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In this paper, the selective cooperation with untrusted relays is studied for wireless multipair two‐way relay networks. We first investigate the feasibility of secure transmission in the presence of cooperative but untrusted relays and then formulate a general optimization problem of secrecy sum‐rate maximization under the constraints of relay selection. By decomposing the original problem into solvable subproblems, we develop a low‐complexity greedy algorithm for selective cooperation, in which the untrusted relays are selected as cooperators or the potential eavesdroppers according to the overall contributions to the secrecy sum rate. Simulation results reveal that the proposed greedy algorithm for selective cooperation with untrusted relays achieves performance gain both in instantaneous and average secrecy sum rate and that the algorithm can converge quickly with the iterations.

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