Transducer Distribution on Spherical Arrays for Ambisonics Recording and Playback

Microphone and loudspeaker arrays are nowadays more and more employed in several applications, such as automotive industry, entertainment, immersive teleconferencing, or remote assistance. The position of the transducers over the surface of the array has a great influence on the beamforming, and so on the spatial performance. In this paper, a recurring geometrical problem is discussed: choosing the optimal locations of transducers for spherical arrays, either microphones or loudspeakers.None of the existing systems is currently relying on a spherical design, or t-design, for the arrangement of the transducers on the sphere. It will be shown that such mathematically optimized geometry is an optimal solution for the design of spherical arrays. They are the only known geometries ensuring a lossless transformation back and forth between the two most common spatial audio format: Ambisonics, which makes use of spherical harmonics, and Spatial PCM Sampling, which relies on unidirectional, high directivity virtual microphones.