Dereverberation in Acoustic Sensor Networks using Weighted Prediction Error with Microphone-dependent Prediction Delays

In the last decades several multi-microphone speech dereverberation algorithms have been proposed, among which the weighted prediction error (WPE) algorithm. In the WPE algorithm, a prediction delay is required to reduce the correlation between the prediction signals and the direct component in the reference microphone signal. In compact arrays with closely-spaced microphones, the prediction delay is often chosen microphone-independent. In acoustic sensor networks with spatially distributed microphones, large time-differences-of-arrival (TDOAs) of the speech source between the reference microphone and other microphones typically occur. Hence, when using a microphone-independent prediction delay the reference and prediction signals may still be significantly correlated, leading to distortion in the dereverberated output signal. In order to decorrelate the signals, in this paper we propose to apply TDOA compensation with respect to the reference microphone, resulting in microphone-dependent prediction delays for the WPE algorithm. We consider both optimal TDOA compensation using crossband filtering in the short-time Fourier transform domain as well as band-to-band and integer delay approximations. Simulation results for different reverberation times using oracle as well as estimated TDOAs clearly show the benefit of using microphone-dependent prediction delays.