Robust Beamforming via Wasserstein Distance: A Data-Driven Distributionally Robust Framework

Abstract

Adaptive beamforming suffers severe performance degradation from uncertainties in the array steering vector and interference-plus-noise covariance matrix. While distributionally robust optimization (DRO) provides a principled framework, existing DRO-based beamformers are often overly conservative and rely on empirically tuned parameters. This paper proposes a unified DRO beamforming framework based on the Wasserstein-2 distance. Ambiguity sets for both the random steering vector and covariance matrix are constructed as Wasserstein balls, with a physically motivated trace support constraint added to the latter to cap unrealistic worst-case power. Leveraging strong duality, the min-max problem is transformed into a tractable convex program. Without the support constraint, it reduces to an adaptive diagonal loading form whose regularization parameter is rigorously data-driven. A bootstrap-based quantile calibration strategy is developed to determine the covariance-related Wasserstein radius and support-set parameter directly from training snapshots, providing finite-sample statistical guarantees and enabling fully automatic selection of these robustness parameters. Extensive simulations demonstrate that the proposed method consistently outperforms state-of-the-art robust beamformers, establishing a new performance benchmark and systematically transitioning the design paradigm from empirical to data-driven.