# Relaying Communications in Energy Scavenging Cognitive Networks: Secrecy Outage Probability Analysis

Authors: Khuong Ho-Van; Thiem Do-Dac
Journal: Wireless Communications and Mobile Computing
 (2019)

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## Abstract

This paper exploits a self-powered secondary relay to not only maintain but also secure communications between a secondary source and a secondary destination in cognitive radio networks when source-destination channel is unavailable. The relay scavenges energy from radio frequency (RF) signals of the primary transmitter and the secondary source and consumes the scavenged energy for its relaying activity. Under the maximum transmit power constraint, Rayleigh fading, the primary outage constraint, and the interference from the primary transmitter, this paper suggests an accurate closed-form expression of the secrecy outage probability to promptly assess the security performance of relaying communications in energy scavenging cognitive networks. The validity of the proposed expression is verified by computer simulations. Numerous results demonstrate the security performance saturation in the range of large maximum transmit power or high required outage probability of primary users. Moreover, the security performance is a function of several system parameters among which the relay’s position, the power splitting factor, and the time splitting factor can be optimized to achieve the minimum secrecy outage probability.


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## Body

## 1. Introduction

Currently low spectrum utilization efficiency is a great motivation for the application of the cognitive radio technology which enables secondary/unlicensed users to access the allocated spectrum of primary/licensed users in order to better exploit the available spectrum [1]. Cognitive radios operate on three (overlay, underlay, and interweave) mechanisms amidst which the underlay one is more preferable owing to its low system design complexity [2]. According to the underlay mechanism, the transmit power of secondary users (SUs) must be adaptively limited to obey the maximum transmit power constraint imposed by hardware design and the primary outage constraint imposed by communication reliability of primary users (PUs) [3]. These power constraints set the upper-bound on the power of secondary transmitters, inflicting unreliable communication through the direct channel between a secondary source and a secondary destination. Another reason for unreliable communication through the direct channel is the blockage of this channel owing to heavy path-loss, severe fading, and strong shadowing. A secondary relay between the source and the destination should be exploited to reduce the path-loss for hop-to-hop communication, mitigate severe fading and strong shadowing, and relax the requirement of high transmit power for long distance communication. Therefore, the relay can bridge the source with the destination in order to maintain reliable connection between them [4]. Nevertheless, as a helper, the relay may be unenthusiastic to utilize its private energy for assistance activity. Currently modern technologies make feasible for self-powered terminals that can scavenge energy with high energy conversion efficiency from green energy sources (e.g., radio frequency signals [5, 6]). Consequently, the relay can utilize its scavenged energy to lengthen the transmission range of the source, better remaining the continuous connection between the source and the destination. However, the scavenged energy may be insufficient, and, hence, the problem is whether the relay can guarantee reliable and secure communication between the source and the destination under the threat of eavesdroppers in the information-theoretic aspect. This aspect confirms that wireless communication is secured when the capacity difference between the desired channel and the wiretap channel is positive [7]. This paper finds the solution to such a problem.


### 1.1. Literature Review

This subsection merely surveys published works related to security performance analysis for relaying communications in energy scavenging cognitive networks. Therefore, published works which did not reflect a complete set of specifications such as power constraints for SUs, security performance analysis, relaying communications, and energy scavenging should not be surveyed (e.g., [8–13] merely dealt with the security performance analysis for direct communications (i.e., without relaying) in energy scavenging cognitive networks). Through this survey, contributions of the current paper will be summarized in the next subsection.The authors in [14] exploited the secondary relay between the secondary source and the secondary destination to not only expand the transmission range of the source but also secure its communication. The system model in [14] considered the decode-and-forward relay, the power splitting based energy scavenging mechanism which allows the relay to scavenge energy from the signals of both the secondary source and the primary transmitter, the maximum transmit power constraint, the interference power constraint, and the interference from the primary transmitter to the relay. Nevertheless, [14] neglected the interference from the primary transmitter to the secondary destination and the eavesdropper. The authors in [15] studied the same problem as [14] but with three different points: (i) the amplify-and-forward relay is used; (ii) the time splitting based energy scavenging mechanism allows the relay to scavenge energy from only the signal of the secondary source; (iii) the interference from the primary transmitter is ignored. To improve the security performance, [16] extended [15] with allowing both the source and the relay to jam the eavesdropper. The authors in [17] continued to expand the work in [16] with relay selection for more secure information transmission. As an alternative approach to enhance the security performance, [18] proposed a path selection scheme where the path with the highest end-to-end channel capacity is selected. The system model in [18] ignored interference from PUs and allowed the relays to scavenge the energy from the signals of dedicated beacons based on the time splitting mechanism. Nevertheless, [18] merely analyzed the connection outage probabilities (the connection outage probability is the probability that the received signal-to-noise ratio is below a threshold) at the destination and the eavesdropper.In summary, [14–18] considered relaying communications in energy scavenging cognitive networks. However, they neglected the secrecy outage analysis (i.e., only simulation results are provided in [14–18]), the primary outage constraint, and the interference from the primary transmitter to all secondary receivers. This paper will complement their shortcomings to complete the framework of the secrecy outage analysis for relaying communications in energy scavenging cognitive networks.


