2402/2402.01259.md

Title: Position Aware 60 GHz mmWave Beamforming for V2V Communications Utilizing Deep Learning

URL Source: https://arxiv.org/html/2402.01259

Markdown Content: Muhammad Baqer Mollah 1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT, Honggang Wang 2 2{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT, and Hua Fang 3 3{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT 1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Dept. of Electrical and Computer Engineering, University of Massachusetts Dartmouth, MA 02747

2 2{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT Dept. of Graduate Computer Science and Engineering, Yeshiva University, NY 10016

3 3{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT Dept. of Computer and Information Science, University of Massachusetts Dartmouth, MA 02747

Emails: mmollah@umassd.edu, honggang.wang@yu.edu, and hfang2@umassd.edu

Abstract

Beamforming techniques are considered as essential parts to compensate the severe path loss in millimeter-wave (mmWave) communications by adopting large antenna arrays and formulating narrow beams to obtain satisfactory received powers. However, performing accurate beam alignment over such narrow beams for efficient link configuration by traditional beam selection approaches, mainly relied on channel state information, typically impose significant latency and computing overheads, which is often infeasible in vehicle-to-vehicle (V2V) communications like highly dynamic scenarios. In contrast, utilizing out-of-band contextual information, such as vehicular position information, is a potential alternative to reduce such overheads. In this context, this paper presents a deep learning-based solution on utilizing the vehicular position information for predicting the optimal beams having sufficient mmWave received powers so that the best V2V line-of-sight links can be ensured proactively. After experimental evaluation of the proposed solution on real-world measured mmWave sensing and communications datasets, the results show that the solution can achieve up to 84.58% of received power of link status on average, which confirm a promising solution for beamforming in mmWave at 60 GHz enabled V2V communications. ††This paper has been accepted to present at 2024 IEEE International Conference on Communications (ICC), Denver, CO, USA.

Index Terms:

Beamforming, Connected and Autonomous Vehicles, Deep Learning, Millimeter-Wave Communications, Out-of-Band Information, Vehicle-to-Vehicle Communications.

I Introduction

††©2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. As a key enabler for communications technologies in connected and autonomous vehicles (CAVs) domain, the utilization of millimeter-Wave (mmWave) bands (e.g., 28 GHz and 57-71 GHz bands) has been promised to bring an abundance of spectrum resources [1, 2]. For example, in the context of cooperative perceptions like high-throughput and low latency demanding applications in CAVs, the connected vehicles mainly exchange a vast amount of 3D point cloud data from LiDAR sensors instead of lightweight textual data [3]. Realizing the high throughput and low latency benefits, mmWave communications enabled by vehicle-to-vehicle (V2V) communications pave the way towards accessible and safe autonomous transportation systems.

On the other side, one inherent property of mmWave band is having high path attenuation of its signals, leading to drastically impact on the link quality performance degradation [4]. In particular, beamforming techniques are utilized to address this bottleneck, whereby massive antenna arrays are typically employed including formulating the narrow beams, thereby achieving desired high throughput from mmWave communications. Likewise, the narrow beams are expected to be aligned precisely and even required to re-direct in accordance with the environmental settings and any changes. Typically, in codebook based beamforming, the beam selection techniques are applied to find the optimal beams over a number of pre-defined beam codebooks.

In practice, with standard defined beam selection techniques, the vehicles usually select the best beam pairs through an exhaustive beam measurements process, which basically introduce computing and latency overheads while applying in highly dynamic moving vehicles. This overhead problem occurs mainly due to tight contact times (the time period of receiver’s received the correct packets), frequent beam realignments, and change of channel state estimation to perform beam computing. Hence, research efforts are crucial to avoid beam misalignment along with reduced and reasonable overheads in order to take the fully potential benefits from mmWave communications.

Considering this challenge in vehicular settings, recent works have suggested effective approaches to configure the communications links through leveraging the out-of-band contextual information, which can be obtained from other lower bands (sub-6 GHz bands) [5, 6], RADAR communications bands [7, 8, 9], or extracted useful sensing information from on-board vehicular non-RF sensing devices [10, 11, 12]. For instance, deployment based the 3GPP 5G NR (New Radio) [13] and IEEE 802.11ad [14] standards might take around 10 milliseconds to select the best beams through searching over all beam directions and need to run over repeatedly when the vehicles move forward. In this regard, combining the surrounding perception capable side-information collected from the vehicle sensors and then, exchanging with sub-6 GHz channels has recently been demonstrated in work [15] as promising results in terms of decreasing the end-to-end latency, which helps to reduce 52.75% on average time in IEEE 802.11ad standard. Besides, another work in [16] has observed regarding the beam search space by utilizing almost similar side-information, 80% and 50% on average overhead caused by beam selection can be reduced for 3GPP 5G NR and IEEE 802.11ad, respectively.

