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arXiv · 1211.4198

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

Yong Zeng·Xiaoli Xu·Yong Liang Guan·Erry Gunawan·Chenwei Wang
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Abstract

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.

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Yong Zeng, Xiaoli Xu, Yong Liang Guan, Erry Gunawan, Chenwei Wang. 2012-11-18. Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel. https://doi.org/10.1109/twc.2014.2315037

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