Monotony properties of relay SER for physical-layer network coding

We focus on relay error performance analysis for physical layer network coding with high-order modulation. This paper derived a specific representation of relay symbol error rate with phase shift-keying modulation in a bidirectional relay scenario over symmetric additive white Gaussian noise channels. And then, we determined the relay error values theoretically and depicted the variation curve comparatively by Monte Carlo simulations. Research shows that causal error function is not monotonic, but fluctuant to a changing power under precondition of another fixed transmitting power for terminal nodes. Additionally, shaking frequency is also not uniform to different power ratios. These monotonous properties may lead to valuable power conservation to extend work lifetime of nodes in wireless networks.