Physical-layer network coded QAM with trellis shaping for the two-way relay channel

Physical-layer network coding (PNC) allows to improve the throughput on the two-way relay channel (TWRC). PNC systems using higher-order modulation present some challenges regarding how to design the PNC mapping at the relay. With higher-order modulation it is also desirable to use constellation shaping which allows to minimize the average transmitted energy. In this paper, we show how low-complexity trellis shaping can be used to provide constellation shaping both at the user nodes and at the relay node. The proposed technique works specifically for sign bit shaping and M-ary quadrature amplitude modulation (QAM). Simulation results show that the proposed scheme provides a significantly increased performance in terms of the achievable BER, with 5.3dB shaping gain available at a BER of 10-3 in the case of 256-QAM signaling.