Differential Beamforming from a Geometric Perspective

Differential microphone arrays (DMAs) have demonstrated a great potential for solving the high-fidelity sound acquisition problem in a wide range of applications as they possess many good properties such as frequency-independent beampatterns with high directivity. A significant number of efforts have been devoted to the design of DMAs and the associated beamformers. As a result, many different types of DMAs and differential beamforming methods have been developed over the last few decades, some of which have been successfully deployed in real systems and commercial products. However, given an application, how to design a DMA to achieve optimal performances is still an open issue. This work studies the problem of designing linear DMAs (LDMAs) from a geometric perspective. Based on the fundamental observation that most practical and interesting DMA beampatterns have nulls in some directions, we define a criterion based on the orthogonality between the beamforming filter and the steering vector in the nulls' directions. We then derive a family of differential beamformers by optimizing the defined criterion, some of which are well known but derived from a different perspective, while others are new. Simulations and experiments are carried out, and the results validate the proposed method and developed differential beamformers.