Secrecy enhancement of RF backhaul system with parallel FSO communication link

This paper analyzes the physical layer secrecy (PLS) performance of a hybrid free space optical and radio frequency (FSO/RF) communication system under a modified selection combining scheme. The transmission scheme takes into account secrecy performance as well as diversity gain and ease of implementation. The effects of FSO link, namely the FSO atmospheric turbulence and the FSO receiver pointing error, are included in the analysis while the power amplifier (PA) inefficiency for the RF transmission is considered to have more realistic understandings on the system performance. The exact analytical expressions for the performance indicators including the average secrecy capacity (ASC) and secrecy outage probability (SOP) of the investigated mixed FSO/RF system are derived. The asymptotic SOP analysis reveals useful insights into the performance of the investigated mixed system. Analytical and simulation results are presented to evaluate the PLS performance of the proposed mixed system as well as to compare the performance of other hybrid systems with different setups.


Research background
The growing demands for extremely high data rate in the next generation mobile systems (5G and beyond) require backhaul links with much higher capacity and reliability relative to previous systems (especially in the context of network densification that makes wired backhaul an expensive solution and of the fact that integrated access backhaul (IAB) solution is officially adopted in 5G standard of 3GPP recently) [1].The conventional RF backhaul can be potentially limited by latency problem due to the limited throughput, but is advantageous of being insensitive to weather effects.The broadcasting nature of radio wave propagation also makes RF communication vulnerable to eavesdropping attack.On the other hand, FSO communication features high-rate and low latency transmission, but it is highly susceptible to the atmospheric conditions and adverse weather effects [2].It is also well accepted by both academia and industry that the point-topoint propagation with extreme narrow divergence of FSO beam makes physical interception and eavesdropping extremely difficult and the chance of an attempted intercept being discovered extremely high, thus making FSO communication an inherently secure technology [3][4][5][6].To combine the advantages of RF communication (in terms of its robustness to atmospheric and weather effects) and FSO communication (in terms of secure transmission with high data rate), the parallel setup of FSO and RF communication systems have been developed as a more reliable candidate solution for backhaul network as an integral part of 5G system as well as in many other applications.The parallel system uses both optical and radio links for information transmission and it can simply adjust the use of both links depending on the wireless interference levels and atmospheric conditions [1].

