Robust adaptive beamforming with minimum sensitivity to correlated random errors

The standard Capon beamformer is subject to substantial performance degradation in the presence of estimation errors of the signal steering vector and the array covariance matrix. In order to address this problem, robust adaptive beamformers (RABs) have been designed. In this study, we propose a novel RAB from the perspective of the beamformer sensitivity. In particular, we consider the general form of the beamformer sensitivity, implying that the random errors may be not white noise but correlated. Then we suggest to use the inverse of the array sample covariance matrix as the random error covariance. Using this, we propose to compute the Capon beamformer with minimum sensitivity to correlated random errors, considering a Euclidean ball as the uncertainty set for the signal steering vector. Moreover, the Lagrange multiplier methodology can be employed to solve the proposed optimization problem. Numerical results demonstrate the superior performance of the proposed beamformer in the presence of large mismatch relative to other existing approaches such as 'diagonal loading', 'robust Capon' and 'maximally robust Capon' beamformers.