  The generalized degrees of freedom (GDoF) region of the MIMO Gaussian
interference channel is obtained for the general case with an arbitrary number
of antennas at each node and where the SNR and interference-to-noise ratios
(INRs) vary with arbitrary exponents to a nominal SNR. The GDoF region reveals
various insights through the joint dependence of optimal interference
management techniques at high SNR on the SNR exponents that determine the
relative strengths of direct-link SNRs and cross-link INRs and the numbers of
antennas at the four terminals. For instance, it permits an in-depth look at
the issue of rate-splitting and partial decoding at high SNR and it reveals
that, unlike in the SISO case, treating interference as noise is not GDoF
optimal always even in the very weak interference regime. Moreover, while the
DoF-optimal strategy that relies just on transmit/receive zero-forcing
beamforming and time-sharing is not GDoF optimal (and thus has an unbounded gap
to capacity) the precise characterization of the very strong interference
regime, where single-user DoF performance can be achieved simultaneously for
both users, depends on the relative numbers of antennas at the four terminals
and thus deviates from what it is in the SISO case. For asymmetric numbers of
antennas at the four nodes the shape of the symmetric GDoF curve can be a
"distorted W" curve to the extent that for certain MIMO ICs it is a "V" curve.
