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This paper addresses the design of hybrid freespace optical/radio frequency (FSO/RF) systems for a highaltitude platform (HAP)-aided relaying satellite communication for mobile networks supported by unmanned aerial vehicle (UAV). While prior work primarily focused on fixed-rate design, which frequently switches between FSO and RF lead reduced the system performance, we propose a rate adaptation design that gradually adjusts the data rate in each link when its channel state fluctuates, under a target bit error rate (BER) constraint. The proposed design's downlink performance is analyzed, taking into account many challenging issues, including beam spreading loss, cloud attenuation, statistical behaviors of the atmospheric turbulence in the dual-hop channel, and pointing misalignment due to the UAV hovering. Different performance metrics are analytically derived based on channel modelings, including outage probability, average transmission rate, and achievable spectrum efficiency. In addition, the average system BER, which satisfies the design constraint, is also numerically obtained. The results quantitatively confirm the effectiveness of our proposed system under the impact of UAV hovering misalignment and atmospheric-related issues like clouds and turbulence. Finally, Monte-Carlo simulations validate the accuracy of theoretical results.

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