SINR Maximizing Distributionally Robust Adaptive Beamforming

TL;DR

This paper develops a distributionally robust adaptive beamforming method that maximizes worst-case SINR by considering uncertainty sets for interference and signal parameters, formulated as a quadratic matrix inequality problem and solved iteratively.

Contribution

It introduces a novel robust beamforming framework using distributional uncertainty sets and quadratic matrix inequality reformulation, with convergence analysis and simulation validation.

Findings

Enhanced SINR performance in simulations.

Effective handling of distributional uncertainties.

Convergence of the iterative solution method.

Abstract

This paper addresses the robust adaptive beamforming (RAB) problem via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization over distributional uncertainty sets for the random interference-plus-noise covariance (INC) matrix and desired signal steering vector. Our study explores two distinct uncertainty sets for the INC matrix and three for the steering vector. The uncertainty sets of the INC matrix account for the support and the positive semidefinite (PSD) mean of the distribution, as well as a similarity constraint on the mean. The uncertainty sets for the steering vector consist of the constraints on the first- and second-order moments of its associated probability distribution. The RAB problem is formulated as the minimization of the worst-case expected value of the SINR denominator over any distribution within the uncertainty set of the INC matrix, subject to the condition that the expected value of the numerator is greater than or equal to one for every distribution within the uncertainty set of the steering vector. By leveraging the strong duality of linear conic programming, this RAB problem is reformulated as a quadratic matrix inequality problem. Subsequently, it is addressed by iteratively solving a sequence of linear matrix inequality relaxation problems, incorporating a penalty term for the rank-one PSD matrix constraint. We further analyze the convergence of the iterative algorithm. The proposed robust beamforming approach is validated through simulation examples, which illustrate improved performance in terms of the array output SINR.