TWR-FSO Communication System under AF Protocol and Its Performance Analysis Method

Abstract

The present invention relates to the field of free space optical communication technology, and particularly to a TWR-FSO communication system under the AF protocol and its performance analysis method. The method includes: S1. constructing a model of the TWR-FSO communication system under the AF protocol; S2. constructing a probability density function of the signal-to-noise ratio of the link of the TWR-FSO communication system; S3. constructing an outage probability function and an average bit error rate function of the TWR-FSO communication system. The present invention establishes a composite fading channel model including atmospheric turbulence and pointing error, and constructs closed expressions for the outage probability and the average bit error rate of the TWR-FSO communication system, which can effectively analyze the performance of the TWR-FSO communication system under the AF protocol. Moreover, the simulation analysis shows that the outage probability and the average bit error rate of the TWR-FSO communication system under the AF protocol are better than those of the TWR-FSO communication system under the DF protocol, indicating that the system can effectively reduce the influence of atmospheric turbulence and pointing error on the communication system.

Description

Technical Field

[0001] The present invention relates to the technical field of free space optical communication, and particularly to a TWR-FSO communication system under the AF protocol and its performance analysis method. Background Art

[0002] Compared with radio frequency (RF) technology, free space optical (FSO) communication technology has a higher transmission rate and bandwidth. In addition, it also has the characteristics of transmission security, strong anti-interference ability, large communication capacity, and small space transmission loss. However, the influence of atmospheric turbulence and pointing error on the system performance will increase with the increase of the communication distance, thereby limiting the transmission distance of FSO, and even causing the communication link to be interrupted in severe cases. To solve this problem, researchers apply relay-assisted technology to the FSO system.

[0003] Due to the fact that relay-assisted technologies can expand the coverage range and improve the performance of communication systems, they have attracted extensive attention in the field of wireless communication. In 2011, Kazemlou et al. (S. Kazemlou, S. Hranilovic and S. Kumar, "All-Optical Multihop Free-Space Optical Communication Systems," in Journal of Lightwave Technology, vol. 29, no. 18, pp. 2663-2669, Sept. 15, 2011, doi: 10.1109 / JLT.2011.2160615.) first applied relay-assisted technology to FSO and proposed an all-optical one-way relay-assisted technology, which can improve the overall error performance and coverage distance of FSO links. On this basis, Puri et al. (P. Puri, N. D. Chatzidiamantis, P. Garg, M. Aggarwal and G. K. Karagiannidis, "Two-Way Relay Selection in Multiple Relayed FSO Networks," in IEEE Wireless Communications Letters, vol. 4, no. 5, pp. 485-488, Oct. 2015, doi: 10.1109 / LWC.2015.2442988) extended the traditional one-way relay (OWR) system to a two-way relay (TWR) system, which further improved the error performance of FSO links while enhancing the spectral efficiency of communication systems. To improve the reliability of the system and effectively combat link failures, researchers have incorporated network coding (NC) technology into FSO links. However, a round of communication between two user terminals via a single relay and double-hop usually requires three or four time slots to complete data exchange. To reduce the number of time slots required for a round of communication, physical layer network coding (PNC) technology was first added to the TWR system, enabling it to make full use of network resources.Physical network coding (PNC) was proposed by Zhang et al. (ZHANG S L, LIEW S C, LAM P P. Hot topic: physical-layer network coding[C] / / Proceedings of the 12th Annual International Conference on Mobile Computing and Networking. New York: ACM Press, 2006: 358-365) in 2006, which increases the throughput by 100% and 50% compared with traditional multi-hop and network coding (NC) schemes respectively. Compared with traditional relay systems, PNC doubles the throughput of the two-way relay (TWR) channel by reducing the number of time slots from four to two. Many literatures have studied relay-assisted free-space optical (FSO) systems under different channel models, including serial and parallel relay-assisted FSO systems, and different forwarding modes are adopted, namely decode-and-forward (DF) protocol and amplify-and-forward (AF) protocol. Al-Ebraheemy et al. (O.M.S. Al-Ebraheemy, A.M.S. Salhab, A. Chaaban, S.A. Zummo and M. Alouini, "Precise Performance Analysis of Dual-Hop Mixed RF / Unified-FSO DF Relaying With Heterodyne Detection and Two IM-DD Channel Models," in IEEE Photonics Journal, vol. 11, no. 1, pp. 1-22, Feb. 2019, Art no. 7900522, doi: 10.1109 / JPHOT.2018.2890722) analyzed the DF-based dual-hop mixed RF / FSO system, derived the closed-form expressions of the outage probability, average bit error rate and ergodic capacity of the system, and carried out an asymptotic analysis of the system performance under high signal-to-noise ratio. It is concluded that at high transmission power, all optical detectors will generate the same diversity order, but their coding gains are different. Wang Yamin (Wang Yamin. Performance study of hybrid RF / FSO systems based on amplify-and-forward[D]. Xidian University, 2020. DOI: 10.27389 / d.cnki.gxadu.2020.000416.) studied the performance of the AF-based hybrid RF / FSO system, derived the theoretical formulas of the outage probability, average bit error rate and capacity of the system, and verified the accuracy of the established system and channel models. The simulation results show that in the system adopting AF relay, the RF link is the main limitation of communication quality.Relay-assisted technologies can reduce the impact of atmospheric turbulence on FSO systems. Existing literature has proposed various FSO relay schemes, such as RF-FSO (A. Sikri, A. Mathur and G. Kaddoum, "Signal Space Diversity-Based Distributed RIS-Aided Dual-Hop Mixed RF-FSO Systems," in IEEE Communications Letters, doi: 10.1109 / LCOMM.2022.3155442.), VLC-FSO

