## 1 Introduction
Under the conditions of considering ocean turbulence and pointing error, the outage probability and average bit error rate of the system were analyzed. Among them, the UWOC link was modeled as underwater path loss described by the Beer-Lambert law, pointing error, and EGG turbulence effect; the RF link used the complex Fisher-Snedecor F distribution to model the influence of small-scale fading and shadowing effects, and the effect of path loss was not considered. In addition, this paper also did not consider the comparison of the system performance of the UWOC link under different receiving and detection schemes such as heterodyne detection (HD) and intensity modulation with direct detection (IM/DD). Synthesizing the above research status of the cross-media FSO/RF-UWOC hybrid two-hop relay system, it can be seen that due to the different communication mechanisms, the channel modeling of the FSO and RF links above the water surface is not comparable. However, just in terms of the operation of the RF link, generally only the influence of small-scale fading is considered while the effects of large-scale shadowing or path loss are ignored. Obviously, the channel modeling of the RF link is far from perfect. On the other hand, for the UWOC link, the Lognormal distribution model directly transplanted from the atmospheric FSO environment or the EGG distribution model, which is not transplanted but relatively complex, is generally used to model the ocean turbulence fading. At the same time, the two unfavorable factors of pointing error and underwater path loss are often ignored. Or, although the influence of path loss is considered, the adopted path loss model is the unreasonable single-exponential Beer-Lambert model [10]. That is to say, there are imperfections or irrationalities in the existing channel modeling of the RF-UWOC system, and it is necessary to conduct special research on the performance of this hybrid two-hop system under a novel and complete channel model. Based on the above background, this paper proposes to model the composite channel fading of the RF link using the Generalized K distribution and atmospheric path loss. Among them, the Generalized K distribution includes Nakagami-m small-scale fading and Lognormal shadowing effects, so that this composite model can comprehensively reflect the complete effects of small-scale fading, large-scale fading, and path loss. The UWOC link is modeled as a novel composite channel fading of the Simple Generalized Gamma Distribution (GGD), zero line-of-sight pointing error(negligible jitter), and Elamassie underwater path loss. Among them, the GGD model, through experimental testing, is an effective model that is simpler in mathematical expression than the EGG model but can perfectly describe the weak-medium-strong, three kinds of turbulence effects [11]. The Elamassie path loss model is also a path loss model that can more accurately describe the path loss including the effects of seawater absorption and scattering, as well as geometric loss than the traditional single-exponential Beer-Lambert law, which has been verified by simulation experiments [10]. Many studies only consider turbulence using the EGG model, but it is too complex and unreasonable, either only considering the pointing error or not considering the path loss, or incomplete consideration. In the system HD (coherent detection), modulation mode (BPSK) was used with devices to realize the underwater complexity less than IM/DD or the OOK complex, but its system performance from the principle is achievable, so the focus of this thesis is to consider the performance of the probability of interruption, and not consider the complexity of its implementation. Based on this novel and complete composite fading channel model of the two links, the theoretical closed-form expression of the average outage probability of the RF-UWOC hybrid two-hop relay transmission system using the Decode-and-Forward (DF) mechanism and its asymptotic expression under high signal-to-noise ratio are derived.