## 4 Slp-macgt Model Design
### Transformation Method Based on a Virtual Coordinate System  
The virtual coordinate system is a technique used to locate nodes in a network. It does not rely on global location information, but it uses relative coordinates to represent the positional relationships between nodes. In this paper, the virtual coordinate system is combined with underwater acoustic sensor networks to protect the source location privacy, assuming that the location information of sensor nodes can be obtained by existing localization algorithms [31]. In underwater acoustic sensor networks, each node can generate virtual coordinates using its own physical location and the relative location information of neighboring nodes. Graph theory is used to model the communication relationships between nodes in underwater acoustic sensor networks in which sensor nodes can be represented as nodes in the graph and the relationships between sensors can be represented as edges in the graph, namely, \(G=(V,E)\). As shown in Figure 2, the graph is traversed according to a breadth-first search to determine virtual coordinates for each node. First, node A is selected as the initial node and given the coordinate (0). All the neighbors of node A are found, and the neighbor nodes are numbered according to the binary representation. For example, node A has three neighboring nodes B, C, and D with numbers 00, 01, and 10, respectively, and the coordinates are \((-1,1)\), \((-1,1)\), and \((1,1)\), respectively. Node B has two neighbors, E and F, whose numbers are 00 and 01 and whose coordinates are \((-2,\,-2,\,-1,\,-1)\) and \((-2,\,-2,\,-1,\,1)\), respectively. Node C has three neighbors D, G, and H. Since node D has virtual coordinates, the coordinates of node D are unchanged, and the coordinates of neighboring nodes G and H are \((-2,\,2,\,-1,\,-1)\), and \((-2,\,2,\,-1,\,1)\), respectively. The remaining nodes are traversed by the same graph traversal method to determine their virtual coordinates.  
The nodes maintain a mapping table that corresponds virtual coordinates to actual locations. These virtual coordinates are only used for internal calculations and do not reveal actual geographic location. When data need to be transmitted, a node can use the virtual coordinate system to select the next-hop transmission node. During data transmission, nodes can map virtual coordinates back to actual geographic coordinates to determine the actual transmission path of the data. This mapping process should take place inside the node and does not need to be propagated outside. Before the source node sends data, the virtual coordinates of the source node can be obfuscated or encrypted to protect the sourcelocation's privacy. Only the nodes inside the network know how to decrypt or restore these coordinates.  
Combined with the virtual coordinate system, the underwater acoustic sensor network can achieve source location privacy protection to a certain degree. The virtual coordinate system allows nodes in the network to perform routing and data transmission according to their relative positions without revealing actual geographic coordinate information, ensuring that the geographic locations of the source nodes are not easily determined by external malicious parties or potential attackers. Moreover, each node only knows the location of itself and its neighboring nodes and does not need to obtain the location information of all nodes in the network, which saves storage space and improves security.