Three-dimensional beamforming for small aperture planar acoustic vector sensor array

A method of three-dimensional beamforming, based on the multipole expansions of the sound field, is proposed in this paper and applied to the small aperture acoustic vector planar array. The desired three-dimensional beam pattern can be synthesized with a two-dimensional array structure by combining the vertical particle velocity component of the sound field and the relationship between the spherical harmonics and the multipole modes. Therefore, the required array structure can be simplified for a three-dimensional beamforming. For illustration, a 3 × 3 rectangular vector sensor array was considered. Simulation results indicate that the error introduced by the approximations for multipole modes extraction can be ignored and the obtained beam pattern approximates the theoretical beam pattern when the spacing of adjacent vector sensors is less than one-fifth of the signal wavelength. Compared to the three-dimensional beamforming based on the spherical harmonic decomposition of the sound field, the proposed method achieves comparable array gain with better robustness in the low frequency band. Therefore, a reliable approach for low-frequency three-dimensional target detection is provided.