Worst-Case Performance Optimization-Based Robust Adaptive Beamformers: An Overview

In practical array systems, traditional adaptive beamforming algorithms are known to degrade if some of exploited assumptions on the environment, sources, or antenna array become wrong or imprecise. Therefore, the robustness of adaptive beamforming techniques against environmental and array imperfections and uncertainties is one of the key issues. In this paper, we present an overview of recent trends and advances in the field of worst-case optimizationbased robust adaptive beamforming. Introduction. The traditional approach to the design of adaptive beamformers assumes that no components of the desired signal are present in the beamformer training data. In such a case, adaptive beamforming is known to be sufficiently robust against errors in the array response to the desired signal and limited training sample size and a variety of rapidly converging techniques have been developed for this case. Although the assumption of signal-free training snapshots may be relevant in certain specific cases (e.g., in some radar and active sonar problems), there are many applications where the interference and noise observations are always “contaminated” by the signal component. Typical examples include wireless communications, passive sonar, microphone array speech processing, and medical imaging. It is well known that even in the ideal case where the signal steering vector (array response) is precisely known at the receiving sensor array, the presence of the desired signal in the training data snapshots can lead to essentially reduced convergence rates of adaptive beamforming algorithms relative to the signal-free training data case. This may cause a severe performance degradation of adaptive beamforming techniques in scenarios with a small training sample size. In practical situations, the performance degradation of adaptive beamforming techniques may become even more substantial because of a possible violation of underlying assumptions on the environment, sources, or sensor array. One of typical causes of such a performance degradation is a mismatch between the nominal (presumed) and actual array responses to the desired signal. Adaptive array techniques are known to be very sensitive even to slight errors of this type because in the presence of such errors adaptive beamformers tend to wrongly interpret the desired signal components as an interference and to suppress these components by means of adaptive nulling instead of maintaining distortionless response towards them. Besides array response errors, performance degradation of adaptive beamforming can be additionally caused by a nonstationary character of the beamformer training data, e.g., by a nonstationary behavior of the propagation channel, interferer and antenna motion, as well as antenna vibration. The same situation occurs in the case of moving antenna arrays, e.g., towed arrays of hydrophones in sonar or moving antenna platforms in airborne applications. Preliminaries. The beamformer output is given by