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We consider a constant $K$-user Gaussian interference channel with $M$antennas at each transmitter and $N$ antennas at each receiver, denoted as a$(K,M,N)$ channel. Relying on a result on simultaneous Diophantineapproximation, a real interference alignment scheme with joint receive antennaprocessing is developed. The scheme is used to provide new proofs for twopreviously known results, namely 1) the total degrees of freedom (DoF) of a$(K, N, N)$ channel is $NK/2$; and 2) the total DoF of a $(K, M, N)$ channel isat least $KMN/(M+N)$. We also derive the DoF region of the $(K,N,N)$ channel,and an inner bound on the DoF region of the $(K,M,N)$ channel.

Multiple-Antenna Interference Channel with Receive Antenna Joint Processing and Real Interference Alignment