On the Design of Robust Differential Beamformers with Uniform Circular Microphone Arrays

While circular microphone arrays (CMAs) have been used in a wide range of applications, e.g., smart speakers and conferencing phones, how to design robust beamformers that can obtain the highest possible directivity with such arrays remains a challenging issue. In this paper, we study this problem and present a method to design robust differential beamformers based on uniform CMAs (UCMAs). The approach casts the differential beamforming problem into one of optimization, which attempts to maximize the directivity factor (DF) subject to some constraints on symmetric nulls in the beampattern and the white noise gain (WNG). The robust beamformers are obtained by transforming the optimization problem into a quadratic eigenvalue problem (QEP). Simulation results show that the deduced beamformers can obtain high DFs and consistent beampatterns, regardless of the steering angle, and the WNG is effectively controlled to be larger than a pre-specified threshold.