## 2 System Model  
Underwater channels have a serious impact on an optical signal, resulting in a limited communication distance. In order to expand the communication range, the transmitter selects a laser (LD) with a smaller divergence angle, and the receiver selects a PMT with a higher detection capability. The transmitter and receiver are aligned along the line of sight [4]. In the case of fixed transmission power, the optical signal's attenuation is more serious when the communication distance is longer. Under the premise of ensuring communication quality, a single QAM cannot meet the changing channel status and the dynamic range of PMT. Therefore, under different link conditions, the adaptive selection of the modulation mode and the control of LCLV can expand the dynamic range of the communication distance and the PMT-received power and improve the reliability and efficiency of the system. The impact of various components contained in water on the optical signal is mainly manifested in two aspects, namely absorption and scattering [19]. The attenuation effect on the optical signal caused by these two factors can be represented by the attenuation coefficient \(c(\lambda)\), which can be expressed as follows:  
\[c(\lambda)=a(\lambda)+b(\lambda), \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & **CPS** & \begin{tabular}{c} **Optical/Electrical** \\ **Domain** \\ \end{tabular} & \begin{tabular}{c} **Modulation** \\ **Method** \\ \end{tabular} & \begin{tabular}{c} **Transmit** \\ **Power** \\ \end{tabular} & \
\begin{tabular}{c} **Link** \\ **Distance** \\ \end{tabular} &
\begin{tabular}{c} **Optimization** \\ **Objective** \\ \end{tabular} \\ \hline Proposed & Yes & Both & QAM & 80 mW & 7–48 m & Distance; \\ [3] & No & Electrical & TDHP & 0.5 W & 11–100 m & Distance \\ [5] & No & Both & OOK & 10–30 mW & 10 m & Distance \\ [6] & No & Optical & OOK & 80 mW & 2 m & Power \\ [8] & No & Electrical & PAM/FPM & 4 W & 0.5–6 m & Distance \\ [12] & No & Electrical & QAM & - & 0.15–0.3 m & Rate \\ [15] & Yes & Electrical & QAM & - & 1–20 m & Rate \\ [16] & Yes & Electrical & QAM & - & 0.5–2 m & Rate \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between the method proposed in this paper and the references above. where \(a(\lambda)\) represents the absorption coefficient, \(b(\lambda)\) represents the scattering coefficient and \(\lambda\) represents the wavelength. According to the Beer-Lambert law, when the distance of the light beam propagating underwater is \(d\), the path loss model is expressed as follows:  
\[L_{loss}=\mathrm{e}^{-c(\lambda)d}. \tag{2}\]  
Assuming the transmitter and receiver are aligned and considering geometric losses, the underwater channel's DC gain can be expressed as follows [20]:  
\[H(0)=\frac{m+1}{2\pi}\cos^{m}(\phi)A_{eff}(d,\psi), \tag{3}\]  
\[A_{eff}(d,\psi)=\frac{\pi D_{r}^{2}\cos(\psi)/4}{\pi(L\tan(\phi_{1/2})+D_{t}/2) ^{2}}, \tag{4}\]  
where \(m=(-\ln 2)/\ln(\cos(\phi_{1/2}))\) is the Lambertian radiation order, \(\phi_{1/2}\) is the half-power angle of the light source, \(\phi\) is the irradiation angle, \(\psi\) represents the incidence angle of the beam to the detector surface, \(D_{t}\) represents the diameter of the light source condenser lens, \(D_{r}\) represents the diameter of the receiving surface, \(d\) represents the beam propagation distance and \(A_{eff}(d,\psi)\) represents the effective area of the detector. The process of light transmission underwater can be regarded as a cumulative loss process. Multiple factors work together to reduce the signal's power [21]. The maximum communication distance is closely related to the received power.