Interference alignment for the K user MIMO interference channel

We consider the K user Multiple Input Multiple Output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver. It is assumed that channel coefficients are fixed and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the total Degrees Of Freedom (DOF) for this channel. Using a new interference alignment technique which has been recently introduced in [1], we show that MN over M+N K degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the total DOF for this channel is derived. This upper-bound coincides with our achievable DOF for K ≥ Ku ≜ M+N over gcd(M,N) where gcd(M,N) denotes the greatest common divisor of M and N. This gives an exact characterization of DOF for MIMO Gaussian interference channel in the case of K ≥ Ku.

[1]  V. Cadambe,et al.  Interference alignment with asymmetric complex signaling , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[2]  G. A. Margulis,et al.  Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions , 2001 .

[3]  Changho Suh,et al.  Interference Alignment for Cellular Networks , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

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

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

[6]  Amir K. Khandani,et al.  Capacity bounds for the Gaussian Interference Channel , 2008, 2008 IEEE International Symposium on Information Theory.

[7]  I. Niven,et al.  An introduction to the theory of numbers , 1961 .

[8]  Aydano B. Carleial,et al.  Interference channels , 1978, IEEE Trans. Inf. Theory.

[9]  Amir K. Khandani,et al.  Forming Pseudo-MIMO by Embedding Infinite Rational Dimensions Along a Single Real Line: Removing Barriers in Achieving the DOFs of Single Antenna Systems , 2009, ArXiv.

[10]  Gerhard Kramer,et al.  A New Outer Bound and the Noisy-Interference Sum–Rate Capacity for Gaussian Interference Channels , 2007, IEEE Transactions on Information Theory.

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

[12]  Victor Beresnevich,et al.  A Groshev Type Theorem for Convergence on Manifolds , 2002 .

[13]  Venugopal V. Veeravalli,et al.  Gaussian Interference Networks: Sum Capacity in the Low-Interference Regime and New Outer Bounds on the Capacity Region , 2008, IEEE Transactions on Information Theory.

[14]  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.

[15]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

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

[17]  Igal Sason,et al.  On achievable rate regions for the Gaussian interference channel , 2004, IEEE Transactions on Information Theory.

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

[19]  Syed Ali Jafar,et al.  Degrees of Freedom for the MIMO Interference Channel , 2006, ISIT.

[20]  Shlomo Shamai,et al.  Interference alignment on the deterministic channel and application to fully connected AWGN interference networks , 2008, 2008 IEEE Information Theory Workshop.

[21]  Amir K. Khandani,et al.  On the Degrees of Freedom of the 3-user Gaussian interference channel: The symmetric case , 2009, 2009 IEEE International Symposium on Information Theory.

[22]  D. R. Heath-Brown,et al.  An Introduction to the Theory of Numbers, Sixth Edition , 2008 .

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

[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]  S. Jafar,et al.  Degrees of freedom of the K user MIMO interference channel , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

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

[27]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

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

[29]  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.

[30]  Erik Ordentlich,et al.  On the Degrees-of-Freedom of the K-user Gaussian interference channel , 2009, 2009 IEEE International Symposium on Information Theory.

[31]  Te Sun Han,et al.  A new achievable rate region for the interference channel , 1981, IEEE Trans. Inf. Theory.

[32]  Amir K. Khandani,et al.  Signaling over MIMO Multi-Base Systems: Combination of Multi-Access and Broadcast Schemes , 2006, 2006 IEEE International Symposium on Information Theory.