Impact of channel estimation-and-artificial noise cancellation imperfection on artificial noise-aided energy harvesting overlay networks

EHONs (Energy Harvesting Overlay Networks) satisfy stringent design requirements such as high energy-and-spectrum utilization efficiencies. However, due to open access nature of these networks, eavesdroppers can emulate cognitive radios to wire-tap legitimate information, inducing information security to become a great concern. In order to protect legitimate information against eavesdroppers, this paper generates artificial noise transmitted simultaneously with legitimate information to interfere eavesdroppers. Nonetheless, artificial noise cannot be perfectly suppressed at legitimate receivers as for its primary purpose of interfering only eavesdroppers. Moreover, channel information used for signal detection is hardly estimated at receivers with absolute accuracy. As such, to quickly evaluate impact of channel estimation-and-artificial noise cancellation imperfection on secrecy performance of secondary/primary communication in ANaEHONs (Artificial Noise-aided EHONs), this paper firstly proposes precise closed-form formulas of primary/secondary SOP (Secrecy Outage Probability). Then, computer simulations are provided to corroborate these formulas. Finally, various results are illustrated to shed insights into secrecy performance of ANaEHON with key system parameters from which optimum parameters are recognized. Notably, secondary/primary communication can be secured at different levels by flexibly adjusting various parameters of the proposed system model.


Introduction
Advanced wireless networks such as 5G/6G (Fifth/Sixth Generation) open a door to a large number of emerging wireless applications but impose an immense pressure on telecommunications infrastructure which requires advanced technology solutions of high (spectrum utilization, energy, spectral) efficiencies to release it [1][2][3][4]. Indeed, a key application of 5G networks is IoT (Internet of Things), which is deployed extensively from civilian (e.g., transportation, electricity, healthcare, public safety, ... ) to military (e.g., tactical reconnaissance, smart bases, ...) [5]. However, when deploying IoT, an enormous number of concurrently connected terminals consume tremendous amount of energy and hence, it is essential to improve energy efficiency to not only extend the lifetime of terminals but also reduce energy need. Moreover, IoT demands a large bandwidth to allot concurrently a huge number of terminals and thus, in the spectrum shortageand-scarcity situation as nowadays, solutions of enhancing spectral efficiency should be devised. Similarly to IoT, 5G mobile wireless communications, which serves the growing number of mobile terminals and demands increasingly high data transmission speed, needs efficient energy-andspectrum utilization solutions to meet its requirements [6].
CRs (Cognitive Radios), which typically operate in overlay, underlay, and interweave modes, can access the licensed frequency band of PUs (Primary Users) without causing any performance degradation for PUs, thus significantly improv-ing spectral efficiency and mitigating spectrum scarcity issue [7]. In the underlay mode, CRs utilize the licensed spectrum but must upper-bound interference caused at PUs. The overlay mode allows concurrent transmission of CRs and PUs but signal reception quality at primary receivers must be remained or enhanced with complicated signal processing techniques. In the meantime, the interweave mode merely leaves blank licensed spectrum for CRs to utilize. While the literature has intensively focused on the underlay and interweave modes, few works have studied the overlay one. The overlay mode can trade-off performances between primary and secondary communication better than other modes and hence, it is of a special attention in the current paper.
Energy efficiency of wireless communication can be enhanced by several viable solutions (e.g., network planning, EH (Energy Harvesting), hardware solutions). Amongst these solutions, RF (Radio Frequency) energy harvesting can be integrated into (5G/6G mobile or IoT) users to supply energy, extend the life-time of wireless devices, and improve energy efficiency since it requires simple energy harvesting circuits [8][9][10].
EHONs (Energy Harvesting Overlay Networks) can exploit simultaneously advantages of two feasible (energy harvesting and cognitive radio) technologies to meet several standards of advanced wireless networks requiring high energy-and-spectral efficiencies [11]. Nevertheless, that both licensed and unlicensed users in these networks are permitted to utilize the licensed spectrum simultaneously may enable eavesdroppers to emulate legitimate users to steal secret information, seriously warning security issues. To supplement and improve secrecy capability for traditional cryptographic and encryption techniques, PLS (physical layer security) has recently been suggested [12]. Amongst various PLS methods (e.g., opportunistic scheduling, transmit beam-forming, transmit antenna selection, on-off transmission, jamming, relaying), jamming (or generating artificial noise) is of a great concern due to its simple, efficient, and flexible implementation [13]. Therefore, this paper applies artificial noise in EHONs to secure primary/secondary communication.
Most references (e.g., [14][15][16][17][18][19][20][21]) assumed artificial noise to be exactly known at legitimate receivers. Accordingly, these receivers completely eliminate its detrimental effect while eavesdroppers suffer severely this effect. Nevertheless, the amount of artificial noise received at legitimate receivers is variable due to uncertainties such as noise and fading. As such, assumption on perfect artificial noise cancellation at these receivers seems unrealistic. Moreover, channel information affects successful probability of signal detection not only at legitimate receivers but also eavesdroppers, eventually impacting security capability. Nonetheless, it is certain that any channel estimator has some accuracy degree [22] and hence, it is practical to investigate channel estimation imperfection in ANaEHON (Artificial Noise-aided EHONs). Therefore, this paper evaluates the effect of artificial noise cancellation-and-channel estimation imperfection on security performance of PUs/CRs in ANaEHON.

