Proactive Eavesdropping Performance for Integrated Satellite–Terrestrial Relay Networks

This work investigates the proactive eavesdropping based legitimate surveillance for integrated satellite-terrestrial relay networks with multiple proactive monitors. To study the eavesdropping non-outage probability, we propose three different presentative proactive eavesdropping cases/modes, where the legitimate monitors could change its roles between eavesdropping and jamming, namely, Case I: Eavesdropping then Jamming, Case II: Jamming then Eavesdropping, Case III: Always Eavesdropping. Particularly, we get the accurate expressions of the eavesdropping non-outage probability for the proposed three proactive eavesdropping modes in the presence of multiple monitors. To derive further insights, we provide the asymptotic analysis of the three eavesdropping non-outage probabilities. Besides, the colluding proactive eavesdropping scenario is considered, in which all the monitors cooperate to overhear or jam the legitimate users. Finally, numerical results are obtained to verify the rightness of the analytical analysis.


I. INTRODUCTION
T HE INCREASING requirements for large data trans- mission and wide coverage in the next wireless communication systems are the major challenges, especially for the beyond the 5-th generation (B5G) networks even the 6-th generation (6G) networks.Focusing on this front, the satellite-terrestrial networks (STNs) have been paid significant attentions, which can overcome the shortages of terrestrial networks, for example, it is restricted by terrain, and having low coverage [1], [2], [3], [4].By considering some obstacles and heavy showings in STNs, the integrated satellite-terrestrial relay networks (ISTRNs) have been viewed as the more promising framework to provide an enhanced coverage, data transmission rate, and the other 6G networks requirements, which is considered as the major part of the Internet of Things (IoT) networks [5], [6], [7], [8].The ISTRN's framework has been regarded as an important factor of the satellite communications (SatComs) that uses the terrestrial nodes to enhance the satellite transmission, which is often utilized into the mobile/fixed satellite systems, such as SiriusXM [9].It has become a realistic case which has been included in Digital Video Broadcasting (DVB) networks [10].Besides, ISTRNs are also contained in "Space-Ground Integrated Information Network Engineering" of China [11].

A. RELATED STUDIES
Till now, outage probability (OP), throughput and the other performance metrics of ISTRNs have been investigated by existing literatures.The authors in [12] researched the OP for an ISTRN with a relay.The work in [13] researched the OP of a cognitive ISTRN with multiple interferences.In [14], the authors utilized a terrestrial relay selection algorithm in an uplink ISTRN with several terrestrial relays and hardware impairments.In [15], the authors utilized a joint optimization scheme for the non-orthogonal multiple access (NOMA)assisted ISTRNs.The authors in [16] researched the performance of a multiuser ISTRN, particularly, the accurate expression for OP was further investigated.Through [17], the authors researched energy efficient algorithm for a satellite-aerial-terrestrial network (SATN), where the relay, i.e., the multi-antenna unmanned aerial vehicle (UAV) is utilized to assist the satellite to transmit the information.The authors in [18] researched the effects of channel estimation errors (CEEs) and hardware impairments (HIs) on the NOMA-based cognitive ISTRNs, especially, the secrecy outage probability (SOP) was further studied.In [19], the authors used the transmit antenna selection scheme on the NOMA-assisted ISTRNs with imperfect CEEs and nonideal successive interference cancellation (SIC).In [20], the authors researched the impact of NOMA on the secrecy performance for the ISTRNs.
It is essential to monitor and legitimately eavesdrop on some suspicious wireless communication, like illegal eavesdropping, mass text, and tampering with communication content, to deal with the case that high-risk events [20], [21].For the wireless surveillance, it could be divided into two scenarios.First scenario is passive eavesdropping, which means the legitimate monitor only overhears the suspicious transmission link.In this scenario, the perfect channel state information (CSI) for each related channel is considered.This scenario works only at the case that the performance of eavesdropping link is preferable to that of the suspicious link.Some related works have investigated the secrecy problem in ISTRNs on the passive eavesdropping scenario [22], [23], [24], [25], [26], [27].The authors in [22] utilized a thresholdbased legitimate user scheduling algorithm and analyzed the secrecy performance for ISTRNs.The authors in [23] researched the secure transmission for the cognitive ISTRNs.In [24], the secrecy performance for the NOMA-assisted ISTRNs was researched, where the detailed investigations for SOP were obtained.In [25], the authors researched the secrecy performance of a downlink ISTRN, where the SOP was investigated with respect to the detailed analysis.In [26], the authors proposed a max user scheduling algorithm for the SatCom, moreover, the SOP was further researched.The authors in [28] researched the SOP for an ISTRN along with several two-way terrestrial nodes.Except the performance, the secrecy beamforming for the ISTRNs is also the popular topic [15], [29], [30].In these papers, the secrecy performance is optimized through different optimization methods.

