Two-Stage Differential Beamforming for Acoustic Vector Sensor Planar Arrays

Multistage differential beamforming has attracted considerable attention for the ability to achieve high spatial gain while maintaining robustness. However, the spatial response of multistage differential beamforming varies with frequency. In order to overcome this limitation, this paper proposes a two-stage differential beamforming for acoustic vector sensor (AVS) planar arrays. Each AVS consists of a sound pressure sensor and two orthogonal particle velocity sensors oriented along thex-axis andy-axis, respectively. In the initial stage, pre-beamforming is performed to maintain uniform differential directivity across all AVSs. The array obtained through pre-beamforming is treated as a virtual array. The steering vector of the virtual array is expanded using the Jacobi-Anger expansion and circular harmonic decomposition, and then compared with the ideal differential beampattern to achieve a frequency-invariant beampattern design. The primary contributions of this paper are as follows: 1) A frequency-invariant two-stage differential beamforming method is proposed, which achieves a maximum WNG improvement of 4.8 dB, attributed to the frequency-independent directivity of the AVSs during pre-beamforming. 2) Simulation results demonstrate that the proposed method exhibits adequate robustness and achieves superior directivity gain. Finally, the effectiveness of the proposed method is validated through first-order and second-order differential beamforming using experimental data collected from a cross-shaped array consisting of five AVSs at a sampling rate of 8 kHz.