Optimal design of modal beamformers for circular arrays

An approach to optimal design of circular harmonics based modal beamformers for circular arrays is presented. Theoretical analysis shows the equivalence between the element-space and circular-harmonics-domain beamformers. By deriving the expression for the signal and noise covariance matrices, array manifold, and the array response in terms of the circular-harmonics-domain beamforming weights, the weights design problem is formulated as one of minimum variance distortionless response beamforming in the circular harmonics domain. It is found that the well-known phase-mode beamformer for circular arrays can be viewed as an ideal minimum variance distortionless response beamformer against the planarly isotropic noise in the circular harmonics domain. This interesting result is useful for analyzing and evaluating the performance of the phase-mode circular arrays. In this circular-harmonics-domain beamformer, additional constraints can be imposed to improve its robustness and control the sidelobes, which is important in practical applications. The developed approach can include both the delay-and-sum and phase-mode beamformers as special cases, which leads to very flexible designs. Simulation and experimental results show excellent performance of the proposed beamforming approach.