Spherical loudspeaker arrays have been recently studied for directional sound radiation, where the compact arrangement of the loudspeaker units around a sphere facilitated the control of sound radiation in three-dimensional space. Directivity of sound radiation, or beamforming, was achieved by driving each loudspeaker unit independently, where the design of beamforming weights was typically achieved by numerical optimization with reference to a given desired beam pattern. This is in contrast to the methods already developed for microphone arrays in general and spherical microphone arrays in particular, where beamformer weights are designed to satisfy a wider range of objectives, related to directivity, robustness, and side-lobe level, for example. This paper presents the development of a physical-model-based, optimal beamforming framework for spherical loudspeaker arrays, similar to the framework already developed for spherical microphone arrays, facilitating efficient beamforming in the spherical harmonics domain, with independent steering. In particular, it is shown that from a beamforming perspective, the spherical loudspeaker array is similar to the spherical microphone array with microphones arranged around a rigid sphere. Experimental investigation validates the theoretical framework of beamformer design.
