## 4 Results and Discussion  
The proposed satellite-ground-underwater OWC system design is demonstrated using the OptiSystem v.21 simulation tool. A BER limit of \(10^{-9}\) is used as a threshold limit for performance evaluation. The simulation results are presented for both satellite-to-ground OWC links and ground-to-underwater UWOC links, taking atmospheric conditions into account for different OAM modes. In both the OWC and UWOC channels, Gamma-Gamma distributions are used as they provide a wide range of turbulence from weak to strong. Figure 3a-d depicts 2D intensity profiles of the generated OAM modes viz. LG[0,0], LG[0,2], LG[0,4], and LG[0,8]. Figure 4a-d present the BER performance of the proposed system for varied satellite-to-ground OWC ranges at LG[0,0], LG[0,2], LG[0,4], and LG[0,8] under weak-, moderate-, and strong-turbulence scenarios. Figure 3: Two-dimensional intensity profiles of (**a**) LG[0,0], (**b**) LG[0,2], (**c**) LG[0,4], and (**d**) LG[0,8]. A weak turbulence is defined as one with a refractive structure parameter of 0.5 \(\times\) 10\({}^{-17}\), a moderate turbulence as one with a refractive structure parameter of 0.5 \(\times\) 10\({}^{-15}\), and a strong turbulence as one with a refractive structure parameter of 0.5 \(\times\) 10\({}^{-12}\) m\({}^{-2/3}\). Here, a BER limit of 10\({}^{-9}\) is considered for system performance evaluation. When the OWC link range is increased from 21,000 to 30,000 km with zero input power at a 1550 nm wavelength, the BER values for all of the modes in diverse turbulent conditions increase. Further, LG[0,0] has a significant increase in transmission range in comparison to any other mode, since it transmits 99% more light than any other mode. Accordingly, in the case of no turbulence, the best performance can be achieved under weak turbulence, followed by moderate turbulence, and the worst under strong turbulence. To evaluate the system's performance under various conditions, the no-turbulence condition has been considered in the simulation as the ideal condition for satellite-to-ground communication over OWC links. Clearly, when the LG[0,0] mode is considered, as shown in Figure 4a, 24,500 km is the maximum range under weak and moderate conditions, while 23,500 km is the maximum range under strong turbulence. For all turbulent conditions, minimum  
Figure 4: BER versus satellite-to-ground OWC range for operating modes of (**a**) LG[0,0], (**b**) LG[0,2], (**c**) LG[0,4], and (**d**) LG[0,8] under diverse turbulent scenarios. logarithm (log) BER values of \(-11\) were obtained compared to the no-turbulence conditions which had a log(BER) range from \(-13\) to \(-9.5\). For the LG[0,2] mode, the maximum OWC link ranges were 24,000 km under weak, 23,800 km under moderate, and 22,000 km under strong turbulence, as depicted in Figure 4b. With respect to the no-turbulence conditions, the minimum log(BER) BER obtained was \(-10.5\). The faithful transmission range for LG[0,4] and LG[0,8] modes was, respectively, 26,000 and 24,000 km for weak turbulence; 22,000 and 22,500 km for moderate turbulence; and 21,500 and 22,000 km for strong turbulence (Figure 4c,d). A summary of the maximum OWC link ranges obtained for different modes and turbulent conditions for satellite-to-ground scenarios can be found in Table 3.  
Figure 5a-f depict the eye patterns observed at different OWC link ranges for different LG modes under weak turbulence. It can be seen that, with an increase in link range from 21,000 to 30,000 km, distorted eye patters are observed under the no-turbulence conditions, as shown in Figure 5a,b.