Mutual Information Based Analysis for Physical-Layer Network Coding with Optimal Phase Control

In this paper two-way relaying networks are considered using physical-layer network coding in a two-phase protocol. In the multiple access phase, both sources transmit their messages to the relay simultaneously. Subsequently, the relay estimates and broadcasts the XOR-based network coded message back to the sources in the broadcast phase. We concentrate on the critical multiple access phase, where several detection and decoding schemes at the relay are studied and compared with respect to mutual information and system throughput. It is shown, that the system performance of the detection and decoding schemes under investigation is highly dependent on the phase difference of the two incoming messages at the relay, motivating a phase control strategy at the sources before transmission. Simulation results confirm our analysis and the superior performance achieved by phase control in practical systems.