the authors in [68] propose a federated learning (FL)-based framework (FairLearn). As shown in part B of Fig. 5, the FairLearn employs three learning modules: (1) Module-D uses RL to dynamically generate training datasets by exploring UAV trajectories, power allocation, and scheduling policies; (2) Module-P employs a DNN trained on these datasets to predict optimal 3D trajectory, transmit power, and user scheduling, maximizing proportional fairness in secrecy rates (defined as the difference between legitimate UAV-user rates and eavesdropper rates); (3) Module-C applies FL to aggregate DNN models across UAVs, enabling collaborative learning while preserving data privacy. Simulation results show that FairLearn's secrecy rate is $26.6\%$ higher than BCD at 1.4W transmit power. After 100s of execution, FairLearn achieves $14.34\%$ , $24.56\%$ , and $108\%$ higher secrecy rates than BCD, MAQ, and QCQP baselines, respectively.
+
+It is worth noting that UAVs can only obtain limited prior environmental information without knowing perfect channel information and the eavesdropper's detection threshold or ex
+
+act location. Some previous methods [59], [65], [68] may find it difficult to solve the optimization problem in such scenarios. In contrast, the generative adversarial network (GAN) has emerged as a new model for solving optimization problems with limited prior information [158], [159]. GAN can effectively model and approximate unknown distributions (such as channel coefficients, detection thresholds, and environmental parameters) through adversarial learning, where the generator continuously improves its strategy by learning from the feedback from the discriminator [158].
+
+The work in [69] addresses challenges related to partial channel distribution information and unknown eavesdropper detection thresholds by proposing a model-driven GAN (MDGAN) framework. The unknown channel coefficients and detection thresholds are treated as trainable weights in the MD-GAN. The MD-GAN transforms the joint trajectory and power optimization problem into a dynamic game between a generator (UAV) and a discriminator (eavesdropper), where the UAV acts as a jammer to protect secondary users from eavesdroppers. The generator optimizes the UAV's 3D trajectory and jamming power, while the discriminator evaluates detection errors. Then, a GAN-based joint trajectory and power optimization (GAN-JTP) algorithm is developed to achieve Nash equilibrium (i.e., maximizing the covert rate and the probability of detection errors). As shown in part C of Fig. 5, the GAN-JTP algorithm consists of two stages: network learning and network training. In the network learning stage, the generator optimizes the UAV's trajectory and transmit power based on the current state and environment. In the network training stage, the generator and discriminator are alternately trained using gradient backpropagation to update their weights. Simulation results show that increasing the training of the discriminator accelerates the convergence of the generator (e.g., when the training step is 10, convergence is achieved within 30 iterations, compared to 89 iterations when
+
+
+Part A. DNN-based Architecture
+
+
+Part B. FL-DNN-based Architecture
+
+
+Part C. MD-GAN-based Architecture
+
+
+Part D. DD-GAN-based Architecture
+
+
+Part E. GDMTD3-based Architecture
+Fig. 5. The overall architecture illustrates various deep learning-based architectures designed to enhance anti-eavesdropping capabilities in UAV deployment scenarios. Part A presents a DNN-based architecture that processes air-ground and ground-ground channel states to determine UAV deployment. Part B shows an FL-DNN-based architecture, incorporating modules for reinforcement learning, DNN-based feature mapping, and FL. Part C depicts an MD-GAN-based architecture, where a generator produces trajectories and power outputs based on location and environment status, while a discriminator evaluates the decisions. Part D introduces a DD-GAN-based architecture, focusing on generating jamming solutions to maximize covert rates, with a discriminator distinguishing between jamming and non-jamming solutions. Part E illustrates a GDMTD3-based architecture, utilizing an experience replay buffer and diffusion reverse process to optimize UAV deployment strategies.
+
+the training step is 1). For a flight period of 100 seconds, the GAN-JTP algorithm achieves a $0.47\%$ increase in covert rate with a $0.15\%$ reduction in detection error probability compared to the BCD-based scheme [160].
+
+The MD-GAN [69] relies on model-driven methods where the unknown channel information and detection threshold are treated as trained weights. Differently, the authors in [70] propose a data-driven GAN (DD-GAN) framework that focuses on generating data consisting of environmental parameters and optimal solutions to train the GAN. Specifically, the DD-GAN transforms the optimization process into an interactive game between the UAV and eavesdropper, where the UAV aims to maximize the covert rate, and the eavesdropper aims to detect the presence of covert communication. To address the non-convexity and lack of eavesdropper detection threshold information in the optimization process, the DD-GAN trains a generator (UAV) and discriminator (eavesdropper) adversarially, using genetic algorithm-generated samples as prior data, as shown in part D of Fig. 5. The generator produces power and trajectory solutions, while the discriminator evaluates the detectability. The loss function of the discriminator is designed to maximize the probability of correctly identifying real data and minimize the probability of being fooled by generated data. The generator's loss function aims to maximize the probability that the generated data is mistaken for real data by the discriminator.
+
+Besides GANs [69], [70], another generative model, the diffusion model, has advanced the effective representation
+
+of multi-dimensional data distributions [161]. The diffusion model can better capture the complex dynamics and the tradeoff in the multi-objective optimization problem concerning secure communication [112]. For example, The diffusion model captures complex state-action distributions, enabling adaptive beamforming and UAV repositioning under eavesdropper mobility. To tackle dynamic environments and high-dimensional action spaces in secure communication and energy efficiency multi-objective optimization problem, the authors in [71] propose GDMTD3, a Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm enhanced with generative diffusion models. Key innovations include integrating diffusion-based reverse processes into the actor network for robust policy generation and addressing continuous action spaces, as shown in part E in Fig. 5. The training process of GDMTD3 involves initializing the online critic and actor networks, interacting with the environment, and updating the network parameters based on the collected experiences. The actor network uses a generative diffusion model to sample actions, while the critic networks evaluate the actions using twin critic networks to reduce overestimation bias. Simulation results show that GDMTD3 outperforms DRL-based benchmarks (including PPO, TD3, and DDPG), achieving about $50\%$ higher cumulative rewards and around $21\%$ higher average secrecy rate than TD3. In addition, when the number of UAVs increases from 4 to 8, the average secrecy rate increases accordingly. However, increasing the number of UAVs from 8 to 16 raises
+
+TABLE VII SUMMARY OF AUTHENTICATION FOR COMMUNICATION CONFIDENTIALITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Techniques | Reference | Algorithm | Pros & Cons |
| PUFs-based authentication | [72] | PUF\(s^1\) | PUF-based dynamic session key generation and mutual authentication protocol
+✓ Lightweight design with no stored secrets
+✗ Potential overhead during temporary identity updates |
| [73] | PUF-fuzzy extractor | PUF-fuzzy extractor mutual authentication with TS-based dynamic session adaptation
+✓ Dynamic session time adaptation minimizes idle periods and enhancing security
+✗ Higher computational cost due to fuzzy extractors |
| [74] | PUFs-fuzzy extractor-AEGIS | Integration of PUFs, fuzzy extractors, and AEGIS for mutual authentication
+✓ The proposed password/biometric update mechanism reduces server dependency
+✗ Multiple cryptographic operations and protocols may be cause delay in the implementation |
| Channel based authentication | [75] | Rician channel | Physical-layer fingerprinting authentication based on Rician channel characteristics
+✓ Optimal power allocation balances data, AN, and authentication tag transmission
+✗ Reliance on encrypted tags requires high demand on UAV processing capabilities |
| [76] | Rayleigh channel | SNR difference-based PLA scheme
+✓ The SNR-based design can be implemented without additional hardware infrastructure
+✗ The simplified Rayleigh channel model may limit to real-world propagation environments |
| [77] | Rayleigh/Rician channels | AD metric2for authentication under Rayleigh/Rician channels
+✓ AD metric-based method improves the detection accuracy of authentication
+✓ Detailed analysis of authentication performance under different propagation conditions
+✗ Computational complexity in Rician channels due to hypergeometric functions |
+
+Physical Unclonable Functions (PUFs) are hardware-based security primitives that exploit inherent and unique physical variations in devices to generate unclonable and unpredictable responses for communication authentication.
+2Authentication Distance (AD) is a metric proposed in [77] to distinguish legitimate and illegitimate signals for communication authentication.
+
+energy consumption but only marginally improves secrecy rates, highlighting a performance-energy trade-off.
+
+Lesson Learned A key lesson learned is that deep learning, particularly through advanced architectures such as GANs [69], [70] and diffusion models [71], can address complex, dynamic environments with partial channel state information and unknown eavesdropper locations, while demonstrating superior performance over traditional methods [59], [65], [66]. These approaches demonstrate that deep learning not only strengthens the resilience of secure communications but also enables autonomous, real-time decision-making to counteract evolving eavesdropping threats in UAV networks.
+
+# B. Communication Authentication
+
+In the LAENet, as UAVs operate in open environments and rely on wireless communication, they are highly vulnerable to security threats such as node capture and man-in-the-middle attacks [46]. Ensuring secure and reliable authentication between UAVs and ground stations/users or among UAVs is critical to preventing unauthorized access [52], [162]. Traditional cryptographic authentication schemes often impose significant computational and memory overheads and incur considerable lantency, making them unsuitable for resource-constrained UAVs [163]. Recently, advancements such as PUFs and Physical-layer Authentication (PLA) mechanisms have opened new possibilities for lightweight and effective authentication in the LAENet.
+
+PUFs are a class of hardware security primitives that leverage the inherent manufacturing variations (such as variations in circuit delay or RF properties) in semiconductor devices to generate unique and unpredictable responses [164]. When a specific input is applied to a PUF, the device generates a corresponding response, forming a challenge-response pair that is unique to this device [164]. Such uniqueness and unpredictability make PUFs highly resistant to cloning and
+
+tampering, making them as a secure means for device authentication and key generation [165]. In addition, employing a PUF in a UAV allows for secure authentication without the need for complex cryptographic operations, making it an efficient solution for resource-constrained scenarios [166].
+
+The work in [72] proposes a lightweight mutual authentication protocol, named SecAuthUAV, for securing UAV-ground station and UAV-UAV communications. SecAuthUAV employs PUFs in each UAV to generate a unique, unclonable session key that functions as a non-reproducible fingerprint. The protocol consists of three phases, as shown in Fig. 6. During UAV registration, a challenge-response pair from the UAV's PUF is stored, and a temporary identity is generated. In the UAV-ground station authentication phase, the UAV and ground station authenticate each other using challenge-response pairs and nonces, establish a session key, and update their identities. Lastly, in the UAV-UAV authentication phase, the GS facilitates secure communication by authenticating a second UAV and generates a session key for both UAVs.
+
+However, the work in [72] ignores the fact that the noise in PUFs can result in significant deviation in the output for the same input at different time points. In addition, [72] does not adjust the session time after establishing an authenticated session between two parties, which may lead to the active session remaining idle for a long time and thus give an opportunity for an adversary to interfere with the communication link. In light of this, the authors in [73] propose an UAV Authentication with Adaptive Session (UAAS) framework to address these challenges. Firstly, they combine PUFs and fuzzy extractors to address PUF noise. The fuzzy extractors consist of two phases: the $Gen(.)$ phase creates a key and non-sensitive helper data, and the $Rep(.)$ phase reconstructs the key from a noisy PUF response using the helper data while tolerating minor deviations. Then, the Thompson Sampling (TS)-based scheme is proposed to dynamically adapt the session time.
+
+
+Fig. 6. The overall architecture of the PUF-based authentication schemes for UAV-GS and UAV-UAV communication in [72]. Part A illustrates the PUF-based authentication process between a UAV and a ground station (GS). The UAV sends its ID and a nonce to the GS, which responds with a hash value based on the PUF, UAV ID, and nonce. The UAV then sends a value derived from the PUF and another nonce, and the GS verifies the authentication by comparing hash values. Part B shows the PUF-based authentication between two UAVs (U1 and U2) through the GS. After establishing a session key with the GS, U1 requests a connection to U2. The GS facilitates the authentication by generating a new session key, which is securely shared between U1 and U2.
+
+TS is a probabilistic approach that balances exploration and exploitation, determining the session time based on the fraction of busy time to minimize idle periods and reduce the risk of adversarial interference. Although the security analysis demonstrates that UAAS improves the security level in the mutual authentication mechanism, its throughput is $20.38\%$ lower and computational cost is 126 ms higher than the baseline [72] due to security overhead.
+
+In the LAENet, while establishing mutual authentication between UAVs and ground stations is critical, it is also important to incorporate role-specific access controls for users to ensure communication confidentiality and preventing unauthorized access [167]. The work in [74] proposes an authentication framework PUF-enabled authentication framework for Internet of Drones (PAF-IoD) to establish mutual authentication among users, UAVs, and ground stations. Users need to authenticate with stations to access the stored data or communicate directly with UAVs, where the users' authentication mechanism includes three factors (identity, password, and biometric data). Similar to [73], PAF-IoD uses PUFs and a fuzzy extractor in the authentication process to generate a unique and tamper-proof session key while tolerating the noise in PUFs. Furthermore, the designed authenticated encryption with associative data (AEAD)-based encryption algorithm is utilized for encrypting and decrypting messages exchanged between the user, ground station server, and UAVs.
+
+In addition to leveraging intrinsic physical properties of hardware for authentication design through PUFs [72]–[74], the characteristics of communication channels can be used for authentication. The PLA mechanism authenticates devices by exploiting the unique physical characteristics of wireless communication channels, such as CSI, received signal strength (RSS), and signal-to-noise ratio (SNR) [168]. The main reason is that the wireless channel between two communicating entities exhibits location-specific and time-varying properties
+
+due to multipath propagation, fading, and environmental factors [169]. These diverse physical channel conditions, which provide a robust set of features for authentication, have been investigated in terrestrial communication networks [168]–[170]. Furthermore, the source of received signals can be accurately and promptly detected [170], making PLA particularly advantageous in the dynamic and complex communication environments of the LAENet.
+
+The authors in [75] leverage the unique properties of the physical layer channel, Rician channel, to develop a PLA for UAV-ground station communication. Given that UAVs receive signals subject to the Rician fading model, the ground station integrates authentication directly into the transmission process. It employs a one-way collision-resistant function (e.g. cryptographic hash function) that combines data symbols with a shared secret key to generate a low-power authentication tag for UAV and seamlessly embeds it into the transmitted signal. The authentication tag is validated by the correlation shaped by the Rician statistical characteristics of the fading channel, i.e., the correlation between the estimated tag (derived from the received signal) and the expected tag (generated using the secret key and decoded data symbols).
+
+However, the work in [75] still partially relies on cryptographic tag generation for authentication, which may not be suitable for UAVs with limited processing capabilities. The study in [76] leverages channel characteristics and geographical locations for PLA design, where the SNR differences between consecutive transmissions are utilized as the authentication metric. Specifically, a legitimate transmitter and a jammer have distinct channel variations due to differences in their geographical locations. The UAV authenticates the legitimate transmitter or jammer by formulating a binary hypothesis test based on the SNR difference between two successive transmissions. If the difference falls within a predefined threshold, the transmission is authenticated as from the legitimate
+
+
+Part A. Channel-based authentication in urban
+
+
+Part B. Channel-based authentication in suburban
+Fig. 7. The overall architecture of the channel-based authentication in urban and suburban environments in [77]. Part A depicts the authentication process in an urban environment under Rayleigh channel conditions. The UAV receiver calculates the SNR, computes the AD, and compares it with a detection threshold to distinguish between legitimate and malicious sensors. Part B illustrates the authentication process in a suburban environment, where the UAV receiver performs similar steps to authenticate legitimate sensors and detect malicious ones under Rayleigh channel conditions.
+
+transmitter; otherwise, it is classified as a jammer. The closed-form expressions for the probability density function of SNR differences, false alarm rate (FAR), and miss detection rate (MDR) are derived under Rayleigh fading channels in single-UAV and dual-UAV scenarios. The non-convex optimization problem of minimizing MDR under FAR constraints is solved using an SCA algorithm, which outperforms the RSS-based baseline [90] by about $40\%$ .
+
+It is worth noting that study [75] may lack a comprehensive analysis of the UAV-PLA performance under different propagation conditions. Additionally, the detection performance may be further improved with other indicators. As shown in Fig. 7, the work in [77] proposes a novel PLA framework under different propagation conditions, including dense urban and suburban environments modeled by Rayleigh and Rician channels, respectively. A new metric, Authentication Distance
+
+(AD), is proposed as the normalized difference in received SNR between adjacent transmissions. For Rayleigh channels, closed-form expressions for FAR and MDR are derived using convolution and integration-by-parts, while Rician channels employ doubly non-central $F$ distributions to model AD statistics. Similar to study [76], this authentication framework minimizes MDR under FAR constraints. In dense urban settings, MDR depends on path loss and transmitter-UAV geometry. For suburban environments, it incorporates elevation angle-dependent Rician factors and path loss exponents to improve discriminability between legitimate and illegitimate signals. The proposed AD-based method outperforms the SNR-difference baseline [171], achieving 40–60% lower MDR.
+
+Lesson Learned. Leveraging physical-layer characteristics, such as PUFs and channel properties, in conjunction with communication models and optimization algorithms, has proven effective in enhancing authentication accuracy and reducing detection errors. However, some methods also reveal limitations. For instance, the assumptions of ideal channel conditions and the neglect of practical implementation constraints may limit the applicability of the proposed solutions [76], [77]. Future research should focus on addressing these limitations by exploring more practical channel models and considering the trade-offs between security and system complexity.
+
+# IV. COMMUNICATION AVAILABILITY FOR LAENET
+
+# A. Anti-Jamming Strategy
+
+Jamming attacks pose significant challenges to communication availability in the LAENet by disrupting legitimate communication links and degrading the performance of aircraft communication networks [79], [172]. As shown in Fig. 10, these attacks can exploit the openness and broadcasting nature of UAV networks, making them particularly vulnerable to interference [79]. Malicious jammers can transmit strong signals that weaken signal strength, degrade signal quality, and increase communication delays, leading to unreliable coverage and potential paralysis of the entire network [172], [173]. This vulnerability underscores the urgent need for effective anti-jamming technologies to ensure reliable communication in the LAENet.
+
+Various anti-jamming strategies have been explored to safeguard the LAENet against malicious jamming, mainly focusing on trajectory adjustment, as well as channel and power control. Overall, by adjusting the trajectory in the spatial domain, an UAV can evade jamming signals while maintaining reliable communication with legitimate devices [80], [173]. Besides the spatial-domain anti-jamming strategy, the UAV can implement a frequency-domain-based anti-jamming scheme. The UAV can select legitimate channels while avoiding jamming signals and control transmit power to minimize energy consumption and latency under jamming attacks [83], [84].
+
+Convex optimization methods can be used to adjust the UAV's trajectory to achieve anti-jamming by strategically guiding its movement to reduce interference and enhance communication reliability [80], [173]. It provides a systematic and efficient approach to handle the complex, non-convex
+
+TABLE VIII SUMMARY OF ANTI-JAMMING STRATEGY FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Techniques | Reference | Algorithm | Pros & Cons |
| Convex optimization | [80] | BCD, SCA | BCD and SCA for UAV 3D trajectory optimization for anti-jamming
+✓ Probabilistic LoS performs well in real-world scenarios such as urban environments
+X High computational complexity may be challenging in resource-constrained environments |
| [81] | SCA, Dinkelbach | SCA and Dinkelbach algorithm for energy-efficient trajectory optimization under malicious jammers
+✓ Balance between throughput and energy consumption in anti-jamming
+X Assume static and LoS-dominated channels |
| [82] | BCD, SCA | BCD and SCA for joint UAV trajectory and transmit power optimization under jamming
+✓ Improve throughput by considering transmit power optimization against jammers
+X Assume a fixed UAV altitude and a static channel environment |
| Multi-agent RL | [87] | MALQL | Collaborative MALQL algorithm for anti-jamming with channel and power allocation
+✓ Accelerate convergence compared to single-agent Q-learning
+X Assume predefined UAV trajectories limits to adaptability |
| [88] | MARL | MARL with adversarial pre-training for dynamic and generalized jamming
+✓ Generalize to various jamming patterns via adversarial populations for pre-training
+X Pre-training for generalized jamming may require significant offline resources |
| [89] | MATD3 | MATD3 algorithm with PER for dynamic resource management under jamming attacks
+✓ Handle high-dimensional continuous action spaces
+X The integration of PER and spectrum sensing may increase the computational complexity |
+
+problems that arise when optimizing UAV trajectories and various constraints under malicious jamming conditions [131]. The work in [80] investigates anti-jamming 3D trajectory design for UAV-enabled wireless sensor networks under a probabilistic LoS channel model. The probabilistic LoS model accounts for elevation angle-dependent shadowing effects in urban environments compared with simplified LoS models. The BCD and SCA algorithms are employed to optimize the UAV's horizontal and vertical trajectory, allowing the UAV to move closer to the ground station for improved transmission rates while dynamically adjusting its elevation angle relative to the jammer to mitigate interference.
+
+However, the anti-jamming trajectory optimization in [80] under the probabilistic LoS model does not consider the energy consumption issue. The study in [81] utilizes SCA and Dinkelbach's algorithm to adjust the UAV's trajectory to avoid areas with jammers while maximizing energy efficiency, which is defined as the ratio of total throughput to propulsion energy consumption during flight. Compared to hovering-centric benchmarks, the optimized trajectory reduced energy consumption by $82\%$ while maintaining $73.16\%$ of the sum throughput. It is worth noting that the transmit power of the UAV and station is fixed in [81], whereas power optimization is also an important factor for energy efficiency. The authors in [82] use the SCA and BCD algorithms to maximize throughput by iteratively optimizing power allocation (via convex reformulation of throughput bounds) and UAV trajectory (via slack variables for distance constraints and jamming mitigation) to avoid jamming signals. The proposed scheme achieves $40\%$ higher throughput compared to the "Line trajectory with fixed power" baseline.
+
+While convex optimization methods [80]–[82] work well for fixed jamming patterns, they may struggle to handle dynamic, intelligent jamming [174] in real-time due to their reliance on global information and the challenges inherent in solving nonconvex problems with increased optimized variables [142]. In contrast, RL and DRL offer significant advantages by enabling autonomous, adaptive decision-making [143], [147]. These
+
+approaches can continuously adjust to environmental changes, learn from past interactions, and optimize performance in real-time [144], [175]. The RL-based anti-jamming methods have emerged as a promising solution due to their ability to operate without excessive prior information (such as unknown environment, CSI, and jamming mode) [147]. Single-agent RL algorithms have been used in previous works to develop anti-jamming strategies in communication networks by regarding jammers and other legitimate users as part of the environment, including independent anti-jamming channel selection methods [83]–[86]. However, these single-agent approaches may fail to converge when dealing with a large number of agents or a high-dimensional action-state space [87], making them impractical for complex, multi-agent scenarios in the LAENet. To address these limitations, multi-agent RL (MARL) methods have been proposed to allow each agent to make decisions based on local information and exchange data with others (such as observations or model parameters).
+
+The study in [87] proposes a collaborative multiagent layered Q-learning (MALQL) algorithm for anti-jamming communication in UAV networks by jointly optimizing channel and power allocation to maximize system Quality of Experience (QoE). The problem is modeled as a local interaction Markov game based on the constructed interference graph. The MALQL divides the problem into two subgames of channel selection (Layer 1) and power allocation (Layer 2), as shown in part B of Fig. 10. The channel layer uses a graph-based interference model to capture mutual interference among UAVs. Each UAV is represented as a node, and edges are formed between UAVs that are within a predefined interference distance. This model allows UAVs to identify and avoid channels that are being used by neighboring UAVs or jammed by external attackers, thereby reducing the jamming likelihood. The power layer optimizes transmit power to meet rate thresholds. Theoretical analysis confirms that MALQL can converge to a pure strategy Nash equilibrium.
+
+Nevertheless, there are still some issues with the anti-jamming mechanism in [87]. Considering that the rapid mo
+
+
+Part A. Overall system model under jamming
+
+
+Part B. MALQL-based anti-jamming scheme
+
+
+Part C. Population update of pre-training for generalized anti-jamming scheme
+
+
+Part D. PER-MATD3-based anti-jamming scheme
+
+
+Actor-Critic network for agent k
+Fig. 8. The overall architecture illustrates various reinforcement learning-based anti-jamming schemes designed to enhance communication reliability in UAV-assisted MEC systems under jamming attacks. Part A presents the overall system model, depicting UAVs and jammers interacting within a dynamic environment. Part B shows the MALQL-based anti-jamming scheme, where agents use layered Q-learning to determine actions based on local observations and rewards. Part C depicts the population update mechanism for pre-training a generalized anti-jamming scheme, involving a jammer population, trajectory encoder, and decoder network to optimize jamming policies. Part D introduces the PER-MATD3-based anti-jamming scheme, incorporating a priority experience replay buffer and actor-critic networks to dynamically allocate resources and optimize UAV deployment strategies.
+
+bility of UAVs may expose them to various and unknown jamming patterns due to frequent transitions to new scenarios, the anti-jamming methods need to be generalized [176], especially in the LAENet. The work [87] randomly initializes strategies and learns from scratch for a particular deployment environment with no pretraining, which may lead to a reduction in the generalization ability of the anti-jamming strategy. In light of this, the authors in [88] introduce an adversarial pre-training stage in the proposed two-stage MARL with a decentralized partially observable Markov decision process. Specifically, the adversarial pre-training stage uses a quality-diverse jammer population (e.g., fixed, random, sweeping, statistic, and RL-based jamming) to bootstrap generalized anti-jamming strategies instead of directly initializing the agents with random anti-jamming policies, as shwon in part C of Fig. 10. This pre-training ensures that UAVs are not overfitted to specific jamming patterns and can generalize to new jamming attacks in real-world deployments. The pre-trained policies are deployed in the fine-tuning stage, where a graph convolutional-based MARL algorithm is proposed to jointly optimize channel selection and power allocation for anti-jamming similar to [87]. Simulation results show that the proposed solution achieves $20 - 30\%$ higher cumulative rewards than collaborative multi-agent Q-learning [177] and independent Q-learning [83] under fixed and sweeping jamming.
+
+Note that previous RL-based anti-jamming strategies [87], [88] mainly rely on the Q-learning method, which is suitable for discrete action spaces but may be limited in dealing with high-dimensional continuous spaces [147], [148]. The authors in [89] propose a PER-MATD3 algorithm against jamming
+
+by integrating spectrum-aware channel selection and prioritized experience replay (PER) into an MADRL framework, as shown in part D of Fig. 10. The proposed spectrum-aware intelligent channel selection uses energy detection-based spectrum sensing, enabling UAVs to identify and avoid jammed channels. The TD3 is specifically designed to handle continuous-valued states and actions, where two critic networks, target policy smoothing, and delayed policy updates are used to further stabilize DRL training. By leveraging PER, the agents can learn from high-error experiences, thereby accelerating adaptation to time-varying CSI, imperfect jamming detection, and co-channel interference. By jointly optimizing CPU frequency, bandwidth allocation, and channel selection to minimize the impact of jamming, PER-MATD3 reduces system cost (a linear combination of latency and energy consumption) by approximately $16.7\%$ , $9.1\%$ , and $1.2\%$ compared to the baselines of Q-learning, MATD3-JSC (without PER), and PER-MATD3 (without channel selection), respectively.
+
+Lesson Learned. Recent advancements in anti-jamming strategies show that intelligent decision-making for trajectory control, channel selection, and power control is essential for effective jamming mitigation. A key takeaway is the successful integration of MARL to develop dynamic and adaptive anti-jamming solutions [75]. By employing intelligent algorithms such as adversarial pre-training and decentralized decision-making, UAV networks can generalize anti-jamming strategies across diverse environments [76], [77]. However, challenges persist in the generalization of these strategies across various jamming types and environmental conditions, as well as balancing the trade-offs between energy consumption,
+
+
+Part A. ML-based spoofing detection
+
+
+Part B. Rule and ML-based spoofing detection
+Fig. 9. The overall framework of ML and rule-based spoofing detection for GPS spoofing detection in the LAENet. Part A depicts an ML-based spoofing detection mechanism in [93], where multiple CNN classifiers are trained with updated sample weights to form an integrated classification model. Each CNN transfers its optimized parameters to subsequent classifiers, enhancing the model's robustness. Part B presents a hybrid rule and ML-based approach in [94], where statistical analysis of path losses between UAVs and multiple base stations (BSs) is performed by edge servers. The analyzed data is processed through MLPs to generate individual predictions, which are aggregated to produce a final spoofing detection decision.
+
+latency, and throughput. Future research could delve into the integration of more adaptive learning frameworks (such as deep learning) into the LAENet for anti-jamming, enabling it to better manage partial or imperfect environmental observations for low-latency, real-time decision-making in multi-UAV systems.
+
+# B. Spoofing Defense
+
+In the LAENet, the openness of A2G transmission channels and the dynamic nature of low-altitude aircraft networks make them particularly susceptible to identity-based spoofing attacks [50]. In such attacks, a malicious entity impersonates a legitimate transmitter using falsified identity information, such as a spoofed media access control address, to gain unauthorized access to the network [52]. Once authenticated, the spoofer can disrupt communications among aircraft by launching more severe attacks, such as rogue access point infiltration and denial-of-service attacks, ultimately leading to network congestion and service outages [75]. Given the limitations of conventional authentication methods that rely on complex cryptographic protocols [52], PLA offers a promising alternative by leveraging the inherent and unique physical characteristics of wireless transmissions for the LAENet, which is introduced in Section III-B. Overall, this type of PLA can defend against spoofing
+
+attacks in the LAENet by exploiting the unique characteristics of the wireless channel (such as RSS, Rayleigh channel, and Rician channel) to identify and separate between legitimate devices and spoofers.
+
+The work in [90] proposes a PLA framework to detect spoofing attacks by exploiting spatial correlations of RSS in A2G channels. The key idea is that the RSS from a legitimate transmitter will remain relatively consistent due to its fixed location, while the RSS from a spoofer will vary significantly because of its different position and channel conditions. Thus, the UAV receiver can perform a hypothesis test to authenticate incoming signals. if the RSS distance between the current signal and a previously authenticated signal is below a predefined threshold, the signal is accepted as legitimate. Otherwise, it is flagged as a spoofing attempt. However, the work [90] is considered under an ideal transmission scenario, where the propagation environment is perfectly exempted from external interference. To address this limitation, the authors in [91] develop a PLA framework that accounts for channel randomness and interference uncertainty. First, they model the G2A link as a Rayleigh fading channel. Then, they introduce jamming signals as external interference. By modeling the jamming power statistically and incorporating it into the analysis of detected power differences, if the difference in power exceeds a predefined threshold, it is identified as a spoofing attempt. Thus, even in real-world scenarios with interference, the proposed framework can better differentiate between natural channel fading and anomalies caused by spoofing attacks.
+
+In addition to using the statistical properties of the Rayleigh channel to design PLA against spoofing in environments with multipath fading (such as urban areas), the channel characteristics in suburban environments should also be considered. To address this, the work [77] proposes a PLA framework to counter spoofing attacks in both urban (Rayleigh channel) and suburban (Rician channel) environments. As mentioned earlier (in Section III-B), a new metric AD is devised to distinguish between legitimate signals and spoofing signals based on differences in channel randomness and geographical factors, such as elevation angles and distances. Adopting the unique fading characteristics of Rayleigh and Rician channels makes it statistically difficult for a spoofer to accurately mimic a legitimate signal. By considering elevation angles and distances in channel modeling, it ensures that a spoofer cannot easily replicate a legitimate signal even if the spoofer knows the legitimate transmitter's location. Simulation results show that the probability of a successful spoofing attack is significantly reduced compared to the baseline [171], where the spoofing miss detection probability drops to 0.014 in suburban environments and 0.371 in dense urban areas.
+
+In the LAENet, in addition to being vulnerable to identity-based spoofing attacks, aircrafts are also susceptible to signal spoofing attacks from the Global Navigation Satellite System (GNSS), particularly GPS spoofing, which poses a significant security threat by generating and transmitting counterfeit satellite signals resulting in severe positioning deviations [25]. By interfering with or suppressing legitimate GNSS signals, attackers can manipulate UAV locations in an imperceptible manner to mislead UAVs, causing deviations from intended
+
+TABLE IX SUMMARY OF SPOOFING DEFENSE FOR COMMUNICATION AVAILABILITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Techniques | Reference | Algorithm | Pros & Cons |
| PLA | [90] | RSS | Spatial correlations of RSS distances in PLA against spoofing attacksUse RSS-based channel characteristics to reduce PLA computational complexityAssume an ideal transmission scenario without external interference |
| [91] | Rayleigh channel | Defend against spoofing attacks by considering channel randomness and jammingSimultaneously address spoofing and jamming attacks via PLAAssume static UAVs and a known jamming distribution |
| [77] | Rayleigh and Rician channels | AD-based PLA for spoofing defense under Rayleigh and Rician channelsProvide a thorough analysis of spoofer identification in urban and suburban environmentsAssume perfect CSI in channel modeling |
| GNSS spoofing detection | [92] | Rule-based detection | Combine cooperative localization mechanism with Stackelberg game against spoofing attacksSpoofing detection is based on neighboring UAV signal sources without predefined thresholdsExtending to larger UAV groups may require complex adjustments |
| [93] | ML-based detection | Improved AdaBoost-CNN for multi-modal spoofing attack identificationHigh accuracy in identifying spoofing attacks with limited data samplesDependence on predefined signal features may lead to model overfitting |
| [94] | Rule & ML-based detection | MLP and statistical feature extraction on path-loss data for detecting GPS spoofingNo additional hardware/energy burden on UAVsRobust performance under sparse base station coverageSpoofing detection performance degrades in areas with unstable cellular signals |
+
+flight paths, violations of no-fly zone regulations, or increased collision risks [46]. Given a critical role of GNSS in UAV operations, effective detection and mitigation strategies for spoofing attacks are essential to ensure flight safety and prevent security breaches in the LAENet. Currently, studies on signal spoofing attack recognition in the LAENet mostly focuses on recognizing GNSS spoofing attack detection, which primarily falls into two categories with respect on rule-based and ML-based methods [19], [25]. Rule-based detection methods typically assess the relative distance and positional deviations of UAVs to determine if they are under GNSS spoofing attack. On the other hand, the ML-based methods pay attention to recognize different spoofing types by learning the characteristics of received signals.
+
+Generally, the simplified rule-based methods determine whether a UAV has encountered spoofing attacks based on whether its trajectory follows a predictable path [178], [179], since a UAV may exhibit deviations from this path due to the false signals imposed by the spoofer. If the measured deviations exceed predefined thresholds, it indicates a potential spoofing attack. However, relying on predefined thresholds for detecting deviations may not dynamically adapt to the spoofing attacks. The study in [92] proposes a defense mechanism based on cooperative localization, where each UAV uses the relative distances and real locations of neighboring UAVs to detect spoofing attacks. Specifically, each UAV measures its relative distances based on alternative signal sources of neighboring UAVs and compares these results with its own GPS-derived location. If inconsistencies are detected (e.g., the GPS-derived location does not match the majority of the calculated locations), the UAV identifies itself or a neighboring UAV as being under attack. To optimize defense deployment, an equilibrium of a dynamic Stackelberg game is derived between the drone operator (leader) and the spoofer (follower). Simulation results show that the proposed scheme can effectively prevent spoofer's capture, while random/deterministic baselines suffer from attackers capturing one to two UAVs.
+
+Recent ML-based methods for spoofing defense primarily focus on binary classification concerning normal GPS signals and spoofing signals [180], [181]. However, they fail to recognize specific types of spoofing attack necessary for countermeasures in complex environments. Hence, there is an urgent need to recognize diverse GPS spoofing attack patterns for effective countermeasures for the LAENet. The authors in [93] propose an improved AdaBoost-CNN algorithm to address the challenge of recognizing diverse GPS spoofing attack patterns for UAVs, as shown in part A of Fig. 9. Three categorized spoofing attack patterns are considered including static and dynamic spoofing based on the UAV's motion state, power-matched and overpowered spoofing based on signal power, and position and time spoofing based on the spoofing targets. The authors select key GPS spoofing signal features such as signal quality monitoring, carrier-to-noise ratio, Doppler shift, and clock error to train the classification model. The improved AdaBoost-CNN algorithm integrates multiple weak CNN classifiers into a strong classification model. Each CNN base classifier uses the updated network parameters from the previous CNN as initial values, enabling iterative refinement of network weights to enhance feature extraction and generalization. With 800 simulated samples, the improved AdaBoost-CNN achieves $100\%$ accuracy, outperforming original AdaBoost-CNN $(94.38\%)$ , CNN $(74.38\%)$ , DNN $(60.94\%)$ , SVM $(40.63\%)$ , and KNN $(53.13\%)$ .
+
+Furthermore, integrating rule-based approaches with machine learning-based methods provides an effective and robust defense against spoofing attacks. The work in [94] leverages statistical features of path losses between UAVs and terrestrial base stations to detect a UAV's trajectory deviation due to GPS spoofing, as shown in part B of Fig. 9. The spoofing detection is formulated as a nonlinear optimization problem that aims to minimize hypothesis test errors by adjusting thresholds, statistical feature weights, and the number of base stations. To further accurately analyze path loss's statistical features for final decisions on predicting GPS spoofing probabilities,
+
+TABLE X SUMMARY OF ANOMALY DETECTION FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Anomaly type | Reference | Algorithm | Pros & Cons |
| Jamming | [98] | HDBN | SA module based on HDBN for detecting jamming anomalies
+✓ UAccurately characterize and detect jamming anomalies via KLD/DB metrics
+✗ Unstable initialization in unsupervised learning affects the performance of the HDBN |
| [99] | GDBN | GDBN to model the radio environment and detect and classify jamming anomalies
+✓ Unsupervised learning eliminates dependency on labeled data in classification of anomalies
+✗ Computational complexity increases with the number of jamming categories |
| [100] | Active-GDBN | Active-GDBN used to model UAV-jammer interactions for anomaly detection
+✓ Actively incorporate UAV's actions for faster adaptation and jamming detection
+✗ M-MJPF requires significant computational resources |
| [101] | Blind channel estimation & ACS | Blind channel estimation based on ACS properties to detect jammer signals
+✓ Does not rely on prior knowledge of the jammer's behavior
+✗ Assumes a specific structure of the multicarrier modulation format |
| Abnormal Power | [102] | Spectrum surveillance | Local and cooperative detection of abnormal power emission
+✓ Handle both aggressive and passive power misuse
+✓ Cloud-based framework enables real-time closed-loop surveillance
+✗ Computational complexity increases with the number of SN |
| Eavesdropping | [103] | SVM & K-means | One-class SVM and K-means clustering for detecting eavesdropping anomalies
+✓ One-class SVM and K-means are stable under varying eavesdropper power
+✗ Detection performance mainly depends on the quality and quantity of the ATD |
+
+multilayer perceptron (MLP) neural networks are deployed on edge cloud servers, where individual MLP models at each BS are used to analyze statistical features of path losses. Simulation results show that the proposed method achieves $97\%$ accuracy with two base stations and $83\%$ accuracy with a single base station, outperforming baseline approaches such as adaptive trustable residence area (ATRA), which necessitates three base stations for triangulation [182].
+
+Lesson Learned. For identity spoofing in the LAENet, leveraging signal features such as received signal strength and channel randomness in PLA design is an effective approach [77], [90], [91]. On the other hand, employing rule-based or ML-based techniques can detect and mitigate GNSS signal spoofing [92]–[94]. While ML-based methods show promising performance, they are limited by factors such as computational complexity and dependency on large datasets. Rule-based methods are simpler but may struggle in dynamic or uncertain environments. Future research could explore the application of RL to develop adaptive and robust spoofing defense mechanisms in the LAENet, which has not yet been extensively studied. Different from the abovementioned approaches, RL dynamically learns from interactions with the environment, and its sequential decision-making ability enables UAVs and ground stations to optimize spoofing defense strategies based on continuous feedback [147], make it a promising direction for enhancing spoofing defense in the LAENet
+
+# V. COMMUNICATION INTEGRITY FOR LAENET
+
+# A. Anomaly Detection
+
+Due to the open nature of wireless channels and the dominant LoS links in the LAENet, communication becomes particularly vulnerable to a diverse range of anomalous behaviors such as abnormal jamming, abnormal transmission power, and covert eavesdropping [46], [49]. Specifically, malicious jammers sense spectrum activity and dynamically adapt their interference patterns to mislead the UAV into taking suboptimal or harmful actions [81], [95]. In parallel, abnormal
+
+power emissions, either due to device faults, selfish behavior, or malicious intent, can violate spectrum policies, introduce harmful interference, and disrupt cooperative spectrum sharing [96]. Additionally, the pervasive risk of eavesdropping is that adversaries exploit the UAV's uplink or downlink transmissions to intercept sensitive data [61], [67]. Thus, it is essential to detect and mitigate these abnormal activities in the LAENet. Different from previously reviewed approaches such as anti-eavesdropping (Section III-A) and anti-jamming (Section IV-A), anomaly detection is a method used to identify and mitigate unexpected deviations from or irregularities in normal operational patterns by monitoring communication channels in the LAENet [127], [183].
+
+Jamming anomalies generally aim to disrupt the normal operation of UAV communication links, such as by injecting disruptive signals to interfere with the legitimate communication process. The study in [98] proposes a novel Self-Awareness (SA) module to leverage the radio to detect abnormal behaviors caused by jamming attacks for Cognitive UAV communications. The SA module unsupervisedly learns a generative model using a Hierarchical Dynamic Bayesian Network (HDBN) [184] to represent the joint distribution of random variables characterizing the radio environment at different levels of abstraction and across time, where the Modified Bayesian Filtering [185] is used to integrate multilevel abnormality measurements for online predictions of radio environmental states at different levels. Since jamming can disrupt and shift the distributions of the radio environment, the abnormalities can be detected by calculating the Kullback-Leibler Divergence (KLD) and Dhattacharyya distance (DB) [186] between predictive messages and diagnostic messages. The predictive messages are generated by the HDBN to capture the expected patterns of normal signals, and diagnostic messages reflect the actual state of the signal. The jammer's impact is characterized by calculating generalized errors based on shifts in amplitude, phase, and frequency of signals, allowing the radio to predict future activities of the jammer. The SA
+
+
+Part A. HDBN-based Scheme
+
+
+Part B. GDBN-based Scheme
+
+
+Part C. Active-GDBN-based Scheme
+Fig. 10. The overall architecture illustrates jamming anomaly detection to enhance communication integrity in the LAEnet. Part A presents an HDBN-based scheme focusing on hierarchical dynamic models to predict and detect abnormal signals caused by jammers. It details the transition probabilities between model states and the prediction of continuous states based on discrete superstates. Part B introduces a GDBN-based scheme, extending the HDBN approach by incorporating generalized states and observations, allowing for more nuanced predictions and error calculations. Part C depicts an Active-GDBN-based scheme, integrating UAV actions into the model to actively infer and adapt to the environment, thereby optimizing resource allocation and anti-jamming measures.
+
+module achieves a near $100\%$ abnormality detection accuracy, approximately $12\%$ higher than the traditional energy detector-based scheme.
+
+Different from the previous work [98], which introduced the SA module using HDBN for anomaly detection, the authors in [99] propose a Generalized Dynamic Bayesian Network (GDBN)-based framework to enhance the SA module by further classifying the detected anomalies caused by multiple jammers. A generalized state-space model [184] is used to represent the evolving radio environment as a GDBN model learned in an unsupervised manner. Different from the KLD/DB metric in [1], Kullback-Leibler divergence and Bhattacharyya distance are used as abnormality measurements between predicted and observed signals to detect jamming. Once an abnormality indicative of jamming is detected, the UAV extracts the interfering signal and compares it with prelearned GDBN models (each representing a different jamming modulation scheme). By evaluating which pre-learned model best explains the extracted jamming signal, the UAV can not only detect the presence of a jammer but also classify its modulation type. Simulation results show that the GDBN-based method achieves an overall classification accuracy of $98\%$ at $\mathrm{SNR} = 10$ dB, outperforming LSTM $(88\%)$ , CNN $(67\%)$ , and SAE $(90\%)$ .
+
+Based on the study [99], the authors in [100] propose an Active-GDBN to model the dynamic interaction between the UAV and jammer for anomaly detection. Similar to [99], the generalized state-space model [184] is used to capture the features and dynamic evolution of UAV signals to represent the radio environment. Differently from passive detection and classification of jamming signals in [99], the Active-GDBN achieves active anomaly detection by incorporating the UAV's actions into the inference process. Specifically, the UAV employs a Modified Markov Jump Particle Filter (M-MJPF) [187] to link the UAV's actions to environmental
+
+states and observations. Meanwhile, the UAV dynamically adjusts physical resource block selections to evade jamming by encoding jammer behavior and updating beliefs. The Active-GDBN achieves about $25\%$ to $37.5\%$ faster convergence on anomaly detection probability than the Q-learning-based baseline under various jamming types.
+
+Different from previous works [98]–[100] that detect jamming anomalies based on the statistical distribution divergence of the signal, study [101] focuses on detecting anomalies by exploiting the time delays, shifts, and modulation of the signal characteristics. Firstly, achieving blind channel estimation involves constructing cyclic correlation matrices to identify distinct Doppler shifts and time delays associated with transmissions by exploiting the inherent almost-cyclostationary (ACS) properties of UAV and jammer signals (e.g., periodic statistics from OFDM modulation). Then, this blind estimation process is combined with a widely linear minimum mean square error (WL-MMSE) filter to provide an initial estimate of the symbol vector by leveraging the non-circular statistics of the received signal, where the initial estimate includes contributions from both the UAV and the jammer. Finally, a post-sorting algorithm (PSA) is employed to iteratively decode and cancel the jammer's contribution by ranking and removing symbols with the highest signal-to-disturbance-plus-noise ratio (SDNR). Simulation results demonstrate that the proposed scheme can effectively detect and separate the jamming signals from UAV signals without requiring prior knowledge of the jammer's characteristics, even when the jammer's power is twice as strong as the UAV's power.
+
+In addition to jamming anomalies, which cause interference and security threats in the LAENet, abnormal power emissions in UAV communication networks also represent a critical type of anomaly, potentially leading to severe disruption of communication quality and violation of spectrum policies. The work in [102] proposes a cloud-based surveillance framework
+
+TABLE XI SUMMARY OF INJECTION DEFENSE FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY.
+
+| Injection type | Reference | Algorithm | Pros & Cons |
| Jamming signal | [98] | HDBN | HDBN-based jamming signal extraction and suppression
+✓ Autonomous learning from raw I/Q data enables adaptability to dynamic jamming patterns
+X Assume the jammer's output power remains constant during attacks |
| [101] | SIC | SIC with blind channel estimation for detecting and eliminating jamming signals
+✓ Eliminate jamming signals regardless of the mobility patterns of jammers
+X Rely on sufficient cyclostationary features in the received signal |
| [104] | DBF | DBF algorithm for nullifying jamming signals
+✓ Effective suppression of jamming signals while maintaining carrier phase integrity
+X May be limited to specific GNSS frequency bands |
| Spoofing signal | [105], [106] | API & LSR | SIC combined with API and LSR to recover legitimate signals from spoofing attacks
+✓ SemperFi with a single antenna does not require additional hardware
+X Limited to attackers with a power advantage lower than 15 dB |
| [107] | Subspace projection | Subspace projection for nullifying spoofing signals
+✓ Low parameter dependency, requiring only code delays and carrier frequencies
+X Suppression performance declines if spoofing and legitimate signals have similar code delays |
+
+to address the detection of abnormal power emissions, where the cloud server assigns spectrum resources to the UAVs and shares UAVs' spectrum usage information with the surveillance center. The surveillance center assigns the detection task to $K$ surveillance nodes (SNs) for local detection of abnormal power emission, where the detection rule is based on the Lagrange multiplier method and the generalized likelihood ratio test. After local decisions, $K$ SNs report results to the surveillance center, where cooperative detection of abnormal power emission is performed using the decision rule that declares an abnormal event when at least $L$ out of $K$ nodes detect an abnormality, where the optimal global threshold of $L$ is determined by solving the constraints on the global false-alarm probabilities. Simulation results show that the global detection probability exceeds 90% when transmit power deviation exceeds 0.02W (allocated power is 0.01W).
+
+Besides the threats of jamming and abnormal power emission, another critical anomaly that requires detection is eavesdropping in the LAENet, where malicious devices covertly intercept sensitive information during UAV-to-ground and UAV-to-UAV transmissions [66], [67]. Note that most previous works on anti-eavesdropping focused on measuring secure performance through secrecy rate and/or secrecy outage probability (such as [71], [76]) rather than emphasizing the detection of eavesdropping attacks. The work in [103] explores anomaly detection for eavesdropping attacks in UAV-aided wireless systems using unsupervised learning. Two datasets are prepared: artificial training data (ATD), simulated without eavesdropping based on CSI (all labeled normal), and a practical dataset extracted from received signal features (mean and variance of amplitude). Two types of unsupervised learning methods are designed for anomaly detection. One-class SVM maps data to a high-dimensional space, defining a normal region where outliers are detected. K-means clustering classifies test data into two clusters, labeling the one nearest to the ATD center as normal.
+
+Lesson Learned For jamming anomalies, the statistical distribution divergence detection and signal structural feature-based detection, such as HDBN, GDBN, and ACS, are used to model the dynamic environment and detect deviations from
+
+learned normal patterns. For abnormal transmission power detection, a cloud-based surveillance framework supports a statistical distribution detection approach to monitor and identify power emission outliers. Leveraging its high computing power, the cloud enables cooperative analysis through multi-source data aggregation, dynamically optimizes detection thresholds using global information, and maintains a feedback loop for adaptive anomaly detection. For eavesdropping detection, unsupervised learning techniques, including One-Class SVM and K-means clustering, achieve the identification of anomalies in received signals. These approaches effectively achieve anomaly detection and demonstrate excellent performance. However, challenges remain, including the reliance on high-quality training data and the complexity of maintaining real-time adaptability in dynamic spectrum environments. Currently, Generative AI such as GANs and generative diffusion models presents a promising research direction for anomaly detection, as demonstrated in the use of generalized models in HDBN and the artificial data generation for training ML and clustering models in [188], [189]. Generative AI could further enrich training datasets and provide a high-level generative model to enhance anomaly detection in the dynamic and uncertain LAENet.
+
+# B. Injection Defense
+
+The low-altitude economy is highly dependent on open communication and network architecture with dense communication links, which brings injection attacks as a significant threat to UAV communication integrity [28], [46]. These attacks involve the deliberate injection of malicious signals, such as jamming and spoofing signals, to disrupt or manipulate legitimate communications [97], [190]. Jamming signal injection can make legitimate signals unrecognizable by emitting high-power electromagnetic interference to degrade signal reception [98]. Additionally, spoofing signal injection can transmit high-power signals to overshadow legitimate GNSS signals. Therefore, eliminating injection signals or separating them from legitimate signals is crucial for ensuring communication integrity in the LAENet.
+
+
+Part A. SNDR-based SIC for jamming injection defense
+
+
+Part B. SIC with API and LSR for spoofing injection defense
+
+
+Part C. Subspace projection for spoofing injection defense
+Fig. 11. The overall architecture of injection defense mechanisms for UAVs in smart city applications. Part A presents the SIC architecture that processes channel state information to defend against jamming injection attacks [101]. Part B shows an SIC architecture integrated with API and LSR modules, which subtracts injection signals from the received signal to recover normal signals [105], [106]. Part C depicts a subspace projection-based architecture for spoofing injection defense, where the received signal is projected onto the orthogonal null space of the spoofing signals to eliminate them [107].
+
+The UAV's communication can be severely disrupted by jammers that exploit LoS propagation to inject jamming signals into the transmission channel, which may effectively mask legitimate signals and render them unrecognizable [101]. The work in [98] proposes an HDBN-based injection defense scheme to extract and remove the jammer's signal. This work first utilizes the HDBN to detect abnormal behaviors caused by jamming attacks, as mentioned earlier in Section V-A. Once the jammer's presence is confirmed, its signal characteristics are analyzed across multiple levels of continuous in-phase (I) and quadrature (Q) components and observation-level state vectors [191]. The extracted jammer signal is then separated from the received observation using frequency-domain subtraction [192], component-wise I/Q processing, and adaptive filtering [191]. The corrected signal is subsequently demodulated and decoded using techniques and error correction coding to restore the original signal. To maintain resilience against evolving jamming tactics, the system continuously updates the HDBN model to improve suppression commands. Simulation results show that the mean square error (MSE) of suppression commands decreases as the JSR increases, meaning that jammers attacking with higher power can be better estimated than jammers attacking with lower power.
+
+Different from the work in [98], which separates the jamming signal by analyzing its I/Q characteristics, the study in [101] proposes a Serial Interference Cancellation (SIC) scheme based on SDNR to eliminate injected anomalous signals in UAV communications, as shown in part A of Fig. 11. First, blind channel estimation and a WL-MMSE filter are used to identify UAV and jammer signals (as detailed in Section V-A). Then, the PSA ranks detected symbols based on SDNR, where the jamming signals rank higher in SDNR due to their higher emitted power. The SIC [193],
+
+[194] is subsequently designed for progressively eliminating jamming signals. Specifically, the high-rank jamming symbol is decoded, reconstructed using estimated channel parameters, and subtracted from the received signal. The process continues iteratively to eliminate previously detected jamming signals until all UAV symbols are successfully recovered, with the receiver dynamically updating channel estimation to adapt to jammer mobility and environmental changes. Simulation results demonstrate that the UAV signal can be recovered with low bit error rates $(< 10^{-4})$ even when the power of the jammer is double that of the UAV.
+
+Jamming attacks not only affect U2G and UAV-to-UAV communications but also cause RF interference, leading to UAVs failing to track GNSS signals in the LAENet. In light of this, the work in [104] proposes a self-calibrating digital beamforming (DBF) algorithm to effectively nullify jamming signals while preserving high-precision carrier phase measurements. It calibrates the antenna array's steering vectors and RF channel characteristics. Once calibration is complete, the system performs jamming detection and direction estimation by analyzing interference patterns across the antenna array. Then, the minimum power distortionless response (MPDR) optimization rule is used to calculate optimal beamforming weights, which aim to create nulls in the beam pattern corresponding to the directions of jamming signals, effectively suppressing them. The calculated beamforming weights are applied to the received signals to produce the beamformer output, which effectively suppresses jamming signals while preserving the carrier phase integrity of the desired signals. The proposed scheme achieves up to 80 dB Jammer-to-Signal Ratio (JSR) suppression, significantly outperforming the conventional Power Inversion (PI) scheme.
+
+In addition to jamming signals, spoofing attacks can easily
+
+transmit fake signals to manipulate GNSS signals due to their open signal structure and weak signal strength [195]. One type of method is based on signal encryption or data encryption to prevent malicious spoofers from injecting illegitimate signals [196]–[198]. However, they may not be suitable for resource-constrained UAVs in the LAENet. Therefore, defending against spoofing signal injection based on different signal characteristics is a promising solution. The authors in [105], [106] propose an anti-spoofing system, called SemperFi, to autonomously recover legitimate signals during active spoofing for UAVs. The system employs two core modules: the Adversarial Peak Identifier (API) and the Legitimate Signal Retriever (LSR), as shown in part B of Fig. 11. The API detects spoofed signals by correlating inertial measurement unit (IMU) data with calculated position-velocity-time (PVT) solutions [199]. The LSR module replicates the spoofing signal once it is identified. Then, similar to the study in [101], the SIC is applied to subtract the replica from the composite received signal that contains legitimate and spoofing signals. SemperFi enters an iterative refinement process if spoofing signals persist after initial cancellation, where replication, subtraction, and reassessment are performed until the spoofing detector no longer triggers an alarm, indicating sufficient attenuation or elimination of spoofing.
+
+Besides recovering legitimate signals by subtracting spoofing signals from the received signal [101], [105], [106], projecting the signal is also a viable injection defense strategy. In the study [107], the GNSS receiver's spoofing mitigation algorithm employs a subspace projection-based interference cancellation method to effectively eliminate spoofing signals, as shown in part C of Fig. 11. Specifically, the receiver on UAVs acquires and tracks incoming signals, identifying potential spoofing signals and reconstructing them based on their power levels, pseudo-random noise (PRN) code delays, and carrier frequencies. Then, the receiver uses these reconstructed spoofing signals to construct a spoofing subspace, which represents all possible linear combinations of spoofing signal characteristics. To effectively remove spoofing signals from the received signal, the receiver performs orthogonal projection to obtain a cleaned signal by mapping the received signal onto a complementary null space that is mathematically orthogonal to the spoofing subspace. Simulation results show that shorter projection lengths suppress spoofing signals more effectively than longer projections, achieving a $20\mathrm{dB}$ gain in Signal-to-Interference Ratio (SIR).
+
+Lesson Learned The above-mentioned studies have demonstrated the effectiveness for mitigating injection signals, such as jamming and spoofing attacks, thereby enhancing UAV communication reliability and security. These advancements leverage techniques that not only detect malicious signal interference but also enable autonomous recovery. One key advantage is that non-cooperative detection techniques, such as blind estimation [101] and self-awareness models [98], allow for efficient attack identification without requiring prior knowledge of the attacker's signal characteristics to adapt to dynamic and adversarial environments. However, several challenges remain in that beamforming-based or spatial filtering techniques rely on multi-antenna configurations [101],
+
+[104], limiting their applicability in cost-sensitive or small UAV systems. Future work should explore lightweight and energy-efficient implementations of injection defense to support stable UAV signal integrity protection. Additionally, more intelligent injection defense strategies combining optimization methods, RL, and ML could enhance resilience against more sophisticated adversaries.
+
+# VI. FUTURE RESEARCH DIRECTIONS
+
+# A. Energy-efficient Physical Layer Security
+
+Future work can focus on exploring more unique physical characteristics of wireless communication, such as exploiting channel characteristics and implementing simple coding schemes, to develop secure and low-energy protocols. Meanwhile, drones in the LAENet need to develop adaptive power control strategies that dynamically adjust transmission power based on channel conditions and security requirements to minimize unnecessary energy consumption [200]. Moreover, dynamic trajectory optimization is equally important for energy efficiency [201]. Future research can explore enabling UAVs to learn attack patterns in real time, share secure trajectory models across swarms, and dynamically adjust flight paths based on real-time security and power consumption feedback.
+
+# B. Multi-drone Collaboration for Secure Communication
+
+Future research on secure physical layer communication in the LAENet should move beyond existing dual-UAV collaboration models and explore distributed multi-UAV coordination (or UAV swarms) for enhanced resilience against jamming, spoofing, and unauthorized access [202]. For example, UAV swarms can collaboratively emit interference signals to obscure unauthorized receivers, thereby enhancing the confidentiality of communications [20]. Additionally, the integration of adaptive trust-based mutual authentication protocols among UAVs is essential [26]. Multiple UAVs with mutually verified identities can enable dynamic and secure spectrum-sharing mechanisms to optimize resource utilization in the LAENet.
+
+# C. AI-driven Security Defense Strategy
+
+Existing AI-based security strategies mainly focus on training AI models to identify anomalous signals while having some limitations. The resource-constrained drones are unable to train high-quality AI models, making the integration of edge computing a promising approach for model training [200]. Note that AI models may be difficult to generalize in recognizing various anomalous signals because they are pre-trained on previously collected datasets of fixed size. Future work can explore leveraging GAN or diffusion models to generate datasets based on real-time captured anomalous signals [203]. Furthermore, emerging generative AI technologies, such as the diffusion model for secure network topology generation in low-altitude domains [189], [204], AI agents for human-aerial vehicle secure interaction [205], and mixture of experts for robust wireless communications [2], [206], can be explored to achieve a more autonomous and intelligent LAENet.
+
+# D. Space-Air-Ground Integrated Security Architecture
+
+Future research can explore establishing a multi-domain physical layer security framework for LAENet to connect space, air, and ground layers, providing seamless communication coverage and cost-effective network access [55], [207]. A potential key research direction is the development of a coordinated multi-tier security mechanism, where satellites, UAVs, and terrestrial base stations collaboratively enhance physical layer security through dynamic resource allocation and interference management based on real-time CSI and environmental conditions, such as UAV mobility, channel fading, and spectrum constraints.
+
+# E. 6G-Enabled Secure UAV Communication
+
+The advent of 6G networks presents new opportunities for LAENet. Terahertz (THz) communication can offer ultrahigh-speed data transmission capabilities for LAENet [208]. Future research can explore the integration of THz with advanced beamforming techniques to focus signals on legitimate users, thereby enhancing security and reducing the risk of interception. Furthermore, Reconfigurable Intelligent Surfaces (RIS) play a crucial role in strengthening physical layer security by intelligently controlling wireless signal propagation [209], [210]. Future work can investigate RIS-based secure beamforming strategies to mitigate adversary interception, and leverage optimization techniques and DRL to adaptively adjust beamforming against eavesdropping or jamming attacks.
+
+# VII. CONCLUSION
+
+This paper has presented a comprehensive survey on secure physical layer communications in the LAENet, emphasizing the importance of safeguarding confidentiality, availability, and integrity in communications. It introduced the concept and architecture of the LAENet and outlined the associated security issues in physical layer communication. Then, the survey provided in-depth reviews of countermeasures for anti-eavesdropping strategies, authentication schemes, anti-jamming strategies, spoofing defenses, anomaly detection, and injection defense. Finally, the paper proposed a set of forward-looking future research directions. These discussions highlighted the critical role of secure physical layer communication in supporting the development of the LAENet and offered valuable insights for ongoing advancements in this emerging domain.
+
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+ "content": "Abstract—The Low-Altitude Economy Networking (LAENet) is emerging as a transformative paradigm that enables an integrated and sophisticated communication infrastructure to support aerial vehicles in carrying out a wide range of economic activities within low-altitude airspace. However, the physical layer communications in the LAENet face growing security threats due to inherent characteristics of aerial communication environments, such as signal broadcast nature and channel openness. These challenges highlight the urgent need for safeguarding communication confidentiality, availability, and integrity. In view of the above, this survey comprehensively reviews existing secure countermeasures for physical layer communication in the LAENet. We explore core methods focusing on anti-eavesdropping and authentication for ensuring communication confidentiality. Subsequently, availability-enhancing techniques are thoroughly discussed for anti-jamming and spoofing defense. Then, we review approaches for safeguarding integrity through anomaly detection and injection protection. Furthermore, we discuss future research directions, emphasizing energy-efficient physical layer security, multi-drone collaboration for secure communication, AI-driven security defense strategy, space-air-ground integrated security architecture, and 6G-enabled secure UAV communication. This survey may provide valuable references and new insights for researchers in the field of secure physical layer communication for the LAENet."
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+ "content": "WITH the rapid development of aerial vehicle technologies and communication networks, the concept of Low-Altitude Economic Networking (LAENet) has emerged to enable more comprehensive, large-scale, and intelligent"
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+ "content": "connectivity to support various low-altitude activities [1]–[4], such as intelligent transportation, logistics delivery, communication enhancement, disaster monitoring, and emergency response [5]–[8], as shown in Fig. 1. The LAENet is built upon earlier frameworks of single Unmanned Aerial Vehicle (UAV) operation and multi-UAV networks. A single UAV typically maintains a direct link to a ground station or base station, operating with simple control procedures and delivering cost-effective services but with limited range and scalability [9]. The UAV network focuses on formation control and multi-UAV collaboration, enabling broader mission areas and stronger fault tolerance [9]–[11]. Advancing from these foundations, the LAENet integrates various aerial vehicles into a high-density communication network, connecting them not only to ground stations but also to other platforms such as base stations, access points, and even satellites [12], [13]. Thus, the LAENet can enable ubiquitous coverage, high reliability, robust fault tolerance, greater autonomy, and intelligence."
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| [19] | A review of cybersecurity threats, countermeasures, and research gaps in UAV networks, with a focus on emerging attack surfaces and commercial UAV applications |
| [20] | A survey of security threats, vulnerabilities, and countermeasures in UAV swarm networks, with a focus on classifying attack types and reviewing emerging defense technologies |
| [21] | A review of security threats, vulnerabilities, and countermeasures in UAVs and Flying Ad Hoc Networks with attack surface analysis with simulation-based evaluation |
| [22] | A survey of vulnerabilities across software, hardware, and communication layers in UAV systems, and an exploration of emerging defense technologies |
| [23] | A survey of security challenges in drone communication and a review of emerging technologies used to enhance the speed, reliability, and security of UAV networks |
| [24] | A review of UAV security challenges, existing controls, and future research directions, with an emphasis on the transformative role of AI in enabling secure UAV systems |
| [25] | A review of security threats classified from a cyberspace security perspective and countermeasures in UAV systems |
| [26] | A survey of security threats, requirements, and counter-measures in UAV-aided Internet of Things (IoT) applications |
| [27] | A survey of cybersecurity vulnerabilities and countermeasures in UAV systems, integrating threat classification, communication protocols, and emerging techniques |
| [28] | A survey of PLS in UAV communications, focusing on key challenges, methodologies, and recent advancements for both static and mobile UAV deployment scenarios |
| [29] | A review of security challenges, practical deployment aspects, and standardization progress associated with integrating UAVs into cellular networks |
| [30] | A survey of layer-wise cybersecurity threats and AI-enabled countermeasures in UAV-assisted IoT applications |
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| Issues | ● Eavesdropping attack [46], [50]● Unauthorized access [31], [51], [52] |
| Solutions | ● Anti-eavesdropping strategies√ Convex optimization-based strategies [53]–[59]√ Reinforcement learning-based strategies [60]–[65]√ Deep learning-based strategies [66]–[71]● Communication authentication√ PUFs-based authentication [72]–[74]√ Channel based-authentication [75]–[77] |
| Section IV, Challenge 2: Communication availability |
| Issues | ● Jamming attack [48], [78], [79]● Spoofing attack [49], [50], [52], [78] |
| Solutions | ● Anti-jamming strategies√ Convex optimization [80]–[82]√ Single-agent RL [83]–[86]√ Multi-agent RL [87]–[89]● Spoofing defense√ PLA [77], [90], [91]√ GNSS spoofing detection [92]–[94] |
| Section V, Challenge 3: Communication Integrity |
| Issues | ● Anomalous behaviors [61], [95], [96]● Injection attacks [28], [46], [97] |
| Solutions | ● Anomaly detection√ Jamming anomaly detection [98]–[101]√ Abnormal power detection [102]√ Eavesdropping anomaly detection [103]● Injection defense√ Jamming signal injection defense [98], [101], [104]● Spoofing signal injection defense [105]–[107] |
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| A2G | Air-to-ground | ABS | Aerial Base Station |
| AN | Artificial Noise | AI | Artificial Intelligence |
| BCD | Block Coordinate Descent | BS | Base Station |
| CNN | Convolutional Neural Network | CSI | Channel State Information |
| DDPG | Deep Deterministic Policy Gradient | DDQN | Double-deep Q-Learning |
| DL | Deep Learning | DNN | Deep Neural Network |
| DQN | Deep Q-Network | eVTOL | Electric Vertical Take-off and Landing |
| DRL | Deep Reinforcement Learning | FAR | False Alarm Rate |
| G2A | Ground-to-air | G2U | Ground-to-UAV |
| GAN | Generative Adversarial Network | GNSS | Global Navigation Satellite System |
| GPS | Global Positioning System | GS | Ground Station |
| IoT | Internet of Things | LAENet | Low-Altitude Economy Networking |
| LSTM | Long Short-Term Memory | LoS | Line-of-sight |
| MARL | Multi-agent Reinforcement Learning | MDP | Markov Decision Process |
| MDR | Miss Detection Rate | MEC | Mobile Edge Computing |
| ML | Machine Learning | MSE | Mean Square Error |
| NOMA | Non-orthogonal Multiple Access | PLA | Physical-layer Authentication |
| PLS | Physical Layer Security | PUF | Physical Unclonable Function |
| QoE | Quality of Experience | RF | Radio Frequency |
| RIS | Reconfigurable Intelligent Surfaces | RL | Reinforcement Learning |
| RNN | Recurrent Neural Network | RSS | Received Signal Strength |
| SCA | Successive Convex Approximation | SDNR | Signal-to-disturbance-plus-noise Ratio |
| SNR | Signal-to-noise Ratio | SOC | Second-Order Cone |
| TDMA | Time-division Multiple Access | THz | Terahertz |
| U2G | UAV-to-ground Communication | UAV | Unmanned Aerial Vehicle |
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+ "content": "able seamless communication, coordination, and management of diverse aerial operations within low-altitude airspace [1], [108]. The LAENet includes numerous different types of constituents, such as flight equipment, base stations, and other communication platforms. Specifically, the LAENet connects various aerial vehicles, including general aviation aircraft for passenger transport and emergency rescue, drones for surveillance and logistics, and eVTOL designed for urban air mobility and last-mile cargo delivery [109], [110]. These aerial vehicles can incorporate ground and aerial base stations, further high-altitude platforms, such as weather balloons and satellites, to receive environmental information and precise navigation [13]."
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+ "content": "Different from traditional aviation networks that rely on centralized air traffic control, the LAENet can independently construct communication and networking by seamlessly interconnecting a variety of aerial and ground-based systems, which enables continuous information exchange, flight path optimization, and autonomous operations [8], [111]. Therefore, the LAENet has opened opportunities for various application scenarios and plays key roles from the perspective of communication coverage and relay [112]–[114]. Specifically, the LAENet can extend the communication coverage by deploying aircraft as ABSs in areas lacking communication infrastructure [115]–[117]. For instance, these ABSs deployed at optimal altitudes can provide connectivity and network services in remote or disaster-stricken areas [118], [119]. Moreover, if the direct communication links between ground base stations and user equipment are unreliable, such as in"
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+ "content": "mountainous regions and densely populated areas, the aircraft can act as mobile relays to improve connectivity by capturing, amplifying, and transmitting communication signals [120]–[122]. It also can be regarded as a surveillance unit to monitor airspace dynamics while simultaneously functioning as a low-altitude network orchestrator to optimize communication and computing resources [118], [123], [124]."
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+ "content": "To integrate and evolve these capabilities, the LAENet needs to establish effective communication infrastructure to ensure reliable connectivity and efficient interaction across various environments [31], [125]. Physical layer communication, as the bottom layer in the network architecture, may directly influence the communication performance of the LAENet across aerial and terrestrial networks [43], [46]. For example, it governs how signals are generated, transmitted, and received between aircraft and base stations [31]. Building on this, it manages the channel and spectrum resources to enhance signal transmission quality and maintain stable connectivity [43]. Therefore, ensuring the security of physical layer communication in the LAENet is crucial for supporting a wide range of applications in low-altitude domains."
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+ "content": "- The confidentiality of physical layer communications in the LAENet can be compromised by security threats such as eavesdropping and unauthorized access [128]. Eavesdropping arises primarily from the broadcast nature of wireless signals and LoS link, making transmissions highly susceptible to interception [46]. An eavesdropper silently capturing or intercepting signals can lead to the exposure of confidential information. Meanwhile, unauthorized access threats exploit the open and broadcast nature of UAV communications [31]. Attackers may gain illegal access to the LAENet by disguising themselves as legitimate UAVs or ground stations, thereby deceiving or interfering with the normal operation of UAVs [51]."
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+ "content": "- Integrity as a microscopic metric measures the deviations of signals, channels, and spectrum in communication under adversaries' influence [129]. The communication integrity of the LAENet can be affected by anomalous behaviors and injection attacks. Anomalous behaviors often use dynamic spectrum access and the open wireless medium, including abnormal jamming, abnormal transmission power, and covert eavesdropping [95]. These anomalous behaviors can introduce harmful interference, violate spectrum policies, and expose sensitive information to eavesdroppers [61], [96]. Moreover, the injection attack exploits the open nature of wireless channels to alter signals or inject illegal signals, such as spoofing signals or malicious GNSS signals, to deceive receivers and interfere with communication, thereby leading to degraded signal quality, false navigation, and network congestion [28], [46], [97]."
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+ "content": "Overall, as illustrated in Fig. 2, this survey reviews existing research on achieving communication confidentiality, availability, and integrity for the LAENet. Specifically, the investigation of anti-jamming strategies and communication authentication schemes aims to enhance communication confidentiality. Studies on anti-jamming techniques and spoofing defense mechanisms have been explored to ensure communication availability. Furthermore, research on communication integrity has focused on anomaly detection and injection attack mitigation approaches."
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+ "content": "In the LAENet, anti-eavesdropping solutions can leverage the controllable mobility of low-altitude aircraft to enhance physical layer security. By dynamically optimizing their trajectories, low-altitude aircraft can actively adapt their flight paths to shape the communication environment [135]. This approach allows them to fly closer to legitimate ground nodes, strengthening communication links and improving channel conditions for intended receivers, while simultaneously distancing themselves from potential eavesdroppers. In this subsection, we present a critical role of UAV trajectory in forming the communication environment, and how PLS can be enhanced through trajectory optimization and resource allocation to mitigate eavesdropping risks. Our analysis focuses on three prominent methodologies in this domain: convex optimization, deep learning, and reinforcement learning."
