Abstract: In physical layer network coding systems, the system performance is affected by forwarding modes used in the relay node. In this paper, we study three different modes in physical layer systems, e.g., amplify and forward, denoise and forward, denoise encode and forward. We first study the constellation diagrams for encoded signals of the three modes where quadrature phase shift keying (QPSK) scheme is used. Then, the s of signal error rate (SER) are derived in the additive white Gaussian noise channel based on the existing s of SER for QPSK and Quadrature Amplitude Modulation (QAM). Simulation results are given to verify the correctness of the derived s and compare the performance of the studied three modes.