On Secrecy Performance of Mixed Generalized Gamma and Málaga RF-FSO Variable Gain Relaying Channel

The emergence of an array of new wireless networks has led researchers to evaluate the prospect of utilizing the physical properties of the wireless medium in order to design secure systems. In this paper, the physical layer secrecy performance of a mixed radio frequency-free space optical (RF-FSO) system with variable gain relaying scheme is investigated in the presence of an eavesdropper. We assume that the eavesdropper can wiretap the transmitted confidential data from the RF link only. It is further assumed that the main and eavesdropper RF links are modeled as generalized Gamma (GG) fading channel, and the free space optical (FSO) link experiences Málaga turbulence with pointing error impairment. Our primary concern is to protect this confidential information from being wiretapped. Besides pointing error, the atmospheric turbulence and two types of detection techniques (i.e. heterodyne detection and intensity modulation with direct detection) are also taken into consideration. Utilizing amplify-and-forward (AF) scheme, the novel mathematical closed-form expressions for average secrecy capacity, lower bound of secrecy outage probability, and strictly positive secrecy capacity are derived. As both the links (RF and FSO) undergo generalized fading channels, the derived expressions are also general. We present a unification of some existing works utilizing the proposed model to better clarify the novelty of this work. Finally, all the derived expressions are justified via Monte-Carlo simulations.


I. INTRODUCTION
A. BACKGROUND Free space optical (FSO) communication is now growing a lot of interest among researchers due to its immunity to interference, lower cost, wider bandwidth, and higher capac-The associate editor coordinating the review of this manuscript and approving it for publication was Christian Esposito .
ity [1], [2]. This communication operates at an unlicensed optical spectrum, thus providing a solution to the scarcity of radio frequency (RF) resources [3]. This technology is applicable in underwater communication, 'last mile' access, military applications, disaster recovery, etc. [4]. However, in the case of long distance communication, some factors like pointing error and atmospheric turbulence deteriorate the overall performance of FSO networks significantly [5]- [7]. VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ A dual-hop mixed RF-FSO system can be considered as a solution to those drawbacks of the FSO technology. In this system, the communication occurs in two hops. The source sends the information to the relay via RF link in the first hop. Subsequently, this signal is converted into optical signal via a relay. That optical signal is finally sent to the receiver via FSO link. The RF-FSO mixed scenario provides an extended cell coverage area. Besides, it also ensures improved received signal quality by employing spatial diversity. These are the main reasons behind widespread interest of the researchers in this technology and such similar systems.

