On Constellations for Physical Layer Network Coded Two-Way Relaying

Abstract: Modulation schemes for two-way bidirectional relay network employing two phases: Multiple access (MA) phase and Broadcast (BC) phase and using physical layer network coding are currently studied intensively. Recently, adaptive modulation schemes using Latin Squares to obtain network coding maps with the denoise and forward protocol have been reported with good end-to-end performance. These schemes work based on avoiding the detrimental effects of distance shortening in the effective receive constellation at the end of the MA phase at the relay. The channel fade states that create such distance shortening called singular fade states, are effectively removed using appropriate Latin squares. This scheme as well as all other known schemes studied so far use conventional regular PSK or QAM signal sets for the end users which lead to the relay using different sized constellations for the BC phase depending upon the fade state. In this work, we propose a 4-point signal set that would always require a 4-ary constellation for the BC phase for all the channel fade conditions. We also propose an 8-point constellation that gives better SER performance (gain of 1 dB) than 8-PSK while still using 8-ary constellation for BC phase like the case with 8-PSK. This is in spite of the fact that the proposed 8-point signal set has more number of singular fade states than for 8-PSK.