## 3 Cross Deployment Networking Method
### UWSN Deployment Process Based on Improved Body-Centered Cubic Lattice  
The UWSN nodes need to be deployed in a certain environment, and they are influenced by the environment and the physical properties of the nodes themselves. The optimal ball-body coverage mode is a body-centered cubic lattice, whose normal coverage (NBCL) is shown in Figure 1a. In NBCL, the body-centered cubic lattices structure is piled up layer by layer by regular ball-bodies. If the boundary effect is ignored, this network topology needs less nodes for certain monitored spaces, but the ratio of energy consumption in the UWSN will become much larger, so we improve the NBCL to a Cross Body-centered Cubic Lattice (CBCL), shown as Figure 1b. In CBCL, the ball-bodies on the higher level are cross stacked over the spaces between ball-bodies on the next layer, and the cubic space is divided into hierarchies and monitors from the top down. The basic idea of CBCL generation is to utilize the vertical movement of sensor nodes to generate a similar body-centered cubic lattice from a planar square lattice. First, randomly distributed nodes on the plane are included into the Voronoi cell of different planar square lattices. Nodes in the same cell decide whether to enter the active state based on the states of other nodes in the cell. At the same time, the monitored space is divided in terms of the Voronoi cells of a body-centered cubic lattice. The moving depth of the sensor nodes is determined by the coverage scope of the body-centered cubic lattice. By moving in a vertical direction the nodes are deployed in the Voronoi cells of the body-centered cubic lattice hierarchically. With an adequate number of active nodes, the CBCL can form a 3D underwater monitoring network, which effectively reduces the energy consumption of the network without affecting the coverage scope. If this CBCL structure is projected onto a plane it forms a planar square lattice CL shown in Figure 1c, and the planar square lattice of NBCL as CL. The Voronoi centre of each layer is distributed on the vertex of CL. Figure 1: (a) NBCL, (b) CBCL and (c) Planar square lattice of NBCL. We assume that the monitored space length is \(x\), width is \(y\), depth is \(z\), detection radius of the sensor is \(d_{b}\), and the number of columns, lines and layers along the direction of \(x\), \(y\), \(z\) are \(n_{1}\), \(n_{2}\), \(n_{3}\), respectively, and the distance between sensor nodes in the same layer is \(a\). The position relationship of sensor nodes in NBCL when the monitored space is overcovered, is shown in Figure 2. In Figure 2a, the relationship between the \(d_{b}\) and \(a\) is \(\sqrt{2}d_{b}\leq a\leq 2d_{b}\). In Figure 2b, \(h\) represents the height of common coverage area among three sensor nodes, then \(h\) meets of \(h=\sqrt{r^{2}-a^{2}/3}\), and the spacing of layers could be expressed with \(H=Q_{1}O_{1}+h\). When \(d=2d_{b}\), \(h=0\) and \(H=\sqrt{2}d_{b}\). Figure 2c is the vertical view of the deployment of sensor nodes, and \(l\) and \(L\) represent the line distance and column distance of the nodes ranked according to the width and the length of the monitored space, respectively, then \(l=a/2\) and \(L=a\). Then the number of sensor nodes for the monitored space is \(N\), hence, the formula (1) will be obtained:  
\[ \begin{split}(n_{1}-1)L\leq x,(n_{1}-1)L+L\geq x,(n_{1}-1)L+\frac {L}{2}\leq x\\ (n_{2}-1)l\geq y,(n_{3}-1)H+2h\geq z\\ N=n_{1}n_{2}n_{3}-\frac{n_{2}}{2}n_{3}\end{split}  \tag{1}\]  
In accordance with space geometry, the relationship between the coverage radius \(R_{bcc}\) of the CBCL and coverage radius \(R_{CL}\) of the planar square lattice CL can be computed. A unit of CBCL is shown in Figure 2a, in which the side length of the cubic body is \(a\). Figure 2b shows the relationship between lattice packing radius \(\rho_{bcc}\) and side length \(a\), thus: \(\rho_{bcc}=\frac{\sqrt{3}a}{4}\) and \(R_{bcc}=\sqrt{\frac{5}{3}}\rho_{bcc}\), \(R_{bcc}=\frac{\sqrt{5}a}{4}\).