Over the recent years, several approaches pursuing efficient beamforming have been introduced based on the out-of-band position specific information. In particular, the solution in [17] has leveraged machine learning technique to investigate how position information can help to reduce the beam training overheads. Likewise, the work in [18] emphasizes on both location and orientation information to perform 3D beam selection by utilizing deep learning technique. Further, the authors in [19] have proposed an approach, where a multi-path fingerprint-based database is maintained which records fingerprints of necessary location information along with channel characteristics so that the knowledge of reliable beamforming can be known in advance. Besides, almost similar concepts have been utilized in [20] and [21]. In [20], the authors utilize spatially indexed historical information so that statistically significant beam sectors can be chosen in specific locations. This proposed work is particularly focused on IEEE 802.11ad standard with an aim of reducing the time of beam sweeping, thereby improving the available time for data communications. And, the work in [21] has utilized the information about spatial correlation of stronger channels in-between the receiver and sender at given locations so that the users are able to track the information beforehand to establish communication link quickly.

However, the aforementioned works are mainly limited to either for vehicle-to-infrastructure (V2I) communications or based on ray-tracing simulations, but utilizing real-world measured wireless data as well as considering the mobility of connected vehicles under V2V connectivity have not been investigated yet. With these limitations in mind, we introduce a solution for mmWave beamforming for V2V communications with the aid of a proposed deep learning model. Specifically, the deep learning model takes vehicular position information as input and predicts a subset of beams, that is, top-M 𝑀 M italic_M beams, thus, significantly lowers down the beam search space. Different from other out-of-band enabled approaches, the proposed solution fully leverages the position data obtained from the global positioning sensors installed in the connected vehicles, subsequently, lowering down the complicacy. Finally, we validate our proposed solution with experiments on real-world 60 GHz mmWave sensing and communications datasets, compare with state-of-the-art approach, and present the results in terms of two meaningful matrices, namely accuracies and received power ratios.

II System Model and Problem Statement

In this section, we first present our considered system model, and then, we describe the problem statement.

II-A System Model

In this work, we consider a mmWave communications system model operating at 60 GHz frequency band as described in Fig. 1. here, the system model is comprised of a moving vehicle v 2 subscript 𝑣 2 v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT to provide communications services, e.g., cooperative perception, to another moving connected vehicle v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT within its coverage area. The v 2 subscript 𝑣 2 v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT works as a transmitter T x subscript 𝑇 𝑥 T_{x}italic_T start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT measures its own location information, that is, latitude and longitude, and shares the information with v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT in real-time manner, while the v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT collects and processes the received location information and works as a receiver R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT. Both vehicles, v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and v 2 subscript 𝑣 2 v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, are connected with each other by vehicle-to-vehicle (V2V) communication links.

Figure 1: Illustration of considered mmWave enabled V2V communications system model.

The connected vehicle v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT consists of N R subscript 𝑁 𝑅 N_{R}italic_N start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT antenna array elements, fixed beam codebooks 𝒬 𝒬\mathbfcal{Q}roman_𝒬, and each codebook describes particular beam orientation, consequently, has received power at every beams. The beam codebooks can be expressed as 𝒬⁢ℑ⁢{∐∞⁢⇔⁢∐∈⁢⇔⁢↙⁢↙⁢↙⁢⇔⁢∐♣⁢𝒬⁢♣⁢¬⁢∐⟩∈𝒞 𝒩 ℛ×∞}𝒬 ℑ subscript∐∞⇔subscript∐∈⇔↙↙↙⇔subscript∐♣𝒬♣¬subscript∐⟩superscript 𝒞 subscript 𝒩 ℛ∞\mathbfcal{Q}={q_{1},q_{2},...,q_{|\mathbfcal{Q}|}:q_{i}\in\mathbb{C}^{N_{R}% \times 1}}roman_𝒬 roman_ℑ { ∐ start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT ⇔ ∐ start_POSTSUBSCRIPT ∈ end_POSTSUBSCRIPT ⇔ ↙ ↙ ↙ ⇔ ∐ start_POSTSUBSCRIPT ♣ roman_𝒬 ♣ end_POSTSUBSCRIPT ¬ ∐ start_POSTSUBSCRIPT ⟩ end_POSTSUBSCRIPT ∈ roman_𝒞 start_POSTSUPERSCRIPT roman_𝒩 start_POSTSUBSCRIPT roman_ℛ end_POSTSUBSCRIPT × ∞ end_POSTSUPERSCRIPT }, where |𝒬♣|\mathbfcal{Q}|| roman_𝒬 ♣ denotes the total number of beamforming vectors. Besides, the antenna array elements enable v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT to perform beamforming so that it can obtain adequate received power. Whereas, the vehicle user v 2 subscript 𝑣 2 v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT has, for the purpose of simplicity, one antenna and assuming it is oriented always towards the v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT. Thus, the total beamforming vector can be represented by (𝒬×∞⇒(\mathbfcal{Q}\times 1)( roman_𝒬 × ∞ ⇒.

