Robust Minimum Sidelobe Beamforming for Spherical Microphone Arrays

A robust minimum sidelobe beamforming approach based on the spherical harmonics framework for spherical microphone arrays is proposed. It minimizes the peaks of sidelobes while keeping the distortionless response in the look direction and maintaining the mainlobe width. A white noise gain constraint is also derived and employed to improve the robustness against array errors. The resulting beamformer can provide optimal tradeoff between the sidelobe level, the beamwidth and robustness, so it could be more practical than the existing spherical array Dolph-Chebyshev modal beamformer in the presence of array errors. The optimal modal beamforming problem is formulated as a tractable convex second-order cone programming program, which is more efficient than conventional element-space based approaches, since the dimension of array weight vectors can be significantly decreased by using the properties of spherical harmonics and Legendre polynomials. For the purpose of performance comparison, we also formulate current robust modal beamformers as equivalent optimization problems based on the proposed array model. Numerical results show the high flexibility and efficiency of the proposed beamforming approach.