A recursive filter approach to adaptive Bayesian beamforming for unknown DOA

Traditional beamforming algorithms require perfect knowledge of the source direction-of-arrival (DOA) to generate beamformer weights that yield high signal-to-interference-plus-noise ratio (SINR). We apply a Bayesian approach to adaptive beamforming such that the algorithm automatically tunes to the underlying DOA that is not known a priori to the user. The proposed beamformer can be viewed as a weighted mixture of minimum variance distortionless response (MVDR) beamformers combined according to the data-driven posterior probability density function (PDF) of the DOA. Previous studies use discrete samples to capture the spatial variation of the posterior PDF. In this work, we show that, in case of uniform linear array (ULA), the posterior PDF can be represented as a product of the prior PDF and a number of von Mises PDF's, each approximated by the frequency response of a recursive filter. The beamformer weights can then be computed from the corresponding recursive filtering operations. This leads to an algorithm that preserves the continuity of the parameter space and is capable to resolve any amount of DOA error.