[21] , etc. Puri et al. (P. Puri, P. Garg, M. Aggarwal and P. K. Sharma, "Multiple user pair scheduling in TWR-FSO systems in presence of building sway," 2014 International Conference on Signal Processing and Communications (SPCOM), 2014, pp. 1-5, doi: 10.1109 / SPCOM.2014.6983920) studied a multi-user scheduling two-way relay-assisted FSO system, namely TWR-FSO. This system applies NC and DF protocols at the relay node and considers the impact of atmospheric turbulence and pointing error on the FSO link, and derives the outage probability under two scheduling schemes of absolute signal-to-noise ratio and normalized signal-to-noise ratio.Garg et al. (P. Puri, P. Garg and M. Aggarwal, "Multiple user pair scheduling in TWR assisted FSO systems," in Journal of Optical Communications and Networking, vol. 8, no. 5, pp. 290-301, May 2016, doi: 10.1364 / JOCN.8.000290.) studied the performance of two scheduling algorithms based on absolute signal-to-noise ratio and normalized signal-to-noise ratio on the basis of the literature (. Puri, P. Garg, M. Aggarwal and P. K. Sharma, "Multiple user pair scheduling in TWR-FSO systems in presence of building sway," 2014 International Conference on Signal Processing and Communications (SPCOM), 2014, pp. 1-5, doi: 10.1109 / SPCOM.2014.6983920), and derived the closed-form expressions of outage probability and bit error rate under different turbulence states. Compared with the direct transmission link, this communication system can significantly reduce the system bit error rate and outage probability. Aggarwal et al. (P. Puri, P. Garg and M. Aggarwal, “Outage and Error Rate Analysis of Network-Coded Coherent TWR-FSO Systems,” in IEEE Photonics Technology Letters, vol. 26, no. 18, pp. 1797-1800, 15 Sept. 15, 2014, doi: 10.1109 / LPT.2014.2333032.) considered a similar system, but only gave the performance analysis of the TWR-FSO system under the DF protocol.

[0004] Currently, no relevant literature has given the performance analysis of the TWR-FSO communication system under the AF protocol.

[0005] Therefore, we propose a method for analyzing the performance of the TWR-FSO communication system under the AF protocol of the present invention. Summary of the Invention

[0006] The object of the present invention is to provide a method for analyzing the performance of a TWR-FSO communication system under the AF protocol, which is used to improve the problem that the performance analysis of the TWR-FSO communication system under the AF protocol is not involved in the existing technology.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] The present invention provides a method for analyzing the performance of a TWR-FSO communication system under the AF protocol, which is characterized by including the following steps:

[0009] S1. Construct a model of the TWR-FSO communication system under the AF protocol;

[0010] S2. Construct the probability density function of the signal-to-noise ratio of the link of the TWR-FSO communication system;

[0011] S3. Construct the outage probability function and the average bit error rate function of the TWR-FSO communication system.

