Outage probability analysis of asymmetrical bi-directional multi-relay system with network coding

In this paper, we construct a practical asymmetrical bi-directional multi-relay system model with considering the effect of distance between source nodes and destination nodes. Then an outage probability expression of the system based on network coding is given. The theoretical analysis is proved to be correct by Monte Carlo simulations. Also we analyze the system average outage probability with different situations of power allocation coefficient, locations of the relay nodes, SNR and the number of relay nodes, indicating the inherent relationship between power allocation coefficient and total system power as well as the number of relay nodes. Simulation results indicate that the optimal power allocation coefficient of the system based on network coding varies with respect to the distance between source nodes and destination nodes. Meanwhile, simulation results show that the system outage probability performance improves with the number of relay nodes increasing.