# Physical Layer Security in Nonorthogonal Multiple Access Wireless Network with Jammer Selection

Authors: Langtao Hu; Xin Zheng; Chunsheng Chen
Journal: Security and Communication Networks
 (2019)

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## Abstract

The physical layer security of downlink nonorthogonal multiple access (NOMA) network is analyzed. In order to improve the secrecy probability, friendly jammers are jointed in the NOMA network. Two jammer schemes are proposed in the NOMA network. All the jammers transmit jamming signal without jammer selection in the first scheme (NO JS scheme). Jammers are selected to transmit jamming signal if their interfering power on scheduled users is below a threshold in the second scheme (JS scheme). A stochastic geometry approach is applied to analyze the outage probability and the secrecy probability. Compared with the NO JS scheme and traditional scheme (without jointing jammers), the jammer selection scheme provides a good balance between the user outage probability and secrecy probability. Numerical results demonstrate that the security performance of the two proposed schemes can be improved by jointing the jammers in the NOMA wireless network.


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## Body

## 1. Introduction

The development of mobile internet and Internet of Things brings lots of challenging requirements to fifth-generation (5G) networks, such as increasing high data rate and low latency [1–3]. The nonorthogonal multiple access has been considered as key promising multiple access candidates for 5G cellular networks. NOMA allows serving multiple users simultaneously using the same frequency/time resources at the cost of increased intracell interference. At the base station side, messages for multiple users are superposed by superposition coding. The successive interference cancellation (SIC) technique is applied to extract the intended message in the receiver side. Security is always an important issue for wireless networks, since the broadcast nature of wireless radio propagation makes it easily be overheard by eavesdroppers.


### 1.1. Related Works

Recently, NOMA has received remarkable attention both in the world of academia and industry [4–6]. Power-domain NOMA has been proposed for the 3GPP long-term evolution initiative in [4]. The authors in [5] investigated the performance of NOMA in a cellular downlink scenario with randomly deployed users. It was shown that NOMA can achieve superior ergodic sum rate performance than traditional orthogonal multiple access (OMA) counter parts. Challenges, opportunities, and future research trends for NOMA design are highlighted to provide some insight into the potential future work of researchers in [6]. The security performance of the NOMA networks can be improved by invoking the protected zone and by generating noise at the BS as shown by Liu et al. [7]. The physical layer security of uplink nonorthogonal multiple access is analyzed by Gerardo Gomez et al. [8]. Tao et al. [9] proposed a new reliable physical layer network coding and cascade-computation decoding scheme. The authors in [10] proposed an opportunistic multiple-jammer selection scheme for enhancing the physical layer security. The authors in [11] studied the security-reliability tradeoff analysis for conventional single-hop networks under a single passive eavesdropper attack. The authors in [12] enhanced physical layer security for downlink heterogeneous networks by using friendly jammers and full-duplex users. Recently, stochastic geometry has been used to model some network, such as large-scale HET wireless networks [10], massive MIMO-enabled HetNets [14], cognitive cellular wireless networks [15], multitier millimeter wave cellular networks [16], and NOMA network [17]. It has been succeeded to develop tractable models to characterize and better understand the performance of these networks, and these models have been shown to provide tractable yet accurate performance bounds for these networks.