B. LITERATURE SURVEY
Mixed RF-FSO frameworks have been investigated thoroughly in recent years because of its promising nature. The authors in [8] considered an amplify-and-forward (AF) fixed gain relaying technique over Rayleigh -Gamma-Gamma( ) fading channel and analyzed the performance of this model by deriving the closed-form expression for Outage probability (OP). In [9], the RF-FSO link was modelled with Nakagami-m and fading channels. The authors here took both HD and IM/DD techniques into consideration and then derived the closed-form expressions for OP, bit error rate (BER), and ergodic capacity (EC). Fixed gain and channel state information (CSI) assisted relaying technique was considered by the authors in [10] for a dual hop mixed RF-FSO system. Here they examined the channels' performance by acquiring the closed-form expressions for OP and bit-error rate (BER). The expressions for OP and average BER for various modulation techniques, such as phase-shift keying (PSK), differential PSK (DPSK), and non-coherent frequency-shift keying (NCFSK), were derived in [11], where the authors used exponentiated-Weibull distribution to model the FSO link. The authors in [12] derived the closed form expressions for EC, OP, and BER over Rayleigh-kappa-mu/inverse Gaussian fading scenarios utilizing the expansion of moment generating function (MGF). The authors in [13] and [14] used identical channel models but different relaying techniques. In [13], closed-form expressions for OP, EC, and BER were obtained for two IM/DD models e.g. input-independent and cost-dependent, using decode-and-forward (DF) relaying, while in [14], OP and EC expressions were obtained for a multi-user scenario using AF relaying technique. The impact of non-zero bore-sight, caused by thermal expansion of the building, was investigated in [15] over Nakagami-m-Málaga mixed channels where the authors derived expressions for OP and average BER (ABER).
Traditional security measures, such as encryption technique is harder to implement in wireless networks consisting of intermediate terminals and relatively simpler end devices. So instead of relying on complicated upper layer security, secured data transmission can be ensured via utilizing the physical properties of the medium that have been proposed in [16]. As the wireless medium is random and inherently time-varying in nature, physical layer security (PLS) has proven to be effective in protecting the secret information from eavesdropping [17]- [20]. Taking advantage of the PLS features, the researchers have performed several analysis to evaluate the secrecy performance of FSO communication systems [21]- [23]. Similar analysis was also performed for mixed RF-FSO systems to show how PLS can protect data [24]- [31]. Considering variable gain relaying technique for both HD and IM/DD techniques, the authors of [24] derived the exact closed-form expression for average secrecy capacity (ASC) over Nakagami-m-Málaga fading model. In [25], a secure simultaneous wireless information and power transfer (SWIPT) system was analyzed over a Nakagami-mdual-hop RF-FSO scenario for various detection techniques. The authors derived expressions for secure OP (SOP) and showed that secrecy diversity order (SDO) is affected by the fading parameters, detection techniques, and the pointing error.
The authors in [26] took the effects of imperfect channel state information into consideration and examined its consequence on the SOP with variable and fixed gain relaying techniques. The expressions for average secrecy rate (ASR) and SOP were derived in [27], where the authors considered a highly secure optical link for communication. So the eavesdropper can wiretap only the RF link. The mathematical expressions for SOP and ASC were obtained in [28] for a mixed RF-FSO communication link. Authors also observed that, in case of variable gain relaying scheme, the RF link has little impact on the secrecy performance of the channel, and the HD technique outperforms the IM/DD technique. In [29], the presence of an eavesdropper was assumed to be in the relay-destination link, and the authors deduced the closed-form expressions for SOP and strictly positive secrecy capacity (SPSC) employing DF relaying scheme. In [30], a SWIPT scenario was proposed where the energy receiver acts as a potential eavesdropper. The authors investigated the secrecy capability of the proposed RF-FSO cooperative system with multiple antennas at the receiver by deriving the closed-form expressions for ASC and SOP. The authors in [31] considered a Nakagami-m fading and Málaga mixed two-way relaying (TWR) model with multiple eavesdroppers. Here they deduced the mathematical expressions for SOP and secrecy throughput (ST) to analyze the secrecy performance. Considering Nakagami-m-Málaga fading scenario, the effects of outdated CSI and transmit antenna selection scheme (TAS) were examined in [32]. The authors observed that a higher number of antennas at the source node doesn't substantially improve the secrecy performance.

C. MOTIVATION
The aforecited literature has revealed that the secrecy analysis over RF-FSO system has been performed considering mainly the multipath fading channels for the RF link. But in practice, generalized fading channels are more likely to be encountered during the data transmission as the wireless fading channels are time varying in nature. Hence, a secrecy analysis over a RF-FSO dual hop link, considering generalized fading channels for both the RF and FSO links, is still an open problem for the researchers. Motivated by aforementioned observations, in this work, a secure framework over generalized Gamma (GG)-Málaga fading mixed RF-FSO scenario is proposed in the presence of an eavesdropper. Here the eavesdropper is considered to be able to wiretap the confidential information via the RF link only, as the directivity of the optical beam in the FSO link is very high, and that's why it is highly unlikely that the eavesdropping will occur in the FSO link. We consider two generalized fading environments (GG and Málaga) because a number of famous classical distributions can be obtained as special cases of both fading distributions. For example Weibull, Nakagami-m, and Rayleigh fading channels can be obtained from GG fading environment and Málaga model includes Gamma-Rician, Log-Normal, , etc. distributions as its special cases [33], [34].

