With the substantial progress in self-interference (SI) cancelation, the full-duplex (FD) technique, which allows the\ncommunication user to transmit and receive signals over the same frequency band simultaneously, enables a\nsignificant enhancement of spectral efficiency (SE) in comparison with the traditional half-duplex (HD) technique.\nRecently, relay-assisted device-to-device (D2D) communications underlaying cellular networks have aroused a great\ndeal of research interests due to its high SE. For the new meaningful paradigm of the combination of the FD and\nthe amplify-and-forward (AF) relay-assisted D2D communications, analyzing the SE and energy efficiency (EE) is\ncrucial, which have not been investigated in the existing works. In this paper, we focus on the EE of the FD twoway\n(FDTW) relay-assisted D2D communications with uplink channel reuse by considering the residual SI at the\nD2D users and compare it with the HD counterpart. Our goal is to find the optimal transmission powers and\namplification gain to maximize the system EE while guaranteeing SE requirements and maximum transmission\npower constraints. A new two-tier alternative iteration optimization algorithm is proposed to solve the optimization\nproblem. Simulation results show that (1) the results obtained by the proposed algorithm is very close to those\nobtained by the exclusive searching method, (2) smaller residual power of SI leads to better performance of EE and\nSE, (3) the SE obtained by FDTW relay-assisted D2D networks is higher than the SE obtained by the HD counterpart,\nand (4) the EE comparison of FDTW relay-assisted D2D networks and its HD counterpart depends on the residual\npower of SI. The EE obtained by FDTW relay-assisted D2D is higher than the EE obtained by HD counterpart only\nwhen the residual power of SI is sufficiently small.
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