Robust minimum variance beamforming with multiple response constraints

Conventional beamformers can be sensitive to mismatches between presumed and actual steering vectors of the signal-of-interest. A recently proposed class of robust beamformers aim to counteract this problem by using a non-attenuation constraint inside a single hypersphere centered at the presumed steering vector of the signal-of-interest. In an effort to strike a balance between robustness to steering vector error and interference-plus-noise suppression, we propose in this manuscript to use multiple concentric hyperspheres instead of one with different degrees of protection in each. We derive several useful properties of this multiply constrained beamformer and use numerical simulations to show that using two constraints yields improved signal-to-interference-plus-noise-ratio compared to one constraint in certain scenarios, particularly at a large input signal-to-noise-ratio.The manuscript also includes an overview of conventional beamforming, the mismatch problem and previously proposed robust beamformers