Robust Adaptive Beamforming Maximizing the Worst-Case SINR over Distributional Uncertainty Sets for Random INC Matrix and Signal Steering Vector

TL;DR

This paper develops a robust adaptive beamforming method that maximizes the worst-case SINR considering distributional uncertainties in the interference-plus-noise covariance and signal steering vector, using a conic programming approach.

Contribution

It introduces a novel distributionally robust formulation for adaptive beamforming that accounts for uncertainties in covariance and steering vector, solved via quadratic matrix inequalities.

Findings

Improved array output SINR demonstrated in simulations.

Effective handling of distributional uncertainties in beamforming.

Iterative LMI relaxation approach enhances robustness.

Abstract

The robust adaptive beamforming (RAB) problem is considered 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. The distributional uncertainty set of the INC matrix accounts for the support and the positive semidefinite (PSD) mean of the distribution, and a similarity constraint on the mean. The distributional uncertainty set for the steering vector consists of the constraints on the known first- and second-order moments. The RAB problem is formulated as a minimization of the worst-case expected value of the SINR denominator achieved by any distribution, subject to the expected value of the numerator being greater than or equal to one for each distribution. Resorting to the strong duality of linear conic programming, such a RAB problem is rewritten as a quadratic matrix inequality problem. It is then tackled by iteratively solving a sequence of linear matrix inequality relaxation problems with the penalty term on the rank-one PSD matrix constraint. To validate the results, simulation examples are presented, and they demonstrate the improved performance of the proposed robust beamformer in terms of the array output SINR.