### 1.2. Contributions

This paper extends the system model in [14–18] with noticeable differences as follows:(i)
The decode-and-forward relay is activated merely when it can exactly restore the source information. This limits the error propagation (e.g., [14])(ii)
The relay exploits the interference from the primary transmitter for energy scavenging. This is helpful in turning unwanted signals to useful energy source and differs from [15–18] where the interference from the primary transmitter is not exploited for energy scavenging(iii)
Periods of two (energy scavenging and information processing) stages are unequal. This facilitates optimizing these periods for minimum secrecy outage probability (SOP). Also, this makes our work distinguished from [14–16] where these stages are of equal times(iv)
This paper proposes the accurate closed-form SOP analysis, which differs from [14–18] in which only simulation results are presentedThe contributions of the paper are highlighted as follows:(i)
Exploit a secondary relay to guarantee secure communications between the secondary source and the secondary destination in case that their direct communication is in outage. The relay is capable of scavenging the energy from both signals of the secondary source and the primary transmitter. Also, it must be successful in restoring the source information before taking part in the relaying activity(ii)
Suggest accurate closed-form expressions for crucial security performance metrics such as the SOP, the probability of strictly positive secrecy capacity (PSPSC), the intercept probability (IP) under both maximum transmit power constraint and primary outage constraint, and interference from the primary transmitters to promptly evaluate the security performance of relaying communications in energy scavenging cognitive networks without time-consuming computer simulations(iii)
Employ the suggested expressions to optimize important system parameters(iv)
Provide numerous results to obtain helpful insights into security performance such as the security performance saturation in the range of large maximum transmit power or high required outage probability of PUs and the minimum secrecy outage probability achievable with appropriate selection of the relay’s position, the time splitting factor, and the power splitting factor


### 1.3. Structure of Paper

The paper continues as follows. System model, signal model, secrecy capacity, and secondary power allocation are described in the next section. Section3 details the derivation of important performance metrics such as the SOP, the PSPSC, and the IP. Section 4 presents simulated/numerical results and Section 5 concludes the paper.


## 1.1. Literature Review

This subsection merely surveys published works related to security performance analysis for relaying communications in energy scavenging cognitive networks. Therefore, published works which did not reflect a complete set of specifications such as power constraints for SUs, security performance analysis, relaying communications, and energy scavenging should not be surveyed (e.g., [8–13] merely dealt with the security performance analysis for direct communications (i.e., without relaying) in energy scavenging cognitive networks). Through this survey, contributions of the current paper will be summarized in the next subsection.The authors in [14] exploited the secondary relay between the secondary source and the secondary destination to not only expand the transmission range of the source but also secure its communication. The system model in [14] considered the decode-and-forward relay, the power splitting based energy scavenging mechanism which allows the relay to scavenge energy from the signals of both the secondary source and the primary transmitter, the maximum transmit power constraint, the interference power constraint, and the interference from the primary transmitter to the relay. Nevertheless, [14] neglected the interference from the primary transmitter to the secondary destination and the eavesdropper. The authors in [15] studied the same problem as [14] but with three different points: (i) the amplify-and-forward relay is used; (ii) the time splitting based energy scavenging mechanism allows the relay to scavenge energy from only the signal of the secondary source; (iii) the interference from the primary transmitter is ignored. To improve the security performance, [16] extended [15] with allowing both the source and the relay to jam the eavesdropper. The authors in [17] continued to expand the work in [16] with relay selection for more secure information transmission. As an alternative approach to enhance the security performance, [18] proposed a path selection scheme where the path with the highest end-to-end channel capacity is selected. The system model in [18] ignored interference from PUs and allowed the relays to scavenge the energy from the signals of dedicated beacons based on the time splitting mechanism. Nevertheless, [18] merely analyzed the connection outage probabilities (the connection outage probability is the probability that the received signal-to-noise ratio is below a threshold) at the destination and the eavesdropper.In summary, [14–18] considered relaying communications in energy scavenging cognitive networks. However, they neglected the secrecy outage analysis (i.e., only simulation results are provided in [14–18]), the primary outage constraint, and the interference from the primary transmitter to all secondary receivers. This paper will complement their shortcomings to complete the framework of the secrecy outage analysis for relaying communications in energy scavenging cognitive networks.


## 1.2. Contributions

This paper extends the system model in [14–18] with noticeable differences as follows:(i)
The decode-and-forward relay is activated merely when it can exactly restore the source information. This limits the error propagation (e.g., [14])(ii)
The relay exploits the interference from the primary transmitter for energy scavenging. This is helpful in turning unwanted signals to useful energy source and differs from [15–18] where the interference from the primary transmitter is not exploited for energy scavenging(iii)
Periods of two (energy scavenging and information processing) stages are unequal. This facilitates optimizing these periods for minimum secrecy outage probability (SOP). Also, this makes our work distinguished from [14–16] where these stages are of equal times(iv)
This paper proposes the accurate closed-form SOP analysis, which differs from [14–18] in which only simulation results are presentedThe contributions of the paper are highlighted as follows:(i)
Exploit a secondary relay to guarantee secure communications between the secondary source and the secondary destination in case that their direct communication is in outage. The relay is capable of scavenging the energy from both signals of the secondary source and the primary transmitter. Also, it must be successful in restoring the source information before taking part in the relaying activity(ii)
Suggest accurate closed-form expressions for crucial security performance metrics such as the SOP, the probability of strictly positive secrecy capacity (PSPSC), the intercept probability (IP) under both maximum transmit power constraint and primary outage constraint, and interference from the primary transmitters to promptly evaluate the security performance of relaying communications in energy scavenging cognitive networks without time-consuming computer simulations(iii)
Employ the suggested expressions to optimize important system parameters(iv)
Provide numerous results to obtain helpful insights into security performance such as the security performance saturation in the range of large maximum transmit power or high required outage probability of PUs and the minimum secrecy outage probability achievable with appropriate selection of the relay’s position, the time splitting factor, and the power splitting factor


## 1.3. Structure of Paper

The paper continues as follows. System model, signal model, secrecy capacity, and secondary power allocation are described in the next section. Section3 details the derivation of important performance metrics such as the SOP, the PSPSC, and the IP. Section 4 presents simulated/numerical results and Section 5 concludes the paper.


