Full-duplex (FD) has emerged as a new communication paradigm with the potential advantage of enhancing the capacity of the wireless communication systems. In this paper, we consider an FD relay-enhanced cellular network, wherein the residual self-interference, the uplink-downlink interference, as well as the relay-access-link interference are the vital restrictions to network performance. To this end, we investigate power control design for the FD relay-enhanced cellular networks, so as to maximize the system spectral efficiency while fulfilling the quality of service (QoS) requirements of both the uplink and downlink user equipments (UEs). We characterize the properties of the optimal transmit power allocation, and propose a power control algorithm based on signomial programming to coordinate the transmit power of the uplink UE, base station, and relay stations to mitigate the interference. Meanwhile, we also derive the closed-form optimal transmit power allocation for the conventional half-duplex (HD) transmission mode. Moreover, we conduct extensive simulation experiments to study the network-level gain of the FD mode over the HD mode in the relay-enhanced cellular networks. Simulation results demonstrate that FD relaying outperforms HD relaying on improving the spectral and energy efficiency, as well as provisioning QoS guarantees for both the uplink and downlink users.INDEX TERMS Wireless networks, full duplex, relaying, power control, spectral efficiency.