D. CONTRIBUTIONS
Our main contributions are summarized as follows.
• At first, we realize the probability density functions (PDF) for SNR of each individual hop of the proposed system and then derive the PDF and cumulative distribution function (CDF) of the dual-hop end-to-end SNR. We take atmospheric turbulence, pointing error, and two detection techniques (HD and IM/DD) into consideration.
• Secondly, we investigate the secrecy capability of the mixed RF-FSO system by deriving the closed-form expressions for SOP and SPSC in terms of Meijer's G function. Additionally, we also represent the ASC in terms of extended generalized bivariate Meijer's G function (EGBMGF). To the best of authors' knowledge bsaed on the open literature, these expressions are novel.
• We present some numerical outcomes based on the derived expressions of ASC, SOP, and SPSC. As both of our channels (RF and FSO) are generalized fading channels, the performance of our dual-hop mixed RF-FSO system unifies the secrecy performance of several existing models in the existing literature [35], [36]. This observation proves the novelty and superiority of our model over all the existing works.
• Finally, the accuracy of our analytical expressions are validated by Monte-Carlo simulations. Our analysis demonstrates that the secrecy performance worsens because of the increment in atmospheric turbulence and pointing error. The results also suggest that the HD technique shows better performance than the IM/DD scheme.

E. ORGANIZATION
The rest of the paper has been arranged in the following way.
The system model has been described in an elaborate manner in Section II. Closed-form expressions for ASC, SOP, and SPSC are derived in Section III. Analytical and simulation results are presented in Section IV, and finally Section V presents the concluding remarks.

II. SYSTEM MODEL AND PROBLEM FORMULATION
A mixed RF-FSO system is considered in Fig. 1, where a single antenna source, P, is transmitting secret information to a legitimate receiver, K , via an intermediate relay, H .
Here, H is equipped with a single transmit aperture and a single receive antenna, and K has one receive aperture.
As the distance between P and K is very large, there is no direct link between them, and the communication occurs only through the relay. A single antenna eavesdropper, W , is also present in the network and trying to decode the confidential information from the source. The channel between P and K is the main channel, and the one between P and W is denoted as the eavesdropper channel. The total communication takes place in two separate phases. In the first phase, P transmits confidential information to H via RF link. The relay then converts the RF signal to optical signal and re-transmits this optical signal via FSO link to K in the second phase. The eavesdroppers are assumed passive and can decode information via RF links only. The RF links of main and eavesdropper channel experience independent and identically distributed (i.i.d.) GG fading while the FSO link undergoes the Málaga turbulence.
We denote the channel gains between P and H as g ph ∈ C 1×1 and that between P and W as l pw ∈ C 1×1 , so the signals at H and W can be expressed in the following manner: respectively. Here, the signal transmitted from P is denoted as z ∼ N (0, P p ), the imposed additive white Gaussian noises (AWGN) at H and W are given by n h ∼ N (0, P h ) and m w ∼ N (0, P w ), respectively, and the terms P h and P w symbolize the noise powers.

A. PDF AND CDF OF SNR FOR RF MAIN CHANNEL
The instantaneous signal-to-noise ratio (SNR) of the main RF channel is denoted by R = P p P h g ph 2 . The PDF of R can be expressed as [37,Eq. (2)] where M 1 =λ r c r cr kλ r cr (c r ) , λ r is the fading severity parameter, and c r is the VOLUME 8, 2020    (4), the CDF of R can be expressed as We consider our RF channels (both main and eavesdropper) experiencing GG distribution due to its flexibility of modeling several well-known small scale fading channels, which are its special cases. This makes it more popular to the researchers to utilize relative to the other conventional models. For instance, some classical distributions modeled from GG Distribution are included in Table 1 [39].

B. PDF AND CDF OF SNR FOR FSO CHANNEL
The Málaga turbulence model is a well-known generalized model that includes some classical turbulence models as its special cases as shown in Table 2. We consider the FSO link experiencing Málaga turbulence with pointing error impairments.
Hence, the PDF of instantaneous SNR of the FSO channel denoted by o is expressed as [33] where β o denotes the fading parameter, α o denotes a parameter which is related to the effective number of large-scale cells of the scattering process, is utilized to refer to the ratio of the equivalent beam radius to the pointing error displacement standard deviation (jitter) at the receiver [40], the electrical SNR is denoted by µ r , r refers to the detection technique utilized i.e. for HD technique (r = 1), , the amount of coupled scattering power to the LOS component is represented by 0 ≤ ρ ≤ 1 parameter, the average power in regard of the coherent contributions is denoted by where R =

