## 3 Cross Deployment Networking Method
### UWSN Deployment Process Based on Improved Body-Centered Cubic Lattice
Figure 1c shows a part of the planar square lattice CL, which is projected from the CBCL onto a plane. The coverage radius of the planar square lattice is the circumscribed circle radius of the Voronoi cell, thus \(R_{CL}=a/2\) and \(R_{CL}=\frac{2\sqrt{5}}{5}R_{bcc}\). As all sensor nodes are deployed on the sea surface in the beginning, they can be seen as being on the same plane. The improved CBCL divides the nodes on the plane into different square cells according to the square lattice CL. We set the coverage radius of the square lattice CL to \(R_{CL}\), then the coordinates of the reference point are \((x_{c}\),\(y_{c})\), thus the coordinates of lattice point in CL are \((x_{c}+u\sqrt{2}R_{CL},y_{c}+v\sqrt{2}R_{CL})\), where \(u\) and \(v\) are integers. A square lattice can be uniformly represented by a binary set (\(u\),\(v\)), thus (\(u\),\(v\)) is used as the ID of the lattice point. The square cell ID of any node on the plane is that of the lattice point closest to the node. In order to complete the 3D network node deployment, the sensor nodes must be sunk to different depths. The network is generated by planar nodes in accordance with the CBCL, so we need to distinguish the type of the square lattice point which the node belong to. According to Figure 1, the CL contains two types lattice point: type 1 and type 2. If the ID of Voronoi cell in type 1 and type 2 are respectively (\(u_{1}\),\(v_{1}\)) and (\(u_{2}\),\(v_{2}\)), we consider the following theorem:  
**Theorem 1**. : _In square lattice CL, the sum of \(u_{1}\) and \(v_{1}\) in type 1 is \(W_{1}=u_{1}+v_{1}\), and the sum of \(u_{2}\) and \(v_{2}\) in type 2 is \(W_{2}=u_{2}+v_{2}\). One of \(W_{1}\) and \(W_{2}\) must always be odd, and the other must always be even._  
Figure 2: (a) Front view, (b) Common coverage area and (c) Vertical view. For example in Figure 1c, if the lattice point Lp\({}_{1}\) is the type 1, then \(W_{1}=u_{1}+v_{1}\). If Lp\({}_{2}\) belongs to type 2, then \(W_{2}=u_{2}+v_{2}=(u_{1}+1)+v_{1}\), so if \(W_{1}\) is an odd integer, that the \(W_{1}\) must be an even integer. Suppose the initial depth of the network monitoring 3D underwater space is \(D_{0}\), and its maximum depth is \(D_{m}\). According to the CBCL in Figure 1, the monitored space is stratified from top to bottom in the light of the plane of the CBCL. The distance between adjacent layers is called inter-laminar space, represented by \(d_{1}\), and as Figure 2a shows, \(d_{1}=\frac{2\sqrt{5}}{5}R_{hcc}\), when the coverage radius of the \(CBCL\) is \(R_{hcc}\). Hence the depth of \(i\) layer in monitored space is \(D_{0}+i.d_{i}\), \(I=0\), \(1\), \(\cdots\), \(n-1\), where \(n=(D_{m}-D_{0})/d_{1}+1\). Assume the square cell ID of a node on the plane is (\(u\),\(v\)). Generally, the sensor nodes are deployed in the even layer when \(u+v\) is even; the sensor nodes are deployed in the odd layer when \(u+v\) is odd. Assume that sensor nodes are continually placed in the lattice points of the planar square CL in Figure 1, and they move down layer by layer according to the above method. In that way the network in the CBCL structure is generated. In practice, the positions of the sensor nodes on the plane are not overlapping. Some redundant nodes can be selected to generate a network in an approximate CBCL structure in the same way. As analyzed above, the network deployment process and topology generation method can be described as in Figure 3.  
From Figure 3, the steps of the method are described as follows:  
1. Place the sensor node randomly on the ocean surface. After anchoring, it calculates the ID of the unit it belongs to according to its coordinates (obtained by GPS) and the pre-designated reference points, then enters into sleep state. The sleep time of nodes obeys the index distribution [7], and the probability density function is \(f(t_{s})=\lambda e^{-\lambda t_{s}}\), where \(\lambda\) is the startup speed; \(t_{s}\) is the sleep interval.