Secrecy Outage Analysis of Mixed RF-FSO Downlink SWIPT Systems††thanks: Manuscript received.
We analyze a secure dual-hop mixed radio frequency-free space optical (RF-FSO) downlink simultaneous wireless information and power transfer (SWIPT) systems. The FSO link and all RF links experience Gamma-Gamma, independent and identical Nakagami- fading, respectively. We analyze the effects of atmospheric turbulence, pointing error, detection technology, path loss, and energy harvesting on secrecy performance. Signal-to-noise ratios at both legitimate and illegitimate receivers are not independent since they are both simultaneously influenced by the FSO link. We derive the closed-form expression of the secrecy outage probability (SOP) as well as the asymptotic result for SOP when signal-to-noise ratios at relay and legitimate destinations tend to infinity. Monte-Carlo simulations are performed to verify the accuracy of our analysis. The results show that the secrecy diversity order (SDO) depends on the fading parameter of the relay-destination link and the number of the destination’s antennas. Additionally, the SDO also depends on the fading parameters, the pointing error parameter, and the detection type of the FSO link.
I-a Background and Related Works
Dual-hop mixed radio frequency-free space optical (RF-FSO) systems are designed to overcome atmospheric turbulence and other factors limiting the applications of FSO systems. They can also effectively improve communication coverage, save spectrum resources, avoid relocating devices, and are considered as a powerful candidate for next generation of wireless communications [1, 2, 3]. In a typical mixed RF-FSO system, users’ signals are transmitted to the base station (which serves as a relay node) via the RF link, converted to optical signals, multiplexed, and transmitted to the data center via the FSO link. We called this “uplink (UL) scenarios”. On the contrary, in “downlink (DL) scenarios”, messages sent from the data center are delivered to the base station/relay through the FSO link, converted to a wireless signal and then sent to the user. Assuming a message sent by the data center is only for specific users, the remaining users within the coverage of the relay node are potential eavesdroppers.
It has been verified that physical layer security (PLS) technology can prevent illegitimate receivers from eavesdropping due to the time-varying nature of the wireless medium -. Numerical studies of PLS over FSO satellite ground systems were performed by Endo et al. . They showed that secrecy communications were possible and that there can be a complementary technologies to balance security and usability issues. But in their study, Endo et al. only considered some idealistic conditions and assumed that the channels were fading-free. Lopez-Martinez et al.  studied PLS based on Wyner’s FSO model and used the probability of strict secrecy capacity to evaluate the secrecy performance. But they considered only two special cases: when the eavesdropper is either near the source or the destination. Sun and Djordievic  studied a secure orbital angular momentum multiplexing FSO system and numerically simulated its secrecy capacity. Their results showed that secrecy performance depends on the location of eavesdroppers and that orbital angular momentum multiplexing technology could improve the secrecy in weak and medium turbulence regimes.
The FSO link is viewed to be highly secure since the laser beam has high directionality -. However, the broadcast nature of the RF link makes the mixed RF-FSO systems vulnerable to wiretap. Recently, the PLS of mixed RF-FSO systems stimulated researchers’ interest and quite a few studies on this topic were reported in the literature, including -. El-Malek et al.  studied the security reliability trade-off of a single-input multiple-output mixed RF-FSO system and derived the closed-form expressions for some generalized performance metrics, such as outage probability (OP), intercept probability (IP), etc. The same authors also analyzed the effect of RF co-channel interference on the secrecy performance of mixed RF-FSO systems and proposed a new power allocation scheme to enhance the secrecy performance . Notice that the all the performance metrics studied in  and  were considered the main channel or wiretap channel separately. By contrast, the secrecy outage probability (SOP) investigated in our work is considered the main channel and wiretap channel simultaneously. We studied the secrecy performance of a UL mixed RF-FSO system with perfect and imperfect channel state information in  and , respectively. The closed-formed expressions for the exact and asymptotic SOP were derived. Our results demonstrated that the turbulence degrades the secrecy performance and that it is difficult to wiretap when the intensity modulation with direct detection (IM/DD) technology is replaced by the heterodyne detection (HD) technology. Furthermore, the secrecy outage performance of a UL mixed RF-FSO system with was investigated in
It is noteworthy that - considered the UL mixed RF-FSO transmission systems, in which the FSO link only influences the signal-to-noise ratio (SNR) at legitimate receivers. Technically speaking, it is much more challenging to analyze the secrecy performance for DL mixed RF-FSO transmission systems compared to analyze the OP/IP/SOP for UL mixed RF-FSO transmission systems. This is because the problem in DL mixed RF-FSO systems becomes complex where all RF destinations are affected by the FSO link.