C. PDF AND CDF OF SNR FOR DUAL-HOP RF-FSO LINK
The end-to-end instantaneous SNR of the dual-hop RF-FSO channel considering variable gain relaying is given by [28, Eq. (7)] The CDF of D can be expressed as [15,Eq. (15)] Substituting (5) and (7) into (9), and utilizing some algebraic manipulations, the CDF of D is obtained as The PDF of equivalent SNR at the destination for the dualhop system can be derived by differentiating (9) with respect to D as [41, Eq. (12)] By substituting (3), (5), (6), and (7) into (11), and utilizing [42, Eq. (2.24.2. 3)] and after some algebraic manipulations and simplifications, the PDF of D is expressed as

D. PDF AND CDF OF SNR FOR EAVESDROPPER CHANNEL
The instantaneous SNR of the eavesdropper channel is denoted by E = P p P w h pw 2 . Similar to (3), the PDF of E can be expressed as (3) where N 1 =λ e c ce e λ ece e (c e ) , N 2 =λ e c e − 1, N 3 = c e −λ e e , λ e = λ e /2, λ e is the fading amplitude, c e is the normalized variance, and the average SNR of eavesdropper channel is e . Like (5), the CDF of E is expressed as

III. PERFORMANCE ANALYSIS A. AVERAGE SECRECY CAPACITY (ASC) ANALYSIS
As the wireless channels are time-varying in nature, ASC is computed as the the average value of instantaneous secrecy capacity that is expressed as [24,Eq. (12)] By substituting (10) and (14) into (15) and considering λ r = λ e = 2, ASC is obtained as (20), as shown at the bottom of the next page. In the following, we derive the termsh 1 ,h 2 , h 3 , andh 4 .

4) DERIVATION OFh 4
The final form ofh 4 has been deduced by following the similar procedures of obtainingh 2 as

B. SECRECY OUTAGE PROBABILITY (SOP) ANALYSIS
The SOP is interpreted as the probability that instantaneous secrecy capacity (C s ) falls below a predetermined threshold, VOLUME 8, 2020 R s . The SOP of mixed RF-FSO channel in the presence of an eavesdropper can be expressed as [28,Eq. (10)] where = 2 R s and R s > 0. The lower bound of the SOP can be derived as [32, Eq. (7)] By substituting (10) and (13) into (22), the SOP is expressed as where L 1 = (c e +p 1 )

C. STRICTLY POSITIVE SECRECY CAPACITY (SPSC) ANALYSIS
In order to ascertain the secrecy of the transmitted information, the secrecy capacity must be a positive quantity.
2) DERIVATION OF 2 Similar to the derivation of 1 , 2 can be expressed as

3) DERIVATION OF 3
The expressions of 3 is deduced as

4) DERIVATION OF 4
Following the similar procedures of obtaining 2 , 4 can be expressed as

D. SIGNIFICANCE OF OUR ANALYSIS
Our main target in this work is to enhance the level of security of the proposed network by taking advantage of the physical properties of RF-FSO propagation medium. To accomplish this task, we relate all the system parameters with three well-known secrecy measures i.e. ASC, SOP, and SPSC. As per the authors' knowledge based on the open literature, we are the first to derive the expressions in (20), (24), and (30) corresponding to our proposed model, and hence our derived expressions are totally novel. It is noteworthy to point out that for the special case of Rayleigh-scenario, our derived expressions in (24) reduce to the expressions of [35,Eqs. (15)]. Again for the scenario of Nakagami-m-fading system as a special case of our model, the expressions presented in (20) and (24) agree with the results of [36,Eqs. (13) & (20)].

