Performance analysis of the Bayesian beamformer

We present an analysis of the performance of Bayesian beamformers that are able to estimate signals from unknown source directions by balancing multiple optimal estimates according to the a posteriori probability mass function (PMF). We show that the conditional mean square error (MSE) of the Bayesian beamformer asymptotically achieves the conditional MSE of an estimator that has prior knowledge of the true direction of arrival. The convergence rate depends on both the signal-to-noise ratio (SNR) and the Kullback Leibler distance between certain probability distributions on which the Bayesian model is defined.