A Chance-Constrained Programming Approach to the Design of Robust Broadband Beamformers With Microphone Mismatches

This paper addresses the design of robust broadband beamformers by taking into account the prior knowledge of uncertain means and variances of microphone mismatches. A chance-constrained programming (CCP) based design approach is proposed, which is a generic extension of the existing worst case mean performance optimization (WMPO) based counterpart by using a chance-constrained stopband level constraint instead of a hard one. The original CCP-based design problem, however, is NP-hard to solve. To deal with the problem, a relaxed convex optimization formulation is developed by exploiting the distribution property of array response distortion due to microphone mismatches. The relation between the proposed CCP- and WMPO-based design approaches is analyzed theoretically. It shows that there always exists a chance constraint probability under which the CCP-based design is comparable to the WMPO-based one, which provides an insight into the overconservatism problem in the WMPO-based design from the perspective of the CCP-based framework. Moreover, a criterion on the setting of the chance constraint probability is also derived for the proposed design approach in order to remedy the overconservatism problem. Simulation and real experimental results are presented to show the superior performance of the proposed design approach compared with its state-of-the-art counterparts.