Design of robust broadband beamformers using worst-case performance optimization for time-domain spherical microphone arrays

Spherical array modal beamformers are known sensitive to microphone mismatches. To combat the problem, robust design of spherical broadband beamformers with the time-domain implementation structure using Worst-Case Performance Optimization (WCPO) is studied. We reveal that the conservativeness of the upper error bound on beamforming response is the primary factor to degrade the performance of the existing WCPO-based approach. Then we propose an improved design approach for spherical broadband beamformers using a stricter upper error bound on beamforming response. Theoretical analysis shows that the cost function of the proposed design is smaller and the range of feasible set of the proposed design is also larger when compared with the existing design. Moreover, we have also proposed a scheme on constraint specification to reduce fluctuation of beamforming response with frequency at steering direction to alleviate signal distortion. Simulation results show that the proposed design outperforms its existing counterpart and exhibits a lower sidelobe level under the same condition of microphone mismatches.