Achievable maximum-directivity beamforming for spherical microphone arrays with random array errors

The maximum-directivity beamformers, or the so-called plane wave decomposition (PWD) beamformers have been widely studied and used for spherical microphone arrays, but they are known to be sensitive to random array errors that exist in practical applications. In this paper, a robust maximum-directivity beamforming approach based on the spherical harmonics framework and worst-case performance optimization techniques is proposed. The approach is developed for both the space domain and the spherical harmonics domain. Given the known maximum level of array errors, it can automatically find and yield the achievable maximum-directivity for spherical microphone array beamformers, and does not require manual tuning of robustness parameters, which is the major advantage over the white noise gain constrained robustness control approaches that have been developed earlier for spherical microphone arrays.