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This paper proposes a full-duplex cooperative device-to-device (D2D) communication system, where the relay employed can receive and transmit signals simultaneously. We adopt such a system to assist with D2D transmission. We first derive the conditional cumulative distribution function and the probability density function (pdf) of a series of channel parameters when the interference to the base station is taken into consideration and power control is applied at the D2D transmitter and the relay node. Then, we obtain an exact expression for the outage probability as an integral and as a closed-form expression for a special case, which can be used as a good approximation to the general case when residual self-interference is small. Additionally, we also investigate the power allocation problem between the source and the relay and formulate a suboptimal allocation problem, which we prove to be quasi-concave …