  We provide innerbound and outerbound for the total number of degrees of
freedom of the $K$ user multiple input multiple output (MIMO) Gaussian
interference channel with $M$ antennas at each transmitter and $N$ antennas at
each receiver if the channel coefficients are time-varying and drawn from a
continuous distribution. The bounds are tight when the ratio
$\frac{\max(M,N)}{\min(M,N)}=R$ is equal to an integer. For this case, we show
that the total number of degrees of freedom is equal to $\min(M,N)K$ if $K \leq
R$ and $\min(M,N)\frac{R}{R+1}K$ if $K > R$. Achievability is based on
interference alignment. We also provide examples where using interference
alignment combined with zero forcing can achieve more degrees of freedom than
merely zero forcing for some MIMO interference channels with constant channel
coefficients.