## 2. System Model, Signal Model, Secrecy Capacity, and Secondary Power Allocation

### 2.1. System Model

Figure1(a) illustrates relaying communications in energy scavenging cognitive networks. Relaying communications experience two stages as shown in Figure 1(b).Figure 1
System model.
(a)
System model (b)
Stage periods (c)
Signal processing at SRIn stage 1, both the secondary sourceSS and the primary transmitter PT simultaneously broadcast their own information to the secondary destination SD and the primary receiver PR, respectively, causing mutual interference signals between the secondary network and the primary network. The interference signals from the secondary network to the primary network are considered in most published works while those from the primary network to the secondary network are usually neglected (e.g., [19–21] and references therein). Therefore, by considering these mutual interference signals, our work is apparently more general than the existing ones but the secrecy outage probability analysis is more sophisticated. The eavesdropper E intends to wire-tap the secondary source’s information. Owing to heavy path-loss, severe fading, and large shadowing, the secondary source’s signals cannot reach SD and E. As such, it is supposed that the secondary relay SR is in the radio coverage of SS and eager to assist SS by forwarding SS’s information to SD according to the decode-and-forward principle. SR is a self-powered terminal for its relaying operation which is capable of scavenging the energy from the received signals according to the power splitting method (e.g., [22, 23]) as observed in Figure 1(c). More specifically, SR scavenges the energy from the RF signals of both SS and PT. This means that SR takes advantage of the interference signal (from PT) for useful purpose of energy scavenging. The power splitting method divides the received signal at SR into two parts: one part for recovering the source information (it is supposed that the information decoder consumes the negligible amount of the energy, which is commonly assumed in most existing publications (e.g., [8–14] and references therein)) and the other for scavenging the energy.In stage 2,SR is idle if it fails to restore the source information. Otherwise, it forwards the restored source information to SD in parallel to the information transmission of PT. At the end of stage 2, SD tries to recover while E eavesdrops the source information from SR’s transmit signal.


### 2.2. Signal Model

In Figure1(a), gab∈{gp1,gp2,gpe,gpd,gpr,gsp,gsr,grp,gre,grd} denotes the channel coefficient between a corresponding pair of the transmitter and the receiver. Although Figure 1(a) only shows one primary transmitter-receiver pair, the realistic scenario may have two pairs communicating in two stages. To reflect such a scenario, two different channel coefficients, gp1 and gp2, are used to represent two different channels for two primary transmitter-receiver pairs in two stages. All frequency nonselective independent Rayleigh fading channels are supposed, producing the zero-mean κab-variance circular symmetric complex Gaussian distribution for gab, i.e., gab~CN(0,κab). When the path-loss is accounted, κab can be represented as κab=lab-ν, with lab denoting the transmitter a-receiver b distance, and ν denoting the path-loss exponent. As such, it is implicit in the sequel that the probability density function (pdf) and the cumulative distribution function (cdf) of the channel gain gab2 are, respectively, given by(1)fgab2x=e-x/κabκab,(2)Fgab2x=1-e-x/κab,where x≥0.In Figure1(b), β with β∈(0,1) and T correspondingly denote the time splitting factor and the total transmission time from SS to SD through SR. In Figure 1(c), α with α∈(0,1) denotes the power splitting factor. With the notations in Figure 1 in mind, the signals are modelled as follows.By denotingus and up1 as the unity-power transmit symbols of SS and PT in stage 1, correspondingly, the received signals at SR and PR can be, respectively, represented as(3)vr=gsrPsus+gprPp1up1+nr,(4)vp1=gspPsus+gp1Pp1up1+np1,where nr~CN0,ϱr2 and np1~CN0,ϱp12 are the additive white Gaussian noises (AWGN) produced by the receive antennas at SR and PR, respectively; Ps and Pp1 are the transmit powers of SS and PT in stage 1, respectively.Based on the operation principle in Figure1(c), the relay SR partitions the received signal vr into two parts: the first part of αvr input to the energy scavenger and the second part of 1-αvr input to the information decoder. Given the energy conversion efficiency of the energy scavenger as μ with μ∈(0,1), the average amount of the energy which SR can scavenge in stage 1 is given by(5)Wrm=μEαvr2βT=μαPsκsr+Pp1κpr+ϱr2βT,where E{·} denotes the statistical average.The maximum transmit power whichSR can use for information transmission in stage 2 is given by(6)Prm=Wrm1-βT=βμα1-βPsκsr+Pp1κpr+ϱr2.The signal input to the information decoder in Figure1(c) can be expressed as(7)v~r=1-αvr+n~r,where n~r~CN0,ϱ~r2 is the noise produced by the passband-to-baseband signal converter.Plugging (3) into (7) results in v~r=1-αPsgsrus+1-αPp1gprup1+1-αnr+n~r from which the SINR (Signal-to-Interference plus Noise Ratio) at the input of the information decoder can be represented as(8)φsr=1-αPsgsr21-αPp1gpr2+1-αϱr2+ϱ~r2=Psgsr2Pp1gpr2+ϱ^r2,where(9)ϱ^r2=ϱr2+ϱ~r21-α.Then, the channel capacity whichSR achieves in stage 1 is Csr=βlog21+φsr bps/Hz where the prelog factor of β is because the period of stage 1 is βT. According to the communication theory, SR can restore the source information when its channel capacity is higher than the required spectral efficiency of SUs, C1, i.e., Csr≥C1. In order words, us is successfully recovered at SR if φsr≥φ1 where φ1=2C1/β-1.In stage 2,SR transmits the recovered source symbol ur with the transmit power Pr if it can successfully restore the source information (i.e., φsr≥φ1 and ur=us). Otherwise, it keeps idle. The information transmission of SR is in parallel to that of PT. As such, SD, E, and PR correspondingly receive the following signals:(10)vrd=grdPrur+gpdPp2up2+nd,φsr≥φ1gpdPp2up2+nd,φsr<φ1,(11)vre=grePrur+gpePp2up2+ne,φsr≥φ1gpePp2up2+ne,φsr<φ1,(12)vrp=grpPrur+gp2Pp2up2+np2,φsr≥φ1gp2Pp2up2+np2,φsr<φ1,where nd~CN0,ϱd2, ne~CN0,ϱe2, and np2~CN0,ϱp22 are the noises produced by the receive antennas at SD, E, and PR, correspondingly; Pp2 and up2 are, respectively, the transmit power and the unity-power transmit symbol of PT in stage 2. That (Pp1,up1) differs from (Pp2,up2) reflects the realistic scenario where two different primary transmitter-receiver pairs may communicate in two stages.


