Mutual Coupling in Continuous Aperture Arrays: Physical Modeling and Beamforming Design

TL;DR

This paper develops a physical model for mutual coupling in continuous aperture arrays, analyzes its effects on beamforming, and proposes methods for optimal array design considering coupling effects.

Contribution

It introduces a comprehensive physical model for mutual coupling in CAPAs, including polarization effects, and derives optimal beamforming structures using calculus of variations.

Findings

Coupling induces anisotropic array gain behavior.

Optimal array gain and beampattern are characterized at large aperture.

Coupled array performance converges to the continuous model, unlike uncoupled models.

Abstract

The phenomenon of mutual coupling in continuous aperture arrays (CAPAs) is studied. First, a general physical model for the phenomenon that accounts for both polarization and surface dissipation losses is developed. Then, the unipolarized coupling kernel is characterized, revealing that polarization induces anisotropic coupling and invalidates the conventional half-wavelength spacing rule for coupling elimination. Next, the beamforming design problem for CAPAs with coupling is formulated as a functional optimization problem, leading to the derivation of optimal beamforming structures via the calculus of variations. To address the challenge of inverting the coupling kernel in the optimal structure, two methods are proposed: 1) the kernel approximation method, which yields a closed-form solution via wavenumber-domain transformation and GaussLegendre quadrature, and 2) the conjugate gradient method, which addresses an equivalent quadratic functional optimization problem iteratively. Furthermore, the optimal array gain and beampattern are analyzed at the large-aperture limit. Finally, the proposed continuous mutual coupling model is extended to spatially discrete arrays (SPDAs), and comprehensive numerical results are provided, demonstrating that: 1) coupled SPDA performance correctly converges to the CAPA limit, while uncoupled models are shown to violate physics, 2) polarization results in anisotropic array gain behavior, and 3) the coupled beampattern exhibits higher directivity than the uncoupled beampattern.