# Impact of Artificial Noise on Security Capability of Energy Harvesting Overlay Networks

Authors: Khuong Ho-Van; Thiem Do-Dac
Journal: Wireless Communications and Mobile Computing
 (2021)

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## Abstract

Artificial noise, energy harvesting, and overlay communications can assure design metrics of modern wireless networks such as data security, energy efficiency, and spectrum utilization efficiency. This paper studies impact of artificial noise on security capability of energy harvesting overlay networks in which the cognitive transmitter capable of self-powering its operation by harvesting radio frequency energy and self-securing its communications against eavesdroppers by generating artificial noise amplifies and forwards the signal of the primary transmitter as well as transmits its individual signal concurrently. To quantify this impact, the current paper firstly suggests accurate expressions of crucial security performance indicators. Then, computer simulations are supplied to corroborate these expressions. Finally, numerous results are demonstrated to expose insights into this impact from which optimum specifications are determined. Notably, primary/cognitive communications can be secured at distinct degrees by flexibly controlling multiple specifications of the suggested system model.


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## Body

## 1. Introduction

Fifth generation (5G) networks provide a huge number of emerging wireless services and thus pressure considerably telecommunication infrastructure [1]. Indeed, one of the 5G network’s pivotal services is Internet of Things (IoT), which is applied extensively from civilian (e.g., healthcare, transportation, electricity, and public safety) to military (e.g., smart bases and tactical reconnaissance) [2]. Nevertheless, when deploying IoT, a large number of simultaneously connected devices consume tremendous amount of energy, and thus it is necessary to enhance energy efficiency to not only linger the life-time of devices but also mitigate energy demand. Moreover, IoT needs a large spectrum to allot instantaneous operation of a huge number of users, and hence in the spectrum shortage-and-scarcity situation as today [3], solutions of upgrading spectral efficiency should be proposed. Similarly to IoT, 5G mobile wireless communications, which also serve the growing number of mobile devices and requires increasingly high data rate, need effective spectrum-and-energy utilization solutions to satisfy its requirements [4]. Such a pressure can be released with modern technology solutions of high (energy, spectrum utilization, spectral) efficiencies as follows.Cognitive users (CUs), which usually operate in underlay, overlay, and interweave mechanisms, can utilize the licensed frequency band (LFB) of primary users (PUs) without harming signal reception of PUs, hence drastically enhancing spectral efficiency and reducing spectrum scarcity problem [5]. In the underlay mechanism, CUs have access permission to the LFB solely if CUs limit interference power induced at PUs under a tolerable degree. CUs working in the overlay mechanism access simultaneously the LFB with PUs; yet, performance indicators of PUs are remained or enhanced with complicated signal processing techniques. On the contrary, the interweave mechanism only leaves unused bandwidth of PUs for CUs’ access. While most literature has intensively studied the underlay and interweave mechanisms, a handful of works have concentrated on the overlay mechanism. Since the overlay mechanism can compromise performances between cognitive and primary communications better than other mechanisms, it greatly attracts this paper.Viable solutions to improve energy efficiency of wireless networks can be listed as network planning, hardware solutions, radio frequency (RF) energy harvesting, etc. Among these solutions, harvesting energy from RF signals neither demands complex energy harvesting equipments nor depends time-variant energy resources. Such advantages of this energy harvesting solution induce it to become a bright candidate deployed in small-size users in 5G mobile communications or IoT to provision energy, linger the life-time, and enhance energy efficiency [6–8]. Currently, this solution can be carried out through SWIPT (simultaneous wireless information and power transfer) [9–11] or relaying communications [12–14].Energy harvesting overlay networks (EHONs) can exploit concurrently advantages of both applicable (energy harvesting and cognitive radio) technologies to satisfy various design metrics of advanced networks including high-energy and spectral efficiencies [15, 16]. Nonetheless, both cognitive and primary users in these networks are allowed to transmit on the LFB concomitantly that may facilitate eavesdroppers in emulating legal users to overhear privacy messages, seriously alerting security problems. To supplement and enhance security performance for conventional encryption and cryptographic solutions, physical layer security (PHY security) has lately been emerged as a promising candidate [17–19]. PHY security can be deployed with numerous techniques, including relaying and jamming. Among these techniques, jamming (or generating artificial noise) has been widely exploited thanks to its efficient, simple, and flexible implementation [20]. Accordingly, this paper generates artificial noise in EHONs to secure communications for both primary and cognitive users.


### 1.1. Existing Publications

This paper studies the impact of artificial noise in EHONs where a primary transmitter cannot connect directly a primary receiver in some scenarios (e.g., heavy shadowing), and hence a cognitive transmitter supports primary communications in exchange for its access to the LFB. The cognitive transmitter operating in the amplify-and-forward (AF) mechanism scavenges RF energy in the primary transmitter’s signals and sends not only its privacy signal but also the primary transmitter’s signal and artificial noise. Message transmission of the cognitive transmitter is overheard by an eavesdropper.Whilst most publications have investigated the PHY security for energy harvesting (interweave/underlay) networks, a handful works have paid attention to the overlay mechanism [5, 21–28]. More specifically, [21] investigated the almost similar system model to ours but EHONs are secured by asking a devoted jammer to jam the eavesdropper. In [22, 23], the primary receiver was exploited to corrupt the eavesdropper rather than the devoted jammer as in [21]. Additionally, [21] disagrees [22, 23] in the energy harvesting (EH) technique, the EH-capable device, and the assistance mechanism. The former utilized the cognitive transmitter as a decode-and-forward (DF) relay and exploited the EH-capable jammer which scavenges energy based on the time switching protocol [29]. Meanwhile, the latter employed the cognitive transmitter as the AF relay and as an energy scavenger that bases on the power splitting protocol [30]. To better secure primary communications, [24] suggested to jam the eavesdropper by the primary receiver as well as the dedicated jammer. Nonetheless, the analysis on the secrecy outage probability (SOP) of both primary and cognitive communications was not reported in [21–24]. In [25], EHONs are secured with the multiuser scheduling and the transmit antenna selection. Moreover, [25] analyzed the SOP/ergodic rate of primary/cognitive communications. Recently, a bulk of dedicated jammers were recommended to secure EHONs, and the SOP of cognitive and primary communications was suggested in closed form [5]. Nevertheless, distinguishing from [21–24], the cognitive user relays the primary signal and sends its privacy signal independently in [5, 25]. This demands at least three phases (phase 1: energy scavenging and PU’s communications, phase 2: CU’s communications to PU, and phase 3: CU’s communications to CU) to complete message communications of both PU and CU, reducing drastically spectral efficiency and analysis complexity. As such, the closed-form analysis on the ergodic rate of cognitive communications and the SOP of cognitive and primary communications in [5, 25] are tractable.Lately, [26–28] suggested that a two-phase ([26, 28] are conference versions where [26] considered Rayleigh fading while [28] generalized [26] with Nakagami-m fading. Because of conference versions, [26, 28] briefly outlined few results without any proof) transmission scheme incorporated with artificial noise generation in EHONs to enhance spectral efficiency and security capability. Moreover, [26–28] analyzed the SOP of cognitive and primary communications in EHONs. Nonetheless, similarly to [5, 25], the authors in [26–28] considered the DF cognitive users, which may cease primary communications if CUs fail to restore primary message.