Literature review and motivations
Due to the great potential of parallel FSO/RF scheme in 5G backhaul network and many other applications, a number of research works have been conducted in the domain of performance analysis of such systems [6][7][8][9][10][11][12].A hybrid radio/optical system with a new implementation of selection combining (SC) scheme was investigated in [6], where the same data is sent over both links concurrently.The work in [6] focused on the analysis of bit error rate (BER) and connection outage probability (COP).A switching-based parallel system was proposed in [7], where the BER and COP performance were analyzed.The COP of a hybrid system with adaptive combining was studied in [8], where the maximal ratio combining (MRC) is applied when the link quality of the optical channel plunges under some predefined level.The BER and COP of a hybrid system were computed in [9] by including various FSO impairments (i.e., atmospheric turbulence and FSO receiver misalignment).In [10], the effect of different power allocation schemes on BER of a hybrid system was studied and a suboptimal allocation strategy was proposed.The throughput of a relaying system was investigated in [11], where two hops employ respectively the RF and parallel FSO/RF techniques.The impact of automatic repeat request (ARQ) schemes on the parallel radio/optical configuration was investigated in [12], which showed significant performance improvement with the parallel implementation of both links compared to using only one of the links.It is clear from [6][7][8][9][10][11][12] and the references therein that most existing work on the parallel FSO/RF system has focused on the BER and COP performance.A thorough search in open literature confirms that the existing works on the physical layer security (PLS) of hybrid FSO and RF systems are confined to the cascaded dual-hop FSO-RF systems [5,[13][14][15][16][17][18], and the PLS of parallel FSO/RF configuration is not yet explored despite the great potential of the system in various applications.
The PLS has been widely viewed as a complementary instrument to conventional cryptographic technique to significantly enhance the security of communication in 5G and beyond [19].It was demonstrated in the pioneering work of Information Theory by Shannon and Bloch, etc., that secure communication is feasible by utilizing the characteristics of the physical channel (e.g., fading, noise, interference, etc.) [20].Therefore, the latest advancements in PLS [5,[13][14][15][16][17][18]] coupled with the great potential of parallel FSO/RF system in various applications have motivated us to analyze the PLS performance of such a system configuration in this research.The choice of SC scheme of the parallel FSO/RF setup in this research paper is justified by the trade-off between connection, secrecy, and complexity.While MRC diversity gain can be obtained while both the FSO and RF transmitters send the confidential information, this approach is also subject to the continuous eavesdropping from the eavesdropper.Additionally, the FSO channel coherence time is normally very small (around 0.1∼1 percent of RF channel coherence time), which poses challenges for the channel estimation required under MRC scheme [10].
Further, to obtain realistic insights into the investigated parallel system performance, we take the practical link impairments into consideration.More specifically, the effects of FSO link turbulence and FSO receiver pointing error are included in the analysis of the FSO subsystem [5].For the RF subsystem, the inefficiency of the power amplifier (PA) is the major hardware constraint limiting the performance [21], which is also included in the analysis.It must be noted that the conducted secrecy analysis in this paper significantly differs from those conducted in [5,[13][14][15][16][17][18], where the FSO link is only part of cascaded FSO-RF dual-hop relay system.The differences in the system structures of parallel FSO/RF and cascaded FSO-RF networks make them have different advantages and also different methods of analysis.The cascaded dual-hop FSO-RF relay system is advantageous in terms of extending the connection distance [5].However, the nature of relaying in the dual-hop FSO-RF system indicates that the end-toend performance can be hindered by either link.The parallel FSO/RF system has the benefits of high data transmission rate enabled by FSO link.At the same time, the additional RF link in the parallel setup makes the system more robust to the adverse weather effects.Thus, contrary to the dual-hop relaying system, the parallel FSO/RF system would be preferred when the communication link requires high-data rate and extremely reliable communication as in the case of backhaul transmission [1].
The major contributions of the paper are the following: (i).Despite great potentials of parallel FSO/RF system as a strong candidate for the backhaul network of future networks as well as in many other applications, the PLS performance of the parallel (ii).To make the conducted analysis more practical, the main impairments or characteristics of the FSO and RF communications (e.g., PA inefficiency for RF sub-system, and atmospheric turbulence, misalignment, detection types for FSO sub-system) are also taken into account.(iii).We derive the exact analytical expressions for the secrecy outage probability (SOP), probability of strictly positive secrecy capacity (SPSC), and the average secrecy capacity (ASC) in this work contrary to previous PLS works on FSO communication systems [13][14][15], where only the lower bounds on SOP were computed.(iv).The asymptotic SOP analysis is performed and the corresponding diversity orders under various conditions are obtained to reveal some useful insights into the PLS performance of the investigated parallel system.

Organization of the paper
The remainder of this work is structured as follows.The investigated SC-based parallel FSO/RF setup is introduced in Section 2 followed by the derivation of ASC in Section 3. In Section 4, the SOP analysis and asymptotic SOP analysis is conducted.The simulation and analytical results with the corresponding discussions are presented in Section 5. Section 6 briefly highlights the conclusions of this research.

Investigated system
The PLS of the investigated SC-based parallel FSO/RF setup in this research work is illustrated as in Fig. 1, where the best link of the RF and FSO links is used for information transmission while the other link is idle.The transmitter (S) of the parallel SC-based optical/radio system transmits confidential messages to a desired receiver (D).Additionally, an eavesdropper (E) tries to intercept the confidential messages from S. Due to the good directivity of FSO signal and broadcasting nature of RF signal, the node  can only eavesdrop the information when the radio part of the parallel configuration is transmitting the confidential information.

Channel models
The FSO link turbulence is statistically characterized by the Gamma-Gamma distribution [2] whereas the fading in RF channels is characterized by the Nakagami- distribution [23].The choice of Nakagami model to describe the RF fading is justified as follows.On the one hand, the simple formed model fits a number of propagation scenarios well [24].On the other hand, the model can degrade to or approach other widely used model well (e.g., Rayleigh, Rician, lognormal, Weibull, etc.) [25].It is further assumed that the phasefront of the FSO signal is perfectly estimated and compensated at the FSO receiver, which enables ideal coherent detection at the receiver [14].

