# Unified Performance Analysis of Direct Air-to-Underwater RF/UWOC Systems
## 1 Introduction
The effective rate of multi-input single-output (MISO) systems under independent and incomplete (i.n.i.d) distributions in EGK fading channels has been studied [24]. Traditionally, relay buoys connect land and underwater vehicles, but relay deployment brings many cost and safety problems. Therefore, it is a promising solution to study the performance of a direct communication system without relay nodes from land to underwater. The author studied pulse response models of water-air channels under different turbulent water surface conditions [25]. Two scenarios are proposed for the uplink and downlink transmissions between the Autonomous Underwater Vehicle (AUV) and the Unmanned Aerial Vehicle (UAV), subject to water-to-air and air-to-water interface impacts direct transmission scenario (DTS) and retro-reflection scenario (RRS) [26]. The outage probability and statistical characteristics of direct air-to-water wireless optical communication without relay are studied by considering the effects of turbulence and fog [27]. The author studied the propagation of Gaussian coherent beams from underwater laser emitters to outdoor receivers in the presence of gravity-generated water waves in the deep-sea plane through direct wireless communication of beams from underwater to airborne platforms [28]. The author statistically models the fading coefficient of direct air-to-water optical wireless communication channels and the statistical photon counting behavior of Single-Photon Avalanche Diode (SPAD) and then evaluates the performance of the communication link by obtaining the analysis relationship of bit error rates [29]. The author derived the outage probability of the without-relay hybrid system with fog conditions in [27]. However, ref. [27] only considered one distribution function of the FSO system and did not consider pointing errors to improve system reliability. This paper considers various distribution functions of atmospheric turbulence and takes into account pointing errors in hybrid systems. In this paper, the major contributions of the proposed work are summarized as follows:  
1. We analyzed the performance of atmospheric turbulence systems with nonzero boresight pointing errors as well as random path loss in foggy conditions with underwater turbulence. We derived PDF and CDF by unifying EGK, \(\mathcal{F}\), and \(\alpha-\mu\) distributions for atmospheric turbulence with nonzero boresight pointing errors as well as random path loss in foggy conditions with the oceanic and the Birnbaum-Saunders (BS) distribution to model the aquatic waves at the air-water interface. It should be mentioned that papers usually use zero boresight pointing errors, and this paper considers nonzero mean single-sided pointing errors in the system. To the best of the author's knowledge, a direct air-to-underwater hybrid system with nonzero mean single-sided pointing error under foggy conditions has been studied for the first time. 3. We used the statistical results to analyze system performance and derived the outage probability, bit error rate, and channel capacity of the system. 4. We validated the derived analytical results using Monte Carlo simulations, demonstrating the effectiveness of direct air-to-underwater systems under various atmospheric turbulence, pointing errors, ocean turbulence, and weather conditions.