Abstract: The bit error rate (BER) performance of a physical-layer network coded two-way relay (PNC-TWR) system which adopts coherent detection is closely related to the carrier synchronization, the residual carrier offset between the transmitter and receiver will result in severe performance degradation. In this paper, we investigate the effect of the carrier offsets on the BER performance of two PNC-TWR systems, where the two source nodes employ same or orthogonal binary phase shift keying (BPSK) constellations. We first determine the decision regions for the received signals at the relay and source nodes based on the maximum likelihood (ML) rule, then by applying Craig’s polar coordinate analyzing method, exact expressions of multiple access channel (MAC), broadcast channel (BC) and sum end-to-end (E2E) BER are derived. The proposed analyzing approach can be generalized to other systems. Computer simulations demonstrate that our theoretical analysis accurately matches with the simulation results and the derived theoretical expressions can effectively evaluate the BER performance of the BPSK modulated PNC-TWR systems. It is also shown that the orthogonal constellation scheme is more sensitive to the carrier offsets than the same constellation scheme, and same carrier offsets result in larger performance loss to the orthogonal constellation scheme.