Efficient Solvers for Coupling-Aware Beamforming in Continuous Aperture Arrays

2026-02-24

AI Summary

This study addresses the significant degradation of beamforming performance in continuous-aperture arrays caused by electromagnetic mutual coupling, a challenge exacerbated by the high computational complexity and low solution efficiency of existing methods when incorporating accurate coupling models. Building upon a physically consistent mutual coupling model, the authors formulate beamforming design as a functional optimization problem and characterize its optimality conditions via a Fredholm integral equation. To solve this efficiently, they propose two strategies: a coordinate-transform-based kernel approximation that preserves operator structure while reducing discretization dimensionality, and a direct solver combining Nyström discretization with LU decomposition, augmented by offline factorization to enable stable and scalable large-scale optimization. Experiments demonstrate that the proposed approaches substantially reduce computational cost while maintaining accuracy, with the LU-based solver exhibiting exceptional efficiency and scalability in large-scale scenarios.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In continuous aperture arrays (CAPAs), careful consideration of the underlying physics is essential, among which electromagnetic (EM) mutual coupling plays a critical role in beamforming performance. Building on a physically consistent mutual coupling model, the beamforming design is formulated as a functional optimization whose optimality condition leads to a Fredholm integral equation. The incorporation of the coupling model, however, substantially increases computational complexity, necessitating efficient and accurate integral equation solvers. In this letter, we propose two efficient solvers: 1) a coordinate-transformation-based kernel approximation that preserves the operator structure while alleviating discretization demands, and 2) a direct lower-upper (LU)-based solver that stably handles the Nystr\"om-discretized system. Numerical results demonstrate improved accuracy and reduced computational overhead compared to conventional methods, with the LU-based solver emerging as an efficient and scalable solution for large-scale CAPA optimization via offline factorization.

Problem

• continuous aperture arrays
• mutual coupling
• beamforming
• integral equation
• computational complexity

Innovation

• continuous aperture arrays
• mutual coupling
• Fredholm integral equation
• kernel approximation
• LU-based solver