Distributionally Robust Linearly Constrained Minimum Variance Beamforming Under Steering-Vector Mismatch

Abstract

Linearly constrained minimum variance (LCMV) beamforming is a fundamental technique for controlling the array response toward multiple desired signals while suppressing interference and noise. In practical systems, however, the steering vectors involved in the response constraints are often affected by direction-of-arrival errors, calibration imperfections, and other array uncertainties. Such mismatches may cause constraint violations and substantial performance degradation. This paper investigates multi-signal LCMV beamforming under steering-vector mismatch and develops probabilistic constraints to guarantee a prescribed reliability level for each desired signal. Several uncertainty-information settings are considered. When the exact mismatch distribution is known and belongs to the class of complex elliptically symmetric distributions (CES), a distribution-informed convex safe reformulation is derived using exact CES quantiles. When the mismatch distribution is unknown, and only partial statistical information or empirical data is available, robust probabilistic reformulations are developed under moment-based ambiguity, support-based uncertainty, and Wasserstein data-driven ambiguity, and the resulting deterministic formulations can be expressed as convex second-order cone programs. Numerical experiments show that the proposed designs improve out-of-sample reliability and reduce beam-gain sensitivity to steering-vector mismatch, while maintaining competitive output signal-to-interference-plus-noise (SINR) ratio and robust beampatterns.