By introducing a novel outer bound, we find a sufficient condition for optimality of K k=1 M k /2 degrees of freedom (half the cake per user) for a K-user multiple-inputmultiple-output (MIMO) interference channel (IC) where the cross-channels have arbitrary rank constraints, and the k th transmitter and receiver are equipped with M k antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the k th user pair has M k antennas.Rank Deficiency Inter-user Asymmetry Inter-user Asymmetry Rank Deficiency K user M × M IC Everyone gets half the cake [1] K user M k × M k IC Half-the-cake optimal if no dominant user [3] K user M k × M k Rank-Def. IC When is Half-the-cake optimal? [This Work] K user M × M Rank-Def. IC Half-the-cake optimal if total interference rank ≥ M [2]Fig. 1: The motivation of this paper.
A. Everyone gets half the cakeIt was shown by Cadambe and Jafar in [1] that in a Kuser M × M MIMO interference channel where each node is