On the Design of Robust Differential Beamformers From the Beampattern Error Perspective

Differential microphone arrays (DMAs), which enhance acoustic signals of interest by measuring both the acoustic pressure field and its spatial derivatives, find extensive use in various practical systems and acoustic products. A critical element of DMAs is the differential beamformer, traditionally designed to ensure that the designed beampattern closely matches the desired target directivity pattern. However, such beamformers may lack sufficient robustness in practice. To address the balance between robustness and beampattern accuracy, this letter proposes two types of beamformers: one prioritizes maximizing the white noise gain (WNG) while maintaining a specified mean-squared beampattern error (MSBE), and the other aims to minimize MSBE while adhering to a specified level of WNG. By transforming these design challenges into quadratic eigenvalue problems (QEPs), we derive explicit solutions for the proposed beamformers. Simulations are conducted to illustrate the performance characteristics of these beamformers.