In this paper, a joint subcarrier and power allocation algorithm is proposed to improve the physical layer security in\r\ncooperative orthogonal frequency division multiple access (OFDMA) networks, where several source-destination pairs\r\nand one untrusted relay are involved. The relay is friendly and intends to help these pairs to enhance their\r\ncommunications. However, it may be overheard by a malicious eavesdropper at the same time. To optimize the joint\r\nsubcarrier and power allocation with low complexity, we divide the optimization problem into two simpler\r\nsubproblems. Firstly, the subcarriers are assigned to the source-destination pairs by employing the dual approach\r\nunder the assumption that the relay power is equally allocated to all the subcarriers. Then, the relay power is allocated\r\nto the subcarriers based on the alternative ascending clock auction mechanism. In addition, we prove that the two\r\nsubproblems can converge after a finite number of iterations. We also find that the proposed auction is cheat-proof\r\nand, thus, can avoid the cheating behaviors in the auction process. Numerical results demonstrate that our proposed\r\nalgorithm can effectively improve the system sum secrecy rate, and the convergence performance is also desirable.
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