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+ "content": "The study in [53] explores physical-layer security in UAV-assisted Mobile Edge Computing (MEC) systems in the presence of multiple ground-based eavesdroppers. The proposed system utilizes dual UAVs for task execution and anti-eavesdropping measures. One UAV operates as a mobile MEC server, while the other emits jamming signals to disrupt eavesdroppers, as shown in Fig. 3. The time-division multiple access (TDMA) scheme and non-orthogonal multiple access (NOMA) scheme are proposed to maximize the minimum secure computing capacity by jointly optimizing communica"
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+ "content": "TABLE IV SUMMARY OF CONVEX OPTIMIZATION FOR ANTI-EAVESDROPPING STRATEGY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
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+ "html": "| Ref | Optimization Objectives | Eavesdropper and Jammer Type | OptimizationConstraints | Pros & Cons |
| [53] | Secure calculation capacity1 | UAV jammer and fixed ground eavesdropper | Transmit power, time allocation, and computation capacity | BCD and P-BCD for secure calculation capacity maximization\n✓ Secure capacity of NOMA and TDMA has been significantly improved\nX High complexity for NOMA due to dual-loop iterations |
| [54] | Secure calculation capacity | Base station jammer and fixed ground eavesdropper | Transmission power, time allocation, and CPU processing frequency | JDPB algorithm with SCA and BCD for secure task offloading\n✓ Reduce complexity via region division\nX Fixed UAV altitude limits 3D trajectory optimization |
| [55] | Average secrecy rate2 | Antenna jammer and fixed aerial eavesdropper | Transmit power and jamming power | BCD and SCA optimization with hybrid FSO/RF links\n✓ Enhance communication security via hybrid FSO/RF links and AN\nX Rely on simplified channel models (e.g., free-space path loss) |
| [56] | Worst-case secrecy rate | UAV jammer and fixed ground eavesdropper | UAV speed, collision avoidance, positioning error, and energy harvesting | Robust 3D trajectory and time switching optimization\n✓ Full mobility of UAVs in 3D for improving secrecy rate\nX The performance may degrade with flying eavesdroppers |
| [57] | Average secrecy rate | None and flying eavesdropper | Transmit power control and user scheduling | Joint trajectory and communication design against mobile eavesdroppers\n✓ Initial trajectory design for keeping away from eavesdroppers\nX Security performance relies on the initial trajectory design |
| [58] | Secure calculation capacity | Ground jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | Integrate a dual-UAV system with a ground jammer in MEC\n✓ Incorporate the UAV server and UAV eavesdropper with a ground jammer\n✓ Allow a UAV server to hover near ground users for secure offloading\nX Numerous flight constraints may require extensive tuning |
| [59] | Secrecy rate | Coastal jammer and flying eavesdropper | Transmit power, time slot, computation capacity, UAV speed, and collision avoidance | A secure communication for UAV-relay-assisted maritime MEC\n✓ Simultaneously optimize multiple parameters for improved secrecy rate\nX Iterative decomposition increases the computational burden\nX Assume prior knowledge of Channel State Information (CSI) of devices |
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| Value-based RL | [60] | DQN | ○ DQN algorithm for UAV trajectory optimization to maximize the secrecy capacity\n✓ Low computational complexity, making it easy to train\n× Q-value overestimation, leading to suboptimal action selection |
| [61] | DDQN | ○ DDQN-based joint trajectory, time allocation, and offloading optimization\n✓ Accelerated convergence via action space pruning\n✓ Real-time optimization of trajectory and resources\n× DDQN is restricted to discrete action spaces\n× DDQN is not suitable for continuous action control |
| Policy Gradient-based RL | [62] | CAA-MADDPG | ○ Multi-Agent DRL with attention mechanisms (CAA-MADDPG) for secrecy rate maximization\n✓ Handle complex multi-agent with the attention mechanism\n× Assume prior knowledge of eavesdropper locations\n× Assume ground devices are static |
| [63] | DDPG | ○ DDPG-based RL for enhancing bi-directional UAV communication security\n✓ Support mobile devices and ensure bi-directional secureit\n× Computational overhead increases with device density\n× performance may be sensitive to hyperparameter selection |
| [64] | PPO+DCCN | ○ Hybrid DCCN and PPO for secrecy rate maximization\n✓ The PPO optimizes the UAV trajectory based on the results from DCCN\n× The performance is sensitive to the choice of clipping factor in PPO |
| [65] | MAPPO+LSTM | ○ MAPPO for multi-agent cooperative anti-eavesdropping and LSTM-enhanced sequential learning\n✓ The MAPPO+LSTM improves the learning capability of sequential sample data\n× Assume perfect knowledge of CSI may be challenging in real-world scenarios |
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| Neural network model | [66] | DNN | ● Use DNN to optimize UAV deployment and jamming strategies for secure communication\n● The DNN model reduces the complexity of exhaustive searches\n● Rely on complete statistical channel knowledge\n● require intensive resources to generate a large amount of training data |
| [67] | CNN-LSTM | ● CNN-LSTM-based SEM prediction for dynamic secure UAV trajectory optimization\n● Efficient spatiotemporal feature extraction via CNN-LSTM\n● Assume fixed UAV height and passive eavesdropper\n● Training CNN-LSTM network requires a substantial amount of data |
| [68] | FL-DNN | ● FL-DNN-RL integration (FairLearn) for maximizing fairness in secrecy rates\n● Collaborative learning via FL improves generalization in anti-eavesdropping strategies\n● Involving multiple learning mechanisms requires significant computational resources\n● Assuming perfect CSI and eavesdropper localization may be impractical |
| Generative AI model | [69] | MD-GAN | ● MD-GAN with unknown CSI as model weights\n● Adapt to dynamic environments via gradient-based training\n● Do not require knowledge of the eavesdropper's detection threshold\n● Training a GAN can be computationally intensive |
| [70] | DD-GAN | ● DD-GAN uses genetic algorithm-generated datasets for GAN training\n● Achieve an effective trade-off between covert rate and detection probability\n● Training relies on the quality and quantity of the genetic algorithm-generated data |
| [71] | GDMTD3 | ● GDMTD3 integrates generative diffusion models into TD3\n● Handle high-dimensional action spaces to adapt mobile eavesdroppers\n● Computational complexity from diffusion denoising steps |
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+ "content": "of multi-dimensional data distributions [161]. The diffusion model can better capture the complex dynamics and the tradeoff in the multi-objective optimization problem concerning secure communication [112]. For example, The diffusion model captures complex state-action distributions, enabling adaptive beamforming and UAV repositioning under eavesdropper mobility. To tackle dynamic environments and high-dimensional action spaces in secure communication and energy efficiency multi-objective optimization problem, the authors in [71] propose GDMTD3, a Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm enhanced with generative diffusion models. Key innovations include integrating diffusion-based reverse processes into the actor network for robust policy generation and addressing continuous action spaces, as shown in part E in Fig. 5. The training process of GDMTD3 involves initializing the online critic and actor networks, interacting with the environment, and updating the network parameters based on the collected experiences. The actor network uses a generative diffusion model to sample actions, while the critic networks evaluate the actions using twin critic networks to reduce overestimation bias. Simulation results show that GDMTD3 outperforms DRL-based benchmarks (including PPO, TD3, and DDPG), achieving about "
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+ "content": " higher average secrecy rate than TD3. In addition, when the number of UAVs increases from 4 to 8, the average secrecy rate increases accordingly. However, increasing the number of UAVs from 8 to 16 raises"
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+ "content": "TABLE VII SUMMARY OF AUTHENTICATION FOR COMMUNICATION CONFIDENTIALITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
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+ "html": "| Techniques | Reference | Algorithm | Pros & Cons |
| PUFs-based authentication | [72] | PUF\\(s^1\\) | PUF-based dynamic session key generation and mutual authentication protocol\n✓ Lightweight design with no stored secrets\n✗ Potential overhead during temporary identity updates |
| [73] | PUF-fuzzy extractor | PUF-fuzzy extractor mutual authentication with TS-based dynamic session adaptation\n✓ Dynamic session time adaptation minimizes idle periods and enhancing security\n✗ Higher computational cost due to fuzzy extractors |
| [74] | PUFs-fuzzy extractor-AEGIS | Integration of PUFs, fuzzy extractors, and AEGIS for mutual authentication\n✓ The proposed password/biometric update mechanism reduces server dependency\n✗ Multiple cryptographic operations and protocols may be cause delay in the implementation |
| Channel based authentication | [75] | Rician channel | Physical-layer fingerprinting authentication based on Rician channel characteristics\n✓ Optimal power allocation balances data, AN, and authentication tag transmission\n✗ Reliance on encrypted tags requires high demand on UAV processing capabilities |
| [76] | Rayleigh channel | SNR difference-based PLA scheme\n✓ The SNR-based design can be implemented without additional hardware infrastructure\n✗ The simplified Rayleigh channel model may limit to real-world propagation environments |
| [77] | Rayleigh/Rician channels | AD metric2for authentication under Rayleigh/Rician channels\n✓ AD metric-based method improves the detection accuracy of authentication\n✓ Detailed analysis of authentication performance under different propagation conditions\n✗ Computational complexity in Rician channels due to hypergeometric functions |
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+ "content": "Physical Unclonable Functions (PUFs) are hardware-based security primitives that exploit inherent and unique physical variations in devices to generate unclonable and unpredictable responses for communication authentication."
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+ "content": "energy consumption but only marginally improves secrecy rates, highlighting a performance-energy trade-off."
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+ "content": "Lesson Learned A key lesson learned is that deep learning, particularly through advanced architectures such as GANs [69], [70] and diffusion models [71], can address complex, dynamic environments with partial channel state information and unknown eavesdropper locations, while demonstrating superior performance over traditional methods [59], [65], [66]. These approaches demonstrate that deep learning not only strengthens the resilience of secure communications but also enables autonomous, real-time decision-making to counteract evolving eavesdropping threats in UAV networks."
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+ "content": "In the LAENet, as UAVs operate in open environments and rely on wireless communication, they are highly vulnerable to security threats such as node capture and man-in-the-middle attacks [46]. Ensuring secure and reliable authentication between UAVs and ground stations/users or among UAVs is critical to preventing unauthorized access [52], [162]. Traditional cryptographic authentication schemes often impose significant computational and memory overheads and incur considerable lantency, making them unsuitable for resource-constrained UAVs [163]. Recently, advancements such as PUFs and Physical-layer Authentication (PLA) mechanisms have opened new possibilities for lightweight and effective authentication in the LAENet."
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+ "content": "PUFs are a class of hardware security primitives that leverage the inherent manufacturing variations (such as variations in circuit delay or RF properties) in semiconductor devices to generate unique and unpredictable responses [164]. When a specific input is applied to a PUF, the device generates a corresponding response, forming a challenge-response pair that is unique to this device [164]. Such uniqueness and unpredictability make PUFs highly resistant to cloning and"
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+ "content": "tampering, making them as a secure means for device authentication and key generation [165]. In addition, employing a PUF in a UAV allows for secure authentication without the need for complex cryptographic operations, making it an efficient solution for resource-constrained scenarios [166]."
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+ "content": "transmitter; otherwise, it is classified as a jammer. The closed-form expressions for the probability density function of SNR differences, false alarm rate (FAR), and miss detection rate (MDR) are derived under Rayleigh fading channels in single-UAV and dual-UAV scenarios. The non-convex optimization problem of minimizing MDR under FAR constraints is solved using an SCA algorithm, which outperforms the RSS-based baseline [90] by about "
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+ "content": "Lesson Learned. Leveraging physical-layer characteristics, such as PUFs and channel properties, in conjunction with communication models and optimization algorithms, has proven effective in enhancing authentication accuracy and reducing detection errors. However, some methods also reveal limitations. For instance, the assumptions of ideal channel conditions and the neglect of practical implementation constraints may limit the applicability of the proposed solutions [76], [77]. Future research should focus on addressing these limitations by exploring more practical channel models and considering the trade-offs between security and system complexity."
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+ "content": "Jamming attacks pose significant challenges to communication availability in the LAENet by disrupting legitimate communication links and degrading the performance of aircraft communication networks [79], [172]. As shown in Fig. 10, these attacks can exploit the openness and broadcasting nature of UAV networks, making them particularly vulnerable to interference [79]. Malicious jammers can transmit strong signals that weaken signal strength, degrade signal quality, and increase communication delays, leading to unreliable coverage and potential paralysis of the entire network [172], [173]. This vulnerability underscores the urgent need for effective anti-jamming technologies to ensure reliable communication in the LAENet."
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| Convex optimization | [80] | BCD, SCA | BCD and SCA for UAV 3D trajectory optimization for anti-jamming\n✓ Probabilistic LoS performs well in real-world scenarios such as urban environments\nX High computational complexity may be challenging in resource-constrained environments |
| [81] | SCA, Dinkelbach | SCA and Dinkelbach algorithm for energy-efficient trajectory optimization under malicious jammers\n✓ Balance between throughput and energy consumption in anti-jamming\nX Assume static and LoS-dominated channels |
| [82] | BCD, SCA | BCD and SCA for joint UAV trajectory and transmit power optimization under jamming\n✓ Improve throughput by considering transmit power optimization against jammers\nX Assume a fixed UAV altitude and a static channel environment |
| Multi-agent RL | [87] | MALQL | Collaborative MALQL algorithm for anti-jamming with channel and power allocation\n✓ Accelerate convergence compared to single-agent Q-learning\nX Assume predefined UAV trajectories limits to adaptability |
| [88] | MARL | MARL with adversarial pre-training for dynamic and generalized jamming\n✓ Generalize to various jamming patterns via adversarial populations for pre-training\nX Pre-training for generalized jamming may require significant offline resources |
| [89] | MATD3 | MATD3 algorithm with PER for dynamic resource management under jamming attacks\n✓ Handle high-dimensional continuous action spaces\nX The integration of PER and spectrum sensing may increase the computational complexity |
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+ "content": "problems that arise when optimizing UAV trajectories and various constraints under malicious jamming conditions [131]. The work in [80] investigates anti-jamming 3D trajectory design for UAV-enabled wireless sensor networks under a probabilistic LoS channel model. The probabilistic LoS model accounts for elevation angle-dependent shadowing effects in urban environments compared with simplified LoS models. The BCD and SCA algorithms are employed to optimize the UAV's horizontal and vertical trajectory, allowing the UAV to move closer to the ground station for improved transmission rates while dynamically adjusting its elevation angle relative to the jammer to mitigate interference."
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| PLA | [90] | RSS | Spatial correlations of RSS distances in PLA against spoofing attacksUse RSS-based channel characteristics to reduce PLA computational complexityAssume an ideal transmission scenario without external interference |
| [91] | Rayleigh channel | Defend against spoofing attacks by considering channel randomness and jammingSimultaneously address spoofing and jamming attacks via PLAAssume static UAVs and a known jamming distribution |
| [77] | Rayleigh and Rician channels | AD-based PLA for spoofing defense under Rayleigh and Rician channelsProvide a thorough analysis of spoofer identification in urban and suburban environmentsAssume perfect CSI in channel modeling |
| GNSS spoofing detection | [92] | Rule-based detection | Combine cooperative localization mechanism with Stackelberg game against spoofing attacksSpoofing detection is based on neighboring UAV signal sources without predefined thresholdsExtending to larger UAV groups may require complex adjustments |
| [93] | ML-based detection | Improved AdaBoost-CNN for multi-modal spoofing attack identificationHigh accuracy in identifying spoofing attacks with limited data samplesDependence on predefined signal features may lead to model overfitting |
| [94] | Rule & ML-based detection | MLP and statistical feature extraction on path-loss data for detecting GPS spoofingNo additional hardware/energy burden on UAVsRobust performance under sparse base station coverageSpoofing detection performance degrades in areas with unstable cellular signals |
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+ "content": "flight paths, violations of no-fly zone regulations, or increased collision risks [46]. Given a critical role of GNSS in UAV operations, effective detection and mitigation strategies for spoofing attacks are essential to ensure flight safety and prevent security breaches in the LAENet. Currently, studies on signal spoofing attack recognition in the LAENet mostly focuses on recognizing GNSS spoofing attack detection, which primarily falls into two categories with respect on rule-based and ML-based methods [19], [25]. Rule-based detection methods typically assess the relative distance and positional deviations of UAVs to determine if they are under GNSS spoofing attack. On the other hand, the ML-based methods pay attention to recognize different spoofing types by learning the characteristics of received signals."
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+ "content": "Furthermore, integrating rule-based approaches with machine learning-based methods provides an effective and robust defense against spoofing attacks. The work in [94] leverages statistical features of path losses between UAVs and terrestrial base stations to detect a UAV's trajectory deviation due to GPS spoofing, as shown in part B of Fig. 9. The spoofing detection is formulated as a nonlinear optimization problem that aims to minimize hypothesis test errors by adjusting thresholds, statistical feature weights, and the number of base stations. To further accurately analyze path loss's statistical features for final decisions on predicting GPS spoofing probabilities,"
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+ "html": "| Anomaly type | Reference | Algorithm | Pros & Cons |
| Jamming | [98] | HDBN | SA module based on HDBN for detecting jamming anomalies\n✓ UAccurately characterize and detect jamming anomalies via KLD/DB metrics\n✗ Unstable initialization in unsupervised learning affects the performance of the HDBN |
| [99] | GDBN | GDBN to model the radio environment and detect and classify jamming anomalies\n✓ Unsupervised learning eliminates dependency on labeled data in classification of anomalies\n✗ Computational complexity increases with the number of jamming categories |
| [100] | Active-GDBN | Active-GDBN used to model UAV-jammer interactions for anomaly detection\n✓ Actively incorporate UAV's actions for faster adaptation and jamming detection\n✗ M-MJPF requires significant computational resources |
| [101] | Blind channel estimation & ACS | Blind channel estimation based on ACS properties to detect jammer signals\n✓ Does not rely on prior knowledge of the jammer's behavior\n✗ Assumes a specific structure of the multicarrier modulation format |
| Abnormal Power | [102] | Spectrum surveillance | Local and cooperative detection of abnormal power emission\n✓ Handle both aggressive and passive power misuse\n✓ Cloud-based framework enables real-time closed-loop surveillance\n✗ Computational complexity increases with the number of SN |
| Eavesdropping | [103] | SVM & K-means | One-class SVM and K-means clustering for detecting eavesdropping anomalies\n✓ One-class SVM and K-means are stable under varying eavesdropper power\n✗ Detection performance mainly depends on the quality and quantity of the ATD |
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+ "content": "multilayer perceptron (MLP) neural networks are deployed on edge cloud servers, where individual MLP models at each BS are used to analyze statistical features of path losses. Simulation results show that the proposed method achieves "
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+ "content": " accuracy with a single base station, outperforming baseline approaches such as adaptive trustable residence area (ATRA), which necessitates three base stations for triangulation [182]."
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+ "content": "Lesson Learned. For identity spoofing in the LAENet, leveraging signal features such as received signal strength and channel randomness in PLA design is an effective approach [77], [90], [91]. On the other hand, employing rule-based or ML-based techniques can detect and mitigate GNSS signal spoofing [92]–[94]. While ML-based methods show promising performance, they are limited by factors such as computational complexity and dependency on large datasets. Rule-based methods are simpler but may struggle in dynamic or uncertain environments. Future research could explore the application of RL to develop adaptive and robust spoofing defense mechanisms in the LAENet, which has not yet been extensively studied. Different from the abovementioned approaches, RL dynamically learns from interactions with the environment, and its sequential decision-making ability enables UAVs and ground stations to optimize spoofing defense strategies based on continuous feedback [147], make it a promising direction for enhancing spoofing defense in the LAENet"
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+ "content": "V. COMMUNICATION INTEGRITY FOR LAENET"
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+ "content": "Due to the open nature of wireless channels and the dominant LoS links in the LAENet, communication becomes particularly vulnerable to a diverse range of anomalous behaviors such as abnormal jamming, abnormal transmission power, and covert eavesdropping [46], [49]. Specifically, malicious jammers sense spectrum activity and dynamically adapt their interference patterns to mislead the UAV into taking suboptimal or harmful actions [81], [95]. In parallel, abnormal"
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+ "content": "power emissions, either due to device faults, selfish behavior, or malicious intent, can violate spectrum policies, introduce harmful interference, and disrupt cooperative spectrum sharing [96]. Additionally, the pervasive risk of eavesdropping is that adversaries exploit the UAV's uplink or downlink transmissions to intercept sensitive data [61], [67]. Thus, it is essential to detect and mitigate these abnormal activities in the LAENet. Different from previously reviewed approaches such as anti-eavesdropping (Section III-A) and anti-jamming (Section IV-A), anomaly detection is a method used to identify and mitigate unexpected deviations from or irregularities in normal operational patterns by monitoring communication channels in the LAENet [127], [183]."
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+ "content": "Jamming anomalies generally aim to disrupt the normal operation of UAV communication links, such as by injecting disruptive signals to interfere with the legitimate communication process. The study in [98] proposes a novel Self-Awareness (SA) module to leverage the radio to detect abnormal behaviors caused by jamming attacks for Cognitive UAV communications. The SA module unsupervisedly learns a generative model using a Hierarchical Dynamic Bayesian Network (HDBN) [184] to represent the joint distribution of random variables characterizing the radio environment at different levels of abstraction and across time, where the Modified Bayesian Filtering [185] is used to integrate multilevel abnormality measurements for online predictions of radio environmental states at different levels. Since jamming can disrupt and shift the distributions of the radio environment, the abnormalities can be detected by calculating the Kullback-Leibler Divergence (KLD) and Dhattacharyya distance (DB) [186] between predictive messages and diagnostic messages. The predictive messages are generated by the HDBN to capture the expected patterns of normal signals, and diagnostic messages reflect the actual state of the signal. The jammer's impact is characterized by calculating generalized errors based on shifts in amplitude, phase, and frequency of signals, allowing the radio to predict future activities of the jammer. The SA"
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+ "content": "Different from previous works [98]–[100] that detect jamming anomalies based on the statistical distribution divergence of the signal, study [101] focuses on detecting anomalies by exploiting the time delays, shifts, and modulation of the signal characteristics. Firstly, achieving blind channel estimation involves constructing cyclic correlation matrices to identify distinct Doppler shifts and time delays associated with transmissions by exploiting the inherent almost-cyclostationary (ACS) properties of UAV and jammer signals (e.g., periodic statistics from OFDM modulation). Then, this blind estimation process is combined with a widely linear minimum mean square error (WL-MMSE) filter to provide an initial estimate of the symbol vector by leveraging the non-circular statistics of the received signal, where the initial estimate includes contributions from both the UAV and the jammer. Finally, a post-sorting algorithm (PSA) is employed to iteratively decode and cancel the jammer's contribution by ranking and removing symbols with the highest signal-to-disturbance-plus-noise ratio (SDNR). Simulation results demonstrate that the proposed scheme can effectively detect and separate the jamming signals from UAV signals without requiring prior knowledge of the jammer's characteristics, even when the jammer's power is twice as strong as the UAV's power."
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+ "content": "TABLE XI SUMMARY OF INJECTION DEFENSE FOR COMMUNICATION INTEGRITY CIRCLES DESCRIBE THE METHODS; CORRECT MARKERS AND CROSS MARKERS REPRESENT PROS AND CONS RESPECTIVELY."
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+ "html": "| Injection type | Reference | Algorithm | Pros & Cons |
| Jamming signal | [98] | HDBN | HDBN-based jamming signal extraction and suppression\n✓ Autonomous learning from raw I/Q data enables adaptability to dynamic jamming patterns\nX Assume the jammer's output power remains constant during attacks |
| [101] | SIC | SIC with blind channel estimation for detecting and eliminating jamming signals\n✓ Eliminate jamming signals regardless of the mobility patterns of jammers\nX Rely on sufficient cyclostationary features in the received signal |
| [104] | DBF | DBF algorithm for nullifying jamming signals\n✓ Effective suppression of jamming signals while maintaining carrier phase integrity\nX May be limited to specific GNSS frequency bands |
| Spoofing signal | [105], [106] | API & LSR | SIC combined with API and LSR to recover legitimate signals from spoofing attacks\n✓ SemperFi with a single antenna does not require additional hardware\nX Limited to attackers with a power advantage lower than 15 dB |
| [107] | Subspace projection | Subspace projection for nullifying spoofing signals\n✓ Low parameter dependency, requiring only code delays and carrier frequencies\nX Suppression performance declines if spoofing and legitimate signals have similar code delays |
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+ "content": "to address the detection of abnormal power emissions, where the cloud server assigns spectrum resources to the UAVs and shares UAVs' spectrum usage information with the surveillance center. The surveillance center assigns the detection task to "
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+ "content": " is determined by solving the constraints on the global false-alarm probabilities. Simulation results show that the global detection probability exceeds 90% when transmit power deviation exceeds 0.02W (allocated power is 0.01W)."
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+ "content": "Besides the threats of jamming and abnormal power emission, another critical anomaly that requires detection is eavesdropping in the LAENet, where malicious devices covertly intercept sensitive information during UAV-to-ground and UAV-to-UAV transmissions [66], [67]. Note that most previous works on anti-eavesdropping focused on measuring secure performance through secrecy rate and/or secrecy outage probability (such as [71], [76]) rather than emphasizing the detection of eavesdropping attacks. The work in [103] explores anomaly detection for eavesdropping attacks in UAV-aided wireless systems using unsupervised learning. Two datasets are prepared: artificial training data (ATD), simulated without eavesdropping based on CSI (all labeled normal), and a practical dataset extracted from received signal features (mean and variance of amplitude). Two types of unsupervised learning methods are designed for anomaly detection. One-class SVM maps data to a high-dimensional space, defining a normal region where outliers are detected. K-means clustering classifies test data into two clusters, labeling the one nearest to the ATD center as normal."
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+ "content": "Lesson Learned For jamming anomalies, the statistical distribution divergence detection and signal structural feature-based detection, such as HDBN, GDBN, and ACS, are used to model the dynamic environment and detect deviations from"
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+ "content": "learned normal patterns. For abnormal transmission power detection, a cloud-based surveillance framework supports a statistical distribution detection approach to monitor and identify power emission outliers. Leveraging its high computing power, the cloud enables cooperative analysis through multi-source data aggregation, dynamically optimizes detection thresholds using global information, and maintains a feedback loop for adaptive anomaly detection. For eavesdropping detection, unsupervised learning techniques, including One-Class SVM and K-means clustering, achieve the identification of anomalies in received signals. These approaches effectively achieve anomaly detection and demonstrate excellent performance. However, challenges remain, including the reliance on high-quality training data and the complexity of maintaining real-time adaptability in dynamic spectrum environments. Currently, Generative AI such as GANs and generative diffusion models presents a promising research direction for anomaly detection, as demonstrated in the use of generalized models in HDBN and the artificial data generation for training ML and clustering models in [188], [189]. Generative AI could further enrich training datasets and provide a high-level generative model to enhance anomaly detection in the dynamic and uncertain LAENet."
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+ "content": "B. Injection Defense"
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+ "content": "The low-altitude economy is highly dependent on open communication and network architecture with dense communication links, which brings injection attacks as a significant threat to UAV communication integrity [28], [46]. These attacks involve the deliberate injection of malicious signals, such as jamming and spoofing signals, to disrupt or manipulate legitimate communications [97], [190]. Jamming signal injection can make legitimate signals unrecognizable by emitting high-power electromagnetic interference to degrade signal reception [98]. Additionally, spoofing signal injection can transmit high-power signals to overshadow legitimate GNSS signals. Therefore, eliminating injection signals or separating them from legitimate signals is crucial for ensuring communication integrity in the LAENet."
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+ "content": "Fig. 11. The overall architecture of injection defense mechanisms for UAVs in smart city applications. Part A presents the SIC architecture that processes channel state information to defend against jamming injection attacks [101]. Part B shows an SIC architecture integrated with API and LSR modules, which subtracts injection signals from the received signal to recover normal signals [105], [106]. Part C depicts a subspace projection-based architecture for spoofing injection defense, where the received signal is projected onto the orthogonal null space of the spoofing signals to eliminate them [107]."
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+ "content": "The UAV's communication can be severely disrupted by jammers that exploit LoS propagation to inject jamming signals into the transmission channel, which may effectively mask legitimate signals and render them unrecognizable [101]. The work in [98] proposes an HDBN-based injection defense scheme to extract and remove the jammer's signal. This work first utilizes the HDBN to detect abnormal behaviors caused by jamming attacks, as mentioned earlier in Section V-A. Once the jammer's presence is confirmed, its signal characteristics are analyzed across multiple levels of continuous in-phase (I) and quadrature (Q) components and observation-level state vectors [191]. The extracted jammer signal is then separated from the received observation using frequency-domain subtraction [192], component-wise I/Q processing, and adaptive filtering [191]. The corrected signal is subsequently demodulated and decoded using techniques and error correction coding to restore the original signal. To maintain resilience against evolving jamming tactics, the system continuously updates the HDBN model to improve suppression commands. Simulation results show that the mean square error (MSE) of suppression commands decreases as the JSR increases, meaning that jammers attacking with higher power can be better estimated than jammers attacking with lower power."
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+ "content": "[1] Z. Li, Z. Gao, K. Wang, Y. Mei, C. Zhu, L. Chen, X. Wu, and D. Niyato, \"Unauthorized uav countermeasure for low-altitude economy: Joint communications and jamming based on mimo cellular systems,\" IEEE Internet of Things Journal, vol. 12, no. 6, pp. 6659-6672, 2025."
+ }
+ ]
+ }
+ ],
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+ }
+ ]
+ }
+ ],
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+ {
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+ "type": "text",
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+ }
+ ]
+ }
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+ }
+ ],
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+ }
+ ]
+ }
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+ "index": 12
+ },
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+ "type": "ref_text",
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+ }
+ ]
+ }
+ ],
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+ },
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+ }
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+ }
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+ }
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diff --git a/data/2025/2504_09xxx/2504.09228/4d91038b-08d1-447d-8037-8ee551148a4c_content_list.json b/data/2025/2504_09xxx/2504.09228/4d91038b-08d1-447d-8037-8ee551148a4c_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..ef45d1d52de48cfe3dda71784a1d66683e786475
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+++ b/data/2025/2504_09xxx/2504.09228/4d91038b-08d1-447d-8037-8ee551148a4c_content_list.json
@@ -0,0 +1,1219 @@
+[
+ {
+ "type": "text",
+ "text": "Learning Occlusion-Robust Vision Transformers for Real-Time UAV Tracking",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "You Wu $^{1\\dagger}$ , Xucheng Wang $^{2\\dagger}$ , Xiangyang Yang $^{1}$ , Mengyuan Liu $^{1}$ , Dan Zeng $^{3}$ , Hengzhou Ye $^{1}$ , Shuiwang Li $^{1*}$",
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "| s | DERIVABLE(qs) |
| l | {T | pmatch(l,T),T ∈ {number, string, boolean}} |
| x | {T | x ≤ n, (n : T) ∈ Γ} |
| (¯p) => e | { (¯p) => T | REACHABLE(DERIVABLE(qe),T)} |
| (e | {T | REACHABLE(DERIVABLE(qe),T)} |
| e ⊙ | {T | ∃S': Γ ↔ e : S ∧ S ⊕ S': T} |
| e( | {R | Γ ↔ e: (¯p) => R} |
| e.a | {S | a ≤ n, Γ ↔ e : T, LOOKUP(T,n) = S} |
",
+ "bbox": [
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+ "page_idx": 11
+ },
+ {
+ "type": "page_number",
+ "text": "171:12",
+ "bbox": [
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+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
+ "bbox": [
+ 339,
+ 81,
+ 907,
+ 98
+ ],
+ "page_idx": 11
+ },
+ {
+ "type": "table",
+ "img_path": "images/a30990f5fbd78a3d5bd03abb5291ed565e72139dbd4b176396fd845291662c23.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Algorithm 2 Our type reachability search algorithm |
| Input: Current type T of some expression e, goal type G |
| Output: Whether G can be reached by extending e |
| 1: function REACHABLE(T, G) |
| 2: if T = G then return true | ▷ The goal type is successfully found |
| 3: if T is marked then return false else mark T | ▷ Type T is marked to avoid cycles |
| 4: for each valid extension step ⌿ from T do |
| 5: S := the resulting type of applying ⌿ on T |
| 6: if PRUNESEARCH(T, G, S) continue | ▷ Prune the search to ensure termination |
| 7: if REACHABLE(S, G) return true | ▷ Recurse to the next round of extension |
| 8: return false | ▷ No suitable extension is found |
",
+ "bbox": [
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+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "The type reachability algorithm, Algorithm 2, implements a depth-first search over this type graph, starting from the current type $T$ , succeeding upon finding goal type $G$ (Line 2), marking any visited types to prevent cycles (Line 3). Then, it proceeds to iterate over all valid extension steps from $T$ (Line 4) and computes the resulting type $S$ after the extension step is applied (Line 5). In the conceptualized type graph, as described in the previous paragraph, this is equivalent to exploring all outgoing edges from $T$ . At Line 7, we proceed to recursively search if $S$ can reach $G$ . If all recursive calls are unsuccessful, the goal type can not be reached (Line 8).",
+ "bbox": [
+ 86,
+ 320,
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+ 437
+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "Some programming languages define self-referential default members, e.g., clone in Java or value0f in TypeScript, which are nullary functions that return a value of the same type as the callee, $(\\mathbf{\\beta})\\Rightarrow T$ for type $T$ . When these members are accessed in functions, higher-order functions can be derived indefinitely. For instance, for a function $f$ with type $(\\mathbf{\\beta})\\Rightarrow S$ , $f.$ value0f has the type $(\\mathbf{\\beta})\\Rightarrow (\\mathbf{\\beta})\\Rightarrow S$ . We therefore need to restrict the type search to a finite set of types to ensure termination. At Line 6 of Algorithm 2, we add a heuristic PRUNESEARCH into the search, which decides where to prune the search process. We develop a simple heuristic based on the results from Gvero et al. [30]. This heuristic prunes exploration of types with higher complexity than goal or source type if they do not contain yet unexplored primitive types, thus preventing exploration of arbitrarily complex types. The details of this heuristic are presented in Appendix A.3. While ensuring termination, our heuristic leads to incompleteness and the potential rejection of well-typed expressions. However, this effect is less pronounced in practical usage, as only highly complex (thus less realistically used) types are avoided.",
+ "bbox": [
+ 86,
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+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "We proceed to prove the soundness of Algorithm 2 below.",
+ "bbox": [
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+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "LEMMA 3. The type search in Algorithm 2 is sound, i.e., for any expression $e$ with $\\Gamma \\vdash e : T$ , if REACHABLE(T,G) holds, then there exists a sequence of extensions $y$ such that $\\Gamma \\vdash e \\circ y : G$ .",
+ "bbox": [
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+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "Proof. By the design of Algorithm 2, if REACHABLE $(T,G)$ returns true, there is a sequence of $n$ recursive calls to REACHABLE $(T_i,G)$ , with $T_0 = T$ and REACHABLE $(T_n,G) = \\text{true}$ . Each $T_i$ ( $i > 0$ ) is derived because some extension $\\diamond_i$ is applicable to $T_{i-1}$ based on the typing rules of $L_B$ . We then convert each $\\diamond_i$ to its concrete, textual version $\\spadesuit_i$ . This representation includes the required well-typed parameters of $\\spadesuit_i$ (i.e., for binary operators and non-nullary functions), which are constructed using literals. Finally, we construct $y$ as $\\spadesuit_1 \\circ \\ldots \\circ \\spadesuit_n$ .",
+ "bbox": [
+ 86,
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+ ],
+ "page_idx": 12
+ },
+ {
+ "type": "text",
+ "text": "Note that using any pruning heuristic at Line 6 of Algorithm 2 preserves soundness, which in turn is sufficient to preserve the required prefix property, as defined in Definition 2. We can conclude that the two-tiered search algorithm soundly determines whether the desired target type can be derived from some partial input. Therefore, we conclude that $A_{e} \\downarrow T$ and $A_{e}$ are prefix automata that parse a subset of well-typed expressions in $L_{B}$ .",
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+ "text": "Type-Constrained Code Generation with Language Models",
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+ "text": "COROLLARY 4. If REACHABLE( DERIVABLE(q), G) holds for any $q \\in \\gamma(I_e, s)$ of a partial expression $s$ , then there exists a suffix $s'$ such that $\\Gamma \\vdash s \\circ s': G$ .",
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+ "text": "Proof. This conclusion follows directly from Lemmas 2 and 3.",
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+ "text": "LEMMA 5. The language parsed by $A_e \\downarrow T$ is thus a subset of the expressions of $L_B$ of type $T$ , i.e., $L(A_e \\downarrow T) \\subseteq \\{s \\mid \\Gamma \\vdash s : T\\}$ . Since $A_e$ recursively involves $A_e \\downarrow T$ , the language parsed by $A_e$ is also a subset of well-typed expressions of $L_B$ , i.e., $L(A_e) \\subseteq \\{s \\mid \\exists T : \\Gamma \\vdash s : T\\}$ .",
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+ "text": "3.5 Prefix Automata for Statements",
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+ "text": "We define the remaining automata to capture the complete language $L_{B}$ . The statement automaton is defined recursively as $A_{s} \\coloneqq A_{\\mathrm{DECL}} \\cup A_{\\mathrm{EXPR}} \\cup A_{\\mathrm{RET}} \\cup A_{\\mathrm{BLOCK}} \\cup A_{\\mathrm{FUN}} \\cup A_{\\mathrm{ITE}}$ . The declaration automaton $A_{\\mathrm{DECL}} \\coloneqq A_{\\mathrm{let} x: T}$ ; captures undefined variable names $x$ by accepting all strings, except for existing identifiers. This automaton is a prefix automaton since an accepting state can always be reached by appending characters to the declared identifier. The return statement automaton is $A_{\\emptyset}$ when outside a function and restricts the parsed expression to the return type of the surrounding function otherwise. The remaining automata are mainly concatenations of previously defined automata and recursive invocations of $A_{s}$ , with small variations detailed in Appendix A.5.",
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+ "text": "Tracking Type Environments. Generally, we follow the typing rules in Figure 6. Identifiers are passed on through all state transitions, matching the rule SEQ, where the type environment of consecutive statements needs to be compatible. However, in the cases of BLOCK, ITE and FUN, we discard the local type environment after parsing, matching the respective typing rules. In FUN additionally, the function signature and parameters are added into the type environment of the function body automaton, and the function signature in the environment of subsequent statements.",
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+ "text": "Guaranteeing Return Types. When parsing the body of a function, the transition function of the function automata $A_{\\mathrm{FUN}}$ maintains information about the declared return type and the encountered return statements (if any). $A_{\\mathrm{FUN}}$ only accepts states where all return values match the declared return type and all execution paths inside the function body return, following $L_B$ 's typing rules in Figure 7. If the current generated statements do not return in all execution paths, another statement is forced to be generated. Since we can always express the requested type through literals, a correct return statement can always be generated and the prefix automaton property is not violated.",
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+ "text": "The described rules are straightforward to implement without violating the prefix property as all restrictions are derived only from already parsed input, e.g., the already defined identifiers or the previously declared function return type. We can therefore deduce that the statement automaton is a prefix automaton. Moreover, the automaton accepts all valid statements of $L_{B}$ , with the exception of well-typed expressions rejected by $A_{e}$ . Therefore the parsed language is a subset of $L_{B}$ .",
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+ "text": "LEMMA 6. With $A_M \\coloneqq A_{\\overline{s}}$ it holds that $A_M$ is a prefix automaton and $L(A_M) \\subseteq L_B$ .",
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+ "text": "4 Extension to TypeScript",
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+ "text": "We extend our completion engine described in §3 to handle a core subset of modern TypeScript. In this section, we selectively discuss the implementation of several interesting TypeScript features. We provide a comprehensive list of supported and unsupported TypeScript features in Appendix B.",
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+ "text": "Constant Variable Declarations. In addition to variable declaration using let, TypeScript supports constant declarations using const. This defines immutable identifiers. We thus additionally track mutability of each identifier in the type environment and disallow applying the assignment operator to immutable identifiers.",
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+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
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+ "text": "Arrays. We add support for array type annotation, parsing array expressions, and reading from and assigning to array fields. In array expressions, we enforce that all array elements have the same type. Moreover, array types introduce another dimension of type nesting. Therefore we adapt the type reachability pruning heuristic to handle this additional dimension to ensure termination.",
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+ "text": "**Loops.** TypeScript supports various loop constructs, including for, while, do-while, and for...of loops. These are implemented mostly as variations of the statement block parser. The for...of loop uniquely constrains the right-hand side of the ..of operator to an array of any type. To adapt the type search, we introduce a generic array type $\\bullet[\\]$ , which matches any array type. For example, both types number[] and string[] match $\\bullet[\\]$ in Line 2 of Algorithm 2.",
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+ "text": "Additional Operators and Types. We add several arithmetic and logic operators, such as modulo $\\%$ , exact equality $= = =$ , logical or $||$ , and the ternary operator $\\text{?}$ :. To handle these operators, we add additional edges to the type search graph. Moreover, we add support for post- and prefix operators such as -- and ++, which are only valid extensions to mutable expressions.",
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+ "text": "Operator Precedence. TypeScript defines an operator precedence, which determines the implicit grouping of expressions. For example $1 + 2$ . toString() is parsed as $1 + (2$ . toString()) . We adapt our expression parsing algorithm in two places to handle operator precedences. First, in the expression automaton, we leverage the knowledge about previously parsed extensions to determine the implicit grouping and thus where the next operator is applied. For example, for state $q^{1} + 2$ , the member access extension $n$ is applied to 2, as opposed to $1 + 2$ . Second, we adapt the type search in Algorithm 2. Concretely, we ensure that only extensions that can be validly applied based on operator precedence are iterated over. For this, we track the operator precedence of previously parsed extensions and extensions considered during the traversal of the type graph and omit operators in Line 5 that violate operator precedence.",
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+ "text": "Global Identifiers and Imports. In TypeScript, many identifiers are defined globally and available in any execution. These global identifiers are incorporated by initializing the type environment of the program automaton accordingly. Identifiers such as Math introduce additional types, which we additionally implement. We also model the import of the crypto library using require.",
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+ "text": "Polymorphic Built-In Members. The TypeScript LOOKUP implementation defines a few polymorphic members for built-in types. For example, for array $\\times$ of type $T[]$ , $x$ . map(f) takes a callback function $f$ and returns a new array $[f(x[0]), f(x[1]), \\ldots]$ . If $f$ has type $(T) => P$ , the returned array has type $P[]$ . Here $P$ is a type parameter, which is instantiated by matching the type of the passed function to the type pattern.",
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+ "text": "We support such polymorphisms by adapting the type search. We track type patterns and enforce that type parameters are instantiated before the goal type is reached. We then continue the search from the instantiated version. In the map example, when searching completions of x.map, we first search for functions that instantiate the type parameter, and then continue the search from the instantiated type. When anonymous functions are generated as call parameters, we enforce that the function matches the searched type pattern.",
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+ "text": "Type Annotations. TypeScript is designed to be flexible, allowing many type annotations to be omitted when they can be automatically inferred. We generally support this, such as inferring types from initial values. However, it can lead to unexpected types when annotations are omitted, often confusing even experienced developers [47, 48]. Moreover, in the context of LLM-based code generation, having more type annotations can provide valuable information for both the model and our type-constraining algorithms. We have identified three situations where generated code often fails to compile without type annotations, prompting us to enforce them. First, we require",
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+ "text": "Type-Constrained Code Generation with Language Models",
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+ "text": "annotations for all function parameters and return types. Second, all variable declarations must either have a type annotation or be initialized with a value. Third, we enforce type annotations for the first parameter of anonymous functions used as callbacks in the polymorphic built-in member reduce. These constraints trade off practical correctness with theoretical language completeness.",
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+ "text": "5 Experimental Evaluation",
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+ "text": "We present an extensive evaluation of our type constraining approach on a variety of tasks and models. We outline our experimental setup (§5.1), evaluate the impact on compilation errors and functional correctness (§5.2), perform runtime analysis (§5.3), and present case studies (§5.4).",
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+ "text": "We now outline our main evaluation setup, covering implementation, evaluated tasks, considered models, compared methods, and metrics. We provide further setup details and hyperparameter choices in Appendix B.",
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+ "text": "Implementation. Our implementation is written in Python and contains 11249 lines of code. To ensure robust implementation, we built a large set of around four hundred unit tests and frequently compared the behaviors of our implementation with the official TypeScript compiler [42].",
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+ "text": "Tasks and Benchmarks. We evaluate three relevant tasks of code generation:",
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+ "- Synthesis: Given a natural language task description and a function header, the task is to generate a solution from scratch.",
+ "- Translation: Given a function written in Python and the header of an equivalent TypeScript function, the task is to generate the body of the equivalent function in TypeScript.",
+ "- Repair: Given a natural language task description, a non-compilable solution, the corresponding compiler error, and the function header, the task is to restore functionality of the flawed solution by resolving the compilation error."
