| Summary: | Unmanned aerial vehicle (UAV) relaying is promising to overcome the challenge of signal blockage in free-space optical (FSO) communications for users in dense urban area. Existing works on UAV relay placement are mostly based on simplified line-of-sight (LOS) channel models or probabilistic channel models, and thus fail to capture the actual LOS status of the optical communication link. By contrast, this paper studies three-dimensional (3D) online placement for a UAV to construct relay links to two ground users in deep shadow with LOS guarantees. By analyzing the properties of the UAV relay placement problem, it is found that searching on a plane that approximates the equipotential surface can achieve a good performance and complexity trade-off for a good placement of the UAV relay in 3D. Based on these insights, a two-stage online search algorithm on an equipotential plane (TOSEP) is developed for a special case where the equipotential surface turns out to be an equipotential plane. For the general case, a strategy called gradient projected online search algorithm on an approximated equipotential plane (GOSAEP) is developed, which approximates the equipotential surface with a perpendicular plane using the gradient projection method. Numerical experiments are conducted over a real-world city topology, and it is shown that the GOSAEP achieves over 95% of the performance of the exhaustive 3D search scheme within a 300-m search length.
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