# Topology Control of Low-Connection UAV Laser Network with Virtual Nodes
## 2 Related Works  
In 2022, [PERSON] and colleagues conducted a study on unmanned-aerial-vehicle-based free space optics (FSO) communication using modulating retro-reflector technology [13]. They developed models that consider atmospheric turbulence and fluctuations in the vehicle's orientation and created analytical expressions for signal-to-noise ratio, outage probability, and bit error rate. Then, in 2023, [PERSON] et al. developed a new FSO channel model to enhance the performance of UAV-based FSO relay systems under pointing errors and atmospheric turbulence, finding that a higher signal-to-noise ratio is needed to maintain low error rates as wind variance increases [14]. The study concluded that relay-assisted UAV-FSO systems perform better than conventional FSO systems in terms of error rate and signal-to-noise ratio. The two papers concentrated on the channel issues of UAV nodes during FSO communication, and, as another important aspect of UAV laser communication, the connectivity capabilities of UAVs are also a topic that requires research.  
In 2021, the team led by [PERSON] at the Wuhan National Information Optoelectronics Innovation Center designed an eight-channel silicon-based optical phased array chip capable of producing 1-5 output beams but with a transmission distance limited to only 15 cm [10]. Similarly, [PERSON] and [PERSON] utilized a managedoptical communication array based on liquid crystal phased array devices, along with time-division multiple access technology, to achieve a laser communication terminal capable of one-to-four-point communication [11]. While these studies enhance the connectivity of laser terminals, they still fail to meet the high connectivity demands of traditional topology control.  
Therefore, developing a topology control algorithm to effectively reduce the upper limit on node degree to the threshold achievable with the current laser communication technology is undoubtedly a feasible and forward-looking solution.  
The research on self-organizing network topology control originated in 1986 [15]. The Gabriel Graph (GG), proposed by [PERSON] in Ref. [16], is constructed based on the following principle: for any two nodes in the graph, if the circle with its diameter equal to the distance between these nodes contains no other nodes, then there exists a connection between the two nodes. The upper node degree limit in a GG graph itself is degree\({}_{+}=n-1\).  
The Relative Neighborhood Graph (RNG), introduced by [PERSON] et al. in Ref. [17], is constructed based on the criterion that, if no other node is closer to both of the two nodes in question than the distance between them, a connection exists between the two nodes. Similarly, the upper node degree limit for an RNG graph itself is also degree\({}_{+}=n-1\).  
[PERSON] and colleagues, in Ref. [18], developed a construction algorithm known as XTC (exceptional topology control) that achieves a node degree upper limit of six by sorting and comparing neighboring nodes. Their algorithm's main idea is that, if there exists a node whose ranking is higher than the rankings of these two nodes in each other's lists, then these two nodes will not connect. If the distances between any node and its neighboring nodes are all distinct, then the outcome of the XTC algorithm is equivalent to an RNG graph. While these approaches can effectively construct neighbor graphs, the node degree limits they impose still do not meet the requirements of UAV laser networks.