Using statistical room acoustics for analysing the output SNR of the MWF in acoustic sensor networks

In the context of acoustic sensor networks with spatially distributed microphones, the selection of the subset of microphones yielding the best performance is of great interest. Subset selection can be achieved by comparing the theoretical performance of different subsets of microphones. In this paper, we derive an analytical expression for the spatially averaged output SNR of the multi-channel Wiener filter (MWF) in a diffuse noise field, exploiting the statistical properties of the acoustic transfer functions (ATFs) between the desired source and the microphones. This analytical expression only requires the room properties and the source-microphone distances to be known. Simulation results show that the spatially averaged 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 the performance of different subsets of microphones.