+ ],
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+ "text": "The benchmarks for these tasks are based on TypeScript-translated tasks from HumanEval [12] and MBPP [5], contained in the MultiPL-E dataset [13], with 159 and 384 instances each. We observe that success in generating valid code for the same sample can vary depending on the random seed used. To obtain more comprehensive results on the small HumanEval dataset, we generate each sample 4 times with different seeds and aggregate the outcomes. In MBPP, we generate each sample once. For Repair, we collect all non-compiling programs from the unconstrained synthesis task for all models, resulting in 292 and 248 instances for HumanEval and MBPP each.",
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+ "text": "Models. We use 6 different open-weight LLMs, covering 3 LLMs of varying parameter sizes from the same model family and 4 models of a similar size from different model families: the Gemma 2 model family with 2B/9B/27B parameters [64], DeepSeekCoder 33B (abbreviated as DSCoder 33B) [28], CodeLlama 34B [59], and Qwen2.5 32B [73]. For all evaluated LLMs we choose the instruction-tuned variants, which are fine-tuned to follow instructions in a chat-style interaction, such that they adequately attempt to resolve the presented tasks.",
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+ "text": "Compared Methods. We run unconstrained LLM sampling, reported as Vanilla. We measure the upper bound improvement of prior syntactic constraining methods [8, 57, 66] by assuming that all syntactically incorrect instances generated by Vanilla could be compiled under syntactic constraining. We refer to this improvement as idealized Syntax. We separately sample using type-constrained decoding based on our completion engine introduced in §3 and §4, and report it as Types. Due to the size and complexity of the full TypeScript compiler, featuring over 427,105 lines of code in 698 files [42], our extension does not cover all features of TypeScript. We therefore",
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+ "text": "171:16",
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+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
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+ {
+ "type": "table",
+ "img_path": "images/9fdda853962702543e4b74b4a4950ce8a8bb257496566563d2784d4fed07cc6e.jpg",
+ "table_caption": [
+ "Table 2. Number of instances with compiler errors in unconstrained generation (Vanilla), idealized syntax-only constraining (Syntax), and our proposed type constraining (Types). Type constraining reduces compiler errors by $74.8\\%$ and $56.0\\%$ in the synthesis of HumanEval and MBPP problems respectively, compared to only $9.0\\%$ and $4.8\\%$ ideal improvement on the two datasets respectively through syntax-only constraining."
+ ],
+ "table_footnote": [],
+ "table_body": " | Vanilla | Types |
| (a) | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split() | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split(' ') |
| (b) | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } // No return } | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } return 1; } |
| (c) | // insert a delimiter between every element return nums.reduce( (acc, curr, index) => { acc.pushurr); return acc; }, []) | // insert a delimiter between every element return nums.reduce( (acc: number[] , num, index) => { acc.pushurr); return acc; }, []) |
",
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+ {
+ "type": "text",
+ "text": "Figure 9. Three examples illustrating the effect of type-constrained sampling. Left are unconstrained generations with problematic tokens highlighted in red, and right are type-constrained results with corrected tokens highlighted in green, adapted for clarity. In (a), Gemma 2 2B attempts to call split, missing required arguments. In (b), DeepSeekCoder 33B attempts to complete a function without a guaranteed return. The issue is resolved by forcing generation of another statement after the main loop. In (c), Gemma 2 9B calls reduce with an anonymous function without type annotation. This leads to an incorrect type inference for the first parameter. The issue is solved by guiding the model to add type annotation.",
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+ "type": "text",
+ "text": "Missing Return Statement. In Figure 9b, to complete function largest_divisor, the model must compute a straightforward divisor loop. DeepSeekCoder 33B Instruct [28] implements a correct loop, but does not guarantee returning a value in every execution path. When the return statement in the loop is never executed, e.g., for negative inputs, the function thus returns undefined, violating the type rules. Our method detects this issue and forces the generation of another statement in the function body, resulting in a correct fallback return statement.",
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+ "type": "text",
+ "text": "Incorrect Type Inference. In Figure 9c, the task is to insert a delimiter between every element in an array. Gemma 2 9B solves this with the reduce function. This generic function accepts two arguments; first, a callback function that is called consecutively for every element in the array and accumulates a result, second, an initial value for the callback function. The type of the accumulator of the callback is derived implicitly from the second argument, which is an empty array in the given example. TypeScript infers special type never[] for the empty array, disallowing inserting curr of type number through push. Therefore, the program fails to compile. This issue is a well-known limitation of the TypeScript compiler, often confusing even expert developers [47, 48]. Our method resolves it by enforcing adequate type annotation on the first argument of the callback function.",
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+ "type": "text",
+ "text": "6 Discussion",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Our general type constraining approach, backed by strong experimental results, opens exciting avenues for future research, which we discuss below.",
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+ "text": "Implementation Effort. Developing a completion engine for a target programming language currently requires manual efforts. However, we expect that the involved effort to adopt our method to other languages will be reduced significantly, as many features transfer from our implementation for $L_{B}$ and TypeScript. Moreover, we believe that, due to the huge impact on LLM's code generation, the effort will pay off. Future programming language developers may consider generally writing",
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+ "text": "171:20",
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+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
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+ {
+ "type": "code",
+ "sub_type": "code",
+ "code_caption": [],
+ "code_body": "function sort_threel(number[]，r：number[]）:number[]{ \nfor（let $\\mathrm{i} = 0$ ；i<1.length; $\\mathrm{i + + }$ ）{ \nr.push(l[i].toString().slice(0,3).concat(l[i].ToString().split())'.split').reverse() .join(')).split''.reverse().join('').ToString() $^+$ l[i].ToString().slice(3).split')…",
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+ "text": "Figure 10. Complications errors remain when the model does not terminate after a corrected token. In this example for synthesis on the HumanEval task #33, CodeLlama 34B is steered away from accessing non-existing member .sort and instead accesses .string.",
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+ "type": "text",
+ "text": "their compilers as an incremental completion engine, which additionally enables automatic adoption for constrained code generation, besides conventional grammar parsing and type checking.",
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+ "text": "Broader Application to More Complex Tasks and Stronger LLMs. Stronger LLMs, such as the latest OpenAI models [33], may make fewer typing errors on the HumanEval and MBPP datasets. Our evaluation results in Table 2 also demonstrate that compilation errors decrease with increasing model size for the Gemma family. However, recent findings showed that currently, even the strongest LLMs struggle with generating compilable code for more complex coding tasks, stricter typing rules, and low-resource languages (e.g., new DSLs). Gusanidas [29] evaluated various state-of-the-art LLMs on difficult code synthesis tasks in Rust, reporting compilation error rates of $18\\%$ for OpenAI o1-mini [33], $39\\%$ for DeepSeek R1 [15] and $27\\%$ for Anthropic's Claude 3.5 Sonnet [2]. For OCaml and Haskell, which are sparsely represented in LLMs' training data, the error rate is even higher at $40\\% - 60\\%$ for all models, matching a trend of worse performance on low-resource languages [24, 36]. Pan et al. [54] compiled a large dataset of code translation and found $44.3\\%$ of GPT-4-generated code to contain compilation errors. Similarly, Shetty et al. [61] report around $25\\%$ compilation errors for C-to-Rust translation using OpenAI o1 models. Our type constraining approach is broadly applicable to all these scenarios and our work presents a promising proof of concept. Future work can consider building upon our approach to address these challenges.",
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+ "type": "text",
+ "text": "Constrained decoding in general requires access to the next-token probability distributions produced by LLMs. Currently, commercially available black-box LLM APIs only return sampled tokens and do not offer complete next-token distributions. A possible solution is to integrate our method into the backend of model providers, as was recently implemented for guaranteeing adherence to JSON Schemas [3, 50].",
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+ "text": "Remaining Compiler Errors. We observe that, even though constrained decoding guarantees a valid result upon termination, a considerable amount of compilation errors remain due to non-termination within the token or time limit. We find this to be caused by generation loops, entered when generation is amended by constraints and the LLM is unable to recover. An example is depicted in Figure 10, where CodeLlama 34B tries to access the invalid member sort on an expression of type number. Future work may add additional constraints to force stopping such unconstructive loops and steer the model more strictly, e.g., by limiting the complexity of generated expressions.",
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+ "text": "7 Related Work",
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+ "text": "Code Language Models. Recently, LLMs have gained traction for diverse coding tasks such as code synthesis, repair, or translation [35]. These models are typically trained on datasets containing billions to trillions of tokens and have billions of parameters, with both factors contributing to improved performance in code-related benchmarks [28, 46, 59, 64]. Meanwhile, LLMs are well known to frequently make mistakes [32, 58], and, as we show in this work, even state-of-the-art open-weight models with over 30 billion parameters frequently make errors in code generation.",
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+ "text": "Improving Language Model Accuracy. Apart from constrained decoding, three primary approaches have been proposed to enhance the accuracy of language models on code tasks: fine-tuning, retrieval augmentation (RAG), and compiler or execution feedback. Fine-tuning adapts the model weights based on specifically collected training data. This process is highly resource intensive [65, 70]. RAG provides the model with additional context based on a database or related code snippets [6, 57]. Compiler and execution feedback is only available after completing the model generation and requires resampling [16, 34, 69]. However, constrained decoding is orthogonal to these methods and, as indicated by Poesia et al. [57] and our experimental results, combining constrained decoding with RAG or compiler feedback additionally improves model performance.",
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+ "text": "Constrained Decoding. Prior work on constrained decoding failed to achieve strong results due to its limitation to syntactic language features. Constraining to context-free languages has been explored extensively in recent work [7, 8, 57, 71]. Simple context-sensitive syntactic features, such as the space indentation in Python and the scope markers in Go have also been implemented [41, 66]. As demonstrated in §5, however, syntax errors on average account for only $6\\%$ of compilation errors in recent code models. The rarity of syntax errors significantly reduces the potential of leveraging them for improvements in code correctness. Meanwhile, our type-constrained decoding more than halved compilation errors.",
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+ "text": "Type Systems for Code Synthesis. Previous work that leveraged type systems for code synthesis was confined to specialized settings and unable to constrain general, complex program generation. Poesia et al. [57] proposed using known column names to guide SQL query generation. Gvero et al. [30] employed a search on the type graph for function call completion. Agrawal et al. [1] leverage language-server-generated type annotations for object member accesses. Blinn et al. [11] use language-server-derived type information to provide additional context to the LLM, but not to enforce hard constraints. Additionally, type constraints have been used to direct code synthesis based on specialized search procedures [22, 56, 69]. However, these methods are not compatible with LLM-based code generation. This limits their ability to exploit the powerful natural language and general-purpose capabilities of LLMs.",
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+ "text": "8 Conclusion",
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+ "text": "In this work, we explored how type systems in programming languages can be used to guide language models during decoding. Concretely, we design and implement prefix automata to perform type constraining for a foundational simply typed language and then extend it to the popular language TypeScript. We extensively evaluate the impact of using such constraints for code synthesis, translation, and repair and observe that we more than halve compilation errors on a diverse set of models and consistently increase functional correctness. We further explore qualitatively how the constraining positively impacts code generation. We conclude that such type constraining should be implemented for more programming languages, and has the potential to generally improve code generation in many domains.",
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+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
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+ "text": "Artifact Availability",
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+ "text": "The artifact for this paper, including source code, datasets, and reproductions scripts, is available on GitHub (https://github.com/eth-sri/type-constrained-code-generation) and Zenodo [45].",
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+ "text": "We would like to thank the anonymous reviewers for their in-depth and constructive feedback, and the artifact reviewers for their feedback on our artifact accessibility.",
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+ "[73] An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, et al. 2024. Qwen2.5 Technical Report. arXiv Preprint (2024). https://doi.org/10.48550/arXiv.2412.15115",
+ "[74] Quanjun Zhang, Chunrong Fang, Yang Xie, Yuxiang Ma, Weisong Sun, Yun Yang, and Zhenyu Chen. 2024. A Systematic Literature Review on Large Language Models for Automated Program Repair. arXiv Preprint (2024). https://doi.org/10.48550/arXiv.2405.01466"
+ ],
+ "bbox": [
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+ "page_idx": 25
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+ {
+ "type": "text",
+ "text": "A Detailed Prefix Automaton Definitions",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "In this section, we provide more detailed definitions and analysis of the various automata for $L_{B}$ .",
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+ "type": "text",
+ "text": "A.1 Base Automata",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We now provide detailed definitions for the base prefix automata introduced at the end of §3.2: union, concatenation, Kleene-Star, and terminal.",
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+ "type": "text",
+ "text": "Union. For the union $A_X \\cup A_Y$ , we define the resulting sets of initial states and accepting states as $I \\coloneqq I_X \\cup I_Y$ and $F \\coloneqq F_X \\cup F_Y$ , respectively. The transition function is defined as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\delta (q, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q, c) & \\text {i f} q \\in Q _ {X} \\\\ \\delta_ {Y} (q, c) & \\text {i f} q \\in Q _ {Y}. \\end{array} \\right.\n$$\n",
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+ "text": "To show that the language parsed by this automaton is indeed the union $L(A_{X} \\cup A_{Y}) = L(A_{X}) \\cup L(A_{Y})$ , we employ a short helper lemma, which can be shown inductively.",
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+ "type": "text",
+ "text": "LEMMA 7. The set of the reachable states from a set of states $\\mathbf{q}$ is equal to the union of reachable states from each state in $\\mathbf{q}$ , i.e., $\\gamma (\\mathbf{q},s) = \\bigcup_{q\\in \\mathbf{q}}\\gamma (q,s)$ .",
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+ "type": "text",
+ "text": "Since the states are distinct and we merely combine the transition functions of both automata, using the lemma, we can quickly see that the language parsed is indeed the union. Moreover, if both $A_{X}$ and $A_{Y}$ are prefix automata, this also holds for $A_{X} \\cup A_{Y}$ .",
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+ "type": "text",
+ "text": "Concatenation. For the concatenation automaton $A_{XY}$ , we define $I \\coloneqq I_X$ , $F \\coloneqq F_Y$ , and the transition function as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\delta_ {X Y} (q, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q, c) & \\text {i f} q \\in Q _ {X} \\backslash F _ {X} \\\\ \\delta_ {X} (q, c) \\cup \\delta_ {Y} (I _ {Y}, c) & \\text {i f} q \\in F _ {X} \\\\ \\delta_ {Y} (q, c) & \\text {i f} q \\in Q _ {Y}. \\end{array} \\right.\n$$\n",
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+ "text": "Informally, concatenation preserves the parsing behavior of both $A_{X}$ and $A_{Y}$ in their respective states. When $A_{XY}$ reaches an accepting state of $A_{X}$ and receives another input character, it either remains in $A_{X}$ or transitions to $A_{Y}$ , as defined in the second case of $\\delta_{XY}$ . Essentially, this maintains outgoing edges from accepting states in $A_{X}$ while adding edges from these accepting states to initial states of $A_{Y}$ .",
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+ "type": "text",
+ "text": "It follows from a similar argument that $L(A_{XY}) = L(A_X) \\circ L(A_Y)$ , where $L(A_X) \\circ L(A_Y)$ is defined as $\\{s_X \\circ s_Y \\mid s_X \\in L(A_X), s_Y \\in L(A_Y)\\}$ . We first show $L(A_{XY}) \\subseteq L(A_X) \\circ L(A_Y)$ . Due to (P1), we can always split any $s \\in L(A_{XY})$ into $s_X$ that extends from $I_X$ to $F_X$ and $s_Y$ that extends from $I_Y$ to $F_Y$ . Then $s_X \\in L(A_X)$ and $s_Y \\in L(A_Y)$ . For $L(A_X) \\circ L(A_Y) \\subseteq L(A_X \\circ A_Y)$ , we pick any $s_X \\circ s_Y$ from $L(A_X) \\circ L(A_Y)$ and parse it using $A_{XY}$ . We observe that it will first traverse from $I_X$ to $F_X$ consuming $s_X$ , and then transition through $I_Y$ to $F_Y$ by consuming $s_Y$ .",
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+ "type": "text",
+ "text": "Moreover $A_{XY}$ is a prefix automaton, if $A_{X}$ and $A_{Y}$ are prefix automata and $L(A_{Y}) \\neq \\emptyset$ . Since $A_{X}$ is a prefix automaton, we can reach $F_{X}$ from any state in $Q_{X}$ . From $F_{X}$ we additionally reach",
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+ {
+ "type": "page_number",
+ "text": "171:26",
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+ "page_idx": 25
+ },
+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
+ "bbox": [
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+ "page_idx": 25
+ },
+ {
+ "type": "text",
+ "text": "$I_{Y} \\subseteq Q_{Y}$ . Since $A_{Y}$ is a prefix automaton, we can reach $F_{Y}$ for any state in $Q_{Y}$ . This construction is a prefix automaton only if $I_{Y} \\neq \\emptyset$ , which, due to the prefix property, is equivalent to $L(A_{Y}) \\neq \\emptyset$ .",
+ "bbox": [
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+ "page_idx": 26
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+ {
+ "type": "text",
+ "text": "Kleene-Star. We define the Kleene-Star automaton $A_{\\overline{X}}$ that parses indefinite repetitions of words accepted by $X$ . First, we consider all initial states as final states, i.e., we ensure $I_X \\subseteq F_{\\overline{X}}$ . Then we add transitions to the transition function $\\delta_X$ from the final states $F_X$ back to the initial states $I_X$ .",
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+ "page_idx": 26
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\delta_ {\\overline {{X}}} (q _ {X}, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q _ {X}, c) & \\text {i f q \\not \\in F _ {X}} \\\\ \\delta_ {X} (q _ {X}, c) \\cup \\delta (I _ {X}, c) & \\text {i f q _ {X} \\in F _ {X}}. \\end{array} \\right.\n$$\n",
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+ "type": "text",
+ "text": "We can quickly see that $L(A_{\\overline{X}}) = \\{\\overline{s} \\mid s \\in L(A_X)\\}$ , with the same argument as the concatenation automaton. Additionally, because the initial states are accepting, the empty word (zero repetitions) is in $L(A_{\\overline{X}})$ . We similarly see that this is a prefix automaton if $A_{X}$ is a prefix automaton. Note that here $L(A_{X}) \\neq \\emptyset$ is not required. This is because if $L(A_{X}) \\neq \\emptyset$ , then $A_{\\overline{X}} = A_{X} = A_{\\emptyset}$ , which is still a prefix automaton.",
+ "bbox": [
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+ "type": "text",
+ "text": "Terminals. The terminal automaton $A_{\\mathsf{S}}$ parses exactly the terminal S. They accept the usual alphabet $\\Sigma$ and feature the states $Q \\coloneqq \\{q_{\\mathsf{s}} \\mid \\mathsf{s} \\text{ is a suffix of S}\\}$ , $F \\coloneqq \\{q_{\\varepsilon}\\}$ , $I \\coloneqq \\{q_{\\mathsf{S}}\\}$ . The transition function $\\delta$ is defined as follows:",
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+ "page_idx": 26
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\delta (q _ {s}, c) := \\left\\{ \\begin{array}{l l} \\{q _ {s ^ {\\prime}} \\} & \\text {i f c \\circ s ^ {\\prime} = s} \\\\ \\varnothing & \\text {o t h e r w i s e .} \\end{array} \\right.\n$$\n",
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+ "type": "text",
+ "text": "Clearly $A_{\\mathfrak{S}}$ is a prefix automaton. We can show inductively that for any $s: \\gamma(q_{s}, s') = \\{q_{\\varepsilon}\\} \\Longleftrightarrow s = s'$ , and thus $L(A_{\\mathfrak{S}}) = \\{\\mathfrak{S}\\}$ . With a simple modification, we introduce $A_{\\mathfrak{s}}^{W}$ , where $W$ denotes whitespace characters. The transition function is defined as $\\delta(q_{\\mathfrak{s}}^{W}, c) := \\{q_{\\mathfrak{s}}^{W}\\}$ if $c \\in W$ ; otherwise, $\\delta(q_{c \\circ s}^{W}, t) := \\{q_{\\mathfrak{s}}^{W}\\}$ . This allows arbitrary whitespace before parsing $s$ . This is how we implement syntactic indifference to whitespace between terminals.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "A.2 Expressions",
+ "text_level": 1,
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Expressions are parsed using recursive automatons as introduced in §3.4. In this part of the Appendix, we describe in more detail how information is passed between states.",
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+ {
+ "type": "text",
+ "text": "Notation. In the following, we will implicitly assume that $\\delta(q, c) = \\emptyset$ if not explicitly defined otherwise, making notation more concise. For any state, we access the following information through dot notation or the special notation on the state, which we assume is passed to subsequent states through the transition function (unless otherwise stated). This information is alternatively passed through to entire automata in composite automata, e.g., in $A_{XY}$ from $A_X$ to $A_Y$ .",
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+ "list_items": [
+ "- $q \\in F_X$ : Whether state $q$ is an accepting state of the automaton $A_X$ .",
+ "- $q. \\Gamma$ : The type environment based on state $q$ currently being parsed.",
+ "- $q$ .LHS: The left-hand side expression of an extending expression represented by state $q$ , i.e., when extending $X$ with $Y$ and currently parsing $q_{Y}$ , then $q_{Y}$ .LHS = $X$ .",
+ "- $q$ .TYP: The described type of the last coherent expression that this state belongs to. This is only defined for accepting states. Generally, we ensure that when some expression $e$ was parsed, the corresponding state $q_{e}$ has attribute $q_{e}$ .TYP such that $q_{e} \\Gamma \\vdash e : q_{e}$ .TYP.",
+ "- $q \\downarrow T$ : Type $T$ to which state $q$ is constrained."
+ ],
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+ "type": "text",
+ "text": "When accessing the properties of $A$ , we access the property of the current state of the automaton $q \\in Q$ , e.g., $A. \\mathrm{LHS} = q. \\mathrm{LHS}$ . For parsed automata, the current state is the final, accepting state. The TYP attribute expresses the type of the expression parsed so far. In expression states $q$ , we leverage the LHS to accurately determine $q. \\mathrm{TYP}$ .",
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+ {
+ "type": "header",
+ "text": "Type-Constrained Code Generation with Language Models",
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+ {
+ "type": "page_number",
+ "text": "171:27",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} q _ {\\mathrm {S T R . T Y P}} := \\text {s t r i n g} \\quad q _ {(e) . \\mathrm {T Y P}} := A _ {e}. \\mathrm {T Y P} \\\\ q _ {\\text {N U M}}. \\text {T Y P} := \\text {n u m b e r} \\quad q _ {\\odot e}. \\text {T Y P} := R, \\text {f o r} q _ {\\odot e}. \\text {L H S}. \\text {T Y P} = S, A _ {e}. \\text {T Y P} = T \\text {a n d} S \\odot T: R \\\\ q _ {\\text {B O O L . T Y P}} := \\text {b o o l e a n} \\quad q _ {(\\overline {{e}}). \\text {T Y P}} := T, \\text {f o r} q _ {(\\overline {{e}}). \\text {L H S . T Y P}} = (\\overline {{p}}) \\Rightarrow T \\\\ q _ {x. \\mathrm {T Y P}} := T \\text {w h e r e} q _ {x}. \\Gamma \\vdash x: T \\quad q. n. \\mathrm {T Y P} := T, \\text {f o r L O O K U P} (q. n. \\mathrm {L H S . T Y P}, n) = T \\\\ q _ {(\\overline {{p}}) = > e. T Y P} := \\left(A _ {\\overline {{p}}} ^ {-}. T Y P\\right) = > A _ {e}. T Y P \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "Unrestricted Expressions. The left-hand side of the currently parsed expression is used in the definition of automata for three extending expressions; arithmetic operators, function call, and member access. The arithmetic operator automaton constrains its states to those with valid operators, i.e.:",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nA_{\\odot e}:= \\bigcup_{\\exists R:A_{\\odot e}.LHS.TYP\\odot T = R}A_{\\odot}(\\circ A_{e}\\downarrow T).\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "For function call, the automaton is only valid if the left-hand side is a function, and accepts only the valid signature.",
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+ {
+ "type": "equation",
+ "text": "\n$$\nA _ {(\\overline {{e}})} := \\left\\{ \\begin{array}{l l} A _ {(} \\circ (A _ {\\overline {{e}}} \\downarrow A _ {\\overline {{p}}}. \\mathrm {T Y P}) \\circ A _ {)} & \\text {i f} A _ {(\\overline {{e}}). \\mathrm {L H S . T Y P}} = (\\overline {{p}}) \\Rightarrow T \\\\ A _ {\\emptyset} & \\text {o t h e r w i s e .} \\end{array} \\right.\n$$\n",
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+ {
+ "type": "text",
+ "text": "Finally, the member access automaton is a union of the automata that parses the attributes of the left-hand side expression. Or formally,",
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+ {
+ "type": "equation",
+ "text": "\n$$\nA_{\\cdot n}:= \\bigcup_{\\exists T:\\text{LOOKUP}(A_{\\cdot n}.LHS.TYP},m) = T}A_{\\cdot \\mathfrak{m}}.\n$$\n",
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+ {
+ "type": "text",
+ "text": "Type-Restricted Expressions. The type-restricted versions of the automata are covered by the definitions presented in §3.4. We therefore do not separately list them here.",
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+ {
+ "type": "text",
+ "text": "A.3 Pruning the Type Search",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We now present our heuristic for pruning the type search recursion from the prefix automaton for type-constrained expressions in §3.4, i.e., our implementation of PRUNESEARCH at Line 6 of Algorithm 2. The heuristic is based on the complexity and novelty of candidate types to explore.",
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+ "type": "text",
+ "text": "Based on the assumptions about the lookup function and the extension expressions in §3.1, we observe a restriction in the reachable types by extensions: from any given type, we reach itself, result types of arithmetic operators via op, return types through CALL, and member types through MEMBER. A higher-order type $(\\cdot) \\Rightarrow T$ does not allow access to types not reachable from $T$ . Consequently, we avoid exploring such higher-order types unless the target type is of higher order, or the higher-order type offers novel, yet unexplored types. For instance, in Figure 11, the type $(\\cdot) \\Rightarrow$ number is not explored, because it is more complex than both the initial and goal types, number and string, and does not contain any unexplored type. Meanwhile, $(\\cdot) \\Rightarrow$ string is explored, as it contains a novel string type.",
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+ "type": "text",
+ "text": "To formalize this understanding, we introduce the concepts about the depth and root types of a given type, denoted as $\\text{DEPTH}$ and $\\text{ROOT}$ , respectively. $\\text{DEPTH}$ measures the complexity of a type, specifically the order of a function, while $\\text{ROOT}$ returns all types of minimal depth (e.g., string, number, and boolean) that constitute a higher-order type. They are defined as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\operatorname {D E P T H} (T) := \\left\\{ \\begin{array}{l l} \\operatorname {D E P T H} (S) + 1 & \\text {i f} T = (\\overline {{p}}) \\Rightarrow S, \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\qquad \\operatorname {R O O T} (T) := \\left\\{ \\begin{array}{l l} \\operatorname {R O O T} (S) & \\text {i f} T = (\\overline {{p}}) \\Rightarrow S, \\\\ \\{T \\} & \\text {o t h e r w i s e .} \\end{array} \\right.\n$$\n",
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+ "type": "text",
+ "text": "We leverage DEPTH and ROOT to implement PRUNESEARCH $(T,G,S)$ for a current type $T$ , a goal type $G$ , and a type $S$ after an extension is applied on $T$ . In general, if $G$ is not directly accessible",
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+ {
+ "type": "page_number",
+ "text": "171:28",
+ "bbox": [
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+ "page_idx": 27
+ },
+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
+ "bbox": [
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+ ],
+ "page_idx": 27
+ },
+ {
+ "type": "image",
+ "img_path": "images/e4f0d79317e2cd79bc15fc30c4d4aeea45c8d0e676e0e7d6a6cc2bb0c53bb505.jpg",
+ "image_caption": [
+ "Figure 11. An example search through the graph for type reachability, starting from $T =$ number with the goal string, e.g., after parsing let x : string; $x = 1$ . States and edges along the final path are marked in green and explored nodes in blue. The () => number node is not explored, as complex types are avoided by our heuristic. The node () => string is explored as it enables reaching new type string."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "text",
+ "text": "from $T$ , it will also not be accessible from expressions with the same root types but greater depth, such as $() \\Rightarrow T$ . When $G$ is of higher order, exploring up to the depth of $G$ can be required, such as when $G = () \\Rightarrow ((.) => \\text{number})$ . Based on these two ideas, we stop exploring $S$ when $\\text{DEPTH}(S) > \\max(\\text{DEPTH}(G), \\text{DEPTH}(T))$ .",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Further, if a higher-depth function returns an unexplored type, we need to explore it. Sticking to the example in Figure 11, type number has the member toString of type () => string. The type string can only be reached by exploring the member access at depth 1. On the contrary, we do not explore a higher-depth function if it does not introduce novel types other than those explored. To achieve this, we adapt Algorithm 2 to additionally define a set of root types $R$ , which is initialized to an empty set and is updated by $R := R \\cup \\mathrm{root}(T)$ . We do not explore $S$ if $\\mathrm{root}(S) \\subseteq R$ .",
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+ "text": "Taking the conjunction of the aforementioned two aspects, our pruning heuristic is implemented as PRUNESEARCH $(T,G,S) \\coloneqq \\mathrm{DEPTH}(S) > \\max(\\mathrm{DEPTH}(T), \\mathrm{DEPTH}(S)) \\wedge \\mathrm{ROOT}(S) \\subseteq R$ . The restrictions based on depth and root types are based on the results of the rigorously analyzed search over succinct types by Gvero et al. [30]. This provides a robust heuristic for exploring as many relevant inhabitable types as possible. However, due to the additional complexity introduced by the lookup function, we can not guarantee completeness and instead refer to the strong empirical results in our evaluation in §5 as evidence of the search's high coverage.",
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+ "type": "text",
+ "text": "A.4 Implementation of DERIVABLE",
+ "text_level": 1,
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+ "text": "Recall that in Table 1, DERIVABLE for function expressions are defined as: $\\mathrm{DERIVABLE}(q_{(\\overline{p})\\Rightarrow e})\\coloneqq \\{(\\overline{p})\\Rightarrow T\\mid \\mathrm{REACHABLE}(\\mathrm{DERIVABLE}(q_e),T)\\}$ . This involves constructing a type reachability graph and collecting all types $T$ reachable from DERIVABLE $(q_{e})$ . However, this process is intractable because $T$ can be of arbitrarily high-order, as such there are infinitely many $T$ to explore. A similar issue exists for grouped expressions, as their DERIVABLE function is also defined to enumerate reachable types. We introduce two optimization heuristics to address this problem.",
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+ "text": "We first observe that DERIVABLE is always called within the context of an invocation of REACHABLE with target type $G$ , e.g., REACHABLE(DERIVABLE(q(\\overline{p}) => e), G) for function expressions. To compute DERIVABLE(q(\\overline{p}) => e), we enumerate all types present on the type graph represented by REACHABLE(DERIVABLE(q_e), G), which is finite due to application of the pruning heuristics in Appendix A.3. In other words, we bound the maximum complexity of considered types $T$ using the pruning heuristic for reachability of target type $G$ . This leads to a sound but potentially incomplete version of DERIVABLE. However, since the final goal is to reach $G$ , this heuristic provides a practically useful set of all relevant derivable types.",
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+ "text": "Type-Constrained Code Generation with Language Models",
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+ "text": "Second, we observe that the resulting two-tiered call REACHABLE( DERIVABLE $(q_{(\\overline{p})} \\Rightarrow e)$ , $G$ ) can be integrated into a single call to further reduce the amount of explored types. Concretely, when discovering some type $M$ in REACHABLE( DERIVABLE $(q_e)$ , $G$ ), as per the previous heuristic, we allow transitioning directly to REACHABLE $(\\overline{p}) \\Rightarrow M, G$ to allow a depth-prioritizing exploration of the search graph. This allows us to efficiently discover a path to $G$ if it exists.",
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+ "text": "A.5 Statements",
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+ "text": "We define the remaining automata to capture the complete language from §3.1. To correctly handle function return types, we pass on related information when entering function bodies:",
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+ "- $q.R$ : The expected return type of the current state $q$ .",
+ "- $q.$ RETURNED: Whether the currently parsed program block has returned in all branches.",
+ "- q.MUSTRETURN: Whether the currently parsed program block must return (i.e., If-Then-Else branches do not need to contain return statements even if a return type is expected of the surrounding code block)."
