Worst-case performance optimization for spherical microphone array modal beamformers

The performance of conventional spherical microphone array modal beamformers is known to degrade in the presence of array errors. White noise gain control has been widely used to control the robustness of modal beamformers, but it is not clear how to properly choose the white noise gain parameters based on the level of array errors. In this paper, a worst-case performance optimization approach is formulated for the spherical array minimum-sidelobe modal beamformer to improve its robustness against random errors occurring in practice, thus the optimal performance can be obtained based on the known maximum level of array errors. The robust optimal modal beamforming problem is reformulated as a tractable convex optimization within the spherical harmonics framework. Compared with conventional element-space approaches, the proposed modal beamforming method enjoys lower optimization complexity and higher flexibility in beam steering.