We further consider that OFDM is used in the downlink communications with 𝒩 𝒩\mathcal{N}caligraphic_N subcarriers. For a given transmitted symbol s n∈ℂ subscript 𝑠 𝑛 ℂ s_{n}\in\mathbb{C}italic_s start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ∈ blackboard_C, the downlink received signal at n t⁢h superscript 𝑛 𝑡 ℎ n^{th}italic_n start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT subcarrier at discrete time instant t 𝑡 t italic_t can be written as:

x n⁢[t]=𝐡 n T⁢[t]⁢q i⁢[t]⁢s n+ω n⁢[t]subscript 𝑥 𝑛 delimited-[]𝑡 superscript subscript 𝐡 𝑛 𝑇 delimited-[]𝑡 subscript 𝑞 𝑖 delimited-[]𝑡 subscript 𝑠 𝑛 subscript 𝜔 𝑛 delimited-[]𝑡 x_{n}[t]=\mathbf{h}{n}^{T}[t]q{i}[t]s_{n}+\omega_{n}[t]italic_x start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT [ italic_t ] = bold_h start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_T end_POSTSUPERSCRIPT [ italic_t ] italic_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT [ italic_t ] italic_s start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT + italic_ω start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT italic_t

where, 𝐡 n⁢[t]∈ℂ N R×1 subscript 𝐡 𝑛 delimited-[]𝑡 superscript ℂ subscript 𝑁 𝑅 1\mathbf{h}{n}[t]\in\mathbb{C}^{N{R}\times 1}bold_h start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT [ italic_t ] ∈ blackboard_C start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT × 1 end_POSTSUPERSCRIPT is the channel vectors between v 2 subscript 𝑣 2 v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and ω n⁢[t]subscript 𝜔 𝑛 delimited-[]𝑡\omega_{n}[t]italic_ω start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT [ italic_t ] is the received noise.

II-B Problem Statement

The primary task of this work is to make optimal beams predictions from the received powers, and from the received signal x n⁢[t]subscript 𝑥 𝑛 delimited-[]𝑡 x_{n}[t]italic_x start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT [ italic_t ], we can get the received power by summing over 𝒩 𝒩\mathcal{N}caligraphic_N subcarriers at the v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT side for the receiver codebook i 𝑖 i italic_i as:

𝒫 i=∑n=1 𝒩|𝐡 n T⁢[t]⁢q i⁢[t]⁢s n|2 subscript 𝒫 𝑖 superscript subscript 𝑛 1 𝒩 superscript superscript subscript 𝐡 𝑛 𝑇 delimited-[]𝑡 subscript 𝑞 𝑖 delimited-[]𝑡 subscript 𝑠 𝑛 2\mathcal{P}{i}=\sum{n=1}^{\mathcal{N}}|\mathbf{h}{n}^{T}[t]q{i}[t]s_{n}|^{2}caligraphic_P start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT = ∑ start_POSTSUBSCRIPT italic_n = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT caligraphic_N end_POSTSUPERSCRIPT | bold_h start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_T end_POSTSUPERSCRIPT [ italic_t ] italic_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT [ italic_t ] italic_s start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT(2)

Given the position sensing data and mmWave received power, determining the optimal beam q isuperscript subscript 𝑞 𝑖 q_{i}^{}italic_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT at the v 1 subscript 𝑣 1 v_{1}italic_v start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT from the beam codebook 𝒬 𝒬\mathbfcal{Q}roman_𝒬 is referred as maximizing the received power. However, if we convert beam codebooks 𝒬⁢ℑ⁢{∐∞⁢⇔⁢∐∈⁢⇔⁢↙⁢↙⁢↙⁢⇔⁢∐♣⁢𝒬⁢♣}𝒬 ℑ subscript∐∞⇔subscript∐∈⇔↙↙↙⇔subscript∐♣𝒬♣\mathbfcal{Q}={q_{1},q_{2},...,q_{|\mathbfcal{Q}|}}roman_𝒬 roman_ℑ { ∐ start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT ⇔ ∐ start_POSTSUBSCRIPT ∈ end_POSTSUBSCRIPT ⇔ ↙ ↙ ↙ ⇔ ∐ start_POSTSUBSCRIPT ♣ roman_𝒬 ♣ end_POSTSUBSCRIPT } into a unique index as ℐ∈{1,2,3,…,ℳ:ℳ≤|𝒬♣}\mathcal{I}\in{1,2,3,...,\mathcal{M}:\mathcal{M}\leq|\mathbfcal{Q}|}caligraphic_I ∈ { 1 , 2 , 3 , … , caligraphic_M : caligraphic_M ≤ | roman_𝒬 ♣ }, predicting optimal beam from beam codebooks can be essentially equivalent to predicting optimal beam index. Then, we can formulate predicting the optimal beam problem as:

ℐ*=arg max i∈{1,2,3,…,|𝒬♣}⁢𝒫⟩\mathcal{I}^{*}=\underset{i\in{1,2,3,...,|\mathbfcal{Q}|}}{\text{arg max}}% \mathcal{P}_{i}caligraphic_I start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = start_UNDERACCENT italic_i ∈ { 1 , 2 , 3 , … , | roman_𝒬 ♣ } end_UNDERACCENT start_ARG arg max end_ARG roman_𝒫 start_POSTSUBSCRIPT ⟩ end_POSTSUBSCRIPT(3)

In this work, our goal is to predict a set of recommended beams ℬ={ℐ 1,ℐ 2,ℐ 3,…,ℐ M}ℬ subscript ℐ 1 subscript ℐ 2 subscript ℐ 3…subscript ℐ 𝑀\mathcal{B}={\mathcal{I}{1},\mathcal{I}{2},\mathcal{I}{3},...,\mathcal{I}% {M}}caligraphic_B = { caligraphic_I start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , caligraphic_I start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , caligraphic_I start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT , … , caligraphic_I start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT } as top-M 𝑀 M italic_M beams such that ℐ∈ℬ superscript ℐ ℬ\mathcal{I}^{}\in\mathcal{B}caligraphic_I start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ∈ caligraphic_B as top-1 beam.

