Degrees of freedom of the K user MIMO interference channel

We provide inner bound and outer bound 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 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 les R and min(M, N) R/R +1 K if K > R. Achievability is based on interference alignment.