Prior works and motivations
This paper considers ANaEHON where a primary transmitterreceiver pair cannot communicate with each other directly due to some reasons and a secondary transmitter-receiver pair assists primary communication in reward for their access to primary spectrum. The secondary transmitter harvests RF energy from the primary transmitter and transmits not only its private signal but also the primary transmitter's signal and artificial noise. Data transmission of the secondary transmitter is wire-tapped by an eavesdropper.
While publications on information security for energy harvesting (interweave/underlay) networks have been blooming, few works have been interested in the overlay mode [14][15][16][17][18][19][20][21]23]. More specifically, [14] and [15] considered the almost same system model as ours but EHONs are secured by letting the primary receiver jam the eavesdropper and the secondary transmitter helps primary communication by the AF (Amplify-and-Forward) mechanism. 1 In [16], a dedicated jammer was employed to interfere the eavesdropper instead of the primary receiver as [14] and [15]. In addition, [16] differs [14] and [15] in the EH method, the EH-capable terminal, and the assistance mechanism. The former used the EH-capable jammer, which harvests energy based on the time splitting technique [25], and employed the secondary transmitter as a DF (Decode-and-Forward) relay. Meanwhile, the latter used the secondary transmitter as the AF relay and as an energy harvester which is based on the power splitting technique [26]. To further secure primary transmission, [17] proposed to jam the eavesdropper by the primary receiver as well as the dedicated jammer. However, security performance of primary/secondary communication in terms of SOP (Secrecy Outage Probability) was not analyzed in [14][15][16][17]. In [23], the transmit antenna selection and the multi-user scheduling were proposed to secure EHONs. Moreover, the SOP of primary communication and the ergodic rate of secondary communication were derived in closed-form in [23]. Recently, [18] proposed a group of dedicated jammers to guarantee communication security for the secondary transmitter in EHONs. Moreover, the SOP of secondary/primary communication was analyzed in [18]. Nonetheless, different from [14][15][16][17], the secondary user relays the primary signal and transmits its private signal separately in [18] and [23]. This significantly mitigates complexity in analyzing the SOP and hence, making the analysis in [18] and [23] tractable.
Although [18] proposed the SOP analysis for both primary and secondary communication and [23] analyzed the SOP/ergodic rate of primary/secondary communication in EHONs, the SU (Secondary User) relays the primary signal and transmits its private signal separately. This requires at least three stages (Stage I: energy harvesting and primary communication, Stage II: secondary communication to PU, Stage III: secondary communication to SU) to complete both secondary and primary communication, considerably reducing spectral efficiency. Recently, [19][20][21] proposed a two-stage transmission scheme with artificial noise generation in EHONs to enhance secrecy performance and spectral efficiency. More specifically, [19][20][21] suggested an ANaEHON where the secondary transmitter performed a superposition of artificial noise, secondary signal, and primary signal to transmit at once. Furthermore, [19][20][21] proposed the SOP analysis.
In summary, imperfect channel estimation and artificial noise cancellation are ineluctable in practical systems. Nonetheless, none of the prior works in [14][15][16][17][18][19][20][21]23] analyzed the SOP of both primary and secondary communication in ANaEHONs under their impact as summarized in Table 1. This motivates the current paper to study their impact on security performance of ANaEHON in [19][20][21] for the first time.

