A Bayesian Framework for Blind Adaptive Beamforming

In this work, the problem of blind adaptive beamforming in the presence of steering-vector uncertainty is addressed within a Bayesian estimation framework. We express the single-input multiple-output (SIMO) observation model in the short-time-Fourier-transform (STFT) domain and employ a variational formulation to obtain iterative closed-form learning rules for inferring approximate posteriors on the steering vector and the target signal. By varying the a priori belief in the top-level statistical model, i.e., modeling a quantity as a random process or an unknown deterministic entity, it is shown that the considered framework yields a variety of beamforming algorithms including the celebrated minimum variance distortionless response (MVDR) beamformer. We highlight these interconnections and show by means of simulation results that the Bayesian approach alleviates signal distortion in noisy and uncertain environments as compared to the conventional MVDR beamformer by adaptively learning and incorporating uncertainty pertaining to the steering vector.