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Contrary to the most existing works about the full-duplex (FD) relaying with perfect channel state information (CSI), this paper studies the outage performance of the two-way FD decode-and-forward relay network under the joint effects of the residual self-interference and imperfect CSI. We first derive the exact closed-form expressions of the system outage probability, based on which we obtain the outage probability under the perfect self-interference cancellation to investigate the impacts of the imperfect CSI on the system performance. In addition, to gain more insights about the imperfect CSI, we analyze the optimal power allocation scheme and an optimal relay node placement strategy, which minimize the system outage probability. The results reveal that the imperfect CSI will only affect the optimal power allocation, and the optimal relay node placement is related to the power ratio between the user nodes. Finally, analytical evaluations are performed to verify the theoretical results, and Monte Carlo simulations guarantee the correctness of the analytical evaluations.

Outage Performance of the Full-Duplex Two-Way DF Relay System Under Imperfect CSI