## 7 Conclusions

Table 11: _Cont._grams (Figures 4-6). We also presented several modelling methods for the underwater channel, including the BLL, VSF/SPF (Figures 7-11), and RTE modelling options, which can be solved analytically, with assumptions, and numerically. Our derived expressions in Section 4 can be used as reference benchmarks and as the \"How\" techniques of evolving reliable simplified analytical solutions. We provided a comprehensive overview of the four numerical methods used to solve the RTE and recent and significant studies of UOWC channel modelling. Additionally, we discussed the primary MCS methods in detail and presented recent studies that provide insight into their simulation parameters. To summarise, the novelty of this work is listed in Table 12. This table provides the novelty statements mapped to the associated equations, tables, and diagrams. In conclusion, the MCS numerical computation technique is at a good maturity level and is a leading trend for designing UOWC systems. Nevertheless, the MCS approach needs a more detailed and unified approach to handle scintillation, turbulence, link configuration, and the inclusion of the photodetector by accounting for the photoelectron generation Poisson process. Conceptualisation, I.R. and Y.A.-H.; Methodology, I.R. and H.M.A. ; Software, I.R., H.M.A. and M.C. ; Validation, I.R., H.M.A. and A.Z.B. ; Formal analysis, I.R. and Y.A.-H.; Investigation, I.R., Y.A.-H., H.M.A. and A.Z.B. ; Writing--original draft, I.R. ; Writing--review and editing, H.M.A., Y.A.-H., M.C. and A.Z.B. ; Visualisation, I.R. All authors have read and agreed to the published version of the manuscript. The Deanship of Scientific Research (DSR) at King Abdulaziz University (KAU), Jeddah, Saudi Arabia, funded this project under grant no. (KEP-PhD: 72-130-1443). The MCS Python codes can be provided upon request through the corresponding author's email. This work was technically supported by the Deanship of Scientific Research (DSR), King Abdulaziz University (KAU), Jeddah, Saudi Arabia. The authors, therefore, gratefully acknowledge the DSR for technical support. Authors are indebted to [PERSON] for his valuable suggestions, mathematical verifications and significant contribution to the execution of the computational modelling and simulation. The authors declare no conflicts of interest. \begin{table}
\begin{tabular}{c c c c} \hline
**Novelty Statement** & **Section** & **Equations** & **Implementation Tables** & **Diagrams** \\ \hline Novel derivation of the core & & & & \\ mathematical equations for the & & & & \\ homogeneous and inhomogeneous & Sections 4.1 and 6.2 & (73)–(78), (83) and (89) & Tables 6–8 & \\ channels, which drive the MCS & & & & \\ numerical computations & & & & \\ \hline The maximum received scattered & & & & \\ photon count for the HG-SPF & & & & \\ regime is consistently higher than & & & & \\ the FURS regime. In other words, & & & \\ the SPF-based computation & & & & \\ overestimates the received & & & \\ scattered photon count compared & & & \\ to the FURS-based computation. & & & \\ This observation is true regardless & & & \\ of the linkspan (\(L\)) and the & & & \\ transmitted pulse width (\(x\)) & & & \\ \hline \end{tabular}
\end{table} 
Table 12: Highlights of the study’s novelty statements.