### 2.3. Secrecy Capacity

The SINRs atSD and E can be achieved from (10) and (11) as(13)φrd=Prgrd2Pp2gpd2+ϱd2,φsr≥φ10,φsr<φ1,(14)φre=Prgre2Pp2gpe2+ϱe2,φsr≥φ10,φsr<φ1.Then,SD and E obtain channel capacities correspondingly as [24](15)Crd=1-βlog21+φrd,(16)Cre=1-βlog21+φre,where the prelog factor of 1-β is because the time of stage 2 is (1-β)T.The secrecy capacity of relaying communications in energy scavenging cognitive networks, which is the difference between the channel capacities of the trusted channel (fromSR to SD) and the wiretap channel (from SR to E), is expressed as [7](17)Csec=Crd-Cre+=1-βlog21+φrd1+φre+,φsr≥φ10,φsr<φ1,where x+ denotes max⁡x,0.


### 2.4. Secondary Power Allocation

The SINR atPR in stage 1 is computed from (4) as(18)φp1=Pp1gp12Psgsp2+ϱp12.Then, the channel capacity thatPR achieves in stage 1 is(19)Cp1=βlog21+φp1.Similarly, the SINR atPR in stage 2 is computed from (12) as(20)φp2=Pp2gp22Prgrp2+ϱp22,φsr≥φ1Pp2gp22ϱp22,φsr<φ1and the channel capacity that PR achieves in stage 2 is(21)Cp2=1-βlog21+φp2.Because the secondary transmitters (SS and SR) opportunistically access the spectrum of the primary users, their transmit powers must be limited such that the outage probability of the primary receiver is below a certain threshold λ. More specifically, Ps and Pr must be constrained by(22)PrCp1≤C2≤λ,(23)PrCp2≤C2≤λ,where C2 is the required spectral efficiency of PR.Constraints in (22) and (23) are, namely, the primary outage constraints.The transmit powers ofSS and SR must be also limited by their maximum transmit powers, Psm and Prm, respectively, which are determined by the hardware implementation and the energy scavenger, correspondingly. Therefore, Ps and Pr are upper-bounded by(24)Ps≤Psm,(25)Pr≤Prm.Constraints in (24) and (25) are, namely, the maximum transmit power constraints.Transmit power constraints forPs in (22) and (24) result in(26)Ps=min⁡Pp1κp1φ21κsp11-λe-φ21ϱp12/Pp1κp1-1+,Psm,where φ21=2C2/β-1.Similarly, transmit power constraints forPr in (23) and (25) result in(27)Pr=minPp2κp2φ22κrp11-λe-φ22ϱp22/Pp2κp2-1+,Prm,where φ22=2C2/1-β-1.In (26) and (27), κp1 and κp2 represent the fading powers of the channels between the primary transmitter and the primary receiver in stage 1 and stage 2, respectively.The derivation of (26) follows [25, eq. (18)] while the derivation of (27) follows [25, eq. (20)] with a note that (27) is obtained with φp2 in the case that SR is active (i.e., φsr≥φ1). The case that SR is idle is of no interest because the source information cannot reach the secondary destination.


## 2.1. System Model

Figure1(a) illustrates relaying communications in energy scavenging cognitive networks. Relaying communications experience two stages as shown in Figure 1(b).Figure 1
System model.
(a)
System model (b)
Stage periods (c)
Signal processing at SRIn stage 1, both the secondary sourceSS and the primary transmitter PT simultaneously broadcast their own information to the secondary destination SD and the primary receiver PR, respectively, causing mutual interference signals between the secondary network and the primary network. The interference signals from the secondary network to the primary network are considered in most published works while those from the primary network to the secondary network are usually neglected (e.g., [19–21] and references therein). Therefore, by considering these mutual interference signals, our work is apparently more general than the existing ones but the secrecy outage probability analysis is more sophisticated. The eavesdropper E intends to wire-tap the secondary source’s information. Owing to heavy path-loss, severe fading, and large shadowing, the secondary source’s signals cannot reach SD and E. As such, it is supposed that the secondary relay SR is in the radio coverage of SS and eager to assist SS by forwarding SS’s information to SD according to the decode-and-forward principle. SR is a self-powered terminal for its relaying operation which is capable of scavenging the energy from the received signals according to the power splitting method (e.g., [22, 23]) as observed in Figure 1(c). More specifically, SR scavenges the energy from the RF signals of both SS and PT. This means that SR takes advantage of the interference signal (from PT) for useful purpose of energy scavenging. The power splitting method divides the received signal at SR into two parts: one part for recovering the source information (it is supposed that the information decoder consumes the negligible amount of the energy, which is commonly assumed in most existing publications (e.g., [8–14] and references therein)) and the other for scavenging the energy.In stage 2,SR is idle if it fails to restore the source information. Otherwise, it forwards the restored source information to SD in parallel to the information transmission of PT. At the end of stage 2, SD tries to recover while E eavesdrops the source information from SR’s transmit signal.


