Dynamic Constellation Mapping and SER Performance for Asynchronized PNC Using QPSK

The increased throughput performance of physical-layer network coding (PNC) has led to rigorous research in this field for two-way relay systems or multi-way systems. For coherent detection of information received by the relay node and decoding the correct symbols transmitted by the user nodes after removing self-information, synchronization in the system is a critical requirement. This paper aims to study the symbol error rate (SER) performance of an asynchronized PNC system, i.e. a system with phase misalignments. The symbols of two end users arrive with a phase difference of $\phi$. We study a mapping scheme for the combined signal at the relay based on its superimposed constellation structure incorporating the phase difference $\phi$. An analytical bound on SER performance at the relay node in presence of phase difference $\phi$ is derived. Simulation results showing identical SER performance for a fixed value of $\phi$, independent of the individual link phase offsets, have been presented. It can be seen that mapping provides better spectral efficiency when compared to the de-noise and forward scheme with a slight tradeoff in SER performance compared to non-mapped case.