Ultraviolet Network Coverage Based on Non-Line-of-Sight Channel

Ultraviolet (UV) networks, owing to their advantages of low eavesdropping rates, low background noise, strong anti-interference abilities, and non–line-of-sight (NLOS) communication, have high prospects for application in the complex electromagnetic environment. In this study, UV network coverage was systematically evaluated based on the NLOS channel. Combined with a designed node model and a specific communication mode, a two-dimensional network coverage model was established and expressions of network coverage area and connectivity were derived mathematically. Subsequently, the effects of the transceiver elevation combination, number of nodes, data rate, and transmission power on the network coverage performance were analyzed, and the communication parameters were optimized to match different network scenarios. The results show that the bigger the transceiver elevation combination, the more stringent the communication parameters required by the UV network coverage. Finally, a coverage evaluation experiment with four-node network was conducted. This study provides theoretical reference information for actual network deployment.


Ultraviolet Network Coverage Based on
Non-Line-of-Sight Channel Cheng Li , Zhiyong Xu , Jingyuan Wang , Jiyong Zhao , and Jianhua Li Abstract-Ultraviolet (UV) networks, owing to their advantages of low eavesdropping rates, low background noise, strong antiinterference abilities, and non-line-of-sight (NLOS) communication, have high prospects for application in the complex electromagnetic environment.In this study, UV network coverage was systematically evaluated based on the NLOS channel.Combined with a designed node model and a specific communication mode, a two-dimensional network coverage model was established and expressions of network coverage area and connectivity were derived mathematically.Subsequently, the effects of the transceiver elevation combination, number of nodes, data rate, and transmission power on the network coverage performance were analyzed, and the communication parameters were optimized to match different network scenarios.The results show that the bigger the transceiver elevation combination, the more stringent the communication parameters required by the UV network coverage.Finally, a coverage evaluation experiment with four-node network was conducted.This study provides theoretical reference information for actual network deployment.
Index Terms-Connectivity, coverage evaluation, UV network.

I. INTRODUCTION
U LTRAVIOLET (UV) communication systems use the scat- tering of UV light in the atmosphere to realize information transmission [1].They have the advantages of low eavesdropping rates, low background noise (owing to the 200-280 nm "solar-blind" band), strong anti-interference abilities, and non-line-of-sight (NLOS) communication [2], [3].However, UV NLOS communication relies on scattering from aerosol particles in the atmosphere, leading to excessive path loss; and with the limitations of light power and photodetectors, the point-to-point communication distance is typically less than 500 m [4].Therefore, combining UV communication with an ad hoc network to construct a UV network can expand the restrictedcommunication distance, meeting the requirements of covert communication.Such networks have high application prospects in secure communication (including military networks), emergency services, disaster recovery, and in other complex electromagnetic environments [5].Unfortunately, high-power UV light sources cause damage to the eyes and skin; therefore, the power of the light source should be strictly controlled according to safety regulations.
Network coverage is a reference standard reflecting the quality of the communication service provided by a UV network, with goals including "coverage of the target area" and "multiconnectivity network" [6].Coverage evaluation is the basis UV network research.
Zhao proposed a coverage optimization strategy based on a genetic algorithm to improve the coverage range of UV networks [7].Ke et al. analyzed the effective coverage of UV networks based on the NLOS single scattering channel model [8].However, these studies only discussed UV network coverage and did not include in-depth research on network connectivity.
Conversely, Vavoulas proposed that the communication parameters affecting the network connectivity primarily include transmission power, supported data rate, and error probability [9].Under the random waypoint mobility model and circular movement-based node motion model [10], Zhao discussed the effects of communication parameters on UV network connectivity.However, the network model was built in a circular area and is not suitable for more general scenarios.
In this study, we systematically analyzed the coverage and connectivity of a UV network combined with a designed node model and specific communication mode.The main contributions of this article are as follows: 1) A two-dimensional network coverage model was mathematically analyzed based on the coverage evaluation parameters.Furthermore, expressions for the network coverage and connectivity were derived separately.
2) The effects of the transceiver elevation combination, number of nodes, data rate, and transmission power on the network coverage were analyzed, and the communication parameters were optimized to match different network scenarios.3) Based on a designed terminal, a coverage evaluation experiment was performed on a four-node UV network.The experimental results were compared with the simulation results, and the differences were analyzed.The remainder of this article is organized as follows.Section II introduces the communication modes coverage evaluation parameters and the designed node model.Section III explains the derivation of the network coverage performance.Section IV discusses the simulation results to analyze the influence of different communication parameters on network coverage.Section V is discusses the four-node UV network coverage  evaluation experiment.Finally, we summarize the conclusions of this study and discuss future prospects in Section VI.

