Using Statistical Room Acoustics for Computing the Spatially Averaged Performance of the Multichannel Wiener Filter Based Noise Reduction

The theoretical 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 microphones. To compute this theoretical performance, either time-consuming measurements of the ATFs and the noise field or simulation of the ATFs, e.g. using the image model, need to be performed. Recently, an analytical expression for the spatially averaged output SNR of the MWF has been proposed, requiring only the room properties and the source-microphone distances to be known. In this paper, we derive similar analytical expressions for other performance measures, namely for the spatially averaged mean square error (MSE), and speech distortion at the reference microphone.