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 γe^jθ, 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 γe^jθ=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.