## 2 System Characteristics  
### Absorption and Scattering  
Light absorption and scattering, inherent optical transmission properties in the underwater channel, would cause the light energy decrease exponentially when the light beam moves in the water. Light scattering would also cause the optical beam to spread in time and space [21]. Two wavelength-related feature parameters, \(a(\lambda_{0})\) and \(b(\lambda_{0})\) (named \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Light Source** & **Power** & **Modulation** & **Detectors** & **Rate** & **Received Optical Power** & **SNR** & **Received Photons per Bit** & **References** \\ \hline
517 nm LD & 100 mW & OOK & PCM & 1.30 Mbps & \(-\)84.1 dBm & +20 dB & \(\sim\)1.0 & [16] \\
520 nm LD & 19.4 mW & OOK & PD & 2.7 Gbps & \(-\)8.24 dBm & +1.8 dB & \(\sim\)10\({}^{5}\) & [17] \\
532 nm SSL & 1.5 W & 256-PPM & PCM & \(\sim\)12 kbps & \(-\)105.04 dBm & +2.5 dB & \(\sim\)0.33 & [9] \\
450 nm LD & 174 uW & PPM & MPPC & 5 MHz & \(-\)39.19 dBm & +2.1 dB & \(\sim\)10\({}^{4}\) & [18] \\
520 nm LD & 7.3 mW & OOK & PD & 500 Mbps & \(-\)19.77 dBm & +2.6 dB & \(\sim\)10\({}^{5}\) & [19] \\
520 nm LD & 10 mW & OOK & SiPM & 1 Gbps & \(-\)40.9 dBm & - & \(\sim\)10\({}^{2}\) & [14] \\
532 nm LD & 10 mW & BPSK & SiPM & 500 Mbps & \(-\)48.2 dBm & - & \(\sim\)10\({}^{2}\) & [20] \\
450 nm LD & 0.47 mW & 32-PPM & PCM & 1.9 Mbps & \(-\)84.0 dBm & +0.1 dB & 0.34 & This work \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the published UWOC system. the absorption coefficient and scattering coefficient, respectively), are used to describe the absorption and scattering effects [22]. The attenuation coefficient \(c(\lambda_{0})\) can then be given as:  
\[c(\lambda_{0})=a(\lambda_{0})+b(\lambda_{0}) \tag{1}\]  
where \(\lambda_{0}\) is the light wavelength. We usually evaluate the performance of UWOC systems under a specific wavelength. The optical characteristics parameters of various water types are shown in Table 2.  
The reason for this is that light scattering involves photon interactions with water molecules, particulate matter, and other dissolved substances in the water [23]. When a photon collides with a particle, the direction of motion will deviate; this deviation angle is called the scattering angle, and is expressed as \(\varphi\). The scatterers in ocean water are randomly distributed, and so the volume scattering phase function, \(\beta(\varphi,\lambda_{0})\), is usually used to describe the angle distribution of the scattering and to predict the moving direction of scattered photons [24]. Moreover, we obtain an expression \(b(\lambda)\) by integrating \(\varphi\) over all angles [21; 25; 26]:  
\[b(\lambda_{0})=2\pi\int_{0}^{\pi}\beta(\varphi,\lambda_{0})\sin\varphi d\varphi \tag{2}\]  
By normalizing the volume scattering phase function \(\beta(\varphi,\lambda_{0})\) with \(b(\lambda_{0})\), we then arrive at the scattering phase function:  
\[\widetilde{\beta}(\lambda_{0},\varphi)=\frac{\beta(\lambda_{0},\varphi)}{b( \lambda_{0})} \tag{3}\]  
Many different types of analytical phase functions have been used over the years. The Henyey-Greenstein (HG) function has been widely used in the research of light scattering in an underwater channel over the years [27; 28]. In more recent years, the Fournier-Forand (FF) scattering phase function [29; 30; 31; 32] has been used, and has been shown to be in good agreement with actual water measurements. The FF scattering phase function is an approximate analytic form of the phase function of an ensemble of particles that have a hyperbolic particle size distribution, with each particle scattering according to the anomalous diffraction approximation to exact Mie theory. The phase is beneficial for modeling both the forward scattering and backscattering of natural waters. \[