Three-dimensional Beamforming Of Miniaturized Aperture Acoustic Vector Sensor Array Based On Multipole Expansions

The conventional beamforming array is designed based on the half-wavelength spacing principle.Therefore,the aperture of low-frequency sonar array is more than hundreds of meters,which is inconvenience for engineering implementation.The small aperture array beamforming method can obtain approximately frequency-invariant beampattern and high spatial gain with a small array aperture and can simultaneously measure the elevation and azimuth of the target,which fulfill the requirements of low-frequency target detection in the deep-sea short-range.In the light of these situations,the three-dimensional beamforming methods based on multipole expansions for small acoustic vector sensor array aperture is proposed in this paper.Above all,a three-dimensional beamforming method of a miniaturized aperture acoustic vector sensor volume array is proposed.Firstly,the frequency independent multipole modes are obtained by approximating the high order sound pressure derivative in this method.Then,the spherical harmonic functions of each order are obtained by combining the relationship between the multipole modes and the spherical harmonic functions.Finally,the desired beam pattern is synthesized by the spherical harmonic functions.In this paper,the performance of the beamformers is simulated and analyzed from the aspects of beam pattern,array gain and white noise gain,and the effects of amplitude and phase errors,position errors and vector sensor pointing errors on the performance of the beamformers are analyzed.The simulation results indicate that the proposed three-dimensional beamformers achieves directivity comparable to the directivity of the pressure spherical array three-dimensional beamformer based on the spherical harmonic function decomposition of the sound field with higher robustness.Furthermore,a three-dimensional beamforming method of miniaturized aperture acoustic vector sensor planar is proposed to simplify the array structure for the complex volume array.The process of this method is basically consistent with that of the miniaturized aperture acoustic vector sensor volume array three-dimensional beamforming method.However,it can be used for three-dimensional beamforming in the absence of partial high-order acoustic pressure derivative components by using the characteristic of interconversion between multipole modes.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 is small and the distortion of obtained beampattern can be neglected when the spacing of adjacent vector sensors is less than one-fifth of the signal wavelength.According to the results of comparison with the miniaturized aperture acoustic vector sensor volume array and the miniaturized aperture acoustic vector sensor planar array threedimensional beamforming,it can be concluded that the performance of both beamforming methods are similar.Therefore,the miniaturized aperture acoustic vector sensor planar array three-dimensional beamforming method also can fulfill the requirements in three-dimensional space,and the field experiment also verifies the feasibility of the method.