### 1.2. Contributions

The current paper contributes the following:(i)
Suggest a new operation principle of the cognitive transmitter which permits it to scavenge energy from the primary transmitter, amplify and forward primary signal, and create a signal combination of primary signal, cognitive signal, and artificial noise. This principle is flexible in trading-off the security capability of primary communications with that of cognitive communications and optimizing system design by appropriately adopting (time switching, power splitting, power allocation) coefficients. It is reminded that compared to the DF cognitive transmitter in [5] and [26–28], the AF cognitive transmitter in this paper is simpler and prevents error propagation. Moreover, the AF cognitive transmitter in this paper always maintains primary communications while the DF cognitive transmitter in [5, 26–28] assures primary communications only when it decodes correctly primary message(ii)
Suggest a novel signal model to represent signals/quantities corresponding to the considered operation principle of the cognitive transmitter, from which the performance metrics are formulated(iii)
Propose accurate pivotal security performance indicator expressions for quickly assessing the impact of artificial noise on the security performance of both cognitive and primary communications. The indicators are the SOP, secrecy throughput, intercept probability, and positive secrecy capacity probability. Furthermore, these expressions are applicable to both nonlinear and linear energy harvesting models(iv)
Show the presence of optimal pivotal specifications for the optimal security capability and the optimal security trade-off between cognitive and primary communications(v)
Supply various insightful results on the security capability of cognitive/primary communications in key specifications


### 1.3. Outline

The next part describes the system model. Derivations of accurate pivotal security performance indicator expressions are presented in part 3. Illustrative results are provided in part 4 and eventually, and part 5 ends the paper.


## 1.1. Existing Publications

This paper studies the impact of artificial noise in EHONs where a primary transmitter cannot connect directly a primary receiver in some scenarios (e.g., heavy shadowing), and hence a cognitive transmitter supports primary communications in exchange for its access to the LFB. The cognitive transmitter operating in the amplify-and-forward (AF) mechanism scavenges RF energy in the primary transmitter’s signals and sends not only its privacy signal but also the primary transmitter’s signal and artificial noise. Message transmission of the cognitive transmitter is overheard by an eavesdropper.Whilst most publications have investigated the PHY security for energy harvesting (interweave/underlay) networks, a handful works have paid attention to the overlay mechanism [5, 21–28]. More specifically, [21] investigated the almost similar system model to ours but EHONs are secured by asking a devoted jammer to jam the eavesdropper. In [22, 23], the primary receiver was exploited to corrupt the eavesdropper rather than the devoted jammer as in [21]. Additionally, [21] disagrees [22, 23] in the energy harvesting (EH) technique, the EH-capable device, and the assistance mechanism. The former utilized the cognitive transmitter as a decode-and-forward (DF) relay and exploited the EH-capable jammer which scavenges energy based on the time switching protocol [29]. Meanwhile, the latter employed the cognitive transmitter as the AF relay and as an energy scavenger that bases on the power splitting protocol [30]. To better secure primary communications, [24] suggested to jam the eavesdropper by the primary receiver as well as the dedicated jammer. Nonetheless, the analysis on the secrecy outage probability (SOP) of both primary and cognitive communications was not reported in [21–24]. In [25], EHONs are secured with the multiuser scheduling and the transmit antenna selection. Moreover, [25] analyzed the SOP/ergodic rate of primary/cognitive communications. Recently, a bulk of dedicated jammers were recommended to secure EHONs, and the SOP of cognitive and primary communications was suggested in closed form [5]. Nevertheless, distinguishing from [21–24], the cognitive user relays the primary signal and sends its privacy signal independently in [5, 25]. This demands at least three phases (phase 1: energy scavenging and PU’s communications, phase 2: CU’s communications to PU, and phase 3: CU’s communications to CU) to complete message communications of both PU and CU, reducing drastically spectral efficiency and analysis complexity. As such, the closed-form analysis on the ergodic rate of cognitive communications and the SOP of cognitive and primary communications in [5, 25] are tractable.Lately, [26–28] suggested that a two-phase ([26, 28] are conference versions where [26] considered Rayleigh fading while [28] generalized [26] with Nakagami-m fading. Because of conference versions, [26, 28] briefly outlined few results without any proof) transmission scheme incorporated with artificial noise generation in EHONs to enhance spectral efficiency and security capability. Moreover, [26–28] analyzed the SOP of cognitive and primary communications in EHONs. Nonetheless, similarly to [5, 25], the authors in [26–28] considered the DF cognitive users, which may cease primary communications if CUs fail to restore primary message.


## 1.2. Contributions

The current paper contributes the following:(i)
Suggest a new operation principle of the cognitive transmitter which permits it to scavenge energy from the primary transmitter, amplify and forward primary signal, and create a signal combination of primary signal, cognitive signal, and artificial noise. This principle is flexible in trading-off the security capability of primary communications with that of cognitive communications and optimizing system design by appropriately adopting (time switching, power splitting, power allocation) coefficients. It is reminded that compared to the DF cognitive transmitter in [5] and [26–28], the AF cognitive transmitter in this paper is simpler and prevents error propagation. Moreover, the AF cognitive transmitter in this paper always maintains primary communications while the DF cognitive transmitter in [5, 26–28] assures primary communications only when it decodes correctly primary message(ii)
Suggest a novel signal model to represent signals/quantities corresponding to the considered operation principle of the cognitive transmitter, from which the performance metrics are formulated(iii)
Propose accurate pivotal security performance indicator expressions for quickly assessing the impact of artificial noise on the security performance of both cognitive and primary communications. The indicators are the SOP, secrecy throughput, intercept probability, and positive secrecy capacity probability. Furthermore, these expressions are applicable to both nonlinear and linear energy harvesting models(iv)
Show the presence of optimal pivotal specifications for the optimal security capability and the optimal security trade-off between cognitive and primary communications(v)
Supply various insightful results on the security capability of cognitive/primary communications in key specifications


## 1.3. Outline

The next part describes the system model. Derivations of accurate pivotal security performance indicator expressions are presented in part 3. Illustrative results are provided in part 4 and eventually, and part 5 ends the paper.


## 2. System Description

### 2.1. System Model

Figure1 demonstrates an EHON where the primary transmitter-receiver pair, T−R, cannot communicate to each other directly owing to channel impairments (e.g., deep fading). Consequently, the cognitive transmitter S, which is in the coverage range of T, can aid T by relaying T’s message to R. It is assumed that S is able to scavenge the RF energy in signals of T and spends the scavenged energy for its operation. Moreover, S operates in the overlay mechanism where it relays T’s message to R and transmits its privacy data to the cognitive receiver D. Communications of S is overheard by an eavesdropper E. In order to mitigate the overhearing capability of E, S sends artificial noise together with messages of T and S.Figure 1
System model.Figure1 denotes hsp, hsd, hse, and hps as (S→R, S→D, S→E, T→S) channel coefficients, respectively. This paper models these channel coefficients as hsp~CN0,μsp, hsd~CN0,μsd, hse~CN0,μse, and hps~CN0,μps, correspondingly. Such a channel coefficient model indicates Rayleigh fading channels. Integrating path loss into channel characteristics models μab with a∈p,s and b∈s,p,d,e as μab=dab−ρ in which ρ is the path-loss exponent and dab is the a−b distance. Then, fgabx=e−x/μab/μab and Fgabx=1−e−x/μab are correspondingly the probability density function (PDF) and the cumulative distribution function (CDF) of the channel gain gab=hab2.The total transmission timeτ for both T and S to finish data transmission to corresponding receivers comprises two phases as seen in Figure 1. In phase 1 of ατ with α∈0,1 being the time switching factor, T with the transmission power of Pp sends its symbol xp for S to harvest energy relied on the power splitting protocol and amplify T’s signal. Such a protocol divides S’s received signal into two parts: one part λys (ys is S’s received signal, and λ∈0,1 is the power splitting factor) for harvesting energy and another part 1−λys for amplifying T’s signal (signal processing at S consumes assumedly negligible energy. Such an assumption is acceptable in previous works (e.g., [5–16, 21–25, 29, 30]). In phase 2 of 1−ατ, S broadcasts a superposition of three signals: amplified primary signal, cognitive signal, and artificial noise.


