A Mixed FSO/RF Integrated Satellite-High Altitude Platform Relaying Networks for Multiple Terrestrial Users with Presence of Eavesdropper: A Secrecy Performance

: In this paper, the secrecy performance of a mixed free space optical (FSO)/radio frequency (RF) integrated satellite-high altitude platform (HAP) relaying networks for terrestrial multiusers with the existence of an eavesdropper is investigated. In this network, FSO is adopted to establish the link between the satellite and HAP for which it experiences Gamma-Gamma distributions under different detection schemes (i.e., heterodyne and intensity modulation direct detection). The transmission between the amplify-and-forward (AF) relaying HAP and terrestrial multiusers is through the RF and is modeled as shadowed-Rician fading distribution. Owning to broadcasting nature of RF link, it is assumed that an eavesdropper attempts to intercept the users’ conﬁdential message, and the eavesdropper link is subjected to Rician distributions. Speciﬁcally, the closed-form expression for the system equivalent end-to-end cumulative distribution function is derived by exploiting the Meijer’s G and Fox’s H functions. Based on this expression, the exact closed-form expressions of the system connection outage probability, secrecy outage probability, and strictly positive secrecy capacity are obtained under the different detection schemes at HAP. Moreover, the asymptotic analyze of the system secrecy outage probability is provided to obtain more physical insights. Furthermore, the accuracy of all the derived analytical closed-form expressions is veriﬁed through the Monte-Carlo simulations. In addition, the impact of atmospheric turbulence, pointing errors, shadowing severity parameters, and Rician factor are thoroughly evaluated. Under the same system conditions, the results depict that heterodyne detection outperforms the intensity modulation direct detection.


Introduction
Recently, there is tremendous growth in the deployment of emergency wireless communication supporting services for large scale disasters in order to provide vital information for both rescue teams and survivors [1]. In this scenario, a fast and reliable communication is highly difficult to establish owing to geographical complexity of the disaster area where the communication infrastructures of such base stations and optical fibers have been destroyed [2]. As a result of this, satellite communication has been suggested as most promising solution due to its large coverage footprint and reliable wireless connectivity for various fixed and mobile users [3]. Conventionally, satellite communication systems are RF-based, in which different frequency bands are used for a particular application. However, this RF-based systems suffer from spectrum congested, licensed band, low security, and interference with other frequency bands [4]. To overcome this problems, FSO has been recently proposed for satellite communication link owing to its ability to offer extremely large bandwidth, high security, unlicensed spectrum, low interference, ease of 1.
The exact closed-form expression for the system equivalent end-to-end cumulative distribution function (CDF) is derived by exploiting the Meijer's G and Fox's H functions. To the best of authors' knowledge, the derived CDF is novel as a mixed Gamma-Gamma and shadowed-Rician structure under AF relaying protocol is not found in the existing literature.

2.
The analytical closed-form expressions of the system performance in terms of connection outage probability (COP), secrecy outage probability (SOP), and strictly positive secrecy capacity (SPSC) are obtained. 3.
The asymptotic expression for the system secrecy outage probability is derived to obtain physical insight. 4.
Relative to Reference [26], where multiple users are considered, the system performance was not based on physical layer secrecy. In addition, the RF link was subjected Photonics 2022, 9, 32 4 of 17 to Nakagami-m distributions. In this paper, the system performance is based on physical layer secrecy, and the RF links are subjected to Rician fading distributions.

5.
Relative to Reference [32], where the HAP relay aided node employed DF relaying protocol, and the system only considered a single terrestrial user. The HAP in this paper is an AF-based relaying protocol, and the multiple legitimate users are considered at the ground station.
The rest of the paper is organized as follows. The system and channel models are provided in Section 2. In Section 3, the exact closed-form expression for the system equivalent end-to-end cumulative distribution function is presented We derive the analytical expressions of the COP, SOP, and SPSC subject to different detection schemes in Section 4. Numerical results and discussions are depicted in Section 5. Finally, concluding remarks are detailed in Section 6.

