Feasibility of interference alignment for the MIMO interference channel: The symmetric square case

Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted to the symmetric square case where all transmitters and receivers have N antennas, and each user desires d transmit dimensions. We prove that alignment is possible if and only if the number of antennas satisfies N ≥ d(K + 1)/2. We also show a necessary condition for feasibility of alignment with arbitrary system parameters. An algebraic geometry approach is central to the results.

[1]  Zhi-Quan Luo,et al.  Linear transceiver design for interference alignment: Complexity and computation , 2010, 2010 IEEE 11th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[2]  T. Willmore.  Algebraic Geometry , 1973, Nature.

[3]  M. Honig,et al.  Beamforming techniques for single-beam MIMO interference networks , 2010, Allerton Conference on Communication, Control, and Computing.

[4]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[5]  Amir K. Khandani,et al.  Communication Over MIMO X Channels: Interference Alignment, Decomposition, and Performance Analysis , 2008, IEEE Transactions on Information Theory.

[6]  Abhay Parekh,et al.  The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference Channels , 2008, IEEE Transactions on Information Theory.

[7]  Robert W. Heath,et al.  Interference alignment via alternating minimization , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

[9]  Robert W. Heath,et al.  Maximum Sum-Rate Interference Alignment Algorithms for MIMO Channels , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[10]  Dimitris S. Papailiopoulos,et al.  Interference Alignment as a Rank Constrained Rank Minimization , 2010, IEEE Transactions on Signal Processing.

[11]  Erik Ordentlich,et al.  The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients , 2009, IEEE Transactions on Information Theory.

[12]  Guy Bresler,et al.  3 User interference channel: Degrees of freedom as a function of channel diversity , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[14]  C. Wampler,et al.  Basic Algebraic Geometry , 2005 .

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

[16]  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.

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