A Bayesian approach to robust adaptive beamforming

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (pdf) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOA’s, where the relative contribution of each MVDR beamformer is determined from the a posteriori pdf of the DOA conditioned on previously observed data. A simple approximation to the a posteriori pdf results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data.