High-order Superdirectivity of Line Acoustic Vector Sensor Arrays

In this paper, the closed form expression of spatial coherence of the noise between the combined vector sensor components in the isotropic noise field is derived, and a superdirective beamformer based on the Gram-Schmidt orthogonal transform is proposed. One such combined directional sensor is composed of a single-degree-of-freedom particle velocity sensor and an omnidirectional acoustic pressure sensor, and its spatial response is directional. The solution to the spatial coherence is solved to constitute the noise covariance matrix of the line array in the endfire direction. Compared to the traditional pressure sensor arrays, the vector sensor arrays can pick up signals at the desired direction and increase the array gain by 4dB - 6dB in a wide frequency band with low side lobes and no left-right ambiguity, which are useful to suppress the unwanted noise and interferences from other sides. The proposed superdirective method is superior to the conventional beamforming and the trade-off can be made between directivity index and robustness. The performance of high-order superdirectivity of the line vector sensor array is analyzed, which is useful to the underwater hydrophone array design.