## 3 Proposed System Model
The probability density function of the irradiance \(I_{r}\) investigates the effect of turbulence on system performance, and various UOWC channel models can be expressed as in [11] as follows:  
\[P(I_{r})=I_{r}^{\psi-1}\;exp(-I_{r}\psi)\cdot\frac{\psi^{\psi}}{\Gamma(\psi)} \tag{2}\]  
where \(\psi\) is a parameter function that represents the effect of the scintillation index \(\delta_{p}^{2}\) as in (3), and \(\Gamma(\psi)\) is the gamma function of \(\psi\). \[\psi=\frac{1}{\delta_{p}^{2}} \tag{3}\]  
The scintillation index \(\delta_{p}^{2}\) can be expressed as follows:  
\[\delta_{p}^{2}=ab+a+b \tag{4}\]  
Figure 2: Proposed OCDMA system for user #n out of N active users: (**a**) Transmitter, (**b**) Receiver, and (**c**) LOS-UOWC channel model. where \(a\) and \(b\) are parameters defined as  
\[a=\left[exp\left(\frac{0.49\sigma_{I_{r}}^{2}}{\left(1+0.18L^{2}+0.56\sigma_{I_{r} }^{12/5}\right)^{7/6}}\right)-1\right] \tag{5}\]  
\[b=\left[exp\left(\frac{0.51\sigma_{I_{r}}^{2}}{\left(1+0.9L^{2}+0.62\sigma_{I_{r }}^{12/5}\right)^{5/6}\left(1+0.62\sigma_{I_{r}}^{12/5}\right)^{5/6}}\right)-1\right] \tag{6}\]  
where \(\sigma_{I_{r}}\) is the normalized intensity variance, and \(L=\sqrt{kD^{2}/(4d)}\), where \(d\) is the transmission distance, \(D\) is the receiver photodetector aperture diameter, and \(k=\frac{2\pi}{\lambda}\) is the wave number. There are two main problems in the case of optical propagation underwater: the high absorption of the optical signal in the water medium and scattering due to the particles in the seawater. In the visible spectrum of light, especially in the 450-470 nm range blue-green region, seawater has a lower absorption and consequently lower attenuation, and the lowest value of this attenuation occurs at 460 nm in clear ocean water. Furthermore, in coastal waters, this wavelength range shifts to 530-550 nm [47; 48]. In the low scattering regime, we can describe the light propagation in water using the spectral attenuation coefficient \(\alpha(\lambda)\), which is the sum of the scattering and absorption coefficients \(S(\lambda)\) and \(A(\lambda)\), respectively. The involvement of water molecules, dissolved colored organic content, and particulate algal/sediment matter are the main factors that determine the absorption and scattering coefficients in m\({}^{-1}\)[50; 51; 52]. In addition to the effect of wavelength on the absorption, the type of particles and level of turbidity significantly affect the absorption and scattering coefficients. Two types of particles are important in seawater: phytoplankton and organic particles, both of which affect the light properties. The first type strongly absorbs the blue and red regions of light. In turbid water, the scattering of photons results in a decrease in the received optical power, and several photons are received with delays, causing ISI. Every type of water is characterized by a value of chlorophyll concentration \(C\), which also affects the values of the absorption and scattering coefficients and can be expressed simply as shown in (7) and (8), respectively [29; 30; 31; 32; 33; 34; 52]:  
\[A(\lambda)=\left[A_{\omega}(\lambda)+0.06A_{C}(\lambda)C^{0.65}\right]\{1+0. 2 exp[-0.014(\lambda-440\,]\} \tag{7}\]  
\[S(\lambda)=0.30\frac{550}{\lambda}C^{0.62} \tag{8}\]  
where \(A_{\omega}(\lambda)\) is the absorption coefficient for pure water, \(A_{C}(\lambda)\) is a statistical dimensionless specific absorption coefficient for chlorophyll, and \(C\) is the chlorophyll concentration of 0.03, 0.1, 0.38, and 3 mg/m\({}^{3}\) for pure seawater, clear ocean water, coastal ocean water, and turbid harbor water, respectively.