Spherical array superdirective beamforming based on spherical harmonic decomposition of the soundfield

This paper provides a new analytical method to calculate superdirective mode coefficients of the spherical array beamforming based on spherical harmonic decomposition of the soundfield. Furthermore, N² law of the spherical receiving arrays is proven: given the highest mode extracted N_max, the Maximum Directivity Factor (DF) is (N_max+1)². Computer simulation is conducted for the spherical array with 20 hydrophones located at the vertex of a dodecahedron, which can be optionally mounted on open sphere or rigid sphere. The resulting directivity index (DI) for N_max=1 and 2 corresponds to the theoretical DI at low frequencies. The operating frequency range is from 100Hz to about 5kHz. The proposed method to calculate the superdirective mode coefficients is also applicable for arrays of any shape and any form of expansion, indicating its wide usage in superdirectivity beamforming.