# Modeling of Satellite-to-Underwater Integrated FSO-PON System Using NOMA-VLC
## 3 Numerical Analysis
### Impact of Losses  
* Geometric loss (GL): GL in FSO links rises owing to the transmitted beam spreading between transmitter and receiver. However, smaller transmitter divergences and larger receiver apertures over an FSO link range (\(Z\) in km) and divergence (\(\theta\) in mrad) cause minimum GL. In general, GL (in dB) is given as [43; 44; 11; 45]: \[GL\ (dB)=10\log\biggl{\{}\frac{D_{r}}{D_{t}+(Z\theta)}\biggr{\}}^{2}\] (19) where \(D_{t}\) (in meters) indicates the transmitter aperture diameters.
* Chromatic dispersion (CD): In the fiber-VLC link the CD, \(d_{Fiber}\) in (ps/nm) at a referred wavelength of 1550 nm is presented as below [46]: \[d_{Fiber}=l[d+c(\lambda-1550)]\] (20) where \(l,d\) and \(c\) present SMF length followed by dispersion and slope coefficient of different wavelengths. The calculated dispersion at 100 km fiber, 10 km FSO and 10 m VLC range at 10/2.5 Gbps transmission rate are tabulated in Table 4.  
In Table 4, the measured positive values indicate the faster progress of short wavelengths than long wavelengths and vice versa for negative values. Therefore, the maximum sustainability attained in downstream (tolerance range = 1176 ps/nm) as well as upstream (tolerance range = 18.817 ps/nm) fiber range is \(\leq\)100 km and \(>\)100 km respectively over integrated fiber-VLC link.  
* Impact of ISI: ISI owing to the existence of overlapped contiguous bit intervals optical pulses, cause pulse broadening represented as \(\Delta b\) as [46]: \[\Delta b=dl\Delta\lambda\] (21) where \(\Delta\lambda\) indicates the pulse spectral line width. As for TWDM-PON as well as WDM-OCDMA, \(\Delta\lambda\) is 0.8 nm and 0.4 nm, respectively, while for FSO and VLC systems, the ISI can be neglected.  
Table 5 tabulates the measured \(\Delta\lambda\) over 10-110 km fiber distance along with 10 km FSO and 10 m VLC range analogous to the DN transmission (highly affected than uplink) at 10 Gbps data rate.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multicolumn{1}{l}{\(\lambda\) **(nm)**} & \multicolumn{3}{c}{**CD (ps/nm)**} \\ \hline  & TWDM-PON & 1596 & 1100 \\  & FSO & 1575 & 1180 \\ DN & FSO & 1550 & 700 \\  & & 625 & 320 \\  & VLC & 525 & 560 \\  & & 455 & 187 \\  & & 1527.2 & 990 \\  & TWDM-PON & 1260 & \(-\)180 \\ UP & FSO & 1550 & 550 \\  & & 625 & \(-\)250 \\  & VLC & 525 & \(-\)240 \\  & & 455 & \(-\)210 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Measured dispersion of proposed hybrid PON-VLC system for distinct wavelengths.  
It is noted that the values of \(\Delta\lambda\) rise as fiber length increases, resulting in a degradation in system performance.
* Impact of FWM: The full range of FWM wavelengths (\(\lambda_{\text{FWM}}\)) for \(i\) wavelength links in the proposed system is presented as [47]: \[\lambda_{\text{FWM}}=\frac{i^{2}}{2(i-1)}\] (22)  
Here, hybrid TWDM-PON produces three FWM wavelengths, while the WDM-OCDMA produces a maximum of four for the MNZCC code. A larger number of wavelengths is caused by more FWM noise in the system. As in FSO and VLC systems, only single and three wavelengths are used, respectively. Hence, produces minimum FWM noise. Additionally, with increasing the transmission rate, the FWM side lobes rise, which results in degrades in system performance.
* Channel noise and beam divergence in VLC: Tables 6 and 7 show the comparisons of the proposed system with integrated fiber-VLC link (50 km fiber + 10 km FSO + 10 m VLC), having Tx and Rx aperture diameter of 10 cm and 20 cm, respectively for downstream and upstream transmission, respectively.