III Proposed Deep Learning Model

In this section, we describe the proposed solution by first discussing the data preprocessing steps, followed by elaborating the proposed deep learning model architecture.

III-A Position Data Preprocessing

The raw position data captured from GPS sensors are basically in Decimal Degrees, specifically the latitude and longitude values are from −90∘superscript 90-90^{\circ}- 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT to +90∘superscript 90+90^{\circ}+ 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT and −180∘superscript 180-180^{\circ}- 180 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT to +180∘superscript 180+180^{\circ}+ 180 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT, respectively. However, in our proposed solution as presented as next subsection, the position data will be fed into a deep learning model as input, and the input is desired to be fixed in size. In this regard, feeding raw position data directly may require developing deep learning model with high complexity in terms of architecture and computational cost. Thus, we first pass through the raw position data into a preprocessing step, namely data normalization, to make fit as well as accelerate the convergence of the proposed deep learning model. We then define the position matrix as X p⁢o⁢s⁢[t]∈ℝ N×2 subscript 𝑋 𝑝 𝑜 𝑠 delimited-[]𝑡 superscript ℝ 𝑁 2 X_{pos}[t]\in\mathbb{R}^{N\times 2}italic_X start_POSTSUBSCRIPT italic_p italic_o italic_s end_POSTSUBSCRIPT [ italic_t ] ∈ blackboard_R start_POSTSUPERSCRIPT italic_N × 2 end_POSTSUPERSCRIPT, where N 𝑁 N italic_N is the total number of samples, and the number 2 2 2 2 is due to having two values at each time instant t 𝑡 t italic_t. After that, we calculate the normalized values of latitude x l⁢t′superscript subscript 𝑥 𝑙 𝑡′x_{lt}^{\prime}italic_x start_POSTSUBSCRIPT italic_l italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and longitude y l⁢g′superscript subscript 𝑦 𝑙 𝑔′y_{lg}^{\prime}italic_y start_POSTSUBSCRIPT italic_l italic_g end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT at each rows of the matrix as: (x l⁢t′,y l⁢g′)=((x l⁢t−x l⁢t⁢⁢m⁢i⁢n)/(x l⁢t⁢_⁢m⁢a⁢x)−x l⁢t⁢_⁢m⁢i⁢n),(x l⁢g−x l⁢g⁢_⁢m⁢i⁢n)/(x l⁢g⁢_⁢m⁢a⁢x−x l⁢g⁢_⁢m⁢i⁢n))(x{lt}^{\prime},y_{lg}^{\prime})=((x_{lt}-x_{lt_min})/(x_{lt_max})-x_{lt_% min}),(x_{lg}-x_{lg_min})/(x_{lg_max}-x_{lg_min}))( italic_x start_POSTSUBSCRIPT italic_l italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_y start_POSTSUBSCRIPT italic_l italic_g end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) = ( ( italic_x start_POSTSUBSCRIPT italic_l italic_t end_POSTSUBSCRIPT - italic_x start_POSTSUBSCRIPT italic_l italic_t _ italic_m italic_i italic_n end_POSTSUBSCRIPT ) / ( italic_x start_POSTSUBSCRIPT italic_l italic_t _ italic_m italic_a italic_x end_POSTSUBSCRIPT ) - italic_x start_POSTSUBSCRIPT italic_l italic_t _ italic_m italic_i italic_n end_POSTSUBSCRIPT ) , ( italic_x start_POSTSUBSCRIPT italic_l italic_g end_POSTSUBSCRIPT - italic_x start_POSTSUBSCRIPT italic_l italic_g _ italic_m italic_i italic_n end_POSTSUBSCRIPT ) / ( italic_x start_POSTSUBSCRIPT italic_l italic_g _ italic_m italic_a italic_x end_POSTSUBSCRIPT - italic_x start_POSTSUBSCRIPT italic_l italic_g _ italic_m italic_i italic_n end_POSTSUBSCRIPT ) ), within Cartesian coordinate system, where x l⁢t subscript 𝑥 𝑙 𝑡 x_{lt}italic_x start_POSTSUBSCRIPT italic_l italic_t end_POSTSUBSCRIPT and x l⁢g subscript 𝑥 𝑙 𝑔 x_{lg}italic_x start_POSTSUBSCRIPT italic_l italic_g end_POSTSUBSCRIPT are the raw latitude and longitude values, while the m⁢a⁢x 𝑚 𝑎 𝑥 max italic_m italic_a italic_x and m⁢i⁢n 𝑚 𝑖 𝑛 min italic_m italic_i italic_n denote their maximum and minimum values, respectively. Finally, the revised matrix with normalized position data is denoted as X p⁢o⁢s′⁢[t]subscript superscript 𝑋′𝑝 𝑜 𝑠 delimited-[]𝑡 X^{\prime}{pos}[t]italic_X start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_p italic_o italic_s end_POSTSUBSCRIPT [ italic_t ], and g t subscript 𝑔 𝑡 g{t}italic_g start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT is considered as a variable representing the vector elements of X p⁢o⁢s′⁢[t]subscript superscript 𝑋′𝑝 𝑜 𝑠 delimited-[]𝑡 X^{\prime}_{pos}[t]italic_X start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_p italic_o italic_s end_POSTSUBSCRIPT [ italic_t ].

