Jammer selection for energy harvesting-aided non-orthogonal multiple access: Performance analysis

Energy harvesting-aided non-orthogonal multiple access (NOMA) meets critical requirements of modern wireless networks in terms of spectral efficiency, communication reliability, and energy efficiency. However, information security for it has not received greatly attentions from both industry and academia. This paper proposes jammer selection to meliorate its security performance. To promptly assess the efficacy of the proposed jammer selection, we propose explicit formulas of connection/secrecy throughput and outage probability for both far and near users accounting for non-linear feature of energy harvesters. These formulas are corroborated by Monte-Carlo simulations and quickly generate innumerable results to reveal a significant/slight influence of energy harvesting nonlinearity on communications reliability/information security. In addition, there exist limits on target data/secrecy rates to avoid complete connection outage (i.e. connection outage probability is one) and achieve complete security (i.e. secrecy outage probability is one). Additionally, the proposed (NOMA-and-proposed jammer selection) scheme significantly outperforms its counterparts (NOMA-and-random jammer selection and orthogonal multiple access-and-proposed jammer selection) in terms of both security and reliability. Nevertheless, there is a trade-off between reliability and security. Notably, the proposed scheme obtains optimum security/reliability performance with proper selection of time/power splitting coefficient.


Backgrounds
Modern wireless networks, namely Fifth/Sixth Generation (5G/6G), offer various wireless services for a tremendous quantity of users.Nevertheless, such massive services and a huge quantity of users impose enormous burden on communications infrastructure, particularly in current circumstance of spectrum scarcity and energy deficiency, in accommodating power and bandwidth sufficiently for such users [1][2][3].Further, securing transmissions for a vast quantity of users in 5G/6G networks against eavesdroppers faces up to severe challenges [4].Consequently, solutions meliorating security-and-reliability performances and spectraland-energy efficiencies become more and more principal.
One of feasible solutions to meliorate spectral efficiency is non-orthogonal multiple access (NOMA) that is proposed for beyond 5G networks [5][6][7].NOMA can be implemented by distributing distinct power levels to different users.Relied on distinct power levels, NOMA can decode user information with successive interference cancellation, which promises to improve reliability performance further.Additionally, energy efficiency can be enhanced with harvesting radio frequency (RF) energy inherently available in wireless signals surrounding RF transmitters.Currently, cheap energy harvesting (EH) circuits are integrated successfully in 5G/6G users [8][9][10].Nonetheless, EH has been modelled to be linear for tractability in most performance analyses [11][12][13][14][15]. Realistically, EH circuits are composed of nonlinear components such as transistors, inductors, capacitors.Therefore, modelling EH should take nonlinearity of circuit components into account.So far, the literature (e.g.[7,[16][17][18][19][20][21]) has proposed various nonlinear energy harvesting (NLEH) models.Further, physical layer security (PLS) that makes use of propagation natures of wireless channels has proved to be an efficient solution to ameliorate security performance [22][23][24][25][26]. Consequently, PLS for EH-aided NOMA has attracted considerable interests from both industry and academia in order to meet concurrently principal demands of high security-and-security performances and energy-and-spectral efficiencies for next generation wireless networks.One of efficient PLS techniques to warrant secure transmission is jamming, which impairs purposely the wire-tapping of eavesdroppers but not harm transmissions of desired users [27,28].
Jammer selection for EH-aided NOMA (JSEHNOMA), e.g.Fig. 1, offers concurrent communications from the NOMA transmitter (S) to two NOMA receivers (N and F) for high spectral efficiency whilst the jammer A j selected from a group of J jammers interrupts the wire-tapping of the eavesdropper (E) for high security performance.S and A j self-power their operations by scavenging energy from a power beacon (B) which can be radio/television broadcasting stations having stable and high transmit power to improve the energy efficiency.Briefly, JSEHNOMA unveils advantages of high reliabilityand-security performances and spectral-and-energy efficiencies.Accordingly, the performance analysis of JSEHNOMA, especially in the realistic scenario of NLEH, is crucial to verify whether JSEHNOMA attains such advantages.Our pioneering work proposes such security/reliability analyses.

