A recursive Bayesian beamforming for steering vector uncertainties

A recursive Bayesian approach to narrowband beamforming for an uncertain steering vector of interest signal is presented. In this paper, the interference-plus-noise covariance matrix and signal power are assumed to be known. The steering vector is modeled as a complex Gaussian random vector that characterizes the level of steering vector uncertainty. Applying the Bayesian model, a recursive algorithm for minimum mean square error (MMSE) estimation is developed. It can be viewed as a mixture of conditional MMSE estimates weighted by the posterior probability density function of the random steering vector given the observed data. The proposed recursive Bayesian beamformer can make use of the information about the steering vector brought by all the observed data until the current short-term integration window and can estimate the mean and covariance of the steering vector recursively. Numerical simulations show that the proposed beamformer with the known signal power and interference-plus-noise covariance matrix outperforms the linearly constrained minimum variance, subspace projection, and other three Bayesian beamformers. After convergence, it has similar performance to the optimal Max-SINR beamformer with the true steering vector.