Design of Maximum Directivity Beamformers with Linear Acoustic Vector Sensor Arrays

This paper studies the design of maximum directivity factor (MDF) beamformers based on uniform linear arrays (ULAs) consisting of acoustic vector sensors (AVSs). We first derive the main lobe constraints, which ensure that the beamformer's beampattern achieves a maximum in the look direction, and prove that any beamformer that satisfies the proposed constraints can be written as the sum of two orthogonal beamformers: The maximum white noise gain (MWNG) beamformer and a reduced-rank beamformer. Then, we derive the MDF beamformer by maximizing the directivity factor (DF) under the deduced constraints. We also derive a robust version of the MDF beamformer, which can keep the WNG above a pre-specified level. Compared to the conventional MDF beamformer based on ULAs with omnidirectional microphones, the designed MDF beamformer with uniform linear AVS arrays (ULAVSAs) can steer the beampattern to any look direction in the 3-dimensional space and achieves a higher directivity. The proposed MDF beamformer also outperforms the two-step MDF beamformer with ULAVSAs since it maximizes the DF. The proposed methods are validated through simulations as well as real experiments.