A. Communication Modes
The UV NLOS communication model is shown in Fig. 1 [11], where V is the effective scatterer, l is the communication distance, and r 1 and r 2 are the distance from the transmitter T to V and the distance from V to the receiver R, respectively.The light signal was transmitted into the atmosphere at T and received at R after being scattered by V.
As shown in Fig. 2, the communication can be divided into three modes, according to the combination of angles θ 1 and θ 2 : NLOS-a for vertical transmission and vertical receiving, NLOSb for nonvertical transmission and vertical receiving, and NLOSc for nonvertical transmission and nonvertical receiving.These correspond to the three coverage models shown in Fig. 3, and a rectangular coordinate system was established [12].
In NLOS-a, the forward and backward scattering of the emitting beam are the same, and its coverage is a circular area.Compared with NLOS-a and NLOS-b, a communication system using the NLOS-c mode has a larger bandwidth, smaller delay, and longer communication distance, and its communication performance is evidently better [12]; however, it can only receive signals in a fixed direction.Because the performance of

B. Coverage Evaluation Parameters
The goal of coverage evaluation is to optimize and improve the network node resources for complete coverage over the regions of interest (ROIs), which is the premise and foundation for the establishment of a communication network [13].The evaluation parameters of network coverage primarily include the coverage and connectivity [14]: 1) Effective Coverage Area: The effective coverage area refers to the unified coverage of all nodes, that is, the remaining area of the coverage of all nodes except the overlapping regions [15].
2) Connectivity: M-connectivity evaluates the degree of connectivity among network nodes.In an m-connectivity network, any node in the network has at least m adjacent nodes that can communicate directly [16].The higher the connectivity, the more robust the network.

C. Node Model
To comprehensively utilize the advantages of the NLOS-c mode with a large bandwidth, small delay, and strong directivity and the reception omnidirectionality of the NLOS-b mode, a

TABLE I UV COMMUNICATION PARAMETERS
hexahedral UV terminal model with directional transmission and omnidirectional reception was creatively designed, as shown in Fig. 4.Each side had separate transmission and reception devices.A UV light-emitting diode (LED) array was used to increase the transmission power and improve communication performance.Furthermore, each side of the terminal was equipped with a photomultiplier (PMT) to increase the efficiency of detection and achieve omnidirectional reception.

A. Node Communication Distance
According to our previous study [17], the UV communication distance for on-off keying (OOK) is as follows: The loss exponent α and loss factor ξ are related to transceiver elevation combinations.R d , P e , P t , c, h, λ, and η are defined in Table I We determined the relationship between transceiver elevation angle and node communication distance, as shown in Fig. 5, for the UV communication parameters listed in Table I.
Fig. 5 demonstrates that the communication distance decreases with increasing transceiver elevation angle.Notably, a slight increase in the communication distance occurs as the transmission elevation angle increases from 40°to 50°.The  distance gain caused by an increase in the effective scatterer with an increase in the angle is greater than the path loss in this case.As elevation angle continues to increase, the path loss increases constantly and the communication distance decreases accordingly.