## 2.2. Signal Model

In Figure1(a), gab∈{gp1,gp2,gpe,gpd,gpr,gsp,gsr,grp,gre,grd} denotes the channel coefficient between a corresponding pair of the transmitter and the receiver. Although Figure 1(a) only shows one primary transmitter-receiver pair, the realistic scenario may have two pairs communicating in two stages. To reflect such a scenario, two different channel coefficients, gp1 and gp2, are used to represent two different channels for two primary transmitter-receiver pairs in two stages. All frequency nonselective independent Rayleigh fading channels are supposed, producing the zero-mean κab-variance circular symmetric complex Gaussian distribution for gab, i.e., gab~CN(0,κab). When the path-loss is accounted, κab can be represented as κab=lab-ν, with lab denoting the transmitter a-receiver b distance, and ν denoting the path-loss exponent. As such, it is implicit in the sequel that the probability density function (pdf) and the cumulative distribution function (cdf) of the channel gain gab2 are, respectively, given by(1)fgab2x=e-x/κabκab,(2)Fgab2x=1-e-x/κab,where x≥0.In Figure1(b), β with β∈(0,1) and T correspondingly denote the time splitting factor and the total transmission time from SS to SD through SR. In Figure 1(c), α with α∈(0,1) denotes the power splitting factor. With the notations in Figure 1 in mind, the signals are modelled as follows.By denotingus and up1 as the unity-power transmit symbols of SS and PT in stage 1, correspondingly, the received signals at SR and PR can be, respectively, represented as(3)vr=gsrPsus+gprPp1up1+nr,(4)vp1=gspPsus+gp1Pp1up1+np1,where nr~CN0,ϱr2 and np1~CN0,ϱp12 are the additive white Gaussian noises (AWGN) produced by the receive antennas at SR and PR, respectively; Ps and Pp1 are the transmit powers of SS and PT in stage 1, respectively.Based on the operation principle in Figure1(c), the relay SR partitions the received signal vr into two parts: the first part of αvr input to the energy scavenger and the second part of 1-αvr input to the information decoder. Given the energy conversion efficiency of the energy scavenger as μ with μ∈(0,1), the average amount of the energy which SR can scavenge in stage 1 is given by(5)Wrm=μEαvr2βT=μαPsκsr+Pp1κpr+ϱr2βT,where E{·} denotes the statistical average.The maximum transmit power whichSR can use for information transmission in stage 2 is given by(6)Prm=Wrm1-βT=βμα1-βPsκsr+Pp1κpr+ϱr2.The signal input to the information decoder in Figure1(c) can be expressed as(7)v~r=1-αvr+n~r,where n~r~CN0,ϱ~r2 is the noise produced by the passband-to-baseband signal converter.Plugging (3) into (7) results in v~r=1-αPsgsrus+1-αPp1gprup1+1-αnr+n~r from which the SINR (Signal-to-Interference plus Noise Ratio) at the input of the information decoder can be represented as(8)φsr=1-αPsgsr21-αPp1gpr2+1-αϱr2+ϱ~r2=Psgsr2Pp1gpr2+ϱ^r2,where(9)ϱ^r2=ϱr2+ϱ~r21-α.Then, the channel capacity whichSR achieves in stage 1 is Csr=βlog21+φsr bps/Hz where the prelog factor of β is because the period of stage 1 is βT. According to the communication theory, SR can restore the source information when its channel capacity is higher than the required spectral efficiency of SUs, C1, i.e., Csr≥C1. In order words, us is successfully recovered at SR if φsr≥φ1 where φ1=2C1/β-1.In stage 2,SR transmits the recovered source symbol ur with the transmit power Pr if it can successfully restore the source information (i.e., φsr≥φ1 and ur=us). Otherwise, it keeps idle. The information transmission of SR is in parallel to that of PT. As such, SD, E, and PR correspondingly receive the following signals:(10)vrd=grdPrur+gpdPp2up2+nd,φsr≥φ1gpdPp2up2+nd,φsr<φ1,(11)vre=grePrur+gpePp2up2+ne,φsr≥φ1gpePp2up2+ne,φsr<φ1,(12)vrp=grpPrur+gp2Pp2up2+np2,φsr≥φ1gp2Pp2up2+np2,φsr<φ1,where nd~CN0,ϱd2, ne~CN0,ϱe2, and np2~CN0,ϱp22 are the noises produced by the receive antennas at SD, E, and PR, correspondingly; Pp2 and up2 are, respectively, the transmit power and the unity-power transmit symbol of PT in stage 2. That (Pp1,up1) differs from (Pp2,up2) reflects the realistic scenario where two different primary transmitter-receiver pairs may communicate in two stages.


## 2.3. Secrecy Capacity

The SINRs atSD and E can be achieved from (10) and (11) as(13)φrd=Prgrd2Pp2gpd2+ϱd2,φsr≥φ10,φsr<φ1,(14)φre=Prgre2Pp2gpe2+ϱe2,φsr≥φ10,φsr<φ1.Then,SD and E obtain channel capacities correspondingly as [24](15)Crd=1-βlog21+φrd,(16)Cre=1-βlog21+φre,where the prelog factor of 1-β is because the time of stage 2 is (1-β)T.The secrecy capacity of relaying communications in energy scavenging cognitive networks, which is the difference between the channel capacities of the trusted channel (fromSR to SD) and the wiretap channel (from SR to E), is expressed as [7](17)Csec=Crd-Cre+=1-βlog21+φrd1+φre+,φsr≥φ10,φsr<φ1,where x+ denotes max⁡x,0.


