Spherical Microphone Array Beam Steering Using Wigner-D Weighting

Spherical microphone arrays, which have been recently developed and proposed for various applications, typically employ beam patterns that are rotationally symmetric about the look direction, providing efficient beam steering in the spherical harmonics domain. However, in some situations, a more general beam pattern may be desired. This letter presents the theory and a simulation example for steering general beam patterns in spherical microphone arrays. Beam steering, formulated as a rotation of the beam pattern, is achieved by weighting the beam pattern coefficients in the spherical harmonics domain with Wigner-D functions that hold the rotation angles as parameters. A matrix formulation is provided, with successive rotations formulated as matrix products.