Previous works
Uplink communications in EH-aided NOMA (UcEHNOMA) was researched in [7] in which numerous NOMA users, who send their data to the same receiver (S), experience two stages as demonstrated in Fig. 1.NOMA users scavenge RF energy from a stable power beacon (B) with nonlinear energy harvesters in Stage 1 whilst they send data to S with scavenged energy in Stage 2.Moreover, [7] optimized duration of each stage.Notwithstanding, [7] did not analyze average secrecy outage probability (SOP) in closed-form.A special case of [7] with two NOMA users was investigated in [29] which proposed countermeasures to maximize the energy efficiency and implement user grouping for NLEH.Additionally, [29] analyzed connection outage probability (COP) but only in approximated-form.
The works in [30][31][32] studied downlink communications in EH-aided NOMA (DcEHNOMA) where S sends NOMA signals simultaneously to two NOMA users (N and F).Subsequently, [33] extended [30][31][32] to the context of multiple NOMA users.The COP and connection throughput (CTP) formulas in approximated-form were proposed in [30][31][32][33].Moreover, [33] proposed a solution to the sum-rate maximization problem.Notwithstanding, S scavenges RF energy from a NOMA user with linear energy harvester (LEH) that is not realistic [30,31,33].Furthermore, F harvests RF energy from S with NLEH yet what harvested energy is for was not explained explicitly in [32].Additionally, [32] proposed three distinct communications modes with divergent utilization degrees of feedback information.A j

E Eavesdropper
DcEHNOMA with two NOMA users (N and F) was studied where communications to F is aided by N in [34][35][36][37][38] or by a relay in [39][40][41], who harvests energy from a NOMA sender.[34] and [41] presented the approximated COP analysis for NLEH at the relay.In the meantime, [39] found a solution to the sum-rate maximization problem for LEH while [36] and [37] maximized data rate of F and optimized both the energy efficiency and the total transmit power for NLEH, correspondingly.[42] and [43] extended [41] to a multiplicity of relays and proposed the relay selection to support NOMA communications from S to both N and F. Additionally, [44] extended [41] by employing two relays who exchange their roles to assist F.Moreover, [44] presented the average CTP yet not in closed-form.In lieu of utilizing several relays as in [42] and [43], the authors in [45] took advantage of multiple near NOMA users and proposed to adopt merely one near NOMA user to assist the far NOMA user.[46] and [47] continue expanding [41] by studying several NOMA receivers.Notwithstanding, [35,38,40,[42][43][44][45][46][47] researched LEH in performance analysis.As an alternative countermeasure, intelligent reflecting surface was employed to substitute the relay in forwarding data from S to N and F [48][49][50].The sum-rate (or throughput) was maximized for NLEH in [48] and LEH in [49] and [50], correspondingly.Nevertheless, [36,37,39,[48][49][50] did not analyze the system performance.
In summary, the previous works relevant for performance analysis for EH-aided NOMA in [7, 29-35, 38, 40-47] researched a trivial system model in which jamming was not exploited for enhanced security performance in [7] and the security problem was ignored in [29-35, 38, 40-47].Thence, the security/reliability analyses for the system model in Fig. 1, which takes NLEH into account, have not been researched in the current literature.This paper pioneers in proposing such analyses which are useful in assessing quickly and optimizing the security/reliability performances before realistic implementation.

Contributions
We contribute the following: • We propose JSEHNOMA in Fig. 1 to ameliorate the security/reliability performances and the spectral-andenergy efficiencies.Moreover, we propose the deployment of the extensively-accepted NLEH model in [17] at S and A j to characterize appropriately nonlinear circuit components in energy scavengers.• We propose the CTP/secrecy throughput (STP) and the SOP/COP analyses for the proposed JSEHNOMA, which takes NLEH into account, to evaluate the reliability/security performances quickly.
• We estimate and optimize the security/reliability performances in different realistic settings.Multifarious results reveal that EH nonlinearity impacts drastically the reliability performance yet slightly the security performance.Additionally, the target data/secrecy rates are limited to prevent complete connection outage (i.e. the COP is one) and attain the complete security (i.e. the SOP is one).Further, the proposed (NOMA-and-proposed jammer selection) scheme drastically outperforms two reference schemes (NOMA-and-random jammer selection and orthogonal multiple access (OMA)-and-proposed jammer selection) in terms of both the security and the reliability.Nonetheless, there is a trade-off between the reliability and the security.Notably, the proposed scheme attains optimum security/reliability performance with proper selection of time/power splitting coefficient.