B. MOTIVATIONS
However, in practical systems, this situation can not be satisfied for the reason that the monitor has a long distance with the suspicious transmitter to avoid being found.To solve this problem, the authors in [31] proposed another scenario with its name as proactive eavesdropping scenario.In this scenario, the monitor has the ability that receives the suspicious signals and sends the jamming information at the same time with a full-duplex mode.With the help of the jamming information, the transmission rate of the suspicious signals can be decreased.In addition, it also can enhance the eavesdropping even though the channel property for the eavesdropping link is worse than that of suspicious links without jamming.The authors considered a three-node surveillance rate maximization problem in [32].On this foundation, the authors in [33] extended the work of [31] by assuming the suspicious transceiver and the monitor equipped with several antennas.The authors in [34] investigated the proactive eavesdropping problem by utilizing the amplify-and-forward relay scheme.In [35], the authors researched a novel wireless surveillance scenario with a reconfigurable intelligent surface (RIS).In [36], the authors proposed a novel objective of eavesdropping energy utilization rate to valuate the eavesdropping quality.The authors in [37] researched the impact of RIS on the proactive eavesdropping case relied on the deep reinforcement learning method.Reference [38] optimized the power and location for the proactive eavesdropping networks with a full-duplex terrestrial relay.In [31], the authors studied the proactive eavesdropping via jamming through the Rayleigh fading channel, especially, the rate maximization was further researched.In [39], the authors utilized the mode selection algorithm for the proactive eavesdropping with jamming to get the best eavesdropping performance.In [40], the authors researched the energy utilization rate for the proactive eavesdropping.In [41], the authors investigated the fairness problems for the UAV-based networks.In [42], the authors still studied the proactive eavesdropping problems for the UAV-based communications.In [43], the proactive problem is analyzed in the full-duplex communication systems along with the multiple antenna node.In [39], the authors researched the mode selection problem for the proactive eavesdropping scheme.In [44], the authors investigated the proactive eavesdropping performance for the 5G uplink systems.especially the multiple antennas were considered.In [45], the authors analyzed the proactive eavesdropping performance for the simultaneously transmitting and reflecting-RIS based networks with statistical CSI.
As mentioned before, ISTRNs and proactive eavesdropping are considered as the major parts for the next wireless transmission networks, thus it is very important for us to investigate the performance of proactive eavesdropping in the ISTRNs.Until now, only the authors in [46] investigated the proactive eavesdropping performance for the ISTRNs with eavesdropping then jamming scenario, which indicates the importance and necessity of our research.

C. OUR CONTRIBUTIONS
However, as the authors know that the investigation of proactive eavesdropping on the ISTRNs has not been published, which motivates our work.Specifically, the major contributions are given in the following: • Firstly, this paper illustrates a general proactive eavesdropping model for the ISTRNs, where a suspicious satellite, a suspicious receiver and multiple monitors are considered in this system model.This system model is new for the ISTRNs when compared with the existed works, which will be considered as the further direction for this topic.• Secondly, three proactive eavesdropping cases/modes are proposed, namely, Case I: Eavesdropping then Jamming, Case II: Jamming then Eavesdropping and Case III: Always Eavesdropping.Particularly, the accurate expressions for eavesdropping non-outage probability (ENOP) for the considered three cases are obtained, which offer valuable ways to valuate the major system and channel parameters on the analyzed systems.
• Thirdly, to reduce the computational complexity and obtain further investigations of the system parameters on the system performance, the approximate investigations for ENOP are provided in high signal-to-noise ratio (SNR) regime.• Some representative simulation results are obtained to prove the analytical results.With these results, the effects of the system parameters are shown with the clear view.The left parts are organized as what follows.In Section II, the illustration of the considered system model is introduced.In Section III, the detailed process for the power control and ENOP is obtained along with the three proposed proactive eavesdropping cases/modes.In Section IV, Monte Carlo (MC) simulations are given to verify the theoretical results.In Section V, the conclusion is obtained to end the whole paper.
Notations: E[•] is the expectation operator, exp(•) denotes the exponential function.The abbreviations and acronyms are provided in TABLE 1, shown at the top of next page.

