Fast adaptive Bayesian beamforming using the FFT

A fast algorithm is developed to implement a Bayesian beam-former that can estimate signals of unknown direction of arrival (DOA). In the Bayesian approach, the underlying DOA is assumed random and its a posteriori probability density function (PDF) is approximated by a discrete probability mass function. A Bayesian beamformer then balances a set of beamformers according to the associated weights. To obtain a close approximation of the a posteriori PDF, the number of samples must be sufficiently large, incurring a significant computational burden. In this paper, we exploit the structure of a uniform linear array (ULA) to show that samples of the a posteriori PDF can be computed efficiently using the fast Fourier transform (FFT). This leads to a fast algorithm for the Bayesian beamformer, which operates in O(MlogM + N²) operations where M is the number of samples and N is the number of sensors.