时域实现结构球面阵的最差性能优化稳健宽带波束形成器设计

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

针对球面阵模态域波束形成器对传声器失配误差敏感的问题，研究了时域实现结构球面阵的最差性能优化稳健宽带波束形成器设计。揭示了波束响应误差上界的保守性是影响现有最差性能优化方法性能的主要原因，进而提出了一种波束响应误差上界更为紧凑的优化设计方法。理论分析表明，与现有最差性能优化方法相比，所提出方法的代价函数更小、且可行解的范围也更大。针对最差性能优化设计方法存在的波束指向上阵列响应随频率变化波动偏大而引起信号失真的问题，还给出了一种减小波束图在指向方向上受信号频率影响的约束方法。仿真分析结果表明：在相同传声器失配误差条件下，所提出的设计方法要优于现有方法，得到的波束图具有更低的旁瓣级。

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.