Synchronization Analysis for Wireless TWRC Operated with Physical-layer Network Coding

Physical-layer network coding (PNC) makes use of the additive nature of the electromagnetic waves to apply network coding arithmetic at the physical layer. With PNC, the destructive effect of interference in wireless networks is eliminated and the capacity of networks can be boosted significantly. This paper addresses a key outstanding issue in PNC: synchronization among transmitting nodes. We first investigate the impact of imperfect synchronization in a 3-node network with a straightforward detection scheme. It is shown that with QPSK modulation, PNC on average still yields significantly higher capacity than straightforward network coding when there are synchronization errors. Significantly, this remains to be so even in the extreme case when synchronization is not performed at all. Moving beyond a 3-node network, we propose and investigate a synchronization scheme for PNC in a general chain network. And we argue that if the synchronization errors can be bounded in the 3-node case, they can also be bounded in the general N-node case. Lastly, we present simulation results showing that PNC is robust to synchronization errors. In particular, for the mutual information performance, there is about 2 dB loss without phase or symbol synchronization.