## 2.4. Secondary Power Allocation

The SINR atPR in stage 1 is computed from (4) as(18)φp1=Pp1gp12Psgsp2+ϱp12.Then, the channel capacity thatPR achieves in stage 1 is(19)Cp1=βlog21+φp1.Similarly, the SINR atPR in stage 2 is computed from (12) as(20)φp2=Pp2gp22Prgrp2+ϱp22,φsr≥φ1Pp2gp22ϱp22,φsr<φ1and the channel capacity that PR achieves in stage 2 is(21)Cp2=1-βlog21+φp2.Because the secondary transmitters (SS and SR) opportunistically access the spectrum of the primary users, their transmit powers must be limited such that the outage probability of the primary receiver is below a certain threshold λ. More specifically, Ps and Pr must be constrained by(22)PrCp1≤C2≤λ,(23)PrCp2≤C2≤λ,where C2 is the required spectral efficiency of PR.Constraints in (22) and (23) are, namely, the primary outage constraints.The transmit powers ofSS and SR must be also limited by their maximum transmit powers, Psm and Prm, respectively, which are determined by the hardware implementation and the energy scavenger, correspondingly. Therefore, Ps and Pr are upper-bounded by(24)Ps≤Psm,(25)Pr≤Prm.Constraints in (24) and (25) are, namely, the maximum transmit power constraints.Transmit power constraints forPs in (22) and (24) result in(26)Ps=min⁡Pp1κp1φ21κsp11-λe-φ21ϱp12/Pp1κp1-1+,Psm,where φ21=2C2/β-1.Similarly, transmit power constraints forPr in (23) and (25) result in(27)Pr=minPp2κp2φ22κrp11-λe-φ22ϱp22/Pp2κp2-1+,Prm,where φ22=2C2/1-β-1.In (26) and (27), κp1 and κp2 represent the fading powers of the channels between the primary transmitter and the primary receiver in stage 1 and stage 2, respectively.The derivation of (26) follows [25, eq. (18)] while the derivation of (27) follows [25, eq. (20)] with a note that (27) is obtained with φp2 in the case that SR is active (i.e., φsr≥φ1). The case that SR is idle is of no interest because the source information cannot reach the secondary destination.


## 3. SOP Analysis

The SOP is a crucial performance metric in assessing information security of wireless communications in the information-theoretic aspect. It is defined as the probability that the secrecy capacityCsec does not reach a required security degree C¯3. As such, the smaller the SOP is, the more secure the wireless communication is. In this section, the SOP of relaying communications in energy scavenging cognitive networks is derived in closed form, which facilitates not only evaluating security performance without exhaustive simulations but also inferring other crucial security performance metrics such as the IP and the PSPSC.The SOP of relaying communications in energy scavenging cognitive networks is given by(28)ΥC¯3=PrCsec<C¯3,where Pr{V} is the probability of the event V.SinceCsec is nonnegative when φsr≥φ1 as seen in (17), one can decompose (28) into two cases as(29)ΥC¯3=Pr⁡1-βlog21+φrd1+φre+<C¯3∣φsr≥φ1Prφsr≥φ1+Pr⁡0<C¯3∣φsr<φ1Prφsr<φ1.Because the required security degreeC¯3 is positive, (29) is rewritten as(30)ΥC¯3=Prlog21+φrd1+φre+<C¯31-β∣φsr≥φ1︸I1Prφsr≥φ1︸1-I2+Prφsr<φ1︸I2.Theorem 1.
The accurate closed-form representation ofI1 is given by(31)I1=CDΨD,C+CΦD,C+e1-2C3BAC2C3C-GΦ2C3B+D,C+e1-2C3BAC2C3C-GD+1C-GΨ2C3B+D,C-Ψ2C3B+D,G,where(32)A=κrdPrκpdPp2,(33)B=ϱd2κrdPr,(34)C=κrePrκpePp2,(35)D=ϱe2κrePr,(36)G=1+2-C3A-1,(37)Ψa,b=-eabEi-ab,(38)Φa,b=1b+aeabEi-ab,(39)C3=C¯31-β,with Ei(·) being the exponential integral in [26].Proof.
Please refer to Appendix.Theorem 2.
The accurate closed-form representation ofI2 is given by(40)I2=1-Ue-Vφ1φ1+U,where(41)U=κsrPsκprPp1,(42)V=ϱ^r2κsrPs.Proof.
By imitating the derivation of (A.5) in the Appendix, it is easy to see that I2 is the cdf of φsr evaluated at φ1. Therefore, I2 can be represented as (40), completing the proof.Plugging (31) and (40) into (30), one obtains the accurate closed-form expression of the SOP for relaying communications in energy scavenging cognitive networks as ΥC¯3=I11-I2+I2. This expression is useful to quickly evaluate the security performance without exhaustive simulations. To the best of the authors’ understanding, this expression is newly reported. Moreover, some crucial security performance metrics (e.g., the IP or the PSPSC) can be easily derived from this expression. More specifically, the IP refers to the probability that the secrecy capacity is negative [27], i.e.,(43)Θ=PrCsec<0=Υ0.Additionally, the PSPSC refers to the probability that the secrecy capacity is strictly positive, i.e.,(44)Ω=PrCsec>0=1-PrCsec<0=1-Υ0.


