Sparse Array Beamformer Design via ADMM

TL;DR

This paper introduces a novel sparse array beamformer design algorithm using ADMM, which efficiently maximizes SINR with proven convergence and superior performance compared to existing methods.

Contribution

The paper presents a new ADMM-based algorithm for sparse array design in adaptive beamforming, with closed-form solutions and convergence analysis, outperforming state-of-the-art approaches.

Findings

Achieves comparable or better SINR than exhaustive search and existing solvers.

Converges to KKT stationary points with proven monotonicity and boundedness.

Outperforms other methods in computational efficiency.

Abstract

In this paper, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes the alternating direction method of multipliers (ADMM), and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, we prove that the proposed algorithm converges to the set of Karush-Kuhn-Tucker stationary points. Numerical results exhibit its excellent performance, which is comparable to that of the exhaustive search approach, slightly better than those of the state-of-the-art solvers, including the semidefinite relaxation (SDR), its variant (SDR-V), and the successive convex approximation (SCA) approaches, and significantly outperforms several other sparse array design strategies, in terms of output SINR. Moreover, the proposed ADMM algorithm outperforms the SDR, SDR-V, and SCA methods, in terms of computational complexity.