III-B Proposed Model Architecture

Figure 2: Proposed deep learning model for mmWave beamforming.

The designed architecture of proposed deep learning model for position data assisted mmWave beamforming task is presented in Fig. 2. The proposed model adopts a convolutional neural network architecture including four components: the convolutional blocks, a flatten layer, and the fully connected layers, followed by a softmax layer, and these components are elaborate as follows.

• Convolutional Blocks: The convolutional blocks, the key building blocks used in our proposed model, are mainly made up of three convolutional blocks. These convolutional blocks are formed together with three sequence of 1D (one-dimensional) convolutional layers, however, each blocks are followed by a max-pooling layer.

• Flatten Layer: After the convolutional blocks, one flatten layer is employed to flatten the output received from the last convolutional block, while not effecting the batch size.

• Fully Connected Layers: Two fully connected layers are incorporated to process the outputs from the flatten layer.

• Softmax Layer: At last, the softmax layer is involved as last layer, where softmax activation function is applied on the output from flatten layer to transform the values into probability scores within the range [0,1]0 1[0,1][ 0 , 1 ] with total value 1, essentially, can be interpreted to eventually determine the top-M 𝑀 M italic_M beams.

Given the sequence vector g t subscript 𝑔 𝑡 g_{t}italic_g start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT as an input to the proposed model, the convolutional block 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 1 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 1\mathsf{ConvNetBlock}{1}sansserif_ConvNetBlock start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT first compute it to extract the features by learning the hidden meaningful representations. This block is repeated two more times as 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2\mathsf{ConvNetBlock}{2}sansserif_ConvNetBlock start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 3 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 3\mathsf{ConvNetBlock}{3}sansserif_ConvNetBlock start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT in the network to make enhanced feature extraction and improved performance. However, the max-pooling layers in both blocks contribute to downsize the feature maps while keeping the most significant features, leading to decreasing the risk of the model becoming overfitted. Then, the output from 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 3 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 3\mathsf{ConvNetBlock}{3}sansserif_ConvNetBlock start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT is passed though the flatten layer. The overall process is presented as follows.

c 1=𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 1⁢(g t)c 2=𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2⁢(c 1)c 3=𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2⁢(c 2)ϝ=𝖥𝗅𝖺𝗍𝗍𝖾𝗇⁢(c 3),subscript 𝑐 1 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 1 subscript 𝑔 𝑡 subscript 𝑐 2 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2 subscript 𝑐 1 subscript 𝑐 3 subscript 𝖢𝗈𝗇𝗏𝖭𝖾𝗍𝖡𝗅𝗈𝖼𝗄 2 subscript 𝑐 2 italic-ϝ 𝖥𝗅𝖺𝗍𝗍𝖾𝗇 subscript 𝑐 3\begin{array}[]{l}c_{1}=\mathsf{ConvNetBlock}{1}(g{t})\ c_{2}=\mathsf{ConvNetBlock}{2}(c{1})\ c_{3}=\mathsf{ConvNetBlock}{2}(c{2})\ \digamma=\mathsf{Flatten}(c_{3}),\end{array}start_ARRAY start_ROW start_CELL italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = sansserif_ConvNetBlock start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_g start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ) end_CELL end_ROW start_ROW start_CELL italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = sansserif_ConvNetBlock start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ) end_CELL end_ROW start_ROW start_CELL italic_c start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT = sansserif_ConvNetBlock start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) end_CELL end_ROW start_ROW start_CELL italic_ϝ = sansserif_Flatten ( italic_c start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) , end_CELL end_ROW end_ARRAY(4)

where, c 1 subscript 𝑐 1 c_{1}italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, c 2 subscript 𝑐 2 c_{2}italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, and c 3 subscript 𝑐 3 c_{3}italic_c start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT are the hidden vectors and ϝ italic-ϝ\digamma italic_ϝ represents the result from the flatten layer. This resulting output ϝ italic-ϝ\digamma italic_ϝ, after that, is forwarded to the two fully connected (dense) layers 𝖥𝖢𝖭 1 subscript 𝖥𝖢𝖭 1\mathsf{FCN}{1}sansserif_FCN start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and 𝖥𝖢𝖭 2 subscript 𝖥𝖢𝖭 2\mathsf{FCN}{2}sansserif_FCN start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT. The two fully connected layers together encompass a prediction by applying weights. If c 1′superscript subscript 𝑐 1′c_{1}^{\prime}italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and c 2′superscript subscript 𝑐 2′c_{2}^{\prime}italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT denote the outputs from the two connected layers, respectively, we can describe as

c 1′=𝖥𝖢𝖭 1⁢(ϝ)c 2′=𝖥𝖢𝖭 2⁢(c 1′).superscript subscript 𝑐 1′subscript 𝖥𝖢𝖭 1 italic-ϝ superscript subscript 𝑐 2′subscript 𝖥𝖢𝖭 2 superscript subscript 𝑐 1′\begin{array}[]{l}c_{1}^{\prime}=\mathsf{FCN}{1}(\digamma)\ c{2}^{\prime}=\mathsf{FCN}{2}(c{1}^{\prime}).\end{array}start_ARRAY start_ROW start_CELL italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT = sansserif_FCN start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_ϝ ) end_CELL end_ROW start_ROW start_CELL italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT = sansserif_FCN start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) . end_CELL end_ROW end_ARRAY(5)

