# Performance Analysis of RIS-Assisted Mixed Dual-Hop FSO-RF Communication Systems over Exponentiated Weibull Channels

Authors: Xinzhong Liu; Jian Zou; Wenwu Xie; Xin Peng; Chunlai Li
Journal: Security and Communication Networks
 (2021)

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## Abstract

Information security is the basis of economic development, information construction, and the protection of people’s and national interest. In this paper, the performance of reconfigurable intelligent surface (RIS)-assisted mixed dual-hop free-space optical-radio frequency (FSO-RF) communication systems is studied and analyzed to ensure the safe transmission of information. In this scheme, it is assumed that the atmospheric turbulence in the fading of the FSO channel follows the exponentiated Weibull distribution model and the fading of the RF channel follows the Rayleigh distribution model. Based on the mathematical function, the probability density function and cumulative distribution function of RIS-assisted mixed dual-hop FSO-RF communication systems are derived. Then, the expression of outage probability and the bit error rate of the system are derived from the channel statistics. Finally, the analysis results are verified by Monte Carlo simulation, and the effects of different parameters on the system performance are analyzed. The simulation results show that the atmospheric turbulence parameters, channel distance of FSO, intensity of atmospheric turbulence, and number of reflectors all affect the system performance.


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## Body

## 1. Introduction

The rapid development of Internet and Internet of Things brings remarkable challenges to information security. It is necessary to take corresponding measures from the aspects of information transmission, information storage, and information interaction to ensure the security of information [1, 2]. Therefore, the field of information security has attracted the attention of researchers and scholars and has achieved a lot of research results [3, 4]. Due to its large capacity, high transmission security, strong anti-interference ability, unregulated spectrum, low cost, and flexible installation, free-space optical (FSO) communication plays an increasingly important role in today’s communication systems [5]. However, the performance of FSO links is significantly affected by transmission distance, environmental factors, and misalignment between the transmitter and receiver [6]. In [7], the outage performance of the FSO communication system is studied in different environments. The system performance of atmospheric turbulence under different probability distribution models is studied in [8–10]. Experimental verification shows that FSO communication is limited by communication distance, and with the increase in communication distance, the performance of the system will significantly decrease. To expand the communication distance of the FSO communication system, the relaying technology has been introduced, which combines the traditional radio frequency (RF) communication and FSO communication to form a hybrid FSO-RF communication system. In [11–13], the performance of the FSO/RF hybrid communication system under amplification and forwarding (AF) and decoding and forwarding (DF) relay schemes is studied and the results show that the performance of the system mainly depends on the FSO link.Reconfigurable intelligent surfaces (RISs) are a flat surface integrated by a large number of passive reflector elements. Due to their low power consumption, high communication quality, programmable full band response, simple deployment, and many other advantages, RISs will become one of the key technologies of 6G [14–16]. In [14], the construction principle, operation mechanism, development prospect, and application scenario of RIS are studied in detail. In [17–19], with the assistance of RIS technology, the performance of the hybrid FSO/RF communication system has been improved to a certain extent, and with the increase in the reflector components, the performance of the system has also been improved.To accurately describe the fluctuation of light intensity based on the effective receiving aperture under the turbulence intensity from weak to strong, Barrios et al. proposed the exponential Weibull (EW) fading model suitable for the aperture average condition [20]. However, the outage probability and BER performance of the RIS-assisted mixed dual-hop FSO-RF communication system based on the EW turbulence distribution model and the influence of pointing error and path loss are rarely reported.In this paper, for an enterprise scenario, signals are transmitted through the mixed dual-hop FSO-RF system and then reflected to the target users by RIS. Then, we investigate the performance of a mixed dual-hop FSO-RF system based on RIS technology. Considering atmospheric turbulence, pointing error, and path loss, not only the expressions of probability density function (PDF) and cumulative distribution function (CDF) of the channel model are derived but also the closed-form expression of outage probability (OP) and the bit error rate (BER) of the system are given. The simulation results show that with the help of RIS technology, the performance of a mixed dual-hop FSO-RF system can be effectively improved.


## 2. System Model

In this section, we consider a RIS-assisted mixed dual-hop FSO-RF communication system as shown in Figure1. A signal source (S) transmits information to the target user (U) with the help of relay node (R) and RIS equipped with N reflectors, and the DF strategy is adopted. The S-R uses FSO link for communication, and R-RIS and RIS-U communicate with the RF link. First, the RF signal is converted to the FSO signal at S and data are transmitted to R through the optical transmitter and optical receiver. Then, the FSO signal is converted to the RF signal at R and data are transmitted to U through RIS. In this scheme, it is assumed that the atmospheric turbulence in the fading of the FSO channel follows the EW distribution model and the fading of the RF channel follows the Rayleigh distribution model.Figure 1
Model diagram of the RIS-assisted mixed dual-hop FSO-RF communication system.