### 2.2. Signal Model

In phase 1,S receives the signal
(1)ys=hpsPpxp+ns,where the received antenna of S creates the additive white Gaussian noise (AWGN) ns~CN0,σs2.Based on Figure1, the harvested energy of S is
(2)Es=ηΞλys2ατ=ηλPpgps+σs2ατ≈αηλPpgpsτ,where η∈0,1 is the energy conversion efficiency, and Ξ· is the expectation operator. The approximation in (2) holds because the signal power dominates the noise power.In phase 2,S has transmission power as
(3)Ps=Es1−ατ≈APpgps,where A=αηλ/1−α.One of the inputs of the signal generator in Figure1 is y~s=1−λys+n~s where n~s~CN0,σ~s2 is the AWGN owing to the passband-to-baseband signal conversion. Superseding (1) into y~s yeilds
(4)y~s=1−λPphpsxp+1−λns+n~s.The signal generator amplifiesy~s before combining with cognitive signal and artificial noise. More specifically, the signal generator creates the signal x¯s=βy~s+θ1−κPsxs+1−θPsxa where β is the amplification factor, θ is the power allocation factor for desired signals and artificial noise, κ is the power allocation factor for cognitive and primary signals, xs is S’s the unit power symbol, and xa is the unit power artificial noise. The amplification factor β is determined so that the total power of S is Ps. Consequently, the power to amplify the primary signal is θκPs from which β is given by
(5)β=θκPsΞy~s2=θκPs1−λPpgps+1−λσs2+σ~s2.In phase 2, the received signals atR,D,E are correspondingly represented as
(6)yp=hspx¯s+np,yd=hsdx¯s+nd,ye=hsex¯s+ne,where the received antennas of R,D,E induce the noises np~CN0,σp2, nd~CN0,σd2, and ne~CN0,σe2, respectively.S purposely generates the artificial noise xa to solely deteriorate the wire tapping of E but not to mitigate the performance of the legitimate receivers (D,R). Such artificial noise generation can be implemented by enabling S to share. For instance, the artificial noise generator at S has the seed that is shared with D and R securely through a collaboration contract solely among S, D, and R prior to any start of message transmission. Open literature widely accepted this artificial noise generating mechanism (e.g., [5, 20, 22, 23]).xa with D and R. Consequently, the legitimate receivers (D,R) are able to reproduce accurately the artificial noise and perfectly annihilate it, eventually yielding the artificial noise-free signals at R and D as
(7)y~p=hspx~s+np,y~d=hsdx~s+nd,where x~s=βy~s+θ1−κPsxs.Insertingy~s in (4) into x~s and then substituting x~s into (7), one rewrites (7) as
(8)y~p=1−λPphspβhpsxp+hspθ1−κPsxs+hspβ1−λns+n~s+np,(9)y~d=1−λPphsdβhpsxp+hsdθ1−κPsxs+hsdβ1−λns+n~s+nd,from which signal-to-interference plus noise ratios (SINRs) for recovering xp at R and xs at D are, respectively, given by
(10)γp=Ξ1−λPphspβhpsxp2Ξhspθ1−κPsxs+hspβ1−λns+n~s+np2=1−λPpgspgpsβ2gspθ1−κPs+gspβ21−λσs2+σ~s2+σp2,(11)γd=Ξhsdθ1−κPsxs2Ξ1−λPphsdβhpsxp+hsdβ1−λns+n~s+nd2=θ1−κPsgsd1−λPpgpsgsdβ2+gsdβ21−λσs2+σ~s2+σd2.SubstitutingPs in (3) and β in (5) into (10) and (11) and after some manipulations, one simplifies (10) and (11) as
(12)γp=GgspHgsp+J,(13)γd=G¯gsdH¯gsd+J¯,where B=σs2+σ~s2/1−λ, J¯=σd2,
(14)G=θκAPp2gps2,(15)H=θAB+1−κPpgpsPpgps,(16)J=Ppgps+Bσp2,(17)G¯=θ1−κAPpgps,(18)H¯=θκAPpgps.Inserting (4) into x¯s and then plugging x¯s into ye in (6), one rewrites (6) for E as
(19)ye=hseβ1−λPphpsxp+hseθ1−κPsxs+hseβ1−λns+n~s+hse1−θPsxa+ne.The understanding of the artificial noisexa is known at R, D, and S for protecting xs and xp; yet, E does not know xa. Consequently, the SINRs at E for recovering xs and xp are derived from (19), respectively, as
(20)γes=Ξhseθ1−κPsxs2Ξhseβ1−λPphpsxp+hseβ1−λns+n~s+hse1−θPsxa+ne2=gseθ1−κPs1−λPpβ2gsegps+gseβ21−λσs2+σ~s2+gse1−θPs+σe2,(21)γep=Ξhseβ1−λPphpsxp2Ξhseθ1−κPsxs+hseβ1−λns+n~s+hse1−θPsxa+ne2=1−λPpβ2gsegpsgseθ1−κPs+gseβ21−λσs2+σ~s2+gse1−θPs+σe2.Equations (20) and (21) expose that S intentionally produces the amount of the artificial noise power, gse1−θPs, to interfere the eavesdropper. As such, boosting this amount would secure message transmission for xs and xp.SubstitutingPs in (3) and β in (5) into (20) and (21) and after some manipulations, one simplifies (20) and (21) as
(22)γes=G¯gseU¯gse+J¯,(23)γep=GgseUgse+J,where
(24)U=AB+1−θκPpgpsPpgps,(25)U¯=1−θ+θκAPpgps,and σs2=σe2=σd2=σp2=σ~s2=N0 is assumed without loss of generality.The channel capacities ofD and R in phase 2 are, respectively, given by
(26)Cd=1−αlog1+γd,(27)Cp=1−αlog1+γp,where phase 2 of 1−ατ induces the prelogarithm factor 1−α.Similarly, the channel capacities atE for decoding xp and xs in phase 2 are deduced, respectively, as
(28)CEp=1−αlog1+γep,(29)CEs=1−αlog1+γes.The capacity difference betweenR and E for restoring xp is defined as the secrecy capacity for xp:
(30)C~p=Cp−CEp+=1−αlog1+γp1+γep+,where x+ denotes maxx,0.Similarly, the capacity difference betweenD and E for restoring xs is the secrecy capacity for xs:
(31)C~s=1−αlog1+γd1+γes+.


