SER Performance Analysis For Asynchronous Physical-layer Network Coding

Physical-layer network coding (PNC) is a novel relaying scheme, which exploits the su-perposition of electromagnetic waves and the broadcast nature of wireless channels to complete packets exchange in bidirectional relay system within two time slots. Compared with network coding and store-and-forward schemes who respectively need three time slots and four time slots, the PNC scheme reduces the needed time slots for packets exchange so that it boosts the throughput of the bidirectional relay system. Therefore, PNC has attracted much interest.Because of the clock asynchrony among the wireless terminals and the difference of the wireless channels, there exist phase offset and symbol misalignment between the superposed signals, which will lead to appreciable symbol error rate (SER) performance penalties when the relay node decodes (demodulate and then code the superposed signals) the superposed sig-nals. Thus, analyzing the SER for Asynchronous PNC is expected to facilitate future practical studies.In this thesis, we derive both the lower bound and upper bound of SER for asynchronous PNC based on the modulation methods of binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). We consider two decoding and mapping methods:multiuser detec-tion (MUD) based XOR network coding (MUD-XOR) and belief propagation (BP) algorithm based maximum a posteriori (MAP) decoding (BP-MAP). And we prove that the error perfor-mances of BP-MAP and MUD-XOR are similar, but BP-MAP provides lower SER. Therefore, based on the BP-MAP scheme, the lower bound is achieved by assuming that part of the over-lapped messages (received by the relay) are known to the relay; while, based on the MUD-XOR scheme, we introduce the definitions of error vector and the decomposition of error vector, and prove that the upper bound only relies on the indecomposable error vectors. The lower and upper bounds we derive in this thesis are suitable for both decoding methods. Our simulation results indicate that the lower and upper bounds are relatively tight.