This paper investigates an optimization problem corresponding to energy minimization of an in-band full-duplex relaying subject to a total data-bits constraint and a flight time constraint. In order to utilize light of sight channels, a fixed-wing unmanned aerial vehicle (UAV) is dispatched as an amplify-and-forward relay to forward messages for the source and destination terminals. To solve the optimization problem, a new received signal-to-noise ratio and a new lower-bound of the data size received by the destination-terminal are derived. Finally, the energy minimization problem is solved, giving the optimal flight speed and flight time of the UAV for energy efficiency. Computer simulation experiments are conducted and the results verified the correctness and the efficiency of the propositions of the paper.
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