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

Abstract

For most multi-microphone noise reduction algorithms, e.g. the multi-channel Wiener filter (MWF), it is well known that the performance depends on the acoustic scenario at hand, i.e. the used microphone array, the position of the desired source and the noise field. Since the position of the desired source is not always known a priori, it is of great interest in many applications to be able to compute the average performance for a specific microphone array, which can be obtained by averaging the performance over all feasible source positions. A possible but either time-consuming or computationally complex approach to achieve this is to use measurements or simulations for a large number of source positions.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.