## 2.1. System Model

Figure1 demonstrates an EHON where the primary transmitter-receiver pair, T−R, cannot communicate to each other directly owing to channel impairments (e.g., deep fading). Consequently, the cognitive transmitter S, which is in the coverage range of T, can aid T by relaying T’s message to R. It is assumed that S is able to scavenge the RF energy in signals of T and spends the scavenged energy for its operation. Moreover, S operates in the overlay mechanism where it relays T’s message to R and transmits its privacy data to the cognitive receiver D. Communications of S is overheard by an eavesdropper E. In order to mitigate the overhearing capability of E, S sends artificial noise together with messages of T and S.Figure 1
System model.Figure1 denotes hsp, hsd, hse, and hps as (S→R, S→D, S→E, T→S) channel coefficients, respectively. This paper models these channel coefficients as hsp~CN0,μsp, hsd~CN0,μsd, hse~CN0,μse, and hps~CN0,μps, correspondingly. Such a channel coefficient model indicates Rayleigh fading channels. Integrating path loss into channel characteristics models μab with a∈p,s and b∈s,p,d,e as μab=dab−ρ in which ρ is the path-loss exponent and dab is the a−b distance. Then, fgabx=e−x/μab/μab and Fgabx=1−e−x/μab are correspondingly the probability density function (PDF) and the cumulative distribution function (CDF) of the channel gain gab=hab2.The total transmission timeτ for both T and S to finish data transmission to corresponding receivers comprises two phases as seen in Figure 1. In phase 1 of ατ with α∈0,1 being the time switching factor, T with the transmission power of Pp sends its symbol xp for S to harvest energy relied on the power splitting protocol and amplify T’s signal. Such a protocol divides S’s received signal into two parts: one part λys (ys is S’s received signal, and λ∈0,1 is the power splitting factor) for harvesting energy and another part 1−λys for amplifying T’s signal (signal processing at S consumes assumedly negligible energy. Such an assumption is acceptable in previous works (e.g., [5–16, 21–25, 29, 30]). In phase 2 of 1−ατ, S broadcasts a superposition of three signals: amplified primary signal, cognitive signal, and artificial noise.


## 2.2. Signal Model

In phase 1,S receives the signal
(1)ys=hpsPpxp+ns,where the received antenna of S creates the additive white Gaussian noise (AWGN) ns~CN0,σs2.Based on Figure1, the harvested energy of S is
(2)Es=ηΞλys2ατ=ηλPpgps+σs2ατ≈αηλPpgpsτ,where η∈0,1 is the energy conversion efficiency, and Ξ· is the expectation operator. The approximation in (2) holds because the signal power dominates the noise power.In phase 2,S has transmission power as
(3)Ps=Es1−ατ≈APpgps,where A=αηλ/1−α.One of the inputs of the signal generator in Figure1 is y~s=1−λys+n~s where n~s~CN0,σ~s2 is the AWGN owing to the passband-to-baseband signal conversion. Superseding (1) into y~s yeilds
(4)y~s=1−λPphpsxp+1−λns+n~s.The signal generator amplifiesy~s before combining with cognitive signal and artificial noise. More specifically, the signal generator creates the signal x¯s=βy~s+θ1−κPsxs+1−θPsxa where β is the amplification factor, θ is the power allocation factor for desired signals and artificial noise, κ is the power allocation factor for cognitive and primary signals, xs is S’s the unit power symbol, and xa is the unit power artificial noise. The amplification factor β is determined so that the total power of S is Ps. Consequently, the power to amplify the primary signal is θκPs from which β is given by
(5)β=θκPsΞy~s2=θκPs1−λPpgps+1−λσs2+σ~s2.In phase 2, the received signals atR,D,E are correspondingly represented as
(6)yp=hspx¯s+np,yd=hsdx¯s+nd,ye=hsex¯s+ne,where the received antennas of R,D,E induce the noises np~CN0,σp2, nd~CN0,σd2, and ne~CN0,σe2, respectively.S purposely generates the artificial noise xa to solely deteriorate the wire tapping of E but not to mitigate the performance of the legitimate receivers (D,R). Such artificial noise generation can be implemented by enabling S to share. For instance, the artificial noise generator at S has the seed that is shared with D and R securely through a collaboration contract solely among S, D, and R prior to any start of message transmission. Open literature widely accepted this artificial noise generating mechanism (e.g., [5, 20, 22, 23]).xa with D and R. Consequently, the legitimate receivers (D,R) are able to reproduce accurately the artificial noise and perfectly annihilate it, eventually yielding the artificial noise-free signals at R and D as
(7)y~p=hspx~s+np,y~d=hsdx~s+nd,where x~s=βy~s+θ1−κPsxs.Insertingy~s in (4) into x~s and then substituting x~s into (7), one rewrites (7) as
(8)y~p=1−λPphspβhpsxp+hspθ1−κPsxs+hspβ1−λns+n~s+np,(9)y~d=1−λPphsdβhpsxp+hsdθ1−κPsxs+hsdβ1−λns+n~s+nd,from which signal-to-interference plus noise ratios (SINRs) for recovering xp at R and xs at D are, respectively, given by
(10)γp=Ξ1−λPphspβhpsxp2Ξhspθ1−κPsxs+hspβ1−λns+n~s+np2=1−λPpgspgpsβ2gspθ1−κPs+gspβ21−λσs2+σ~s2+σp2,(11)γd=Ξhsdθ1−κPsxs2Ξ1−λPphsdβhpsxp+hsdβ1−λns+n~s+nd2=θ1−κPsgsd1−λPpgpsgsdβ2+gsdβ21−λσs2+σ~s2+σd2.SubstitutingPs in (3) and β in (5) into (10) and (11) and after some manipulations, one simplifies (10) and (11) as
(12)γp=GgspHgsp+J,(13)γd=G¯gsdH¯gsd+J¯,where B=σs2+σ~s2/1−λ, J¯=σd2,
(14)G=θκAPp2gps2,(15)H=θAB+1−κPpgpsPpgps,(16)J=Ppgps+Bσp2,(17)G¯=θ1−κAPpgps,(18)H¯=θκAPpgps.Inserting (4) into x¯s and then plugging x¯s into ye in (6), one rewrites (6) for E as
(19)ye=hseβ1−λPphpsxp+hseθ1−κPsxs+hseβ1−λns+n~s+hse1−θPsxa+ne.The understanding of the artificial noisexa is known at R, D, and S for protecting xs and xp; yet, E does not know xa. Consequently, the SINRs at E for recovering xs and xp are derived from (19), respectively, as
(20)γes=Ξhseθ1−κPsxs2Ξhseβ1−λPphpsxp+hseβ1−λns+n~s+hse1−θPsxa+ne2=gseθ1−κPs1−λPpβ2gsegps+gseβ21−λσs2+σ~s2+gse1−θPs+σe2,(21)γep=Ξhseβ1−λPphpsxp2Ξhseθ1−κPsxs+hseβ1−λns+n~s+hse1−θPsxa+ne2=1−λPpβ2gsegpsgseθ1−κPs+gseβ21−λσs2+σ~s2+gse1−θPs+σe2.Equations (20) and (21) expose that S intentionally produces the amount of the artificial noise power, gse1−θPs, to interfere the eavesdropper. As such, boosting this amount would secure message transmission for xs and xp.SubstitutingPs in (3) and β in (5) into (20) and (21) and after some manipulations, one simplifies (20) and (21) as
(22)γes=G¯gseU¯gse+J¯,(23)γep=GgseUgse+J,where
(24)U=AB+1−θκPpgpsPpgps,(25)U¯=1−θ+θκAPpgps,and σs2=σe2=σd2=σp2=σ~s2=N0 is assumed without loss of generality.The channel capacities ofD and R in phase 2 are, respectively, given by
(26)Cd=1−αlog1+γd,(27)Cp=1−αlog1+γp,where phase 2 of 1−ατ induces the prelogarithm factor 1−α.Similarly, the channel capacities atE for decoding xp and xs in phase 2 are deduced, respectively, as
(28)CEp=1−αlog1+γep,(29)CEs=1−αlog1+γes.The capacity difference betweenR and E for restoring xp is defined as the secrecy capacity for xp:
(30)C~p=Cp−CEp+=1−αlog1+γp1+γep+,where x+ denotes maxx,0.Similarly, the capacity difference betweenD and E for restoring xs is the secrecy capacity for xs:
(31)C~s=1−αlog1+γd1+γes+.