In the end, softmax layer (𝖲𝗈𝖿𝗍𝗆𝖺𝗑 𝖲𝗈𝖿𝗍𝗆𝖺𝗑\mathsf{Softmax}sansserif_Softmax) helps to give the final top-M 𝑀 M italic_M beam prediction result as ℐ^=𝖲𝗈𝖿𝗍𝗆𝖺𝗑⁢(h 2′)^ℐ 𝖲𝗈𝖿𝗍𝗆𝖺𝗑 superscript subscript ℎ 2′\hat{\mathcal{I}}=\mathsf{Softmax}(h_{2}^{\prime})over^ start_ARG caligraphic_I end_ARG = sansserif_Softmax ( italic_h start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) by converting the unnormalized output from the connected layers into normalized values (a probability distribution). However, since our proposed model is particularly designed to predict the top-M 𝑀 M italic_M beams, the cross-entropy is utilized as a loss function with an aim to minimize the loss, which can be calculated by

ℒ⁢(ℐ^,ℐ)=−1 N b⁢∑k=0 N b−1∑l=0 M−1 ℐ(k)⁢log⁡ℐ^(l),ℒ^ℐ ℐ 1 subscript 𝑁 𝑏 superscript subscript 𝑘 0 subscript 𝑁 𝑏 1 superscript subscript 𝑙 0 𝑀 1 superscript ℐ 𝑘 superscript^ℐ 𝑙\mathcal{L}(\hat{\mathcal{I}},\mathcal{I})=-\frac{1}{N_{b}}\sum_{k=0}^{N_{b}-1% }\sum_{l=0}^{M-1}\mathcal{I}^{(k)}\log\hat{\mathcal{I}}^{(l)},caligraphic_L ( over^ start_ARG caligraphic_I end_ARG , caligraphic_I ) = - divide start_ARG 1 end_ARG start_ARG italic_N start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT end_ARG ∑ start_POSTSUBSCRIPT italic_k = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT - 1 end_POSTSUPERSCRIPT ∑ start_POSTSUBSCRIPT italic_l = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_M - 1 end_POSTSUPERSCRIPT caligraphic_I start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT roman_log over^ start_ARG caligraphic_I end_ARG start_POSTSUPERSCRIPT ( italic_l ) end_POSTSUPERSCRIPT ,(6)

where, N b subscript 𝑁 𝑏 N_{b}italic_N start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT represents the number of samples in each batches, M 𝑀 M italic_M denotes the total number of beam indices, ℐ(k)superscript ℐ 𝑘\mathcal{I}^{(k)}caligraphic_I start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT is the ground truth beams indices for k t⁢h superscript 𝑘 𝑡 ℎ k^{th}italic_k start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT sample, and ℐ^(l)superscript^ℐ 𝑙\hat{\mathcal{I}}^{(l)}over^ start_ARG caligraphic_I end_ARG start_POSTSUPERSCRIPT ( italic_l ) end_POSTSUPERSCRIPT is the predicted probabilities of beams indices by softmax for l t⁢h superscript 𝑙 𝑡 ℎ l^{th}italic_l start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT sample. Further, we utilize a stochastic optimization technique namely adaptive moment estimation (Adam) [22] for faster convergence on minimizing the loss function while training the model.

(a)For scenario 36

(b)For scenario 37

(c)For scenario 38

(d)For scenario 39

Figure 3: Visual representation of receiver vehicle’s GPS location data points (400 samples) along with corresponding best beam indices out of 64 beams on Google Map satellite view.

IV Experimental Results

In this section, we describe the results obtained from a series of experiments, followed by datasets description and implementation settings.

IV-A Datasets Description

In this work, we consider the DeepSense6G dataset [23], a collection of real-world mmWave sensing and communications measurements, to evaluate the effectiveness of our proposed top-M 𝑀 M italic_M beam prediction solution presented in Section III. Specifically, following the consistency of our considered system model and formulated problem, we adopt scenario 36 (24,800 samples), scenario 37 (31,000 samples), scenario 38 (36,000 samples), and 39 (20,400 samples). These scenarios are captured with a testbed setup including two moving vehicles (namely, unit 1 1 1 1 and unit 2 2 2 2) deployed in diverse outdoor inter-city and urban scenarios having long and shorter distances, respectively, and the data is collected at Tempe, Phoenix, Scottsdale, and Chandler of Arizona during both day as well as night times.

Here, the unit 1 1 1 1 acts as a receiver R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT, whereas the another unit 2 2 2 2 acts as a transmitter T x subscript 𝑇 𝑥 T_{x}italic_T start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT, and both are operating at 60 GHz carrier frequency. Besides, the unit 1 1 1 1 employs four numbers of mmWave phased arrays, and each phased array has 16 elements (N R=16 subscript 𝑁 𝑅 16 N_{R}=16 italic_N start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT = 16) uniform linear arrays (ULA) facing right, left, back, and front directions on the vehicle. Further, the number of pre-defined and over-sampled codebook beams at each phased array of unit 1 1 1 1 is 64 64 64 64 (|𝒬♣ℑ/△|\mathbfcal{Q}|=64| roman_𝒬 ♣ roman_ℑ / △), whereas the unit 2 2 2 2 has one antenna element, leading to total 64×1 64 1 64\times 1 64 × 1 = 64 64 64 64 beam pairs.

