Robust minimum variance beamforming under distributional uncertainty

This paper investigates distributionally robust minimum variance beamforming under first-order moment uncertainty. In contrast to deterministic modeling of the array response, our approach employs a distributional set to describe the uncertainty. The distributional set we introduce consists of two constraints: the probability measure constraint and a first-order moment constraint. The weights are selected to minimize the combined output power, subject to the modified distortionless response constraint that the expected real part of the array gain exceeds unity for all distributions in the uncertainty set. We begin our discussion by revealing the intrinsic connection between the distributionally robust minimum variance beamformers (DRMVB) and the robust minimum variance beamformer (RMVB). Then for the sample space described by a union of ellipsoids, the DRMVB is reformulated as the optimal solution of a semidefinite program (SDP). Finally, we demonstrate the performance of the DRMVB via several numerical examples.