# A Biologically Inspired Self-Organizing Underwater Sensor Network
## 3 Problem Statement and Solution  
The problem that we seek to solve in this paper is to obtain a scheme to coordinate the wireless communication of nodes in a large-scale wireless underwater sensor network. As shown in Figure 1, \(N\) sensor nodes are randomly deployed into the area of interest by a ship or a plane, where \(N\) can reach tens, hundreds, or thousands. Once deployed, these nodes sink underwater and float at a certain depth, collecting information within their detection ranges. As all nodes are underwater, they can only communicate with each other via acoustic signals, with the communication range being \(r\). Here it is assumed that a high-frequency acoustic signal is adopted, and thus \(r\) is of hundreds of meters, with communication speed being several Kbps. Among these nodes, there is a special node called a base station that is connected to an antenna floating at the surface of the water. Thus, the data collected by other nodes are transmitted to the base station node jump-by-jump via acoustic communication and are finally sent to the control center via radio signals by the base station node. Consequently, even though nodes can be deployed randomly, they must form a connected graph (treating nodes as vertexes and assigning an edge between a pair of nodes whose distance is less than \(r\)), otherwise messages from some nodes are unable to reach the base station. With acoustic communication, if one node hears multiple signals at the same time, or it hears signals while speaking at the same time, the node is unable to parse the information contained in the signal. In this paper, this phenomenon is called communication collision. To define this concept formally, let us define \(dis(i,j)\) as the distance between Nodes \(i\) and \(j\). If \(dis(i,j)<r,i\
eq j\), we call Node \(j\) the first-order neighbor of Node \(i\), and vice versa. Further, if there exists Node \(k\) that satisfies:  
\[dis(i,j)<r\wedge dis(j,k)<r\wedge dis(i,k)>r,\]  
then we call Node \(k\) the second-order neighbor of Node \(i\). Intuitively, a second-order neighbor represents a neighbor's neighbor. Note that the neighbor relationship is defined based on the relative position of nodes. If the nodes' positions change, the neighbor relationship may also change. In the following sections, variables defined for first-order neighbors are  
Figure 1: Illustration of a wireless underwater sensor network. Nodes are randomly deployed and float at a certain depth. The nodes communicate with each other via underwater acoustic communication. There is a special node called a base station that is connected with a radio antenna floating at the surface of the water. Information obtained by sensor nodes is sent to the base station, and the base station sends messages to the control center via radio. As communication collision can happen if acoustic signals are sent improperly, each node is equipped with a controller called a communication coordinator, which is used to control when and what a node broadcasts via acoustic signals. The communication coordinator is designed in this paper. indicated with subscript \({}_{1-neighbor}\) and for second-order neighbors with subscript \({}_{2-neighbor}\). The subscript \({}_{12-neighbor}\) indicates variables with both first-order neighbors and second-order neighbors. The definition of the neighborhood is shown in Figure 2.  
According to the definition of communication collision and neighborhood relationship, it can be obtained that for Node \(i\), let \(S_{1-neighbor}\) be the set of all its first-order neighbors and \(S_{2-neighbor}\) be the set of all its second-order neighbors. If the following conditions are satisfied, no communication collision will happen on Node \(i\). The conditions are:  
* At most one member in \(S_{1-neighbor}\cup i\) speaks at the same time. * When \(i\) speaks, no node in \(S_{2-neighbor}\) speaks.