  Hand-crafted spatial features (e.g., inter-channel phase difference, IPD)
play a fundamental role in recent deep learning based multi-channel speech
separation (MCSS) methods. However, these manually designed spatial features
are hard to incorporate into the end-to-end optimized MCSS framework. In this
work, we propose an integrated architecture for learning spatial features
directly from the multi-channel speech waveforms within an end-to-end speech
separation framework. In this architecture, time-domain filters spanning signal
channels are trained to perform adaptive spatial filtering. These filters are
implemented by a 2d convolution (conv2d) layer and their parameters are
optimized using a speech separation objective function in a purely data-driven
fashion. Furthermore, inspired by the IPD formulation, we design a conv2d
kernel to compute the inter-channel convolution differences (ICDs), which are
expected to provide the spatial cues that help to distinguish the directional
sources. Evaluation results on simulated multi-channel reverberant WSJ0 2-mix
dataset demonstrate that our proposed ICD based MCSS model improves the overall
signal-to-distortion ratio by 10.4% over the IPD based MCSS model.