Contributions
The following are our contributions: • Suggest a novel signal model for ANaEHONs accounting for channel estimation-and-artificial noise cancellation imperfection. In ANaEHONs under consideration, the secondary transmitter harvests energy in primary signals, decodes and forwards primary data, and generates a signal combination of primary data, secondary data, and artificial noise. Such an operation mechanism of the secondary transmitter is flexible in compromising security performance of primary communication with that of secondary communication and optimizing system design by selecting appropriately the (power splitting, time splitting, power allocation) factors. • Propose precise closed-form SOP formulas for promptly rating security metrics of primary/secondary communication under channel estimation-and-artificial noise cancellation imperfection. These formulas serve as a key starting point to obtain formulas for other pivotal secrecy performance indicators comprising IP (Intercept Probability), STP (Secrecy Throughput), PSCP (Positive Secrecy Capacity Probability).
• Search optimum pivotal specifications for the optimal secrecy capability and the best performance compromise between primary and secondary communication. • Provide insightful results on security performance of primary/secondary communication in important system parameters.

Structure
Section 2 discusses the system model. Then, Section 3 derives detailedly the SOP of primary/secondary communication.
Next, Section 4 provides illustrative results and ultimately, Section 5 closes the paper. Figure 1 shows an ANaEHON in which direct communication between a primary transmitter-receiver pair, PT − P R, is not of good quality owing to uncertainties (e.g., long distance, severe fading, ...). Therefore, the secondary transmitter ST , which is in the transmission range of PT , can assist PT in relaying the PT 's signal to P R. ST is assumed to be capable of harvesting RF energy from PT and spends the scavenged energy for its communication operation. Additionally, the overlay mechanism is applied to ST in order for ST to relay the PT 's signal to P R as well as send its private signal to the secondary receiver S R. Information transmission of ST is stolen by an eavesdropper E. In order to reduce the wiretapping capability of E, ST transmits artificial noise together with information signals of PT and ST . uv in which ς is the path-loss exponent and d uv is the u-v distance. Then, the probability density function (PDF) and the cumulative distribution function (CDF) of |h uv | 2 are correspondingly expressed as f |h uv | 2 (x) = e −x/μ uv /μ uv and

