Integrating high altitude platforms (HAPs) and free-space optical (FSO) communications is a promising solution to establish high data rate aerial links for the next-generation wireless networks. However, practical limitations such as pointing errors and angle-of-arrival (AOA) fluctuations of the optical beam due to the orientation deviations of hovering HAPs make it challenging to implement HAP-based FSO links. For a ground-to-HAP FSO link, tractable, closed-form statistical channel models are derived in this paper to simplify the optimal design of such systems. The proposed models include the combined effects of atmospheric turbulence regimes (i.e., log-normal and gamma-gamma), pointing error induced geometrical loss, pointing jitter variance caused by beam wander, detector aperture size, beam-width, and AOA fluctuations of the received optical beam. The analytical expressions are corroborated by performing Monte-Carlo simulations. Furthermore, closed-form expressions for the outage probability of the considered link under different turbulence regimes are derived. Detailed analysis is carried out to optimize the transmitted laser beam and the field-of-view of the receiver for minimizing outage probability under different channel conditions. The obtained analytical results can be applied to finding the optimal parameter values and designing ground-to-HAP FSO links without resorting to time-consuming simulations.
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