  Despite successful applications of end-to-end approaches in multi-channel
speech recognition, the performance still degrades severely when the speech is
corrupted by reverberation. In this paper, we integrate the dereverberation
module into the end-to-end multi-channel speech recognition system and explore
two different frontend architectures. First, a multi-source mask-based weighted
prediction error (WPE) module is incorporated in the frontend for
dereverberation. Second, another novel frontend architecture is proposed, which
extends the weighted power minimization distortionless response (WPD)
convolutional beamformer to perform simultaneous separation and
dereverberation. We derive a new formulation from the original WPD, which can
handle multi-source input, and replace eigenvalue decomposition with the matrix
inverse operation to make the back-propagation algorithm more stable. The above
two architectures are optimized in a fully end-to-end manner, only using the
speech recognition criterion. Experiments on both spatialized wsj1-2mix corpus
and REVERB show that our proposed model outperformed the conventional methods
in reverberant scenarios.