System and Channel Models
A mixed FSO/RF integrated satellite-HAP relaying network is illustrated in Figure 1, where the satellite (S) transmits confidential information to the legitimate terrestrial users (D) through an AF HAP relay (R) in the presence of an eavesdropper attempting to wiretap confidential information. It is assumed that there is no direct link between satellite and the terrestrial users due to masking effects as a result of weather, environmental obstacles, long distance, etc. It is assumed that the FSO link follows Gamma-Gamma fading distribution, while the RF link between the HAP relay and the terrestrial users follows Shadowed-Rician fading distribution. In addition, the eavesdroppers RF link between the E and R is considered to undergo Rician distribution. In addition, the HAP relay in the network employs AF relaying protocol, which will introduce a fixed gain into the receive signal irrespective of the fading amplitude on the FSO link. Thus, the network end-to-end signalto-noise ratio (SNR) can be defined as [33]: where C denotes the fixed relay gain parameter, γ 1 = γ 1 |h 1 | 2 represents the instantaneous SNR at the HAP with γ 1 , and |h 1 | 2 , respectively, signifies the average SNR and channel power gain of satellite-to-HAP relay link, while the γ 2 = γ 2 h 2 indicates the instantaneous SNR at the destination, with γ 2 and h 2 representing the average SNR and channel power gain of HAP-to-terrestrial users link, respectively.
Photonics 2022, 9, x FOR PEER REVIEW 4 of 18 3. The asymptotic expression for the system secrecy outage probability is derived to obtain physical insight. 4. Relative to Reference [26], where multiple users are considered, the system performance was not based on physical layer secrecy. In addition,, the RF link was subjected to Nakagami-m distributions. In this paper, the system performance is based on physical layer secrecy, and the RF links are subjected to Rician fading distributions. 5. Relative to Reference [32], where the HAP relay aided node employed DF relaying protocol, and the system only considered a single terrestrial user. The HAP in this paper is an AF-based relaying protocol, and the multiple legitimate users are considered at the ground station.
The rest of the paper is organized as follows. The system and channel models are provided in Section 2. In Section 3, the exact closed-form expression for the system equivalent end-to-end cumulative distribution function is presented We derive the analytical expressions of the COP, SOP, and SPSC subject to different detection schemes in Section 4. Numerical results and discussions are depicted in Section 5. Finally, concluding remarks are detailed in Section 6.

System and Channel Models
A mixed FSO/RF integrated satellite-HAP relaying network is illustrated in Figure 1, where the satellite (S) transmits confidential information to the legitimate terrestrial users (D) through an AF HAP relay (R) in the presence of an eavesdropper attempting to wiretap confidential information. It is assumed that there is no direct link between satellite and the terrestrial users due to masking effects as a result of weather, environmental obstacles, long distance, etc. It is assumed that the FSO link follows Gamma-Gamma fading distribution, while the RF link between the HAP relay and the terrestrial users follows Shadowed-Rician fading distribution. In addition, the eavesdroppers RF link between the E and R is considered to undergo Rician distribution. In addition, the HAP relay in the network employs AF relaying protocol, which will introduce a fixed gain into the receive signal irrespective of the fading amplitude on the FSO link. Thus, the network end-to-end signal-to-noise ratio (SNR) can be defined as [33]:

FSO Link Statistical Distributions
Since the FSO link experiences Gamma-Gamma fading distribution, the probability density function (PDF) of the instantaneous SNR γ 1 under different detection techniques can be defined as [5]: where ω = ξ 2 r(Γ(α)Γ(α)) , M = ξ 2 αβ (1+ξ 2 ) , Γ(.) signifies the Gamma function, ξ signifies the pointing error, α and β are the scintillation parameters which are specified in references [34,35], the r parameter shows the type of detection at the HAP relay node (i.e., r = 1 for heterodyne detection, and r = 2 for IM/DD), µ r indicates the average electrical SNR of the link. Specifically, for heterodyne detection, µ 1 = γ 1 with γ 1 represents the average instantaneous SNR of the link, and, for IM/DD, By integrating (2) through the integral identity detailed in Reference [36] (Equation (26)), the cumulative density function (CDF) of the instantaneous SNR γ 1 can be expressed as: where

