Degrees of Freedom of the Three-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the three-user M
_T
× M
_R
multiple-input-multipleoutput (MIMO) interference channel (IC) with rank-deficient channel matrices, where each transmitter is equipped with M
_T
antennas and each receiver with M
_R
antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks D
₁
and D
₂
, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., D
₁
+ D
₂
≤ min(M
_T
, M
_R
), zero forcing is sufficient to achieve the optimal DoF. On the other hand, when D
₁
+ D
₂
> min(M
_T
, M
_R
), a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.