[0012] Further, the TWR-FSO communication system under the AF protocol includes:

[0013] A target node A, a target node B, and a relay node R;

[0014] The relay node R includes 2 directional antennas, which communicate with the target node A and the target node B respectively;

[0015] In the relay node R, an amplifier using the AF protocol amplifies the received signal, and PNC is used to establish two-stage communication between the target node A and the target node B.

[0016] Further, the two-stage communication includes:

[0017] The first stage:

[0018] The target node A and the target node B send the signals carrying information to the relay node R through the FSO link, and the relay node R amplifies the received signals and performs PNC operations;

[0019] The second stage:

[0020] The relay node R sends the data packets to the target node A and the target node B simultaneously. After receiving the data packets, the target node A and the target node B perform exclusive OR operations with their own data packets to decode the data packets of the other party.

[0021] Further, in S2, to construct the probability density function of the signal-to-noise ratio of the link of the TWR-FSO communication system, the method is as follows:

[0022] S21. Let the fading of the signal transmission in the TWR - FSO communication system caused by atmospheric turbulence be \(h\). a ;

[0023] The a probability density function of \(h\) is:

[0024]

[0025] where \(K\) α-β (·) is the modified Bessel function of the second kind, \(\Gamma(·)\) is the gamma function, \(\alpha\) and \(\beta\) represent the large - scale and small - scale turbulence respectively, and the expressions are:

[0026]

[0027]

[0028] In the formula is the Rytov variance, is the refractive index structure parameter, \(k = 2\pi / \lambda\) is the optical wave number, and \(z\) is the transmission distance of the signal laser;

[0029] S22. Let the pointing error of the signal transmission in the TWR - FSO communication system caused by atmospheric turbulence be \(H\). p ;

[0030] The p probability density function of \(H\) is:

[0031]

[0032] In the formula, \(A_0\) is the fraction of the collected optical power, \(\xi=\omega\) e / (2\(\sigma\) s ) is the pointing error coefficient, \(\omega\) e is the equivalent beam width, and \(\sigma\) s is the standard deviation of the pointing error displacement;

[0033] S23. Let the signal - to - noise ratio of the link of the TWR - FSO communication system be \(\gamma\). cd , which is defined as:

[0034]

[0035] where \(\{c,d\}\in\{A,R,B\}\); \(P\) t is the transmitted optical power, \(P\) l is the local oscillator power, \(N_0\) is the power spectral density of the additive white Gaussian noise, \(\chi=\eta q / hf\) is the responsivity of the photodetector, \(\eta\) is the quantum efficiency of the photodetector, \(q\) is the charge of an electron, \(h\) is Planck's constant, and \(f\) is the frequency of light;

[0036] Since \(H = H\)a ×H p ;

[0037] obtain γ cd The probability density function of is:

[0038]

[0039] where, is the Meijer’s G function, is the average signal-to-noise ratio between the target node and the relay node.

[0040] Furthermore, the outage probability is expressed as follows:

[0041]

[0042] where, represents the end-to-end instantaneous signal-to-noise ratio of the system, γ AR represents the signal-to-noise ratio between the target node A and the relay node R link, γ RB represents the signal-to-noise ratio between the target node B and the relay node R link, and γ AR and γ RB are independent and identically distributed, C is a constant determined by the relay gain G, γ th represents the communication system threshold;

[0043] According to Bayes' theorem, the outage probability can be expressed as:

[0044]

[0045] where,

[0046] Given that γ RB > 0, Rewrite Ψ as

[0047]

[0048] Substitute Equation (9) into Equation (8) and simplify to obtain:

[0049]

[0050] where,

[0051] Furthermore, the average bit error rate is expressed as:

[0052] Substitute γ = γ th to obtain:

[0053]

[0054] The present invention also provides a TWR-FSO communication system under the AF protocol, which is characterized in that the TWR-FSO communication system under the AF protocol includes:

[0055] A target node A, a target node B, and a relay node R;

[0056] The relay node R includes 2 directional antennas, which communicate with the target node A and the target node B respectively;

[0057] In the relay node R, an amplifier using the AF protocol amplifies the received signal, and PNC is used to establish two-stage communication between the target node A and the target node B.

[0058] Furthermore, the two-stage communication includes:

[0059] The first stage:

[0060] The target node A and the target node B send the signals carrying information to the relay node R through the FSO link, and the relay node R amplifies the received signals and performs PNC operation;

[0061] The second stage:

[0062] The relay node R sends the data packets to the target node A and the target node B simultaneously. After receiving the data packets, the target node A and the target node B perform an exclusive OR operation with their own data packets to decode the data packets of the other party.