Organization
Section 2 describes the proposed JSEHNOMA.Next, Section 3 presents the COP/SOP/CTP/STP analyses.Then, Section 4 provides analytical/simulated results in divergent realistic settings.Ultimately, Section 5 closes the paper.Table 1 tabulates frequently-used notations.

Jammer selection for EH-aided NOMA
Figure 1 shows the proposed system model of JSEHNOMA 1 with B, S, N, F, E and A j , j = 1, ..., J .Such a JSEHNOMA can stand for downlink communications in mobile communications networks.As energy-constrained users, S and A j self-power their operations by scavenging energy from B which may be an available power beacon (e.g.radio broadcasting stations, television broadcasting stations).For the proposed JSEHNOMA, B transfers energy to S and A j in a time fraction of transmission block T, viz.Stage 1, while S implements NOMA downlink communications to N and F and the selected jammer A j among J jammers jams the eavesdropping of E in the remaining of T, viz.Stage 2. We denote g bs , g sn , g sf , and g se as channel gains between B and S, S and N, S and F, S and E, respectively whilst g bj , g jn , g jf , g je as channel gains between B and A j , A j and N, A j and F, A j and E, correspondingly.We also suppose flat block Rayleigh fading channels.Therefore, g kl with kl = {bs, sn, sf , se, bj, jn, jf , je} is expo- nentially distributed with the mean of kl = E g kl .To account for path loss, kl is modelled as d − kl wherein is the fading power at the reference distance of 1 meter (m), d kl is the corresponding transmitter-to-receiver dis- tance and is the path-loss exponent [19].Moreover, the PDF, the CDF, and the CCDF of g kl are correspondingly expressed to be g kl (a) = e −a∕ kl ∕ kl , g kl (a) = 1 − e −a∕ kl , and ̄ g kl (a) = e −a∕ kl .It is noted that the following denotes where h kl is the channel coefficient.
In Stage 1, B transfers energy wirelessly to S and A j .Consequently, S and A j accumulate the amount of energy as E u = T Pg bu where P is the power of B and ∈ (0, 1) represents the energy converting efficiency; u = {s, j} .Since Stage 2 lasts (1 − )T , the power for communica- tions in Stage 2 transformed from E u is E u (1− )T .In accordance with NLEH in [17], the power of S and A j consumed in Stage 2 is where A = P 1− , C = 1− , B = P , and is the power saturation threshold.
It is worth noticing that NLEH is evidently featured by (1).To be more specific, NLEH outputs the power of Ag bu , which is proportional linearly to the input power as it subceeds ; otherwise, its output power is saturated at .Additionally, NLEH reduces to LEH as is large ( → ∞).
In Stage 2, the NOMA downlink communications and the jamming operation are executed simultaneously, viz.S sends concurrently the symbols ( x n and x f ) with transmit power P s in the NOMA representation of √ P s x n + √ (1 − )P s x f to N and F while the selected jammer, namely A j , sends the jamming signal x j to interfere the wire-tapping of E with transmit power P j where x n and x f are the desired symbols intended to N and F, respectively.In agreement with the NOMA mechanism, N is allocated less power than F and thence,  < 0.5 .Consequently, {N, F, E} receives the signal to be This paper selects the jammer A j such that it causes the most interference among all jammers to E. This means the index j is expressed as j = max i∈ [1,J] g ie P i .The selection of A j can be implemented in numerous ways.For example, each jammer A i can set its timer independently with the threshold inversely proportional to g ie P i .Then, A j is the jammer whose timer expires earliest2 .

