Mutual Coupling-Aware Beamforming in Multi-User Continuous Aperture Array Systems

TL;DR

This paper introduces a mutual coupling-aware beamforming method for multi-user continuous aperture arrays, improving performance by explicitly modeling coupling effects and extending to MIMO systems.

Contribution

It develops a novel kernel approximation-based WMMSE algorithm that explicitly captures mutual coupling effects in CAPA systems, with extensions to MIMO configurations.

Findings

The proposed algorithm outperforms benchmark schemes in simulations.

Modeled coupling effects are physically rational, with discrete arrays converging to CAPA performance.

CAPA-to-CAPA MIMO systems achieve higher degrees of freedom with close transceiver placement.

Abstract

A mutual coupling-aware beamforming design for continuous aperture array (CAPA)-aided multi-user systems is investigated. First, a transmit coupling kernel is characterized to explicitly capture the mutual coupling effects inherent in CAPAs, based on which a mutual coupling-aware sum-rate maximization functional optimization problem is formulated. To address this problem, a kernel approximation (KA)-based weighted minimum mean-squared error (WMMSE) algorithm is developed. The optimal beamforming condition is derived within the WMMSE framework using the calculus of variations, while KA is employed to obtain a closed-form beamforming solution via wavenumber-domain Fourier transforms and Gauss-Legendre quadrature. Furthermore, the proposed framework is extended to CAPA-to-CAPA multiple-input multiple-output (MIMO) systems. Finally, numerical results demonstrate that: 1) the proposed algorithm achieves improved performance compared to benchmark schemes; 2) the modeled coupling effects are physically rational, where the performance of spatially discrete arrays converges to that of CAPAs; and 3) CAPA-to-CAPA MIMO systems can achieve higher degrees of freedom when the transceivers are placed in close proximity.