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

TL;DR

This paper characterizes the degrees of freedom for a 3-user MIMO interference channel with rank-deficient channels, showing when zero forcing suffices and when interference alignment is needed for optimality.

Contribution

It provides a unified DoF characterization for rank-deficient MIMO ICs, extending existing results and introducing a method to convert rank-deficient channels into full-rank equivalents.

Findings

Zero forcing achieves optimal DoF when interference ranks are weak.

Interference alignment is necessary when interference ranks are strong.

The results unify and extend previous DoF characterizations.

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.