B. Network Coverage Area
We used the Boolean model to study the coverage [18].The Boolean coverage model is also known as the "0-1 model" because it has only two states: covered and not being covered, as shown in Fig. 6.Assuming that the coverage radius of node O is R, the coverage rate p(X) of node O at a certain point X is given as where d(O, X) represents the distance between nodes O and X. 1) UV Node: Without loss of generality, one side of the hexahedral node model described in Section II-C was randomly selected for the UV node coverage analysis.A single-side coverage model of the UV node was established, as shown in Fig. 7. Here, TO is the central axis; T and O are the vertex and center of the emitting light cone, respectively; Φ 1 is the beam divergence angle; θ 1 is the transmission elevation angle; and R 1 is the communication radius of the transmitter.The projection of From the geometric relationship between T AA , T OD and T OO , we obtain where The triangular area S B T D is given as The elliptical area S B C D A is given as where O D and O A are the semi-major and semi-minor axes of the ellipse, respectively.Forward scattering is evidently stronger than back scattering in the NLOS-c mode; therefore, the coverage of forward scattering is the primary factor to be considered.The coverage 2) UV Network: The square network deploys nodes efficiently and is convenient for networking, which is conducive to the rapid formation of network topology.Currently, square network deployment is widely used when the nodes are arranged to form communication networks [19], [20].Therefore, the coverage and connectivity of the UV network were analyzed on the basis of square networks in this study.The following assumptions were made during the performance analysis: a) All UV nodes have the same structure and communication parameter settings, including transmission power, data rate, and communication angles.b) The analysis is based on a two-dimensional plane.The communication distance of the UV node is l, and the coverage of the directional transmission of the multi-sides is a circular region with radius l. c) Each node can be considered as an integrated transceiver terminal with both transmission and reception devices.The four-node square network deployment is shown in Fig. 8 with a network side length EF of 3l.Further, a rectangular coordinate system was established, with point D as the origin.
The equation of circle A is given as The equation of line EF is given as The effective coverage of the four-node square network is the union of the coverage of all nodes, which is expressed as where S 1 and S 2 are shown in Fig. 8(blue and yellow areas, respectively) and the square area S EF GH with side length 3l is given as Based on ( 8) and ( 9), the following can be obtained: The sector area S P BQ is given as thus, According to (10), ( 11), (12), and ( 14), we obtain When any UV node is added to a square network, the increased effective coverage area is S eff (gray area in Fig. 8), which is also the maximum effective coverage area achieved by a single communication node in the network (except the boundary node).
The sector area S P QCB is given as By symmetry,

C. Network Connectivity
The connectivity analysis was based on a two-dimensional area C, with area S ROI .In a square network, n nodes are evenly deployed.The probability density function of the square network is given as As shown in Fig. 9, the coverage S node (t x , ϕ x ) of any node x(t x , ϕ x ) is a circular area, with (t x , ϕ x ) as the center and l as the radius: When the distance d between x(t x , ϕ x ) and origin O is greater than or equal to l, as in Fig. 9(a), from (19) we obtain Here, ϕ 1 and ϕ 2 and t 1 and t 2 represent the upper and lower bounds of the integral area, respectively.When d < l, as in Fig. 9 The probability P(t x , ϕ x , l) that node x(t x , ϕ x ) has adjacent nodes is given as The remaining nodes within the coverage of node x(t x , ϕ x ) obey the binomial distribution Bin(n-1, P(t x , ϕ x , l)); therefore, the probability that x(t x , ϕ x ) has m adjacent nodes is expressed as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Then, the probability that x(t x , ϕ x ) has more than m adjacent nodes is given as The probability that an arbitrary node has more than m adjacent nodes is given by The probability that each node has more than m adjacent nodes is approximated as the probability of an m-connected network it and can be obtained as follows [21]: Hence, the probability of an m-connected network is expressed as