[0063] The present invention has at least the following beneficial effects:

[0064] In view of the fact that the influence of atmospheric turbulence and pointing error on the system performance becomes more and more serious as the communication distance increases, based on the amplify-and-forward protocol, the present invention proposes a TWR-FSO communication system solution;

[0065] The present invention establishes a composite fading channel model including atmospheric turbulence and pointing error, and the channel fading satisfies the Gamma-Gamma distribution, and constructs closed expressions for the outage probability and average bit error rate of the TWR-FSO communication system. Under different turbulence intensities and threshold conditions, the outage probability and average bit error rate performance are compared and analyzed. The performance of the TWR-FSO communication system under the AF protocol can be effectively analyzed.

[0066] The simulation results show that under the same parameter conditions, the TWR-FSO communication system under the AF protocol can effectively reduce the influence of atmospheric turbulence and pointing error on the communication system. Compared with the direct link, the system of the present invention can also effectively improve the influence of the threshold on the system outage performance to improve the system stability. Description of the Drawings

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0068] Figure 1 It is a diagram of the TWR-FSO communication system;

[0069] Figure 2 It is a comparison diagram of the system outage probability of the direct link and the link with relay;

[0070] Figure 3 It is a comparison diagram of the system outage probability of the direct link and the link with relay under different threshold levels;

[0071] Figure 4 It is a comparison diagram of the outage probability corresponding to different pointing errors ξ;

[0072] Figure 5 It is a comparison diagram of the outage probability of the system under different turbulence intensities;

[0073] Figure 6 It is a comparison diagram of the outage probability of the system under different threshold levels;

[0074] Figure 7 It is a comparison diagram of the system bit error rate corresponding to different pointing errors ξ;

[0075] Figure 8 It is a comparison diagram of the system bit error rate under different turbulence intensities;

[0076] Figure 9 It is a comparison diagram of the system bit error rate under different transmission distances. Specific Embodiments

[0077] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0078] Embodiment 1:

[0079] 1. System and Channel Model

[0080] The TWR-FSO communication system adopts coherent heterodyne detection (HD), consists of a target node A, a target node B and a relay node R, and the relay node R includes 2 directional antennas. The transmission distances of A-R and R-B are both z, as Figure 1As shown, the same receiver structure as in

[25] is used. Since the distance between the target nodes A and B is relatively long or there are obstacles, line-of-sight (LOS) communication between the two nodes is not possible. At this time, a relay node R is used to establish communication between them. In the relay node R, an amplifier based on the AF protocol is used to amplify the received signal, and PNC is used here. Due to the adoption of PNC, the relay node R establishes two-stage communication between the target nodes A and B. In the first stage, namely the multiple access stage (MAC), the target nodes A and B send the information-bearing signals to the relay node R through the FSO link. The relay node R amplifies the received signals and performs PNC operations. In the second stage, namely the broadcast stage (BC), the relay node R sends the data packets to the target nodes A and B simultaneously. After receiving the data packets, the target nodes A and B perform exclusive OR operations with their own data packets to decode the data packets of the other party.

[0081] In the FSO system, the signal laser transmission is subject to fading (H a ) and pointing error (H p ) caused by atmospheric turbulence. h a obeys the double Gamma distribution, and this distribution model is applicable to weak turbulence to strong turbulence. The probability density function of h a is:

[0082]

[0083] where K α-β (·) is the modified Bessel function of the second kind, Γ(·) is the Gamma function, and α and β represent the large turbulence scale and the small turbulence scale respectively. They depend on the aperture diameter of the receiver, and the specific expressions are:

[0084]

[0085]

[0086] In the formula is the Rytov variance, which can be directly measured from the atmospheric parameters. is the refractive index structure parameter, and its value changes with the altitude. k = 2π / λ is the optical wave number, and z is the laser propagation distance.

[0087] The radial displacement at the receiving end caused by the pointing error H p is determined by the Rayleigh distribution, and the corresponding probability density function is:

[0088]

[0089] In the formula, A0 is the fraction of the collected optical power, and ξ = ω e / (2σs ) is the pointing error coefficient, ω e is the equivalent beam width, σ s is the standard deviation of the pointing error displacement.

