In this paper, we propose an optimal time and power allocation scheme in a wireless power supply full-duplex (FD) relay system, where we consider the number of relay antennas in the energy harvesting stage. At the same time, the energy efficiency optimization problem of the system is structured, where optimization issues related to time allocation factors and power allocation are established. For the FD dual-antenna and the FD single-antenna energy harvesting system, energy efficiency function is proven to be a concave function over the time-switch factor, and the optimal time-switching factor is theoretically obtained using the Lambert function. Then, according to the given value range of the optimal time switching factor, the optimal power distribution scheme is obtained by analyzing the derivative function of the system energy efficiency and using the properties of the Lambert function. The time-switching factor and transmission power are optimally selected at the wireless power supply FD relay. Results reveal that the performance of energy efficiency of the dual-antenna energy harvesting at the FD relay outperforms that of the single-antenna. Moreover, our results demonstrate that FD relay systems always substantially boost the energy efficiency compared with half-duplex (HD) relay systems.
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