## 3. Security Analysis

The vital performance indicator to rate the security performance of wireless transmission is the SOP that is the probability of the secrecy capacity below the required security degreeC0. In this section, accurate SOP expressions are firstly proposed to quickly assess the security performance for xp and xs without time-consuming simulations. Then, other vital security capability indicators including the positive secrecy capacity possibility (PSCP), the intercept possibility (IP), and the secrecy throughput (ST) are derived from the SOP formulas.


### 3.1. SOP for the Primary Messagexp

The SOP for the primary messagexp is defined as
(32)OpC0=PrC~p<C0.PluggingC~p in (30) into (32) results in
(33)OpC0=ΞgpsΨgps,where X=1+Ggsp/Hgsp+J, Y=1+Ggse/Ugse+J, D=2C0/1−α, and
(34)Ψgps=PrX<DYgps.To numerically assess (33), one needs the exact closed-form expression of Ψgps in (34), which is presented as follows.The accurate expression ofΨgps is
(35)Ψgps=1−ReJμspH+JμseUΛ,K<V1−ReJμspH+JμseUφ,1≤V<K1,V<1,where
(36)L=GH+1,(37)K=GU+1,(38)V=LD,(39)M=1K−1−1K−V,(40)N=1V−1+1K−V,(41)Q=JGμspH2D,(42)R=JGμseU2,(43)Λ=eQK−V1Re−RK−1−QK−V2eRV−KEi−RM+∑g=2∞Qg−Rg−1K−V2gg!g−1!e−RK−1∑c=1g−1c−1!−RMc−eRV−KEi−RM,(44)φ=eR/V−KV−K2∑g=0∞Rg−Qg+1V−K2gg!g+1!e−QV−1∑c=1g+1c−1!−QNc−eQK−VEi−QN,with Eixbeing the exponential-integral function [31].Ψgps in (35) can be shown with the help of Appendix C in [27] and some proper variable changes.BecauseΨgps is a function of random variables (G, H, J, U) which are also functions of the random variable gps according to (14), (15), (16), and (24), OpC0 in (33) is computed through the single-variable integral as
(45)OpC0=∫0∞Ψxfgpsxdx=∫0∞Ψxe−x/μpsμpsdx.In order to compute (45), one must determine Ψx in (35) for the specific value of x. Towards this end, one considers two expressions, K−V and V−1, which are functions of x=gps. By using K in (37) and V in (38), one can, respectively, express K−V and V−1 as
(46)K−V=D−1+θκ−Dκx−x1x−x2,(47)V−1=Dκ−D+1x−BD−1/Pp,where x1=−B/Pp and x2=−BD−1/PpD−1+θκ−Dκ.It is straightforward to infer cases in Table1 where x¯=BD−1/PpDκ−D+1. Based on Table 1, three cases are considered to compute (45) as follows.Case 1.
D<1−θκ/1−κ.
This case results in(48)x>x2,K<Vx¯<x<x2,1<V<Kx<x¯,V<1,and hence
(49)OpC0=∫0x¯e−x/μpsμpsdx+∫x¯x21−ReJμspH+JμseUφe−x/μpsμpsdx+∫x2∞1−ReJμspH+JμseUΛe−x/μpsμpsdx=1−A1μps,where A1=∫x¯x2RφeJ/μspH+J/μseU−x/μpsdx+∫x2∞RΛeJ/μspH+J/μseU−x/μpsdx.Case 2.
1−θκ/1−κ<D<1/1−κ.
This case results in(50)x¯<x,1<V<Kx<x¯,V<1,and thus
(51)OpC0=∫0x¯e−x/μpsμpsdx+∫x¯∞1−ReJμspH+JμseUφe−x/μpsμpsdx=1−A2μps,where A2=∫x¯∞RφeJ/μspH+J/μseU−x/μpsdx.Case 3.
1/1−κ<D.
This case results inV<1, and thus
(52)OpC0=1.Table 1
Inequalities:K>V and V>1.
D>1−θκ1−κD<1−θκ1−κD<11−κD>11−κV<KV>KV<KV>1V<1V<1x>x2x<x2x>x¯x<x¯In summary, the SOP for the primary messagexp is expressed as
(53)OpC0=1−A1μps,D<1−θκ1−κ1−A2μps,1−θκ1−κ<D<11−κ1,11−κ<D.


### 3.2. SOP for the Cognitive Messagexs

The SOP for the cognitive messagexs is expressed as
(54)OsC0=PrC~s<C0.InsertingC~s in (31) into (54) yields
(55)OsC0=ΞgpsYgps,where
(56)Ygps=Pr1+G¯gsd/H¯gsd+J¯1+G¯gse/U¯gse+J¯<Dgps.BothY in (56) and Ψ in (34) share a similar form. Accordingly, by substituting variables appropriately into Ψ in (35), one achieves the accurate expression of Y. More specifically, Y is computed by using Ψ in (35) with G→G¯, H→H¯, J→J¯, U→U¯, and μsp→μsd. Consequently, the derivation of Y is ignored here for compactness.SinceYgps is a function of random variables (G¯, H¯, U¯) which are also functions of the random variable gps according to (17), (18), and (25), OsC0 in (55) is computed as
(57)OsC0=∫0∞Yxfgpsxdx.In order to compute (57), it should be noted that K¯=G¯/U¯+1=1/1−θ+θκ and V¯=L¯/D=G¯/H¯+1/D=1/Dκ are constants. Therefore, (57) is explicitly rewritten as
(58)OsC0=1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsΛ¯dx,K¯<V¯1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsφ¯dx,1≤V¯<K¯1,V¯<1=1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsΛ¯dx,D<1−θ+θκκ1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsφ¯dx,1−θ+θκκ≤D<1κ1,D>1κ,where x=gps and R¯, Λ¯, φ¯ are correspondingly achieved from R, Λ, ad φ with G→G¯, H→H¯, J→J¯, U→U¯, and μsp→μsd.


### 3.3. Comments

#### 3.3.1. Absolute Unsecurity

SinceD=2C0/1−α, (53) and (58) show that the SOP for the primary/cognitive message takes different values dependent on the correlation among C0, α, θ, and κ. Especially, the primary (or cognitive) communications are absolutely unsecured when κ<1−2−C0/1−α or κ>2−C0/1−α.