[0090] The instantaneous signal-to-noise ratio (SNR) of the link between the target node and the relay node is defined as follows:

[0091]

[0092] where, γ cd represents the SNR of the link between the source node and the relay node, {c, d} ∈ {A, R, B}. P t is the transmitted optical power, P l is the local oscillator power, N0 is the power spectral density of additive white Gaussian noise, χ = ηq / hf is the responsivity of the photodetector, η is the quantum efficiency of the photodetector, q is the charge of an electron, h is Planck's constant, and f is the frequency of light.

[0093] Since H = H a × H p , substituting Eqs. (1) and (4) into Eq. (5), the probability density function of γ cd can be obtained as

[0094]

[0095] where, is the Meijer’s G function, is the average SNR between the target node and the relay node.

[0096] Performance Analysis of 2TWR-FSO

[0097] 2.1 Analysis of the Outage Probability of TWR-FSO

[0098] For the TWR-FSO communication system, an outage occurs when the link A-R or the link R-B fails. Since the AF protocol is adopted at the relay node, when the end-to-end instantaneous SNR is lower than the threshold, the system cannot communicate, and the outage probability is expressed by the following formula

[0099]

[0100] In the above formula, represents the end-to-end instantaneous SNR of the system, γ AR represents the SNR between the target node A and the relay node R link, γ RB represents the SNR between the target node B and the relay node R link, and γ AR and γ RBare independent and identically distributed, C is a constant determined by the relay gain G, which is taken as 1 here, γ th represents the threshold of the communication system. According to Bayes' theorem, the outage probability can be expressed as:

[0101]

[0102] where

[0103] Given that γ RB > 0, using the literature (C.S. Meijer, “Expansion theorems for the G-function. II,” in Indagationes Mathematicae, vol. 55. Amsterdam, The Netherlands: Elsevier, 1952, pp. 483–487), Ψ is rewritten as

[0104]

[0105] Substituting Equation (9) into Equation (8) and simplifying using Equation (07.34.21.0086.01) in the literature (Wolfram [OL], http: / / functions.wolfram.com / HypergeometricFunctions / MeijerG / , 2018) gives

[0106]

[0107] where

[0108] When there is no relay node for direct communication between the destination nodes A and B, the outage probability can be expressed as:

[0109]

[0110] In the above equation, represents the average signal-to-noise ratio of the link between the destination nodes A and B, γ th represents the threshold of the communication system.

[0111] 2.2 Average Bit Error Rate Analysis of TWR-FSO

[0112] Since TWR-FSO uses differential binary phase shift keying (DBPSK) modulation, the expression is Calculate and simplify according to Equation (07.34.21.0088.01) in the literature (Wolfram[OL], http: / / functions.wolfram.com / HypergeometricFunctions / MeijerG / , 2018.), and substitute γ = γ th into the following formula to obtain the closed-loop formula for the average bit error rate, as follows

[0113]

[0114] 3. Simulation and Analysis

[0115] To analyze the transmission performance of the TWR-FSO communication system under the AF protocol, perform simulation analysis using the outage probability and average bit error rate expressions derived previously. Let The transmission distances z of the A-R link and the R-B link are the same. The specific settings of the relevant parameters are shown in Table 1.

[0116] Table 1 FSO Link Parameters

[0117]

[0118] To compare the system outage probability performance of the direct link (without relay nodes) and the TWR-FSO link, perform simulation analysis under the given parameters, where the refractive index structure parameter The weak pointing error coefficient ξ = 6.7, the transmission distance z = 4 km, and the threshold γ th = 10 dB. It can be seen from Figure 2 that compared with the direct link, the outage performance of the TWR-FSO link has been significantly improved. This is because the relay node bypasses obstacles such as buildings and vegetation on the transmission path of the communication system, overcomes the influence of large-scale fading to a certain extent, reduces the path loss, and improves the anti-interference performance of the system. When SNR = 20 dB and the other parameter conditions remain unchanged, as Figure 3 shown, as the threshold increases, the outage probability of the system gradually increases. Since the influence of the pointing error can be ignored at this time, that is, ξ = 6.7, it shows that the TWR-FSO link can effectively improve the influence of the threshold on the system outage performance compared with the direct link.

