# Efficient Data Gathering in 3D Linear Underwater Wireless Sensor Networks Using Sink Mobility
## 4 Framework and Formal Definition of the Problem
### Energy Consumption Model in UWSNs  
Nodes deployed in the underwater network field are powered by batteries. Energy consumed in sensing and processing data is negligible as compared to the data transmission and reception. Transmission power depends on the distance and transmission range. With the propagation model, we estimate the transmit power for a specified signal-to-noise ratio (SNR). We use the energy consumption model for the acoustic communication given in [20]. The SNR equation for passive sonar is calculated in Equation (24):  
\[SNR=SL-TL-NL+DI\geq DT \tag{24}\]  
where SL represents the source level, TL is the transmission loss and \(NL\) is the noise level of the receiver and the environment. The directive index is denoted by DI. The sonar's detection threshold is DT. The TL for nodes in the underwater environment is calculated in Equation (25) by the Thorp model in [4], _i.e._,  
\[TL=10 log(d)+\alpha d\times 10^{-3} \tag{25}\]  
where \(d\) denotes the distance between the sender and receiver and \(\alpha\) is the absorption coefficient. In Equation (24), noise loss is calculated by Equation (23). \(SL\) can be calculated from Equation (24):  
\[SL=SNR+TL+NL-DI \tag{26}\]  
Transmitted signal intensity is calculated as:  
\[I_{T}=10^{5L/10}\times 0.67\times 10^{-18} \tag{27}\]  
and transmitted power by source is:  
\[P_{T}(d)=2\pi\times 1m\times H\times 10^{5L/10}\times 0.67\times 10^{-18} \tag{28}\]  
Equation (29) determines the energy required for the transmission of \(k\) bits over a distance \(d\):  
\[E_{tx}(k,d)=P_{T}(d)\times T_{tx} \tag{29}\]where \(T_{tx}\) is the time in seconds that \(k\) bits take to reach the destination by covering \(d\) distance. Consider a network with \(N\) number of battery-operated wireless nodes; they are randomly deployed in the field, and they will remain stationary afterwards. All of the nodes in the network have an equal sensing range and an equal amount of initial energy. A node performs four major tasks: sensing, computing, reception and transmissions. In UWSNs, nodes use acoustic communication for data transmission, and this has a large propagation delay. To save energy, a sleep/awake mechanism can be introduced into the network. However, due to the long propagation delay, nodes may not be able to receive the control message from the MS and become active immediately. In our proposed scheme, nodes stay active till their death. UWSNs are different from terrestrial WSNs in terms of the low communication bandwidth and ocean current. This scheme follows the following two steps:  
* **Association phase:** i The MS has the information of its location \((X_{tt},Y_{n},Z_{n})\), where \(n=1\), \(2\), \(3\), \(4\). ii The MS collects data from in range neighbors by calculating the distance, _i.e._, \(d(n_{i0})=\sqrt{(x_{i0}-X_{n})^{2}+(y_{i0}-Y_{n})^{2}+(z_{i0}-Z_{n})^{2}}\leq R\), where \(n_{i0}\) is a single node with location coordinates \((x_{i0},y_{i0},z_{i0})\) and \(R\) is the radius of the sensing range of the MS. iii Nodes that are non-neighbors of the MS find the \(C_{i}\) for data forwarding. They find minimum distance \(C_{i}\), \(d(n_{i1})=\sqrt{(x_{i1}-x_{ci})^{2}+(y_{i1}-y_{ci})^{2}+(z_{i1}-z_{ci})^{2}} \leq r\), where \(n_{i1}\) is the single node with location coordinates \((x_{i1},y_{i1},z_{i1})\), _i.e._, the non-neighbor of the MS, and \(r\) is the sensing and transmission radius of \(C_{i}\). iv A node sends the sensed data to the MS directly if \(d(n_{i})\leq R\); otherwise, it waits until the MS arrives at the nearest stop. The same condition applies for those nodes that send their data to \(C_{i}\), if \(d(n_{i})\leq r\). * **Collection phase:** After the start of network operation, all nodes are in active mode and sense data from the field.