  The key advantage of using multiple microphones for speech enhancement is
that spatial filtering can be used to complement the tempo-spectral processing.
In a traditional setting, linear spatial filtering (beamforming) and
single-channel post-filtering are commonly performed separately. In contrast,
there is a trend towards employing deep neural networks (DNNs) to learn a joint
spatial and tempo-spectral non-linear filter, which means that the restriction
of a linear processing model and that of a separate processing of spatial and
tempo-spectral information can potentially be overcome. However, the internal
mechanisms that lead to good performance of such data-driven filters for
multi-channel speech enhancement are not well understood. Therefore, in this
work, we analyse the properties of a non-linear spatial filter realized by a
DNN as well as its interdependency with temporal and spectral processing by
carefully controlling the information sources (spatial, spectral, and temporal)
available to the network. We confirm the superiority of a non-linear spatial
processing model, which outperforms an oracle linear spatial filter in a
challenging speaker extraction scenario for a low number of microphones by 0.24
POLQA score. Our analyses reveal that in particular spectral information should
be processed jointly with spatial information as this increases the spatial
selectivity of the filter. Our systematic evaluation then leads to a simple
network architecture, that outperforms state-of-the-art network architectures
on a speaker extraction task by 0.22 POLQA score and by 0.32 POLQA score on the
CHiME3 data.
