## 2 Research Problem
### Underwater Optical Channel Model  
Due to the unique physical characteristics of underwater light propagation, absorption and scattering are the two major factors that impact the channel loss. The absorption and scattering coefficients highly depend on the water types. The work in [27] investigated the attenuation coefficients for different water types, such as pure sea, clear ocean, coastal, and harbor. In Table 2, some typical attenuation coefficients are illustrated. From the results in this table, the pure sea water has the smallest absorption and scattering coefficients, which result in the least signal attenuation.  
\begin{table}
\begin{tabular}{c l} \hline \(a(\lambda)\): & absorption attenuation \\ \(b(\lambda)\): & scattering attenuation \\ \(a\): & clipping coefficient \\ \(\beta\): & modulation index \\ \(h\): & channel loss \\ \(A_{r}\): & size of the photodetector \\ \(d\): & propagation distance \\ \(N\): & Number of subcarriers for OFDM \\ \(x_{\mathrm{D}}[m]\) & \(m\)th sample for the DCO-OFDM signal \\ \(x_{\mathrm{U}}[m]\) & \(m\)th sample for the UCO-OFDM signal \\ \(x_{\mathrm{A}}[m]\) & \(m\)th sample for the ACO-OFDM signal \\ \(b_{\mathrm{DC}}\) & DC bias for DCO-OFDM \\ \(f_{\mathrm{D}}\) & probability density function of the DCO-OFDM signal \\ \(f_{\mathrm{U}}\) & probability density function of the UCO-OFDM signal \\ \(f_{\mathrm{A}}\) & probability density function of the ACO-OFDM signal \\ \(\mathsf{P}\) & average optical power \\ \(P_{m}\) & peak transmitted power \\ \hline \end{tabular}
\end{table}
Table 1: Notation list. DCO, DC-biased optical; ACO, asymmetrically-clipped optical.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Water Types** & **Absorption (\(\mathbf{m^{-1}}\))** & **Scattering (\(\mathbf{m^{-1}}\))** \\ \hline Pure Sea Water & 0.053 & 0.003 \\ Clear Ocean & 0.114 & 0.037 \\ Coastal Ocean & 0.179 & 0.219 \\ Turbid Harbor & 0.295 & 1.875 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Typical attenuation coefficients for different water types [27].  
Light with different wavelengths experience different signal attenuation. Figure 1 shows the attenuation coefficient in pure sea water [28].  
For different light wavelengths and water conditions (deep water or harbor area), the absorption and scattering may vary. In this paper, the effects of water conditions are beyond the scope; therefore, the effect of light wavelength is considered only. In UOWC, the overall attenuation of absorption and scattering can be described as [4]:  
\[c(\lambda)=a(\lambda)+b(\lambda), \tag{1}\]  
where \(a(\lambda)\) and \(b(\lambda)\) are absorption and scattering attenuation coefficients, respectively. The unit of the overall attenuation coefficient, \(c(\lambda)\), is m\({}^{-1}\). The channel loss can be represented as:  
\[h_{o}(d)=L(\lambda,d)\frac{A_{r}\cos\theta\cos\varphi}{2\pi d^{2}}, \tag{2}\]  
where \(A_{r}\) is the size of the photodetector (PD) in the receiver. \(\theta\) and \(\varphi\) are the irradiation and incident angles between the LED and the user. \(d\) is the propagation distance between the LED and the user. \(L(\lambda,d)\) represents the link attenuation, which is calculated as:  
\[L(\lambda,d)=\exp(-c(\lambda)\cdot d). \tag{3}\]  
To simplify the problem, we assume that the propagation distance and attenuation of absorption and scattering mainly impact the channel loss.