An Inner SOCP Approximate Algorithm for Robust Adaptive Beamforming for General-Rank Signal Model

TL;DR

This paper introduces an efficient inner SOCP approximation algorithm for robust adaptive beamforming in general-rank signal models, avoiding heavy SDP relaxations and demonstrating improved computational performance.

Contribution

It proposes a novel inner SOCP-based algorithm that converges to a local (often global) optimum without using computationally intensive SDP relaxations.

Findings

The algorithm converges to a locally optimal solution in simulations.

It demonstrates faster convergence and reduced CPU time compared to SDP-based methods.

The method performs well in high SNR scenarios.

Abstract

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio (SINR), incorporating a positive semidefinite constraint on the actual covariance matrix of the desired signal. In the literature, semidefinite program (SDP) techniques, together with others, have been applied to approximately solve this problem. Herein an inner second-order cone program (SOCP) approximate algorithm is proposed to solve it. In particular, a sequence of SOCPs are constructed and solved, while the SOCPs have the nondecreasing optimal values and converge to a locally optimal value (it is in fact a globally optimal value through our extensive simulations). As a result, our algorithm does not use computationally heavy SDP relaxation technique. To validate our inner approximation results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformer in terms of the averaged cpu-time (indicating how fast the algorithms converge) in a high signal-to-noise region.