###### Abstract  
Free-space optical (FSO) communication with unmanned aerial vehicles (UAVs) as relays is a promising technology for future aeronautical communication systems. In this paper, a multiple UAV-based aeronautical communication system is proposed, wherein a hybrid FSO/radio frequency (RF) link is established to connect the Airborne Warning and Control System (AWACS) with the mobile ground station (GS). Initially, we consider the velocity variance of both AWACS and the mobile GS, along with the influence of the Doppler effect. Furthermore, four relay selection modes are proposed, and exact closed expressions are derived for the end-to-end outage probability and bit error rate (BER) of the considered system. Numerical simulations demonstrate the impact of velocity variance variation on system performance. Additionally, we analyze the applicability of these four relay modes under different platform mobility characteristics through simulation results, while discussing the optimal numbers and the deployment altitude of UAVs. Finally, effective design guidelines that can be useful for aeronautical communication system designers are presented. UAV relay; FSO/RF; aeronautical communication; relay selection mode model over a log-normal atmospheric turbulence environment under weak turbulence conditions was proposed in [5]. In [6], a multi-rotor UAV-based FSO link in the presence of atmospheric turbulence by considering angle-of-arrival (AOA) fluctuations was considered. Moreover, UAV relays are flexible enough to maneuver and adjust their positions based on channel conditions [7; 8; 9], such as cloud obstacles. In addition, extensive research has been conducted on the combined utilization of serial and parallel UAV relays to achieve significant performance enhancements by reducing hops in multi-hop systems [10; 11; 12]. Therefore, the main motivations of our paper can be summarized as follows:  
* The current literature extensively studies the use of UAV relay-assisted communication. However, these studies are rarely studied in aeronautical communication systems and the mobility of source and destination nodes is neglected. * To the best of our knowledge, existing research almost ignores the impact of varying velocity variance among mobile platforms on system performance. * Currently, extensive research has been conducted on relay selection modes; however, there is a lack of performance comparison and applicability analysis for various modes in mobile scenarios. * In aeronautical communication scenarios, a single FSO link is susceptible to platform movement and atmospheric interference, thereby compromising information transmission reliability. Therefore, incorporating an RF backup link is crucial for enhancing the overall system performance. Motivated by the aforementioned discussions, we consider a parallel UAV relay-assisted aeronautical communication system from an Airborne Warning and Control System (AWACS) to a mobile ground station (GS). In order to reduce the impact of complex atmospheric conditions on air-to-ground links, we adopted a hybrid FSO/RF link and activated an RF backup link when the FSO link failed to meet the requirement of quality of service (QoS). The key contributions of this paper are summarized as follows:  
* First, we propose a novel air-to-ground aeronautical communication system model based on multiple parallel UAV relays. To ensure reliable communication, we consider employing a hybrid RF/FSO communication link between the AWACS and the mobile GS. * Next, the mobility of the AWACS platform, UAV relays, and mobile GS is considered. The impacts of velocity variance variation of the AWACS and GS on the outage and average BER performance in the aeronautical communication system are analyzed in detail. Additionally, the influence of the Doppler effect is also discussed. * Moreover, four relay selection modes are proposed, and the exact closed-form expressions for end-to-end outage probability under different modes are derived.