Detection at N and F
Because A j creates the jamming message x j to interfere deliberately only E without harming communications of N and F, the desired receivers (N and F) can predict accurately this jamming signal, which can be interpreted as being transmitted through the null space to N and F [56][57][58][59][60][61]. Accordingly, N and F can completely suppress the jamming signal out of y d , ultimately producing the no-jamming signal as Conditioned on ỹd , N and F detect x n and x f in accordance with the NOMA-based detection principle.Because  < 0.5 , N detects x f first by behaving x n as the interference.Subse- quently, N detects x f from ỹn with signal-to-interference plus noise ratio (SINR) as By suppressing the interference3 created by x f , N keeps restoring (1 − )P s g sn g sn P s + n .
= h sn √ P s x n + n .Consequently, conditioned on ŷn , N restores x n with the signal-to-noise ratio (SNR) as In the meanwhile, F detects x f by behaving x n as the inter- ference.Accordingly, F detects x f directly from ỹf with the SINR to be

Detection at E
The eavesdropper is blind with the jamming information x j .Thence, conditioned on ( 2), E performs the detection of x n and x f conforming to the NOMA-based detection principle.Since  < 0.5 , E detects x f first by behaving x n as the inter- fe r e n c e .S u b s e q u e n t ly, E d e t e c t s

SINR to be
By suppressing the interference induced by x f , E keeps detecting x n from ŷe = y e − h se √ (1 − )P s x f = h se √ P s x n + h je √ P j x j + e .Accordingly, conforming to ŷe , E detects x n with the SINR to be One sees from ( 6) and ( 7) that A j impairs E by the quan- tity of jamming power to be g je P j , which drastically mitigates the probability of successful detection of x n and x f at E and thence, ameliorating dramatically the security performance.

Performance analysis for JSEHNOMA
At first, this section analyzes the COP/SOP of JSEHNOMA.The COP is determined as the possibility that the achieved channel capacity at the desired receiver subceeds the target data rate R b .In the meantime, the SOP is determined as the likelihood that the obtained channel capacity at the eavesdropper subceeds the redundant secrecy rate R b − R s reserved against eavesdropping where R s is the target secrecy rate.Therefore, the COP/SOP represents the reliability/security of information transmission.Subsequently, the proposed COP/SOP analyses are extended to the CTP/STP analyses.(5) (1 − )P s g se g se P s + g je P j + e .
(7) Φ n e = g se P s g je P j + e .
Those analyses facilitate the quick COP/SOP/CTP/STP evaluation without exhaustive simulations.

Reliability analysis
The reliability performance is characterized by the COP at N and F. As a result, the lower the COP at N and F, the higher the reliability performance.

The COP at F
The COP at F is represented as where , m = B 2 m + 1 , and I stands for the complexity-accuracy trade-off of the Gaussian-Chebyshev quadrature in [62] which is used to approximate the first integral in (11).Section 4 adopts I = 50 which guarantees a very high preciseness.

The COP at N
Two events cause N to be in a connection outage as follows: (8) • The first event happens as N decodes x f unsuccessfully (namely, (1 − )log In accordance with the total probability law, the COP at N is represented as Remark 1 (9) and (13) indicate that since and finally causing distinct COP degrees for F and N.More specifically, F and N suffer a complete connection outage ; otherwise, a complete connection outage does not happen at F and N.This implies that the system designer must set the limit for the target data rate R b such that R b < −(1 − )log 2  to prevent the complete connection outage at F and N.
Remark 2 Both Δ f and Δ n depend on parameters (R b , , P, , , ) , meaning that N and F can attain the desired reliability by establishing properly these parameters.( 12)

Asymptotic reliability analysis
The following finds the upper-bound on the communications reliability of JSEHNOMA in the regime of high transmit power, namely P → ∞ .It is recalled that NLEH is com- pletely saturated as P → ∞ .Therefore, P u → C as P → ∞ .Following the analysis in Subsections 3.1.1and 3.1.2yields the COPs at F and N, respectively, as and

Connection throughput
For JSEHNOMA with delay-limited communications, the CTPs of N and F are expressed to be It is recalled that the higher the CTP, the higher the reliability performance.Moreover, (17) indicates that the CTPs of N and F are also jointly determined by a specification set (R b , , P, , , ) since this set influences Δ n and Δ f .Consequently, the desired CTPs are accomplished by establishing flexibly and properly this set conditioned on its preset value range.

Security analysis
The security performance is represented by the SOP at E. Accordingly, the lower the SOP at E, the lower the security (15) performance.Additionally, the SOP at E is defined in the same manner as the COP at N and F. As such, the SOPs of F and N are respectively given by and where Φ s = 2 (Rb−Rs)∕(1− ) − 1.

