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<sub>T</sub> × M<sub>R</sub> multiple-input-multipleoutput (MIMO) interference channel (IC) with rank-deficient channel matrices, where each transmitter is equipped with M<sub>T</sub> antennas and each receiver with M<sub>R</sub> antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks D<sub>1</sub> and D<sub>2</sub>, 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<sub>1</sub> + D<sub>2</sub> ≤ min(M<sub>T</sub>, M<sub>R</sub>), zero forcing is sufficient to achieve the optimal DoF. On the other hand, when D<sub>1</sub> + D<sub>2</sub> > min(M<sub>T</sub> , M<sub>R</sub>), 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.

[1]  Syed Ali Jafar,et al.  A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks , 2011, IEEE Transactions on Information Theory.

[2]  Aly El Gamal,et al.  Degrees of Freedom of Interference Channels With CoMP Transmission and Reception , 2011, IEEE Transactions on Information Theory.

[3]  Shlomo Shamai,et al.  Degrees of Freedom Region of the MIMO $X$ Channel , 2008, IEEE Transactions on Information Theory.

[4]  Syed A. Jafar,et al.  Interference Alignment: A New Look at Signal Dimensions in a Communication Network , 2011, Found. Trends Commun. Inf. Theory.

[5]  Vahid Tarokh,et al.  On the degrees-of-freedom of the MIMO interference channel , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[6]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[7]  Theodore S. Rappaport,et al.  Overview of spatial channel models for antenna array communication systems , 1998, IEEE Wirel. Commun..

[8]  Xiaoli Xu,et al.  On the degrees of freedom of the 3-user rank-deficient MIMO interference channels , 2013, 2013 IEEE International Conference on Communications (ICC).

[9]  Amir K. Khandani,et al.  Real Interference Alignment with Real Numbers , 2009, ArXiv.

[10]  Hua Wang,et al.  Gaussian Interference Channel Capacity to Within One Bit , 2007, IEEE Transactions on Information Theory.

[11]  Sundar R. Krishnamurthy,et al.  Degrees of Freedom of Rank-Deficient MIMO Interference Networks , 2015 .

[12]  Aria Nosratinia,et al.  The multiplexing gain of wireless networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[13]  Syed Ali Jafar,et al.  Degrees of Freedom of the K User M times N MIMO Interference Channel , 2008, IEEE Trans. Inf. Theory.

[14]  Syed Ali Jafar,et al.  Interference Alignment and Degrees of Freedom of the $K$-User Interference Channel , 2008, IEEE Transactions on Information Theory.

[15]  Syed Ali Jafar,et al.  Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[16]  Sae-Young Chung,et al.  On the degrees of freedom of rank deficient interference channels , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[17]  Syed Ali Jafar,et al.  Degrees of Freedom of the K User M×N MIMO Interference Channel , 2008, ArXiv.

[18]  Sundar R. Krishnamurthy,et al.  Degrees of freedom of 2-user and 3-user rank-deficient MIMO interference channels , 2012, 2012 IEEE Global Communications Conference (GLOBECOM).

[19]  Y. Guan,et al.  Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel , 2014 .

[20]  Syed Ali Jafar,et al.  Interference Alignment With Asymmetric Complex Signaling—Settling the Høst-Madsen–Nosratinia Conjecture , 2009, IEEE Transactions on Information Theory.