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In this paper, we consider an amplify-and-forward (AF) full-duplex relay network (FDRN) using simultaneous wireless information and power transfer, where a battery-free relay node harvests energy from the received radio frequency (RF) signals from a source node and uses the harvested energy to forward the source information to destination node. The time-switching relaying (TSR) protocol is studied, with the assumption that the channel state information (CSI) at the relay node is imperfect. We deliver a rigorous analysis of the outage probability of the proposed system. Based on the outage probability expressions, the optimal time switching factor are obtained via the numerical search method. The simulation and numerical results provide practical insights into the effect of various system parameters, such as the time switching factor, the noise power, the energy harvesting efficiency, and the channel estimation error on the performance of this network. It is also observed that for the imperfect CSI case, the proposed scheme still can provide acceptable outage performance given that the channel estimation error is bounded in a permissible interval.