Finite data performance analysis of MVDR beamformer with and without spatial smoothing

The finite-data performance of a minimum-variance distortionless response (MVDR) beamformer is analyzed with and without spatial smoothing, using first-order perturbation theory. In particular, expressions are developed for the mean values of the power gain in any direction of interest, the output power, and the norm of the weight-error vector, as a function of the number of snapshots and the number of smoothing steps. It is shown that, in general, the smoothing, in addition to decorrelating the sources, can alleviate the effects of finite-data perturbations. The above expressions are reduced to the case in which no spatial smoothing is used. These expressions are valid for an arbitrary array and for arbitrarily correlated signals. For this case, an expression for the variance of the power gain is also developed. For a single interference case it is shown explicitly how the SNR, spacing of the interference from the desired signal and the correlation between them influence the beamformer performance. Simulations verify the usefulness of the theoretical expressions