# Energy-Efficient Clustering Multi-Hop Routing Protocol in a UWSN
## 3 Energy-Efficient Clustering Multi-Hop Routing Protocol  
### Network Model  
The network scenario consists of \(N\) dynamic nodes which are randomly and sparsely deployed in a three-dimensional scenario \(L\times L\times L\). Figure 1 illustrates the network. The data source is the sensed data in the water medium. The data are collected by the underwater sensor nodes. The sensed data are temperature, current flow, and pressure [1; 2; 3; 4]. Underwater sensor nodes are equipped with acoustic modems to communicate with other nodes in the water medium. The sink node is deployed at the center of the surface and equipped with both acoustic and radio frequency (RF) modems; the sink's acoustic modems receive data from the underwater sensor nodes, and the RF modem transmits data to the base station on the shore. We assumed that our network scenario was similar to the networks in [8; 9; 10]. The underwater sensor nodes are mobile due to water currents with velocities of around 1-3 m/s; therefore, the topology changes rapidly. A table of notations is listed in Table 1. The assumptions of the network can be described as follows:  
* The node knows its location and the location of the sink node upon first deployment. * Nodes can become either the cluster head, cluster relay, or cluster member. * The cluster head is rotated between the sensor nodes to conserve energy. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Description** \\ \hline \(N\) & Number of nodes \\ \(S_{0}\) & Sink node \\ \(S_{\text{i}}\) & Sensor node index \(i\), \(1\leq i\leq N\) \\ \(L\times L\times L\) & Three-dimensional network deployment \\ \(Tx\) & Transmission range of node \\ \(n_{depth}\) & Number of layers \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of notations. The depth of deployment can be divided into layers, where each layer is defined by the transmission range of the node or sink, as given in (1):  
\[n_{depth}=\frac{L}{Tx}, \tag{1}\]  
where \(L\) is the depth of network deployment and \(Tx\) is the transmission range of the node or sink. In the paper, we divide the depth of the network, as shown in Figure 1. The depth of the network is divided into four cases: (1) the sink node at the surface, denoted \(D_{0}\); (2) nodes stay near the surface, whose depth is \(D_{1}\); (3) nodes stay in the water, whose depth is \(D_{2}\); (4) nodes stay near the seabed, whose depth is \(D_{3}\), where \(D_{3}>D_{2}>D_{1}>D_{0}\). The role of the nodes can be explained as follows:  
* Each layer has several clusters, each cluster having one cluster head and a cluster member. For example, node \(S_{3}\) is the cluster head at depth \(D_{1}\) and node \(S_{9}\) is the cluster head at depth \(D_{2}\). * Nodes located at the border of two layers can adopt the role of cluster relay, which forwards the data of the deeper layer to the sink. For example, node \(S_{5}\) becomes a cluster relay which forwards the data of cluster \(S_{9}\) to cluster \(S_{3}\) and then transmits to the sink node. * Node \(S_{13}\) located at the seabed takes the multi-hop routing path to the sink via clusters of \(S_{12}\)-\(S_{9}\)-\(S_{5}\)-\(S_{3}\)-\(S_{1}\)-sink. The propagation loss model of the underwater acoustic channel is assumed, as in [3]. Since the signals propagate vertically, attenuation increases, which is proportional to increasing distance. The transmission loss is calculated as follows: \[TL=k_{TL}\times 10\lg r+\alpha_{TL}r\times 10^{-3},\] (2) where \(TL\) represents the transmission loss in dB; \(k_{TL}\) is the spreading factor, which indicates the spreading loss, its value depending on the water depth and corresponding to the propagation geometry; \(k_{TL}=1\) in shallow water and cylindrical spreading; \(k_{TL}=2\) for deep water and spherical spreading; \(\alpha_{TL}\) represents the absorption coefficient of the medium, which depends on the frequency, its unit being dB/km; \(r\) is the distance between the receiver and transmitter.