  The K-user symmetric multiple input multiple output (MIMO) Gaussian
interference channel (IC) where each transmitter has M antennas and each
receiver has N antennas is studied from a generalized degrees of freedom (GDOF)
perspective. An inner bound on the GDOF is derived using a combination of
techniques such as treating interference as noise, zero forcing (ZF) at the
receivers, interference alignment (IA), and extending the Han-Kobayashi (HK)
scheme to K users, as a function of the number of antennas and the log (INR) /
log (SNR) level. Three outer bounds are derived, under different assumptions of
cooperation and providing side information to receivers. The novelty in the
derivation lies in the careful selection of side information, which results in
the cancellation of the negative differential entropy terms containing signal
components, leading to a tractable outer bound. The overall outer bound is
obtained by taking the minimum of the three outer bounds. The derived bounds
are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the
generalized degrees of freedom (GDOF). Several interesting conclusions are
drawn from the derived bounds. For example, when K > N/M + 1, a combination of
the HK and IA schemes performs the best among the schemes considered. When N/M
< K <= N/M + 1, the HK-scheme outperforms other schemes and is shown to be GDOF
optimal. In addition, when the SNR and INR are at the same level, ZF-receiving
and the HK-scheme have the same GDOF performance. It is also shown that many of
the existing results on the GDOF of the Gaussian IC can be obtained as special
cases of the bounds, e.g., by setting K=2 or the number of antennas at each
user to 1.