FSO communications
By assuming the fading on the FSO link to follow Gamma-Gamma turbulence model and taking into account of the FSO pointing errors caused by jitter, the probability distribution function (PDF) In (1),  and  imply the severity of fading resulting from turbulent flow [26],   is the link's SNR with heterodyne detection (HD) for  = 1 or with intensity modulation under direct detection (IM/DD) for  = 2 being used at receiver [2],  2 denotes the ratio between squared radius of equivalent ray and variance of the FSO receiver jitting movement [15], and ℎ =  2  2 +1 .Hereinafter, we apply the following simplifications: Therefore, the PDF     () can be alternatively expressed as: ) .
From ( 1), the cumulative distribution function (CDF)     (⋅) of    is expressed as [27] For simplicity, the following notations will be used in the rest of the paper: 2 ), (, ), (, ), 0. As a result, the CDF     () is expressed by ) .
Remark 1.It is noteworthy that another widely used model to describe the FSO turbulence is the Málaga model that was proposed in [28].By observing the distribution functions of the Gamma-Gamma and Málaga models, it is evident that they exhibit similar form.Thus, the analytical method applied in this work can be straightforwardly expanded to the case assuming the Málaga fading for the FSO turbulence.■

RF communications
With the Nakagami fading of the RF channels, the PDF    , (⋅) and CDF    , (⋅) of the instantaneous SNR   , for the RF link between the transmitter S and receiver X are given by [29,30] where   , =   ⋅   is average SNR between transmitter S and receiver X,   is the transmit power,   and   respectively are shape factor and average channel gain of corresponding Nakagami fading link.
To account for the effect of non-ideal PA in the RF link, we utilize the following relationship for the PA efficiency [21]:  where   ,    , and    respectively denote amplifier's output power, output power limit, and input power of amplifier; the parameter  represents the amplifier efficiency limit that is reached when   =    , and the parameter  is related to the class of the PA.Both parameters  and  are within the range of 0 and 1.The PA efficiency model in (5) has been widely used in the analysis that includes non-ideal amplifier [31][32][33].Additionally, the accuracy of the model on different classes of amplifiers has been verified by efficiency measurements conducted in the microwave electronics lab of Chalmers University of Technology, Sweden [34].The relationship between the consumed power    and the PA efficiency defined as for different classes of PAs, where   = 18 mW and  = 0.5.The relationship between the output power   and consumed power    for imperfect PAs is shown in Fig. 3.It can be seen that the output power of PA does not improve much as the power    is small due to low efficiency as well as low power.

Remark 2.
As illustrated in Fig. 2, the efficiency of imperfect PAs improves as the input power increases until some saturation point is reached.With other factors being the same, the saturation point for the PA with larger maximum efficiency is found to be lower than that with lower maximum efficiency.■

Selection combining scheme
With the receiver employing the SC scheme, the equivalent SNR   of the parallel setup relies upon the SNRs of optical communication channel    and legitimate RF communication link   , , i.e. [35,Chpt. 9.7], The CDF    (⋅) of the SNR   can be obtained directly as Then, the PDF    (⋅) of the SNR   can be obtained from the differentiation of the CDF given in (7) and is obtained as

