In this paper, we propose a full-duplex orthogonal frequency-division multiplexing (OFDM) device-to-device (D2D) system in two-hop networks, where multiple full-duplex decode-andforward (DF) relays assist the transmission from D2D user equipment (DUE) transmitter to DUE receiver. By such a transmission mechanism, the signal transmitted by the DUE transmitter does not need to go through a base station (BS). Meanwhile, due to the adoption of underlay D2D communication protocol, power control

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... nisms are thereby necessary to be applied to mitigate the interference to conventional cellular communications. Based on these considerations, we analyze the outage performance of the proposed system, and derive the exact expressions of outage probabilities when bulk and per-subcarrier relay selection criteria are applied. Furthermore, closed-form expressions of outage probabilities are also obtained for special cases when the instantaneous channel state information (CSI) between BS and cellular user equipments (CUEs) is not accessible, so that a static power control mechanism is applied. Subsequently, we also investigate the outage performance optimization problem by coordinating transmit power among DUE transmitter and relays, and provide a suboptimal solution, which is capable of improving the outage performance. All analyses are substantiated by numerical results provided by Monte Carlo simulations. The analytical and numerical results demonstrated in this paper can provide an insight into the full-duplex relay-assisted OFDM D2D systems, and serve as a guideline for its implementation in next generation networks.