In particular, the unit 2 2 2 2 continually performs omni-directional transmission by utilizing its one antenna element, at the same time, the unit 1 1 1 1 collects the measurements of received power at each beams by making a full beam sweeping. The obtained received power at beams are represented as beam indices (ℐ∈{1,2,3⁢…,64}ℐ 1 2 3…64\mathcal{I}\in{1,2,3…,64}caligraphic_I ∈ { 1 , 2 , 3 … , 64 }). Moreover, both the unit 1 1 1 1 and unit 2 2 2 2 carry GPS Real Time Kinematics sensors to obtain the real-time vehicle position data, i.e., latitude and longitude values. The data collection maintains a gap between two consecutive samples is 0.1 0.1 0.1 0.1 second, which makes sampling rate as 10 10 10 10 samples/second. At each time instant, the unit 1 1 1 1 records the synchronous data of location coordinates of unit 2 2 2 2 along with corresponding received powers and optimal beam indices (referred as ground truth indices). As an example, the Figs. 3a, b, c, and d illustrate the visual representation of 400 400 400 400 location data points of R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT corresponding to individual ground truth beams associated with maximum received powers for all V2V scenarios.

(a)Accuracies: For scenario 36 and scenario 37

(b)Accuracies: For scenario 38 and scenario 39

(c)Received power: For scenario 36 and scenario 37

(d)Received power: For scenario 38 and scenario 39

Figure 4: Performance comparison of average achieved accuracies and received power ratio in percentage for all considered vehicle-to-vehicle scenarios.

IV-B Implementation Details

We carry out two sets of experiments, for the designed deep learning model as well as a baseline work, on the considered real-world datasets. For the baseline work, we consider the work proposed in [19], and the key reason behind this choosing is because of having same beam search overhead with ours, that is, the overhead is dependent on M 𝑀 M italic_M.

In particular, the baseline work consists of four steps for beam selection: (i) first, the receiver R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT divides the coverage zone into a number of uniform location bins, and contributing vehicles help to perform channels measurements so that the R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT can build a database including fingerprints of channel characteristics (e.g., received power strengths) and corresponding beams for specific locations bins in advance, (ii) then, the intended transmitter T x subscript 𝑇 𝑥 T_{x}italic_T start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT makes a training request and a query along with its position information to the receiver R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT using sub-6GHz bands, (iii) after that, the R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT acknowledges and shares the candidate beams from its database to the T x subscript 𝑇 𝑥 T_{x}italic_T start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT to initiate beam training, and (iv) at the end, upon received the acknowledgement, the T x subscript 𝑇 𝑥 T_{x}italic_T start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT proceed to beam training following the candidate beams and establish communications over mmWave link after receiving the feedback on the best beam index (among the candidates) from the R x subscript 𝑅 𝑥 R_{x}italic_R start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT.

Settings and Parameters: The experiments are conducted on a computing device having Intel Core i7-10875H CPU with 32 GB RAM and NVIDIA GeForce RTX 2080 Super GPU with 8 GB memory. In particular, the deep learning model is developed by PyTorch and CUDA toolkit 11.7.

The fixed learning rate and weight decay values of the utilized Adam optimizer are set to 0.01 0.01 0.01 0.01 and 1×10−4 1 superscript 10 4 1\times 10^{-4}1 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT, respectively, while the batch size N b subscript 𝑁 𝑏 N_{b}italic_N start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT is 128, and the model is trained up to total 30 30 30 30 epochs. We split the data resources of each scenario into 60 60 60 60%, 20 20 20 20%, and 20 20 20 20% for training, validation, and testing, respectively. We utilize this ratio in the proposed solution, whereas we use 80 80 80 80% for training and 20 20 20 20% for testing in the baseline work. Particularly, we keep the same testing part in both experiments for the purpose of fair comparison.

IV-C Performance Evaluation

For better analysis and illustration of the performance evaluation, we adopt the following two important metrics to measure the performances. Both matrices are averaged over total number of testing samples.

• Top-M 𝑀 M italic_M Accuracy: The results of number of correct top-M 𝑀 M italic_M predictions from the model during testing time in relation to the total number of predictions, which can be defined as follows.