[0119] For the turbulent channel under different pointing error coefficients, it will affect the outage probability of the communication system. Among them, ξ = 2 and ξ = 6.7 represent the strong pointing error coefficient and the weak pointing error coefficient respectively. Given the refractive index structure parameter The threshold γ th = 10 dB, and the transmission distance z = 4 km, as Figure 4As shown. It can be observed from the figure that as the value of ξ increases, the system outage probability performance is significantly improved. This is because the larger ξ is, the smaller the beam jitter is, and the weaker the influence of ξ on the FSO channel. When SNR = 25 dB, the system outage probability under the AF protocol is at about the order of 10-4, while the system outage probability under the DF protocol is at about the order of 10-1. As SNR increases, the gap between the two becomes larger and larger, indicating that the system under the AF protocol has a smaller outage probability. Because the system can obtain multiple diversity gains under the AF protocol, while the DF protocol does not have it. Although the AF protocol will amplify noise compared with the DF protocol, the multiple diversity gain plays a major role in improving the system performance at this time.

[0120] The turbulent channels with different turbulence intensities will affect the outage probability of the communication system. Among them, the refractive index structure parameter The smaller it is, the weaker the turbulence intensity. Given the weak pointing error coefficient ξ = 6.7, the threshold γ th = 10 dB, and the transmission distance z = 10 km. From Figure 5 it can be seen that when SNR is below 6 dB, the system outage probability is basically not affected by atmospheric turbulence. However, as SNR increases, the influence of atmospheric turbulence on the system outage probability becomes more obvious. When changes from 4.8×10 -16 to 4.0×10 -15 , when the outage probability is at the order of 10-7, the system will have a loss of about 7 dB. To study the change of the system outage probability performance under different threshold values, the parameters are set as the refractive index structure parameter weak pointing error ξ = 6.7, and the transmission distance z = 10 km. From Figure 6 it can be clearly seen that the threshold has a direct impact on the system outage probability. When the outage probability is at the order of 10-7, when γ th decreases from 10 dB to 6 dB, the system has a gain of 1.5 dB; when γ th decreases from 4 dB to 1 dB, the system has a gain of 3 dB, indicating that choosing an appropriate threshold is of great significance for improving the system outage probability performance.

[0121] The turbulent channels with different pointing error coefficients will affect the system bit error rate of the communication system. Given the refractive index structure parameter the transmission distance z = 6 km, where there is no threshold γ th , as Figure 7 shown. When BER is at the order of 10-8, ξ increasing from 2 to 2.5 and ξ increasing from 2.5 to 6.7 have approximately the same performance gain. At this time, the system under the AF protocol has a gain of about 1.5 dB. Figure 7The BER of the TWR-FSO communication system operating under the AF protocol and the DF protocol is also given. When SNR = 40 dB, the BER under the DF protocol can drop to about the order of 10-4, while the BER under the AF protocol can drop to about the order of 10-4 only when SNR = 22 dB, indicating that the BER performance of the TWR-FSO communication system under the AF protocol has been significantly improved.

[0122] To study the different effects of the turbulent channel under different turbulence intensities on the system bit error rate, where the smaller the value of the refractive index structure parameter , the weaker the corresponding turbulence intensity. The parameter is set as the weak pointing error coefficient ξ = 6.7 and the transmission distance z = 10 km. It can be found from Figure 8 that as the atmospheric turbulence intensity increases, the bit error rate of the system gradually increases. When the BER is at the order of 10-8, increasing from 4.8×10 -16 to 4.0×10 -15 , the BER loss is close to 8 dB. When SNR = 40 dB and , the BER of the system will approximately reach the order of 10-12, while under the same conditions , the BER of the system can only reach about the order of 10-9, indicating that the atmospheric turbulence intensity has a direct impact on the BER performance of the system. Regarding the influence of different transmission distances on the system bit error rate, the BER performance of the TWR-FSO communication system operating under the AF protocol and the DF protocol is also compared. The parameters are set as the refractive index structure parameter and the weak pointing error coefficient ξ = 6.7, as shown in Figure 9 . Comparing z = 5 km under the AF protocol with z = 5 km under the DF protocol, the former has more excellent BER performance, indicating that the TWR-FSO communication system under the AF protocol can reduce the system BER and increase the system reliability at the same transmission distance.