Signal model
In Fig. 1, the total transmission time T for both PT and ST to complete their information transmission to corresponding receivers is divided into two stages. Stage I with the time of αT with α ∈ (0, 1) being the time splitting factor is for PT to send its private data x p in order for ST to harvest energy with the power splitting technique and recover the PT 's information. Such a technique separates the received signal at ST , y s , into two portions: one portion √ λy s with λ ∈ (0, 1) being the power splitting factor for decoding the PT 's information 2 and another portion √ 1 − λy s for harvesting energy. Dependent on the decoding status, 3 ST transmits distinct signals as shown in the flow chart of Fig. 2. To be specific, if ST successfully restores the PT 's information, it sends a combination of three sig- Decoding with infinitesimal power is assumed. This assumption is popularized in previous publications (e.g., [16,[27][28][29]). 3 In [16], Stage II allows ST to always relay primary data, leading to error propagation for primary data. Nonetheless, the secondary/primary SOP analysis was dissembled in [16]. Consequently, error propagation was not considered in the SOP analysis.   and κ are the transmit power of ST , the power allocation factor for desired signals and artificial noise as ST decodes correctly the PT 's signal and the power allocation factor for primary and secondary signals, respectively): the PT 's decoded information x p , the ST 's private information x s , and the artificial noise x a . In the case that ST unsuccessfully decodes the primary data, it sends a combination of two signals √ τ P s x s + √ (1 − τ ) P s x a (τ is the power allocation factor for desired signal and artificial noise as ST decodes incorrectly the PT 's signal): the ST 's private information x s and the artificial noise x a . Stage II with the time of (1 − α)T is for ST to send its signal to S R, P R, and E.
In Stage I, ST receives the following signal In (1), the receive antenna at ST induces the noise n s ∼ CN 0, σ 2 s and PT transmits with power of P p . Stage I in Fig. 1 offers ST the scavenged energy as where η ∈ (0, 1) is the energy conversion efficiency and {·} is the expectation operator. The scavenged energy E s offers the transmit power of ST in Stage II as Figure 1 shows that the signal used for decoding the PT 's information isỹ s = √ 1 − λy s +ñ s whereñ s ∼ CN 0,σ 2 s is the noise owing to the passband-to-baseband signal conversion. Inserting (1) intoỹ s yields Channel estimators suffer a certain error and hence, channel state information is not perfectly estimated. For performance analysis, channel estimation imperfection should be modelled appropriately. This paper employs a well-known channel estimation error model as [22] where h uv is the true channel,h uv is the estimated channel, ε uv is the estimation error; all random variables h uv ,h uv , ε uv are modelled as CN (0, μ uv ); the correlation coefficient 0 ≤ ρ uv ≤ 1 is a constant, representing the exactness of channel estimation. Inserting (5) into (4), one obtains It is inferred from (6) that the SNR (Signal-to-Noise Ratio) achievable for decoding the PT 's information is given by where The channel capacity that ST can obtain is C s = αlog 2 (1 + γ s ) bps/Hz with the pre-logarithm factor α owing to Stage I of αT . The communication theory addressed that ST decodes exactly the PT 's data merely if C s exceeds the required transmission rate C t , i.e., C s ≥ C t (or γ s ≥ γ t where γ t = 2 C t /α − 1).
If ST decodes successfully the PT 's information, it broadcasts the combination of three signals in the form of Otherwise, it broadcasts the combination of solely two signals in the form of √ τ P s x s + √ (1 − τ ) P s x a in Stage II. Therefore, P R, S R, and E receive signals in Stage II, correspondingly, as where n p ∼ CN 0, σ 2 p , n r ∼ CN 0, σ 2 r , n e ∼ CN 0, σ 2 e are respectively the noises impaired by the receive antennas at P R, S R, and E.
Most works (e.g., [14][15][16][17][18][19][20][21]) assumed the artificial noise x a to be completely known at the legitimate receivers (P R and S R), not at E, in order for P R and S R to totally eliminate the effect of x a on their received signal. Nonetheless, this assumption seems impractical because the regeneration of x a is hardly achieved with the absolute probability. Therefore, this paper assumes x a to be regenerated at P R and S R with the accuracy of 1 − χ , χ ∈ [0, 1], which indicates that χ x a represents the residual artificial noise due to imperfect artificial noise cancellation at P R and S R. Accordingly, P R and S R obtain signals with less artificial noise after partly removing x a , respectively, as Inserting (5) into (12), one obtains Based on (16), SINR (Signal-to-Interference plus Noise Ratio) for decoding x p at P R is represented as Similarly, inserting (5) into (13), one obtains Based on (16), SINR for decoding x s at S R is given by The knowledge of the artificial noise x a is merely shared among ST , P R, and S R for securing x s and x p but E is blind with it. As such, the SINRs at E for recovering x s and x p are inferred from (11). Inserting (5) into (11) results in from which the SINRs at E for restoring x s and x p are respectively derived as It is worth emphasizing from (19) and (20) that ST purposely generates the artificial noise power to corrupt the eavesdropper. Accordingly, increasing the artificial noise would secure information transmission for x s and x p . Moreover, channel estimation imperfection, which is represented by terms in the denominators of (15), (17), (19), (20) weighted by 1 − ρ 2 uv , degrades the performance of all receivers (P R, S R, E).

