On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients

In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.

[1]  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.

[2]  Manfred Gilli,et al.  Matchings, covers, and Jacobian matrices☆ , 1996 .

[3]  Moe Z. Win,et al.  The feasibility conditions of interference alignment for MIMO interference networks , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[4]  Inkyu Lee,et al.  Spatial Multiplexing Gain for Two Interfering MIMO Broadcast Channels Based on Linear Transceiver , 2010, IEEE Transactions on Wireless Communications.

[5]  Inkyu Lee,et al.  Degrees of Freedom of Multiple Broadcast Channels in the Presence of Inter-Cell Interference , 2011, IEEE Transactions on Communications.

[6]  Yanjun Ma,et al.  On Feasibility of Interference Alignment for L-Cell Constant Cellular Interfering Networks , 2012, IEEE Communications Letters.

[7]  Carlos Beltrán,et al.  A general test to check the feasibility of linear interference alignment , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[8]  Bruno Clerckx,et al.  Spatial Degrees of Freedom of the Multicell MIMO Multiple Access Channel , 2011, 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011.

[9]  Namyoon Lee,et al.  On the Design of Interference Alignment Scheme for Two-Cell MIMO Interfering Broadcast Channels , 2011, IEEE Transactions on Wireless Communications.

[10]  David Gesbert,et al.  Interference Alignment in Partially Connected Interfering Multiple-Access and Broadcast Channels , 2011, 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011.

[11]  Moe Z. Win,et al.  The Feasibility Conditions for Interference Alignment in MIMO Networks , 2013, IEEE Transactions on Signal Processing.

[12]  David Tse,et al.  Downlink Interference Alignment , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[13]  David Tse,et al.  Feasibility of interference alignment for the MIMO interference channel: The symmetric square case , 2011, 2011 IEEE Information Theory Workshop.

[14]  Zhi-Quan Luo,et al.  On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel , 2011, IEEE Transactions on Signal Processing.

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

[16]  David Tse,et al.  Geometry of the 3-user MIMO interference channel , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[17]  Syed Ali Jafar,et al.  Approaching the Capacity of Wireless Networks through Distributed Interference Alignment , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

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

[19]  A. H. Kayran,et al.  On Feasibility of Interference Alignment in MIMO Interference Networks , 2009, IEEE Transactions on Signal Processing.

[20]  Hua Sun,et al.  Genie chains and the degrees of freedom of the K-user MIMO interference channel , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[21]  Reinaldo A. Valenzuela,et al.  Network coordination for spectrally efficient communications in cellular systems , 2006, IEEE Wireless Communications.

[22]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[23]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

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

[25]  Michael L. Honig,et al.  Interference alignment in MIMO cellular networks , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).