In this paper, we investigate the performance of a mixed radio-frequency-underwater wireless optical communication (RF-UWOC) system where an unmanned aerial vehicle (UAV), as a low-altitude mobile aerial base station, transmits information to an autonomous underwater vehicle (AUV) through a fixed-gain amplify-and-forward (AF) or decode-and-forward (DF) relay. Our analysis accounts for the main factors that affect the system performance, such as the UAV height, air bubbles, temperature gradient, water salinity variations, and detection techniques. Employing fixed-gain AF relaying and DF relaying, we derive closed-form expressions for some key performance metrics, e.g., outage probability (OP), average bit error rate (ABER), and average channel capacity (ACC). In addition, in order to get further insights, asymptotic analyses for the OP and ABER are also carried out. Furthermore, assuming DF relaying, we derive analytical expressions for the optimal UAV altitude that minimizes the OP. Simulation results show that the UAV altitude influences the system performance and there is an optimal altitude which ensures a minimum OP. Moreover, based on the asymptotic results, it is demonstrated that the diversity order of fixed-gain AF relaying and DF relaying are respectively determined by the RF link and by the detection techniques of the UWOC link.
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