Application of Acoustic Radiation Modes in the Directivity Control by a Spherical Loudspeaker Array

Abstract

This work concerns the theoretical analysis and synthesis of sound fields by a compact spherical loudspeaker array. Such an electroacoustic device consists of several transducers mounted on a sphere-like structure, which are driven independently in order to achieve non-uniform directivity patterns. The control strategy usually adopted is to provide the array with some preprogrammed basic directivities corresponding to spherical harmonic functions. Thus, an arbitrary radiation pattern can be approximately achieved by changing the gains associated with these basic directivities. Here, a different approach based on the acoustic radiation modes of the array is proposed. Unlike spherical harmonics, radiation modes constitute a finite set of vectors that spans a subspace on which any radiation pattern the array is able to reproduce can be projected. Furthermore, radiation modes radiate sound energy independently. Since the eigenvalue analysis that must be carried out in order to obtain the modes leads also to their radiation efficiencies, the low frequency constraint in the directivity synthesis by a spherical array is naturally evaluated. Finally, it is useless to drive inefficient radiation modes. Therefore, the radiation mode approach leads to a reduced number of active channels, and to minimum source voltages for a given target directivity pattern.