  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.