Analysis of average secrecy rate
By definition, the secrecy rate that indicates the maximum achievable perfect secrecy rate in Wyner's wiretap model is [36]   (  ,   , ) = max { 0, ln where   , and   respectively denote instantaneous SNRs of the radio wiretap link and legitimate link that consists of the parallel radio and optical channels.
In case of active eavesdropping scenario, the source node can adapt the achievable secrecy rate accordingly and the ASC is the secrecy performance metric that is of central importance in this case.From instantaneous secrecy capacity, the ASC   is mathematically expressed as [37] Noticing that the FSO communication is secure while RF transmission is subject to eavesdropping, the ASC of investigated parallel setup under proposed combining scheme is further given by Evaluation of  1 : The probability  1 indicates the scenario, where the optical link's SNR is larger than RF link's.We can solve the probability  1 as Substituting ( 2) and ( 3) into (12) and rewriting the exponential term with the G-function [38,Eq. (8.4)] and further employing property [38, Eq. (2.24)], the exact expression of the probability  1 can be obtained as follows: Evaluation of  1 : By definition, the average capacity  1 = {ln(  + 1)} can be obtained as follows: where  1 and  1 can be further expressed as To solve the integrals  1 and  1 , we utilize the following transformations involving the Meijer G-function [38,Chpt. 8.4], [39, Eq. ( 8)]: and the following relationship that is obtained by making use of the identity [40, Eq. (2. 3)] and the relationship [38, Eq. (8.3.2.21)]: ) . ( In (18),  ,∶,∶, ,∶,∶, (⋅) represents the extended generalized bivariate Fox H-function (EGBFHF) [40].This function can be conveniently evaluated using mathematical softwares such as Mathematica [41,Table I] and Matlab [42,Appx A].
Expressing the relevant functions in ( 15) and ( 16) into Meijer Gfunction using the above equalities in (17), we can solve the resultant integrals with the aid of (18) as given in Box I.
To solve the single integral  2 , we first express the lower incomplete Gamma functions in (23) in series [15, Eq. ( 2)], convert to relevant terms in Meijer G-function, and then solve the resultant integrals with the identity (18) to obtain where ) .

(26c)
Finally, substituting the expressions of  1 ,  1 , and  2 into (11), the exact closed-form solution for ASC of the investigated system is obtained.

Connection outage probability analysis
Before analyzing the SOP, we first evaluate the COP of the investigated system.The COP implies the scenario that the legitimate receiver is unable to decode the sent information correctly.This occurs while   is smaller than a given threshold  ℎ [45].Therefore, the investigated COP can be directly derived from CDF of   as follows: ) . (27)

Secrecy outage probability analysis
In the passive eavesdropping case, the transmitter resorts to encode and transmit the confidential information into codewords with some constant rate   .If   (  ,   , ) ≥   , perfectly secure information transmission can be achieved, otherwise information secrecy is subject to be undermined [46].Under such scenario, SOP is the most essential performance indicator, which describes the likelihood the secrecy capacity is below some threshold [47].The SOP is mathematically expressed as [47] where  = exp(  ) ≥ 1.
Again, noticing that the eavesdropper can only eavesdrop via the RF link, the SOP of the parallel FSO/RF setup under investigation is further written as where the probability  1 has already been solved in ( 12)-( 13).
Evaluation of  0 : It is obvious that when the capacity of the eavesdropping link is zero, the SOP of the investigated system equals the COP.Hence,  0 is solved as Evaluation of  2 : The probability  2 is the SOP when the eavesdropper's link has nonzero channel capacity.The probability  2 can be written as follows: Substituting ( 3) and ( 7) into (31),  2 can be further expressed as The single integral in ( 32) is solved by using the transformation:  = +1  − 1 and then writing the resultant polynomial in series, where Expressing the relevant functions in (34) into Meijer G-functions using identities in (17) and further using (18), we obtain (1, 1) (  , 1), (0, 1) ) . ( The term   can be efficiently evaluated by the definite integral in (35) using numerical softwares.Next, we compute the closed-form solution of   in following way: first we write the lower incomplete Gamma function in series with the help of [44,Eq. ( Finally, substituting the expressions of probabilities  0 ,  1 , and  2 into (29), the exact solution of the SOP for the investigated SC-based FSO/RF setup is obtained.Remark 3. The probability of SPSC is another important performance metric, whose exact expression is evaluated directly by putting   = 0 or  = 1 in corresponding SOP expression.■

Asymptotic SOP analysis
In this subsection, we conduct the asymptotic SOP analysis under different conditions to gain in-depth understandings on the PLS performance of considered system.

𝜇 𝑡 → ∞
When   → ∞ (i.e.,  → 0) with limited SNRs for the RF links, the SC-based FSO/RF setup will employ the optical link for confidential information transmission while the radio channel will not be utilized.In this case, the SOP is actually equivalent to the COP with the expression given in (27).Then, by making use of asymptotic expression of Gfunction [5,Eq. (30)] in (27), we obtain the following asymptotic expression: where and the parameters   and   represent the th and th terms of  1 and  2 respectively.Recalling that the lowest power of   dominates the asymptotic expression, it is concluded that as   → ∞, the diversity order with respect to   will be minimum of terms {  2  ,   ,   }.
Remark 4. The secrecy diversity of parallel FSO/RF setup under investigation relies largely upon the utilized FSO detection technique.More specifically, the diversity order for the configuration using IM/DD will only be half of that with the HD under the same FSO channel conditions.■

Table 1
Simulation parameters of the optical fading link and RF amplifier.