A⁢c⁢c t⁢o⁢p−M=1 N t⁢e⁢s⁢t⁢∑i=0 N t⁢e⁢s⁢t−1∣I t∩I^t∣∣I^t∣𝐴 𝑐 subscript 𝑐 𝑡 𝑜 𝑝 𝑀 1 subscript 𝑁 𝑡 𝑒 𝑠 𝑡 superscript subscript 𝑖 0 subscript 𝑁 𝑡 𝑒 𝑠 𝑡 1 delimited-∣∣subscript superscript 𝐼 𝑡 subscript^𝐼 𝑡 delimited-∣∣subscript^𝐼 𝑡 Acc_{top-M}=\frac{1}{N_{test}}\sum_{i=0}^{N_{test}-1}\frac{\mid I^{}{t}\cap% \hat{I}{t}\mid}{\mid\hat{I}_{t}\mid}italic_A italic_c italic_c start_POSTSUBSCRIPT italic_t italic_o italic_p - italic_M end_POSTSUBSCRIPT = divide start_ARG 1 end_ARG start_ARG italic_N start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT end_ARG ∑ start_POSTSUBSCRIPT italic_i = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT - 1 end_POSTSUPERSCRIPT divide start_ARG ∣ italic_I start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ∩ over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ∣ end_ARG start_ARG ∣ over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ∣ end_ARG

where, N t⁢e⁢s⁢t subscript 𝑁 𝑡 𝑒 𝑠 𝑡 N_{test}italic_N start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT, I tsubscript superscript 𝐼 𝑡 I^{}{t}italic_I start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT, and I^t subscript^𝐼 𝑡\hat{I}{t}over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT denote the number of test samples, optimal beams at t t⁢h superscript 𝑡 𝑡 ℎ t^{th}italic_t start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT time, and top-M 𝑀 M italic_M beams at t t⁢h superscript 𝑡 𝑡 ℎ t^{th}italic_t start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT time, respectively.

• Received Power Ratio: The ratio between received power in downlink associated with predicted beams and received power from ground-truth beams. Intuitively, this metric in terms of percentage can represent how much percentage of received power can be possibly obtained from the link status. It can be defined as follows.

R 𝒫 t=1 N t⁢e⁢s⁢t⁢∑i=0 N t⁢e⁢s⁢t−1 𝒫 t^𝒫 t(g⁢t)subscript 𝑅 subscript 𝒫 𝑡 1 subscript 𝑁 𝑡 𝑒 𝑠 𝑡 superscript subscript 𝑖 0 subscript 𝑁 𝑡 𝑒 𝑠 𝑡 1^subscript 𝒫 𝑡 superscript subscript 𝒫 𝑡 𝑔 𝑡 R_{\mathcal{P}{t}}=\frac{1}{N{test}}\sum_{i=0}^{N_{test}-1}\frac{\hat{% \mathcal{P}{t}}}{\mathcal{P}{t}^{(gt)}}italic_R start_POSTSUBSCRIPT caligraphic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_POSTSUBSCRIPT = divide start_ARG 1 end_ARG start_ARG italic_N start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT end_ARG ∑ start_POSTSUBSCRIPT italic_i = 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT - 1 end_POSTSUPERSCRIPT divide start_ARG over^ start_ARG caligraphic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG end_ARG start_ARG caligraphic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( italic_g italic_t ) end_POSTSUPERSCRIPT end_ARG

where, 𝒫 t^^subscript 𝒫 𝑡\hat{\mathcal{P}{t}}over^ start_ARG caligraphic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_ARG and 𝒫 t(g⁢t)superscript subscript 𝒫 𝑡 𝑔 𝑡\mathcal{P}{t}^{(gt)}caligraphic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( italic_g italic_t ) end_POSTSUPERSCRIPT are the received power from predicted beams and ground-truth beams, respectively, at time instant t 𝑡 t italic_t.

First, we compare the performance of this proposed solution with the baseline in terms of accuracy under Top-M 𝑀 M italic_M beams, in particular, we choose the top beam candidates M∈{1,5,9,13}𝑀 1 5 9 13 M\in{1,5,9,13}italic_M ∈ { 1 , 5 , 9 , 13 }. As depicted in Figs. 4a and 4b, we present the results for four scenarios, and it can be observed that our proposed solution outperforms the baseline almost at every top-M 𝑀 M italic_M beam selection accuracies. For instance, with the same beam search overheads, the top-1 prediction in scenario 36 is performed nearly 19.67 19.67 19.67 19.67% increased average accuracy than the baseline, which is made possible by applying trained deep learning model. For another, we also depict the results of received power ratio performances in Figs. 4c and 4d. For example, the results show that with top-1 predicted beams, 84.58 84.58 84.58 84.58% received power ratio can be possibly achieved on average in scenario 36. All average results obtained from the experiments after running 5 5 5 5 times. While quantifying the end-to-end latency performance has already been explored in other works, our emphasis of this proposed solution lies in accomplishing the maximum received power from the communications links. The implementation codes are publicly available at Github 1 1 1https://github.com/mbaqer/V2V-mmWave-Beamforming.

V Conclusion

In this paper, we have presented a proposed beam selection solution to improve the achieved downlink received power in vehicle-to-vehicle connectivity enabled by 60 GHz mmWave communications. In this solution, we have utilized deep learning model to learn from the out-of-band vehicular position information and predict the top-M 𝑀 M italic_M beams (a subset of beams). This predicted beams has also helped to reduce the beam searching space, thereby addressing the beam searching overheads limitation of mmWave communications. At the end, experiments on real-world datasets have shown the effectiveness and applicability of the proposed solution, which has indicated the benefits of exploring the side-information in mmWave beamforming. As a future work, this work can be potentially extended by including multiple sensing information together and performing the model fusion.

Acknowledgment: This research is supported by National Science Foundation (NSF) under the grant number # 2010366.

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