Interference Alignment and the Degrees of Freedom of Wireless $X$ Networks

We explore the degrees of freedom of M times N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to [(MN)/(M+N-1)] per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M=2 or N=2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1) . For these cases the degrees of freedom outer bound is exactly achievable.

[1]  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.

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

[3]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[4]  Shashibhushan Prataprao Borade,et al.  MAXIMIZING DEGREES OF FREEDOM IN WIRELESS NETWORKS , 2004 .

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

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

[7]  David Tse,et al.  DIMACS Series in Discrete Mathematics and Theoretical Computer Science On the Capacity of the Multiple Antenna Broadcast Channel , 2002 .

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

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

[10]  VishwanathSriram,et al.  Generalized degrees of freedom of the symmetric Gaussian K user interference channel , 2010 .

[11]  Syed Ali Jafar,et al.  Degrees of Freedom on the MIMO X Channel - the Optimality of the MMK Scheme , 2006 .

[12]  Andrea J. Goldsmith,et al.  Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels , 2003, IEEE Trans. Inf. Theory.

[13]  Shlomo Shamai,et al.  A layered lattice coding scheme for a class of three user Gaussian interference channels , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

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

[15]  Suhas N. Diggavi,et al.  A Deterministic Approach to Wireless Relay Networks , 2007, ArXiv.

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

[17]  Helmut Bölcskei,et al.  Distributed orthogonalization in large interference relay networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[18]  Andrea J. Goldsmith,et al.  The "Z" channel , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[19]  Lizhong Zheng,et al.  Diversity-multiplexing tradeoff in multiple-access channels , 2004, IEEE Transactions on Information Theory.

[20]  Helmut Bölcskei,et al.  Capacity scaling laws in MIMO relay networks , 2006, IEEE Transactions on Wireless Communications.

[21]  David Tse,et al.  Sum capacity of the multiple antenna Gaussian broadcast channel , 2002, Proceedings IEEE International Symposium on Information Theory,.

[22]  Syed A. Jafar,et al.  Interference Alignment and the Degrees of Freedom for the 3 User Interference Channel , 2007 .

[23]  Shlomo Shamai,et al.  On the Compound MIMO Broadcast Channel , 2007 .

[24]  Sriram Vishwanath,et al.  Capacity of Symmetric K-User Gaussian Very Strong Interference Channels , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[25]  Shlomo Shamai,et al.  The Capacity Region of the Degraded MIMO Compound Broadcast Channel , 2007, 2007 IEEE International Symposium on Information Theory.

[26]  Natasha Devroye,et al.  The Multiplexing Gain of MIMO X-Channels with Partial Transmit Side-Information , 2007, 2007 IEEE International Symposium on Information Theory.

[27]  Wei Yu,et al.  Sum capacity of Gaussian vector broadcast channels , 2004, IEEE Transactions on Information Theory.

[28]  Sriram Vishwanath,et al.  Generalized Degrees of Freedom of the Symmetric Gaussian $K$ User Interference Channel , 2010, IEEE Transactions on Information Theory.