Flexible and Optimal Design of Spherical Microphone Arrays for Beamforming

This paper describes a methodology for designing a flexible and optimal spherical microphone array for beamforming. Using the approach presented, a spherical microphone array can have very flexible layouts of microphones on the spherical surface, yet optimally approximate a desired beampattern of higher order within a specified robustness constraint. Depending on the specified beampattern order, our approach automatically achieves optimal performances in two cases: when the specified beampattern order is reachable within the robustness constraint we achieve a beamformer with optimal approximation of the desired beampattern; otherwise we achieve a beamformer with maximum directivity, both robustly. For efficient implementation, we also developed an adaptive algorithm for computing the beamformer weights. It converges to the optimal performance quickly while exactly satisfying the specified frequency response and robustness constraint in each step. One application of the method is to allow the building of a real-world system, where microphones may not be placeable on regions, such as near cable outlets and/or a mounting base, while having a minimal effect on the performance. Simulation results are presented