II. SYSTEM DESCRIPTION
As shown in Fig. 1, we investigate the performance of proactive eavesdropping in ISTRNs, where includes a suspicious satellite (S), a suspicious terrestrial receiver (D), N monitors (E) aim to overhear or jam the information between S and D. All the legitimate monitors cooperate together to overhear or jam the signals [48], [49], [50].A half-duplex (R) is used to forward the signal from S to D. 1 R is working with the decode-and-forward (DF) protocol.It has the assumption that all transmission nodes having the single antenna. 2 Owing to the heavy shadowing fading, the direct transmission link is 1.Although only one terrestrial relay is employed for the considered system, the derived results can be considered as a special case of multiple terrestrial relays scenario.
2. It is mentioned that, in this paper, the terrestrial nodes are equipped with only one antenna, while the results are also suitable to the case that transmission nodes are equipped with multiple antennas and beamforming (BF) is utilized at each multiple antenna node.not contained in this paper, which has been widely assumed in existing works [18], [19], [20]. 3,4 As a common scene, 2 time slots are required for the whole communication.During the first time slot, R receives the information of S, then transmits the decoded signal to D during the second time slot.The multiple monitors may select either jamming or eavesdropping among the two time slots, which are mainly judged by the channel quality.Three proactive eavesdropping Cases are investigated in this paper, namely Case I: Eavesdropping then Jamming, 3. Owing to obstacles, weather conditions like rain, fog and the other reasons, only one direct link is considered in this paper, which is a widely used assumption [18], [20].
4. In this paper, we consider that the user D was not equipped with the satellite antenna, thus it can not receive the signal from the satellite, it needs the help of the terrestrial relay.Case II: Jamming then Eavesdropping, and Case III: Always Eavesdropping. 5  In Case I, during the first time slot, N monitors first eavesdrop the target signal from S, then jam the received signal at D. s(t) which comes from the suspicious transmitter with E[|s(t)| 2 ] = 1 will be sent to the suspicious R, while the multiple monitors E overhear the signals.Thus, the derived signals at R and the j-th E are, respectively, obtained as where P S denotes the transmission power of S, h SR and h SE j represent the channel fading between S and R, the channel fading between S and the j-th E, respectively, either of them suffers the shadowed-Rician (SR) fading [47].n R (t) and n E j (t) denote the additive Gaussian white noise (AWGN) at R and the j-th E, respectively, with distribution as n R (t) ∼ CN (0, δ 2 R ) and n E j (t) ∼ CN (0, δ 2 E j ).By utilizing (1) and ( 2), the SNRs at R and the j-th E are, respectively, obtained as As colluding scheme is utilized at the legitimate monitors, so the obtained SNR at E is given by 6 For the second time slot, the jamming signal I j (t) which obeys E[|I j (t)| 2 ] = 1 with its suspicious information is 5.This system model is a general model, which not only suits for the terrestrial networks but also the vehicle networks.
6.In this paper, every node has the equal position, so all nodes can receive the interference of the monitors.This consideration has appeared in so many former papers, such as [9], [20], [51], [52].The other reason is to simplify the analysis, thus every node is considered to have the same power, however, different eavesdropping scheme is applied into different node will be an interesting topic, which will be investigated in the near future.
transmitted by the j-th E as the destination is terrestrial receiver D. At the same time, R forwards the decoded signal to the suspicious terrestrial receiver D. By utilizing colluding scheme, the gotten signal at terrestrial receiver D is derived as (6) where P R and P E j represent the transmission power at R and the j-th E, respectively.h RD and g E j D represent the channel coefficient between R and terrestrial receiver D, the channel coefficient between the j-th E and terrestrial receiver D, respectively, which are both modeled as Rayleigh fading.
. By utilizing ( 6), the final signal-to-interference plus noise ratio (SINR) can be obtained as where Owing to the reason that DF protocol is utilized at R, the SINR at terrestrial receiver D is given by In Case II, in the first time slot, S forwards the signal to R, which N monitors transmit the jamming interference I j (t) to R. Thus, the signal received at R is obtained as (9) where g E j R depicts the channel coefficient between the j-th E and R which obeys the Rayleigh fading.
Through the second time slot, R re-transmits the decoded signals to terrestrial receiver D, while at the same time, N monitors try to overhear the signals, relied on this consideration, the gotten signal at D is shown as By utilizing the similar way, the final SINR for Case II at R is given by where . The final SNR for the second time slot at terrestrial receiver D for Case II is obtained as By using the DF protocol, the final SINR at terrestrial receiver D for Case II is given by By using the same method, the gotten signal for Case II at the j-th E can be obtained as where h RE j depicts the channel coefficient between R and the j-th E modeled as Rayleigh fading.For all the monitors cooperate together [48], [49], [50], hence the SNR at E is obtained as In Case III, the monitors only act as the eavesdropper for the whole two time slots, thus through the first time slot, the received SNR at R is obtained as At this time, the received SNR for the first time slot at the E can be derived as Then, for the second time slot, the derived SNR at terrestrial receiver D is represented as The obtained SNR at the E for the second time slot is shown as where γ E 3 represents the received SNR at E for Case III.Due to the DF protocol, the final SNR for Case III at D is given by Owing to the reason that E can receive two independent signals, thus we utilize the maximal ratio combining (MRC) algorithm to guarantee the eavesdropping performance.On this foundation, the final effective SNR at E after MRC is obtained as

