A New Class of Differential Beamformers

Differential microphone arrays (DMAs) have been used in a wide range of applications for high-fidelity acoustic signal acquisition and enhancement. In the design of differential beamformers, three of the widely used measures are the directivity factor (DF), the front-to-back ratio (FBR), and the white noise gain (WNG). The former two have been used to obtain optimal differential beamformers, e.g., the hypercardioid and supercardioid, and the third one is generally used to analyze and control the robustness of the beamformer with respect to array imperfections due to sensors' self noise, mismatch among sensors, and sensors' placement errors. In this paper, we present a new measure called directivity factor and front-to-back ratio (DFBR), which is a generalization of DF and FBR. With this new measure, three different kinds of beamformers are derived. The first one is the maximum DFBR beamformer, which is deduced by maximizing DFBR with a joint diagonalization method. The second one is the ψ-cardioid beamformer, which is the maximum DFBR beamformer corresponding to a distortionless constraint. The last one is the reduced-rank differential beamformer, which is obtained by properly choosing the dimension of the signal subspace and maximizing WNG subject to the distortionless constraint. The developed beamformers have many interesting properties, which are justified by both simulations and experiments.