Derivation of 7 f
Inserting Φ f e in ( 6) into ( 18), one obtains Based on the proposed jammer selection, ( 20) is further simplified as where q se = P s g se , q ke = P k g ke , and q je = P j g je .
For notation simplicity, we assume that all jammers are close enough in order for average statistics from S to all jammers and from all jammers to E to be identical, i.e. bj = b and je = e for all j ∈ [1, J] .Then, all the terms inside the summation in (21) are also identical and thence, ( 18) (1 − )P s g se g se P s + g je P j + e ≤ Φ s . ( To complete the derivation of ( 22), one needs the CDF and the PDF of q ue = P u g ue with u ∈ {s, k, j} .Towards this end, we follow the steps in deriving B(⋅, ⋅, ⋅) in (11) as Taking the derivative of q ue (x) with respect to x yields the PDF of q ue to be where , and Using (25) to simplify L in (23) as Similarly to (27), one can simplify q ke (x) as q ue (x) = Pr P u g ue ≤ x C ue e where Given (28), one can express G in (23) after using the multinomial theorem and the closely located jammers as where Using (26), (27), and (29) to express (23) in closedform as Similarly, ( 24) is also expressed in closed-form as (28)

G = �
q ke (x) Υ f to accept distinct levels and lastly inducing divergent SOP degrees for F. Therefore, the target data/secrecy rates {R b , R s } should be set appropriately in relation to { , } to achieve the desired security performance for F.

Derivation of 7 n
Inserting Φ f e in (6) and Φ n e in ( 7) into (19), one obtains where Based on the proposed jammer selection and the closely located jammers, ( 33) is rewritten as (32) Υ n = 1 − Pr (1 − )P s g se g se P s + g je P j +  e ≥ Φ s , g se P s g je P , Before deriving (34), one simplifies U by invoking ( 25) as where Now inserting U in (35), G in ( 29) and f q je in ( 26) into (34) yields Remark 4 Similarly to Remark 1, (32) indicates that selecting {R b , R s , , } leads to 1−  > Φ s or 1− ≤ Φ s , causing Υ n to accept different values and finally causing divergent SOP degrees for N.More specifically, N is completely secured ; other- wise, N suffers a certain insecurity.This implies that the system designer must set the limit for the target data/secrecy rates {R b , R s } such that R b − R s ≥ −(1 − )log 2 to attain the complete security for N.
Remark 5 Both Υ f and Υ n depend on parameters (R b , R s , , P, , , J, ) , meaning that N and F can attain the desired security performances by setting properly these parameters.

Asymptotic security analysis
The following finds the upper-bound on the information security of JSEHNOMA in the regime of high transmit power, ( 35) It is recalled that NLEH is completely satu- rated as P → ∞ .Therefore, P u → C as P → ∞ .Then, and q ue (x) → 1 . Using these results and following the analysis in Subsections 3.2.1 and 3.2.2,one attains the SOPs for F and N, respectively, as and where Now we express Ῡ∞ f , Υ∞ f , and Ῡ∞ n explicitly by using the binomial expansion and the explicit forms of g ue (x) and g ue (x) .Therefore, we obtain (37)

Secrecy throughput
For JSEHNOMA with delay-limited communications, the STPs of N and F are given by It is reminded that the higher the STP, the less security N and F attain.Also, (45) indicates that the STPs of N and F are also jointly determined by a specification set (R b , R s , , P, , , J, ) since this set influences Υ n and Υ f .Therefore, the desired STPs are attained by establishing properly and flexibly this set conditioned on its preset value range.( 42)