#### 3.3.2. Vital Security Performance Measures

The accurate expressions ofOp and Os can be numerically computed by multiple softwares such as Mathematica and Matlab. Accordingly, such expressions are useful in quickly rating the influence of artificial noise on the secrecy performance of both cognitive and primary transmission in EHONs without exhaustive simulations. Upon our knowledge, these formulas are novel. Furthermore, they facilitate in deriving the formulas for other vital security performance measures. More specifically, the IP is the possibility of the negative secrecy capacity. Accordingly, the IP of primary/cognitive communications is obtained as
(59)IPv=PrC~v<0=Ov0,where v=s,p.The PSCP is the possibility of the positive secrecy capacity. Consequently, the PSCP of primary/cognitive communications is represented as(60)PSCPv=PrC~v>0=1−Ov0.Eventually, the ST is the multiplication of the secrecy communication possibility at a certain secrecy capacity with that secrecy capacity. Consequently, the ST of primary/cognitive communications is achieved as(61)STv=1−OvC0C0.


#### 3.3.3. Nonlinear Energy Harvesting

This paper mainly focuses on the linear energy harvesting (LEH) model in (2). Nonetheless, our analytical results are still extended to the nonlinear energy harvesting (NLEH) models (e.g., [32, 33]). Indeed, for the NLEH models, Ps in (3) is a nonlinear function of gps. Therefore, the forms of γp in (12), γd in (13), γes in (22), and γep in (23) are unchanged for the NLEH models. Nonetheless, some quantities in (12), (13), (22), and (23), which are functions of Ps, are different for the LEH and NLEH models. More specifically, for the NLEH models, γp in (12), γd in (13), γes in (22), and γep in (23) are correspondingly expressed as
(62)γ~p=G~gspH~gsp+σp2,(63)γ~d=G¯~gsdH¯~gsd+σd2,(64)γ~es=G¯~gseU¯~gse+σe2,(65)γ~ep=G~gseU~gse+σe2,where G~=1−λPpgpsβ2, H~=θ1−κPs+β21−λσs2+σ~s2, G¯~=θ1−κPs, H¯~=1−λPpgpsβ2+β21−λσs2+σ~s2, U¯~=1−λPpβ2gps+β21−λσs2+σ~s2+1−θPs, and U~=θ1−κPs+β21−λσs2+σ~s2+1−θPs.Sinceβ is a function of gps, the quantities (G~, H~, G¯~, H¯~, U¯~, U~) are just functions of gps. Therefore, for the NLEH models, the SOP for the primary message, OpC0, and the SOP for the cognitive message, OsC0, can be, respectively, computed by using (45) and (57) with appropriate variable changes.


## 3.1. SOP for the Primary Messagexp

The SOP for the primary messagexp is defined as
(32)OpC0=PrC~p<C0.PluggingC~p in (30) into (32) results in
(33)OpC0=ΞgpsΨgps,where X=1+Ggsp/Hgsp+J, Y=1+Ggse/Ugse+J, D=2C0/1−α, and
(34)Ψgps=PrX<DYgps.To numerically assess (33), one needs the exact closed-form expression of Ψgps in (34), which is presented as follows.The accurate expression ofΨgps is
(35)Ψgps=1−ReJμspH+JμseUΛ,K<V1−ReJμspH+JμseUφ,1≤V<K1,V<1,where
(36)L=GH+1,(37)K=GU+1,(38)V=LD,(39)M=1K−1−1K−V,(40)N=1V−1+1K−V,(41)Q=JGμspH2D,(42)R=JGμseU2,(43)Λ=eQK−V1Re−RK−1−QK−V2eRV−KEi−RM+∑g=2∞Qg−Rg−1K−V2gg!g−1!e−RK−1∑c=1g−1c−1!−RMc−eRV−KEi−RM,(44)φ=eR/V−KV−K2∑g=0∞Rg−Qg+1V−K2gg!g+1!e−QV−1∑c=1g+1c−1!−QNc−eQK−VEi−QN,with Eixbeing the exponential-integral function [31].Ψgps in (35) can be shown with the help of Appendix C in [27] and some proper variable changes.BecauseΨgps is a function of random variables (G, H, J, U) which are also functions of the random variable gps according to (14), (15), (16), and (24), OpC0 in (33) is computed through the single-variable integral as
(45)OpC0=∫0∞Ψxfgpsxdx=∫0∞Ψxe−x/μpsμpsdx.In order to compute (45), one must determine Ψx in (35) for the specific value of x. Towards this end, one considers two expressions, K−V and V−1, which are functions of x=gps. By using K in (37) and V in (38), one can, respectively, express K−V and V−1 as
(46)K−V=D−1+θκ−Dκx−x1x−x2,(47)V−1=Dκ−D+1x−BD−1/Pp,where x1=−B/Pp and x2=−BD−1/PpD−1+θκ−Dκ.It is straightforward to infer cases in Table1 where x¯=BD−1/PpDκ−D+1. Based on Table 1, three cases are considered to compute (45) as follows.Case 1.
D<1−θκ/1−κ.
This case results in(48)x>x2,K<Vx¯<x<x2,1<V<Kx<x¯,V<1,and hence
(49)OpC0=∫0x¯e−x/μpsμpsdx+∫x¯x21−ReJμspH+JμseUφe−x/μpsμpsdx+∫x2∞1−ReJμspH+JμseUΛe−x/μpsμpsdx=1−A1μps,where A1=∫x¯x2RφeJ/μspH+J/μseU−x/μpsdx+∫x2∞RΛeJ/μspH+J/μseU−x/μpsdx.Case 2.
1−θκ/1−κ<D<1/1−κ.
This case results in(50)x¯<x,1<V<Kx<x¯,V<1,and thus
(51)OpC0=∫0x¯e−x/μpsμpsdx+∫x¯∞1−ReJμspH+JμseUφe−x/μpsμpsdx=1−A2μps,where A2=∫x¯∞RφeJ/μspH+J/μseU−x/μpsdx.Case 3.
1/1−κ<D.
This case results inV<1, and thus
(52)OpC0=1.Table 1
Inequalities:K>V and V>1.
D>1−θκ1−κD<1−θκ1−κD<11−κD>11−κV<KV>KV<KV>1V<1V<1x>x2x<x2x>x¯x<x¯In summary, the SOP for the primary messagexp is expressed as
(53)OpC0=1−A1μps,D<1−θκ1−κ1−A2μps,1−θκ1−κ<D<11−κ1,11−κ<D.


## 3.2. SOP for the Cognitive Messagexs

The SOP for the cognitive messagexs is expressed as
(54)OsC0=PrC~s<C0.InsertingC~s in (31) into (54) yields
(55)OsC0=ΞgpsYgps,where
(56)Ygps=Pr1+G¯gsd/H¯gsd+J¯1+G¯gse/U¯gse+J¯<Dgps.BothY in (56) and Ψ in (34) share a similar form. Accordingly, by substituting variables appropriately into Ψ in (35), one achieves the accurate expression of Y. More specifically, Y is computed by using Ψ in (35) with G→G¯, H→H¯, J→J¯, U→U¯, and μsp→μsd. Consequently, the derivation of Y is ignored here for compactness.SinceYgps is a function of random variables (G¯, H¯, U¯) which are also functions of the random variable gps according to (17), (18), and (25), OsC0 in (55) is computed as
(57)OsC0=∫0∞Yxfgpsxdx.In order to compute (57), it should be noted that K¯=G¯/U¯+1=1/1−θ+θκ and V¯=L¯/D=G¯/H¯+1/D=1/Dκ are constants. Therefore, (57) is explicitly rewritten as
(58)OsC0=1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsΛ¯dx,K¯<V¯1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsφ¯dx,1≤V¯<K¯1,V¯<1=1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsΛ¯dx,D<1−θ+θκκ1−1μps∫0∞R¯eJ¯μsdH¯+J¯μseU¯−xμpsφ¯dx,1−θ+θκκ≤D<1κ1,D>1κ,where x=gps and R¯, Λ¯, φ¯ are correspondingly achieved from R, Λ, ad φ with G→G¯, H→H¯, J→J¯, U→U¯, and μsp→μsd.