RF Link Statistical Distributions
It is assumed that the RF link between the HAP and terrestrial users link follows Shadowed-Rician fading distribution and the PDF of instantaneous SNR γ 2 can be expressed as [17,25,37]: with Ω, m h , and 2b being the average power of LOS, Nakagami fading severity parameter with 0 < m h < ∞, and the multipath component, respectively, and 1 F 1 (x; y; z) denotes the confluent hypergeometric function. By using the identity detail in Reference [38], the confluent hypergeometric function in (4) can be expressed as: where (.) q denotes the Pochhammer symbol. By invoking (5) into (4), the Shadowed-Rician distribution of the RF link can be further simplified as: where Since the sum of SNR at the terrestrial users can be expressed as then, by following the same approach detailed in Reference [17], the PDF of instantaneous SNR γ 2 Shadowed-Rician distribution can be expressed as: Photonics 2022, 9, 32 with B(., .) denoting Beta function. By integration (7) using the integral identity detailed in Reference [38] (Equation (3.351(1), the CDF of the link can be obtained as: where γ(., .) is the lower incomplete Gamma function. By converting the incomplete Gamma function to Meijer-G function using the identity detailed in Reference [39] (Equation (8.4.16(1))), then, (9) can be further expressed as: Owing to broadcast nature of RF link, the eavesdropper attempts to intercept the secret information of the ground users from the HAP relay node. As a result of this, the eavesdropper link is assumed to follow Rican distribution with the PDF of instantaneous SNR γ e defined as [40,41]: where K is the Rician fading factor which is defined as the ratio of the power of the line-of-sight component to the scattered components, and I o (.) denotes the zero-order modified Bessel function of the first kind. By using the identity detailed in Reference [38], where
By substituting (3) and (19) into (13), the concerned system equivalent end-to-end CDF can be obtained as:

Performance Analysis
In this section, the exact closed-form expression of the system connection outage probability (COP), secrecy outage probability, and strictly positive secrecy capacity (SPSC) are derived. In addition, to gain more insight about the derived expression, the asymptotic expression of the concerned system is obtained.

Connection Outage Probability (COP)
This metric characterizes the attainable reliability performance of the proposed system. It describes a situation, whereby the eavesdropper is unable to decode the confidential message of terrestrial users. This usually occurs when the end-to-end instantaneous SNR of the concerned system falls below a predefined threshold value γ th and can be formulated as [46]: Thus, by substituting (20) into (21), the COP of the concerned system under different detection schemes can be obtained as:  These are the most vital performance indices which describe the probability that the instantaneous secrecy capacity falls below a predefined threshold rate of confidential information R s and can be defined mathematically as follows [6]: where Θ = e R s . By invoking (12) and (22) into (23), the system SOP can be expressed as: Thus, By utilizing the integral identity detailed in Reference [38] (Equation (7.813(1))), the I 1 term of (25) can be expressed as: Similarly, By converting the H-Fox function to integral form using the identity detailed in Reference [45], (27) can be expressed as: By applying the integral identity defined in Reference [38] (Equation (3.326(2))), the I 3 term of (28) can be solved as: Putting (29) into (28) and apply the identity given in Reference [45], the I 2 term of (28) can be obtained as: By substituting (26) and (30) into (24), the system SOP can be obtained as: ×H 0,1:1,2:1,3 1,0:3,1:3,3 where ψ 3 = −l, 1, ψ 1 , and ψ 4 = ψ 2 , 0.

