6. Optimal Beam Pattern Design

Beamforming with spherical microphone arrays was presented in Chap. 5 as an instrument to achieve directional filtering, characterized by the beam pattern of the array. It may be desired to control the beam pattern in a more explicit manner to achieve specific properties. For example, beamformers that achieve maximum directivity index may be useful to enhance a desired plane wave relative to undesired plane waves arriving from the entire range of directions. Beamformers that achieve maximum white noise gain (WNG) may be desired if robustness to system uncertainty is important. We may also be interested in enhancing a desired plane wave while guaranteeing a specific reduction level for undesired plane waves in other directions. This can be achieved by restricting the side-lobe level in the beam pattern using the Dolph-Chebyshev design. Design objectives can also be combined into a single objective, or integrated into a more complex constrained optimization formulation. In summary, this chapter presents methods for beam pattern design formulated explicitly for spherical arrays, with the aim of providing tools for matching the properties of the array to specific performance aspects.