III. POWER CONTROL AND EAVESDROPPING NON-OUTAGE PROBABILITY ANALYSIS
The power control and ENOP analysis will be given in this Section.

A. PRELIMINARY RESULTS
Before investigating the power control and performance analysis, the probability density function (PDF) and cumulative distribution function (CDF) for the transmission channels are first given.

1) SATELLITE CHANNEL MODEL
During this work, the geosynchronous earth orbit (GEO) satellite is assumed.In addition, the satellite is considered to own several transmission beams.Moreover, time division multiple access (TDMA) [53] scheme is considered that leads to the result that only one terrestrial is used at each slot.The channel coefficient h X , X ∈ {{SR}, {SE j }} is represented as where f X denotes the random SR factor of the satellite channel, and C X is the effect of antenna pattern and the free space loss (FSL), which can be written as where λ denotes the wavelength of the frequency carrier, d represents the length from terrestrial relay/eavesdroppers to the satellite beam' center.d 0 ≈ 35786km is the antenna gain for terrestrial relay/eavesdroppers/monitors, furthermore, G Re is the satellite on-board beam gain.
With the help of [20], G Re can be approximated as where G max represents the maximum beam gain, and ϑ denotes the off-boresight's angle.Considering G X , by assuming θ k being the angle, and θk is regarded as the 3dB angle shown as [18], [22] where G max is the maximal beam gain, u k = 2.07123 sin θ k / sin θ k , K 1 and K 3 are the 1st-kind bessel function of order 1 and 3, respectively.To gain the best beam performance, θ k → 0 is considered which leads to G X ≈ G max .Owing on this consideration, we get h X = C max X f X .For f X , a popular SR model was mentioned in [54], which suits for land mobile satellite (LMS) systems [22].By utilizing [54], the PDF of where γ X denotes the average SNR from the satellite to terrestrial relay/eavesdroppers/monitors, , where m X ≥ 0 represents the fading severity parameter, 2b Q denotes the multipath component's average power and X represents the line of sight (LoS) component's average power.Through this work, m X is considered as an integer [14], [18], [22], when m X → ∞, the shadowed-Rician channel will be reduced to the Rician fading.(•) k x denotes the Pochhammer symbol [55].
Next, by utilizing (26), the CDF for γ X is derived as From [14], the PDF of γ SE has the following expression as where , B(., .)represents the Beta function [55].

2) THE TERRESTRIAL CHANNEL
As announced before, the channel coefficient between the relay and the ground users/eavesdroopers is considered to be shadowed as i.i.d Rayleigh fading.when colluding scheme is used at N monitors, the PDF of γ V , V ∈ (ED, RE) and γ RD are, respectively, given by and where denote the distinct diagonal elements in decreasing order, τ i (A V ) are the multiplicity of γ i , and χ i,j (A V ) represents the (i, j)-th characteristic coefficient of A V [56].By utilizing (30), the CDF for γ RD is written as Besides, when γ1 = γ2 =, . . ., = γV , (29) can be written as

B. EAVESDROPPING NON-OUTAGE PROBABILITY
Based on [31] and [57], the ENOP is given by The accurate expressions for the ENOP of the considered three cases are, respectively, given in the following.

1) CASE I: EAVESDROPPING THEN JAMMING
In this case, the ENOP is derived as With the help of (34), this case can be observed as follows: • If γ E > γ SR , it will satisfy that E can eavesdrop the signal successfully without any help, hence no more power is needed to jam the signal, namely γ ED = 0 is set.
is also satisfied to overhear the signal successfully with no help, which also means γ ED is set as 0.
, E can just its transmit power to maintain E can eavesdrop successfully.
Then, the final expressions for the ENOP is obtained in Theorem 1.

