# Energy-Efficient Clustering Multi-Hop Routing Protocol in a UWSN
## 3 Energy-Efficient Clustering Multi-Hop Routing Protocol
### Network Model
The absorption coefficient for the medium is measured in dB/km for \(f\) in kHz; the equation for calculation is as follows: \[\alpha_{TL}(f)=0.11\frac{f^{2}}{1+f^{2}}+44\frac{f^{2}}{4100+f^{2}}+2.75\times 1 0^{-4}f^{2}+0.003,\] (3)  
The absorption coefficient increases with increasing frequency. In UWSNs, the frequency is approximately 30 kHz; the absorption coefficient is less than 10 dB/km. The absorption coefficient is derived for chemical absorption in seawater in terms of acoustic frequency, pressure, acidity, temperature, and salinity. The constant values are calculated using [PERSON]'s expression, which denotes the relaxation frequency for different chemical \begin{table}
\begin{tabular}{c c} \hline
**Notations** & **Description** \\ \hline _Nei(\(S_{i}\))_ & List of neighbors of node \(S_{i}\) \\ \(D_{m}\) & Depth layer index \(m\), \(0\leq m\leq n_{depth}\) \\ \(Lst(D_{m})\) & List of sensor nodes at depth \(D_{m}\) \\ \(TL\) & Transmission loss of acoustic signal \\ \(\alpha_{TL}(f)\) & Absorption coefficient for the medium \\ \(W_{i}\) & Weight of sensor node \(S_{i}\) \\ \(d(i,j)\) & Distance between node \(S_{i}\) and node \(S_{j}\) \\ \(d(i,S_{0})\) & Distance between node \(S_{i}\) and the sink \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._absorptions, the value of the acidic component and pH of the seawater, and the depth pressure of the seawater. Interested readers can refer to [22] for more details. Based on the energy consumption model presented in [3,8,9], the least transmission power required at the transmitter to achieve power level \(P_{0}\) at the receiver can be expressed by  
\[P_{tx}=P_{0}\times d^{2}\times 10^{(\alpha_{TL}(f)/10)}, \tag{4}\]  
where \(P_{0}\) is the received power, \(d\) is the distance between the transmitter and receiver, and \(\alpha_{TL}(f)\) is the absorption coefficient, which is shown in Figure 2.  
Since the characteristic of an acoustic wave in an underwater transmission medium is different from that of a radio wave, the energy consumption of wireless sensor networks cannot be applied to UWSNs. In the present paper, we apply the energy consumption model of the underwater acoustic channel as adopted in [3,12]. To transmit \(k\) bits of data over distance \(d\) with a data rate \(R\), the energy consumed is defined as follows:  
\[E_{Tx}(k,d)=k\times E_{elc}+\frac{k}{R}P_{tx}, \tag{5}\]  
where \(E_{elc}\) is the energy consumption to route 1 bit of data, and \(P_{Tx}\) is the transmitted power, which is shown in equation (4). To receive \(k\) bits of data, the receiver radio energy consumption can be expressed as  
\[E_{Rx}(k)=kP_{r}, \tag{6}\]  
where \(P_{r}\) is a constant dependent on the device. To fuse \(k\) bits of data, the energy consumption can be defined as  
\[E_{DA}(k)=k\times E_{DA0} \tag{7}\]  
where \(E_{DA0}\) is the energy consumed by fusing one bit of data, which can be taken as \(5\,\mathrm{nJ}/\mathrm{bit}\). Since nodes are mobile due to the water current, we deploy random movement for nodes during the operating time. The current velocity is 1-3 m/s.