Robust adaptive beamformer with feasibility constraint on the steering vector

The standard MVDR beamformer has high resolution and interference rejection capability when the array steering vector is accurately known. However, it is known to degrade if steering vector error exists. Motivated by recent work in robust adaptive beamforming, we develop variants of the constrained robust adaptive beamformer that attempt to limit the search in the underlying optimization problem to a feasible set of steering vectors thereby achieving improved performance. The robustness against steering vector error is provided through a spherical uncertainty set constraint, while a set of magnitude constraints is enforced on each element of the steering vector to better constrain the search in the space of feasible steering vectors. By appropriately changing the variables, the optimization problem is modified such that the need for the magnitude constraints are avoided. The developed algorithm is tested in the context of speech enhancement using a microphone array and shown to be superior to existing algorithms.