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In order to gain new insights into MIMO interference networks, the optimalityof $\sum_{k=1}^K M_k/2$ (half the cake per user) degrees of freedom is exploredfor a $K$-user multiple-input-multiple-output (MIMO) interference channel wherethe cross-channels have arbitrary rank constraints, and the $k^{th}$transmitter and receiver are equipped with $M_k$ antennas each. The resultconsolidates and significantly generalizes results from prior studies byKrishnamurthy et al., of rank-deficient interference channels where all usershave $M$ antennas, and by Tang et al., of full rank interference channels wherethe $k^{th}$ user pair has $M_k$ antennas. The broader outcome of this work isa novel class of replication-based outer bounds for arbitrary rank-constrainedMIMO interference networks where replicas of existing users are added asauxiliary users and the network connectivity is chosen to ensure that anyachievable scheme for the original network also works in the new network. Thereplicated network creates a new perspective of the problem, so that evensimple arguments such as user cooperation become quite powerful when applied inthe replicated network, giving rise to stronger outer bounds, than when applieddirectly in the original network. Remarkably, the replication based bounds arebroadly applicable not only to MIMO interference channels with arbitraryrank-constraints, but much more broadly, even beyond Gaussian settings.

Replication-based Outer bounds and the Optimality of "Half the Cake" for Rank-Deficient MIMO Interference Networks