# Performance Analysis of FSO-UWOC Mixed Dual-Hop Relay System with Decode-and-Forward Protocol
## 5 Simulation Results and Analysis
### Average BER Simulation Results and Analysis  
Figure 5 illustrates the curves of the average BER versus average SNR for the hybrid dual-hop FSO-UWOC system under conditions of weak atmospheric turbulence Rytov variance \(\sigma_{R}^{2}=0.6\), strong pointing error in the first hop \(\xi_{1}=1.14\), and weak pointing error in the second hop \(\xi_{2}=4.00\). As depicted in Figure 5, the atmospheric transmission distance is fixed at \(Z=200\) m, while the underwater transmission distance is set to \(d=20\) m. Additionally, three distinct underwater turbulence scintillation index parameters are established as \(\sigma_{I}^{2}=0.1074/0.2066/0.4548\). From the simulation results presented in Figure 5, it can be observed that, with the parameters of the FSO link (such as atmospheric turbulence, atmospheric transmission distance, and pointing error) fixed, the BER performance significantly degrades as the intensity of underwater turbulence increases, regardless of whether the system employs IM/DD or HD. This observation underscores the severe impact of oceanic turbulence intensity on the average BER performance. However, when the scintillation index, which characterizes the intensity of oceanic turbulence, begins to increase, the deterioration in system performance is not immediately apparent; for instance, at \(\sigma_{I}^{2}=0.1074\) and \(0.2066\), the two performance curves almost overlap, while at \(\sigma_{I}^{2}=0.4548\), a significant disparity in performance becomes evident. To further analyze the reasons, the asymptotic formula for the average BER, as given by Equation (43), reveals that the asymptotic average BER is influenced by five system fading parameters that characterize atmospheric and oceanic turbulence, as well as the pointing errors of the two hops. Solid lines represent the theoretical values of IM/DD detection, dashed lines represent the theoretical values of HD detection, circles represent the simulated values of IM/DD detection, and triangles represent the simulated values of HD detection. When the oceanic turbulence scintillation index is set to \(0.1074\) and \(0.2066\) (corresponding to ac = \(3.60\) and \(2.02\)), and other parameters are configured as \((\alpha,\beta)=(5.41,3.78)\), \(\xi_{1}=1.14\), \(\xi_{2}=4.00\). It is evident that in high-SNR regions, the asymptotic value of the average BER is primarily determined by the pointing error of the FSO link, \(\xi_{1}=1.14\). This implies that, under these conditions, the average BER performance is largely independent of the intensity of oceanic turbulence. Conversely, as the oceanic turbulence intensity increases to \(\sigma_{I}^{2}=0.4548\), the associated parameter \(ac=1.01\) becomes smaller than the other four parameters \(\alpha\), \(\beta\), \(\xi_{1}^{2}\), \(\xi_{2}^{2}\), leading to the asymptotic value of this curve being dominated by the oceanic turbulence coefficient. Clearly, the BER curve corresponding to the oceanic turbulence \(\sigma_{I}^{2}=0.4548\) is significantly worse when compared to those for \(\sigma_{I}^{2}=0.1074/0.2066\). Additionally, the simulation results reveal a high degree of agreement between the theoretical calculations and MC simulations. This consistency further validates the accuracy of the derived closed-form expressions for the BER and its asymptotic value. Figures 4 and 6 demonstrate the impact of varying link transmission distances on the average BER of the FSO-UWOC system. The analysis is conducted under strong atmospheric turbulence (Rytov variance \(\sigma_{R}^{2}=2\)) and moderate marine turbulence conditions (scintillation index \(\sigma_{I}^{2}=0.1074\)). Pointing error parameters for the two hops are configured as \(\xi_{1}=1.14\) and \(\xi_{2}=4.00\), respectively. Figure 6a depicts theoretical and MC simulation results for the average BER as a function of the average SNR.