### 2.1. FSO Transmission Link

According to the design of the system model, the signal atS is given by(1)St=PsϑRt+B,where Ps represents the transmitted power, B represents the DC bias, and ϑ represents the photoelectric conversion coefficient. Then, the signal received at R can be expressed as(2)ySR=hSRRθASt+nSR,where Rθ and A represent photoelectric response and photoelectric physical area, respectively, and hSR represents random attenuation in the propagation channel. In our model, hSR includes three factors: path losshl, pointing error hp, and atmospheric turbulence ha. nSR represents the noise produced by the signal between S and R. In (2), hSR can be obtained as(3)hSR=hlhahp.The path loss caused by the absorption and scattering of the optical signals emitted by the wireless optical communication system satisfies the Beer–Lambert’s law:(4)hl=exp−ςl,where ς is the atmospheric attenuation constant and l is the distance of the S-R link. In the Kim model, the atmospheric attenuation constant is defined as ς=13/V2×107×λ/11ψV, where λ represents the wavelength of light, V represents the visible distance, and ψV is a function of visibility given in [21].EW can describe channel fading under different atmospheric turbulence intensities. Therefore, the PDF can be expressed as [22](5)fhax=mnρxρn−1exp−xρn1−exp−xρnm−1,where m, n, and ρ are parameters related to the scintillation factor and the mean value of light intensity, respectively, and they satisfy m>0, n>0, and ρ>0 [22].According to the results in [23], the pointing error obeys Rayleigh distribution, so hp=A0e−2r2/w2/e, where r is the radial displacement, A0=erf2v, v=π/2Ra/wb, erf(.) is the error function, Ra/wb denotes the beam waist normalized by the radius of the receiver aperture, and we=πerfvwb2ev2/2V represents the equivalent beam waist. Hence, the PDF can be obtained as(6)fhpx=ξ2A0ξ2xξ2−1,x∈0,A0,where ξ=we/2σs is the ratio of the beam width to the jitter standard deviation. Using Eq. (4), Eq. (5), and Eq. (6), the joint PDF can be obtained as(7)fhy=mnρnξ2hlA0ξ2yξ2−1∫y/A0hl∞xn−1−ξ2exp−xρn1−exp−xρnm−1dx.According to Newton’s general binomial theorem, PDF can be rewritten as(8)fhy=C1yξ2−1∑j=0∞CjΓ1−ξ2n,1+jA0hlρnyn,where C1=mξ2/ρhlA0ξ2andCj=−1jΓm/Γm−jj!1+jξ2/n−1.At R, we need to convert an optical signal into an electrical signal through a photoelectric converter, and we can obtain(9)ySR′=ηhSRRθAPsςRt+n1t,where η represents the photoelectric conversion efficiency. Hence,(10)γSR=γ¯SRha2hp2,where γ¯SR=η2hl2Rθ2A2Psς2/N1. Here, γSR represents the instantaneous signal-to-noise ratio. Under the assumptions of atmospheric turbulence, pointing error, and path loss, the PDF of γSR is given by(11)fγSRγ=B1γξ2−2/2∑j=0∞CjΓB2,Bjγn/2,where B1=1/2C1γ¯SRξ2/2,Bj=1+j/A0hlργ¯SRn,andB2=1−ξ2/n. Then, the CDF can be expressed as(12)FγSRγ=2B1n∑j=0∞Cjγξ2/2G2,32,1Bjγn/2|0,B2,−ξ2n1−∈ξ2/n,1.


### 2.2. RF Transmission Main Link

We assumeφi and ψi are the phases, u represents the path loss coefficient, d1 is the distance of the R-RIS link, and d2 is the distance of the RIS-U link. Then, the channel gain of the R-RIS link can be expressed as hi=d1−u/2αie−jφi, and the channel of gain of the RIS-U link can be expressed as gi=d2−u/2βie−jψi. So, the signal received by the user can be expressed as(13)yRD=PR∑i=1Nhivigix+nRD,where PR is the average transmitting power at R and nRU represents additive white Gaussian noise. According to the results in [24], vi=ρiϕiejϕi represents the reflection coefficient of the i-th reflector, whereρiϕi=1. From [24], we assume ϕi=φi+ψi in order to obtain the maximum signal-to-noise ratio. Then, yRD can be rewritten as(14)yRD=PR∑i=1Nαiβix+nRD=PREx+nRD.According to the results in [14], αiβi follows the Rayleigh distribution with a mean value of π/4 and a variance of 1−π2/16. Thus, the instantaneous SNR obtained by the user can be written as(15)γRD=γ¯RDE2,where γ¯RU=PRd1d2−u/N2. The PDF of γRU is given by [21](16)fγRDx=12σ2xλ−1/4exp−x+λ2σ2I−1/2xλσ2.The CDF can be obtained as(17)FγRDγth=1−Q1/2λσ,γthσ,where Qca,b is the Marcum Q-function [25]. According to the Gaussian Q-function, we can obtain(18)Q1/2a,b=Qa+b+Qb−a.


