Robust adaptive beamforming with imprecise steering vector and noise covariance matrix due to finite sample size

Minimum variance beamformers are widely used for array signal processing. It is known that the diagonal loading method can improve the robustness against mismatches caused by the imprecise steering vector (or the channel vector) and the noise covariance matrix. Instead of concentrating on one aspect of the mismatches and assuming perfect knowledge of the other, we handle both estimation error in the steering vector and the noise covariance matrix caused by the finite sample size simultaneously. We employ high-dimensional asymptotics to reflect the finite sample size, and estimate the optimal loading factor based on random matrix theory. In an asymptotic setting where the number of samples is comparable to the array dimension, we obtain a beamformer that is as good as the beamformer with optimal diagonal loading. Monte Carlo simulations show the advantage of our beamformer in the finite sample size regime.