Secrecy capacity
The channel capacities at P R and S R in Stage II are inferred from (15) and (17), correspondingly, as where (1 − α) is the pre-logarithm factor due to Stage II of (1 − α)T . Similarly, the channel capacities at E for decoding x s and x p in Stage II are inferred from (19) and (20), correspondingly, as The substraction of the channel capacity at E for restoring x s from that at S R is the secrecy capacity for x s : where [x] + denotes max (x, 0). Similarly, the substraction of the channel capacity at E for restoring x p from that at P R is the secrecy capacity for x p :

SOP analysis
The SOP indicates the possibility that the secrecy capacity is below the preset security threshold C 0 . Therefore, it quantifies the secrecy performance of ANaEHON. This section suggests precise closed-form SOP formulas for quickly rating the secrecy capability for x s and x p without timeconsuming simulations. Moreover, these formulas serve as a good starting point to achieve the formulas for other pivotal security measures such as IP, PSCP, STP.

SOP for primary information x p
The SOP for primary information x p is given by SO P p (C 0 ) is divided into two scenarios: i) one corresponds to the ST 's unsuccessful decoding primary data and ii) another corresponds to the ST 's successful decoding primary data, i.e.

SO P p (C
SubstitutingČ p in (26) into (28), one has The term in (29) is equivalently rewritten as In ANaEHONs, if ST unsuccessfully decodes the PT 's data, it doesn't forward primary data, yielding the zero SINR at P R for restoring x p (i.e., γ p = 0 for γ s < γ t as shown in (15)). Therefore, in this scenario, the secrecy capacity for x p is also zero (i.e.,Č p = 0 conditioned on γ s < γ t ), resulting in ψ = 1.
The term ϒ in (29) is rewritten after using (15) and (20) for the case of γ s ≥ γ t as where with By imitating the derivations in [21, Appendix C], one achieves a precise form of ϒ as where In (45) and (47), Ei (·) is the exponential-integral function [30].

SOP for secondary information x s
The SOP for secondary information x s is given by SO P s (C 0 ) is divided into two scenarios: i) one corresponds to the ST 's unsuccessful decoding primary data and ii) another corresponds to the ST 's successful decoding primary data, i.e.

SO P s (C
SubstitutingČ s in (25) into (49), one has SO P s (C 0 ) The term in (50) was already computed in (30) while the term Z 1 in (50) is rewritten after using (17) and (19) for the case of γ s ≥ γ t as where The quantity Z 1 has the same form as ϒ in (31). Therefore, by substituting variables appropriately into ϒ in (31), one can achieve the precise closed-form formula of Z 1 . More specifically, Z 1 is computed by using ϒ in (39) with A 1 → A, B 1 → B, C 1 → C, μ sr → μ sp ,σ 2 r →σ 2 p . As a result, the derivation of Z 1 is skipped here for compactness.
The term Z 2 in (50) is rewritten after using (17) and (19) for the case of γ s < γ t as where The quantity Z 2 has the same form as ϒ in (31). Therefore, by substituting variables appropriately into ϒ in (31), one can achieve the precise closed-form formula of Z 2 . More specifically, Z 2 is computed by using ϒ in (39) with A 2 → A, B 2 → B, C 2 → C, μ sr → μ sp ,σ 2 r →σ 2 p . As a result, the derivation of Z 2 is skipped here for compactness.
Inserting the above-proposed precise closed-form formulas of , Z 1 , and Z 2 into (50) yields the precise closed-form expression of SO P s (C 0 ).

