  Time-domain training criteria have proven to be very effective for the
separation of single-channel non-reverberant speech mixtures. Likewise,
mask-based beamforming has shown impressive performance in multi-channel
reverberant speech enhancement and source separation. Here, we propose to
combine neural network supported multi-channel source separation with a
time-domain training objective function. For the objective we propose to use a
convolutive transfer function invariant Signal-to-Distortion Ratio (CI-SDR)
based loss. While this is a well-known evaluation metric (BSS Eval), it has not
been used as a training objective before. To show the effectiveness, we
demonstrate the performance on LibriSpeech based reverberant mixtures. On this
task, the proposed system approaches the error rate obtained on single-source
non-reverberant input, i.e., LibriSpeech test_clean, with a difference of only
1.2 percentage points, thus outperforming a conventional permutation invariant
training based system and alternative objectives like Scale Invariant
Signal-to-Distortion Ratio by a large margin.