## 2.1. FSO Transmission Link

According to the design of the system model, the signal atS is given by(1)St=PsϑRt+B,where Ps represents the transmitted power, B represents the DC bias, and ϑ represents the photoelectric conversion coefficient. Then, the signal received at R can be expressed as(2)ySR=hSRRθASt+nSR,where Rθ and A represent photoelectric response and photoelectric physical area, respectively, and hSR represents random attenuation in the propagation channel. In our model, hSR includes three factors: path losshl, pointing error hp, and atmospheric turbulence ha. nSR represents the noise produced by the signal between S and R. In (2), hSR can be obtained as(3)hSR=hlhahp.The path loss caused by the absorption and scattering of the optical signals emitted by the wireless optical communication system satisfies the Beer–Lambert’s law:(4)hl=exp−ςl,where ς is the atmospheric attenuation constant and l is the distance of the S-R link. In the Kim model, the atmospheric attenuation constant is defined as ς=13/V2×107×λ/11ψV, where λ represents the wavelength of light, V represents the visible distance, and ψV is a function of visibility given in [21].EW can describe channel fading under different atmospheric turbulence intensities. Therefore, the PDF can be expressed as [22](5)fhax=mnρxρn−1exp−xρn1−exp−xρnm−1,where m, n, and ρ are parameters related to the scintillation factor and the mean value of light intensity, respectively, and they satisfy m>0, n>0, and ρ>0 [22].According to the results in [23], the pointing error obeys Rayleigh distribution, so hp=A0e−2r2/w2/e, where r is the radial displacement, A0=erf2v, v=π/2Ra/wb, erf(.) is the error function, Ra/wb denotes the beam waist normalized by the radius of the receiver aperture, and we=πerfvwb2ev2/2V represents the equivalent beam waist. Hence, the PDF can be obtained as(6)fhpx=ξ2A0ξ2xξ2−1,x∈0,A0,where ξ=we/2σs is the ratio of the beam width to the jitter standard deviation. Using Eq. (4), Eq. (5), and Eq. (6), the joint PDF can be obtained as(7)fhy=mnρnξ2hlA0ξ2yξ2−1∫y/A0hl∞xn−1−ξ2exp−xρn1−exp−xρnm−1dx.According to Newton’s general binomial theorem, PDF can be rewritten as(8)fhy=C1yξ2−1∑j=0∞CjΓ1−ξ2n,1+jA0hlρnyn,where C1=mξ2/ρhlA0ξ2andCj=−1jΓm/Γm−jj!1+jξ2/n−1.At R, we need to convert an optical signal into an electrical signal through a photoelectric converter, and we can obtain(9)ySR′=ηhSRRθAPsςRt+n1t,where η represents the photoelectric conversion efficiency. Hence,(10)γSR=γ¯SRha2hp2,where γ¯SR=η2hl2Rθ2A2Psς2/N1. Here, γSR represents the instantaneous signal-to-noise ratio. Under the assumptions of atmospheric turbulence, pointing error, and path loss, the PDF of γSR is given by(11)fγSRγ=B1γξ2−2/2∑j=0∞CjΓB2,Bjγn/2,where B1=1/2C1γ¯SRξ2/2,Bj=1+j/A0hlργ¯SRn,andB2=1−ξ2/n. Then, the CDF can be expressed as(12)FγSRγ=2B1n∑j=0∞Cjγξ2/2G2,32,1Bjγn/2|0,B2,−ξ2n1−∈ξ2/n,1.