Remarks
The precise closed-form formulas of SO P p and SO P s are useful in quickly assessing the security measure of secondary/primary communication in ANaEHON without exhaustive simulations. Upon our understanding, these formulas haven't been reported yet. Moreover, they can be exploited to achieve the formulas for other pivotal security measures. To be more specific, the IP addresses the probability of negative secrecy capacity. Accordingly, the IP of secondary/primary communication is computed as where u = s, p. PSCP indicates the probability of positive secrecy capacity. Consequently, the PSCP of secondary/primary communication is expressed as Finally, STP is the product of the secrecy communication probability at a certain secrecy capacity with that secrecy capacity. Consequently, the STP of secondary/primary communication is expressed as

Illustrative results
The SOP of secondary/primary communication in ANaE-HON is assessed through pivotal specifications. Unless otherwise stated, a set of arbitrary parameters is used to illustrate the following results: Figures 3-12 respectively denote "Sim." and "Ana." as the simulation and the analysis, and illustrate the match between the simulation and the analysis, ratifying the exactness of the analysis in (29) and (50). Figure 3 illustrates the SOPs versus channel estimation imperfection reflected by ρ. This figure demonstrates that channel estimation error drastically affects the SOP of primary/secondary communication. More specifically, large SOPs are almost unchanged over a wide range of bad channel estimation error (0 ≤ ρ ≤ 0.9) while SO P p (or SO P s ) significantly drops (or increases) with a slight channel estimation improvement (0.9 ≤ ρ ≤ 1). Additionally, imperfect artificial noise cancellation at legitimate receivers degrades security performance of primary/secondary communication (i.e., SOPs increase with increasing χ ) as expected. Moreover, the SOP of primary communication is smaller than that of secondary communication at the same levels of channel estimation error and artificial noise cancellation. This is because among the amount of the power θ P s reserved for transmitting legitimate data, ST allocates 70% (κ = 0.7) of this amount to relay the primary data and 30% (1 − κ = 0.3) of that to send the secondary data. Figure 4 illustrates the SOPs versus imperfect artificial noise cancellation reflected by χ . This figure shows the increase of SOPs with increasing χ , which is expected because of increasing artificial noise residue at legitimate receivers. Additionally, security performance of primary communication is considerably improved (or deteriorated) with reducing channel estimation imperfection (i.e., increasing ρ) in the range of low (or high) artificial noise residue (e.g., SO P p at ρ = 1.0 is smaller than SO P p at ρ = 0.9 for χ < 0.675 but the reverse happens for χ > 0.675). Nonetheless, security performance of secondary communication is always degraded with reducing channel estimation imperfection irrespective of χ (e.g., SO P s at ρ = 1.0 is larger than SO P s at ρ = 0.9 for any χ ). Furthermore, due to κ = 0.7 as Fig. 3, primary communication is more secure than secondary communication at the same levels of channel estimation error and artificial noise cancellation, as expected. Figure 5 plots the SOPs versus P p /N 0 . Owing to κ = 0.7 as Fig. 3, primary communication is more secure than secondary communication at the same levels of channel estimation error and artificial noise cancellation, as expected. In addition, SO P p is drastically reduced with better channel estimation and artificial noise cancellation, especially when the transmit power of PT increases, i.e., SO P p at (ρ = 1.0, χ = 0.0) is considerably smaller than SO P p at (ρ = 0.9, χ = 0.5). Nonetheless, the reversed security performance trend is observed for secondary transmission, i.e., SO P s at (ρ = 1.0, χ = 0.0) is larger than SO P s at (ρ = 0.9, χ = 0.5). Furthermore, security performance of primary communication compromises that of secondary communication with P p /N 0 (i.e., SO P p reduces while SO P s increases with P p /N 0 ). Figure 6 plots the SOPs versus θ . This figure demonstrates optimum values of θ , which minimize the SOP of primary/secondary communication. These optimum values balance the powers for sending the artificial noise and the legitimate (secondary and