Interference alignment for the K user MIMO interference channel

We consider the K user Multiple Input Multiple Output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver. It is assumed that channel coefficients are fixed and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the total Degrees Of Freedom (DOF) for this channel. Using a new interference alignment technique which has been recently introduced in, we show that MN/M+N K degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the total DOF for this channel is derived. This upper-bound coincides with our achievable DOF for K ≥ K_u =^Δ M+N/gcd(M,N) where gcd(M,N) denotes the greatest common divisor of M and N. This gives an exact characterization of DOF for MIMO Gaussian interference channel in the case of K ≥ K_u.