2) CASE II: JAMMING THEN EAVESDROPPING
In this case, the ENOP is given by From (38), this case can be analyzed in the following as , it is sure that E could eavesdrop the signal successfully with no help, so we need not waste power to jam the signal, namely γ ER = 0 is set.
is also satisfied to overhear the signal successfully with no help, which also means γ ER is set as 0.
, E can just its transmit power to maintain E can eavesdrop successfully.Then, the final expression for the ENOP is given in Theorem 2.
Theorem 2: The final expression for the ENOP in Case II is presented as where Besides, when γ1 = γ2 =, . . ., = γRE , (39) can be written as Proof: Please see Appendix B.

3) CASE III: ALWAYS EAVESDROPPING
In this case, the ENOP can be expressed as Then, the final expression for the ENOP is given as Theorem 3.
Theorem 3: The final expression for the ENOP in Case III is given by Besides, when γ1 = γ2 =, . . ., = γRE , (43) can be written as Proof: See Appendix C.

C. ASYMPTOTIC ANALYSIS FOR ENOP
To derive further investigations on the system performance, in this subsection, the asymptotic analysis for the ENOP of three cases will given in the following.For the convenience, we assume that γRD = γSR = γ .So, when γ → ∞, namely 1/ γ → 0.
For Case I in (35), Ei(x) can be re-written as where σ = 0.57721566 is Euler-Mascheroni constant.
During high SNR regimes, in this paper which means x → 0, then the high order components of the series can be omitted, thus we can get the asymptotic expression of (45) as where o(x) represents the higher order of x.By substituting ( 46) into (35), the asymptotic expression of ENOP for Case I can be obtained.
For Case II, with the similar method, when at high SNRs which means z → 0 in this paper, by utilizing the [55], we derive The asymptotic ENOP of Case II can be obtained by taking (47) into (39).
For Case III, we attempt to use a different way to calculate the asymptotic analysis, when γSR = γRD = γ → ∞, (27) and ( 31) can be re-written as and Then, by substituting ( 48) and ( 49) into the derivation of Theorem 3 and utilizing the same method, after some mathematical steps, the asymptotic expression will be derived as From the former analysis, we summarize the advantages and disadvantages of the three modes in TABLE 2, which shown at the top of next page.

