On Constellations for Physical Layer Network Coded Two-Way Relaying

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 8PSK. 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. I. BACKGROUND AND PRELIMINARIES Physical layer network coding for wireless networks is a promising new area of research and a lot of work has been done in this area in recent times. Wireless two-way relay network shown in Fig 1, in which bidirectional data transfer takes place between the end nodes A and B with the help of the relay R is considered in this work. All the wireless links are assumed to be half-duplex. The De-noise and Forward (DNF) protocol for this case which consists of two phases: the multiple access (MA) phase, during which both A and B simultaneously transmit to R and the broadcast (BC) phase during which R transmits the network coded information to A and B is considered. Network coding map, also called the de-noising map, is used at R during the BC phase to broadcast a symbol to A and B in such a way that A (B) can decode the message of B (A), given that A (B) knows its own message. This scheme, however, results in Multiple Access Interference (MAI) at the relay node and strategies to mitigate MAI for two way relay channel were studied in [1]. Design of coding schemes and network coding maps for uncoded transmission was studied in [2], and that for coded transmission was reported in [3] and [4]. It was observed in [2] that for uncoded transmission, the network coding map used at the relay needs to be changed adaptively according to the channel fade coefficients, in order R A B hA hB