Frequency-Domain Design of Asymmetric Circular Differential Microphone Arrays

Circular differential microphone arrays (CDMAs) facilitate compact superdirective beamformers whose beampatterns are nearly frequency invariant. In contrast to linear differential microphone arrays where the optimal steering direction is at the endfire, CDMAs provide perfect steering for all azimuthal directions. Herein, we extend the traditional symmetric model of DMAs and establish an analytical asymmetric model for Nth-order CDMAs. This model exploits the circular geometry to eliminate the inherent limitation of symmetric beampatterns associated with a linear geometry and allows also asymmetric beampatterns. This new model is then used to develop asymmetric versions of two optimal commonly used beampatterns namely the hypercardioid and the supercardioid. Experimental results demonstrate the advantages of the asymmetric model compared to the traditional symmetric one, when additional directional constraints are imposed. The proposed model yields superior performance in terms of white noise gain, directivity factor, and front-to-back ratio, as well as more flexible design of nulls for the interfering signals.