Closed form solution and useful signal power maximization for interference alignment in multi-pair two-way relay networks

In this paper, bidirectional pair-wise communication between 2K nodes is considered. Each node has N antennas and wants to transmit d data streams to its communication partner. A single non-regenerative half-duplex relay with R antennas supports the communication. In this scenario, the process of interference alignment can be decomposed into partial signal alignment (PSA), partial channel alignment (PCA) and zero forcing (ZF). PSA and PCA are dual problems and we focus on PSA in this paper. PSA is a bilinear problem. A closed form solution is possible only when there is a sufficient number of variables in the system. In this paper, a closed form solution is proposed and the condition for the feasibility of the closed form solution is derived in terms of K;N;R; and d. Besides this, in order to improve the performance at low and medium signal to noise ratios (SNRs), a gradient based algorithm to maximize the useful signal power is also proposed. It is shown through simulations that in some cases, it is better to serve less node pairs and utilize the additional degrees of freedom in the system to maximize the useful signal power.

[1]  Tobias Weber,et al.  Pair-Aware Interference Alignment in Multi-User Two-Way Relay Networks , 2013, IEEE Transactions on Wireless Communications.

[2]  Roger S. Cheng,et al.  Achieve the Degrees of Freedom of K-User MIMO Interference Channel with a MIMO Relay , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[3]  Anja Klein,et al.  Interference alignment using a MIMO relay and partially-adapted transmit/receive filters , 2012, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[4]  Chi-Huang Shih On the Study of Analogue Network Coding for Multi-Pair, Bidirectional Relay Channels , 2010, IEEE Transactions on Wireless Communications.

[5]  Verzekeren Naar Sparen,et al.  Cambridge , 1969, Humphrey Burton: In My Own Time.

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

[7]  Long Chen INTRODUCTION TO FINITE ELEMENT METHODS , 2003 .

[8]  Armin Wittneben,et al.  Spectral efficient protocols for half-duplex fading relay channels , 2007, IEEE Journal on Selected Areas in Communications.

[9]  Tobias Weber,et al.  Interference Alignment in Multi-User Two Way Relay Networks , 2011, 2011 IEEE 73rd Vehicular Technology Conference (VTC Spring).

[10]  Jon C. Dattorro,et al.  Convex Optimization & Euclidean Distance Geometry , 2004 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Anja Klein,et al.  Cooperative zero forcing in multi-pair multi-relay networks , 2012, 2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC).

[13]  Raymond Knopp,et al.  Multi-Pair Two-Way Relay Channel with Multiple Antenna Relay Station , 2010, 2010 IEEE International Conference on Communications.

[14]  Hussein Al-Shatri,et al.  Interference alignment aided by non-regenerative relays for multiuser wireless networks , 2011, 2011 8th International Symposium on Wireless Communication Systems.

[15]  P. N. Godbole Introduction to Finite Element Methods , 2013 .

[16]  Amir K. Khandani,et al.  Relay-aided Interference Alignment for the quasi-static interference channel , 2010, 2010 IEEE International Symposium on Information Theory.

[17]  Kin K. Leung,et al.  Relay-aided interference alignment: Feasibility conditions and algorithm , 2010, 2010 IEEE International Symposium on Information Theory.

[18]  A. Robert Calderbank,et al.  MIMO Wireless Communications , 2007 .