Robust adaptive beamforming using a Bayesian steering vector error model

We propose a Bayesian approach to robust adaptive beamforming which entails considering the steering vector of interest as a random variable with some prior distribution. The latter can be tuned in a simple way to reflect how far is the actual steering vector from its presumed value. Two different priors are proposed, namely a Bingham prior distribution and a distribution that directly reveals and depends upon the angle between the true and presumed steering vector. Accordingly, a non-informative prior is assigned to the interference plus noise covariance matrix R$\mathbf{R}$, which can be viewed as a means to introduce diagonal loading in a Bayesian framework. The minimum mean square distance estimate of the steering vector as well as the minimum mean square error estimate of R$\mathbf{R}$ are derived and implemented using a Gibbs sampling strategy. Numerical simulations show that the new beamformers possess a very good rate of convergence even in the presence of steering vector errors.