It is expected that the next generation of wireless communications will comprise a lot of simpler and cheaper wireless nodes which are powered by batteries. For these nodes, it is quite difficult or even impossible to replace the batteries. Then the simultaneous wireless information and power transfer (SWIPT) technology was proposed to solve this problem -. Since part of energy is used to charge the battery at receivers, the power for information delivery will decrease, which will lead to the degraded secrecy capacity . Thus many literature recently focused on the security of SWIPT systems -. The security for SWIPT systems was first considered in  and the resource allocation design for secure MISO SWIPT systems was formulated as a non-convex optimization problem and an efficient resource allocation algorithm was proposed to obtain the global optimal solution. The secrecy performance of SIMO and MISO SWIPT systems were investigated and the closed-form expressions for SOP were derived in  and , respectively. The secrecy outage performance of an underlay multiple-input-multiple-output cognitive radio networks with energy harvesting and transmit antenna selection was studied in . And all these works just considered the RF systems. Pan et al. investigated the secrecy performance of a hybrid visible light communication (VLC)-RF system with light energy harvesting and derived analytical expressions for exact and asymptotic SOP in . Makki et al. analyzed the throughput and OP for the hybrid RF-FSO SWIPT systems and a power allocation scheme was proposed in . But all these works considered the hybrid systems, in which the FSO/VLC and RF links were parallel and backup/backhaul. In our work, a dual-hop mixed RF-FSO system is considered. It is assumed that SWIPT is used to collect energy for all RF receivers from the wireless signals sent by the relay node.
I-B Motivation and Contributions
To our best knowledge, there is no literature studying the physical layer security of DL mixed RF-FSO SWIPT systems. In this work, we study a secure DL mixed RF-FSO system and analyze the effects of misalignment, different detection schemes, SWIPT, and multiple antenna techniques on secrecy performance of mixed systems. In summary:
We study the secrecy outage performance of the DL mixed RF-FSO SWIPT systems over Gamma-Gamma - Nakagami- fading channels with DF relaying schemes. We investigate the effects of misalignment, different detection schemes, SWIPT, and multiple antenna techniques and deduct the closed-form expressions for the exact and asymptotic SOPs.
We present a selected figures illustrating Monte-Carlo simulations and analytic results in order to validate our analysis. Results show that the HD detection method can lead to lower secrecy outage compared to IM/DD, and that the SOP can also be improved with less pointing error or/and weak turbulence. The path-loss degrades the security of the DL mixed RF-FSO systems when the FSO link is the bottleneck of the transmission, and vice versa. Moreover, our results show that the secrecy diversity order (SDO) is determined by the fading parameter of the relay-destination link and the number of the destination’s antennas. Additionally, the SDO also depends on the fading parameters, the pointing error parameter, and the detection type of the FSO link.
The correlation of the SNR at legitimate and illegitimate receivers is considered and is eliminated by using the law of total probability. The results in our work does not only apply to the mixed RF-FSO systems but also can be utilized to investigate the secrecy performance of all the dual-hop cooperative systems with DF scheme when there is not direct link between the source and the receiver.
Although the secrecy performance of DL mixed RF-FSO systems was investigated in , the correlation of the SNR at both legitimate and illegitimate receivers was not considered. Furthermore, SWIPT, path-loss fading, and multiple antennas are considered in this work.
The rest of the paper is organized as follows. Section II describes the system model. The exact SOP analysis is presented in Section III, while Section IV analyzes the asymptotic SOP. Simulation results are given in Section V, while Section VI concludes this paper.
Ii System Models
We consider a DL mixed RF-FSO SWIPT system (shown in Fig. 1), with confidential signals transmitted from the data center to the legitimate destination node through the relay . There is an eavesdropper who is attempting to wiretap the information, and and are equipped with and antennas, respectively. We assume that the FSO link follows a unified Gamma-Gamma fading and that all the RF links experience independent and identical Nakagami- fading. The maximum ratio combining (MRC) scheme is utilized at both and to improve the received SNR.
All the receivers (both and ) are equipped with a rechargeable battery harvesting the RF energy broadcasted from , and power splitting (PS) method is used to coordinate the processes of information decoding and energy harvesting from the received signal [16, 23, 24]. This means that the received signal is divided into information decoding (ID) part and harvesting energy (EH) part. In other words, the portion of the signal power is used to decode information, and the remaining portion of power is used for harvesting the energy. The linear EH model is not practical since an EH circuit usually comprises diodes, inductors and capacitors. The new non-linear EH model was proposed in  and , respectively. Actually, the EH model does not influence the secrecy performance of the mixed RF-FSO system because the different EH model just influence the energy harvested at the receivers ( and ) and does not influence the SNR at the receivers. Only the portion of signal power used to ID influences the SNR at receivers. The situation is similar to the case with the infinity capacity EH buffer and finite capacity EH buffer scenarios. Our results are also fit to the case with time splitting method. It should be noted that the splitting factors in our work are assumed to be fixed. The secrecy performance might be affected with the splitting factors which are dynamically varying depending on the non-linear EH model, which will be addressed in our future work.
The probability density function (PDF) and cumulative distribution function (CDF) of can be expressed as 
respectively, where , , . and are the fading parameters, represents the detection scheme used at , i.e. for HD and for IM/DD, is the pointing error at the destination . , represents the electrical SNR of the FSO link, , , , , and is Meijer’s -function, as defined by (9.301) of .
The effects of path-loss and small-scale fading of the RF link are considered and the received signals at the th antennas of are expressed as
where is the transmit power at , is the propagation loss constant, is the distance between and , is the path-loss exponent ( means that the effect of path loss is ignored), denotes the transmitted symbol from , is the channel coefficient, and represent the additive white Gaussian noise and the signal processing noise at the th antenna of , which are additive white Gaussian noise with zero means and variances and , respectively.
The SNR of the signal at is then written as
Using Lemma 1 of , we obtain the PDF and CDF for the received SNR on as
respectively, where , is the expectation of , , and is the Gamma function, as defined by eq. (8.310) of .
Similarly, we obtain the PDF and CDF of as
respectively, where , is the average power channel gains between and , and .
Iii Secrecy Outage Probability Analysis
As defined in , we obtain the secrecy capacity of DF relaying scheme as
Remark 1: From (11), one can easily find that when , the secrecy capacity of mixed RF-FSO systems with DF scheme can be rewritten as
Eq. (12) means that the link is the bottleneck for the equivalent SNR at . This equation is easy to understand but very useful since the two parts in (12) are independent. It should be noted that the secrecy capacity in this case (when ) may be equal to zero.
Remark 2: On the other side, when , which means - link is the bottleneck for the equivalent SNR at , the secrecy capacity in this case must be zero because the equivalent SNR at cannot be greater than the one at , which can be expressed as
Thus SOP can be expressed as
where represents the target secrecy rate, , , and are expressed as
Remark 3: Based on (15) and (16), one can easily find that and means that the bottleneck of equivalent SNR at is and link, respectively. The corresponding secrecy capacity in these two cases is positive but less than , which cause the secrecy outage.
Remark 4: Moreover, one can find that (17) has no relationship with . Because of , based on (17), we can observe that denotes the probability of . Then signifies the probability for since the secrecy capacity of mixed RF-FSO systems equals zero when .
It should also note that the previous results (Eqs. (11)- (17), Remark 1 - 4) does not only apply to the mixed RF-FSO systems but also can be utilized to investigate the secrecy performance of all the dual-hop cooperative systems with DF scheme when there is not direct link between the source and the receiver.
Iii-a Derivations of
We can rewrite as
Since , can be rewritten as
where and is the lower incomplete Gamma function, defined by (8.350.1) of . The closed-form expression of is given in Appendix A.
Using of (1.111) and (3.351.1) of , we have as
where , , and . The closed-form expression of is given in Appendix B.
Iii-B Derivations of
Similar to the derivation of , we have
where , , and .
where and .
Similarly, using of (184.108.40.206) of  leads to the following expression for as
where is given by (49) in Appendix A.
After exchanging the order of the integral, we can rewrite as
Iii-C Derivation of
The PDF of can be expressed as :
Iv Asymptotic analysis of secrecy outage probability
In this section, we analyze the asymptotic SOP in high-SNR region. We assume that , where is a constant and .
The asymptotic CDF and PDF of can be given by 
respectively, where .
In the following, we derive the closed-form expressions of asymptotic , , , , , , and , respectively.