Design of Robust Broadband Beamformers Using Worst-Case Performance Optimization: A Semidefinite Programming Approach

Broadband beamformers are known sensitive to microphone mismatches, especially for small-sized arrays. To address the problem, the worst-case performance optimization (WCPO) criterion has been used to design robust broadband beamformers. Recently, a circular-model-based design using the WCPO criterion was proposed, which has been shown superior to the existing second-order cone programming (SOCP) based design also using the WCPO criterion. In this paper, however, we find that the circular-model-based design is sensitive to stopband level constraint. If the constraint is chosen tightly, it may become less robust and degrades even worse than the SOCP-based design. To achieve a better tradeoff between robustness and beamforming performance, we propose a semidefinite programming based approach for robust broadband beamformer design using the WCPO criterion. The relations of the proposed design to its existing counterparts are also theoretically analyzed. In particular, we show that the proposed design is less conservative than the SOCP-based design, and is also less sensitive to the setting of stopband level constraint and more robust when compared to the circular model-based design. Another contribution of this paper is that the relation between the SOCP- and the circular-model-based designs is theoretically revealed. Simulation results and real experimental results are presented to show the superior of the proposed design over its existing counterparts.