Plane wave decomposition and beamforming for directional spatial sound localization

Sound field decomposition using spherical microphone arrays has become a focus of interest for spatio-temporal analysis of the sound field in room acoustics, spatial audio rendering applications, and an estimation of the direction and localization of acoustic sources. The existing methods to localize acoustics sources and describe the sound field normally depend on omnidirectional sound field capturing by utilizing a few pairs of microphones and employing traditional correlation techniques. Therefore, these methods yield an approximate estimation of an overall acoustic analysis and parameters estimation of the captured sound field. In this paper, we performed sound field decomposition and beamforming to analyze the spatio-temporal structures of the captured impulse responses (IRs) using a 32-channel spherical microphone array in an anechoic chamber hall and in a real auditorium. We propose an approach based on a combination of plane wave decomposition (PWD), using spherical harmonics (SH) analysis, and an adaptive beamforming technique, as weighting filters for the PWD. Among adaptive beamforming techniques minimum variance distortionless response (MVDR) is investigated and used to compute the directional behavior of sound fields in the form of directional impulse responses (DIRs), in order to explain the influence of surrounding space on the propagation of the direct sound and several reflections. Furthermore, simultaneous localization of multiple sources and the variation in their temporal behavior is investigated and presented. The comparison between the results of computed directions of incidence of sound and the directions known beforehand showed a good agreement with each other inferring an effective application of spherical microphone arrays to sound field analysis.