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 {\em asymmetric} MIMO Interference Channel (IC) with square direct link channel matrices, that is, the $u$-th transmitter and its intended receiver have $M_u\in \mathbb{N}$ antennas each, where $M_u$ need not be the same for all $u\in [1:K]$. 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 {\it dominant} user, i.e., a user that has more antennas than the other two users combined, %(say $M_1\geq M_2+M_3$), it is DoF optimal to let that user transmit alone on the IC. Otherwise, it is DoF optimal to {\em decompose} and operate the 3-user MIMO IC as an $(M_1+M_2+M_3)$-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.