## 4 Systematic Performances Analysis of UWSNs
### Systematic Quar-Performance Calculation Model of UWSN
#### 4.2.1 Measurement Formula of Coverage  
Coverage is denoted as \(\Theta\), which is determined by the coverage scope and the detection capacity within the coverage scope. Assuming the underwater detection scope of the sensor node is a standard ball-body, then the coverage volume of each node is about \(\frac{4}{3}\cdot\pi\cdot d_{b}^{3}\), for all sensor nodes, and the coverage scope of the network is about \(\frac{n_{b}\cdot\frac{4}{3}\cdot\pi\cdot d_{b}^{3}}{c_{b}}\). Because an UUV can move to a specified location in underwater space, its contribution rate to the network coverage scope is related to its location: when an UUV locates inside an UWSN, its contribution is zero; when an UUV locates at the edge of an UWSN, there is a direct proportional relationship between its contribution and its detection scope. The coverage scope of the UWSN can be measured by Equation (2):  
\[\frac{n_{b}\cdot\pi\cdot d_{b}^{3}}{c_{b}}+\theta\cdot n_{u}\cdot d_{u}^{3} \tag{2}\]  
In this equation \(\theta\) represents coefficients. \(\theta>0\) stands for the average contribution rate of the UUV to the coverage scope, and it is dominated by the proportion of the vehicle cruise route inside and outside the UWSN.  
Detection performance of the network is dominated mainly by the average degree of coverage and the precision of node detection. A wider average degree of coverage and higher detection precision guarantees stronger detection performance of the network. The average degree of coverage is mainly  
\begin{table}
\begin{tabular}{l c l c} \hline \hline
**Sensor Node Parameters** & **Label** & **Master and Mobile Node Parameters** & **Label** \\ \hline underwater communication radius & \(r_{b}\) & mobile node velocity & \(v_{u}\) \\ underwater communication bandwidth & \(b_{b}\) & mobile node underwater communication bandwidth & \(b_{u}\) \\ overwater communication bandwidth & \(b_{b}\) & mobile node detected radius & \(d_{u}\) \\ detected radius & \(d_{b}\) & mobile node detected precision & \(h_{u}\) \\ detected precision & \(h_{b}\) & mobile node number & \(n_{u}\) \\ number & \(n_{b}\) & mobile node total energy & \(e_{u}\) \\ total energy & \(e_{b}\) & mobile node energy consumption & \(p_{u}\) \\ average energy consumption & \(p_{b}\) & master node velocity & \(v_{s}\) \\ average connectivity & \(k_{b}\) & master node underwater communication bandwidth & \(b_{s}\) \\ average coverage & \(c_{b}\) & master node number & \(n_{s}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters and labels.  
influenced by the number of sensor nodes. In addition, UUVs can detect the nearby area while cruising, so detection performance can be represented by Equation (3):  
\[\left[1-\left(1-h_{b}\right)^{c_{h}}\right]+\varphi\cdot h_{u} \tag{3}\]  
In this equation, \(\varphi\) represents coefficients, and \(\varphi>0\) indicates the UUV's average contribution rate to detection performance, which depends on the proportion inside and outside the UWSN when the UUV is cruising. In summary, the coverage of network can be measured by Equation (4):  
\[\Theta=\alpha\cdot\frac{n_{b}\cdot\pi\cdot d_{b}^{3}}{c_{b}}\cdot\left[1-\left( 1-h_{b}\right)^{c_{b}}\right]+\beta\cdot n_{u}\cdot d_{u}^{3}\cdot h_{u} \tag{4}\]  
In the equation, \(\alpha\), \(\beta>0\) represents the relative contribution coefficient between the sensor network and the UUV.