## 2 System Model
### Underwater Channel Model  
Aquatic media contain dozens of different elements suspended or dissolved in water with different concentrations, as well as some marine animals and plants [38]. Therefore, the water medium exhibits two basic physical effects, namely absorption and scattering. According to [PERSON]'s law, the absorption and the scattering effects of the water medium can be combined as the seawater extinction coefficient c(\(\lambda\)) via the following formula:  
\[\mathrm{c(\lambda)}\mathrm{=a(\lambda)+b(\lambda)} \tag{1}\]  
where \(\lambda\), \(\mathrm{a(\lambda)}\), and \(\mathrm{b(\lambda)}\) represent the wavelength, the absorption coefficient, and the scattering coefficient, respectively. The key absorption elements include pure seawater, chlorophyll, and colored dissolved organic matter. Seawater contains pure water and dissolved salt. Chlorophyll plays a significant role in photosynthesis. It can absorb light energy in a wide wavelength range. The organic substances, mainly composed of humic and fulvic acid, can also absorb light in seawater. As for the scattering effect, it mainly comes from diverse kinds of particles, whose refractive indices can be defined from 1.03 to 1.15 [39].  
As in [40], the underwater light absorption model can be established as follows:  
\[\mathrm{a(\lambda)}\mathrm{=a_{w}(\lambda)+a_{cl}(\lambda)+a_{cl}^{0}C_{f}e^{- k_{f}\lambda}+a_{b}^{0}C_{h}e^{-k_{b}\lambda}} \tag{2}\]  
\[\mathrm{C_{f}}=1.74098C_{c}e^{0.12327(\frac{C_{h}}{C_{f}})} \tag{3}\]  
\[\mathrm{C_{h}}=0.19334C_{c}e^{0.12343(\frac{C_{f}}{C_{f}})} \tag{4}\]  
Figure 1: The network model employed for the proposed LE-KCR algorithm.  
where \(\mathrm{a}_{w}(\lambda)\) denotes the absorption coefficient of pure water, \(\mathrm{a}_{\mathrm{cl}}(\lambda)\) denotes the chlorophyll absorption coefficient [38; 39], \(\mathrm{a}_{\mathrm{h}}^{0}\) and \(\mathrm{a}_{\mathrm{f}}^{0}\) denote the absorption coefficients of humic and fulvic acid, respectively, and \(\mathrm{C}_{\mathrm{h}}\) and \(\mathrm{C}_{\mathrm{f}}\) denote the concentrations of humic and fulvic acid, respectively, which can be determined by chlorophyll concentration \(\mathrm{C}_{\mathrm{c}}\) (\(\mathrm{C}_{\mathrm{c}}^{0}=1\) mg/m\({}^{3}\), \(0<\mathrm{C}_{\mathrm{c}}<12\) mg/m\({}^{3}\). \(\mathrm{K}_{\mathrm{f}}\) and \(\mathrm{k}_{\mathrm{h}}\) are model constants.  
As for the scattering model, it can be calculated as follows [38]:  
\[\mathrm{b}(\lambda) =\mathrm{b}_{\mathrm{w}}(\lambda)+\mathrm{b}_{\mathrm{s}}^{0}( \lambda)\mathrm{C}_{\mathrm{s}}+\mathrm{b}_{\mathrm{l}}^{0}(\lambda)\mathrm{C }_{\mathrm{l}} \tag{5}\] \[\mathrm{C}_{\mathrm{s}} =0.01739(\mathrm{g}/\mathrm{mg})\mathrm{C}_{\mathrm{c}}\mathrm{e} ^{0.11631(\frac{\mathrm{C}_{\mathrm{c}}}{\mathrm{C}})}\] (6) \[\mathrm{C}_{\mathrm{l}} =0.76284\left(\frac{\mathrm{g}}{\mathrm{mg}}\right)\mathrm{C}_{ \mathrm{c}}\mathrm{e}^{0.03092(\frac{\mathrm{C}_{\mathrm{c}}}{\mathrm{C}})} \tag{7}\]  
where \(\mathrm{b}_{\mathrm{w}}(\lambda)\), \(\mathrm{b}_{\mathrm{s}}^{0}(\lambda)\), and \(\mathrm{b}_{\mathrm{l}}^{0}(\lambda)\) denote the scattering coefficients of pure water, small particles, and large particles, respectively. \(\mathrm{C}_{\mathrm{s}}\) denotes the concentrations of small particles with \(\mathrm{C}_{\mathrm{l}}\) denoting those of large particles in seawater.