## 4 Performance Investigation  
We investigate the performance of the proposed LE-KCR algorithm in an underwater wireless sensor network employing optical waves. The network parameters are selected according to the channel and energy model described in Section 2. The initial energy of each sensor node is 5 J and is equipped with the components, such as an optical transmitter, receiver, and signal generator. The maximum transmission range of the signal is set as 50 m, and the minimum receiving power is set as 0.0025 mW. Power control is used to assign just enough transmitting power to guarantee this value at the receiver. The network is comprised of 100 sensor nodes, which are deployed in an area of 100*100 m\({}^{2}\) following a Poisson process. Regarding the characteristics of the underwater channel and the resource constraints of the nodes, most of the simulation parameters are set based on [46], while the maximum transmission range is set by considering the \"exponential\" characteristics of energy consumption in Figure 3. We employ the k-means technique to cluster the network and determine the number of clusters by the gap statistical method. Due to the small number of nodes in the model, the clustering algorithm converges in less than one second. It can select the best clustering number and identify the centroid of the cluster. We set an energy threshold as 2 J. When the node remaining energy is below this threshold, it will not be selected as a cluster-head, and will be regarded as a \"dead node\". However, it is not really a dead node, because it can still be used as an ordinary node to collect information for the network. The simulations are performed in multiple rounds. A non-cluster-head node transmits 1-bit information to the corresponding cluster-head in each round. The cluster-head processes the collected information before forwarding it to the nearest anchor node. Then, the information can be further transmitted to the receiver on the sea surface. The simulations are carried out in MATLAB. The parameters set in the simulations can be found in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Space of topology & 100 \(\times\) 100 m\({}^{3}\) \\ Number of sensors & 100 \\ E\({}_{\text{init}}\) & 5 J \\ Pr & 0.0025 mW \\ E\({}_{\text{elec}}\) & 1 mJ \\ K(\(\lambda\)) & 0.5 \\ R\({}_{\text{max}}\) & 50 m \\ R\({}_{\text{b}}\) & 100 Mbps \\ \(\sigma\) & 1 \\ \(\eta_{\text{t}}\) & 0.8000 \\ \(\eta_{\text{r}}\) & 0.7452 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 5 shows the simulation results on dead nodes with different rounds, when the basic LEACH, the LEACH k-means, and the proposed LE-KCR algorithms are adopted. As shown in Figure 5, the LEACH algorithm dies more than half of the nodes in less than 30 rounds. The Leach-k algorithm dies nearly 40% of nodes after running 100 rounds and, in order to ensure the consistency of the comparison, we set the same conditions for the proposed LE-KCR algorithm. Before reaching the energy threshold condition, only 4% of the nodes die by running 100 rounds. In the proposed LE-KCR algorithm, the selected cluster-heads are close to most nodes, so less energy is required for each round. This shows that the proposed algorithm is extraordinarily energy-saving. Figure 6 depicts the variety of nodes' total remaining energy with a diverse number of transmission rounds when the basic LEACH, the LEACK K-Means, and the proposed LE-KCR algorithms are adopted. Remaining energy is another important criterion to estimate the energy efficiency of wireless sensor networks [47]. It can evaluate the network lifetime based on different algorithms. As shown in Figure 6, we consider the area under the curve under the same remaining energy threshold. The proposed LE-KCR algorithm has a better network lifetime than both the LEACH and the LEACK K-Means algorithms with different numbers of transmissions. Compared with LEACH, the performance of the proposed LE-KCR algorithm improves by more than 90%.