# Research on the Coverage of Ultraviolet Communication Network in the Arbitrary Polygon Area
## 1 Introduction  
With the rapid development of communication technology, the communication system applied in the complex electromagnetic environment is gradually developed for the integration of communication and resistance. Traditional wireless communication has been unable to meet the requirements of the complex and changeable electromagnetic environment, and its problems such as low confidentiality and susceptibility to interference are gradually exposed. \"Solar blind zone\" ultraviolet (UV) communication has excellent characteristics rarely available in other signal sources such as low background light interference, non-line-of-sight (NLOS) scattering communication, strong anti-jamming ability and high confidentiality, showing its potential as a supplement to traditional radio communication means [1]. The integration of UV communication and the Ad hoc network can give full play to their unique advantages. In addition, the distance of UV communication has been greatly expanded with the multi-hop transmission performance of the Ad hoc network. Therefore it has broad application prospects in the field of wireless, secure communication in unmanned aerial vehicle (UAV) terminals. It should be noted that the high-power UV light source can cause some damage to the eyes and skin. Therefore, when it is used, the power of the light source should be strictly controlled according to safety regulations. As early as the 1960s, the U.S. Navy began to pay attention to UV communication, hoping to realize NLOS scattered light communication [2, 3]. [PERSON] et al. proposed three improvement measures for the Monte Carlo method commonly used in UV scattering simulation [4]. In 2019, a UV scattering model applied in both strong and weak turbulence was proposed [5]. [PERSON] et al. took the lead in using a UV source pumped by an electron beam to test and analyze the characteristics of the UV scattering link [6]. In 2020, the bit error rate of the system was reduced by using diversity technology at the receiver end of the UV communication system [7]. The UV network needs to cover the entire target area in order to achieve reliable communication. [PERSON] et al. deduced the probability expression of isolated nodes in a circular area for UV network coverage and used a network model based on multi-hop nodes to expand its communication range [8]. The literature [8] simulated and analyzed the influence of transmitted power, node density, data rate and bit error rate on network coverage under OOK and PPM modulation modes but only discusses the working mode of vertical transmission and vertical reception. [PERSON] et al. took the lead in discussing the impact of various parameters on the performance of the UV network under different working modes, while the connected state under discussion is only a 1-connected network [9]. At present, the studies on the coverage of the UV network are all based on the circular area. In our previous research, the UV network connectivity in the circular area under different working modes also has been studied [10]. However, in reality, most distribution areas of the UV nodes are irregular shapes rather than the standard circle. This article creatively analyzes the UV coverage under the condition that the UV nodes are uniformly distributed in an arbitrary convex polygon area and mathematically discusses the influence of different parameters on network performance. The research on the connectivity of the UV network in an arbitrary polygon region can break the restriction of the regular circular distribution region and provide a higher reference value for practical network construction. The rest of the paper is organized as follows. The UV communication model and the basic concepts of network coverage are introduced first in Section 2. Then the influence parameters of the UV node communication radius are studied. The mathematical expression of k-connectivity of UV network in an arbitrary convex polygon is derived in Section 3. Section 4 gives the mathematical analysis of the simulation results.