Optimal Microphone Array Observation for Clear Recording of Distant Sound Sources

We propose the principle for deriving an optimum design for a microphone array that uses mutual information to segregate distant sound sources. Many conventional studies on array signal processing have focused on methods for estimating sound sources from array observations. To record distant sound sources clearly, designing an optimum array structure to segregate a target from other noise is also necessary. In this study, we reveal that the optimum array observation was achieved by receiving signals that are physically decorrelated between microphones, which homogenizes the eigenvalues of the spatial correlation matrix. We theoretically explain this underlying principle using mutual information between sound sources and microphone observations whose relation to the existing minimum mean square error criterion for source separation is also discussed. The implementation of such a microphone array is possible by placing microphones in front of parabolic reflectors since the phase/amplitude around the focal point of the reflectors drastically varies with small perturbation of the microphone position. Crosscorrelation between observed signals can be reduced by optimally placing microphones. An array structure based on our proposed principle was tested by implementing minimum variance distortion-less response beamforming and postfiltering in the observations of a prototype microphone array. We experimentally confirmed that 1) the eigenvalues of the spatial correlation matrix were asymptotically homogenized and 2) the target source could be extracted clearly even when the sound sources were positioned 16.5 m from the array.