[0123] 4. Summary

[0124] Since the impacts of atmospheric turbulence and pointing errors on communication systems increase with the increase of transmission distance and may even cause the communication link to break down severely, this paper proposes a TWR-FSO communication system scheme under the AF protocol and analyzes its performance from the perspectives of outage probability and average bit error rate. The system uses differential binary phase shift keying modulation to establish a TWR-FSO communication system with coherent heterodyne detection, where the FSO link is modeled as a Gamma-Gamma distribution affected by atmospheric turbulence and pointing errors. Closed-form expressions for the system outage probability and average bit error rate are derived based on the Meijer’s G function. Simulation results show that the TWR-FSO link can effectively improve the impact of the threshold on the system outage performance compared with the direct link. Under the same conditions, the outage probability and average bit error rate of the TWR-FSO communication system under the AF protocol are better than those of the TWR-FSO communication system under the DF protocol, indicating that the system can effectively reduce the impacts of atmospheric turbulence and pointing errors on the communication system.

[0125] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification is only the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection required by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the performance of a TWR-FSO communication system under the AF protocol, characterized in that, It includes the following steps: S1. Construct a model of a two-way relay-free space optical TWR-FSO communication system under the amplify-and-forward AF protocol; S2. Construct the probability density function of the signal-to-noise ratio of the link of the TWR-FSO communication system; S3. Construct the outage probability function and the average bit error rate function of the TWR-FSO communication system; The outage probability function is: ； Among them, , is the pointing error coefficient, is the equivalent beam width, is the standard deviation of the pointing error displacement, is the gamma function, and respectively represent the large turbulence scale and the small turbulence scale, is the average signal-to-noise ratio between the target node and the relay node, represents the communication system threshold, is the Meijer’s G function; The average bit error rate function is ； Under different turbulence intensities and threshold conditions, compare and analyze the outage probability and the average bit error rate, and analyze the performance of the TWR-FSO communication system under the AF protocol.

2. The performance analysis method of the TWR-FSO communication system under the AF protocol according to claim 1, characterized in that The TWR-FSO communication system under the AF protocol includes: A target node A, a target node B, and a relay node R; The relay node R includes 2 directional antennas, which communicate with the target node A and the target node B respectively; In the relay node R, an amplifier using the AF protocol amplifies the received signal, and physical layer network coding PNC is used to establish two-stage communication between the target node A and the target node B.

3. The performance analysis method of the TWR-FSO communication system under the AF protocol according to claim 2, wherein The two-stage communication includes: The first stage: The target node A and the target node B send the signals carrying information to the relay node R through the FSO link, and the relay node R amplifies the received signals and performs PNC operations; The second stage: The relay node R sends the data packets to the target node A and the target node B simultaneously. After receiving the data packets, the target node A and the target node B perform exclusive OR operations with their own data packets to decode the data packets of the other party.

4. The performance analysis method of the TWR-FSO communication system under the AF protocol according to claim 1, characterized in that, In S2, to construct the probability density function of the signal-to-noise ratio of the link of the TWR-FSO communication system, the method is as follows: S21. Assume that the signal transmission of the TWR-FSO communication system is subject to fading caused by atmospheric turbulence as ; The probability density function is: （1） wherein, is the second kind of modified Bessel function, is the gamma function, and represent the large turbulence scale and the small turbulence scale respectively, and the expressions are: （2） （3） where is the Rytov variance, is the refractive index structure parameter, is the wave number of the light wave, λ is the wavelength of the light wave, is the transmission distance of the signal laser; S22. Assume that the signal transmission of the TWR-FSO communication system is subject to a pointing error caused by atmospheric turbulence as ; The said has a probability density function as follows: （4） In the formula, is the fraction of the collected optical power, is the pointing error coefficient, is the equivalent beam width, is the standard deviation of the pointing error displacement; S23. Let the signal-to-noise ratio of the link of the TWR-FSO communication system be , which is defined as follows: （5） Among them, ; is the transmitted optical power, the local oscillator power, is the power spectral density of additive white Gaussian noise, is the responsivity of the photodetector, is the quantum efficiency of the photodetector, is the charge of an electron, is Planck's constant, is the frequency of light; Due to ; Obtained The probability density function of is as follows: （6） Among them, is the Meijer’s G function, is the average signal-to-noise ratio between the target node and the relay node; The outage probability is expressed as follows: (7) Among them, represents the end-to-end instantaneous signal-to-noise ratio of the system, represents the signal-to-noise ratio between the target node A and the relay node R link, represents the signal-to-noise ratio between the target node B and the relay node R link, and and are independent and identically distributed, is a constant determined by the relay gain G, represents the communication system threshold; According to Bayes' theorem, the outage probability can be expressed as: (8) Among them, ; Known in the case of , convert to (9) Substitute Equation (9) into Equation (8) and simplify to obtain: (10) Among them, .

Images