# Modeling of Satellite-to-Underwater Integrated FSO-PON System Using NOMA-VLC
## 3 Numerical Analysis
### BER Performance Analysis  
The light waves propagating in the oceanic medium undergo attenuation and signals' broadening in the polarization, temporal, spatial and angular domains. These attenuated and broadened signals are input wavelengths dependents and derive absorption as well as light signals multi-scattering by water molecules or marine organic matter/minerals. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Channel** & **Parameters** & & **Value** \\ \hline \multirow{8}{*}{UOWC} & VLC Range & & 1-15 m \\  & Beam divergence angle & & 1108 mrad \\  & & Clear ocean & 0.21 dB/m \\  & Attenuation & Coastal ocean & 0.39 dB/m \\  & & Turbid harbor & 11 dB/m \\  & & Transmitter & 10 cm \\  & Aperture diameter & Receiver & 20 cm \\  & & & (15, 10, 5) m; \\  & Location co-ordinates & & (12, 8, 3) m; \\  & & & (5, 10, 15) m \\ \hline \multirow{8}{*}{FSO} & \multirow{8}{*}{Beam divergence} & Additional & 2 dB \\  & Loss & Transmitter & 2.5 dB \\ \cline{1-1}  & & Receiver & 2.5 dB \\ \cline{1-1}  & Beam divergence & & 2 mrad \\ \cline{1-1}  & Scintillation model & Gamma-Gamma & Yes \\ \cline{1-1}  & Geometric loss & & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._Therefore, the aquatic channel extinction coefficient, \(y(\lambda)\) is regulated by absorption and two scattering coefficients viz. \(\alpha(\lambda)\) and \(\beta(\lambda)\) as [37]:  
\[y(\lambda)=\alpha(\lambda)+\beta(\lambda) \tag{4}\]  
Table 3 presents the conventional values of absorption and scattering in distinct kinds of water at the different operating wavelength (\(\lambda\)) ranges. As the turbidity increases drastically, \(y(\lambda)\) rises in 0.1 m\({}^{-1}\) to 2 m\({}^{-1}\) range from clear water to turbid water. The propagation loss factor, \(L_{s}(\lambda,l)\) for length (\(l\)) is given as [37]:  
\[L_{s}(\lambda,l)=e^{[-y(\lambda)l]} \tag{5}\]  
Moreover, considering the LOS link in the VLC system, i.e., the transmitter transferring the light beam in a specific direction to the receiver, the received optical signal(\(P_{r}\)), obtained via multiplication of launch power with telescope losses is described as [37]:  
\[P_{r}=P_{t}\mu_{t}\mu_{r}L_{p}(\lambda,l)\left(\lambda,\frac{d}{cos\Omega} \right)\frac{Acos\Omega}{2\pi d^{2}(1-cos\Omega_{0})} \tag{6}\]  
where \(P_{t}\) means Tx power, \(\mu_{t}\) indicates Tx optical efficiency, \(\mu_{r}\) means Rx optical efficiency, \(d\) implies upright distance in Tx and Rx, \(\Omega\) means angle in Tx and Rx trajectory, \(A\) means beam divergence angle and \(\Omega_{0}\) indicates the receiver aperture area. Furthermore, to evaluate the system BER performance under the direct-detection OOK modulation technique, the BER is presented as [37]:  
\[BER=\frac{1}{2}erfc\Bigg{[}\frac{d_{1}T-d_{0}T}{\sqrt{2}\Big{\{}\big{(}d_{1}T \big{)}^{1/2}+\big{(}d_{2}T\big{)}^{1/2}\Big{\}}}\Bigg{]} \tag{7}\]  
Here, \(d_{1}=d_{d}+d_{bg}+d_{s}\) and \(d_{0}=d_{d}+d_{bg}\), where \(d_{d}\) and \(d_{bg}\) indicate the additive noise sources due to dark counts as well as background illumination correspondingly. Also, \(erfc\) presents an error function. Again, the proposed work performance can be evaluated by measuring system BER, which relies on an SNR ratio. The output SNR at PD includes prime noise sources such as shot, thermal and dark currents in the system. In view of a Gaussian distribution of noise, \(SNR_{0}\) in the absence of turbulence regimes at the receiver side is expressed as [39]:  
\[SNR_{0}=\frac{P_{t}}{\sqrt{\Big{(}\frac{2 hfB}{\eta}\Big{)}P_{t}+\Big{(}\frac{ hf}{\eta e}\Big{)}^{2}\Big{(}\frac{4\pi TB}{R_{n}}\Big{)}}} \tag{8}\]  
where \(h,f,\eta\) and \(B\) imply the Plank's constant, frequency, PD quantum efficiency as well as receiver filter bandwidth, respectively; \(e\), \(R_{n}\) and \(K\) represent the electronic charge, input noise resistance and Boltzmann constant, respectively.