Strictly Positive Secrecy Capacity (SPSC)
This illustrates the probability of the existence of positive secrecy capacity so as to offer a secure transmission and can be expressed as [32]: Thus,
The COP performance of the system under the variation of threshold SNR γ th is illustrated in Figure 2 under different atmospheric turbulence. It can be deduced from the results that the increase in atmospheric turbulence significantly deteriorates the system COP performance for the two detection schemes at the HAP. In addition, a similar impact of atmospheric turbulence on the system SOP performance can be observed in Figure 3 as the system SOP gets degraded due to severities of the atmospheric turbulence. In both secrecy performances, it is depicted by the results that heterodyne detection offers the system better performance than IMDD detection. The results also depict that the analytical results perfectly matched with the simulation results, which indicate the accuracy of the derived expressions.
detection. It can also be observed from the result that the asymptotic results follow the SOP results at high SNR. This shows that the quality of eavesdropper channel improves at higher valves of ̅ , which significantly leads to degradation in system SOP performance. The effect of Rican factor level of the eavesdropper link on the system SOP performance is depicted in Figure 6. It can be observed that the higher value of factor has lower system SOP performance. This is because, at large values of factor, there is strong LOS for the eavesdropper to wiretap the confidential message from HAP, and this degrades the system SOP performance. The analytical results match well with simulation results, confirming the validity of the derived expressions.       Figure 3. Impact of atmospheric turbulence on the system SOP performance under different detection schemes when ̅ 2 = 10 dB, ̅ = 5 dB, and = 6.5. r = 2 Figure 3. Impact of atmospheric turbulence on the system SOP performance under different detection schemes when γ 2 = 10 dB, γ e = 5 dB, and ξ = 6.5.
The impact of pointing error on the system SOP performance under the different detection schemes is presented in Figure 4. Under both detections, the lower pointing error value (ξ = 1.1) causes an increase in the effect of pointing errors, which leads to degradation in the system SOP performance. On the other hand, higher values of PE (ξ = 6.5) decrease the effect of PE and improve the system SOP. It is observed from the results that the system performance is better under the heterodyne detection compared to the IMDD detection.   In Figure 5, the effect of γ e level on the system SOP performance is demonstrated under the different detection schemes. It can be seen that the analytical results collaborate perfectly with the simulation results, which proves the accuracy of the derived expressions. Moreover, it can be deduced from the results that the higher the values of γ e , the worse the system SOP performance, with heterodyne detection outperforming the IMDD detection. It can also be observed from the result that the asymptotic results follow the SOP results at high SNR. This shows that the quality of eavesdropper channel improves at higher valves of γ e , which significantly leads to degradation in system SOP performance. The effect of Rican factor level of the eavesdropper link on the system SOP performance is depicted in Figure 6. It can be observed that the higher value of K factor has lower system SOP performance. This is because, at large values of K factor, there is strong LOS for the eavesdropper to wiretap the confidential message from HAP, and this degrades the system SOP performance. The analytical results match well with simulation results, confirming the validity of the derived expressions.     The system SOP performance under different shadowing fading severities is presented in Figure 7. It can be observed that the system becomes degraded as the shadowing fading effect increases from AS to FHS. Under the same channel conditions, the results show that heterodyne detection offers the system better SOP performance compared with IMDD detection. In addition, analytical results of the system SOP closely match with simulation results, showing the accuracy of our derivations.
performance compared to the IMDD detection.
The SPSC performance of the system under the different shadowing fading effect is illustrated in Figure 9 under the heterodyne detection at HAP. It can be observed that the system becomes degraded as the shadowing fading effect get severer. The results also demonstrate that the analytical results perfectly agree with the simulation results, which justify the accuracy of the derived expressions.  The effect of the number of terrestrial users on the system SOP performance under strong turbulence condition is presented in Figure 8. It can be deduced that the system SOP performance significantly improves as the number of ground users increases. This is because multiuser diversity gain is achieved, which, in turn, enhances the system SOP performance. The results indicate that the heterodyne detection offers the system better performance compared to the IMDD detection.  The SPSC performance of the system under the different shadowing fading effect is illustrated in Figure 9 under the heterodyne detection at HAP. It can be observed that the system becomes degraded as the shadowing fading effect get severer. The results also demonstrate that the analytical results perfectly agree with the simulation results, which justify the accuracy of the derived expressions.

Conclusions
The secrecy performance of a mixed FSO/RF integrated satellite-HAP relaying networks in the presence of an eavesdropper is evaluated. The FSO and RF links are model Figure 9. SPSC performance of the system under shadowing fading severities for heterodyne detection at γ 1 = 45 dB, γ e = 5 dB, and ξ = 6.5.

Conclusions
The secrecy performance of a mixed FSO/RF integrated satellite-HAP relaying networks in the presence of an eavesdropper is evaluated. The FSO and RF links are model as Gamma-Gamma distribution and Rican fading distribution, respectively. The exact closed-form expression of the system equivalent end-to-end CDF is derived under different detection schemes. Based on this, the analytical closed form expressions of the concerned system COP, SOP, and SPSC are determined. To obtain more insight about the system performance, the asymptotic analysis of the system SOP is provided. The results shows that the pointing errors, atmospheric turbulence, and shadowing severity significantly degrade the system performance. In addition, the results indicate that heterodyne detection offers the system better performance compared to IM/DD detection. The future work of this paper could be tailored toward the non-orthogonal multiple access (NOMA) for better system spectrum efficiency.