Demonstrative results
A multiplicity of simulated/analytical results are presented to measure the CTP/STP of N and F in JSEHNOMA in multitudinous specifications in this section.The CTP/STP of N/F is denoted as N/F-Reliability/Security in the subsequent figures.Analytical results are generated by the theoretical expressions in Section 3 while simulated results are produced by Monte-Carlo simulations.Both simulated and analytical results are then compared to validate the analysis in Section 3.For illustration, users are located in a 2D plane.Unless otherwise stated, parameters are adopted in Table 2.For performance comparison, two reference schemes are considered.The reference schemes differ the proposed scheme only in Stage 2.More specifically, in the first reference scheme, a jammer is randomly selected and S implements NOMA.In the second reference scheme, the jammer selection of the proposed scheme is implemented and S carries out OMA by dividing Stage 2 into two equal sub-stages in which S transmits sequentially x n to N and x f to F. In the following figures, the proposed scheme, the first and the second reference schemes are respectively denoted as "Proposed", "Random", and "OMA".Therefore, the reliability performances of the proposed and the first reference schemes are similar (denoted as "N/F: Proposed & Random" in the following figures) and the security performances of N and F in the second reference scheme are identical (denoted as "F-Security = N-Security" in the following figures).The security/reliability analyses for two reference schemes are proceeded in the same manner as the proposed scheme and thence, we omitted them for compactness.
Figure 2 illustrates the CTP/STP versus P.This figure unveils the match between the simulation and the analysis for the proposed scheme, validating the exactness of the analysis in Section 3. Also this figure reveals the considerable reliability enhancement (i.e., higher CTP) yet the slight security mitigation (i.e. higher STP) with accreting P for both N and F. This originates from increasing harvested energy.Indeed, the higher harvested energy (i.e., higher transmit power of S) makes N and F receive their desired signals more reliably.However, the higher harvested energy not only increases the transmit power of S but also accretes the transmit power of A j , making E receive more both desired signal power and jamming power.Thence, the SINRs for E to decode x n and x f increase slightly, eventually degrad- ing slightly the security performance.Moreover, due to the increase of both the CTP and the STP with increasing P, the trade-off between the reliability and the security arises.Nevertheless, that the security is mitigated slightly whilst the reliability is improved significantly with accreting P reveals the efficacy of the jamming operation in remaining communications secured with higher reliability.Furthermore, the security/reliability performance is saturated at high P as analyzed4 in Subsections 3.1.3and 3.2.3.Further, the CTP of the proposed (NOMA) scheme is almost double that of the second reference (OMA) scheme as expected, showing the superiority of the proposed scheme in comparison with its OMA counterpart in terms of the reliability.In addition, the STP is in the increasing order for the proposed (NOMAand-proposed jammer selection) scheme, the second (OMAand-proposed jammer selection) reference scheme, and the first (NOMA-and-random jammer selection) reference scheme, unveiling the significantly higher security of the proposed scheme as compared to the reference ones.This also exposes the efficacy of the proposed jammer selection and the NOMA in securing communications as compared to the random jammer selection and the OMA.Briefly, the proposed scheme outperforms the reference ones in terms of both the reliability and the security.Owing to the match between the analytical and simulated results of the proposed scheme, the subsequent figures show merely the analytical results to reduce the number of curves, ultimately making the figures readable.Figure 3 unveils the influence of the number of jammers J on the CTP/STP of N and F. As expected, the communications reliability of all the considered schemes and the information security of the first (NOMA-and-random jammer selection) reference scheme are independent of J. Additionally, the CTP of the proposed (NOMA) scheme is twice that of the second (OMA) reference scheme, showing that the proposed scheme outperforms its OMA counterpart in terms of the reliability.Moreover, the proposed scheme is more secure than the reference schemes, exposing the efficacy of the proposed jammer selection in meliorating the information security.Moreover, the security of the proposed scheme is meliorated with increasing J, as expected.Meanwhile, the security of the second (OMA) reference scheme is almost unchanged with increasing J.In summary, the proposed scheme attains higher reliability and security than the reference ones.
