Wasserstein Distributionally Robust Adaptive Beamforming

TL;DR

This paper introduces a Wasserstein distributionally robust optimization approach for adaptive beamforming, providing a data-driven, unified framework that enhances robustness against model uncertainties in signal processing.

Contribution

It proposes a novel Wasserstein DRO-based beamformer that unifies and generalizes existing robust beamforming models through the choice of cost functions.

Findings

Wasserstein metric defines uncertainty sets for robust beamforming.

Choice of cost function influences the resulting beamforming model.

Framework bridges deterministic and distributionally robust methods.

Abstract

Distributionally robust optimization (DRO)-based robust adaptive beamforming (RAB) enables enhanced robustness against model uncertainties, such as steering vector mismatches and interference-plus-noise covariance matrix estimation errors. Existing DRO-based RAB methods primarily rely on uncertainty sets characterized by the first- and second-order moments. In this work, we propose a novel Wasserstein DRO-based beamformer, using the worst-case signal-to-interference-plus-noise ratio maximization formulation. The proposed method leverages the Wasserstein metric to define uncertainty sets, offering a data-driven characterization of uncertainty. We show that the choice of the Wasserstein cost function plays a crucial role in shaping the resulting formulation, with norm-based and Mahalanobis-like quadratic costs recovering classical norm-constrained and ellipsoidal robust beamforming models, respectively. This insight highlights the Wasserstein DRO framework as a unifying approach, bridging deterministic and distributionally robust beamforming methodologies.