A Bayesian approach to robust adaptive beamforming

TLDR

The study derives a Bayesian adaptive beamformer robust to source DOA uncertainty. The beamformer is a weighted sum of MVDR beamformers over candidate DOAs, with weights derived from the posterior PDF of a discrete DOA model, and a simple approximation enables efficient implementation. Its performance exceeds that of LCMV beamformers and data‑driven approaches that estimate signal characteristics or steering vectors from data.

Abstract

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 DOAs, 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.