𝛾 𝑅𝐹 ,𝐷 → ∞
In this case, the parallel FSO/RF communication system will always utilize radio channel for confidential information transmission, and the eavesdropper will also continuously intercept the information through the RF link.Therefore, the SOP under this scenario is equivalent to the probability  2 with the expression given in (31).By utilizing the asymptotic property of lower incomplete Gamma function (i.e., lim →0  (, ) ≅    [44, Eq. (06.06.06.0004.02)]), the asymptotic Substituting ( 3) and ( 39) into ( 31) and utilizing similar rationale as in ( 31)-( 37) to derive  2 , the asymptotic SOP under the scenario   , → ∞ can be expressed by where Substituting ( 41) and ( 42) into (40), we obtain the asymptotic expression for SOP when   , → ∞.Noting that the diversity order is decided by the least exponent of   , in ( 40)- (42), it is obvious that the secrecy diversity order is   in terms of   , .Remark 5.If both   , and   , increase with the transmission power   with the ratio   ,   , being a constant, the diversity order when   → ∞ will be   +   with respect to the transmission power   .■

Simulation results and discussions
The PLS performance of the considered parallel communication setup having varying channel conditions is discussed in this section.The utilized simulation parameters for the FSO link fading and PA characteristics are given in Table 1.For the SOP analysis, we set the secrecy rate threshold as 0.5 nats per second per unit bandwidth.
Before elaborating on secrecy performance, we first examine the COP of parallel configuration versus that of single FSO system in Fig. 4, which shows the COP in terms of varying threshold SNRs for different link and hardware conditions.It is seen that the strong turbulence condition leads to poor FSO link connection, which is significantly enhanced using the parallel setup.Also, the non-ideal PA of  the RF sub-system of the hybrid system largely degrades the connection performance compared to that with ideal PA.

ASC performance
Fig. 5 illustrates how PA nonideality affects ASC of the investigated parallel setup.It can be seen that the ASC for the case with ideal PA appears as an upper limit compared to the cases with imperfect PAs.This is due to the fact that the secrecy capacity depends on the ergodic capacity difference between the legitimate and eavesdropping transmissions.When the transmitted power of RF link (i.e., the output power of PA) increases, the ergodic capacities of both transmissions will increase.However, the increase for the legitimate transmission appears to be larger than that of the eavesdropping link due to the diversity transmission of the legitimate transmission.This implies that as the output power of the PA increases, the ASC will also increase.Since with the same PA input power, the output power for ideal PA will always be larger than that from the imperfect PA, thus leading to the fact that the ASC will be larger in the former case than the latter with the same input power of PA    .In other words, the ASC for the case with ideal PA appears as an upper bound compared to the cases with imperfect PAs.It is also observed that the PA inefficiency exhibits a significantly adverse impact on the system's secrecy.Resulting from the characteristics of  imperfect PA as shown in Fig. 2 (i.e., the efficiency of any imperfect PA becomes lower when the consumed power of the PA is smaller), the ASC stays stagnant when     is small that leads to even smaller output power   due to further impairment from the imperfect PA (as can be seen in Fig. 3).After the consumed power of PA    grows to some threshold and the PA's output power limit (i.e.,    ) is reached, further increasing the consumed power of the PA does not change the output power of the PA   , which thus results in a stagnant ASC again.
In Fig. 6, ASC of investigated parallel FSO/RF setup is plotted against average SNR of legitimate radio communication link.It is seen the investigated parallel setup has much improved ASC compared to RF-only system even when optical communication link undergoes strong turbulent situations.As another point of view, the inclusion of the radio communication link into the parallel system makes the system more robust to the FSO turbulence.
In Fig. 7, the impacts of optical link turbulence and receiver misalignment on ASC are depicted.It is observed that both FSO receiver misalignment and turbulence have adverse effects on the ASC performance, and they exhibit greater impact on the ASC performance as the optical link quality becomes better.However, it can also be seen from Fig. 7 that the atmospheric turbulence poses less performance variation on the ASC for the parallel RF-FSO system compared to the FSO-only or cascaded RF/FSO system in [5,15].Moreover, intersection between the  curves corresponding to varying turbulence is found in Fig. 7.It occurs because when the optical SNR  2 is below some threshold, the hybrid system with more severe turbulence will have slightly higher capacity.While the opposite trend is true when the optical SNR is large enough.This intersection of the ergodic capacity of the legitimate transmission translates to the intersection of the ASC curves with the RF power being unchanged.The similar intersection for curves of ergodic capacity v.s.optical SNR under varying turbulence levels has also been reported for the parallel RF/FSO system with selection combining in [48, Fig. 3].It can also be observed from Fig. 7 that the ASC variations due to the pointing errors caused by jitter are much less before the aforementioned intersection due to the small values of the ASCs when the optical SNR  2 is below the threshold corresponding to the intersection.

