## 3 Experimental Setup
### Underwater Channel Characterization  
In the experiment, the water tank with dimensions of 5 \(\times\) 0.8 \(\times\) 0.8 m shown in Figure 5a was used to simulate an underwater channel, and Figure 5b was the view of received light spots with an emitted spot diameter of 2 mm after transporting in the tank water. In particular, Magnesium hydroxide (Mg(OH)\({}_{2}\)) powder, as shown in Figure 5c, was added to the water to vary the attenuation coefficient. The effect of turbulence was enhanced by the wave-making air pump shown in Figure 5d that was used to generate the air bubbles. Here, we did not consider the effect of turbulence caused by temperature and salinity gradients. Figure 4: Frame acquisition sequence. Figure 5: The simulated underwater channel: (**a**) the water tank, (**b**) the view of the received optical spot in the water, (**c**) Mg(OH)\({}_{2}\) powder, (**d**) the wave-making air pump. The transparency of water can greatly affect the performance of UWOC, thus the effect of power loss in the underwater channel is one of the important factors needed to be considered due to the variability of the underwater channel. Parameters characterizing the quality of water include the absorption coefficient \(c\), the scattering coefficient \(b\), the scattering albedo \(\omega\), and the attenuation coefficient \(c\). In this experiment, we applied [PERSON]'s water-typed parameters, and the value of \(a\), \(b\), and \(c\), \(\omega\) are shown in Table 1. The Beer-Lambert law is commonly used to describe the power loss as a function of transmission distance in UWOC [22], which can be:  
\[P(z)=P(0)e^{-c(\lambda_{0})z} \tag{23}\]  
where \(z\) is the communication length. To obtain the attenuation coefficient \(c\) of the experimental water tank. As shown in Figure 6a, we tested the power loss of measured water over different transmission distances. The blue prismatic points are the measured data, and the red fitting curve is based on the Beer-Lambert model with \(c=0.51\) m\({}^{-1}\), here we ignored the geometric loss because the received optical spot was smaller than the receiver aperture size in this experiment. The water quality in the experimental tank was close to that of the Jerlov II water according to the data in Table 1. However, the Beer-Lambert law assumes that all scattered light is lost from the propagation beam and no multiply scattered light returns to the beam, which results in the gain because the photons scattering back into the central beam are not considered [45]. Instead, in consideration of energy conservation, the radiance transmission equation (RTE), which is derived to theoretically describe all photons moving through the water along a path toward a given direction [46], is given as:  
\[ \begin{split}&\cos\theta^{\prime}\frac{dI(z,\lambda,\varphi^{ \prime},\theta^{\prime})}{dz}=-c(\lambda)I(z,\lambda,\varphi^{\prime},\theta^{ \prime})\\ &+\int_{0}^{\pi}\int_{0}^{2\pi}\beta(z,\lambda,\varphi\to\varphi^ {\prime},\theta\to\theta^{\prime})I(z,\lambda,\varphi^{\prime},\theta^{\prime} )\sin\psi_{1}d\theta^{\prime}d\varphi^{\prime}\end{split}  \tag{24}\]  
where _I(z, \(\lambda\), \(\varphi\), \(\theta\))_ is the radiance energy in the direction with the scattering angle \(\varphi_{i}\) (_i_ = 1,2)and the azimuth angle \(\theta_{i}\) (_i_ = 1,2), and the angle \(\varphi_{i}\) is obtained by the scattering phase function described in Equation (4). In Equation (24), the first term on the right is [PERSON]'s law loss, and the second term is the gain from light scattering from the angles \(\varphi\), \(\theta\) into \(\varphi^{\prime}\), \(\theta^{\prime}\). The analytical solution of the equation is extremely difficult since it involves integrals and derivatives. The Monte Carlo (MC) simulation tool has been widely used to solve the RTE [46; 46]. In this approach, the interaction of each photon with the medium is statistically modeled, and the photon propagation paths from the transmitter to the receiver are traced step by step.