A penalized inequality-constrained minimum variance beamformer with applications in hearing aids

A well known challenge in linearly-constrained beamforming is how to suppress multiple interferences when the degrees of freedom (DoF) provided by the array are fewer than the number of sources in the environment. In this paper, we propose a beamformer design to address this challenge. Specifically, we propose a min-max beam-former design that penalizes the spatial responses on all interferences' directions. The new design can efficiently mitigate the total interference power regardless of whether the number of interfering sources is less than the array DoF or not. We formulate this min-max beamformer design as a convex second-order cone programming (SOCP) and proposed a low complexity iterative algorithm based on alternating direction method of multipliers (ADMM) method to solve it. In the simulation, we compare the proposed beamfomer with the linearly constrained minimum variance (LCMV) beamformer and a recently proposed inequality-constrained minimum variance (ICMV) beamformer [1]. The ability of the proposed beamformer to handle more interferences is demonstrated.