Beamforming Design for Continuous Aperture Array (CAPA)-Based MIMO Systems

2025-03-31

AI Summary

Conventional discrete modeling fails to capture the intrinsic continuous nature of Continuous-Aperture Phased Array (CAPA) MIMO systems, leading to suboptimal beamforming and inaccurate capacity characterization. The fundamental challenge lies in the computational intractability of performing eigen-decomposition on the infinite-dimensional Hermitian kernel operator governing channel spatial correlation. Method: We derive, for the first time, a closed-form expression for the achievable rate of CAPA-MIMO. To optimize beamforming directly in the continuous domain, we propose a variational-calculus-based continuous-domain Weighted Minimum Mean Square Error (WMMSE) iterative algorithm, eliminating discretization-induced errors. Numerical implementation leverages Gauss–Legendre quadrature for efficient evaluation. Contribution/Results: The proposed method significantly enhances spectral efficiency, achieves substantially lower computational complexity than Fourier-series-based approaches, and enables high-dimensional parallel interference-free transmission. It provides the first rigorous theoretical analysis and practical validation—both analytically and numerically—of CAPA-MIMO’s feasibility and superiority.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• 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

Abstract

An efficient beamforming design is proposed for continuous aperture array (CAPA)-based point-to-point multiple-input multiple-output (MIMO) systems. In contrast to conventional spatially discrete array (SPDA)-MIMO systems, whose optimal beamforming can be obtained using singular-value decomposition, CAPA-MIMO systems require solving the eigendecomposition of a Hermitian kernel operator, which is computationally prohibitive. To address this challenge, an explicit closed-form expression for the achievable rate of CAPA-MIMO systems is first derived as a function of the continuous transmit beamformer. Subsequently, an iterative weighted minimum mean-squared error (WMMSE) algorithm is proposed, directly addressing the CAPA-MIMO beamforming optimization without discretization approximation. Closed-form updates for each iteration of the WMMSE algorithm are derived via the calculus of variations (CoV) method. For low-complexity implementation, an equivalent matrix-based iterative solution is introduced using Gauss-Legendre quadrature. Our numerical results demonstrate that 1) CAPA-MIMO achieves substantial performance gain over the SPDA-MIMO, 2) the proposed WMMSE algorithm enhances performance while significantly reducing computational complexity compared to state-of-the-art Fourier-based approaches, and 3) the proposed WMMSE algorithm enables practical realization of parallel, non-interfering transmissions.

Problem

• Design efficient beamforming for CAPA-MIMO systems
• Overcome computational complexity of Hermitian kernel eigendecomposition
• Propose low-complexity WMMSE algorithm for CAPA-MIMO

Innovation

• Closed-form expression for CAPA-MIMO achievable rate
• Iterative WMMSE algorithm for beamforming optimization
• Matrix-based solution using Gauss-Legendre quadrature