  To date, mainstream target speech separation (TSS) approaches are formulated
to estimate the complex ratio mask (cRM) of the target speech in time-frequency
domain under supervised deep learning framework. However, the existing deep
models for estimating cRM are designed in the way that the real and imaginary
parts of the cRM are separately modeled using real-valued training data pairs.
The research motivation of this study is to design a deep model that fully
exploits the temporal-spectral-spatial information of multi-channel signals for
estimating cRM directly and efficiently in complex domain. As a result, a novel
TSS network is designed consisting of two modules, a complex neural spatial
filter (cNSF) and an MVDR. Essentially, cNSF is a cRM estimation model and an
MVDR module is cascaded to the cNSF module to reduce the nonlinear speech
distortions introduced by neural network. Specifically, to fit the cRM target,
all input features of cNSF are reformulated into complex-valued representations
following the supervised learning paradigm. Then, to achieve good hierarchical
feature abstraction, a complex deep neural network (cDNN) is delicately
designed with U-Net structure. Experiments conducted on simulated multi-channel
speech data demonstrate the proposed cNSF outperforms the baseline NSF by 12.1%
scale-invariant signal-to-distortion ratio and 33.1% word error rate.