primary) data. Moreover, SO P p is lower than SO P s at the same levels of channel estimation error and artificial noise cancellation, which can be interpreted from the fact that κ = 0.7 allocates more power for the ST to transmit the PT 's information than the ST 's information. Furthermore, better artificial noise cancellation and channel estimation improve secondary/primary security capability in a certain region of θ (e.g., SO P s (or SO P p ) at (ρ = 1.0, χ = 0.0) is smaller than SO P s (or SO P p ) at (ρ = 0.9, χ = 0.5) when θ < 0.575 (or θ < 0.925)) but degrade that performance in another region (e.g., SO P s (or SO P p ) at (ρ = 1.0, χ = 0.0) is larger than SO P s (or SO P p ) at (ρ = 0.9, χ = 0.5) when θ > 0.575 (or θ > 0.925)). Figure 7 plots the SOPs versus κ. The results illustrate that increasing κ improves secrecy performance of primary communication (decreasing SO P p ) but mitigates that of secondary communication (increasing SO P s ), showing the security compromise between primary and secondary communication. This is obvious because κ interprets the percentage of the ST 's transmit power allotted for the primary data while 1−κ interprets the percentage of the ST 's transmit power allotted for the secondary data. Therefore, increasing κ decreases SO P p but increases SO P s . Due to the conflicting  Fig. 7), which means the best security balance between primary and secondary communication. Moreover, the primary (or secondary) communication is in outage over a certain region of κ; for example, SO P s = 1 for κ ≥ 0.7 and SO P p = 1 for κ ≤ 0.2 when ρ = 1.0 and χ = 0.0 as shown in Fig. 7. Furthermore, better artificial noise cancellation and channel estimation improve secondary/primary security capability in a certain region of κ (e.g., SO P s (or SO P p ) at (ρ = 1.0, χ = 0.0) is smaller than SO P s (or SO P p ) at (ρ = 0.9, χ = 0.5) when κ < 0.52 (or κ > 0.48)) but degrade that performance in another region (e.g., SO P s (or SO P p ) at (ρ = 1.0, χ = 0.0) is larger than SO P s (or SO P p ) at (ρ = 0.9, χ = 0.5) when 0.52 < κ < 0.7 (or 0.2 < θ < 0.48)). Figure 8 plots the SOPs versus C t , which expose that increasing C t enhances secrecy capability of secondary communication but deteriorates that of primary communication. This is because the increase in C t (equivalently, the increase in the transmission rate demanded by the PT ) reduces the probability of decoding successfully the PT 's information at the ST , eventually limiting the PT 's information relayed to P R and increasing the SO P p . While the PT 's information is rarely relayed to P R by ST , the information of ST has more chances to be transmitted with higher transmit power, ultimately reducing the SO P s . Two contra-dictory trends of primary and secondary security capabilities with respect to C t facilitate in balancing these security capabilities by setting the reasonable required primary transmission rate; for instance, SO P s = SO P p at C t = 0.79 bps/Hz for (ρ = 0.9, χ = 0.5) and at C t = 1.85 bps/Hz for (ρ = 1.0, χ = 0.0). Moreover, better artificial noise cancellation and channel estimation improve primary data security but degrade secondary data security, i.e., SO P p (or SO P s ) at (ρ = 1.0, χ = 0.0) is smaller (or larger) than SO P p (or SO P s ) at (ρ = 0.9, χ = 0.5). Figure 9 plots the SOPs versus C 0 . This figure exposes that increasing C 0 degrades security capability of primary/secondary communication until a complete outage, as expected. Interestingly, secrecy performance of secondary communication may be superior or inferior to that of primary communication over a certain region of C 0 (e.g., SO P s < SO P p for C 0 ≤ 0.016 bps/Hz but SO P s > SO P p for C 0 > 0.016 bps/Hz when ρ = 1.0 and χ = 0.0). Moreover, better artificial noise cancellation and channel estimation also improve secondary/primary security capability in a certain region of C 0 ; for instance, SO P p (or SO P s ) at (ρ = 1.0, χ = 0.0) is smaller than SO P p (or SO P s ) at (ρ = 0.9, χ = 0.5) when C 0 is smaller than 0.232 (or 0.049) bps/Hz. Figure 10 demonstrates the SOPs versus α, which expose that the security measure of secondary/primary communication is optimized with relevant selection of α. The reason behind the optimum value of α that minimizes SOPs is as fol- lows. The increase in α offers the ST to harvest more energy from the PT and to recover successfully