+ ],
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+ "text": "The single statement automaton is another recursive definition, since some statements, e.g., If-Then-Else, can themselves contain statements. The statement automaton is defined recursively as $A_{s} \\coloneqq A_{\\mathrm{DECL}} \\cup A_{\\mathrm{EXPR}} \\cup A_{\\mathrm{RET}} \\cup A_{\\mathrm{BLOCK}} \\cup A_{\\mathrm{FUN}} \\cup A_{\\mathrm{ITE}}$ . The expression statement automaton and block automaton are simply defined as $A_{\\mathrm{EXPR}} \\coloneqq A_{e}$ ; and $A_{\\mathrm{BLOCK}} \\coloneqq A_{\\{\\overline{s}\\}}$ . The declaration automaton $A_{\\mathrm{DECL}} \\coloneqq A_{\\mathrm{let} x:T}$ ; captures variable names $x$ using an automaton for non-existing identifiers, which works the same way as $A_{x}$ except that it rejects terminals that match an existing variable. This automaton is a prefix automaton as well, since indefinite additional characters can be added to the variable name and there are only finitely many defined variables. The If-Then-Else automaton is defined using standard concatenation: $A_{\\mathrm{ITE}} \\coloneqq A_{\\mathrm{if}(e) s \\text{else}s}$ . The statements automaton $A_{\\overline{s}}$ , based on the Kleene-Star automaton definition and the single statement automaton. Return statements are only non-empty when the expected return type is set, i.e. when parsing inside a function:",
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+ "text": "\n$$\nA _ {\\mathrm {R E T}} := \\left\\{ \\begin{array}{l l} A _ {\\mathrm {r e t u r n}} \\circ A _ {e} \\downarrow T & \\text {i f} A _ {\\mathrm {R E T}}. R = T \\\\ A _ {\\emptyset} & \\text {o t h e r w i s e .} \\end{array} \\right.\n$$\n",
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+ "text": "For functions, the automaton is based on the standard concatenation $A_{\\text{FUN}} \\coloneqq A_{\\text{function } x(\\overline{p}):T(\\overline{s})}$ . However, the transition function updates the states of the statement automata inside the function:",
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+ "- $q.R \\coloneqq T$ , i.e., the return type of these statements is set to the return type of the function. This value is propagated recursively to all sub-automata.",
+ "- $q$ .MUSTRETURN := true, for the outermost statement block automaton. It is set to false for deeper nested statement blocks and as soon as a parsed statement $X$ has $q_{X}$ .RETURNED set to true - i.e. one of the main body statements returned in every branch.",
+ "- $q. \\text{RETURNED} :=$ false, per default in every statement, except a) in return automata, b) inside a multi-statement automaton where the previous statement has RETURNED = true and c) in ITE-automata where both branching statements have RETURNED = true."
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+ "text": "As long as a state $q$ in a multi-statement automaton has $X. \\text{RETURNED} = \\text{false}$ and $q. \\text{MUSTRETURN} = \\text{true}$ , it can not accept but instead forces the generation of another statement. Since we can always express the requested type through literals and can always generate a return statement to fulfill this requirement, the prefix automaton property is not violated.",
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+ "type": "text",
+ "text": "B Details about Experimental Evaluation",
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+ "text": "In this section, we detail how executable code is extracted from the model responses and a slight modification to the decoding algorithm used, that increases throughput heuristically.",
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+ {
+ "type": "header",
+ "text": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev",
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+ "text": "Implementation Details. We have two main external dependencies. To implement the regular-expression-based literal automata, we leverage the regex library, as it allows checking if the current string can be completed to match a regular expression. To implement LLM inference, we leverage the transformers library. We provide an exhaustive list of supported and unsupported features of the TypeScript language in our final implementation in Tables 5 and 6, respectively.",
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+ "text": "Hyperparameters. We run the models on A100 NVidia GPUs with 80 GB of VRAM and CUDA version 12.4. We set the sampling temperature to 1. We set seeds to 0 to 4 on the four HumanEval runs and 0 on the one MBPP run, respectively. We limit the completions to 1000 tokens and time out after 300 seconds. We compute syntactic correctness using the Oxidation toolchain [52] as the official TypeScript compiler does not clearly distinguish between syntactic and semantic errors.",
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+ "text": "Excluded MBPP Instances. We discovered that a number of TypeScript translations in the MultiPL-E dataset [13] contained invalidly generated nested tuples. After reporting them to the developers, they have been resolved in the latest version of MBPP and we include them in our evaluation. Still, we find that the TypeScript translation of a number of MBPP instances contains too broad type annotation, annotating elements as any or array of any. We therefore exclude the following 6 instances from the evaluation:",
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+ "sub_type": "text",
+ "list_items": [
+ "- mbpp_405_check_tuplex\n- mbpp_612_merge",
+ "- mbpp_563extract_values -mbpp_725.extract_quotation",
+ "- mbpp_580.extract_even\n- mbpp_791_removeNSTed"
+ ],
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+ "type": "text",
+ "text": "Complete Prompts. We provide the complete LLM prompts for our evaluated tasks (synthesis, translation, and repair) in Figures 12-14. The prompts are templates, instantiated with instructions specific to each task and problem instance. If system prompts are not available for a given LLM, we pretend the system prompt to the first user prompt. The model completion starts from a pre-filled function signature, enabling unified unit testing. For the repair prompt, we add the non-compilable model output as assistant output and use a second turn to pass back compiler outputs. Compiler errors contain line numbers for localization, so we annotate the output with line numbers. We find that Qwen2.5 32B tends to always generate test cases, which leads to errors during compilation. We therefore append the sentence Do not include test cases in the code. to its prompt.",
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+ "text": "Extracting Output Code. Given our prompts, LLMs are expected to output the resulting programs. However, they often produce additional outputs, such as generated test cases and explanations. Now we describe our heuristics for extracting the generated code. We first extract the corresponding TypeScript code block (i.e., ``` typescript`, or do not cut off if the block is not closed. Inside the code block, we cut off after the closing curly brace of the last balanced pair of curly braces, if it is followed by a newline or semicolon. This determines the last statement block generated, and avoids cutting off, e.g., inside a template literal. Again, if no such case is found, we do not prune the output. We demonstrate the operation of our cutoff heuristics in Figure 15.",
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+ "type": "text",
+ "text": "C Case Study Full Outputs",
+ "text_level": 1,
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+ "text": "In §5.4, we present the shortened versions of three qualitative examples showcasing the effectiveness of our approach. In Figures 16-18, we provide the full code outputs of these examples, with detailed descriptions in the respective captions.",
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+ "text": "Type-Constrained Code Generation with Language Models",
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+ "type": "page_footnote",
+ "text": "3https://pypi.org/project/regex/",
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+ "type": "page_footnote",
+ "text": "4 https://huggingface.co/docs/transformers",
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+ "table_caption": [
+ "Table 5. Supported TypeScript features."
+ ],
+ "table_footnote": [],
+ "table_body": "| Supported TypeScript Features | Examples |
| Expressions, Statements, Function Declarations | (LB as introduced in §3) |
| Additional Literals: BigInt, Regex, Template Strings | 10n, /\\d*, 'hello ${user}' |
| Additional Types: void, null, undefined | void, undefined, null |
| Index Signature Types and Literals | let x: {{y: number}: string} = 1: "hi"; |
| Anonymous Functions | function(): bool {return true} |
| Lambda Functions with and without Function Bodies | x => {return y}, x => y |
| Ternary and LogicOperators | ? :, |, && |
| Arithmetic and Boolean Operations | +, -, **, &, ! |
| Assigning Pre-and Postfix Operators | ++, -- |
| Arrays | [1, 2, 3] |
| Access and Assignment to Computed Members | x[10] = y[i]; |
| Constructors and "new" Calls | let x = new Number(1); |
| Calls with Optional and Rest Parameters | function foo(x?: number, y...: string) |
| Sets and Maps | Map<string, number>}() |
| Parameterized Constructor Calls | new Set<string>}() |
| Tuples | let x: [int, string] = [1, "hello"]; |
| Optional Chaining | x.get("hi").get("world") |
| Spread Operator | [...xs] |
| Type Assertions | "hello" as any |
| For Loops | for(int x = 0; i < 10; i++) |
| For Of Loops | for(x of xs) |
| For Of Loops with Tuple Destructuring | for([x, y] of xys) |
| Do-While and While Loops | while (true) {...} |
| Typed and Untyped Variable Declarations | let x: number = 1; let y = 100; |
| Comments, Multiline Comments | // Comment |
| Returning without Expressions | return; |
| Try-Catch Statements with a Fixed Exception Type | try {...} catch (e) {...} |
| Throw Statements | throw new Error("..." |
| Importing the crypto Library | require("crypto") |
| Global Scope Objects | Math, parseInt |
| Automatic Semicolon Insertion | |
",
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+ "table_caption": [
+ "Table 6.Unsupported TypeScript features."
+ ],
+ "table_footnote": [],
+ "table_body": "| s | DERIVABLE(qs) |
| l | {T | pmatch(l,T),T ∈ {number, string, boolean}} |
| x | {T | x ≤ n, (n : T) ∈ Γ} |
| (¯p) => e | { (¯p) => T | REACHABLE(DERIVABLE(qe),T)} |
| (e | {T | REACHABLE(DERIVABLE(qe),T)} |
| e ⊙ | {T | ∃S': Γ ↔ e : S ∧ S ⊕ S': T} |
| e( | {R | Γ ↔ e: (¯p) => R} |
| e.a | {S | a ≤ n, Γ ↔ e : T, LOOKUP(T,n) = S} |
"
+ }
+ ],
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+ {
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+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
+ },
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+ "type": "page_number",
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+ "type": "table",
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+ "angle": 0,
+ "content": "| Algorithm 2 Our type reachability search algorithm |
| Input: Current type T of some expression e, goal type G |
| Output: Whether G can be reached by extending e |
| 1: function REACHABLE(T, G) |
| 2: if T = G then return true | ▷ The goal type is successfully found |
| 3: if T is marked then return false else mark T | ▷ Type T is marked to avoid cycles |
| 4: for each valid extension step ⌿ from T do |
| 5: S := the resulting type of applying ⌿ on T |
| 6: if PRUNESEARCH(T, G, S) continue | ▷ Prune the search to ensure termination |
| 7: if REACHABLE(S, G) return true | ▷ Recurse to the next round of extension |
| 8: return false | ▷ No suitable extension is found |
"
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+ "content": "The type reachability algorithm, Algorithm 2, implements a depth-first search over this type graph, starting from the current type \\( T \\), succeeding upon finding goal type \\( G \\) (Line 2), marking any visited types to prevent cycles (Line 3). Then, it proceeds to iterate over all valid extension steps from \\( T \\) (Line 4) and computes the resulting type \\( S \\) after the extension step is applied (Line 5). In the conceptualized type graph, as described in the previous paragraph, this is equivalent to exploring all outgoing edges from \\( T \\). At Line 7, we proceed to recursively search if \\( S \\) can reach \\( G \\). If all recursive calls are unsuccessful, the goal type can not be reached (Line 8)."
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+ "content": "Some programming languages define self-referential default members, e.g., clone in Java or value0f in TypeScript, which are nullary functions that return a value of the same type as the callee, \\((\\mathbf{\\beta})\\Rightarrow T\\) for type \\(T\\). When these members are accessed in functions, higher-order functions can be derived indefinitely. For instance, for a function \\(f\\) with type \\((\\mathbf{\\beta})\\Rightarrow S\\), \\(f.\\) value0f has the type \\((\\mathbf{\\beta})\\Rightarrow (\\mathbf{\\beta})\\Rightarrow S\\). We therefore need to restrict the type search to a finite set of types to ensure termination. At Line 6 of Algorithm 2, we add a heuristic PRUNESEARCH into the search, which decides where to prune the search process. We develop a simple heuristic based on the results from Gvero et al. [30]. This heuristic prunes exploration of types with higher complexity than goal or source type if they do not contain yet unexplored primitive types, thus preventing exploration of arbitrarily complex types. The details of this heuristic are presented in Appendix A.3. While ensuring termination, our heuristic leads to incompleteness and the potential rejection of well-typed expressions. However, this effect is less pronounced in practical usage, as only highly complex (thus less realistically used) types are avoided."
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+ "content": "We proceed to prove the soundness of Algorithm 2 below."
+ },
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+ "content": "LEMMA 3. The type search in Algorithm 2 is sound, i.e., for any expression \\( e \\) with \\( \\Gamma \\vdash e : T \\), if REACHABLE(T,G) holds, then there exists a sequence of extensions \\( y \\) such that \\( \\Gamma \\vdash e \\circ y : G \\)."
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+ "content": "Proof. By the design of Algorithm 2, if REACHABLE\\((T,G)\\) returns true, there is a sequence of \\(n\\) recursive calls to REACHABLE\\((T_i,G)\\), with \\(T_0 = T\\) and REACHABLE\\((T_n,G) = \\text{true}\\). Each \\(T_i\\) (\\(i > 0\\)) is derived because some extension \\(\\diamond_i\\) is applicable to \\(T_{i-1}\\) based on the typing rules of \\(L_B\\). We then convert each \\(\\diamond_i\\) to its concrete, textual version \\(\\spadesuit_i\\). This representation includes the required well-typed parameters of \\(\\spadesuit_i\\) (i.e., for binary operators and non-nullary functions), which are constructed using literals. Finally, we construct \\(y\\) as \\(\\spadesuit_1 \\circ \\ldots \\circ \\spadesuit_n\\)."
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+ "content": "Note that using any pruning heuristic at Line 6 of Algorithm 2 preserves soundness, which in turn is sufficient to preserve the required prefix property, as defined in Definition 2. We can conclude that the two-tiered search algorithm soundly determines whether the desired target type can be derived from some partial input. Therefore, we conclude that \\( A_{e} \\downarrow T \\) and \\( A_{e} \\) are prefix automata that parse a subset of well-typed expressions in \\( L_{B} \\)."
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+ },
+ {
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+ "angle": 0,
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ },
+ {
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+ "content": "COROLLARY 4. If REACHABLE( DERIVABLE(q), G) holds for any \\( q \\in \\gamma(I_e, s) \\) of a partial expression \\( s \\), then there exists a suffix \\( s' \\) such that \\( \\Gamma \\vdash s \\circ s': G \\)."
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+ "content": "Proof. This conclusion follows directly from Lemmas 2 and 3."
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+ "content": "LEMMA 5. The language parsed by \\( A_e \\downarrow T \\) is thus a subset of the expressions of \\( L_B \\) of type \\( T \\), i.e., \\( L(A_e \\downarrow T) \\subseteq \\{s \\mid \\Gamma \\vdash s : T\\} \\). Since \\( A_e \\) recursively involves \\( A_e \\downarrow T \\), the language parsed by \\( A_e \\) is also a subset of well-typed expressions of \\( L_B \\), i.e., \\( L(A_e) \\subseteq \\{s \\mid \\exists T : \\Gamma \\vdash s : T\\} \\)."
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+ "content": "3.5 Prefix Automata for Statements"
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+ "content": "We define the remaining automata to capture the complete language \\( L_{B} \\). The statement automaton is defined recursively as \\( A_{s} \\coloneqq A_{\\mathrm{DECL}} \\cup A_{\\mathrm{EXPR}} \\cup A_{\\mathrm{RET}} \\cup A_{\\mathrm{BLOCK}} \\cup A_{\\mathrm{FUN}} \\cup A_{\\mathrm{ITE}} \\). The declaration automaton \\( A_{\\mathrm{DECL}} \\coloneqq A_{\\mathrm{let} x: T} \\); captures undefined variable names \\( x \\) by accepting all strings, except for existing identifiers. This automaton is a prefix automaton since an accepting state can always be reached by appending characters to the declared identifier. The return statement automaton is \\( A_{\\emptyset} \\) when outside a function and restricts the parsed expression to the return type of the surrounding function otherwise. The remaining automata are mainly concatenations of previously defined automata and recursive invocations of \\( A_{s} \\), with small variations detailed in Appendix A.5."
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+ "content": "Tracking Type Environments. Generally, we follow the typing rules in Figure 6. Identifiers are passed on through all state transitions, matching the rule SEQ, where the type environment of consecutive statements needs to be compatible. However, in the cases of BLOCK, ITE and FUN, we discard the local type environment after parsing, matching the respective typing rules. In FUN additionally, the function signature and parameters are added into the type environment of the function body automaton, and the function signature in the environment of subsequent statements."
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+ "content": "Guaranteeing Return Types. When parsing the body of a function, the transition function of the function automata \\( A_{\\mathrm{FUN}} \\) maintains information about the declared return type and the encountered return statements (if any). \\( A_{\\mathrm{FUN}} \\) only accepts states where all return values match the declared return type and all execution paths inside the function body return, following \\( L_B \\)'s typing rules in Figure 7. If the current generated statements do not return in all execution paths, another statement is forced to be generated. Since we can always express the requested type through literals, a correct return statement can always be generated and the prefix automaton property is not violated."
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+ "content": "The described rules are straightforward to implement without violating the prefix property as all restrictions are derived only from already parsed input, e.g., the already defined identifiers or the previously declared function return type. We can therefore deduce that the statement automaton is a prefix automaton. Moreover, the automaton accepts all valid statements of \\( L_{B} \\), with the exception of well-typed expressions rejected by \\( A_{e} \\). Therefore the parsed language is a subset of \\( L_{B} \\)."
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+ "content": "LEMMA 6. With \\( A_M \\coloneqq A_{\\overline{s}} \\) it holds that \\( A_M \\) is a prefix automaton and \\( L(A_M) \\subseteq L_B \\)."
+ },
+ {
+ "type": "title",
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+ "content": "4 Extension to TypeScript"
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+ "content": "We extend our completion engine described in §3 to handle a core subset of modern TypeScript. In this section, we selectively discuss the implementation of several interesting TypeScript features. We provide a comprehensive list of supported and unsupported TypeScript features in Appendix B."
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+ "content": "Constant Variable Declarations. In addition to variable declaration using let, TypeScript supports constant declarations using const. This defines immutable identifiers. We thus additionally track mutability of each identifier in the type environment and disallow applying the assignment operator to immutable identifiers."
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+ ],
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+ {
+ "type": "header",
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+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
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+ "content": "171:15"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Arrays. We add support for array type annotation, parsing array expressions, and reading from and assigning to array fields. In array expressions, we enforce that all array elements have the same type. Moreover, array types introduce another dimension of type nesting. Therefore we adapt the type reachability pruning heuristic to handle this additional dimension to ensure termination."
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+ "content": "**Loops.** TypeScript supports various loop constructs, including for, while, do-while, and for...of loops. These are implemented mostly as variations of the statement block parser. The for...of loop uniquely constrains the right-hand side of the ..of operator to an array of any type. To adapt the type search, we introduce a generic array type \\(\\bullet[\\]\\), which matches any array type. For example, both types number[] and string[] match \\(\\bullet[\\]\\) in Line 2 of Algorithm 2."
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+ "content": "Additional Operators and Types. We add several arithmetic and logic operators, such as modulo \\(\\%\\) , exact equality \\(= = =\\) , logical or \\(||\\) , and the ternary operator \\(\\text{?}\\) :. To handle these operators, we add additional edges to the type search graph. Moreover, we add support for post- and prefix operators such as -- and ++, which are only valid extensions to mutable expressions."
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+ "content": "Operator Precedence. TypeScript defines an operator precedence, which determines the implicit grouping of expressions. For example \\( 1 + 2 \\). toString() is parsed as \\( 1 + (2 \\). toString()) . We adapt our expression parsing algorithm in two places to handle operator precedences. First, in the expression automaton, we leverage the knowledge about previously parsed extensions to determine the implicit grouping and thus where the next operator is applied. For example, for state \\( q^{1} + 2 \\), the member access extension \\( n \\) is applied to 2, as opposed to \\( 1 + 2 \\). Second, we adapt the type search in Algorithm 2. Concretely, we ensure that only extensions that can be validly applied based on operator precedence are iterated over. For this, we track the operator precedence of previously parsed extensions and extensions considered during the traversal of the type graph and omit operators in Line 5 that violate operator precedence."
+ },
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+ "content": "Global Identifiers and Imports. In TypeScript, many identifiers are defined globally and available in any execution. These global identifiers are incorporated by initializing the type environment of the program automaton accordingly. Identifiers such as Math introduce additional types, which we additionally implement. We also model the import of the crypto library using require."
+ },
+ {
+ "type": "text",
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+ "content": "Polymorphic Built-In Members. The TypeScript LOOKUP implementation defines a few polymorphic members for built-in types. For example, for array \\( \\times \\) of type \\( T[] \\), \\( x \\). map(f) takes a callback function \\( f \\) and returns a new array \\( [f(x[0]), f(x[1]), \\ldots] \\). If \\( f \\) has type \\( (T) => P \\), the returned array has type \\( P[] \\). Here \\( P \\) is a type parameter, which is instantiated by matching the type of the passed function to the type pattern."
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+ "content": "We support such polymorphisms by adapting the type search. We track type patterns and enforce that type parameters are instantiated before the goal type is reached. We then continue the search from the instantiated version. In the map example, when searching completions of x.map, we first search for functions that instantiate the type parameter, and then continue the search from the instantiated type. When anonymous functions are generated as call parameters, we enforce that the function matches the searched type pattern."
+ },
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+ "type": "text",
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+ "content": "Type Annotations. TypeScript is designed to be flexible, allowing many type annotations to be omitted when they can be automatically inferred. We generally support this, such as inferring types from initial values. However, it can lead to unexpected types when annotations are omitted, often confusing even experienced developers [47, 48]. Moreover, in the context of LLM-based code generation, having more type annotations can provide valuable information for both the model and our type-constraining algorithms. We have identified three situations where generated code often fails to compile without type annotations, prompting us to enforce them. First, we require"
+ }
+ ],
+ [
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+ "type": "page_number",
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+ },
+ {
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+ "angle": 0,
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "annotations for all function parameters and return types. Second, all variable declarations must either have a type annotation or be initialized with a value. Third, we enforce type annotations for the first parameter of anonymous functions used as callbacks in the polymorphic built-in member reduce. These constraints trade off practical correctness with theoretical language completeness."
+ },
+ {
+ "type": "title",
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+ "content": "5 Experimental Evaluation"
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+ "angle": 0,
+ "content": "We present an extensive evaluation of our type constraining approach on a variety of tasks and models. We outline our experimental setup (§5.1), evaluate the impact on compilation errors and functional correctness (§5.2), perform runtime analysis (§5.3), and present case studies (§5.4)."
+ },
+ {
+ "type": "title",
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+ "content": "5.1 Experimental Setup"
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+ "content": "We now outline our main evaluation setup, covering implementation, evaluated tasks, considered models, compared methods, and metrics. We provide further setup details and hyperparameter choices in Appendix B."
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Implementation. Our implementation is written in Python and contains 11249 lines of code. To ensure robust implementation, we built a large set of around four hundred unit tests and frequently compared the behaviors of our implementation with the official TypeScript compiler [42]."
+ },
+ {
+ "type": "text",
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+ "content": "Tasks and Benchmarks. We evaluate three relevant tasks of code generation:"
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+ "angle": 0,
+ "content": "- Synthesis: Given a natural language task description and a function header, the task is to generate a solution from scratch."
+ },
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+ "angle": 0,
+ "content": "- Translation: Given a function written in Python and the header of an equivalent TypeScript function, the task is to generate the body of the equivalent function in TypeScript."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "- Repair: Given a natural language task description, a non-compilable solution, the corresponding compiler error, and the function header, the task is to restore functionality of the flawed solution by resolving the compilation error."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "content": "The benchmarks for these tasks are based on TypeScript-translated tasks from HumanEval [12] and MBPP [5], contained in the MultiPL-E dataset [13], with 159 and 384 instances each. We observe that success in generating valid code for the same sample can vary depending on the random seed used. To obtain more comprehensive results on the small HumanEval dataset, we generate each sample 4 times with different seeds and aggregate the outcomes. In MBPP, we generate each sample once. For Repair, we collect all non-compiling programs from the unconstrained synthesis task for all models, resulting in 292 and 248 instances for HumanEval and MBPP each."
+ },
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+ "content": "Models. We use 6 different open-weight LLMs, covering 3 LLMs of varying parameter sizes from the same model family and 4 models of a similar size from different model families: the Gemma 2 model family with 2B/9B/27B parameters [64], DeepSeekCoder 33B (abbreviated as DSCoder 33B) [28], CodeLlama 34B [59], and Qwen2.5 32B [73]. For all evaluated LLMs we choose the instruction-tuned variants, which are fine-tuned to follow instructions in a chat-style interaction, such that they adequately attempt to resolve the presented tasks."
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+ "content": "Compared Methods. We run unconstrained LLM sampling, reported as Vanilla. We measure the upper bound improvement of prior syntactic constraining methods [8, 57, 66] by assuming that all syntactically incorrect instances generated by Vanilla could be compiled under syntactic constraining. We refer to this improvement as idealized Syntax. We separately sample using type-constrained decoding based on our completion engine introduced in §3 and §4, and report it as Types. Due to the size and complexity of the full TypeScript compiler, featuring over 427,105 lines of code in 698 files [42], our extension does not cover all features of TypeScript. We therefore"
+ }
+ ],
+ [
+ {
+ "type": "header",
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+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
+ },
+ {
+ "type": "page_number",
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+ "angle": 0,
+ "content": "171:17"
+ },
+ {
+ "type": "table_caption",
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+ "angle": 0,
+ "content": "Table 2. Number of instances with compiler errors in unconstrained generation (Vanilla), idealized syntax-only constraining (Syntax), and our proposed type constraining (Types). Type constraining reduces compiler errors by \\(74.8\\%\\) and \\(56.0\\%\\) in the synthesis of HumanEval and MBPP problems respectively, compared to only \\(9.0\\%\\) and \\(4.8\\%\\) ideal improvement on the two datasets respectively through syntax-only constraining."
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": " | Vanilla | Types |
| (a) | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split() | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split(' ') |
| (b) | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } // No return } | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } return 1; } |
| (c) | // insert a delimiter between every element return nums.reduce( (acc, curr, index) => { acc.pushurr); return acc; }, []) | // insert a delimiter between every element return nums.reduce( (acc: number[] , num, index) => { acc.pushurr); return acc; }, []) |
"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 9. Three examples illustrating the effect of type-constrained sampling. Left are unconstrained generations with problematic tokens highlighted in red, and right are type-constrained results with corrected tokens highlighted in green, adapted for clarity. In (a), Gemma 2 2B attempts to call split, missing required arguments. In (b), DeepSeekCoder 33B attempts to complete a function without a guaranteed return. The issue is resolved by forcing generation of another statement after the main loop. In (c), Gemma 2 9B calls reduce with an anonymous function without type annotation. This leads to an incorrect type inference for the first parameter. The issue is solved by guiding the model to add type annotation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Missing Return Statement. In Figure 9b, to complete function largest_divisor, the model must compute a straightforward divisor loop. DeepSeekCoder 33B Instruct [28] implements a correct loop, but does not guarantee returning a value in every execution path. When the return statement in the loop is never executed, e.g., for negative inputs, the function thus returns undefined, violating the type rules. Our method detects this issue and forces the generation of another statement in the function body, resulting in a correct fallback return statement."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Incorrect Type Inference. In Figure 9c, the task is to insert a delimiter between every element in an array. Gemma 2 9B solves this with the reduce function. This generic function accepts two arguments; first, a callback function that is called consecutively for every element in the array and accumulates a result, second, an initial value for the callback function. The type of the accumulator of the callback is derived implicitly from the second argument, which is an empty array in the given example. TypeScript infers special type never[] for the empty array, disallowing inserting curr of type number through push. Therefore, the program fails to compile. This issue is a well-known limitation of the TypeScript compiler, often confusing even expert developers [47, 48]. Our method resolves it by enforcing adequate type annotation on the first argument of the callback function."
+ },
+ {
+ "type": "title",
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+ "content": "6 Discussion"
+ },
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+ "angle": 0,
+ "content": "Our general type constraining approach, backed by strong experimental results, opens exciting avenues for future research, which we discuss below."
+ },
+ {
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+ "angle": 0,
+ "content": "Implementation Effort. Developing a completion engine for a target programming language currently requires manual efforts. However, we expect that the involved effort to adopt our method to other languages will be reduced significantly, as many features transfer from our implementation for \\( L_{B} \\) and TypeScript. Moreover, we believe that, due to the huge impact on LLM's code generation, the effort will pay off. Future programming language developers may consider generally writing"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
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+ "content": "Type-Constrained Code Generation with Language Models"
+ },
+ {
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+ "angle": 0,
+ "content": "171:21"
+ },
+ {
+ "type": "code",
+ "bbox": [
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+ "angle": 0,
+ "content": "function sort_threel(number[]，r：number[]）:number[]{ \nfor（let \\(\\mathrm{i} = 0\\) ；i<1.length; \\(\\mathrm{i + + }\\) ）{ \nr.push(l[i].toString().slice(0,3).concat(l[i].ToString().split())'.split').reverse() .join(')).split''.reverse().join('').ToString() \\(^+\\) l[i].ToString().slice(3).split')…"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 10. Complications errors remain when the model does not terminate after a corrected token. In this example for synthesis on the HumanEval task #33, CodeLlama 34B is steered away from accessing non-existing member .sort and instead accesses .string."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "their compilers as an incremental completion engine, which additionally enables automatic adoption for constrained code generation, besides conventional grammar parsing and type checking."
+ },
+ {
+ "type": "text",
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+ "content": "Broader Application to More Complex Tasks and Stronger LLMs. Stronger LLMs, such as the latest OpenAI models [33], may make fewer typing errors on the HumanEval and MBPP datasets. Our evaluation results in Table 2 also demonstrate that compilation errors decrease with increasing model size for the Gemma family. However, recent findings showed that currently, even the strongest LLMs struggle with generating compilable code for more complex coding tasks, stricter typing rules, and low-resource languages (e.g., new DSLs). Gusanidas [29] evaluated various state-of-the-art LLMs on difficult code synthesis tasks in Rust, reporting compilation error rates of \\(18\\%\\) for OpenAI o1-mini [33], \\(39\\%\\) for DeepSeek R1 [15] and \\(27\\%\\) for Anthropic's Claude 3.5 Sonnet [2]. For OCaml and Haskell, which are sparsely represented in LLMs' training data, the error rate is even higher at \\(40\\% - 60\\%\\) for all models, matching a trend of worse performance on low-resource languages [24, 36]. Pan et al. [54] compiled a large dataset of code translation and found \\(44.3\\%\\) of GPT-4-generated code to contain compilation errors. Similarly, Shetty et al. [61] report around \\(25\\%\\) compilation errors for C-to-Rust translation using OpenAI o1 models. Our type constraining approach is broadly applicable to all these scenarios and our work presents a promising proof of concept. Future work can consider building upon our approach to address these challenges."
+ },
+ {
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+ "angle": 0,
+ "content": "Constrained decoding in general requires access to the next-token probability distributions produced by LLMs. Currently, commercially available black-box LLM APIs only return sampled tokens and do not offer complete next-token distributions. A possible solution is to integrate our method into the backend of model providers, as was recently implemented for guaranteeing adherence to JSON Schemas [3, 50]."
+ },
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+ "content": "Remaining Compiler Errors. We observe that, even though constrained decoding guarantees a valid result upon termination, a considerable amount of compilation errors remain due to non-termination within the token or time limit. We find this to be caused by generation loops, entered when generation is amended by constraints and the LLM is unable to recover. An example is depicted in Figure 10, where CodeLlama 34B tries to access the invalid member sort on an expression of type number. Future work may add additional constraints to force stopping such unconstructive loops and steer the model more strictly, e.g., by limiting the complexity of generated expressions."
+ },
+ {
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+ "content": "7 Related Work"
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+ "content": "Code Language Models. Recently, LLMs have gained traction for diverse coding tasks such as code synthesis, repair, or translation [35]. These models are typically trained on datasets containing billions to trillions of tokens and have billions of parameters, with both factors contributing to improved performance in code-related benchmarks [28, 46, 59, 64]. Meanwhile, LLMs are well known to frequently make mistakes [32, 58], and, as we show in this work, even state-of-the-art open-weight models with over 30 billion parameters frequently make errors in code generation."
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+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
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+ "content": "Improving Language Model Accuracy. Apart from constrained decoding, three primary approaches have been proposed to enhance the accuracy of language models on code tasks: fine-tuning, retrieval augmentation (RAG), and compiler or execution feedback. Fine-tuning adapts the model weights based on specifically collected training data. This process is highly resource intensive [65, 70]. RAG provides the model with additional context based on a database or related code snippets [6, 57]. Compiler and execution feedback is only available after completing the model generation and requires resampling [16, 34, 69]. However, constrained decoding is orthogonal to these methods and, as indicated by Poesia et al. [57] and our experimental results, combining constrained decoding with RAG or compiler feedback additionally improves model performance."
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+ "content": "Constrained Decoding. Prior work on constrained decoding failed to achieve strong results due to its limitation to syntactic language features. Constraining to context-free languages has been explored extensively in recent work [7, 8, 57, 71]. Simple context-sensitive syntactic features, such as the space indentation in Python and the scope markers in Go have also been implemented [41, 66]. As demonstrated in §5, however, syntax errors on average account for only \\(6\\%\\) of compilation errors in recent code models. The rarity of syntax errors significantly reduces the potential of leveraging them for improvements in code correctness. Meanwhile, our type-constrained decoding more than halved compilation errors."
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+ "content": "Type Systems for Code Synthesis. Previous work that leveraged type systems for code synthesis was confined to specialized settings and unable to constrain general, complex program generation. Poesia et al. [57] proposed using known column names to guide SQL query generation. Gvero et al. [30] employed a search on the type graph for function call completion. Agrawal et al. [1] leverage language-server-generated type annotations for object member accesses. Blinn et al. [11] use language-server-derived type information to provide additional context to the LLM, but not to enforce hard constraints. Additionally, type constraints have been used to direct code synthesis based on specialized search procedures [22, 56, 69]. However, these methods are not compatible with LLM-based code generation. This limits their ability to exploit the powerful natural language and general-purpose capabilities of LLMs."
