The DoF of the asymmetric MIMO interference channel with square direct link channel matrices

This paper studies the sum Degrees of Freedom (DoF) of K-user asymmetric MIMO Interference Channel (IC) with square direct link channel matrices, that is, the u-th transmitter and its intended receiver have M_u ϵ N antennas each, where M_u need not be the same for all u ϵ [1 : K]. Starting from a 3-user example, it is shown that existing cooperation-based outer bounds are insufficient to characterize the DoF. Moreover, it is shown that two distinct operating regimes exist. With a dominant user, i.e., a user that has more antennas than the other two users combined, it is DoF optimal to let that user transmit alone on the IC. Otherwise, it is DoF optimal to decompose and operate the 3-user MIMO IC as an (M₁ + M₂ + M₃)-user SISO IC. This indicates that MIMO operations are useless from a DoF perspective in systems without a dominant user. The main contribution of the paper is the derivation of a novel outer bound for the general K-user case that is tight in the regime where a dominant user is not present; this is done by generalizing the insights from the 3-user example to an arbitrary number of users.