Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the 3-user MT×MR multiple-input multiple-output (MIMO) interference channel (IC) with rank-deficient channel matrices, where each transmitter is equipped with MT antennas and each receiver with MR antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks D1 and D2, 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 MIMOIC 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., D1 +D2 ≤ min(MT ,MR), zero forcing is sufficient to achieve the optimal DoF. On the other hand, when D1 +D2 > min(MT ,MR), 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.