Average output SNR of the multichannel Wiener filter using statistical room acoustics

The performance of the multi-channel Wiener filter (MWF), which is often used for noise reduction in speech enhancement applications, depends on the noise field and on the acoustic transfer functions (ATFs) between the desired source and the microphone array. Recently, using statistical room acoustics an analytical expression for the spatially averaged output SNR, given the relative distance between the source and the microphone array, has been derived for the MWF in a diffuse noise field, requiring only the room properties to be known. In this paper, we show that this analytical expression can be extended to compute the average output SNR of the MWF for a specific microphone configuration, enabling to compare the performance of different microphone configurations, e.g. in an acoustic sensor network. Simulation results show that the average output SNR obtained using the statistical properties of ATFs is similar to the average output SNR obtained using simulated ATFs, therefore providing an efficient way to compare different microphone configurations.