## 2.2. RF Transmission Main Link

We assumeφi and ψi are the phases, u represents the path loss coefficient, d1 is the distance of the R-RIS link, and d2 is the distance of the RIS-U link. Then, the channel gain of the R-RIS link can be expressed as hi=d1−u/2αie−jφi, and the channel of gain of the RIS-U link can be expressed as gi=d2−u/2βie−jψi. So, the signal received by the user can be expressed as(13)yRD=PR∑i=1Nhivigix+nRD,where PR is the average transmitting power at R and nRU represents additive white Gaussian noise. According to the results in [24], vi=ρiϕiejϕi represents the reflection coefficient of the i-th reflector, whereρiϕi=1. From [24], we assume ϕi=φi+ψi in order to obtain the maximum signal-to-noise ratio. Then, yRD can be rewritten as(14)yRD=PR∑i=1Nαiβix+nRD=PREx+nRD.According to the results in [14], αiβi follows the Rayleigh distribution with a mean value of π/4 and a variance of 1−π2/16. Thus, the instantaneous SNR obtained by the user can be written as(15)γRD=γ¯RDE2,where γ¯RU=PRd1d2−u/N2. The PDF of γRU is given by [21](16)fγRDx=12σ2xλ−1/4exp−x+λ2σ2I−1/2xλσ2.The CDF can be obtained as(17)FγRDγth=1−Q1/2λσ,γthσ,where Qca,b is the Marcum Q-function [25]. According to the Gaussian Q-function, we can obtain(18)Q1/2a,b=Qa+b+Qb−a.


## 3. System Performance Analysis

### 3.1. Outage Probability

For the communication system, the OP is one of the important indicators to measure the transmission reliability of the communication system, which can be expressed as the probability that the SNR of the receiver signal is lower than the threshold value of the set SNR. Therefore, the OP of this system can be written as(19)Po=PrγSR<γthorγRD<γth=1−1−FγSRγth1−FγRDγth.Combining (12), (17), and (19), the OP can be obtained as(20)Po=1−1−2B1n∑j=0∞Cjγξ2/2G2,32,1Bjγn2|0,B2,−ξ2/n1−ξ2/n,1Q1/2λσ,γthσ.


### 3.2. Asymptotic Outage Probability Analysis

In order to observe the influence of different parameters on the system OP performance, it is necessary to carry out an asymptotic analysis. In the case of high SNR, the system outage performance is mainly determined by the FSO link. Hence, we can obtain(21)Po=PrγSR<γthorγRD<γth≈FγSRγth=2B1n∑j=0∞Cjγthξ2/2G2,32,1Bjγthn2|0,B2,−ξ2/n1−ξ2/n,1.According to [26], we have(22)Po=1nC1∑j=0∞Cj∑k=12∏i=1,i≠k2Γbi−bkΓbk+ξ2/nΓ1−bkΓ1+ξ2/n+bk1+jA0hlρnbkγthγ¯SRnbk/2+ξ2/2,where bk∈0,B2,−ξ2/n. When γ¯SR⟶∞, the diversity order of the system can be expressed as(23)d=−limρ⟶∞logPologρ=n4minbk+ξ22=n4min0,B2,−ξ2n+ξ22.From (23), the asymptotic outage performance of the system depends on the minimum value of 0,B2,−ξ2/n.


### 3.3. Exact Bit Error Rate Analysis

BER refers to the percentage of error information in the total amount of information in a data transmission process. In the relay system model designed by us, the bit error ratePE1 generated in the FSO link and the bit error rate PE2 generated in the RF link are mainly considered. According to [22], the BER of the system can be written as(24)PBER=PE1+PE2−2PE1PE2.According to the results of [27], we can obtain(25)PE=qp2Γp∫0∞e−qγγp−1Fγdγ.The precondition is binary modulation. Combining (12) and (25), PE1 can be written as(26)PE1=B1n2B2−3/2nξ2+1/22πn/2∑j=0∞Cj4+n,64,2+nBj2nn4|0,1/2,1/2B2,1/2B2+1,−ξ2/2n,1/21−ξ2/n−ξ2/2n,…,1/nn−ξ2/2−1,1/21−ξ2/n,1/22−ξ2/n,1/2,1.We will only consider DBPSK modulation here, sop=1 and q = 1. Combining (17) and (25), PE2 can be written as [25](27)PE2=121+2σ2e−λ/2σ2F1112,12,λ2σ2+4σ4.


## 3.1. Outage Probability

For the communication system, the OP is one of the important indicators to measure the transmission reliability of the communication system, which can be expressed as the probability that the SNR of the receiver signal is lower than the threshold value of the set SNR. Therefore, the OP of this system can be written as(19)Po=PrγSR<γthorγRD<γth=1−1−FγSRγth1−FγRDγth.Combining (12), (17), and (19), the OP can be obtained as(20)Po=1−1−2B1n∑j=0∞Cjγξ2/2G2,32,1Bjγn2|0,B2,−ξ2/n1−ξ2/n,1Q1/2λσ,γthσ.


