Physical Layer Network Coding for Two-Way Relaying with QAM

The design of modulation schemes for the physical layer network-coded two-way relay network has been studied in literature and it is known that every network coding map that satisfies the exclusive law is representable by a Latin Square. This relationship has been used to get network coding maps satisfying the exclusive law. But, only the scenario in which the end nodes use M-PSK signal sets has been addressed previously. In this paper, we address the case in which the end nodes use M-QAM signal sets. In a fading scenario, for certain channel conditions γejθ, termed singular fade states, the end-to-end performance is greatly reduced. By formulating a procedure for finding the exact number of singular fade states for QAM, we show that square QAM signal sets give lesser number of singular fade states compared to PSK signal sets. This reduces the computational complexity at the relay node. It is shown that the criterion for partitioning the complex plane, for the purpose of using a particular network code for a particular fade state, is different from that used for M-PSK. Using a modified criterion, we describe a procedure to analytically partition the complex plane representing the channel condition. We show that when M-QAM (M >4) signal set is used, the conventional XOR network mapping fails to remove the ill effects of γejθ=1, which is a singular fade state for all signal sets of arbitrary size. We show that a doubly block circulant Latin Square removes this singular fade state for M-QAM. Finally it is shown that M-QAM gives superior performance over M-PSK.

[1]  C. Nemeroff,et al.  Hot Topics , 1998, Pediatric Research.

[2]  B. Sundar Rajan,et al.  Physical layer network coding for two-way relaying with QAM and Latin Squares , 2012, 2012 IEEE Global Communications Conference (GLOBECOM).

[3]  Diane Donovan,et al.  The completion of partial Latin squares , 2000, The Australasian Journal of Combinatorics.

[4]  B. Sundar Rajan,et al.  Wireless bidirectional relaying and Latin Squares , 2011, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[5]  Toshiaki Koike-Akino,et al.  Optimized constellations for two-way wireless relaying with physical network coding , 2009, IEEE Journal on Selected Areas in Communications.

[6]  Chris A. Rodger.  Recent results on the embedding of latin squares and related structures, cycle systems and graph design , 1993 .

[7]  Petar Popovski,et al.  The Anti-Packets Can Increase the Achievable Throughput of a Wireless Multi-Hop Network , 2006, 2006 IEEE International Conference on Communications.

[8]  Toshiaki Koike-Akino,et al.  Denoising Strategy for Convolutionally-Coded Bidirectional Relaying , 2009, 2009 IEEE International Conference on Communications.

[9]  Krishna R. Narayanan,et al.  Multilevel coding schemes for compute-and-forward , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[10]  Patrick Mitran,et al.  Performance Bounds for Bidirectional Coded Cooperation Protocols , 2007, IEEE Transactions on Information Theory.

[11]  P. Doyle.  The number of Latin rectangles , 2007, math/0703896.

[12]  Athanasios V. Vasilakos,et al.  Differential Modulation for Bidirectional Relaying With Analog Network Coding , 2010, IEEE Transactions on Signal Processing.

[13]  B. Sundar Rajan,et al.  Performance analysis of adaptive physical layer network coding for wireless two-way Relaying , 2012, 2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC).

[14]  Petar Popovski,et al.  Physical Network Coding in Two-Way Wireless Relay Channels , 2007, 2007 IEEE International Conference on Communications.

[15]  Soung Chang Liew,et al.  Hot topic: physical-layer network coding , 2006, MobiCom '06.

[16]  B. Sundar Rajan,et al.  Channel quantization for physical layer network-coded two-way relaying , 2012, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[17]  B. Sundar Rajan,et al.  An adaptive modulation scheme for two-user fading MAC with quantized fade state feedback , 2012, 2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC).