Secrecy Outage Analysis of Mixed RFFSO Downlink SWIPT Systems^{†}^{†}thanks: Manuscript received.
Abstract
We analyze a secure dualhop mixed radio frequencyfree space optical (RFFSO) downlink simultaneous wireless information and power transfer (SWIPT) systems. The FSO link and all RF links experience GammaGamma, 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. Signaltonoise ratios at both legitimate and illegitimate receivers are not independent since they are both simultaneously influenced by the FSO link. We derive the closedform expression of the secrecy outage probability (SOP) as well as the asymptotic result for SOP when signaltonoise ratios at relay and legitimate destinations tend to infinity. MonteCarlo 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 relaydestination 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 Introduction
Ia Background and Related Works
Dualhop mixed radio frequencyfree space optical (RFFSO) 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 RFFSO 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 timevarying nature of the wireless medium [4][8]. Numerical studies of PLS over FSO satellite ground systems were performed by Endo et al. [9]. 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 fadingfree. LopezMartinez et al. [10] 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 [11] 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 [12][15]. However, the broadcast nature of the RF link makes the mixed RFFSO systems vulnerable to wiretap. Recently, the PLS of mixed RFFSO systems stimulated researchers’ interest and quite a few studies on this topic were reported in the literature, including [12][15]. ElMalek et al. [12] studied the security reliability tradeoff of a singleinput multipleoutput mixed RFFSO system and derived the closedform expressions for some generalized performance metrics, such as outage probability (OP), intercept probability (IP), etc. The same authors also analyzed the effect of RF cochannel interference on the secrecy performance of mixed RFFSO systems and proposed a new power allocation scheme to enhance the secrecy performance [13]. Notice that the all the performance metrics studied in [12] and [13] 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 RFFSO system with perfect and imperfect channel state information in [14] and [15], respectively. The closedformed 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 RFFSO system with was investigated in
It is noteworthy that [12][15] considered the UL mixed RFFSO transmission systems, in which the FSO link only influences the signaltonoise ratio (SNR) at legitimate receivers. Technically speaking, it is much more challenging to analyze the secrecy performance for DL mixed RFFSO transmission systems compared to analyze the OP/IP/SOP for UL mixed RFFSO transmission systems. This is because the problem in DL mixed RFFSO 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 [16][20]. 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 [21]. Thus many literature recently focused on the security of SWIPT systems [22][26]. The security for SWIPT systems was first considered in [22] and the resource allocation design for secure MISO SWIPT systems was formulated as a nonconvex 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 closedform expressions for SOP were derived in [23] and [24], respectively. The secrecy outage performance of an underlay multipleinputmultipleoutput cognitive radio networks with energy harvesting and transmit antenna selection was studied in [25]. 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 [26]. Makki et al. analyzed the throughput and OP for the hybrid RFFSO SWIPT systems and a power allocation scheme was proposed in [27]. 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 dualhop mixed RFFSO 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.
IB Motivation and Contributions
To our best knowledge, there is no literature studying the physical layer security of DL mixed RFFSO SWIPT systems. In this work, we study a secure DL mixed RFFSO 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 RFFSO SWIPT systems over GammaGamma  Nakagami fading channels with DF relaying schemes. We investigate the effects of misalignment, different detection schemes, SWIPT, and multiple antenna techniques and deduct the closedform expressions for the exact and asymptotic SOPs.

We present a selected figures illustrating MonteCarlo 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 pathloss degrades the security of the DL mixed RFFSO 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 relaydestination 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 RFFSO systems but also can be utilized to investigate the secrecy performance of all the dualhop cooperative systems with DF scheme when there is not direct link between the source and the receiver.

Although the secrecy performance of DL mixed RFFSO systems was investigated in [28], the correlation of the SNR at both legitimate and illegitimate receivers was not considered. Furthermore, SWIPT, pathloss 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 RFFSO 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 GammaGamma 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 nonlinear EH model was proposed in [29] and [30], respectively. Actually, the EH model does not influence the secrecy performance of the mixed RFFSO 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 nonlinear 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 [31]
(1) 
(2) 
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 [32]. , represents the electrical SNR of the FSO link, , , , , and is Meijer’s function, as defined by (9.301) of [33].
The effects of pathloss and smallscale fading of the RF link are considered and the received signals at the th antennas of are expressed as
(3) 
where is the transmit power at , is the propagation loss constant, is the distance between and , is the pathloss 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
(4) 
where .
Using Lemma 1 of [34], we obtain the PDF and CDF for the received SNR on as
(5) 
(6) 
respectively, where , is the expectation of , , and is the Gamma function, as defined by eq. (8.310) of [33].
Similarly, we obtain the PDF and CDF of as
(7) 
(8) 
respectively, where , is the average power channel gains between and , and .
Iii Secrecy Outage Probability Analysis
As defined in [36], we obtain the secrecy capacity of DF relaying scheme as
(11)  
Remark 1: From (11), one can easily find that when , the secrecy capacity of mixed RFFSO systems with DF scheme can be rewritten as
(12) 
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
(13) 
Thus SOP can be expressed as
(14)  
where represents the target secrecy rate, , , and are expressed as
(15) 
(16) 
(17)  
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 RFFSO systems equals zero when .
We can easily obtain another useful secrecy metric, probability of strictly positive secrecy capacity [37, 38], as
(18) 
It should also note that the previous results (Eqs. (11) (17), Remark 1  4) does not only apply to the mixed RFFSO systems but also can be utilized to investigate the secrecy performance of all the dualhop cooperative systems with DF scheme when there is not direct link between the source and the receiver.
Iiia Derivations of
We can rewrite as
(19) 
where .
Since , can be rewritten as
(20)  
where
By substituting (1), (5) and (8) into , we obtain
(21) 
where and is the lower incomplete Gamma function, defined by (8.350.1) of [33]. The closedform expression of is given in Appendix A.
Using of (1.111) and (3.351.1) of [33], we have as
(23)  
where , , and . The closedform expression of is given in Appendix B.
IiiB Derivations of
Similar to the derivation of , we have
(24) 
where , , and .
Substituting (1), (5) and (8) into and using (07.34.21.0084.01) of [39], we can achieve
(25)  
where and .
Similarly, using of (2.24.2.1) of [40] leads to the following expression for as
(26)  
where is given by (49) in Appendix A.
After exchanging the order of the integral, we can rewrite as
(27)  
IiiC Derivation of
The PDF of can be expressed as [41]:
(30) 
Iv Asymptotic analysis of secrecy outage probability
In this section, we analyze the asymptotic SOP in highSNR region. We assume that , where is a constant and .
In the following, we derive the closedform expressions of asymptotic , , , , , , and , respectively.