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

We provide the degrees of freedom (DoF) characterization for the $3$-user $M_T\times M_R$ multiple-input multiple-output (MIMO) interference channel (IC) with \emph{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., $D_1+D_2\leq \min(M_T, M_R)$, 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.Comment: 28 pages, 7 figures. To appear in IEEE transactions on wireless communication

Degrees of freedom of 2-user and 3-user rank-deficient MIMO interference channels

We study the degrees of freedom (DoF) of 2-user and 3-user multiple input multiple output (MIMO) interference channels with rank deficient channel matrices. Only achievable DoF results and trivial outer bounds were previously available for these problems, restricted to symmetric settings. For the 2- user rank deficient MIMO interference channel we prove the optimality of previously known achievable DoF in the symmetric case and generalize the result to fully asymmetric settings. For the 3-user rank deficient MIMO interference channel, we improve the achievable DoF and provide a tight outer bound to establish optimality. Linear precoding based achievable schemes are found to be DoF optimal in both cases