Linear Receive Beamforming for CAPA Systems

TL;DR

This paper analyzes linear receive beamforming techniques for CAPA systems, deriving closed-form solutions for MRC, ZF, and MMSE, and demonstrating their superiority over traditional arrays through numerical results.

Contribution

It introduces and mathematically characterizes three novel continuous beamforming methods for CAPA systems, including their optimality and performance analysis.

Findings

CAPA systems outperform SPDAs in sum-rate and MSE.

Closed-form beamformers are derived for MRC, ZF, and MMSE.

Numerical results confirm the effectiveness of the proposed techniques.

Abstract

The performance of linear receive beamforming in continuous-aperture array (CAPA)-based uplink communications is analyzed. Three continuous beamforming techniques are proposed under the criteria of maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-squared error (MMSE). \romannumeral1) For \emph{MRC beamforming}, a closed-form expression for the beamformer is derived to maximize per-user signal power. The achieved uplink rate and mean-squared error (MSE) in detecting received data symbols are analyzed. \romannumeral2) For \emph{ZF beamforming}, a closed-form beamformer is derived based on channel correlation to eliminate interference. As a further advance, its optimality in maximizing effective channel gain while ensuring zero inter-user interference is proven. \romannumeral3) \emph{MMSE beamforming} is established as the optimal linear receive approach for CAPAs in terms of maximizing per-user rate and minimizing MSE. Closed-form expressions are derived for the MMSE beamformer and the achievable sum-rate and sum-MSE. It is mathematically proven that all proposed beamformers lie within the signal subspace spanned by users' spatial responses. Numerical results demonstrate that CAPAs outperform conventional spatially-discrete arrays (SPDAs) by achieving higher sum-rates and lower sum-MSEs under the proposed linear beamforming techniques.