Phase modes circular array superdirective beamforming

Circular arrays are widely used in underwater acoustics array signal processing due to their two dimensional symmetrical characteristics. In this paper a new method to analytically calculate the superdirective mode coefficients of the phase modes circular array beamforming is proposed. The maximum Directivity Index (DI) achievable for phase modes circular array beamforming is also derived. Computer simulation is held for a circular array composed of 12 separate hydrophones mounted on either open sphere or rigid sphere. The calculated DI achieved by the proposed superdirective beamforming corresponds to the theoretical maximum DI for up to the 5^th order. The proposed method to calculate the superdirective mode coefficients is also applicable for calculating mode coefficients for arrays of any shape and any kind of expansion, indicating its wide range of applications in superdirectivity beamforming.