IV. SIMULATION AND ANALYSIS
A. Coverage Area 1) UV Node: According to the analysis in Fig. 5, large elevation angles shorten the communication distance and cannot be used in actual networking.Similarly, excessively small elevation angles cannot be used to achieve NLOS communication.Transmission elevation angles of 30°and 50°were selected for the simulation in this study.Generally, the beam divergence angle should not exceed 20°to avoid power diffusion of the UV emission beam.Fig. 10 shows that the trends of the covered area of a single side of UV nodes with respect to the beam divergence angle Φ 1 are approximately identical for different transceiver elevation combinations.Therefore, with an increase in Φ 1 , the coverage of the single side increases.Comparing the coverage horizontally reveals that, when Φ 1 remains the same, the smaller the transceiver elevation combination, the larger the coverage.When the transceiver elevation combination is 30°-30°, the coverage of a single side is 8.07 × 10 2 m 2 , with a divergence angle of 15°, which is approximately 122.15% and 297.51% of those of the 30°-50°(6.61× 10 2 m 2 ) and 50°-50°(2.71× 10 2 m 2 ) transceiver elevation combinations, respectively.
2) UV Network: Figs.11 and 12 show the four-node effective coverage area and single-node effective coverage area versus the transmission power P t for varying transceiver elevation combinations, respectively.Similar trends are observed for both coverages: an increase in the communication distance leads to an increase in coverage as P t increases.
Figs. 11 and 12 illustrate that the smaller the transceiver elevation angles, the faster the coverage increases with an increase in P t .When the transceiver elevation combination is 30°-30°, the four-node effective coverage area is 1.15 × 10 5 m 2 , with a transmission power of 0.5 W, which is approximately 257.84% and 197.25% of those of the 30°-50°(4.46× 10 4 m 2 ) and 50°-30°( 5.83 × 10 4 m 2 ) transceiver elevation combinations, respectively.
Figs. 13 and 14 show the four-node effective coverage area and single-node effective coverage area versus the data rate R d for varying transceiver elevation combinations, respectively.As Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.By horizontally comparing the results in Figs. 13 and 14, we deduced that the choice of transceiver elevation angles has a great impact on the effective coverage area with the same R d .Fig. 14 shows that the single-node effective coverage area increases by approximately 81.86% from 50°-50°(5.83× 10 3 m 2 ) to 30°-50°(1.06× 10 4 m 2 ), and by 343.26% from 50°-50°t o 30°-30°(2.58× 10 4 m 2 ) when R d is 50 kbps.
The maximum effective coverage ratio of UV node η eff was defined as the ratio of the maximum effective coverage area to the coverage area of a single node [19], which is given as In the area S ROI shown in Fig. 15, the minimum number of nodes n min required to achieve completely seamless coverage when deploying a square UV network is Equation ( 29) provides a theoretical reference for the number of nodes required for the deployment of UV networks.Assuming that S ROI is a square area with a side length of 1.0 × 10 3 m, to achieve full coverage of the target area, the number of UV nodes n min is theoretically required to be 96 with a transceiver elevation combination of 30°-50°.However, owing to the boundary effect, the UV node required in actual deployment is generally greater than the theoretical value.

B. Connectivity
According to the analysis in Section IV-A, the effective coverage area of UV nodes for actual communication networks are far less than those in cases where the transceiver elevation angles are large.To obtain better communication coverage and achieve NLOS communication, four transceiver elevation combinations were selected: 30°-30°, 30°-50°, 50°-30°, and 50°-50°.The network connectivity simulations were performed in a square area with a side length of 1.0 × 10 3 m.
1) Number of Nodes: Fig. 16 shows that the UV network connectivity has similar growth trends with the number of nodes n under different transceiver elevation combinations (R d = 50 kbps; P t = 0.5 W).Initially, a near-linear trend is observed in the connectivity growth with n as more nodes are deployed.With a continuous increase in the number of nodes, the connectivity growth decreases and the connectivity gradually approaches 100%.Owing to the fact that a large number of node resources are needed to increase the connectivity to 100%, 90% connectivity is considered as the evaluation standard of connectivity in actual UV networking.
Fig. 16 illustrates the more stringent conditions for achieving a multi-connected network under the same communication parameters for larger multi-connectivities.In the 30°-30°t ransceiver elevation combination, the number of nodes required to reach 90% connectivity increases by 51.02% for a twoconnected network (73 nodes) compared to a one-connected network (48), and the number of nodes increases by 106.12% for three-connectivity (101).
The two-connected network is robust, and the channel parameter requirements are less stringent than multi-connectivities. Horizontal comparison reveals that the smaller the transceiver elevation combination, the smaller the number of nodes required to form a two-connected network.A total of 73 nodes must be deployed to the network to achieve two-connectivity with the 30°-30°transceiver elevation combination.The number of nodes required with 50°-30°and 50°-50°transceiver elevation Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.combinations are 135 and 301, respectively, which are approximately 183.78% and 408.10% of that of the 30°-30°elevation combination.
2) Data Rate: Fig. 17 shows the connectivity versus data rate R d for different transceiver elevation combinations (n = 300, P t = 0.5 W).The results indicate that the network connectivity decreases with an increase in R d .The higher the value of m in the connected network, the lower the supported R d .The data rate supported by the one-connected network is 117 kbps with the 30°-50°transceiver elevation combination, and the rates supported by the two-and three-connected networks are 73 kbps and 58 kbps, respectively, which are reduced by 37.61% and 50.43% compared to that of the one-connected state.
3) Transmission Power: Fig. 18 shows the connectivity versus transmission power P t for different transceiver elevation combinations (n = 300, R d = 50 kbps).The network connectivity increases with increasing P t and gradually approaches 100%.For the same transceiver elevation combinations, multiconnected states require a higher transmission power.Compared to the one-connected state (0.24 W), the transmission power P t of the network increases by 41.66% for the two-connected state (0.34 W) and by 75.00% for a three-connected state (0.42 W), Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.with the 30°-50°transceiver elevation combination, as shown in Fig. 18(b).
Comparing Figs.16-18 reveals that the bigger the transceiver elevation combination, the more stringent the communication parameters (number of nodes, data rate, and transmission power) required by the connected UV network.Therefore, the selected elevation combination should be as small as possible for NLOS communication in actual UV networking.
Overall, compared to the blind coverage area, the isolation of communication terminals causes more serious damage to the network performance.Therefore, it is appropriate to construct  a UV network with two-connectivity and one coverage area for practical applications.