## 3.3. Comments

### 3.3.1. Absolute Unsecurity

SinceD=2C0/1−α, (53) and (58) show that the SOP for the primary/cognitive message takes different values dependent on the correlation among C0, α, θ, and κ. Especially, the primary (or cognitive) communications are absolutely unsecured when κ<1−2−C0/1−α or κ>2−C0/1−α.


### 3.3.2. Vital Security Performance Measures

The accurate expressions ofOp and Os can be numerically computed by multiple softwares such as Mathematica and Matlab. Accordingly, such expressions are useful in quickly rating the influence of artificial noise on the secrecy performance of both cognitive and primary transmission in EHONs without exhaustive simulations. Upon our knowledge, these formulas are novel. Furthermore, they facilitate in deriving the formulas for other vital security performance measures. More specifically, the IP is the possibility of the negative secrecy capacity. Accordingly, the IP of primary/cognitive communications is obtained as
(59)IPv=PrC~v<0=Ov0,where v=s,p.The PSCP is the possibility of the positive secrecy capacity. Consequently, the PSCP of primary/cognitive communications is represented as(60)PSCPv=PrC~v>0=1−Ov0.Eventually, the ST is the multiplication of the secrecy communication possibility at a certain secrecy capacity with that secrecy capacity. Consequently, the ST of primary/cognitive communications is achieved as(61)STv=1−OvC0C0.


### 3.3.3. Nonlinear Energy Harvesting

This paper mainly focuses on the linear energy harvesting (LEH) model in (2). Nonetheless, our analytical results are still extended to the nonlinear energy harvesting (NLEH) models (e.g., [32, 33]). Indeed, for the NLEH models, Ps in (3) is a nonlinear function of gps. Therefore, the forms of γp in (12), γd in (13), γes in (22), and γep in (23) are unchanged for the NLEH models. Nonetheless, some quantities in (12), (13), (22), and (23), which are functions of Ps, are different for the LEH and NLEH models. More specifically, for the NLEH models, γp in (12), γd in (13), γes in (22), and γep in (23) are correspondingly expressed as
(62)γ~p=G~gspH~gsp+σp2,(63)γ~d=G¯~gsdH¯~gsd+σd2,(64)γ~es=G¯~gseU¯~gse+σe2,(65)γ~ep=G~gseU~gse+σe2,where G~=1−λPpgpsβ2, H~=θ1−κPs+β21−λσs2+σ~s2, G¯~=θ1−κPs, H¯~=1−λPpgpsβ2+β21−λσs2+σ~s2, U¯~=1−λPpβ2gps+β21−λσs2+σ~s2+1−θPs, and U~=θ1−κPs+β21−λσs2+σ~s2+1−θPs.Sinceβ is a function of gps, the quantities (G~, H~, G¯~, H¯~, U¯~, U~) are just functions of gps. Therefore, for the NLEH models, the SOP for the primary message, OpC0, and the SOP for the cognitive message, OsC0, can be, respectively, computed by using (45) and (57) with appropriate variable changes.


## 3.3.1. Absolute Unsecurity

SinceD=2C0/1−α, (53) and (58) show that the SOP for the primary/cognitive message takes different values dependent on the correlation among C0, α, θ, and κ. Especially, the primary (or cognitive) communications are absolutely unsecured when κ<1−2−C0/1−α or κ>2−C0/1−α.


## 3.3.2. Vital Security Performance Measures

The accurate expressions ofOp and Os can be numerically computed by multiple softwares such as Mathematica and Matlab. Accordingly, such expressions are useful in quickly rating the influence of artificial noise on the secrecy performance of both cognitive and primary transmission in EHONs without exhaustive simulations. Upon our knowledge, these formulas are novel. Furthermore, they facilitate in deriving the formulas for other vital security performance measures. More specifically, the IP is the possibility of the negative secrecy capacity. Accordingly, the IP of primary/cognitive communications is obtained as
(59)IPv=PrC~v<0=Ov0,where v=s,p.The PSCP is the possibility of the positive secrecy capacity. Consequently, the PSCP of primary/cognitive communications is represented as(60)PSCPv=PrC~v>0=1−Ov0.Eventually, the ST is the multiplication of the secrecy communication possibility at a certain secrecy capacity with that secrecy capacity. Consequently, the ST of primary/cognitive communications is achieved as(61)STv=1−OvC0C0.


## 3.3.3. Nonlinear Energy Harvesting

This paper mainly focuses on the linear energy harvesting (LEH) model in (2). Nonetheless, our analytical results are still extended to the nonlinear energy harvesting (NLEH) models (e.g., [32, 33]). Indeed, for the NLEH models, Ps in (3) is a nonlinear function of gps. Therefore, the forms of γp in (12), γd in (13), γes in (22), and γep in (23) are unchanged for the NLEH models. Nonetheless, some quantities in (12), (13), (22), and (23), which are functions of Ps, are different for the LEH and NLEH models. More specifically, for the NLEH models, γp in (12), γd in (13), γes in (22), and γep in (23) are correspondingly expressed as
(62)γ~p=G~gspH~gsp+σp2,(63)γ~d=G¯~gsdH¯~gsd+σd2,(64)γ~es=G¯~gseU¯~gse+σe2,(65)γ~ep=G~gseU~gse+σe2,where G~=1−λPpgpsβ2, H~=θ1−κPs+β21−λσs2+σ~s2, G¯~=θ1−κPs, H¯~=1−λPpgpsβ2+β21−λσs2+σ~s2, U¯~=1−λPpβ2gps+β21−λσs2+σ~s2+1−θPs, and U~=θ1−κPs+β21−λσs2+σ~s2+1−θPs.Sinceβ is a function of gps, the quantities (G~, H~, G¯~, H¯~, U¯~, U~) are just functions of gps. Therefore, for the NLEH models, the SOP for the primary message, OpC0, and the SOP for the cognitive message, OsC0, can be, respectively, computed by using (45) and (57) with appropriate variable changes.