## 3.2. Asymptotic Outage Probability Analysis

In order to observe the influence of different parameters on the system OP performance, it is necessary to carry out an asymptotic analysis. In the case of high SNR, the system outage performance is mainly determined by the FSO link. Hence, we can obtain(21)Po=PrγSR<γthorγRD<γth≈FγSRγth=2B1n∑j=0∞Cjγthξ2/2G2,32,1Bjγthn2|0,B2,−ξ2/n1−ξ2/n,1.According to [26], we have(22)Po=1nC1∑j=0∞Cj∑k=12∏i=1,i≠k2Γbi−bkΓbk+ξ2/nΓ1−bkΓ1+ξ2/n+bk1+jA0hlρnbkγthγ¯SRnbk/2+ξ2/2,where bk∈0,B2,−ξ2/n. When γ¯SR⟶∞, the diversity order of the system can be expressed as(23)d=−limρ⟶∞logPologρ=n4minbk+ξ22=n4min0,B2,−ξ2n+ξ22.From (23), the asymptotic outage performance of the system depends on the minimum value of 0,B2,−ξ2/n.


## 3.3. Exact Bit Error Rate Analysis

BER refers to the percentage of error information in the total amount of information in a data transmission process. In the relay system model designed by us, the bit error ratePE1 generated in the FSO link and the bit error rate PE2 generated in the RF link are mainly considered. According to [22], the BER of the system can be written as(24)PBER=PE1+PE2−2PE1PE2.According to the results of [27], we can obtain(25)PE=qp2Γp∫0∞e−qγγp−1Fγdγ.The precondition is binary modulation. Combining (12) and (25), PE1 can be written as(26)PE1=B1n2B2−3/2nξ2+1/22πn/2∑j=0∞Cj4+n,64,2+nBj2nn4|0,1/2,1/2B2,1/2B2+1,−ξ2/2n,1/21−ξ2/n−ξ2/2n,…,1/nn−ξ2/2−1,1/21−ξ2/n,1/22−ξ2/n,1/2,1.We will only consider DBPSK modulation here, sop=1 and q = 1. Combining (17) and (25), PE2 can be written as [25](27)PE2=121+2σ2e−λ/2σ2F1112,12,λ2σ2+4σ4.


## 4. Numerical Results

According to the expression of OP and BER derived above, we give the simulation results of the proposed communication system model and mainly analyze the influence of different parameter values on the system OP and BER. For this purpose, the following parameters are assumed:λ=10−9km, V=1.2km, Rθ=1, Ps=50, ς=0.8A=0.1, d1=2, d2=2, u=2, and PR=1.Figure2 demonstrates the influence of SNR threshold and channel distance on system outage probability under different SNRs. It is obvious from Figure 2 that when the SNR threshold is constant, the OP of the system increases with the increase in the channel distance. When the channel distance is constant, the OP of the system increases with the increase in the SNR threshold. In other words, the setting of SNR threshold and channel length has a significant impact on the performance of the communication system.Figure 2
OP with different values of SNR threshold and channel distance.In Figure3, the variation curves of the parameters ξ, m, n, and ρ with the system outage probability under different SNRs are analyzed. According to the curve in the figure, it can be concluded that when the parameters m, n, and ρ are constant, the outage probability of the system decreases with the increase in the parameter ξ. The reason is that the parameter ξ is inversely proportional to the jitter standard deviation, and the larger the pointing error, the lower the system performance.Figure 3
OP with different values of parameters (ξ, (m), n, ρ).Figure4 illustrates the change in BER under different SNR conditions and the number of reflectors N for the considered mixed dual-hop FSO-RF-RIS communication system. It can also be seen from Figure 4 that the BER of the system tends to be stable at a high SNR regardless of the value of N. As the number of reflectors N increases, the BER of the system decreases. With the assistance of RIS, the BER of the mixed dual-hop FSO-RF relay communication system decreases with the increase in the number of reflectors N.Figure 4
BER with a different number of reflectors.Figure5 compares the system outage performance under different SNR conditions and different atmospheric turbulence intensities. According to the simulation results, when the SNR is constant, the OP of the system increases with the increase in the atmospheric turbulence intensity.Figure 5
OP with different intensities of atmospheric turbulence.


## 5. Conclusion

In this paper, the RIS technology is introduced on the basis of the mixed dual-hop FSO-RF relay communication system. Considering pointing error, path loss, and atmospheric turbulence, PDF and CDF of the composite channel are derived and the OP and BER of the communication system are obtained by using mathematical function. The simulation results show that channel distance and SNR threshold are inversely proportional to system performance. The larger the pointing error, the lower the system performance. With the assistance of RIS technology, the BER of the system is significantly reduced with the increase in the number of reflectors N.



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