Distributionally Robust Adaptive Beamforming

As a fundamental technique in array signal processing, beamforming plays a crucial role in amplifying signals of interest (SoI) while mitigating interference plus noise (IPN). When uncertainties exist in the signal model or the data size of snapshots is limited, the performance of beamformers significantly degrades. In this article, we comprehensively study the conceptual system, theoretical analysis, and algorithmic design for robust beamforming against uncertainties in the assumed snapshot or IPN covariances. Since such robustness is specific to the probabilistic uncertainties of snapshots or IPN signals, it is referred to as distributional robustness. Particularly, four technical approaches for distributionally robust beamforming are proposed, including locally distributionally robust beamforming, globally distributionally robust beamforming, regularized beamforming, and Bayesian-nonparametric beamforming. In addition, we investigate the equivalence among the four technical approaches and suggest a unified distributionally robust beamforming framework. Moreover, we show that the resolution of power spectra estimation using distributionally robust beamforming can be greatly refined by incorporating the characteristics of subspace methods, and hence, the accuracy of IPN covariance reconstruction can be improved, especially when the interferers are close to the SoI. As a result, the robustness of beamformers based on IPN covariance estimation can be further enhanced.