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+ "content": "8 Conclusion"
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+ "angle": 0,
+ "content": "In this work, we explored how type systems in programming languages can be used to guide language models during decoding. Concretely, we design and implement prefix automata to perform type constraining for a foundational simply typed language and then extend it to the popular language TypeScript. We extensively evaluate the impact of using such constraints for code synthesis, translation, and repair and observe that we more than halve compilation errors on a diverse set of models and consistently increase functional correctness. We further explore qualitatively how the constraining positively impacts code generation. We conclude that such type constraining should be implemented for more programming languages, and has the potential to generally improve code generation in many domains."
+ }
+ ],
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+ "type": "header",
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+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
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+ "type": "title",
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+ "angle": 0,
+ "content": "Artifact Availability"
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+ "type": "text",
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+ "angle": 0,
+ "content": "The artifact for this paper, including source code, datasets, and reproductions scripts, is available on GitHub (https://github.com/eth-sri/type-constrained-code-generation) and Zenodo [45]."
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "Acknowledgements"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We would like to thank the anonymous reviewers for their in-depth and constructive feedback, and the artifact reviewers for their feedback on our artifact accessibility."
+ },
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+ },
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+ "type": "title",
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+ "content": "A Detailed Prefix Automaton Definitions"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "In this section, we provide more detailed definitions and analysis of the various automata for \\(L_{B}\\)."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "A.1 Base Automata"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We now provide detailed definitions for the base prefix automata introduced at the end of §3.2: union, concatenation, Kleene-Star, and terminal."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Union. For the union \\( A_X \\cup A_Y \\), we define the resulting sets of initial states and accepting states as \\( I \\coloneqq I_X \\cup I_Y \\) and \\( F \\coloneqq F_X \\cup F_Y \\), respectively. The transition function is defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.361,
+ 0.402,
+ 0.632,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\delta (q, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q, c) & \\text {i f} q \\in Q _ {X} \\\\ \\delta_ {Y} (q, c) & \\text {i f} q \\in Q _ {Y}. \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "To show that the language parsed by this automaton is indeed the union \\( L(A_{X} \\cup A_{Y}) = L(A_{X}) \\cup L(A_{Y}) \\), we employ a short helper lemma, which can be shown inductively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "LEMMA 7. The set of the reachable states from a set of states \\(\\mathbf{q}\\) is equal to the union of reachable states from each state in \\(\\mathbf{q}\\), i.e., \\(\\gamma (\\mathbf{q},s) = \\bigcup_{q\\in \\mathbf{q}}\\gamma (q,s)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Since the states are distinct and we merely combine the transition functions of both automata, using the lemma, we can quickly see that the language parsed is indeed the union. Moreover, if both \\( A_{X} \\) and \\( A_{Y} \\) are prefix automata, this also holds for \\( A_{X} \\cup A_{Y} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Concatenation. For the concatenation automaton \\( A_{XY} \\), we define \\( I \\coloneqq I_X \\), \\( F \\coloneqq F_Y \\), and the transition function as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.287,
+ 0.632,
+ 0.709,
+ 0.695
+ ],
+ "angle": 0,
+ "content": "\\[\n\\delta_ {X Y} (q, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q, c) & \\text {i f} q \\in Q _ {X} \\backslash F _ {X} \\\\ \\delta_ {X} (q, c) \\cup \\delta_ {Y} (I _ {Y}, c) & \\text {i f} q \\in F _ {X} \\\\ \\delta_ {Y} (q, c) & \\text {i f} q \\in Q _ {Y}. \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Informally, concatenation preserves the parsing behavior of both \\( A_{X} \\) and \\( A_{Y} \\) in their respective states. When \\( A_{XY} \\) reaches an accepting state of \\( A_{X} \\) and receives another input character, it either remains in \\( A_{X} \\) or transitions to \\( A_{Y} \\), as defined in the second case of \\( \\delta_{XY} \\). Essentially, this maintains outgoing edges from accepting states in \\( A_{X} \\) while adding edges from these accepting states to initial states of \\( A_{Y} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
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+ 0.908,
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+ ],
+ "angle": 0,
+ "content": "It follows from a similar argument that \\( L(A_{XY}) = L(A_X) \\circ L(A_Y) \\), where \\( L(A_X) \\circ L(A_Y) \\) is defined as \\( \\{s_X \\circ s_Y \\mid s_X \\in L(A_X), s_Y \\in L(A_Y)\\} \\). We first show \\( L(A_{XY}) \\subseteq L(A_X) \\circ L(A_Y) \\). Due to (P1), we can always split any \\( s \\in L(A_{XY}) \\) into \\( s_X \\) that extends from \\( I_X \\) to \\( F_X \\) and \\( s_Y \\) that extends from \\( I_Y \\) to \\( F_Y \\). Then \\( s_X \\in L(A_X) \\) and \\( s_Y \\in L(A_Y) \\). For \\( L(A_X) \\circ L(A_Y) \\subseteq L(A_X \\circ A_Y) \\), we pick any \\( s_X \\circ s_Y \\) from \\( L(A_X) \\circ L(A_Y) \\) and parse it using \\( A_{XY} \\). We observe that it will first traverse from \\( I_X \\) to \\( F_X \\) consuming \\( s_X \\), and then transition through \\( I_Y \\) to \\( F_Y \\) by consuming \\( s_Y \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.883,
+ 0.908,
+ 0.917
+ ],
+ "angle": 0,
+ "content": "Moreover \\( A_{XY} \\) is a prefix automaton, if \\( A_{X} \\) and \\( A_{Y} \\) are prefix automata and \\( L(A_{Y}) \\neq \\emptyset \\). Since \\( A_{X} \\) is a prefix automaton, we can reach \\( F_{X} \\) from any state in \\( Q_{X} \\). From \\( F_{X} \\) we additionally reach"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.09,
+ 0.083,
+ 0.496,
+ 0.097
+ ],
+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "171:27"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.118,
+ 0.907,
+ 0.153
+ ],
+ "angle": 0,
+ "content": "\\(I_{Y} \\subseteq Q_{Y}\\). Since \\(A_{Y}\\) is a prefix automaton, we can reach \\(F_{Y}\\) for any state in \\(Q_{Y}\\). This construction is a prefix automaton only if \\(I_{Y} \\neq \\emptyset\\), which, due to the prefix property, is equivalent to \\(L(A_{Y}) \\neq \\emptyset\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Kleene-Star. We define the Kleene-Star automaton \\( A_{\\overline{X}} \\) that parses indefinite repetitions of words accepted by \\( X \\). First, we consider all initial states as final states, i.e., we ensure \\( I_X \\subseteq F_{\\overline{X}} \\). Then we add transitions to the transition function \\( \\delta_X \\) from the final states \\( F_X \\) back to the initial states \\( I_X \\)."
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.7,
+ 0.262
+ ],
+ "angle": 0,
+ "content": "\\[\n\\delta_ {\\overline {{X}}} (q _ {X}, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q _ {X}, c) & \\text {i f q \\not \\in F _ {X}} \\\\ \\delta_ {X} (q _ {X}, c) \\cup \\delta (I _ {X}, c) & \\text {i f q _ {X} \\in F _ {X}}. \\end{array} \\right.\n\\]"
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+ {
+ "type": "text",
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+ ],
+ "angle": 0,
+ "content": "We can quickly see that \\( L(A_{\\overline{X}}) = \\{\\overline{s} \\mid s \\in L(A_X)\\} \\), with the same argument as the concatenation automaton. Additionally, because the initial states are accepting, the empty word (zero repetitions) is in \\( L(A_{\\overline{X}}) \\). We similarly see that this is a prefix automaton if \\( A_{X} \\) is a prefix automaton. Note that here \\( L(A_{X}) \\neq \\emptyset \\) is not required. This is because if \\( L(A_{X}) \\neq \\emptyset \\), then \\( A_{\\overline{X}} = A_{X} = A_{\\emptyset} \\), which is still a prefix automaton."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.36,
+ 0.907,
+ 0.409
+ ],
+ "angle": 0,
+ "content": "Terminals. The terminal automaton \\( A_{\\mathsf{S}} \\) parses exactly the terminal S. They accept the usual alphabet \\( \\Sigma \\) and feature the states \\( Q \\coloneqq \\{q_{\\mathsf{s}} \\mid \\mathsf{s} \\text{ is a suffix of S}\\} \\), \\( F \\coloneqq \\{q_{\\varepsilon}\\} \\), \\( I \\coloneqq \\{q_{\\mathsf{S}}\\} \\). The transition function \\( \\delta \\) is defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.36,
+ 0.414,
+ 0.635,
+ 0.458
+ ],
+ "angle": 0,
+ "content": "\\[\n\\delta (q _ {s}, c) := \\left\\{ \\begin{array}{l l} \\{q _ {s ^ {\\prime}} \\} & \\text {i f c \\circ s ^ {\\prime} = s} \\\\ \\varnothing & \\text {o t h e r w i s e .} \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.464,
+ 0.907,
+ 0.548
+ ],
+ "angle": 0,
+ "content": "Clearly \\( A_{\\mathfrak{S}} \\) is a prefix automaton. We can show inductively that for any \\( s: \\gamma(q_{s}, s') = \\{q_{\\varepsilon}\\} \\Longleftrightarrow s = s' \\), and thus \\( L(A_{\\mathfrak{S}}) = \\{\\mathfrak{S}\\} \\). With a simple modification, we introduce \\( A_{\\mathfrak{s}}^{W} \\), where \\( W \\) denotes whitespace characters. The transition function is defined as \\( \\delta(q_{\\mathfrak{s}}^{W}, c) := \\{q_{\\mathfrak{s}}^{W}\\} \\) if \\( c \\in W \\); otherwise, \\( \\delta(q_{c \\circ s}^{W}, t) := \\{q_{\\mathfrak{s}}^{W}\\} \\). This allows arbitrary whitespace before parsing \\( s \\). This is how we implement syntactic indifference to whitespace between terminals."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.089,
+ 0.561,
+ 0.257,
+ 0.578
+ ],
+ "angle": 0,
+ "content": "A.2 Expressions"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.582,
+ 0.907,
+ 0.615
+ ],
+ "angle": 0,
+ "content": "Expressions are parsed using recursive automatons as introduced in §3.4. In this part of the Appendix, we describe in more detail how information is passed between states."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.624,
+ 0.907,
+ 0.708
+ ],
+ "angle": 0,
+ "content": "Notation. In the following, we will implicitly assume that \\(\\delta(q, c) = \\emptyset\\) if not explicitly defined otherwise, making notation more concise. For any state, we access the following information through dot notation or the special notation on the state, which we assume is passed to subsequent states through the transition function (unless otherwise stated). This information is alternatively passed through to entire automata in composite automata, e.g., in \\(A_{XY}\\) from \\(A_X\\) to \\(A_Y\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.712,
+ 0.696,
+ 0.728
+ ],
+ "angle": 0,
+ "content": "- \\( q \\in F_X \\): Whether state \\( q \\) is an accepting state of the automaton \\( A_X \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.729,
+ 0.697,
+ 0.744
+ ],
+ "angle": 0,
+ "content": "- \\( q. \\Gamma \\): The type environment based on state \\( q \\) currently being parsed."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.745,
+ 0.907,
+ 0.778
+ ],
+ "angle": 0,
+ "content": "- \\( q \\).LHS: The left-hand side expression of an extending expression represented by state \\( q \\), i.e., when extending \\( X \\) with \\( Y \\) and currently parsing \\( q_{Y} \\), then \\( q_{Y} \\).LHS = \\( X \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.779,
+ 0.907,
+ 0.828
+ ],
+ "angle": 0,
+ "content": "- \\( q \\).TYP: The described type of the last coherent expression that this state belongs to. This is only defined for accepting states. Generally, we ensure that when some expression \\( e \\) was parsed, the corresponding state \\( q_{e} \\) has attribute \\( q_{e} \\).TYP such that \\( q_{e} \\Gamma \\vdash e : q_{e} \\).TYP."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.829,
+ 0.513,
+ 0.844
+ ],
+ "angle": 0,
+ "content": "- \\( q \\downarrow T \\): Type \\( T \\) to which state \\( q \\) is constrained."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.109,
+ 0.712,
+ 0.907,
+ 0.844
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.849,
+ 0.907,
+ 0.916
+ ],
+ "angle": 0,
+ "content": "When accessing the properties of \\( A \\), we access the property of the current state of the automaton \\( q \\in Q \\), e.g., \\( A. \\mathrm{LHS} = q. \\mathrm{LHS} \\). For parsed automata, the current state is the final, accepting state. The TYP attribute expresses the type of the expression parsed so far. In expression states \\( q \\), we leverage the LHS to accurately determine \\( q. \\mathrm{TYP} \\)."
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.092,
+ 0.084,
+ 0.138,
+ 0.096
+ ],
+ "angle": 0,
+ "content": "171:28"
+ },
+ {
+ "type": "header",
+ "bbox": [
+ 0.34,
+ 0.083,
+ 0.908,
+ 0.098
+ ],
+ "angle": 0,
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.113,
+ 0.117,
+ 0.898,
+ 0.204
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} q _ {\\mathrm {S T R . T Y P}} := \\text {s t r i n g} \\quad q _ {(e) . \\mathrm {T Y P}} := A _ {e}. \\mathrm {T Y P} \\\\ q _ {\\text {N U M}}. \\text {T Y P} := \\text {n u m b e r} \\quad q _ {\\odot e}. \\text {T Y P} := R, \\text {f o r} q _ {\\odot e}. \\text {L H S}. \\text {T Y P} = S, A _ {e}. \\text {T Y P} = T \\text {a n d} S \\odot T: R \\\\ q _ {\\text {B O O L . T Y P}} := \\text {b o o l e a n} \\quad q _ {(\\overline {{e}}). \\text {T Y P}} := T, \\text {f o r} q _ {(\\overline {{e}}). \\text {L H S . T Y P}} = (\\overline {{p}}) \\Rightarrow T \\\\ q _ {x. \\mathrm {T Y P}} := T \\text {w h e r e} q _ {x}. \\Gamma \\vdash x: T \\quad q. n. \\mathrm {T Y P} := T, \\text {f o r L O O K U P} (q. n. \\mathrm {L H S . T Y P}, n) = T \\\\ q _ {(\\overline {{p}}) = > e. T Y P} := \\left(A _ {\\overline {{p}}} ^ {-}. T Y P\\right) = > A _ {e}. T Y P \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.211,
+ 0.91,
+ 0.276
+ ],
+ "angle": 0,
+ "content": "Unrestricted Expressions. The left-hand side of the currently parsed expression is used in the definition of automata for three extending expressions; arithmetic operators, function call, and member access. The arithmetic operator automaton constrains its states to those with valid operators, i.e.:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.335,
+ 0.278,
+ 0.66,
+ 0.315
+ ],
+ "angle": 0,
+ "content": "\\[\nA_{\\odot e}:= \\bigcup_{\\exists R:A_{\\odot e}.LHS.TYP\\odot T = R}A_{\\odot}(\\circ A_{e}\\downarrow T).\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.317,
+ 0.908,
+ 0.351
+ ],
+ "angle": 0,
+ "content": "For function call, the automaton is only valid if the left-hand side is a function, and accepts only the valid signature."
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.233,
+ 0.358,
+ 0.762,
+ 0.401
+ ],
+ "angle": 0,
+ "content": "\\[\nA _ {(\\overline {{e}})} := \\left\\{ \\begin{array}{l l} A _ {(} \\circ (A _ {\\overline {{e}}} \\downarrow A _ {\\overline {{p}}}. \\mathrm {T Y P}) \\circ A _ {)} & \\text {i f} A _ {(\\overline {{e}}). \\mathrm {L H S . T Y P}} = (\\overline {{p}}) \\Rightarrow T \\\\ A _ {\\emptyset} & \\text {o t h e r w i s e .} \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.407,
+ 0.908,
+ 0.441
+ ],
+ "angle": 0,
+ "content": "Finally, the member access automaton is a union of the automata that parses the attributes of the left-hand side expression. Or formally,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.347,
+ 0.446,
+ 0.649,
+ 0.485
+ ],
+ "angle": 0,
+ "content": "\\[\nA_{\\cdot n}:= \\bigcup_{\\exists T:\\text{LOOKUP}(A_{\\cdot n}.LHS.TYP},m) = T}A_{\\cdot \\mathfrak{m}}.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.492,
+ 0.908,
+ 0.526
+ ],
+ "angle": 0,
+ "content": "Type-Restricted Expressions. The type-restricted versions of the automata are covered by the definitions presented in §3.4. We therefore do not separately list them here."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.088,
+ 0.539,
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+ 0.555
+ ],
+ "angle": 0,
+ "content": "A.3 Pruning the Type Search"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.087,
+ 0.559,
+ 0.91,
+ 0.608
+ ],
+ "angle": 0,
+ "content": "We now present our heuristic for pruning the type search recursion from the prefix automaton for type-constrained expressions in §3.4, i.e., our implementation of PRUNESEARCH at Line 6 of Algorithm 2. The heuristic is based on the complexity and novelty of candidate types to explore."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.609,
+ 0.911,
+ 0.759
+ ],
+ "angle": 0,
+ "content": "Based on the assumptions about the lookup function and the extension expressions in §3.1, we observe a restriction in the reachable types by extensions: from any given type, we reach itself, result types of arithmetic operators via op, return types through CALL, and member types through MEMBER. A higher-order type \\((\\cdot) \\Rightarrow T\\) does not allow access to types not reachable from \\(T\\). Consequently, we avoid exploring such higher-order types unless the target type is of higher order, or the higher-order type offers novel, yet unexplored types. For instance, in Figure 11, the type \\((\\cdot) \\Rightarrow\\) number is not explored, because it is more complex than both the initial and goal types, number and string, and does not contain any unexplored type. Meanwhile, \\((\\cdot) \\Rightarrow\\) string is explored, as it contains a novel string type."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.759,
+ 0.91,
+ 0.825
+ ],
+ "angle": 0,
+ "content": "To formalize this understanding, we introduce the concepts about the depth and root types of a given type, denoted as \\( \\text{DEPTH} \\) and \\( \\text{ROOT} \\), respectively. \\( \\text{DEPTH} \\) measures the complexity of a type, specifically the order of a function, while \\( \\text{ROOT} \\) returns all types of minimal depth (e.g., string, number, and boolean) that constitute a higher-order type. They are defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.119,
+ 0.831,
+ 0.892,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {D E P T H} (T) := \\left\\{ \\begin{array}{l l} \\operatorname {D E P T H} (S) + 1 & \\text {i f} T = (\\overline {{p}}) \\Rightarrow S, \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\qquad \\operatorname {R O O T} (T) := \\left\\{ \\begin{array}{l l} \\operatorname {R O O T} (S) & \\text {i f} T = (\\overline {{p}}) \\Rightarrow S, \\\\ \\{T \\} & \\text {o t h e r w i s e .} \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.882,
+ 0.908,
+ 0.916
+ ],
+ "angle": 0,
+ "content": "We leverage DEPTH and ROOT to implement PRUNESEARCH \\((T,G,S)\\) for a current type \\(T\\), a goal type \\(G\\), and a type \\(S\\) after an extension is applied on \\(T\\). In general, if \\(G\\) is not directly accessible"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.09,
+ 0.083,
+ 0.496,
+ 0.098
+ ],
+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.863,
+ 0.084,
+ 0.909,
+ 0.097
+ ],
+ "angle": 0,
+ "content": "171:29"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.25,
+ 0.114,
+ 0.745,
+ 0.242
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.088,
+ 0.247,
+ 0.912,
+ 0.314
+ ],
+ "angle": 0,
+ "content": "Figure 11. An example search through the graph for type reachability, starting from \\( T = \\) number with the goal string, e.g., after parsing let x : string; \\( x = 1 \\). States and edges along the final path are marked in green and explored nodes in blue. The () => number node is not explored, as complex types are avoided by our heuristic. The node () => string is explored as it enables reaching new type string."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.358,
+ 0.909,
+ 0.425
+ ],
+ "angle": 0,
+ "content": "from \\( T \\), it will also not be accessible from expressions with the same root types but greater depth, such as \\( () \\Rightarrow T \\). When \\( G \\) is of higher order, exploring up to the depth of \\( G \\) can be required, such as when \\( G = () \\Rightarrow ((.) => \\text{number}) \\). Based on these two ideas, we stop exploring \\( S \\) when \\( \\text{DEPTH}(S) > \\max(\\text{DEPTH}(G), \\text{DEPTH}(T)) \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.425,
+ 0.91,
+ 0.525
+ ],
+ "angle": 0,
+ "content": "Further, if a higher-depth function returns an unexplored type, we need to explore it. Sticking to the example in Figure 11, type number has the member toString of type () => string. The type string can only be reached by exploring the member access at depth 1. On the contrary, we do not explore a higher-depth function if it does not introduce novel types other than those explored. To achieve this, we adapt Algorithm 2 to additionally define a set of root types \\( R \\), which is initialized to an empty set and is updated by \\( R := R \\cup \\mathrm{root}(T) \\). We do not explore \\( S \\) if \\( \\mathrm{root}(S) \\subseteq R \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.525,
+ 0.911,
+ 0.643
+ ],
+ "angle": 0,
+ "content": "Taking the conjunction of the aforementioned two aspects, our pruning heuristic is implemented as PRUNESEARCH\\((T,G,S) \\coloneqq \\mathrm{DEPTH}(S) > \\max(\\mathrm{DEPTH}(T), \\mathrm{DEPTH}(S)) \\wedge \\mathrm{ROOT}(S) \\subseteq R\\). The restrictions based on depth and root types are based on the results of the rigorously analyzed search over succinct types by Gvero et al. [30]. This provides a robust heuristic for exploring as many relevant inhabitable types as possible. However, due to the additional complexity introduced by the lookup function, we can not guarantee completeness and instead refer to the strong empirical results in our evaluation in §5 as evidence of the search's high coverage."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.089,
+ 0.659,
+ 0.421,
+ 0.675
+ ],
+ "angle": 0,
+ "content": "A.4 Implementation of DERIVABLE"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.68,
+ 0.909,
+ 0.78
+ ],
+ "angle": 0,
+ "content": "Recall that in Table 1, DERIVABLE for function expressions are defined as: \\(\\mathrm{DERIVABLE}(q_{(\\overline{p})\\Rightarrow e})\\coloneqq \\{(\\overline{p})\\Rightarrow T\\mid \\mathrm{REACHABLE}(\\mathrm{DERIVABLE}(q_e),T)\\}\\). This involves constructing a type reachability graph and collecting all types \\(T\\) reachable from DERIVABLE \\((q_{e})\\). However, this process is intractable because \\(T\\) can be of arbitrarily high-order, as such there are infinitely many \\(T\\) to explore. A similar issue exists for grouped expressions, as their DERIVABLE function is also defined to enumerate reachable types. We introduce two optimization heuristics to address this problem."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.78,
+ 0.911,
+ 0.915
+ ],
+ "angle": 0,
+ "content": "We first observe that DERIVABLE is always called within the context of an invocation of REACHABLE with target type \\( G \\), e.g., REACHABLE(DERIVABLE(q(\\overline{p}) => e), G) for function expressions. To compute DERIVABLE(q(\\overline{p}) => e), we enumerate all types present on the type graph represented by REACHABLE(DERIVABLE(q_e), G), which is finite due to application of the pruning heuristics in Appendix A.3. In other words, we bound the maximum complexity of considered types \\( T \\) using the pruning heuristic for reachability of target type \\( G \\). This leads to a sound but potentially incomplete version of DERIVABLE. However, since the final goal is to reach \\( G \\), this heuristic provides a practically useful set of all relevant derivable types."
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.092,
+ 0.084,
+ 0.138,
+ 0.096
+ ],
+ "angle": 0,
+ "content": "171:30"
+ },
+ {
+ "type": "header",
+ "bbox": [
+ 0.34,
+ 0.083,
+ 0.908,
+ 0.097
+ ],
+ "angle": 0,
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.119,
+ 0.907,
+ 0.203
+ ],
+ "angle": 0,
+ "content": "Second, we observe that the resulting two-tiered call REACHABLE( DERIVABLE \\((q_{(\\overline{p})} \\Rightarrow e)\\), \\(G\\)) can be integrated into a single call to further reduce the amount of explored types. Concretely, when discovering some type \\(M\\) in REACHABLE( DERIVABLE \\((q_e)\\), \\(G\\)), as per the previous heuristic, we allow transitioning directly to REACHABLE \\((\\overline{p}) \\Rightarrow M, G\\) to allow a depth-prioritizing exploration of the search graph. This allows us to efficiently discover a path to \\(G\\) if it exists."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.089,
+ 0.216,
+ 0.25,
+ 0.231
+ ],
+ "angle": 0,
+ "content": "A.5 Statements"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "We define the remaining automata to capture the complete language from §3.1. To correctly handle function return types, we pass on related information when entering function bodies:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.276,
+ 0.57,
+ 0.291
+ ],
+ "angle": 0,
+ "content": "- \\( q.R \\): The expected return type of the current state \\( q \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.292,
+ 0.868,
+ 0.308
+ ],
+ "angle": 0,
+ "content": "- \\( q. \\) RETURNED: Whether the currently parsed program block has returned in all branches."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.308,
+ 0.907,
+ 0.357
+ ],
+ "angle": 0,
+ "content": "- q.MUSTRETURN: Whether the currently parsed program block must return (i.e., If-Then-Else branches do not need to contain return statements even if a return type is expected of the surrounding code block)."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.109,
+ 0.276,
+ 0.907,
+ 0.357
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
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+ 0.909,
+ 0.546
+ ],
+ "angle": 0,
+ "content": "The single statement automaton is another recursive definition, since some statements, e.g., If-Then-Else, can themselves contain statements. The statement automaton is defined recursively as \\( A_{s} \\coloneqq A_{\\mathrm{DECL}} \\cup A_{\\mathrm{EXPR}} \\cup A_{\\mathrm{RET}} \\cup A_{\\mathrm{BLOCK}} \\cup A_{\\mathrm{FUN}} \\cup A_{\\mathrm{ITE}} \\). The expression statement automaton and block automaton are simply defined as \\( A_{\\mathrm{EXPR}} \\coloneqq A_{e} \\); and \\( A_{\\mathrm{BLOCK}} \\coloneqq A_{\\{\\overline{s}\\}} \\). The declaration automaton \\( A_{\\mathrm{DECL}} \\coloneqq A_{\\mathrm{let} x:T} \\); captures variable names \\( x \\) using an automaton for non-existing identifiers, which works the same way as \\( A_{x} \\) except that it rejects terminals that match an existing variable. This automaton is a prefix automaton as well, since indefinite additional characters can be added to the variable name and there are only finitely many defined variables. The If-Then-Else automaton is defined using standard concatenation: \\( A_{\\mathrm{ITE}} \\coloneqq A_{\\mathrm{if}(e) s \\text{else}s} \\). The statements automaton \\( A_{\\overline{s}} \\), based on the Kleene-Star automaton definition and the single statement automaton. Return statements are only non-empty when the expected return type is set, i.e. when parsing inside a function:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.317,
+ 0.553,
+ 0.677,
+ 0.598
+ ],
+ "angle": 0,
+ "content": "\\[\nA _ {\\mathrm {R E T}} := \\left\\{ \\begin{array}{l l} A _ {\\mathrm {r e t u r n}} \\circ A _ {e} \\downarrow T & \\text {i f} A _ {\\mathrm {R E T}}. R = T \\\\ A _ {\\emptyset} & \\text {o t h e r w i s e .} \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.606,
+ 0.91,
+ 0.638
+ ],
+ "angle": 0,
+ "content": "For functions, the automaton is based on the standard concatenation \\( A_{\\text{FUN}} \\coloneqq A_{\\text{function } x(\\overline{p}):T(\\overline{s})} \\). However, the transition function updates the states of the statement automata inside the function:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.109,
+ 0.643,
+ 0.907,
+ 0.675
+ ],
+ "angle": 0,
+ "content": "- \\( q.R \\coloneqq T \\), i.e., the return type of these statements is set to the return type of the function. This value is propagated recursively to all sub-automata."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- \\( q \\).MUSTRETURN := true, for the outermost statement block automaton. It is set to false for deeper nested statement blocks and as soon as a parsed statement \\( X \\) has \\( q_{X} \\).RETURNED set to true - i.e. one of the main body statements returned in every branch."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.726,
+ 0.906,
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+ ],
+ "angle": 0,
+ "content": "- \\( q. \\text{RETURNED} := \\) false, per default in every statement, except a) in return automata, b) inside a multi-statement automaton where the previous statement has RETURNED = true and c) in ITE-automata where both branching statements have RETURNED = true."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.109,
+ 0.643,
+ 0.907,
+ 0.775
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+ "angle": 0,
+ "content": null
+ },
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+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.781,
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+ ],
+ "angle": 0,
+ "content": "As long as a state \\( q \\) in a multi-statement automaton has \\( X. \\text{RETURNED} = \\text{false} \\) and \\( q. \\text{MUSTRETURN} = \\text{true} \\), it can not accept but instead forces the generation of another statement. Since we can always express the requested type through literals and can always generate a return statement to fulfill this requirement, the prefix automaton property is not violated."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.089,
+ 0.861,
+ 0.492,
+ 0.877
+ ],
+ "angle": 0,
+ "content": "B Details about Experimental Evaluation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.882,
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+ ],
+ "angle": 0,
+ "content": "In this section, we detail how executable code is extracted from the model responses and a slight modification to the decoding algorithm used, that increases throughput heuristically."
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.09,
+ 0.083,
+ 0.496,
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+ ],
+ "angle": 0,
+ "content": "Type-Constrained Code Generation with Language Models"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.863,
+ 0.084,
+ 0.906,
+ 0.096
+ ],
+ "angle": 0,
+ "content": "171:31"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.118,
+ 0.912,
+ 0.203
+ ],
+ "angle": 0,
+ "content": "Implementation Details. We have two main external dependencies. To implement the regular-expression-based literal automata, we leverage the regex library, as it allows checking if the current string can be completed to match a regular expression. To implement LLM inference, we leverage the transformers library. We provide an exhaustive list of supported and unsupported features of the TypeScript language in our final implementation in Tables 5 and 6, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.21,
+ 0.911,
+ 0.295
+ ],
+ "angle": 0,
+ "content": "Hyperparameters. We run the models on A100 NVidia GPUs with 80 GB of VRAM and CUDA version 12.4. We set the sampling temperature to 1. We set seeds to 0 to 4 on the four HumanEval runs and 0 on the one MBPP run, respectively. We limit the completions to 1000 tokens and time out after 300 seconds. We compute syntactic correctness using the Oxidation toolchain [52] as the official TypeScript compiler does not clearly distinguish between syntactic and semantic errors."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.301,
+ 0.911,
+ 0.402
+ ],
+ "angle": 0,
+ "content": "Excluded MBPP Instances. We discovered that a number of TypeScript translations in the MultiPL-E dataset [13] contained invalidly generated nested tuples. After reporting them to the developers, they have been resolved in the latest version of MBPP and we include them in our evaluation. Still, we find that the TypeScript translation of a number of MBPP instances contains too broad type annotation, annotating elements as any or array of any. We therefore exclude the following 6 instances from the evaluation:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.151,
+ 0.406,
+ 0.646,
+ 0.422
+ ],
+ "angle": 0,
+ "content": "- mbpp_405_check_tuplex\n- mbpp_612_merge"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.152,
+ 0.423,
+ 0.765,
+ 0.438
+ ],
+ "angle": 0,
+ "content": "- mbpp_563extract_values -mbpp_725.extract_quotation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.152,
+ 0.44,
+ 0.725,
+ 0.454
+ ],
+ "angle": 0,
+ "content": "- mbpp_580.extract_even\n- mbpp_791_removeNSTed"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.151,
+ 0.406,
+ 0.765,
+ 0.454
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.46,
+ 0.912,
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+ ],
+ "angle": 0,
+ "content": "Complete Prompts. We provide the complete LLM prompts for our evaluated tasks (synthesis, translation, and repair) in Figures 12-14. The prompts are templates, instantiated with instructions specific to each task and problem instance. If system prompts are not available for a given LLM, we pretend the system prompt to the first user prompt. The model completion starts from a pre-filled function signature, enabling unified unit testing. For the repair prompt, we add the non-compilable model output as assistant output and use a second turn to pass back compiler outputs. Compiler errors contain line numbers for localization, so we annotate the output with line numbers. We find that Qwen2.5 32B tends to always generate test cases, which leads to errors during compilation. We therefore append the sentence Do not include test cases in the code. to its prompt."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.619,
+ 0.912,
+ 0.753
+ ],
+ "angle": 0,
+ "content": "Extracting Output Code. Given our prompts, LLMs are expected to output the resulting programs. However, they often produce additional outputs, such as generated test cases and explanations. Now we describe our heuristics for extracting the generated code. We first extract the corresponding TypeScript code block (i.e., ``` typescript`, or do not cut off if the block is not closed. Inside the code block, we cut off after the closing curly brace of the last balanced pair of curly braces, if it is followed by a newline or semicolon. This determines the last statement block generated, and avoids cutting off, e.g., inside a template literal. Again, if no such case is found, we do not prune the output. We demonstrate the operation of our cutoff heuristics in Figure 15."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.089,
+ 0.763,
+ 0.357,
+ 0.78
+ ],
+ "angle": 0,
+ "content": "C Case Study Full Outputs"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.088,
+ 0.785,
+ 0.911,
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+ ],
+ "angle": 0,
+ "content": "In §5.4, we present the shortened versions of three qualitative examples showcasing the effectiveness of our approach. In Figures 16-18, we provide the full code outputs of these examples, with detailed descriptions in the respective captions."
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.089,
+ 0.887,
+ 0.305,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "3https://pypi.org/project/regex/"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.089,
+ 0.902,
+ 0.38,
+ 0.915
+ ],
+ "angle": 0,
+ "content": "4 https://huggingface.co/docs/transformers"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.089,
+ 0.887,
+ 0.38,
+ 0.915
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+ "angle": 0,
+ "content": null
+ }
+ ],
+ [
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "171:32"
+ },
+ {
+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.345,
+ 0.117,
+ 0.651,
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+ ],
+ "angle": 0,
+ "content": "Table 5. Supported TypeScript features."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.092,
+ 0.136,
+ 0.905,
+ 0.641
+ ],
+ "angle": 0,
+ "content": "| Supported TypeScript Features | Examples |
| Expressions, Statements, Function Declarations | (LB as introduced in §3) |
| Additional Literals: BigInt, Regex, Template Strings | 10n, /\\d*, 'hello ${user}' |
| Additional Types: void, null, undefined | void, undefined, null |
| Index Signature Types and Literals | let x: {{y: number}: string} = 1: "hi"; |
| Anonymous Functions | function(): bool {return true} |
| Lambda Functions with and without Function Bodies | x => {return y}, x => y |
| Ternary and LogicOperators | ? :, |, && |
| Arithmetic and Boolean Operations | +, -, **, &, ! |
| Assigning Pre-and Postfix Operators | ++, -- |
| Arrays | [1, 2, 3] |
| Access and Assignment to Computed Members | x[10] = y[i]; |
| Constructors and "new" Calls | let x = new Number(1); |
| Calls with Optional and Rest Parameters | function foo(x?: number, y...: string) |
| Sets and Maps | Map<string, number>}() |
| Parameterized Constructor Calls | new Set<string>}() |
| Tuples | let x: [int, string] = [1, "hello"]; |
| Optional Chaining | x.get("hi").get("world") |
| Spread Operator | [...xs] |
| Type Assertions | "hello" as any |
| For Loops | for(int x = 0; i < 10; i++) |
| For Of Loops | for(x of xs) |
| For Of Loops with Tuple Destructuring | for([x, y] of xys) |
| Do-While and While Loops | while (true) {...} |
| Typed and Untyped Variable Declarations | let x: number = 1; let y = 100; |
| Comments, Multiline Comments | // Comment |
| Returning without Expressions | return; |
| Try-Catch Statements with a Fixed Exception Type | try {...} catch (e) {...} |
| Throw Statements | throw new Error("..." |
| Importing the crypto Library | require("crypto") |
| Global Scope Objects | Math, parseInt |
| Automatic Semicolon Insertion | |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.334,
+ 0.67,
+ 0.663,
+ 0.686
+ ],
+ "angle": 0,
+ "content": "Table 6.Unsupported TypeScript features."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.093,
+ 0.689,
+ 0.905,
+ 0.905
+ ],
+ "angle": 0,
+ "content": "| s | DERIVABLE(qs) |
| l | {T | pmatch(l,T),T ∈ {number, string, boolean}} |
| x | {T | x ≤ n, (n : T) ∈ Γ} |
| (¯p) => e | { (¯p) => T | REACHABLE(DERIVABLE(qe),T)} |
| (e | {T | REACHABLE(DERIVABLE(qe),T)} |
| e ⊙ | {T | ∃S': Γ ↔ e : S ∧ S ⊕ S': T} |
| e( | {R | Γ ↔ e: (¯p) => R} |
| e.a | {S | a ≤ n, Γ ↔ e : T, LOOKUP(T,n) = S} |
+
+| Algorithm 2 Our type reachability search algorithm |
| Input: Current type T of some expression e, goal type G |
| Output: Whether G can be reached by extending e |
| 1: function REACHABLE(T, G) |
| 2: if T = G then return true | ▷ The goal type is successfully found |
| 3: if T is marked then return false else mark T | ▷ Type T is marked to avoid cycles |
| 4: for each valid extension step ⌿ from T do |
| 5: S := the resulting type of applying ⌿ on T |
| 6: if PRUNESEARCH(T, G, S) continue | ▷ Prune the search to ensure termination |
| 7: if REACHABLE(S, G) return true | ▷ Recurse to the next round of extension |
| 8: return false | ▷ No suitable extension is found |
+
+The type reachability algorithm, Algorithm 2, implements a depth-first search over this type graph, starting from the current type $T$ , succeeding upon finding goal type $G$ (Line 2), marking any visited types to prevent cycles (Line 3). Then, it proceeds to iterate over all valid extension steps from $T$ (Line 4) and computes the resulting type $S$ after the extension step is applied (Line 5). In the conceptualized type graph, as described in the previous paragraph, this is equivalent to exploring all outgoing edges from $T$ . At Line 7, we proceed to recursively search if $S$ can reach $G$ . If all recursive calls are unsuccessful, the goal type can not be reached (Line 8).
