Optimization of loudspeaker and microphone configurations for sound reproduction system based on boundary surface control principle - An optimizing approach using Gram-Schmidt orthogonalization and its evaluation

We propose a 3-D sound reproduction system based on the boundary surface control principle (BoSC system) and evaluate its performance via demonstration and exhibition. The BoSC reproduction system, dome-shaped and constructed of wood, consists of 62 full-range loudspeakers and eight subwoofer loudspeakers. The BoSC recording system is designed from C80 fullerene consisting of 70 microphones of a 46-cm diameter. In the listening room, 62 full-range loudspeakers assisted by the designed inverse filters reproduce sound fields identical to the primary sound fields by reproducing sound pressure on the 70 microphones which surround the listener's head. The BoSC system requires huge numerical calculation to reproduce authentic 3-D sound fields. Consequently, a pre-convolution calculation of the inverse filters is required to reproduce and transmit these fields. Therefore, to realize a real-time 3-D sound field reproduction system, we investigated optimization of the loudspeaker and microphone configuration using Gram-Schmidt orthogonalization. In the BoSC system, the inverse filters are determined by an inverse system of a transfer function matrix measured between each loudspeaker and microphone pair. Therefore, a transfer function matrix with a huge condition number degrades the accuracy of the reproduced sound fields. The selection of loudspeakers in the active control system that includes the BoSC system is equal to the selection of a vertical vector in the transfer function matrix. This means that for the reduction of the number of loudspeakers the vertical vector is selected up to the required numbers. By applying Gram-Schmidt orthogonalization to the selection of loudspeakers, the loudspeaker is selected in the order of linear independence from highest to lowest. In this paper, the effect of the reduction of loudspeakers and microphones is evaluated by the subjective assessment of a sound image localization test. Copyright