IV. NUMERICAL RESULTS
This section illustrates the analytical results corresponding to the closed-form expressions of ASC, SPSC, and SOP. Additionally, the impact of fading, pointing errors, and atmospheric turbulence on the secrecy performance of the proposed framework are also determined. Besides, we also present Monte-Carlo simulations via MATLAB in order to validate the derived analytical expressions. We assume λ r = λ e = 2 while deriving the expressions in closed-form, but impact of λ r and λ e on the system performance are demonstrated below via numerical methods. Other parameters used for both the simulations and analysis are set as (α o , β o ) = (2.296, 2) for strong turbulence, (α o , β o ) = (4.2, 3) for moderate turbulence, and (α o , β o ) = (8, 4) for weak turbulence similar to [33], r = 1 (HD technique) and 2 (IM/DD technique), and R s = 0.5 bits/sec/Hz.  In order to investigate the effect of e on the secrecy capacity, the ASC is plotted against k for selected values of e in Fig. 2. An increase in e reduces the ASC, as testified in [24]. This is because the lower value of e indicates weaker SNR at the eavesdropper terminal. The simulated results demonstrate exact similarities with the analytic results which ensures that our derived expressions are correct.
In Fig. 3, we investigate the impact of fading severity parameters on the ASC for specific values of λ e and λ r . We observe that ASC improves for a higher value of λ r as a higher value of λ r signifies lower amount of fading in the main channel. On the other hand, ASC decreases for a higher value of λ e . This is expected because higher value of λ e denotes weak fading between the source and eavesdropper channel.
A comparison between the two detection techniques is performed in terms of ASC, SPSC, and SOP in Figs. 4, 5,  = 1, g p = 2, = 6.7, e = −10dB, and 10 =¯ 20 = 25dB. and 6, respectively, where HD technique (r = 1) outperforms the IM/DD technique (r = 2). Compared to IM/DD technique, the SNR at destination tends to be higher for HD technique, thus it demonstrates better performance, as testified in [9], [46], and [47]. In addition, we observe that the secrecy performance also varies significantly with various levels of turbulence. It can clearly be seen that better performance is obtained for weaker turbulence compared to stronger turbulence for both HD and IM/DD techniques. This indicates that stronger turbulence affects the SNR at K more significantly than the weaker turbulence. Same conclusions were also made in [9].
Since the main RF link is modelled as generalized Gamma fading channel, the SOP is plotted versus k in Fig. 7 to demonstrate the generic nature of this generalized fading channel. It is observed that several multipath fading scenarios  can be obtained from this fading model simply by tweaking the fading parameter and normalized variance. It is evident that the SOP is worst for Rayleigh fading model whereas it is considerably better for Nakagami-m fading channel.
The impact of pointing error is examined in Figs. 8 and 9. For this purpose ASC and SOP are plotted versus average SNR of RF channel for selected values of λ r , λ e , and . It is observed that both the secrecy capacity and the secure outage performance improve significantly when pointing error is negligible ( = 6.7), whereas the performances deteriorate when the pointing error is strong ( = 1). This improvement in secrecy capacity occurs as higher values of leads to better pointing accuracy that matches well with the results of [9].
Comparison With Existing Works: We consider two generalized fading scenarios to model the RF and FSO links e.g. the RF link experiences generalized Gamma fading while the  FSO link experiences Málaga turbulence with pointing errors. Hence, our proposed model unifies the secrecy performance of several classical RF-FSO fading scenarios [34], [37] that are available in the existing literature. For example, Rayleighmodel [35] is obtained by setting λ r = 2, c r = 1, ρ = 1 and = 1. Again for λ r = 2, ρ = 1, and = 1, we obtain Nakagami-m-scenario [36], where c r denotes Nakagami-m fading parameter. To generate a Rayleigh-Lognormal mixed fading scenario, the parameters would be λ r = 2, c r = 1, ρ = 0 and g p → 0. Besides these special cases, Weibull fading model also exhibits accurate fit to the measurements of experimental fading channels. We can use our proposed model to easily generate a secure Weibull-/Lognormal/Gamma environment with c r = 1 where λ r represents the Weibull fading parameter. This mixed combination of Weibull distribution with , Lognormal,  and Gamma distributions to model the RF and FSO links is totally absent in the existing literature. The above mentioned generic nature of our proposed model has been demonstrated in Fig. 10 by plotting the SOP against k . The results demonstrate that our model unifies the performance of various distributions which are summarized in Table 3.
Based on the observations it is trustworthy that our proposed work is novel and most generalized relative to all other existing works.

V. CONCLUSION
This paper deals with the secrecy performance analysis of dual-hop mixed RF-FSO system in the presence of an eavesdropper. The novel closed-form expressions for ASC, SOP, and SPSC are derived and validated through Monte-Carlo simulations. HD and IM/DD techniques were utilized to detect the signals at the receiver. Based on the numerical results, we can confirm that HD technique is a superior approach for obtaining improved secrecy performance because of its enhanced ability to reduce the detrimental impacts of fading, atmospheric turbulence, and pointing error, compared to the IM/DD technique.