+
+Some programming languages define self-referential default members, e.g., clone in Java or value0f in TypeScript, which are nullary functions that return a value of the same type as the callee, $(\mathbf{\beta})\Rightarrow T$ for type $T$ . When these members are accessed in functions, higher-order functions can be derived indefinitely. For instance, for a function $f$ with type $(\mathbf{\beta})\Rightarrow S$ , $f.$ value0f has the type $(\mathbf{\beta})\Rightarrow (\mathbf{\beta})\Rightarrow S$ . We therefore need to restrict the type search to a finite set of types to ensure termination. At Line 6 of Algorithm 2, we add a heuristic PRUNESEARCH into the search, which decides where to prune the search process. We develop a simple heuristic based on the results from Gvero et al. [30]. This heuristic prunes exploration of types with higher complexity than goal or source type if they do not contain yet unexplored primitive types, thus preventing exploration of arbitrarily complex types. The details of this heuristic are presented in Appendix A.3. While ensuring termination, our heuristic leads to incompleteness and the potential rejection of well-typed expressions. However, this effect is less pronounced in practical usage, as only highly complex (thus less realistically used) types are avoided.
+
+We proceed to prove the soundness of Algorithm 2 below.
+
+LEMMA 3. The type search in Algorithm 2 is sound, i.e., for any expression $e$ with $\Gamma \vdash e : T$ , if REACHABLE(T,G) holds, then there exists a sequence of extensions $y$ such that $\Gamma \vdash e \circ y : G$ .
+
+Proof. By the design of Algorithm 2, if REACHABLE $(T,G)$ returns true, there is a sequence of $n$ recursive calls to REACHABLE $(T_i,G)$ , with $T_0 = T$ and REACHABLE $(T_n,G) = \text{true}$ . Each $T_i$ ( $i > 0$ ) is derived because some extension $\diamond_i$ is applicable to $T_{i-1}$ based on the typing rules of $L_B$ . We then convert each $\diamond_i$ to its concrete, textual version $\spadesuit_i$ . This representation includes the required well-typed parameters of $\spadesuit_i$ (i.e., for binary operators and non-nullary functions), which are constructed using literals. Finally, we construct $y$ as $\spadesuit_1 \circ \ldots \circ \spadesuit_n$ .
+
+Note that using any pruning heuristic at Line 6 of Algorithm 2 preserves soundness, which in turn is sufficient to preserve the required prefix property, as defined in Definition 2. We can conclude that the two-tiered search algorithm soundly determines whether the desired target type can be derived from some partial input. Therefore, we conclude that $A_{e} \downarrow T$ and $A_{e}$ are prefix automata that parse a subset of well-typed expressions in $L_{B}$ .
+
+COROLLARY 4. If REACHABLE( DERIVABLE(q), G) holds for any $q \in \gamma(I_e, s)$ of a partial expression $s$ , then there exists a suffix $s'$ such that $\Gamma \vdash s \circ s': G$ .
+
+Proof. This conclusion follows directly from Lemmas 2 and 3.
+
+LEMMA 5. The language parsed by $A_e \downarrow T$ is thus a subset of the expressions of $L_B$ of type $T$ , i.e., $L(A_e \downarrow T) \subseteq \{s \mid \Gamma \vdash s : T\}$ . Since $A_e$ recursively involves $A_e \downarrow T$ , the language parsed by $A_e$ is also a subset of well-typed expressions of $L_B$ , i.e., $L(A_e) \subseteq \{s \mid \exists T : \Gamma \vdash s : T\}$ .
+
+# 3.5 Prefix Automata for Statements
+
+We define the remaining automata to capture the complete language $L_{B}$ . The statement automaton is defined recursively as $A_{s} \coloneqq A_{\mathrm{DECL}} \cup A_{\mathrm{EXPR}} \cup A_{\mathrm{RET}} \cup A_{\mathrm{BLOCK}} \cup A_{\mathrm{FUN}} \cup A_{\mathrm{ITE}}$ . The declaration automaton $A_{\mathrm{DECL}} \coloneqq A_{\mathrm{let} x: T}$ ; captures undefined variable names $x$ by accepting all strings, except for existing identifiers. This automaton is a prefix automaton since an accepting state can always be reached by appending characters to the declared identifier. The return statement automaton is $A_{\emptyset}$ when outside a function and restricts the parsed expression to the return type of the surrounding function otherwise. The remaining automata are mainly concatenations of previously defined automata and recursive invocations of $A_{s}$ , with small variations detailed in Appendix A.5.
+
+Tracking Type Environments. Generally, we follow the typing rules in Figure 6. Identifiers are passed on through all state transitions, matching the rule SEQ, where the type environment of consecutive statements needs to be compatible. However, in the cases of BLOCK, ITE and FUN, we discard the local type environment after parsing, matching the respective typing rules. In FUN additionally, the function signature and parameters are added into the type environment of the function body automaton, and the function signature in the environment of subsequent statements.
+
+Guaranteeing Return Types. When parsing the body of a function, the transition function of the function automata $A_{\mathrm{FUN}}$ maintains information about the declared return type and the encountered return statements (if any). $A_{\mathrm{FUN}}$ only accepts states where all return values match the declared return type and all execution paths inside the function body return, following $L_B$ 's typing rules in Figure 7. If the current generated statements do not return in all execution paths, another statement is forced to be generated. Since we can always express the requested type through literals, a correct return statement can always be generated and the prefix automaton property is not violated.
+
+The described rules are straightforward to implement without violating the prefix property as all restrictions are derived only from already parsed input, e.g., the already defined identifiers or the previously declared function return type. We can therefore deduce that the statement automaton is a prefix automaton. Moreover, the automaton accepts all valid statements of $L_{B}$ , with the exception of well-typed expressions rejected by $A_{e}$ . Therefore the parsed language is a subset of $L_{B}$ .
+
+LEMMA 6. With $A_M \coloneqq A_{\overline{s}}$ it holds that $A_M$ is a prefix automaton and $L(A_M) \subseteq L_B$ .
+
+# 4 Extension to TypeScript
+
+We extend our completion engine described in §3 to handle a core subset of modern TypeScript. In this section, we selectively discuss the implementation of several interesting TypeScript features. We provide a comprehensive list of supported and unsupported TypeScript features in Appendix B.
+
+Constant Variable Declarations. In addition to variable declaration using let, TypeScript supports constant declarations using const. This defines immutable identifiers. We thus additionally track mutability of each identifier in the type environment and disallow applying the assignment operator to immutable identifiers.
+
+Arrays. We add support for array type annotation, parsing array expressions, and reading from and assigning to array fields. In array expressions, we enforce that all array elements have the same type. Moreover, array types introduce another dimension of type nesting. Therefore we adapt the type reachability pruning heuristic to handle this additional dimension to ensure termination.
+
+**Loops.** TypeScript supports various loop constructs, including for, while, do-while, and for...of loops. These are implemented mostly as variations of the statement block parser. The for...of loop uniquely constrains the right-hand side of the ..of operator to an array of any type. To adapt the type search, we introduce a generic array type $\bullet[\]$ , which matches any array type. For example, both types number[] and string[] match $\bullet[\]$ in Line 2 of Algorithm 2.
+
+Additional Operators and Types. We add several arithmetic and logic operators, such as modulo $\%$ , exact equality $= = =$ , logical or $||$ , and the ternary operator $\text{?}$ :. To handle these operators, we add additional edges to the type search graph. Moreover, we add support for post- and prefix operators such as -- and ++, which are only valid extensions to mutable expressions.
+
+Operator Precedence. TypeScript defines an operator precedence, which determines the implicit grouping of expressions. For example $1 + 2$ . toString() is parsed as $1 + (2$ . toString()) . We adapt our expression parsing algorithm in two places to handle operator precedences. First, in the expression automaton, we leverage the knowledge about previously parsed extensions to determine the implicit grouping and thus where the next operator is applied. For example, for state $q^{1} + 2$ , the member access extension $n$ is applied to 2, as opposed to $1 + 2$ . Second, we adapt the type search in Algorithm 2. Concretely, we ensure that only extensions that can be validly applied based on operator precedence are iterated over. For this, we track the operator precedence of previously parsed extensions and extensions considered during the traversal of the type graph and omit operators in Line 5 that violate operator precedence.
+
+Global Identifiers and Imports. In TypeScript, many identifiers are defined globally and available in any execution. These global identifiers are incorporated by initializing the type environment of the program automaton accordingly. Identifiers such as Math introduce additional types, which we additionally implement. We also model the import of the crypto library using require.
+
+Polymorphic Built-In Members. The TypeScript LOOKUP implementation defines a few polymorphic members for built-in types. For example, for array $\times$ of type $T[]$ , $x$ . map(f) takes a callback function $f$ and returns a new array $[f(x[0]), f(x[1]), \ldots]$ . If $f$ has type $(T) => P$ , the returned array has type $P[]$ . Here $P$ is a type parameter, which is instantiated by matching the type of the passed function to the type pattern.
+
+We support such polymorphisms by adapting the type search. We track type patterns and enforce that type parameters are instantiated before the goal type is reached. We then continue the search from the instantiated version. In the map example, when searching completions of x.map, we first search for functions that instantiate the type parameter, and then continue the search from the instantiated type. When anonymous functions are generated as call parameters, we enforce that the function matches the searched type pattern.
+
+Type Annotations. TypeScript is designed to be flexible, allowing many type annotations to be omitted when they can be automatically inferred. We generally support this, such as inferring types from initial values. However, it can lead to unexpected types when annotations are omitted, often confusing even experienced developers [47, 48]. Moreover, in the context of LLM-based code generation, having more type annotations can provide valuable information for both the model and our type-constraining algorithms. We have identified three situations where generated code often fails to compile without type annotations, prompting us to enforce them. First, we require
+
+annotations for all function parameters and return types. Second, all variable declarations must either have a type annotation or be initialized with a value. Third, we enforce type annotations for the first parameter of anonymous functions used as callbacks in the polymorphic built-in member reduce. These constraints trade off practical correctness with theoretical language completeness.
+
+# 5 Experimental Evaluation
+
+We present an extensive evaluation of our type constraining approach on a variety of tasks and models. We outline our experimental setup (§5.1), evaluate the impact on compilation errors and functional correctness (§5.2), perform runtime analysis (§5.3), and present case studies (§5.4).
+
+# 5.1 Experimental Setup
+
+We now outline our main evaluation setup, covering implementation, evaluated tasks, considered models, compared methods, and metrics. We provide further setup details and hyperparameter choices in Appendix B.
+
+Implementation. Our implementation is written in Python and contains 11249 lines of code. To ensure robust implementation, we built a large set of around four hundred unit tests and frequently compared the behaviors of our implementation with the official TypeScript compiler [42].
+
+Tasks and Benchmarks. We evaluate three relevant tasks of code generation:
+
+- Synthesis: Given a natural language task description and a function header, the task is to generate a solution from scratch.
+- Translation: Given a function written in Python and the header of an equivalent TypeScript function, the task is to generate the body of the equivalent function in TypeScript.
+- Repair: Given a natural language task description, a non-compilable solution, the corresponding compiler error, and the function header, the task is to restore functionality of the flawed solution by resolving the compilation error.
+
+The benchmarks for these tasks are based on TypeScript-translated tasks from HumanEval [12] and MBPP [5], contained in the MultiPL-E dataset [13], with 159 and 384 instances each. We observe that success in generating valid code for the same sample can vary depending on the random seed used. To obtain more comprehensive results on the small HumanEval dataset, we generate each sample 4 times with different seeds and aggregate the outcomes. In MBPP, we generate each sample once. For Repair, we collect all non-compiling programs from the unconstrained synthesis task for all models, resulting in 292 and 248 instances for HumanEval and MBPP each.
+
+Models. We use 6 different open-weight LLMs, covering 3 LLMs of varying parameter sizes from the same model family and 4 models of a similar size from different model families: the Gemma 2 model family with 2B/9B/27B parameters [64], DeepSeekCoder 33B (abbreviated as DSCoder 33B) [28], CodeLlama 34B [59], and Qwen2.5 32B [73]. For all evaluated LLMs we choose the instruction-tuned variants, which are fine-tuned to follow instructions in a chat-style interaction, such that they adequately attempt to resolve the presented tasks.
+
+Compared Methods. We run unconstrained LLM sampling, reported as Vanilla. We measure the upper bound improvement of prior syntactic constraining methods [8, 57, 66] by assuming that all syntactically incorrect instances generated by Vanilla could be compiled under syntactic constraining. We refer to this improvement as idealized Syntax. We separately sample using type-constrained decoding based on our completion engine introduced in §3 and §4, and report it as Types. Due to the size and complexity of the full TypeScript compiler, featuring over 427,105 lines of code in 698 files [42], our extension does not cover all features of TypeScript. We therefore
+
+Table 2. Number of instances with compiler errors in unconstrained generation (Vanilla), idealized syntax-only constraining (Syntax), and our proposed type constraining (Types). Type constraining reduces compiler errors by $74.8\%$ and $56.0\%$ in the synthesis of HumanEval and MBPP problems respectively, compared to only $9.0\%$ and $4.8\%$ ideal improvement on the two datasets respectively through syntax-only constraining.
+
+ | Vanilla | Types |
| (a) | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split() | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split(' ') |
| (b) | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } // No return } | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } return 1; } |
| (c) | // insert a delimiter between every element return nums.reduce( (acc, curr, index) => { acc.pushurr); return acc; }, []) | // insert a delimiter between every element return nums.reduce( (acc: number[] , num, index) => { acc.pushurr); return acc; }, []) |
+
+Figure 9. Three examples illustrating the effect of type-constrained sampling. Left are unconstrained generations with problematic tokens highlighted in red, and right are type-constrained results with corrected tokens highlighted in green, adapted for clarity. In (a), Gemma 2 2B attempts to call split, missing required arguments. In (b), DeepSeekCoder 33B attempts to complete a function without a guaranteed return. The issue is resolved by forcing generation of another statement after the main loop. In (c), Gemma 2 9B calls reduce with an anonymous function without type annotation. This leads to an incorrect type inference for the first parameter. The issue is solved by guiding the model to add type annotation.
+
+Missing Return Statement. In Figure 9b, to complete function largest_divisor, the model must compute a straightforward divisor loop. DeepSeekCoder 33B Instruct [28] implements a correct loop, but does not guarantee returning a value in every execution path. When the return statement in the loop is never executed, e.g., for negative inputs, the function thus returns undefined, violating the type rules. Our method detects this issue and forces the generation of another statement in the function body, resulting in a correct fallback return statement.
+
+Incorrect Type Inference. In Figure 9c, the task is to insert a delimiter between every element in an array. Gemma 2 9B solves this with the reduce function. This generic function accepts two arguments; first, a callback function that is called consecutively for every element in the array and accumulates a result, second, an initial value for the callback function. The type of the accumulator of the callback is derived implicitly from the second argument, which is an empty array in the given example. TypeScript infers special type never[] for the empty array, disallowing inserting curr of type number through push. Therefore, the program fails to compile. This issue is a well-known limitation of the TypeScript compiler, often confusing even expert developers [47, 48]. Our method resolves it by enforcing adequate type annotation on the first argument of the callback function.
+
+# 6 Discussion
+
+Our general type constraining approach, backed by strong experimental results, opens exciting avenues for future research, which we discuss below.
+
+Implementation Effort. Developing a completion engine for a target programming language currently requires manual efforts. However, we expect that the involved effort to adopt our method to other languages will be reduced significantly, as many features transfer from our implementation for $L_{B}$ and TypeScript. Moreover, we believe that, due to the huge impact on LLM's code generation, the effort will pay off. Future programming language developers may consider generally writing
+
+```javascript
+function sort_threel(number[]，r：number[]）:number[]{
+for（let $\mathrm{i} = 0$ ；i<1.length; $\mathrm{i + + }$ ）{
+r.push(l[i].toString().slice(0,3).concat(l[i].ToString().split())'.split').reverse() .join(')).split''.reverse().join('').ToString() $^+$ l[i].ToString().slice(3).split')…
+```
+
+Figure 10. Complications errors remain when the model does not terminate after a corrected token. In this example for synthesis on the HumanEval task #33, CodeLlama 34B is steered away from accessing non-existing member .sort and instead accesses .string.
+
+their compilers as an incremental completion engine, which additionally enables automatic adoption for constrained code generation, besides conventional grammar parsing and type checking.
+
+Broader Application to More Complex Tasks and Stronger LLMs. Stronger LLMs, such as the latest OpenAI models [33], may make fewer typing errors on the HumanEval and MBPP datasets. Our evaluation results in Table 2 also demonstrate that compilation errors decrease with increasing model size for the Gemma family. However, recent findings showed that currently, even the strongest LLMs struggle with generating compilable code for more complex coding tasks, stricter typing rules, and low-resource languages (e.g., new DSLs). Gusanidas [29] evaluated various state-of-the-art LLMs on difficult code synthesis tasks in Rust, reporting compilation error rates of $18\%$ for OpenAI o1-mini [33], $39\%$ for DeepSeek R1 [15] and $27\%$ for Anthropic's Claude 3.5 Sonnet [2]. For OCaml and Haskell, which are sparsely represented in LLMs' training data, the error rate is even higher at $40\% - 60\%$ for all models, matching a trend of worse performance on low-resource languages [24, 36]. Pan et al. [54] compiled a large dataset of code translation and found $44.3\%$ of GPT-4-generated code to contain compilation errors. Similarly, Shetty et al. [61] report around $25\%$ compilation errors for C-to-Rust translation using OpenAI o1 models. Our type constraining approach is broadly applicable to all these scenarios and our work presents a promising proof of concept. Future work can consider building upon our approach to address these challenges.
+
+Constrained decoding in general requires access to the next-token probability distributions produced by LLMs. Currently, commercially available black-box LLM APIs only return sampled tokens and do not offer complete next-token distributions. A possible solution is to integrate our method into the backend of model providers, as was recently implemented for guaranteeing adherence to JSON Schemas [3, 50].
+
+Remaining Compiler Errors. We observe that, even though constrained decoding guarantees a valid result upon termination, a considerable amount of compilation errors remain due to non-termination within the token or time limit. We find this to be caused by generation loops, entered when generation is amended by constraints and the LLM is unable to recover. An example is depicted in Figure 10, where CodeLlama 34B tries to access the invalid member sort on an expression of type number. Future work may add additional constraints to force stopping such unconstructive loops and steer the model more strictly, e.g., by limiting the complexity of generated expressions.
+
+# 7 Related Work
+
+Code Language Models. Recently, LLMs have gained traction for diverse coding tasks such as code synthesis, repair, or translation [35]. These models are typically trained on datasets containing billions to trillions of tokens and have billions of parameters, with both factors contributing to improved performance in code-related benchmarks [28, 46, 59, 64]. Meanwhile, LLMs are well known to frequently make mistakes [32, 58], and, as we show in this work, even state-of-the-art open-weight models with over 30 billion parameters frequently make errors in code generation.
+
+Improving Language Model Accuracy. Apart from constrained decoding, three primary approaches have been proposed to enhance the accuracy of language models on code tasks: fine-tuning, retrieval augmentation (RAG), and compiler or execution feedback. Fine-tuning adapts the model weights based on specifically collected training data. This process is highly resource intensive [65, 70]. RAG provides the model with additional context based on a database or related code snippets [6, 57]. Compiler and execution feedback is only available after completing the model generation and requires resampling [16, 34, 69]. However, constrained decoding is orthogonal to these methods and, as indicated by Poesia et al. [57] and our experimental results, combining constrained decoding with RAG or compiler feedback additionally improves model performance.
+
+Constrained Decoding. Prior work on constrained decoding failed to achieve strong results due to its limitation to syntactic language features. Constraining to context-free languages has been explored extensively in recent work [7, 8, 57, 71]. Simple context-sensitive syntactic features, such as the space indentation in Python and the scope markers in Go have also been implemented [41, 66]. As demonstrated in §5, however, syntax errors on average account for only $6\%$ of compilation errors in recent code models. The rarity of syntax errors significantly reduces the potential of leveraging them for improvements in code correctness. Meanwhile, our type-constrained decoding more than halved compilation errors.
+
+Type Systems for Code Synthesis. Previous work that leveraged type systems for code synthesis was confined to specialized settings and unable to constrain general, complex program generation. Poesia et al. [57] proposed using known column names to guide SQL query generation. Gvero et al. [30] employed a search on the type graph for function call completion. Agrawal et al. [1] leverage language-server-generated type annotations for object member accesses. Blinn et al. [11] use language-server-derived type information to provide additional context to the LLM, but not to enforce hard constraints. Additionally, type constraints have been used to direct code synthesis based on specialized search procedures [22, 56, 69]. However, these methods are not compatible with LLM-based code generation. This limits their ability to exploit the powerful natural language and general-purpose capabilities of LLMs.
+
+# 8 Conclusion
+
+In this work, we explored how type systems in programming languages can be used to guide language models during decoding. Concretely, we design and implement prefix automata to perform type constraining for a foundational simply typed language and then extend it to the popular language TypeScript. We extensively evaluate the impact of using such constraints for code synthesis, translation, and repair and observe that we more than halve compilation errors on a diverse set of models and consistently increase functional correctness. We further explore qualitatively how the constraining positively impacts code generation. We conclude that such type constraining should be implemented for more programming languages, and has the potential to generally improve code generation in many domains.
+
+# Artifact Availability
+
+The artifact for this paper, including source code, datasets, and reproductions scripts, is available on GitHub (https://github.com/eth-sri/type-constrained-code-generation) and Zenodo [45].
+
+# Acknowledgements
+
+We would like to thank the anonymous reviewers for their in-depth and constructive feedback, and the artifact reviewers for their feedback on our artifact accessibility.
+
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+
+# A Detailed Prefix Automaton Definitions
+
+In this section, we provide more detailed definitions and analysis of the various automata for $L_{B}$ .
+
+# A.1 Base Automata
+
+We now provide detailed definitions for the base prefix automata introduced at the end of §3.2: union, concatenation, Kleene-Star, and terminal.
+
+Union. For the union $A_X \cup A_Y$ , we define the resulting sets of initial states and accepting states as $I \coloneqq I_X \cup I_Y$ and $F \coloneqq F_X \cup F_Y$ , respectively. The transition function is defined as follows:
+
+$$
+\delta (q, c) := \left\{ \begin{array}{l l} \delta_ {X} (q, c) & \text {i f} q \in Q _ {X} \\ \delta_ {Y} (q, c) & \text {i f} q \in Q _ {Y}. \end{array} \right.
+$$
+
+To show that the language parsed by this automaton is indeed the union $L(A_{X} \cup A_{Y}) = L(A_{X}) \cup L(A_{Y})$ , we employ a short helper lemma, which can be shown inductively.
+
+LEMMA 7. The set of the reachable states from a set of states $\mathbf{q}$ is equal to the union of reachable states from each state in $\mathbf{q}$ , i.e., $\gamma (\mathbf{q},s) = \bigcup_{q\in \mathbf{q}}\gamma (q,s)$ .
+
+Since the states are distinct and we merely combine the transition functions of both automata, using the lemma, we can quickly see that the language parsed is indeed the union. Moreover, if both $A_{X}$ and $A_{Y}$ are prefix automata, this also holds for $A_{X} \cup A_{Y}$ .
+
+Concatenation. For the concatenation automaton $A_{XY}$ , we define $I \coloneqq I_X$ , $F \coloneqq F_Y$ , and the transition function as follows:
+
+$$
+\delta_ {X Y} (q, c) := \left\{ \begin{array}{l l} \delta_ {X} (q, c) & \text {i f} q \in Q _ {X} \backslash F _ {X} \\ \delta_ {X} (q, c) \cup \delta_ {Y} (I _ {Y}, c) & \text {i f} q \in F _ {X} \\ \delta_ {Y} (q, c) & \text {i f} q \in Q _ {Y}. \end{array} \right.
+$$
+
+Informally, concatenation preserves the parsing behavior of both $A_{X}$ and $A_{Y}$ in their respective states. When $A_{XY}$ reaches an accepting state of $A_{X}$ and receives another input character, it either remains in $A_{X}$ or transitions to $A_{Y}$ , as defined in the second case of $\delta_{XY}$ . Essentially, this maintains outgoing edges from accepting states in $A_{X}$ while adding edges from these accepting states to initial states of $A_{Y}$ .
+
+It follows from a similar argument that $L(A_{XY}) = L(A_X) \circ L(A_Y)$ , where $L(A_X) \circ L(A_Y)$ is defined as $\{s_X \circ s_Y \mid s_X \in L(A_X), s_Y \in L(A_Y)\}$ . We first show $L(A_{XY}) \subseteq L(A_X) \circ L(A_Y)$ . Due to (P1), we can always split any $s \in L(A_{XY})$ into $s_X$ that extends from $I_X$ to $F_X$ and $s_Y$ that extends from $I_Y$ to $F_Y$ . Then $s_X \in L(A_X)$ and $s_Y \in L(A_Y)$ . For $L(A_X) \circ L(A_Y) \subseteq L(A_X \circ A_Y)$ , we pick any $s_X \circ s_Y$ from $L(A_X) \circ L(A_Y)$ and parse it using $A_{XY}$ . We observe that it will first traverse from $I_X$ to $F_X$ consuming $s_X$ , and then transition through $I_Y$ to $F_Y$ by consuming $s_Y$ .
+
+Moreover $A_{XY}$ is a prefix automaton, if $A_{X}$ and $A_{Y}$ are prefix automata and $L(A_{Y}) \neq \emptyset$ . Since $A_{X}$ is a prefix automaton, we can reach $F_{X}$ from any state in $Q_{X}$ . From $F_{X}$ we additionally reach
+
+$I_{Y} \subseteq Q_{Y}$ . Since $A_{Y}$ is a prefix automaton, we can reach $F_{Y}$ for any state in $Q_{Y}$ . This construction is a prefix automaton only if $I_{Y} \neq \emptyset$ , which, due to the prefix property, is equivalent to $L(A_{Y}) \neq \emptyset$ .
+
+Kleene-Star. We define the Kleene-Star automaton $A_{\overline{X}}$ that parses indefinite repetitions of words accepted by $X$ . First, we consider all initial states as final states, i.e., we ensure $I_X \subseteq F_{\overline{X}}$ . Then we add transitions to the transition function $\delta_X$ from the final states $F_X$ back to the initial states $I_X$ .
+
+$$
+\delta_ {\overline {{X}}} (q _ {X}, c) := \left\{ \begin{array}{l l} \delta_ {X} (q _ {X}, c) & \text {i f q \not \in F _ {X}} \\ \delta_ {X} (q _ {X}, c) \cup \delta (I _ {X}, c) & \text {i f q _ {X} \in F _ {X}}. \end{array} \right.
+$$
+
+We can quickly see that $L(A_{\overline{X}}) = \{\overline{s} \mid s \in L(A_X)\}$ , with the same argument as the concatenation automaton. Additionally, because the initial states are accepting, the empty word (zero repetitions) is in $L(A_{\overline{X}})$ . We similarly see that this is a prefix automaton if $A_{X}$ is a prefix automaton. Note that here $L(A_{X}) \neq \emptyset$ is not required. This is because if $L(A_{X}) \neq \emptyset$ , then $A_{\overline{X}} = A_{X} = A_{\emptyset}$ , which is still a prefix automaton.
+
+Terminals. The terminal automaton $A_{\mathsf{S}}$ parses exactly the terminal S. They accept the usual alphabet $\Sigma$ and feature the states $Q \coloneqq \{q_{\mathsf{s}} \mid \mathsf{s} \text{ is a suffix of S}\}$ , $F \coloneqq \{q_{\varepsilon}\}$ , $I \coloneqq \{q_{\mathsf{S}}\}$ . The transition function $\delta$ is defined as follows:
+
+$$
+\delta (q _ {s}, c) := \left\{ \begin{array}{l l} \{q _ {s ^ {\prime}} \} & \text {i f c \circ s ^ {\prime} = s} \\ \varnothing & \text {o t h e r w i s e .} \end{array} \right.
+$$
+
+Clearly $A_{\mathfrak{S}}$ is a prefix automaton. We can show inductively that for any $s: \gamma(q_{s}, s') = \{q_{\varepsilon}\} \Longleftrightarrow s = s'$ , and thus $L(A_{\mathfrak{S}}) = \{\mathfrak{S}\}$ . With a simple modification, we introduce $A_{\mathfrak{s}}^{W}$ , where $W$ denotes whitespace characters. The transition function is defined as $\delta(q_{\mathfrak{s}}^{W}, c) := \{q_{\mathfrak{s}}^{W}\}$ if $c \in W$ ; otherwise, $\delta(q_{c \circ s}^{W}, t) := \{q_{\mathfrak{s}}^{W}\}$ . This allows arbitrary whitespace before parsing $s$ . This is how we implement syntactic indifference to whitespace between terminals.
+
+# A.2 Expressions
+
+Expressions are parsed using recursive automatons as introduced in §3.4. In this part of the Appendix, we describe in more detail how information is passed between states.
+
+Notation. In the following, we will implicitly assume that $\delta(q, c) = \emptyset$ if not explicitly defined otherwise, making notation more concise. For any state, we access the following information through dot notation or the special notation on the state, which we assume is passed to subsequent states through the transition function (unless otherwise stated). This information is alternatively passed through to entire automata in composite automata, e.g., in $A_{XY}$ from $A_X$ to $A_Y$ .
+
+- $q \in F_X$ : Whether state $q$ is an accepting state of the automaton $A_X$ .
+- $q. \Gamma$ : The type environment based on state $q$ currently being parsed.
+- $q$ .LHS: The left-hand side expression of an extending expression represented by state $q$ , i.e., when extending $X$ with $Y$ and currently parsing $q_{Y}$ , then $q_{Y}$ .LHS = $X$ .
+- $q$ .TYP: The described type of the last coherent expression that this state belongs to. This is only defined for accepting states. Generally, we ensure that when some expression $e$ was parsed, the corresponding state $q_{e}$ has attribute $q_{e}$ .TYP such that $q_{e} \Gamma \vdash e : q_{e}$ .TYP.
+- $q \downarrow T$ : Type $T$ to which state $q$ is constrained.
+
+When accessing the properties of $A$ , we access the property of the current state of the automaton $q \in Q$ , e.g., $A. \mathrm{LHS} = q. \mathrm{LHS}$ . For parsed automata, the current state is the final, accepting state. The TYP attribute expresses the type of the expression parsed so far. In expression states $q$ , we leverage the LHS to accurately determine $q. \mathrm{TYP}$ .
+
+$$
+\begin{array}{l} q _ {\mathrm {S T R . T Y P}} := \text {s t r i n g} \quad q _ {(e) . \mathrm {T Y P}} := A _ {e}. \mathrm {T Y P} \\ q _ {\text {N U M}}. \text {T Y P} := \text {n u m b e r} \quad q _ {\odot e}. \text {T Y P} := R, \text {f o r} q _ {\odot e}. \text {L H S}. \text {T Y P} = S, A _ {e}. \text {T Y P} = T \text {a n d} S \odot T: R \\ q _ {\text {B O O L . T Y P}} := \text {b o o l e a n} \quad q _ {(\overline {{e}}). \text {T Y P}} := T, \text {f o r} q _ {(\overline {{e}}). \text {L H S . T Y P}} = (\overline {{p}}) \Rightarrow T \\ q _ {x. \mathrm {T Y P}} := T \text {w h e r e} q _ {x}. \Gamma \vdash x: T \quad q. n. \mathrm {T Y P} := T, \text {f o r L O O K U P} (q. n. \mathrm {L H S . T Y P}, n) = T \\ q _ {(\overline {{p}}) = > e. T Y P} := \left(A _ {\overline {{p}}} ^ {-}. T Y P\right) = > A _ {e}. T Y P \\ \end{array}
+$$
+
+Unrestricted Expressions. The left-hand side of the currently parsed expression is used in the definition of automata for three extending expressions; arithmetic operators, function call, and member access. The arithmetic operator automaton constrains its states to those with valid operators, i.e.:
+
+$$
+A_{\odot e}:= \bigcup_{\exists R:A_{\odot e}.LHS.TYP\odot T = R}A_{\odot}(\circ A_{e}\downarrow T).
+$$
+
+For function call, the automaton is only valid if the left-hand side is a function, and accepts only the valid signature.
+
+$$
+A _ {(\overline {{e}})} := \left\{ \begin{array}{l l} A _ {(} \circ (A _ {\overline {{e}}} \downarrow A _ {\overline {{p}}}. \mathrm {T Y P}) \circ A _ {)} & \text {i f} A _ {(\overline {{e}}). \mathrm {L H S . T Y P}} = (\overline {{p}}) \Rightarrow T \\ A _ {\emptyset} & \text {o t h e r w i s e .} \end{array} \right.
+$$
+
+Finally, the member access automaton is a union of the automata that parses the attributes of the left-hand side expression. Or formally,
+
+$$
+A_{\cdot n}:= \bigcup_{\exists T:\text{LOOKUP}(A_{\cdot n}.LHS.TYP},m) = T}A_{\cdot \mathfrak{m}}.
+$$
+
+Type-Restricted Expressions. The type-restricted versions of the automata are covered by the definitions presented in §3.4. We therefore do not separately list them here.
+
+# A.3 Pruning the Type Search
+
+We now present our heuristic for pruning the type search recursion from the prefix automaton for type-constrained expressions in §3.4, i.e., our implementation of PRUNESEARCH at Line 6 of Algorithm 2. The heuristic is based on the complexity and novelty of candidate types to explore.
+
+Based on the assumptions about the lookup function and the extension expressions in §3.1, we observe a restriction in the reachable types by extensions: from any given type, we reach itself, result types of arithmetic operators via op, return types through CALL, and member types through MEMBER. A higher-order type $(\cdot) \Rightarrow T$ does not allow access to types not reachable from $T$ . Consequently, we avoid exploring such higher-order types unless the target type is of higher order, or the higher-order type offers novel, yet unexplored types. For instance, in Figure 11, the type $(\cdot) \Rightarrow$ number is not explored, because it is more complex than both the initial and goal types, number and string, and does not contain any unexplored type. Meanwhile, $(\cdot) \Rightarrow$ string is explored, as it contains a novel string type.
+
+To formalize this understanding, we introduce the concepts about the depth and root types of a given type, denoted as $\text{DEPTH}$ and $\text{ROOT}$ , respectively. $\text{DEPTH}$ measures the complexity of a type, specifically the order of a function, while $\text{ROOT}$ returns all types of minimal depth (e.g., string, number, and boolean) that constitute a higher-order type. They are defined as follows:
+
+$$
+\operatorname {D E P T H} (T) := \left\{ \begin{array}{l l} \operatorname {D E P T H} (S) + 1 & \text {i f} T = (\overline {{p}}) \Rightarrow S, \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \qquad \operatorname {R O O T} (T) := \left\{ \begin{array}{l l} \operatorname {R O O T} (S) & \text {i f} T = (\overline {{p}}) \Rightarrow S, \\ \{T \} & \text {o t h e r w i s e .} \end{array} \right.
+$$
+
+We leverage DEPTH and ROOT to implement PRUNESEARCH $(T,G,S)$ for a current type $T$ , a goal type $G$ , and a type $S$ after an extension is applied on $T$ . In general, if $G$ is not directly accessible
+
+
+Figure 11. An example search through the graph for type reachability, starting from $T =$ number with the goal string, e.g., after parsing let x : string; $x = 1$ . States and edges along the final path are marked in green and explored nodes in blue. The () => number node is not explored, as complex types are avoided by our heuristic. The node () => string is explored as it enables reaching new type string.