## 4. Illustrative Results

The SOPs of both primary and cognitive communications in EHONs are assessed through pivotal specifications. For demonstration purposes, some specifications are randomly specified as the primary receiverR at 0.4,−0.2, the primary transmitter T at −0.2,0.2, the eavesdropper E at 0.5,−0.1, the cognitive receiver D at 0.5,0.0, the cognitive transmitter S at d,0.0, the energy conversion efficiency η=0.9, and the path-loss exponent ρ=3. In the following figures, the simulated result is denoted as “Sim,” while the theoretical results in (53) and (58) are denoted as “The.”. Furthermore, these figures are generated with a set of specifications (the primary transmission power-to-noise variance ratio Pp/N0=10 dB, d=0.0, the power splitting factor λ=0.6, the power allocation factor for primary and cognitive signals κ=0.6, the power allocation factor for desired signals and artificial noise θ=0.7, and the target security degree C0=0.1 bits/s/Hz) unless stated otherwise. These figures expose that the theoretical and simulated results are in a perfect match, validating the exactness of (53) and (58).Figure2 demonstrates the SOPs with respect to (w.r.t) Pp/N0. This figure exposes that the security performance is proportional to Pp/N0, which is interpreted as follows. Increasing Pp/N0 facilitates S to scavenge more energy from T and thus increasing the SINRs in phase 2 and reducing the SOPs. Furthermore, the security performance of primary communications outperforms that of cognitive communications. This is because among the amount of the power θPs reserved for transmitting legitimate data, and S allocates 60% (κ=0.6) of this amount to amplify and forward the primary signal and 40% (1−κ=0.4) of that to send the cognitive data. Moreover, increasing the time switching factor α degrades the security performance of both cognitive and primary communications (i.e., Op (or Os) at α=0.6 that is larger than Op (or Os) at α=0.4). The reason is that although increasing α helps S scavenge more energy from T in phase 1 (i.e., the SINRs at receivers in phase 2 also increase), the secrecy capacities in phase 2 reduce since they are weighted by 1−α. Therefore, Op and Os may increase with α.Figure 2
SOPs w.r.tPp/N0.Figure3 shows the SOPs w.r.t θ, which expose that the security performance of both cognitive and primary transmission is maximized at optimal values of θ, which balance the transmission powers for the legal (primary and cognitive) messages and the artificial noise. Additionally, the best security performance of both primary and cognitive communications increases with increasing α. The reason is that increasing α permits S to scavenge more energy from T and thus, increasing transmission power for both privacy message and the artificial noise. Therefore, the amount of the artificial noise at E increases, eventually improving the security performance. Moreover, the best security performance of primary communications is higher than that of cognitive communications. This can be comprehended from the fact that κ=0.6 allots more power for S to transmit T’s message than S’s message.Figure 3
SOPs w.r.tθ.Figure4 demonstrates the SOPs w.r.t κ. The results illustrate that increasing κ enhances the security performance of primary communications (i.e., Op decreases) while degrades that of cognitive communications (i.e., Os increases). This is apparent because κ interprets the percentage of S’s transmission power allocated for T’s signal while 1−κ interprets the percentage of S’s transmission power allocated for S’s signal. Consequently, increasing κ mitigates Op but boosts Os. Thanks to the contradictory security performance propensity of Op and Os w.r.t κ, there exists a value of κ where Op and Os are similar (e.g., κ≃0.524 for α=0.4 as seen in Figure 4). Additionally, increasing α degrades the security capability at Op=Os, which is comprehended similarly as Figure 2. Moreover, primary (or cognitive) communications 1s always in outage for some range of κ, for instance, Op=1 for κ≤0.23 and Os=1 for κ≥0.84 when α=0.4 as seen in Figure 4. This is comprehended as follows. Small κ means that the percentage of S’s transmission power allocated for T’s signal is small, and hence R receives less power for decoding T’s message, leading to the outage event. Also, large κ means that the percentage of S’s transmission power allocated for S’s signal is small, and thus D receives less power for decoding S’s message, leading to the outage event.Figure 4
SOPs w.r.tκ.Figure5 plots the SOPs w.r.t C0. This figure exposes that increasing C0 deteriorates the security performance of both primary and cognitive communications until a complete outage as expected. Moreover, primary communications are more secured than cognitive communications, which is comprehended similarly as Figure 2 due to κ=0.6. Furthermore, increasing α does not always enhance the security capability of both primary and cognitive communications. For instance, when C0 is smaller than 0.078 (or 0.086) bits/s/Hz, increasing α improves message security for the cognitive (or primary) communications; nevertheless, when C0 is greater than 0.078 (or 0.086) bits/s/Hz, this performance tendency is reversed. This is because the value of α must be selected to poise the harvested energy in phase 1 with the secrecy capacities in phase 2.Figure 5
SOPs w.r.tC0.Figure6 plots the SOPs w.r.t α, which expose that the security capability of both cognitive and primary communications is maximized with the optimum selection of α. The optimum value of α, which minimizes SOPs, was recognized and explained as in the previous figures. Additionally, the security capability compromise between cognitive and primary communications is achieved by adopting κ appropriately to allot S‘s transmission power for messages of S and T. This remark was also pointed out from Figure 4. Furthermore, the security performance of both primary and cognitive communications is in a complete outage for a large value of α (e.g., α≥0.75 causes Op=1 when κ=0.5). This is attributed to the fact that the large value of α significantly reduces the secrecy capacities in phase 2, causing the secrecy outage.Figure 6
SOPs w.r.tα.Figure7 demonstrates the SOPs w.r.t λ. The results demonstrate that increasing λ improves the security capability of cognitive communications. The reason is that increasing λ boosts the harvested energy but reduces the power of T’s signal in the received signal at S before amplifying T’s signal; thus, the power for transmitting S’s data is higher in Phase 2, intimately mitigating Os. Nevertheless, λ is adopted reasonably to optimize the security performance of primary communications. The optimal λ for minimum Op is to balance between the harvested energy and the power of T’s signal in the received signal at S. Additionally, the best security performance of primary communications is higher than that of cognitive communications due to κ=0.6, which is a similar remark observed from the previous figures. Moreover, α significantly affects the security capability of cognitive communications while slightly impacts that of primary communications.Figure 7
SOPs w.r.tλ.Locations of users in energy harvesting overlay networks affect the harvested energy in phase 1 as well as the secrecy capacities in phase 2, eventually impacting the SOPs. Figure8 plots the SOPs w.r.t the variation of S’s location. The results demonstrate that when S is close to (E, D, R) yet distant from T (i.e., d increases), the security capability of primary communications is degraded, which is comprehended as follows. As d rises, the power of T’s signal in the received signal at S decreases, leading to a reduction in the power of T’s signal at corresponding receivers (R, D, E) after relayed by S and an increase in Op. Nevertheless, this performance tendency is reversed for cognitive communications. This is because xs is not affected by d while received at corresponding receivers (R, D, E) with higher power due to lower path loss between S and corresponding receivers (R, D, E), leading to the decrease in Os. The opposite secrecy capability tendencies of cognitive and primary communications with d represent the performance compromise between them, which can be flexibly established by choosing the appropriate location of S. Furthermore, increasing α degrades the security performance of both primary and cognitive communications. This is apprehended similarly as the previous figures.Figure 8
SOPs w.r.td.


## 5. Conclusions

This paper investigated EHONs where the cognitive transmitter operating in the amplify-and-forward mechanism relays the signal of the primary transmitter as well as transmits its privacy signal. The cognitive transmitter self-powers its operation by harvesting RF energy and self-secures both primary and cognitive communications against eavesdroppers by generating the artificial noise. The security performance of both cognitive and primary communications was measured through numerous important indicators (SOP, IP, PSCP, ST), which were numerically evaluated by the recommended accurate formulas. Multiple results are supplied to validate these formulas as well as shed insights into the influence of the artificial noise on the security performance of EHONs with respect to pivotal specifications. Additionally, optimum specifications were found through exhaustive searches relied on the recommended formulas, which well serves as a design instruction. Moreover, the security capability compromise between cognitive and primary communications can be adjusted by selecting specifications reasonably.



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*Source: 9976837-2021-06-21.xml*