SOP performance
The effects of PA nonideality on SOP are depicted in Fig. 8.It can be observed that the SOP for the case with ideal PA is the lower limit compared to the cases with imperfect PAs due to the same reason as analyzed for the ASC in Fig. 5.For non-ideal PA, the SOP will stay stagnant when the consumed power    is small.This is because the output power of the PA   is too small due to low consumed power and low PA efficiency as can be seen in Figs. 2 and 3, which makes the  RF SNRs still worse compared to the optical communication link; thus, the SOP performance is still dominated by the FSO communication link quality.It is also observed that the SOP will stay stagnant again when the consumed power    is larger than some threshold.This is because the maximum output power of the imperfect PA has reached and further increasing the input power of imperfect PA cannot further improve the transmission power of the PA, thus resulting in a stagnant SOP again.
In Fig. 9, SOP of the investigated parallel FSO/RF setup is plotted against average SNR of the legitimate radio link.The results in Fig. 9 again demonstrate the improved secrecy of the proposed SC-based parallel setup in this paper compared to the isolated RF system.For the analytical curve corresponding to strong turbulence with   = 3.2, the SOP at the SNR   , of 35 dB and 25 dB are 5.595 ⋅ 10 −10 and 8.401 ⋅ 10 −7 , respectively.Then, the slope of the curve is calculated as log 10 The SOP of the hybrid system under varying turbulence conditions and detection techniques is plotted in terms of optical communication link's SNR in Fig. 10.Clearly, the FSO receiver detection type has a large impact on the SOP.Additionally, when the optical link's SNR is smaller than some threshold value, the hybrid system with the FSO sub-system employing HD ( = 1) has superior SOP performance than that with IM/DD ( = 2).Instead, when the optical link quality is above some level, the system with IM/DD technique exhibits better performance than that with HD technique in terms of SOP.This is related to the statistics of the instantaneous SNR for the FSO receiver with different detection types.As the optical SNR   is lower than some threshold, the probability of the SC-based setup using FSO signals for demodulation (namely the probability  1 ) is larger when the FSO system is equipped with IM/DD technique compared to the case using HD technique; and the opposite trend holds when the electrical SNR is larger than the threshold.This is verified numerically by the plot of probability  1 in Fig. 11, where an interaction is observed between the curves corresponding to IM/DD and HD detections due to the above reasons.

Summary and conclusions
The PLS performance analysis of a parallel optical and RF setup with SC was conducted in this paper.Exact closed-form expressions for performance indicators such as connection outage probability, average secrecy capacity, and secrecy outage probability were derived by including the effects of FSO channel atmospheric turbulence and RF hardware nonideality.Furthermore, the secrecy diversity analysis was also performed to obtain in-depth understandings into the PLS performance of the investigated parallel setup.The results show that the FSO turbulence and the RF PA inefficiency largely affect the connectivity of the investigated parallel system.Meanwhile, the investigated SC-based parallel system is more robust than the FSO-only system in connectivity and is superior to the isolated RF system in secrecy performance.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .
Fig. 2. PA efficiency v.s.   for PAs with varying levels of PA efficiency.