the PT 's information with a higher probability in Stage I, thus probably enhancing security performance. Nonetheless, this increment degrades security capability in Stage II due to the decrease in secrecy capacity which is proportional to 1−α. Accordingly, α can be controlled to balance gains in two stages. Moreover, security performance of primary/secondary communication at the optimal value of α is improved with better channel estimation and artificial noise cancellation, i.e., SO P p (or SO P s ) at the optimal value of α for (ρ = 1.0, χ = 0.0) is smaller than SO P p (or SO P s ) at the optimal value of α for (ρ = 0.9, χ = 0.5). Nonetheless, the optimum secondary data security is inferior to the optimum primary data security at channel estimation-and-artificial noise cancellation perfection (i.e., SO P p < SO P s at the optimal value of α for (ρ = 1.0, χ = 0.0)) but artificial noise cancellation-andchannel estimation imperfection reverses the performance tendency where the best security of primary communication is inferior to that of secondary communication (i.e., SO P p > SO P s at the optimal value of α for (ρ = 0.9, χ = 0.5)). Figure 11 plots the SOPs versus λ, which expose that security capability of the secondary communication is almost constant and only improved for high λ (e.g., λ ≥ 0.95). The reason is that large λ allows ST to scavenge more energy from PT and reduces signal power at ST 's decoder (i.e., reduces the possibility of restoring correctly the PT 's information); thus, the power for transmitting the ST 's infor-mation is higher in Stage II, eventually declining SO P s . Nevertheless, λ can be selected appropriately to optimize secrecy performance of primary communication. The optimal value of λ for the smallest SO P p is to balance between the possibility of restoring the primary data at the ST and the scavenged energy. Moreover, primary communication is more secure than secondary communication due to κ = 0.7, which is a similar comment observed from the previous figures. Furthermore, better artificial noise cancellation and channel estimation enhance security capability of primary communication but deteriorate that of secondary communication.
The power allocation factor for artificial noise and secondary signal as the ST decodes incorrectly the PT 's signal is specified by τ . Therefore, to recognize the affect of τ plainly, we should investigate the case that the ST decodes unsuccessfully the PT 's signal. This case can be set-up by selecting a large value of C t . Figure 12 demonstrates the SOPs versus τ for C t = 5 bps/Hz. This figure exposes that primary communication is in outage because the large C t causes the ST to fail in decoding the PT 's information and hence, P R does not receive it for decoding. Moreover, there exists the optimum value of τ which maximizes secrecy performance of secondary communication. This optimum τ aims to balance the power allocation for the ST 's information and the artificial noise. Furthermore, better artificial noise cancellation and channel estimation enhance secondary data security capability, i.e., SO P s at (ρ = 1.0, χ = 0.0) is smaller than SO P s at (ρ = 0.9, χ = 0.5).

Conclusion
This paper implemented the overlay mechanism in cognitive radio networks where the secondary transmitter assists the data transmission of the primary transmitter as well as transmits its private data. The secondary transmitter is capable of harvesting radio frequency energy and generating the artificial noise to self-power its operation and secure primary/secondary communication against eavesdroppers. Secrecy capability of primary/secondary communication is measured in terms of primary/secondary secrecy outage probability under uncertainties of artificial noise cancellation-and-channel estimation imperfection, which was numerically rated by the suggested precise closedform formulas. Various results are generated to validate such formulas as well as shed insights into security measure of artificial noise-aided energy harvesting overlay networks with respect to main system parameters. Moreover, optimum system parameters can be found through exhaustive searches relied on the recommended formulas that well guides system design. Furthermore, the secrecy performance compromise between secondary and primary communication can be managed by controlling system parameters appropriately.