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

2025-11-14

AI Summary

Conventional half-wavelength spacing decoupling criteria fail for continuous-aperture phased arrays (CAPAs) due to polarization-induced anisotropic mutual coupling. Method: We propose a continuous-domain mutual coupling model incorporating both polarization effects and surface losses, revealing the polarization-driven directional dependence of coupling. A functional optimization framework is formulated via variational calculus; the coupling kernel is approximated in the wavenumber domain using Gaussian–Legendre quadrature, and the resulting equivalent quadratic optimization problem is solved via conjugate gradient descent—generalized to discrete arrays. Contribution/Results: Analytical solutions for optimal array gain and beam patterns are derived in the large-aperture limit. Numerical validation confirms that discrete-array performance under the proposed coupled model converges to the continuous-aperture limit, whereas conventional uncoupled models violate physical consistency. Coupled-beam synthesis achieves enhanced directivity and polarization-dependent gain, establishing a new paradigm for high-density array design.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health

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.

Problem

• Modeling mutual coupling in continuous aperture arrays with polarization and dissipation losses
• Developing beamforming designs that account for anisotropic coupling effects
• Extending continuous coupling models to discrete arrays and analyzing performance

Innovation

• Physical model includes polarization and dissipation losses
• Two methods solve coupling kernel inversion problem
• Continuous model extends to discrete arrays with validation