tasks/engineering-sciences/electrical-engineering/uav-array-codesign/authoring/provenance/PROVENANCE.md

Provenance of Physical Models and Verification Thresholds

1. Electromagnetic Forward Model (/app/hfss_sim/em_solver.py)

All electromagnetic quantities are computed deterministically from analytical antenna and microwave network theory (no oracle outputs are used as ground truth):

• Self and Mutual Impedance Matrix $\mathbf{Z}_{\text{ant}}(f)$: Carter's Induced-EMF formulation for parallel and echelon finite-radius center-fed dipoles of length $L$ and wire radius $a = 0.8\text{ mm}$ at $f_0 = 2.45\text{ GHz}$ (C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., Ch. 8, Eqs. 8-60 to 8-71), evaluated via 24-node Gauss-Legendre quadrature.
• Conducting Carbon-Fiber Airframe Reflector: Modeled via image theory across the conducting fuselage plane $z_{\text{body}} = 0$ at standoff distance $h = \text{substrate_height_m}$ with imperfect surface reflection coefficient $\rho_{\text{cf}} = -0.96 e^{-j 0.03}$.
• Multi-Port Active Reflection and L-Section Matching: Per-port shunt susceptance $B_p(f)$ and series reactance $X_s(f)$ transform $\mathbf{Z}{\text{ant}}(f)$ to $\mathbf{Z}{\text{port}}(f)$ and $\mathbf{S}(f) = (\mathbf{Z}{\text{port}} + Z_0\mathbf{I})^{-1}(\mathbf{Z}{\text{port}} - Z_0\mathbf{I})$ with $Z_0 = 50,\Omega$ (D. M. Pozar, Microwave Engineering, 4th ed., Ch. 4–5). Total Active Reflection Coefficient is $\text{TARC}(f, \mathbf{w}) = |\mathbf{S}(f)\mathbf{w}|_2 / |\mathbf{w}|_2$ (M. Manteghi and Y. Rahmat-Samii, IEEE Trans. Antennas Propag., vol. 53, no. 1, 2005).

2. 6-DoF Flight & Contested Channel Model (/app/hfss_sim/flight_env.py)

• Attitude Transformations: Aerospace ZYX Euler rotation $\mathbf{R}_{\text{world}\leftarrow\text{body}}(\phi_r, \theta_p, \psi_y) = \mathbf{R}_z(\psi_y)\mathbf{R}_y(\theta_p)\mathbf{R}_x(\phi_r)$.
• Two-Ray Multipath: Coherent sum of direct line-of-sight and ground-reflected ray over dielectric soil ($\varepsilon_r = 15 - j1.2$) with Fresnel reflection coefficient $\Gamma_\perp(\psi_g)$.
• PA Thermal & Queue Dynamics: First-order thermal RC ODE driven by wasted DC power plus $2.8 P_{\text{refl}}$ (VSWR foldback heating) with airspeed-dependent convective thermal resistance $R_{\text{th}}(v_{\text{air}}) = 14.5 / (1 + 0.055 v_{\text{air}})\text{ }^\circ\text{C/W}$.

3. Structural Independence of Verification Bounds

Thresholds in /tests/test_outputs.py are objective physical engineering requirements (return loss $\le -18\text{ dB}$, $-10\text{ dB}$ bandwidth $\ge 120\text{ MHz}$, nadir realized gain $\ge 10.5\text{ dBi}$, scan TARC $\le 0.32$, packet delivery ratio $\ge 0.95$, PA temperature $\le 78^\circ\text{C}$) validated against two structurally distinct implementations:

1. solution/ (Oracle): Analytical quadratic L-network impedance synthesis + coupled active-TARC-regularized MVDR matrix inversion + link-budget lookahead power/MCS selector.
2. authoring/evidence/independent_solution.py: Derivative-free Nelder-Mead simplex S-parameter optimization + Gram-Schmidt Jammer Null-Space Projection beamformer + Proportional-Integral (PI) feedback power/MCS controller.