+
+from $T$ , it will also not be accessible from expressions with the same root types but greater depth, such as $() \Rightarrow T$ . When $G$ is of higher order, exploring up to the depth of $G$ can be required, such as when $G = () \Rightarrow ((.) => \text{number})$ . Based on these two ideas, we stop exploring $S$ when $\text{DEPTH}(S) > \max(\text{DEPTH}(G), \text{DEPTH}(T))$ .
+
+Further, if a higher-depth function returns an unexplored type, we need to explore it. Sticking to the example in Figure 11, type number has the member toString of type () => string. The type string can only be reached by exploring the member access at depth 1. On the contrary, we do not explore a higher-depth function if it does not introduce novel types other than those explored. To achieve this, we adapt Algorithm 2 to additionally define a set of root types $R$ , which is initialized to an empty set and is updated by $R := R \cup \mathrm{root}(T)$ . We do not explore $S$ if $\mathrm{root}(S) \subseteq R$ .
+
+Taking the conjunction of the aforementioned two aspects, our pruning heuristic is implemented as PRUNESEARCH $(T,G,S) \coloneqq \mathrm{DEPTH}(S) > \max(\mathrm{DEPTH}(T), \mathrm{DEPTH}(S)) \wedge \mathrm{ROOT}(S) \subseteq R$ . The restrictions based on depth and root types are based on the results of the rigorously analyzed search over succinct types by Gvero et al. [30]. This provides a robust heuristic for exploring as many relevant inhabitable types as possible. However, due to the additional complexity introduced by the lookup function, we can not guarantee completeness and instead refer to the strong empirical results in our evaluation in §5 as evidence of the search's high coverage.
+
+# A.4 Implementation of DERIVABLE
+
+Recall that in Table 1, DERIVABLE for function expressions are defined as: $\mathrm{DERIVABLE}(q_{(\overline{p})\Rightarrow e})\coloneqq \{(\overline{p})\Rightarrow T\mid \mathrm{REACHABLE}(\mathrm{DERIVABLE}(q_e),T)\}$ . This involves constructing a type reachability graph and collecting all types $T$ reachable from DERIVABLE $(q_{e})$ . However, this process is intractable because $T$ can be of arbitrarily high-order, as such there are infinitely many $T$ to explore. A similar issue exists for grouped expressions, as their DERIVABLE function is also defined to enumerate reachable types. We introduce two optimization heuristics to address this problem.
+
+We first observe that DERIVABLE is always called within the context of an invocation of REACHABLE with target type $G$ , e.g., REACHABLE(DERIVABLE(q(\overline{p}) => e), G) for function expressions. To compute DERIVABLE(q(\overline{p}) => e), we enumerate all types present on the type graph represented by REACHABLE(DERIVABLE(q_e), G), which is finite due to application of the pruning heuristics in Appendix A.3. In other words, we bound the maximum complexity of considered types $T$ using the pruning heuristic for reachability of target type $G$ . This leads to a sound but potentially incomplete version of DERIVABLE. However, since the final goal is to reach $G$ , this heuristic provides a practically useful set of all relevant derivable types.
+
+Second, we observe that the resulting two-tiered call REACHABLE( DERIVABLE $(q_{(\overline{p})} \Rightarrow e)$ , $G$ ) can be integrated into a single call to further reduce the amount of explored types. Concretely, when discovering some type $M$ in REACHABLE( DERIVABLE $(q_e)$ , $G$ ), as per the previous heuristic, we allow transitioning directly to REACHABLE $(\overline{p}) \Rightarrow M, G$ to allow a depth-prioritizing exploration of the search graph. This allows us to efficiently discover a path to $G$ if it exists.
+
+# A.5 Statements
+
+We define the remaining automata to capture the complete language from §3.1. To correctly handle function return types, we pass on related information when entering function bodies:
+
+- $q.R$ : The expected return type of the current state $q$ .
+- $q.$ RETURNED: Whether the currently parsed program block has returned in all branches.
+- q.MUSTRETURN: Whether the currently parsed program block must return (i.e., If-Then-Else branches do not need to contain return statements even if a return type is expected of the surrounding code block).
+
+The single statement automaton is another recursive definition, since some statements, e.g., If-Then-Else, can themselves contain statements. The statement automaton is defined recursively as $A_{s} \coloneqq A_{\mathrm{DECL}} \cup A_{\mathrm{EXPR}} \cup A_{\mathrm{RET}} \cup A_{\mathrm{BLOCK}} \cup A_{\mathrm{FUN}} \cup A_{\mathrm{ITE}}$ . The expression statement automaton and block automaton are simply defined as $A_{\mathrm{EXPR}} \coloneqq A_{e}$ ; and $A_{\mathrm{BLOCK}} \coloneqq A_{\{\overline{s}\}}$ . The declaration automaton $A_{\mathrm{DECL}} \coloneqq A_{\mathrm{let} x:T}$ ; captures variable names $x$ using an automaton for non-existing identifiers, which works the same way as $A_{x}$ except that it rejects terminals that match an existing variable. This automaton is a prefix automaton as well, since indefinite additional characters can be added to the variable name and there are only finitely many defined variables. The If-Then-Else automaton is defined using standard concatenation: $A_{\mathrm{ITE}} \coloneqq A_{\mathrm{if}(e) s \text{else}s}$ . The statements automaton $A_{\overline{s}}$ , based on the Kleene-Star automaton definition and the single statement automaton. Return statements are only non-empty when the expected return type is set, i.e. when parsing inside a function:
+
+$$
+A _ {\mathrm {R E T}} := \left\{ \begin{array}{l l} A _ {\mathrm {r e t u r n}} \circ A _ {e} \downarrow T & \text {i f} A _ {\mathrm {R E T}}. R = T \\ A _ {\emptyset} & \text {o t h e r w i s e .} \end{array} \right.
+$$
+
+For functions, the automaton is based on the standard concatenation $A_{\text{FUN}} \coloneqq A_{\text{function } x(\overline{p}):T(\overline{s})}$ . However, the transition function updates the states of the statement automata inside the function:
+
+- $q.R \coloneqq T$ , i.e., the return type of these statements is set to the return type of the function. This value is propagated recursively to all sub-automata.
+- $q$ .MUSTRETURN := true, for the outermost statement block automaton. It is set to false for deeper nested statement blocks and as soon as a parsed statement $X$ has $q_{X}$ .RETURNED set to true - i.e. one of the main body statements returned in every branch.
+- $q. \text{RETURNED} :=$ false, per default in every statement, except a) in return automata, b) inside a multi-statement automaton where the previous statement has RETURNED = true and c) in ITE-automata where both branching statements have RETURNED = true.
+
+As long as a state $q$ in a multi-statement automaton has $X. \text{RETURNED} = \text{false}$ and $q. \text{MUSTRETURN} = \text{true}$ , it can not accept but instead forces the generation of another statement. Since we can always express the requested type through literals and can always generate a return statement to fulfill this requirement, the prefix automaton property is not violated.
+
+# B Details about Experimental Evaluation
+
+In this section, we detail how executable code is extracted from the model responses and a slight modification to the decoding algorithm used, that increases throughput heuristically.
+
+Implementation Details. We have two main external dependencies. To implement the regular-expression-based literal automata, we leverage the regex library, as it allows checking if the current string can be completed to match a regular expression. To implement LLM inference, we leverage the transformers library. We provide an exhaustive list of supported and unsupported features of the TypeScript language in our final implementation in Tables 5 and 6, respectively.
+
+Hyperparameters. We run the models on A100 NVidia GPUs with 80 GB of VRAM and CUDA version 12.4. We set the sampling temperature to 1. We set seeds to 0 to 4 on the four HumanEval runs and 0 on the one MBPP run, respectively. We limit the completions to 1000 tokens and time out after 300 seconds. We compute syntactic correctness using the Oxidation toolchain [52] as the official TypeScript compiler does not clearly distinguish between syntactic and semantic errors.
+
+Excluded MBPP Instances. We discovered that a number of TypeScript translations in the MultiPL-E dataset [13] contained invalidly generated nested tuples. After reporting them to the developers, they have been resolved in the latest version of MBPP and we include them in our evaluation. Still, we find that the TypeScript translation of a number of MBPP instances contains too broad type annotation, annotating elements as any or array of any. We therefore exclude the following 6 instances from the evaluation:
+
+- mbpp_405_check_tuplex
+- mbpp_612_merge
+- mbpp_563extract_values -mbpp_725.extract_quotation
+- mbpp_580.extract_even
+- mbpp_791_removeNSTed
+
+Complete Prompts. We provide the complete LLM prompts for our evaluated tasks (synthesis, translation, and repair) in Figures 12-14. The prompts are templates, instantiated with instructions specific to each task and problem instance. If system prompts are not available for a given LLM, we pretend the system prompt to the first user prompt. The model completion starts from a pre-filled function signature, enabling unified unit testing. For the repair prompt, we add the non-compilable model output as assistant output and use a second turn to pass back compiler outputs. Compiler errors contain line numbers for localization, so we annotate the output with line numbers. We find that Qwen2.5 32B tends to always generate test cases, which leads to errors during compilation. We therefore append the sentence Do not include test cases in the code. to its prompt.
+
+Extracting Output Code. Given our prompts, LLMs are expected to output the resulting programs. However, they often produce additional outputs, such as generated test cases and explanations. Now we describe our heuristics for extracting the generated code. We first extract the corresponding TypeScript code block (i.e., ``` typescript`, or do not cut off if the block is not closed. Inside the code block, we cut off after the closing curly brace of the last balanced pair of curly braces, if it is followed by a newline or semicolon. This determines the last statement block generated, and avoids cutting off, e.g., inside a template literal. Again, if no such case is found, we do not prune the output. We demonstrate the operation of our cutoff heuristics in Figure 15.
+
+# C Case Study Full Outputs
+
+In §5.4, we present the shortened versions of three qualitative examples showcasing the effectiveness of our approach. In Figures 16-18, we provide the full code outputs of these examples, with detailed descriptions in the respective captions.
+
+Table 5. Supported TypeScript features.
+
+| Supported TypeScript Features | Examples |
| Expressions, Statements, Function Declarations | (LB as introduced in §3) |
| Additional Literals: BigInt, Regex, Template Strings | 10n, /\d*, 'hello ${user}' |
| Additional Types: void, null, undefined | void, undefined, null |
| Index Signature Types and Literals | let x: {{y: number}: string} = 1: "hi"; |
| Anonymous Functions | function(): bool {return true} |
| Lambda Functions with and without Function Bodies | x => {return y}, x => y |
| Ternary and LogicOperators | ? :, |, && |
| Arithmetic and Boolean Operations | +, -, **, &, ! |
| Assigning Pre-and Postfix Operators | ++, -- |
| Arrays | [1, 2, 3] |
| Access and Assignment to Computed Members | x[10] = y[i]; |
| Constructors and "new" Calls | let x = new Number(1); |
| Calls with Optional and Rest Parameters | function foo(x?: number, y...: string) |
| Sets and Maps | Map<string, number>}() |
| Parameterized Constructor Calls | new Set<string>}() |
| Tuples | let x: [int, string] = [1, "hello"]; |
| Optional Chaining | x.get("hi").get("world") |
| Spread Operator | [...xs] |
| Type Assertions | "hello" as any |
| For Loops | for(int x = 0; i < 10; i++) |
| For Of Loops | for(x of xs) |
| For Of Loops with Tuple Destructuring | for([x, y] of xys) |
| Do-While and While Loops | while (true) {...} |
| Typed and Untyped Variable Declarations | let x: number = 1; let y = 100; |
| Comments, Multiline Comments | // Comment |
| Returning without Expressions | return; |
| Try-Catch Statements with a Fixed Exception Type | try {...} catch (e) {...} |
| Throw Statements | throw new Error("..." |
| Importing the crypto Library | require("crypto") |
| Global Scope Objects | Math, parseInt |
| Automatic Semicolon Insertion | |
+
+Table 6.Unsupported TypeScript features.
+
+| s | DERIVABLE(qs) |
| l | {T | pmatch(l,T),T ∈ {number, string, boolean}} |
| x | {T | x ≤ n, (n : T) ∈ Γ} |
| (¯p) => e | { (¯p) => T | REACHABLE(DERIVABLE(qe),T)} |
| (e | {T | REACHABLE(DERIVABLE(qe),T)} |
| e ⊙ | {T | ∃S': Γ ↔ e : S ∧ S ⊕ S': T} |
| e( | {R | Γ ↔ e: (¯p) => R} |
| e.a | {S | a ≤ n, Γ ↔ e : T, LOOKUP(T,n) = S} |
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| Input: Current type T of some expression e, goal type G |
| Output: Whether G can be reached by extending e |
| 1: function REACHABLE(T, G) |
| 2: if T = G then return true | ▷ The goal type is successfully found |
| 3: if T is marked then return false else mark T | ▷ Type T is marked to avoid cycles |
| 4: for each valid extension step ⌿ from T do |
| 5: S := the resulting type of applying ⌿ on T |
| 6: if PRUNESEARCH(T, G, S) continue | ▷ Prune the search to ensure termination |
| 7: if REACHABLE(S, G) return true | ▷ Recurse to the next round of extension |
| 8: return false | ▷ No suitable extension is found |
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+ "content": "The type reachability algorithm, Algorithm 2, implements a depth-first search over this type graph, starting from the current type "
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+ "content": " (Line 2), marking any visited types to prevent cycles (Line 3). Then, it proceeds to iterate over all valid extension steps from "
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+ "type": "text",
+ "content": " after the extension step is applied (Line 5). In the conceptualized type graph, as described in the previous paragraph, this is equivalent to exploring all outgoing edges from "
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+ "content": ". At Line 7, we proceed to recursively search if "
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+ "type": "text",
+ "content": ". If all recursive calls are unsuccessful, the goal type can not be reached (Line 8)."
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+ "type": "text",
+ "content": "Some programming languages define self-referential default members, e.g., clone in Java or value0f in TypeScript, which are nullary functions that return a value of the same type as the callee, "
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+ "type": "inline_equation",
+ "content": "(\\mathbf{\\beta})\\Rightarrow (\\mathbf{\\beta})\\Rightarrow S"
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+ "type": "text",
+ "content": ". We therefore need to restrict the type search to a finite set of types to ensure termination. At Line 6 of Algorithm 2, we add a heuristic PRUNESEARCH into the search, which decides where to prune the search process. We develop a simple heuristic based on the results from Gvero et al. [30]. This heuristic prunes exploration of types with higher complexity than goal or source type if they do not contain yet unexplored primitive types, thus preventing exploration of arbitrarily complex types. The details of this heuristic are presented in Appendix A.3. While ensuring termination, our heuristic leads to incompleteness and the potential rejection of well-typed expressions. However, this effect is less pronounced in practical usage, as only highly complex (thus less realistically used) types are avoided."
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+ "content": "We proceed to prove the soundness of Algorithm 2 below."
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+ "content": "L(A_e \\downarrow T) \\subseteq \\{s \\mid \\Gamma \\vdash s : T\\}"
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+ "content": " by accepting all strings, except for existing identifiers. This automaton is a prefix automaton since an accepting state can always be reached by appending characters to the declared identifier. The return statement automaton is "
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+ "content": " when outside a function and restricts the parsed expression to the return type of the surrounding function otherwise. The remaining automata are mainly concatenations of previously defined automata and recursive invocations of "
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+ "content": " in Line 2 of Algorithm 2."
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| (a) | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split() | // find all words with consonants function select_words(s: string): string[] { for (const word of s. split(' ') |
| (b) | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } // No return } | function largest_divisor(n: number): number { for(let i = n - 1; i > 0; i-- ) { if(n % i == 0) return i; } return 1; } |
| (c) | // insert a delimiter between every element return nums.reduce( (acc, curr, index) => { acc.pushurr); return acc; }, []) | // insert a delimiter between every element return nums.reduce( (acc: number[] , num, index) => { acc.pushurr); return acc; }, []) |
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+ "content": "Figure 9. Three examples illustrating the effect of type-constrained sampling. Left are unconstrained generations with problematic tokens highlighted in red, and right are type-constrained results with corrected tokens highlighted in green, adapted for clarity. In (a), Gemma 2 2B attempts to call split, missing required arguments. In (b), DeepSeekCoder 33B attempts to complete a function without a guaranteed return. The issue is resolved by forcing generation of another statement after the main loop. In (c), Gemma 2 9B calls reduce with an anonymous function without type annotation. This leads to an incorrect type inference for the first parameter. The issue is solved by guiding the model to add type annotation."
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+ "content": "Incorrect Type Inference. In Figure 9c, the task is to insert a delimiter between every element in an array. Gemma 2 9B solves this with the reduce function. This generic function accepts two arguments; first, a callback function that is called consecutively for every element in the array and accumulates a result, second, an initial value for the callback function. The type of the accumulator of the callback is derived implicitly from the second argument, which is an empty array in the given example. TypeScript infers special type never[] for the empty array, disallowing inserting curr of type number through push. Therefore, the program fails to compile. This issue is a well-known limitation of the TypeScript compiler, often confusing even expert developers [47, 48]. Our method resolves it by enforcing adequate type annotation on the first argument of the callback function."
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+ "content": "In this work, we explored how type systems in programming languages can be used to guide language models during decoding. Concretely, we design and implement prefix automata to perform type constraining for a foundational simply typed language and then extend it to the popular language TypeScript. We extensively evaluate the impact of using such constraints for code synthesis, translation, and repair and observe that we more than halve compilation errors on a diverse set of models and consistently increase functional correctness. We further explore qualitatively how the constraining positively impacts code generation. We conclude that such type constraining should be implemented for more programming languages, and has the potential to generally improve code generation in many domains."
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+ "content": "Informally, concatenation preserves the parsing behavior of both "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{X}"
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+ {
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+ "type": "text",
+ "content": " and "
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+ "type": "inline_equation",
+ "content": "A_{Y}"
+ },
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+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " in their respective states. When "
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+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{XY}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " reaches an accepting state of "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " and receives another input character, it either remains in "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " or transitions to "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{Y}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", as defined in the second case of "
+ },
+ {
+ "bbox": [
+ 42,
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta_{XY}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". Essentially, this maintains outgoing edges from accepting states in "
+ },
+ {
+ "bbox": [
+ 42,
+ 503,
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+ ],
+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
+ 42,
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+ ],
+ "type": "text",
+ "content": " while adding edges from these accepting states to initial states of "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{Y}"
+ },
+ {
+ "bbox": [
+ 42,
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 17
+ },
+ {
+ "bbox": [
+ 42,
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
+ {
+ "bbox": [
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+ "spans": [
+ {
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+ "type": "text",
+ "content": "It follows from a similar argument that "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{XY}) = L(A_X) \\circ L(A_Y)"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", where "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_X) \\circ L(A_Y)"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " is defined as "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "\\{s_X \\circ s_Y \\mid s_X \\in L(A_X), s_Y \\in L(A_Y)\\}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". We first show "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{XY}) \\subseteq L(A_X) \\circ L(A_Y)"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". Due to (P1), we can always split any "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s \\in L(A_{XY})"
+ },
+ {
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+ "type": "text",
+ "content": " into "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "s_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " that extends from "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "I_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " to "
+ },
+ {
+ "bbox": [
+ 42,
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+ 441,
+ 635
+ ],
+ "type": "inline_equation",
+ "content": "F_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " and "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s_Y"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " that extends from "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "I_Y"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " to "
+ },
+ {
+ "bbox": [
+ 42,
+ 563,
+ 441,
+ 635
+ ],
+ "type": "inline_equation",
+ "content": "F_Y"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ". Then "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s_X \\in L(A_X)"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " and "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "s_Y \\in L(A_Y)"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". For "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_X) \\circ L(A_Y) \\subseteq L(A_X \\circ A_Y)"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", we pick any "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s_X \\circ s_Y"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " from "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_X) \\circ L(A_Y)"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " and parse it using "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{XY}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". We observe that it will first traverse from "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "I_X"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " to "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "F_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " consuming "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "s_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", and then transition through "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "I_Y"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " to "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "F_Y"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " by consuming "
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+ "type": "inline_equation",
+ "content": "s_Y"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 18
+ },
+ {
+ "bbox": [
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+ 441,
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
+ {
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+ "spans": [
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+ "type": "text",
+ "content": "Moreover "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "A_{XY}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " is a prefix automaton, if "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " and "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "A_{Y}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " are prefix automata and "
+ },
+ {
+ "bbox": [
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+ 441,
+ 660
+ ],
+ "type": "inline_equation",
+ "content": "L(A_{Y}) \\neq \\emptyset"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". Since "
+ },
+ {
+ "bbox": [
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+ 441,
+ 660
+ ],
+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " is a prefix automaton, we can reach "
+ },
+ {
+ "bbox": [
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+ 441,
+ 660
+ ],
+ "type": "inline_equation",
+ "content": "F_{X}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " from any state in "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "Q_{X}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". From "
+ },
+ {
+ "bbox": [
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+ 660
+ ],
+ "type": "inline_equation",
+ "content": "F_{X}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " we additionally reach"
+ }
+ ]
+ }
+ ],
+ "index": 19
+ }
+ ],
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+ "type": "text",
+ "content": "171:26"
+ }
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+ "type": "text",
+ "content": "Niels Mündler*, Jingxuan He*, Hao Wang, Koushik Sen, Dawn Song, Martin Vechev"
+ }
+ ]
+ }
+ ],
+ "index": 1
+ }
+ ],
+ "page_size": [
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+ {
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+ "spans": [
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+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ". Since "
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+ {
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+ "type": "text",
+ "content": " is a prefix automaton, we can reach "
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+ "type": "inline_equation",
+ "content": "F_{Y}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " for any state in "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "Q_{Y}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". This construction is a prefix automaton only if "
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+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "I_{Y} \\neq \\emptyset"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", which, due to the prefix property, is equivalent to "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{Y}) \\neq \\emptyset"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 2
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+ "type": "text",
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+ "spans": [
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+ "bbox": [
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+ ],
+ "type": "text",
+ "content": "Kleene-Star. We define the Kleene-Star automaton "
+ },
+ {
+ "bbox": [
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+ 115,
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+ 151
+ ],
+ "type": "inline_equation",
+ "content": "A_{\\overline{X}}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " that parses indefinite repetitions of words accepted by "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "X"
+ },
+ {
+ "bbox": [
+ 42,
+ 115,
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+ 151
+ ],
+ "type": "text",
+ "content": ". First, we consider all initial states as final states, i.e., we ensure "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "I_X \\subseteq F_{\\overline{X}}"
+ },
+ {
+ "bbox": [
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+ 440,
+ 151
+ ],
+ "type": "text",
+ "content": ". Then we add transitions to the transition function "
+ },
+ {
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+ 151
+ ],
+ "type": "inline_equation",
+ "content": "\\delta_X"
+ },
+ {
+ "bbox": [
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+ 151
+ ],
+ "type": "text",
+ "content": " from the final states "
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+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "F_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " back to the initial states "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "I_X"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 3
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "interline_equation",
+ "angle": 0,
+ "lines": [
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+ "spans": [
+ {
+ "bbox": [
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+ ],
+ "type": "interline_equation",
+ "content": "\\delta_ {\\overline {{X}}} (q _ {X}, c) := \\left\\{ \\begin{array}{l l} \\delta_ {X} (q _ {X}, c) & \\text {i f q \\not \\in F _ {X}} \\\\ \\delta_ {X} (q _ {X}, c) \\cup \\delta (I _ {X}, c) & \\text {i f q _ {X} \\in F _ {X}}. \\end{array} \\right.",
+ "image_path": "7bd7f054612c4b5ce3ec157716303576583113e6a0fcb2d75dc6408106b57761.jpg"
+ }
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
+ {
+ "bbox": [
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+ ],
+ "spans": [
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": "We can quickly see that "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{\\overline{X}}) = \\{\\overline{s} \\mid s \\in L(A_X)\\}"
+ },
+ {
+ "bbox": [
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+ 252
+ ],
+ "type": "text",
+ "content": ", with the same argument as the concatenation automaton. Additionally, because the initial states are accepting, the empty word (zero repetitions) is in "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{\\overline{X}})"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". We similarly see that this is a prefix automaton if "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "A_{X}"
+ },
+ {
+ "bbox": [
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+ 252
+ ],
+ "type": "text",
+ "content": " is a prefix automaton. Note that here "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{X}) \\neq \\emptyset"
+ },
+ {
+ "bbox": [
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+ 252
+ ],
+ "type": "text",
+ "content": " is not required. This is because if "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{X}) \\neq \\emptyset"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", then "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "A_{\\overline{X}} = A_{X} = A_{\\emptyset}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", which is still a prefix automaton."
+ }
+ ]
+ }
+ ],
+ "index": 5
+ },
+ {
+ "bbox": [
+ 42,
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
+ {
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+ ],
+ "spans": [
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+ "bbox": [
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+ ],
+ "type": "text",
+ "content": "Terminals. The terminal automaton "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "A_{\\mathsf{S}}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " parses exactly the terminal S. They accept the usual alphabet "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\Sigma"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " and feature the states "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "Q \\coloneqq \\{q_{\\mathsf{s}} \\mid \\mathsf{s} \\text{ is a suffix of S}\\}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "F \\coloneqq \\{q_{\\varepsilon}\\}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ", "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "I \\coloneqq \\{q_{\\mathsf{S}}\\}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". The transition function "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " is defined as follows:"
+ }
+ ]
+ }
+ ],
+ "index": 6
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "interline_equation",
+ "angle": 0,
+ "lines": [
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+ "bbox": [
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+ "type": "interline_equation",
+ "content": "\\delta (q _ {s}, c) := \\left\\{ \\begin{array}{l l} \\{q _ {s ^ {\\prime}} \\} & \\text {i f c \\circ s ^ {\\prime} = s} \\\\ \\varnothing & \\text {o t h e r w i s e .} \\end{array} \\right.",
+ "image_path": "b8dd3da9566767a457ff25647916a8656a65423e1b578756cff759a72841a378.jpg"
+ }
+ ]
+ }
+ ],
+ "index": 7
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
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+ "spans": [
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+ ],
+ "type": "text",
+ "content": "Clearly "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "A_{\\mathfrak{S}}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " is a prefix automaton. We can show inductively that for any "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s: \\gamma(q_{s}, s') = \\{q_{\\varepsilon}\\} \\Longleftrightarrow s = s'"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", and thus "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "L(A_{\\mathfrak{S}}) = \\{\\mathfrak{S}\\}"
+ },
+ {
+ "bbox": [
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+ 440,
+ 394
+ ],
+ "type": "text",
+ "content": ". With a simple modification, we introduce "
+ },
+ {
+ "bbox": [
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+ 440,
+ 394
+ ],
+ "type": "inline_equation",
+ "content": "A_{\\mathfrak{s}}^{W}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", where "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "W"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " denotes whitespace characters. The transition function is defined as "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta(q_{\\mathfrak{s}}^{W}, c) := \\{q_{\\mathfrak{s}}^{W}\\}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " if "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "c \\in W"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": "; otherwise, "
+ },
+ {
+ "bbox": [
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+ 334,
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta(q_{c \\circ s}^{W}, t) := \\{q_{\\mathfrak{s}}^{W}\\}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". This allows arbitrary whitespace before parsing "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "s"
+ },
+ {
+ "bbox": [
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+ 394
+ ],
+ "type": "text",
+ "content": ". This is how we implement syntactic indifference to whitespace between terminals."
+ }
+ ]
+ }
+ ],
+ "index": 8
+ },
+ {
+ "bbox": [
+ 43,
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+ 124,
+ 416
+ ],
+ "type": "title",
+ "angle": 0,
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+ ],
+ "type": "text",
+ "content": "A.2 Expressions"
+ }
+ ]
+ }
+ ],
+ "index": 9
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "angle": 0,
+ "lines": [
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+ "spans": [
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+ "type": "text",
+ "content": "Expressions are parsed using recursive automatons as introduced in §3.4. In this part of the Appendix, we describe in more detail how information is passed between states."
+ }
+ ]
+ }
+ ],
+ "index": 10
+ },
+ {
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+ "type": "text",
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+ "lines": [
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+ "spans": [
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+ "type": "text",
+ "content": "Notation. In the following, we will implicitly assume that "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta(q, c) = \\emptyset"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " if not explicitly defined otherwise, making notation more concise. For any state, we access the following information through dot notation or the special notation on the state, which we assume is passed to subsequent states through the transition function (unless otherwise stated). This information is alternatively passed through to entire automata in composite automata, e.g., in "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "A_{XY}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " from "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "A_X"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " to "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "A_Y"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 11
+ },
+ {
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+ "type": "list",
+ "angle": 0,
+ "index": 17,
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+ "type": "text",
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+ "content": "- "
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+ {
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+ "type": "inline_equation",
+ "content": "q \\in F_X"
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+ {
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+ "type": "text",
+ "content": ": Whether state "
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+ "type": "inline_equation",
+ "content": "q"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " is an accepting state of the automaton "
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+ {
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+ "type": "inline_equation",
+ "content": "A_X"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 12
+ },
+ {
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+ "type": "text",
+ "angle": 0,
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+ "type": "text",
+ "content": "- "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "q. \\Gamma"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ": The type environment based on state "
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+ ],
+ "type": "inline_equation",
+ "content": "q"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " currently being parsed."
+ }
+ ]
+ }
+ ],
+ "index": 13
+ },
+ {
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+ "type": "text",
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+ "lines": [
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+ "type": "inline_equation",
+ "content": "q"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ".LHS: The left-hand side expression of an extending expression represented by state "
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+ {
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+ "type": "inline_equation",
+ "content": "q"
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+ {
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+ ],
+ "type": "text",
+ "content": ", i.e., when extending "
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+ {
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+ "type": "inline_equation",
+ "content": "X"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " with "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "Y"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " and currently parsing "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "q_{Y}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ", then "
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+ "content": "X"
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+ "type": "text",
+ "content": "."
+ }
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+ }
+ ],
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+ {
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+ "type": "text",
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+ "type": "inline_equation",
+ "content": "q"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ".TYP: The described type of the last coherent expression that this state belongs to. This is only defined for accepting states. Generally, we ensure that when some expression "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "e"
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+ "type": "text",
+ "content": " was parsed, the corresponding state "
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+ "type": "inline_equation",
+ "content": "q_{e}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " has attribute "
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+ {
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+ "type": "inline_equation",
+ "content": "q_{e}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ".TYP such that "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "q_{e} \\Gamma \\vdash e : q_{e}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ".TYP."
+ }
+ ]
+ }
+ ],
+ "index": 15
+ },
+ {
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+ "type": "text",
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+ "content": "- "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "q \\downarrow T"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ": Type "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "T"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " to which state "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "q"
+ },
+ {
+ "bbox": [
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+ ],
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+ "content": " returns all types of minimal depth (e.g., string, number, and boolean) that constitute a higher-order type. They are defined as follows:"
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+ "content": ". States and edges along the final path are marked in green and explored nodes in blue. The () => number node is not explored, as complex types are avoided by our heuristic. The node () => string is explored as it enables reaching new type string."
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+ }
+ ],
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+ "content": ", it will also not be accessible from expressions with the same root types but greater depth, such as "
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+ "content": "G = () \\Rightarrow ((.) => \\text{number})"
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+ "content": ". Based on these two ideas, we stop exploring "
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+ "content": "\\text{DEPTH}(S) > \\max(\\text{DEPTH}(G), \\text{DEPTH}(T))"
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+ "type": "text",
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+ }
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+ "type": "text",
+ "content": "Further, if a higher-depth function returns an unexplored type, we need to explore it. Sticking to the example in Figure 11, type number has the member toString of type () => string. The type string can only be reached by exploring the member access at depth 1. On the contrary, we do not explore a higher-depth function if it does not introduce novel types other than those explored. To achieve this, we adapt Algorithm 2 to additionally define a set of root types "
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+ "content": ". We do not explore "
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+ }
+ ]
+ }
+ ],
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+ },
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+ "content": "Taking the conjunction of the aforementioned two aspects, our pruning heuristic is implemented as PRUNESEARCH"
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+ "type": "inline_equation",
+ "content": "(T,G,S) \\coloneqq \\mathrm{DEPTH}(S) > \\max(\\mathrm{DEPTH}(T), \\mathrm{DEPTH}(S)) \\wedge \\mathrm{ROOT}(S) \\subseteq R"
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+ "content": ". The restrictions based on depth and root types are based on the results of the rigorously analyzed search over succinct types by Gvero et al. [30]. This provides a robust heuristic for exploring as many relevant inhabitable types as possible. However, due to the additional complexity introduced by the lookup function, we can not guarantee completeness and instead refer to the strong empirical results in our evaluation in §5 as evidence of the search's high coverage."
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+ "content": "\\mathrm{DERIVABLE}(q_{(\\overline{p})\\Rightarrow e})\\coloneqq \\{(\\overline{p})\\Rightarrow T\\mid \\mathrm{REACHABLE}(\\mathrm{DERIVABLE}(q_e),T)\\}"
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+ "content": " to explore. A similar issue exists for grouped expressions, as their DERIVABLE function is also defined to enumerate reachable types. We introduce two optimization heuristics to address this problem."
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+ ]
+ }
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+ "content": " using the pruning heuristic for reachability of target type "
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+ "content": ". This leads to a sound but potentially incomplete version of DERIVABLE. However, since the final goal is to reach "
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+ "content": ", this heuristic provides a practically useful set of all relevant derivable types."
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+ "content": ") can be integrated into a single call to further reduce the amount of explored types. Concretely, when discovering some type "
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+ "content": " in REACHABLE( DERIVABLE "
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+ "content": "(q_e)"
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+ "type": "text",
+ "content": "), as per the previous heuristic, we allow transitioning directly to REACHABLE "
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+ "type": "inline_equation",
+ "content": "(\\overline{p}) \\Rightarrow M, G"
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+ "content": " to allow a depth-prioritizing exploration of the search graph. This allows us to efficiently discover a path to "
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+ "type": "text",
+ "content": " if it exists."
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+ "content": "We define the remaining automata to capture the complete language from §3.1. To correctly handle function return types, we pass on related information when entering function bodies:"
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+ }
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+ "type": "text",
+ "content": " RETURNED: Whether the currently parsed program block has returned in all branches."
+ }
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+ }
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+ "content": "- q.MUSTRETURN: Whether the currently parsed program block must return (i.e., If-Then-Else branches do not need to contain return statements even if a return type is expected of the surrounding code block)."
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+ }
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+ }
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+ "type": "text",
+ "content": "The single statement automaton is another recursive definition, since some statements, e.g., If-Then-Else, can themselves contain statements. The statement automaton is defined recursively as "
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+ "content": "A_{s} \\coloneqq A_{\\mathrm{DECL}} \\cup A_{\\mathrm{EXPR}} \\cup A_{\\mathrm{RET}} \\cup A_{\\mathrm{BLOCK}} \\cup A_{\\mathrm{FUN}} \\cup A_{\\mathrm{ITE}}"
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+ "type": "text",
+ "content": ". The expression statement automaton and block automaton are simply defined as "
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+ "content": "A_{\\mathrm{BLOCK}} \\coloneqq A_{\\{\\overline{s}\\}}"
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+ "content": ". The declaration automaton "
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+ "type": "inline_equation",
+ "content": "A_{\\mathrm{DECL}} \\coloneqq A_{\\mathrm{let} x:T}"
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| Expressions, Statements, Function Declarations | (LB as introduced in §3) |
| Additional Literals: BigInt, Regex, Template Strings | 10n, /\\d*, 'hello ${user}' |
| Additional Types: void, null, undefined | void, undefined, null |
| Index Signature Types and Literals | let x: {{y: number}: string} = 1: "hi"; |
| Anonymous Functions | function(): bool {return true} |
| Lambda Functions with and without Function Bodies | x => {return y}, x => y |
| Ternary and LogicOperators | ? :, |, && |
| Arithmetic and Boolean Operations | +, -, **, &, ! |
| Assigning Pre-and Postfix Operators | ++, -- |
| Arrays | [1, 2, 3] |
| Access and Assignment to Computed Members | x[10] = y[i]; |
| Constructors and "new" Calls | let x = new Number(1); |
| Calls with Optional and Rest Parameters | function foo(x?: number, y...: string) |
| Sets and Maps | Map<string, number>}() |
| Parameterized Constructor Calls | new Set<string>}() |
| Tuples | let x: [int, string] = [1, "hello"]; |
| Optional Chaining | x.get("hi").get("world") |
| Spread Operator | [...xs] |
| Type Assertions | "hello" as any |
| For Loops | for(int x = 0; i < 10; i++) |
| For Of Loops | for(x of xs) |
| For Of Loops with Tuple Destructuring | for([x, y] of xys) |
| Do-While and While Loops | while (true) {...} |
| Typed and Untyped Variable Declarations | let x: number = 1; let y = 100; |
| Comments, Multiline Comments | // Comment |
| Returning without Expressions | return; |
| Try-Catch Statements with a Fixed Exception Type | try {...} catch (e) {...} |
| Throw Statements | throw new Error("..." |
| Importing the crypto Library | require("crypto") |
| Global Scope Objects | Math, parseInt |
| Automatic Semicolon Insertion | |
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