Figure 4 illustrates the influence of the time splitting coefficient on the CTP/STP of N and F. This figure reveals that the reliability performance is deteriorated with increasing (i.e. the CTP reduces with increasing ).This is because the CTP is inversely proportional to as seen in (17).In addition, high causes the zero CTP, which was already analyzed in Section 3.More specifically, Remark 1 indicates the zero CTP (or the complete connection outage) for . Given the system parameters ( R b = 1 bps/Hz, = 0.2 ) in Table 2, it is obvious that the zero CTP of the proposed scheme occurs when ≥ 0.5693 , which coincides with the results in Fig. 4. Addi- tionally, the proposed (NOMA) scheme attains the CTP almost twice that of the second (OMA) reference scheme, showing the efficacy of the NOMA in improving the reliability.Moreover, all the considered schemes have lower STP with increasing , indicating the security improvement.Therefore, the security-and-reliability trade-off is observed since the reliability is mitigated but the security is meliorated with increasing .Furthermore, the proposed scheme has the lower STP than two reference schemes, again verifying the efficacy of the proposed jammer selection and the NOMA in improving both the security and the reliability.
Figure 5 illustrates the influence of the energy converting efficiency on the CTP/STP of N and F. This figure shows that the communications reliability is slightly meliorated with accreting due to the increasing harvested energy which eventually increases the received power at N and F for decoding x n and x f more reliably.However, the security performance is almost unchanged with increasing .This is because the increasing harvested energy due to increasing accretes both powers of the desired signal and the jamming signal and thence, the SINR for E to decode x n and x f is almost constant.Additionally, the CTP of the proposed (NOMA) scheme is almost double that of the second (OMA) reference scheme, indicating the efficiency of the NOMA in improving the reliability.Further, the proposed scheme is more secure than both reference schemes.In brief, the proposed scheme accomplishes higher reliability and security than the reference ones.
Figure 6 demonstrates the influence of the power splitting coefficient , which represents the power portion allocated to x n , on the CTP/STP of N and F. One sees that the reli- ability performance of the second (OMA) reference scheme is independent of as predicted.Moreover, the reliability performance of F for the proposed scheme is mitigated with increasing , which is because of less power allocated to transmit x f and direct decoding of x f at F. Nevertheless, N in the proposed scheme can attain the highest CTP with the optimal selection of (e.g.= 0.238 makes the CTP of N the highest in Fig. 6).This is because N must decode x f prior to decoding x n .Therefore, should be selected optimally to balance the SINR for decoding x f and the SNR for decoding x n .In addition, high causes the zero CTP, which was already analyzed in Section 3.More specifically, Remark 1 indicates the zero CTP (or the complete connection outage) for R b ≥ −(1 − )log 2 or  > 2 − R b 1− .Given the system parameters ( R b = 1 bps/Hz, = 0.4 ) in Table 2, it is obvious that the zero CTP of the proposed scheme occurs when ≥ 0.315 , which coincides with the results in Fig. 6.Further, the proposed (NOMA) scheme attains the CTP almost twice that of the second (OMA) reference scheme, showing the efficacy of the NOMA in improving the reliability.Moreover, the proposed scheme has the lower STP than two reference schemes, again verifying the efficacy of the proposed jammer selection and the NOMA in improving both the security and the reliability.
Figure 7 exposes the effect of the power saturation threshold on the CTP/STP of N and F. The results show the considerable reliability improvement with accreting , which is because of the increasing harvested energy.Additionally, the CTP is saturated at high because high makes the energy harvester linear.In addition, the proposed (NOMA) scheme attains the CTP almost twice that of the second (OMA) reference scheme, showing the efficacy of the NOMA in improving the reliability.Nevertheless, the STP can be optimized with the appropriate selection of .This is because increasing accretes both powers of the jamming signal and the desired signal.Thence, E can attain the best STP (the worst security for N and F) by balancing between the jamming power and the desired power with the optimal value of .Further, the proposed scheme is more secure than two reference schemes, again verifying the efficacy of the proposed jammer selection and the NOMA in meliorating both the reliability and the security.

Conclusions
This paper proposed the jammer selection in EH-aided NOMA to improve the reliability-and-security performances and the spectral-and-energy efficiencies for downlink communications.For prompt security/reliability performance evaluation, this paper proposed the closed-form COP/SOP/ CTP/STP formulas.Multifarious results corroborated the proposed formulas and reveal that EH nonlinearity, which is characterized by , dramatically affects the communications reliability but slightly the information security.In addition, there exists limits on the target data rate R b and the target secrecy rate R s to avoid the complete connection outage (i.e. the COP is one) and achieve the complete security (i.e. the SOP is one).Moreover, the proposed (NOMA-andproposed jammer selection) scheme attains significantly higher security and reliability than its counterparts (NOMAand-random jammer selection and OMA-and-proposed jammer selection).However, there is a trade-off between the reliability and the security.Remarkably, the proposed scheme attains the optimum security/reliability performance with the proper selection of and .

Fig. 2 CTP
Fig. 2 CTP/STP versus the power of B