Three-Dimensional Sound Field Reproduction Using Multiple Circular Loudspeaker Arrays

Three-dimensional spatial sound field reproduction enables enhanced immersive acoustic experience for a listener. Recreating an arbitrary 3-D spatial sound field using a practically realizable array of loudspeakers is a challenging problem in acoustic signal processing. This paper exploits the underlying characteristics of wavefield propagation to devise a strategy for accurate 3-D sound field reproduction inside a 3-D region of interest with practical array geometries. Specifically, we use the properties of the associated Legendre functions and the spherical Hankel functions, which are part of the solution to the wave equation in spherical coordinates, for loudspeaker placement on a set of multiple circular arrays and provide a technique for spherical harmonic mode-selection to control the reproduced sound field. We also analyze the artifacts of spatial aliasing due to the use of discrete loudspeaker arrays in the region of interest. As an illustration, we design a third-order reproduction system to operate at a frequency of 500 Hz with 18 loudspeakers arranged in a practically realizable configuration.