Design of Robust Differential Beamformers with Microphone Arrays of Arbitrary Planar Geometry

Differential microphone arrays (DMAs) have garnered significant attention in recent research and development due to their high directivity and frequency-invariant beampatterns. However, DMAs frequently encounter substantial white noise amplification, which limits their practical applications. This paper addresses this issue by introducing a general method for designing robust DMAs with microphone arrays of arbitrary planar topology. The proposed approach approximates the beampattern using the Jacobi-Anger series expansion and constrains the white noise gain (WNG) to a specified value. This minimizes the error between the beampattern and the ideal directivity pattern while ensuring a reasonable level of robustness. A closed-form solution for the robust differential beamformer filter is derived using the quadratic eigenvalue problem (QEP) method. Simulation results demonstrate the feasibility and effectiveness of the proposed approach.