# High-Efficiency Clustering Routing Protocol in AUV-Assisted Underwater Sensor Networks
## 2 System Model  
The underwater sensor network consists of sink nodes, sensor nodes, and an AUV. The sink nodes are deployed on the water surface, and after satellite relaying, they can transmit data to and from the ground base station via radio communication. Each sensor node may become a cluster head (CH) node or a cluster member (CM) node. In each round of communication, the CHs fuse the data from the CMs and send the information to the sink node through one-hop or multihop communication, while the AUV acts as a dynamic relay node for relaying messages between CHs that cannot communicate owing to long distances. The network model is shown in Figure 1.  
Within this study, the energy consumption model for hydroacoustic communication described in the literature [17] is used to describe the energy scenario of the network, assuming that a sensor node transmits kb bits of data at a transmission rate \(T_{r}\) over a distance \(d\). The energy consumed by the sensor node is defined as follows:  
\[E_{T}=\frac{kb}{T_{r}}*P_{rx} \tag{1}\]  
where \(P_{rx}\) is the transmission power of the node.  
If a sensor node receives \(kb\) bits of data, the energy consumed by that sensor node is defined as follows:  
\[E_{R}=\frac{kb}{T_{r}}*P_{rx} \tag{2}\]  
where \(P_{rx}\) is the received power of the node.  
It is also important to consider the data fusion energy consumption, which is the amount of energy required to fuse \(kb\) bits of data:  
\[E_{A}=kb*E_{DA} \tag{3}\]  
Figure 1: Network model.  
where \(E_{DA}\) is the energy consumed to fuse the data per unit length.  
In underwater sensor networks, the movement of nodes with ocean currents is a crucial factor. In this paper, we use the meandering current mobility model (MCM) [18] to simulate node movement. The MCM uses a two-dimensional model to simulate the movement of underwater nodes because oceans are rotating stratified fluids, and most of the vertical motion can be ignored. Assuming that the coordinates of the plane of the node with deployment number \(i\) are \((x_{i},y_{i})\), the movement function of this node in time \(t_{m}\) can be given by the following equation:  
\[\Psi(x_{i},y_{i},t_{m})=-\text{tanh}\left[\frac{y_{i}-B(t_{m})\text{sin}(k(x_{i }-ct_{m}))}{\sqrt{1+k^{2}B^{2}(t_{m})\text{cos}^{2}(k(x_{i}-ct_{m}))}}\right] \tag{4}\]  
where \(k\) is the number of meanders in the unit length, which is usually \(2\pi/7.5\). \(c\) is the phase speed at which the phases shift downstream, usually \(0.12\).  
\(B(t_{m})\) is the current amplitude function, defined as follows:  
\[B(t_{m})=A+\varepsilon\text{cos}(\omega t_{m}) \tag{5}\]  
where \(A\) denotes the average width of the ocean current; usually \(1.2\). \(\varepsilon\) is the modulation amplitude, usually \(0.3\). \(\omega\) is the modulation frequency, which can be taken as \(0.4\).  
Therefore, the plane coordinates \(\left(\dot{x}_{i},\dot{y}_{i}\right)\) of sensor node \(i\) after moving with the ocean current after time \(t_{m}\) can be calculated by the following equation:  
\[\dot{x}_{i}=-\frac{\partial\Psi(x_{i},y_{i},t_{m})}{\partial y_{i}} \tag{6}\]  
\[\dot{y}_{i}=\frac{\partial\Psi(x_{i},y_{i},t_{m})}{\partial x_{i}} \tag{7}\]