Error probability of physical-layer network coding in multiple-antenna two-way relay channel

In this paper, we investigate the error probability and the diversity order of physical-layer network coding (PNC) in the two-way relay channel (TWRC), where two users communicate with the help of a relay. Each user has one antenna and the relay has two antennas. The system operates in a half-duplex mode with binary phase shift keying (BPSK) modulation. All the channels are Rayleigh faded. In particular, we consider a general asymmetric case, where two users have different average signal-to-noise ratio (SNR) to the relay. The upper and lower bounds on the instantaneous and average error probability of the uplink channel are derived based on the maximum-likelihood (ML) criterion. We also investigate the diversity order of the uplink channel. Numerical result demonstrates that the bounds are much tighter than other existing work, especially at low SNR, and the analytical result shows that the diversity is two for the asymmetric uplink channel.