## 4. Results and Discussions

Simulated/numerical results in this section are collected to assess the security performance of relaying communications in energy scavenging cognitive networks in terms of the SOP through typical parameters. Numerical results are produced by (30) while simulated ones are generated by Monte-Carlo simulation with 107 channel realizations. Without loss of generality, equal noise variances are supposed (i.e., ϱp12=ϱp22=ϱd2=ϱe2=ϱr2=ϱ~r2=N0) and only one primary transmitter-receiver pair is considered (i.e., κp1=κp2=κpp and Pp1=Pp2=Pp). Simulation parameters under investigation are specified in Table 1.Table 1
Simulation parameters.
PARAMETER VALUE Path-loss exponent ν = 4  Energy conversion efficiency μ = 0.9  Coordinate ofSS S S at (0.0, 0.0)  Coordinate ofSD S D at (1.0, 0.0)  Coordinate ofPT P T at (0.2, 0.8)  Coordinate ofPR P R at (0.9, 0.7)  Coordinate ofE E at (1.0, 0.4)  Coordinate ofSR S R at (d,0.0)Figure2 shows the SOP versus the maximum transmit power-to-noise variance ratio Psm/N0 for d=0.5, λ=0.1, C1=0.2 bps/Hz, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, α=0.8, β=0.6, and Pp/N0=10,15,20 dB. This figure verifies the accuracy of (30) due to the exact agreement between the analysis and the simulation. Additionally, the SOP decreases with increasing Psm/N0. This is attributed to the fact that increasing Psm/N0 offers SR more opportunities to correctly recover the source information and to scavenge more energy from the RF signals of SS, eventually decreasing the outage probability in stage 2. Nevertheless, the SOP suffers the error floor in the range of high Psm/N0. This error floor originates from the power allocation mechanism for SS and SR (please recall (26) and (27)) where SS and SR transmit signals with powers independent of Psm/N0 in the range of large Psm/N0 (i.e., the maximum transmit power constraint is ignored when Psm/N0 is large), resulting in the constant SOP. Furthermore, the SOP increases with increasing Pp/N0. This is because increasing the power of the primary transmitter inflicts more interference to secondary receivers which cannot be compensated by the increase in the energy of SR scavenged from the transmit signals of PT. However, when Psm/N0 is greater than a certain value, the SOP decreases with increasing Pp/N0. For example, when Psm/N0 is greater than 15.5 dB, the SOP with Pp/N0=10 dB is larger than the SOP with Pp/N0=15 dB. This can be explained as follows. When Psm/N0 is greater than a certain value, the transmit power of SS is large according to (26). Therefore, the relay can scavenge more energy from the transmit signal of SS according to (6). This increases the transmit power of the relay according to (27), which can better compensate for more interference from the primary transmitter due to larger value of Pp/N0, ultimately reducing the SOP.Figure 2
SOP versusPsm/N0. “Sim.” and “Ana.” represent “Simulation” and “Analysis,” respectively.Figure3 demonstrates the SOP versus the required outage probability of PUs, λ, for Psm/N0=15 dB, d=0.5, α=0.8, β=0.6, C1=0.2 bps/Hz, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure validates (30) due to the match between the simulation and the analysis. Moreover, increasing the required outage probability of PUs decreases the SOP. This is because such an increase allows PUs to tolerate more interference from SUs. Therefore, SUs can transmit signals with higher powers, eventually reducing the outage in stage 2. Nevertheless, the SOP is saturated in the range of large λ (e.g., λ>0.5). Such a SOP saturation is because of the power allocation mechanism in (26) and (27) where the second term in Ps (or Pr) is independent of λ. Therefore, Ps (or Pr) is constant for large values of λ at which the first term dominates the second term in Ps (or Pr), causing the error floor in the SOP. Furthermore, the SOP saturation level increases with increasing Pp/N0. This can be comprehended from increasing the interference on SUs when Pp/N0 increases.Figure 3
SOP versusλ.Figure4 shows the SOP versus the relay’s position (i.e., d) for Psm/N0=15 dB, β=0.6, λ=0.1, α=0.8, C1=0.2 bps/Hz, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure confirms the validity of (30) due to the exact agreement between the simulation and the analysis. We are reminded that the secrecy outage event occurs as R cannot successfully recover the source information (i.e., SS is distant from SR) or SR cannot reliably send the decoded source information to SD (i.e., SD is distant from SR). As such, it is obvious that there is always an existence of the relay’s optimum position, which optimally trades off the probability that SR can correctly restore the source information with the probability that SR can reliably send the decoded source information to SD to minimize the SOP. Figure 4 confirms this fact which achieves the minimum SOP as SR is dopt=0.86,0.87,0.79 distant from SS for Pp/N0=10,15,20 dB, respectively. Moreover, the minimum SOP corresponding to the relay’s optimum position increases with increasing the interference from PUs (i.e., increasing Pp/N0) as expected. However, when d is smaller than a certain value, the SOP decreases with increasing Pp/N0. For instance, when d is smaller than 0.48, the SOP with Pp/N0=10 dB is larger than the SOP with Pp/N0=15 dB. This can be interpreted as follows. When d is smaller than a certain value (i.e., SR is nearer to SS), SR can correctly decode the source information with a higher probability and scavenge more energy from the transmit signal of SS. This increases the transmit power of the relay, which can better compensate for more interference from the primary transmitter due to larger value of Pp/N0, ultimately reducing the SOP.Figure 4