V. EXPERIMENT AND ANALYSIS
We conducted a coverage evaluation experiment with a fournode UV network based on the designed terminals.The experimental results were compared with the simulation results, and the differences were analyzed.

A. Experimental Conditions
According to the node model described in Section II-C, a hexagonal terminal model was designed as shown in Fig. 19; each side had separate transmission and reception devices.A 1 × 5 UV LED array was used at the transmission end to improve communication distance and the total power of a single side was 0.5 W. The PMT was used at the reception end, with a response time at the nanometer level.The communication mode of NLOS-c with OOK modulation was used for each side with an elevation angle combination of 30°-50°.
Each node can be considered an integrated transceiver terminal with both transmission and reception devices.In the communication network, a UV networking protocol previously proposed by our team was used [22], and each node could transmit and receive data.The four terminals were deployed according to a square network.The experiment scene is shown in Fig. 20.

B. Experimental Results
The measured communication distance between terminals was 75.1 m, and the effective coverage area of the four-node network was 4.48×10 4 m 2 .Compared to the simulation results, where the coverage area of the four-node network was 4.62×10 4 m 2 under the same parameter conditions (Fig. 11), the area in the experiments was slightly smaller.
Although the "solar blind" UV band was selected, a small amount of background interference was still present in the experiments.This background noise was ignored in the simulations, thus the effective coverage area in the simulations was higher.

VI. CONCLUSION
UV network has great potential in covert communication and has high prospects for application in the complex electromagnetic environment.In this study, we systematically evaluated UV network coverage based on an NLOS channel.A twodimensional network coverage model was established, which was combined with a designed node model and a specific communication mode.Furthermore, the expressions of the effective coverage area and connectivity were derived mathematically.Subsequently, the effects of communication parameters on the network coverage performance were analyzed.We observed that the bigger the transceiver elevation combination, the more stringent the communication parameters (number of nodes, data rate, and transmission power) required by the UV network coverage.Finally, a coverage evaluation experiment with a four-node network was conducted.The experimental results were consistent with the simulation results.Thus, comprehensive consideration of the network coverage and connectivity can guide node deployment in practical UV networking.
Network life is another factor affecting coverage performance.Owing to the limitation of the energy of the node, stable and efficient strategies are urgently needed to improve the energy utilization efficiency of the nodes and extend the working lives of UV networks as much as possible.Therefore, in subsequent research, we aim to examine the rational utilization of energy in the construction of UV networks.

Fig. 6 .
Fig. 6.Boolean coverage model: point X is considered covered when it lies within radius R and not covered when d(O, X) ≥ R.

Fig. 9 .
Fig. 9. Connectivity analysis diagram for distances d between point x and the origin O (a) d > l and (b) d < l.

Fig. 11 .
Fig. 11.Four-node effective coverage area versus transmission power for different transceiver elevation combinations.

Fig. 12 .
Fig. 12. Single-node effective coverage area versus transmission power for different transceiver elevation combinations.