Analysis of the average performance of the multi-channel Wiener filter for distributed microphone arrays using statistical room acoustics

In this paper, we propose to use the statistical properties of the acoustical transfer functions (ATFs) between the desired source and the microphones to derive analytical expressions for the spatially averaged performance measures (output SNR, noise reduction, speech distortion) of the MWF, assuming a homogeneous and known noise field. In addition, we show that although the spatially averaged performance measures do not express the performance of the MWF for a given position of the source and/or the microphones, they can be used to derive approximate analytical expressions for the average performance of the MWF for a given position of the microphones. Experimental results show that the proposed analytical expressions can be used to easily compare the performance of different microphone arrays, e.g. in an acoustic sensor network, without having to measure or numerically simulate a large number of ATFs.