SOP versus the relay’s position.Figure5 illustrates the SOP versus β for d=0.5, Psm/N0=15 dB, λ=0.1, α=0.5, C1=0.2 bps/Hz, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure validates (30) because the simulation perfectly matches the analysis. In addition, there exist optimum values of β (e.g., βopt=0.51,0.46,0.56 for Pp/N0=10,15,20 dB, correspondingly as shown in Figure 5) for the minimum SOPs. The existence of βopt can be interpreted as follows. Increasing β prolongs the period of stage 1, and thus, SR can scavenge more energy and correctly restore the source information with a higher probability. Nevertheless, increasing β can also mitigate the secrecy capacity in stage 2, and thus, the SOP increases. Consequently, β should be selected to optimally compromise the periods of two stages for the minimum SOP. Furthermore, the minimum SOP corresponding to the optimum value of β increases with Pp/N0 as expected. However, when β is outside a certain range, the SOP decreases with increasing Pp/N0. For instance, when β is outside [0.47,0.66], the SOP with Pp/N0=10 dB is larger than the SOP with Pp/N0=15 dB. This can be interpreted as follows. The value of β affects the required SINRs of PR (i.e., φ21=2C2/β-1 and φ22=2C2/(1-β)-1 as seen in (26) and (27)). Therefore, the primary receiver has more chances to obtain the required SINRs when Pp/N0 increases. Accordingly, it can be more tolerable with the interference from the secondary transmitters. Furthermore, the relay has more chances to scavenge more energy from the transmit signal of PT when Pp/N0 increases. As such, the relay transmits signals with higher power, which can better compensate for more interference from the primary transmitter due to larger value of Pp/N0, eventually mitigating the SOP.Figure 5
SOP versus the time splitting factor.Figure6 demonstrates the SOP versus α for Psm/N0=15 dB, λ=0.1, d=0.5, β=0.6, C1=0.2 bps/Hz, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure exposes an exact agreement between the simulation and the analysis, validating (30). Moreover, the SOP can be minimized by optimally selecting α. The existence of the optimal value of α for the minimum SOP can be explained as follows. Increasing α permits SR to scavenge more energy, and thus, SR can enhance its transmission reliability in stage 2, ultimately decreasing the SOP. Nevertheless, increasing α also decreases the energy for the information decoder, decreasing the probability that SR can correctly restore the source information in stage 1 and inflicting more secrecy outage in stage 2. Consequently, α should be optimally adopted to compromise transmission reliability of SS and SR in both stages. Furthermore, the minimum SOP corresponding to the optimum value of α increases with Pp/N0 as expected.Figure 6
SOP versus the power splitting factor.Figure7 illustrates the SOP versus the required spectral efficiency of SUs, C1, for Psm/N0=15 dB, β=0.6, λ=0.1, d=0.5, α=0.8, C2=0.3 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure verifies a perfect match between the simulation and the analysis, confirming the precision of (30). In addition, the SOP increases with increasing C1. This is apparent because the higher the required spectral efficiency of SUs, the lower the probability for the relay to correctly restore the source information, and, hence, the higher the probability for the system to be outage in stage 2. Moreover, the SOP is higher for larger values of Pp/N0 as expected.Figure 7
SOP versus the required spectral efficiency of SUs.Figure8 demonstrates the SOP versus the required spectral efficiency of PUs, C2, for Psm/N0=15 dB, β=0.6, λ=0.1, d=0.5, α=0.8, C1=0.2 bps/Hz, C¯3=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure confirms an exact agreement between the analysis and the simulation, validating (30). Additionally, the SOP increases with increasing C2. This is because for the fixed value of λ (please see (22) and (23)) the higher the required spectral efficiency of PUs is, the lower the interference at PUs caused by SUs must be, and, hence, the lower the transmit power of SUs must be, leading to the higher SOP. Nevertheless, the system is always in outage at large values of C2. This is because according to (26) and (27), the terms inside [·]+ are inversely proportional to φ21 and φ22 (or C2). As such, increasing C2 up to a certain value (e.g., 1.53 bps/Hz for Pp/N0=15 dB) incurs [·]+=0 and, hence, Ps and Pr are always zero when C2 exceeds a threshold, causing the system outage all the time. Furthermore, the SOP is affected by Pp/N0 as expected. More noticeably, when C2 is greater than a certain value, the SOP decreases with increasing Pp/N0. For example, when C2 is greater than 0.31 bps/Hz, the SOP with Pp/N0=10 dB is larger than the SOP with Pp/N0=15 dB. This can be interpreted as follows. The primary receiver has more chances to obtain the required spectral efficiency C2 when Pp/N0 increases. As such, it can be more tolerable with the interference from the secondary transmitters. Moreover, the relay has more chances to scavenge more energy from the transmit signal of PT when Pp/N0 increases. Accordingly, the relay transmits signals with higher power, which can better compensate for more interference from the primary transmitter due to larger value of Pp/N0, eventually reducing the SOP.Figure 8
SOP versus the required spectral efficiency of PUs.Figure9 shows the SOP versus the required security degree C¯3 for Psm/N0=15 dB, β=0.6, λ=0.1, d=0.5, α=0.8, C1=0.2 bps/Hz, C2=0.1 bps/Hz, and Pp/N0=10,15,20 dB. This figure validates (30) because of the match between the analysis and the simulation. Additionally, the SOP increases with increasing C¯3. This is because, given system parameters, the higher the required security degree, the higher the SOP. Moreover, the SOP is influenced by Pp/N0 as expected.Figure 9
SOP versus the required security degree.


## 5. Conclusion

This paper evaluated the security performance of relaying communications in energy scavenging cognitive networks in terms of the SOP. For quick performance assessment, the accurate closed-form expression of the SOP was derived under consideration of Rayleigh fading, the primary outage constraint, the interference from PUs, and the maximum transmit power constraint. The validity of the proposed expression was verified by computer simulations. Various results exposed that the self-powered relay considerably enhances the security performance even when the source-destination channel is unavailable owing to deep fading, severe path-loss, and strong shadowing. Moreover, the security performance suffered the error floor in the range of large maximum transmit power or high required outage probability of PUs. Furthermore, the security performance of relaying communications in energy scavenging cognitive networks depends on several system parameters among which the time splitting factor, the relay’s position, and the power splitting factor should be optimally selected to minimize the SOP.



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*Source: 2109837-2019-05-06.xml*