Microphone array source enhancement using subtractive PSD estimation model

Wiener post-filtering is a method for sound source enhancement that is known to be practically effective in various acoustic environments. To calculate an Wiener post-filter, the power spectral density (PSD) of the target source as well as that of noise needs to be estimated. Although a previous method known as PSD-estimation-in-beamspace was invented for estimating the PSD of sound sources using multiple beamformers, heuristic design of the beamformers may degrade the accuracy in source PSD estimation. To avoid selecting such beamformers, this study proposes an analytical beamformer design method using subtractive PSD estimation model, i.e. the target source PSD is described by subtraction of the PSD of noise-dominant signals from the PSD of a target source-dominant signal. The study reveals that beamformers suitable for PSD estimation can be analytically designed when a PSD mixing matrix consisting of the beamformer's directivity gains is circulant and its inverse becomes an M-matrix to make the PSD estimation model subtractive. The results of numerical simulations and practical experiments prove that the performance of the sound source enhancement will be improved when beamformers designed with the proposed method are utilized even in practical acoustic environments.