Bayesian robust adaptive beamforming based on random steering vector with bingham prior distribution

We consider robust adaptive beamforming in the presence of steering vector uncertainties. A Bayesian approach is presented where the steering vector of interest is treated as a random vector with a Bingham prior distribution. Moreover, in order to also improve robustness against low sample support, the interference plus noise covariance matrix R is assigned a non informative prior distribution which enforces shrinkage to a scaled identity matrix, similarly to diagonal loading. The minimum mean square distance estimate of the steering vector as well as the minimum mean square error estimate of R are derived and implemented using a Gibbs sampling strategy. The new beamformer is shown to converge within a limited number of snapshots, despite the presence of steering vector errors.