User Pair-Relay Matching in a Multiple User Pair and Multiple Untrusted Relay Network

In this paper, considering a multi-user pair and multi-untrusted relay two-way transmission network, a user pair-relay matching scheme is proposed. To maximize the achievable secrecy rate and reduce the complexity, we model the proposed matching problem as a bipartite graph and utilize the Kuhn-Munkres (KM) algorithm to find the maximum weighted complete matching. Furthermore, considering the fairness among the user pairs, we put a constraint on the minimum quality of service (QoS) requirements into the previous optimization problem. The existence of optimal matching is studied and the corresponding optimal solution is then presented after modifying the weight matrix. Simulation results finally validate that the proposed matching schemes can achieve improvement of average secrecy rate and harvest the diversity with more relays.