  The majority of multichannel speech enhancement algorithms are two-step
procedures that first apply a linear spatial filter, a so-called beamformer,
and combine it with a single-channel approach for postprocessing. However, the
serial concatenation of a linear spatial filter and a postfilter is not
generally optimal in the minimum mean square error (MMSE) sense for noise
distributions other than a Gaussian distribution. Rather, the MMSE optimal
filter is a joint spatial and spectral nonlinear function. While estimating the
parameters of such a filter with traditional methods is challenging, modern
neural networks may provide an efficient way to learn the nonlinear function
directly from data. To see if further research in this direction is worthwhile,
in this work we examine the potential performance benefit of replacing the
common two-step procedure with a joint spatial and spectral nonlinear filter.
  We analyze three different forms of non-Gaussianity: First, we evaluate on
super-Gaussian noise with a high kurtosis. Second, we evaluate on inhomogeneous
noise fields created by five interfering sources using two microphones, and
third, we evaluate on real-world recordings from the CHiME3 database. In all
scenarios, considerable improvements may be obtained. Most prominently, our
analyses show that a nonlinear spatial filter uses the available spatial
information more effectively than a linear spatial filter as it is capable of
suppressing more than $D-1$ directional interfering sources with a
$D$-dimensional microphone array without spatial adaptation.