IV. NUMERICAL RESULTS
Analytical analysis is verified by the several simulations below in this Section.In general, we assume the GEO satellite, 7 and for Case I and Case II, besides, γSE = γRE = γE .The channel and system parameters of satellite-terrestrial channel are provided in Table 3 [14] and Table 4 [18], respectively. 8 From the simulation figures, we can easily get that our theoretical solutions are well consistent with MC simulations, which means that the correctness of our theoretical derivation has been proved.Besides, in high SNR regime, it can be clearly found that the asymptotic investigations are in line with theoretical analysis, which verifies the effectiveness of our asymptotic results.
7. Although in this paper GEO satellite is assumed, our derivations are still for the cases for medium earth orbit (MEO) satellite and low earth orbit (LEO) satellite.
8.Although in this paper, these assumptions are set, the other assumptions will be investigated in our near future.The derived results will give some guidance for the future analysis.Fig. 2(a) illustrates the ENOP of Case I versus different N with γ E = 20dB.It can be clearly observed that the active eavesdropping performance of the system improves with the numbers of monitors increasing, which verifies the superiority of our considered scheme.Furthermore, ENOP is higher under favorable satellite-terrestrial channel conditions, which shows that the better channel condition bring better eavesdropping performance.In addition, when γ ED increases, the jamming will interference the users easier.Moreover, we find that when N increases, the ENOP will be larger for the reason that more monitors work together to jam or overhear the legitimate signals.
Fig. 2(b) shows that the ENOP of Case I versus different γ E with setting N = 2.We can find that the ENOP enhances as the γ E increases.This is because the larger γ E will enhance the jamming or eavesdropping ability.
Both from Fig. 2(a) and Fig. 2(b), when the power of monitors becomes larger enough, the ENOP will be always 1, which is the inherent character of the proactive eavesdropping scenario.
Fig. 3(a) depicts the ENOP of Case II versus different N with γ E = 20dB.It can be found that ENOP increases with the enhancement of N as well as γ ER , which is similar to the results of Case I.However, an improved system performance is obtained with worse channel condition of SR fading, which is opposite of case I.The reason can be explained by the fact that monitors improve eavesdropping performance by interfering the relay in Case II.However, when the system is under light channel fading, the ENOP will be lower, which means the channel fading has great impact on the system performance.Fig. 3(b) plots the ENOP of Case II versus different γ E .Similar to Case I, the degradation of γ E will lead to the deterioration of ENOP.The similar conclusion with Fig. 2(a), when N increases, the ENOP will be larger for the reason that more monitors join to jam or overhear the legitimate signals.
The similar results with Fig. 2, in Fig. 3, when the power of monitors becomes larger enough, the ENOP will be always 1, which is caused by the proactive scenario.
Fig. 4(a) examines the ENOP of Case III for the system with γE =6dB.It should be pointed out that the simulation settings of Fig. 4 is different from that of Fig. 2 or Fig. 3.In this figure, γ is not fixed, it is shown as the abscissa varying from 0 to 40dB.This is very different from the former simulation settings.From Fig. 4(a), we can derive that when the number of eavesdroppers grows larger, the ENOP would be larger, which means the eavesdropping will be interrupted at a high probability.Finally, we can derive that the light channel fading brings a lower ENOP., the interesting thing is that, the ENOP will lower when the transmitted power for the legitimate link grows larger, which results from the reason that when the legitimate link's power grows larger, the performance for the legitimate links is enhanced, it is hard to overhear the legitimate link.It is not hard to understand that when the power for the eavesdroppers becomes larger, the performance for the eavesdropper will be better in a reasonable manner.
Fig. 5 examines the ENOP versus different γED or γER for three Cases with γ =20dB, N=2 and γE =15dB in ILS scenario.From Fig. 5, we can find that when ( γED or γER ) is smaller than a fixed value, Case III has the largest ENOP, however, when ( γED or γER ) is larger than this value, Case II will gain the largest ENOP, which will guide us how to allocate ( γED or γER ) to have the largest ENOP, which has the same phenomenon as [58].In Fig. 5, we can also find that when all the simulation settings are the same, the ENOP for Case III will be a constant, which is not affected by γED or γER .This is because, jamming does not exist in Case III.

V. CONCLUSION
Through this paper, the proactive eavesdropping based legitimate surveillance in ISTRNs with multiple monitors was investigated.Specifically, three proactive eavesdropping modes were proposed in our paper, besides, the theoretical and asymptotic analysis of ENOP for the three cases were further, respectively, derived.The numerical results indicated the characters of the three proactive eavesdropping cases.In addition, the impacts of major system and channel parameters were investigated on the considered system.The results showed that the power for the legitimate users, the power of the monitors, the number of the monitors, and the channel fading had serious impacts on the proactive eavesdropping performance.

APPENDIX A PROOF OF THEOREM 1
From (34), the P out is given by From (51), the important thing is to derive C 11 and C 12 , the detailed steps are shown in the following.
For the scenario with γ1 = γ2 =, . . ., = γED , by replacing ( 29) with (32), then with the similar method of the former presentations, (37) will be obtained, the final expression for ENOP in Case II can be derived.
The proof of Theorem 1 is over.
The proof of Theorem 2 is gotten.
The proof of Theorem 3 is over.

FIGURE 1 .
FIGURE 1. Illustration of the system model.

Fig. 4 (
Fig.4(b) illustrates the ENOP of Case III for the system with different γE with FHS scenario.The insightful results from this figure is that a larger γE brings a larger ENOP.Both from Fig.4(a) and Fig.4(b), the interesting thing is that, the ENOP will lower when the transmitted power for the legitimate link grows larger, which results from the reason that when the legitimate link's power grows larger, the performance for the legitimate links is enhanced, it is hard to overhear the legitimate link.It is not hard to understand that when the power for the eavesdroppers becomes larger, the performance for the eavesdropper will be better in a reasonable manner.Fig.5examines the ENOP versus different γED or γER for three Cases with γ =20dB, N=2 and γE =15dB in ILS scenario.From Fig.5, we can find that when ( γED or γER ) is smaller than a fixed value, Case III has the largest ENOP, however, when ( γED or γER ) is larger than this value, Case II will gain the largest ENOP, which will guide us how to allocate ( γED or γER ) to have the largest ENOP, which has the same phenomenon as[58].In Fig.5, we can also find that when all the simulation settings are the same, the ENOP for Case III will be a constant, which is not affected by γED or γER .This is because, jamming does not exist in Case III.