## 3 Underwater Wireless Optical Communication System
### LED Light Attenuation with Communication Distance  
When the distance between the LED transmitter and receiver reaches \(d\), the LED attenuation and communication noise may be considered in terms of the additive white Gaussian noise (AWGN). Also, the intensity of the light emitted by the LED may be referred to as \(I(\lambda)\), and the attenuated intensity of the corresponding light, \(dI(\lambda)\), at the underwater distance, \(d\), can be described using Beer's law, as shown in Equation (6) below [23].  
\[dI(\lambda)=-c(\lambda)I(\lambda)dz \tag{6}\]  
By integrating the above equation, the intensity of light with respect to the distance, \(d\), can be expressed as shown in Equation (7).  
\[I(\lambda)=I_{0}(\lambda)e^{-c(\lambda)d} \tag{7}\]  
The variables for the corresponding equation are as follows:  
\(d\): communication distance;  
\(I(\lambda)\): intensity of light reaching the receiver;  
\(I_{0}(\lambda)\): initial intensity of light emitted by the LED, etc.;  
\(c(\lambda)\): attenuation coefficient obtained underwater.  
Table 2 shows the absorption and scattering coefficients calculated at the wavelength of 514 nm.  
In UWOC, the intensity of light detected by the receiver is inversely proportional to the square of the receiving distance and is inversely proportional to the gain of the receiver sensor. The intensity of light detected by the receiver, \(P_{r}\), can be expressed as shown in Equation (8) [23].  
\[P_{r}=P_{o}\frac{A_{r}}{4\pi d^{2}}e^{-c(\lambda)d} \tag{8}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Water Quality** & **Absorption Coefficient** & **Scattering Coefficient** \\  & **[m\({}^{-1}\)]** & **[m\({}^{-1}\)]** \\ \hline Pure Seawater & 0.0405 & 0.0025 \\ Ocean & 0.114 & 0.037 \\ Coast & 0.179 & 0.219 \\ Harbor & 0.266 & 1.824 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Absorption and scattering coefficients of water at 514 nm wavelength.  
Figure 6: Configuration of underwater UWOC.  
As the variables for this equation, \(P_{o}\) is the light intensity of the LED, etc., \(A_{r}\) is the area of the receiver, and d is the distance between the LED and the receiver. Therefore, when the underwater attenuation coefficient is high, the intensity of light detected by the receiver is exponentially reduced.  
Modifying Equation (8) yields  
\[\ln A=\ln(\frac{1}{d^{2}}e^{-cd}) \tag{9}\]  
where A = \(\frac{P_{c}}{P_{0}}\), \(\frac{4\pi}{A_{r}}\).  
Equation (9) can be arranged to relate the damping coefficient equation, \(c\), with the distance, \(d\), as follows:  
\[c=-\frac{1}{d}(\ln A+2\ln d) \tag{10}\]  
The researchable communication distance of the UWOC and damping coefficient \(c\) are exponentially related to turbidity, and the turbidity is related to the damping coefficient. Finding the communication distance of the UWOC is important. For this, after finding the damping coefficient, as the derived Equation (10), the communication distance can be estimated by measuring the intensity of the received light and the sensor area. The intensity of emitting light and the area of the receiving light can be designed for a better researchable communication distance of the UWCOM.