### 1.2. Motivations and Contributions

In this paper, we investigate the physical layer security of NOMA with friendly jammers and multiple noncolluding eavesdroppers (EVEs) in large-scale networks with stochastic geometry. For the sake of easy deployment, all nodes in NOMA wireless network are equipped with single antenna, and eavesdroppers are randomly distributed along the whole plane. The jammers are assumed to transmit friendly artificial noise. To enhance the physical layer security, two schemes are proposed with jointing jammers in NOMA network. In order to alleviate the interference from jammers to scheduled users, a jammer selection policy is discussed based on the received jamming power at the user. When the jammer power is below a threshold, the jammer around the scheduled user is active; otherwise, the jammer is idle. Unlike the scheme in [7, 8], the security performance of the NOMA networks can be improved by generating noise at the BS in [7], and physical layer security in uplink NOMA is discussed in [8]. In this paper, friendly jammers will be jointed, which can enhance the physical layer security in downlink NOMA wireless network. The main contributions of this paper are summarized as follows:(1)
Two physical layer security schemes are proposed, where friendly jammers are jointed in NOMA wireless network. Jammers transmit friendly artificial noise. A jammer selection policy is discussed based on the received jamming power at user.(2)
Using stochastic geometry tools, the downlink NOMA performance is analyzed in terms of outage probability and secrecy probability. In particular, the BSs and user positions are model Poisson point process (PPP) on a 2-D plane. The active jammer positions are model Poisson hole process.(3)
All the analytical results are validated by system-level simulations. Our proposed schemes provide a better security performance compared with the traditional scheme.The rest of the paper is organized as follows. In Section2, we introduce the system model. In Section 3, the outage probability performance of proposed schemes is investigated. In Section 4, the user secrecy probability performance of proposed schemes is investigated. In Section 5, numerical simulation and analysis are discussed to verify these results. A conclusion is drawn in Section 6.Notation: the expectation of functionfx with respect to x is denoted as Efx. Cumulative distribution function of fx is denoted as Ff. The Laplace transform of fx is denoted by Lfs. An exponential distributed random variable with mean 1 is denoted by x∼exp1. Let I1 be a set and I2 be a subset of I1; then, I1\I2 denotes the set of elements of I1 that do not belong to I2.


## 1.1. Related Works

Recently, NOMA has received remarkable attention both in the world of academia and industry [4–6]. Power-domain NOMA has been proposed for the 3GPP long-term evolution initiative in [4]. The authors in [5] investigated the performance of NOMA in a cellular downlink scenario with randomly deployed users. It was shown that NOMA can achieve superior ergodic sum rate performance than traditional orthogonal multiple access (OMA) counter parts. Challenges, opportunities, and future research trends for NOMA design are highlighted to provide some insight into the potential future work of researchers in [6]. The security performance of the NOMA networks can be improved by invoking the protected zone and by generating noise at the BS as shown by Liu et al. [7]. The physical layer security of uplink nonorthogonal multiple access is analyzed by Gerardo Gomez et al. [8]. Tao et al. [9] proposed a new reliable physical layer network coding and cascade-computation decoding scheme. The authors in [10] proposed an opportunistic multiple-jammer selection scheme for enhancing the physical layer security. The authors in [11] studied the security-reliability tradeoff analysis for conventional single-hop networks under a single passive eavesdropper attack. The authors in [12] enhanced physical layer security for downlink heterogeneous networks by using friendly jammers and full-duplex users. Recently, stochastic geometry has been used to model some network, such as large-scale HET wireless networks [10], massive MIMO-enabled HetNets [14], cognitive cellular wireless networks [15], multitier millimeter wave cellular networks [16], and NOMA network [17]. It has been succeeded to develop tractable models to characterize and better understand the performance of these networks, and these models have been shown to provide tractable yet accurate performance bounds for these networks.


## 1.2. Motivations and Contributions

In this paper, we investigate the physical layer security of NOMA with friendly jammers and multiple noncolluding eavesdroppers (EVEs) in large-scale networks with stochastic geometry. For the sake of easy deployment, all nodes in NOMA wireless network are equipped with single antenna, and eavesdroppers are randomly distributed along the whole plane. The jammers are assumed to transmit friendly artificial noise. To enhance the physical layer security, two schemes are proposed with jointing jammers in NOMA network. In order to alleviate the interference from jammers to scheduled users, a jammer selection policy is discussed based on the received jamming power at the user. When the jammer power is below a threshold, the jammer around the scheduled user is active; otherwise, the jammer is idle. Unlike the scheme in [7, 8], the security performance of the NOMA networks can be improved by generating noise at the BS in [7], and physical layer security in uplink NOMA is discussed in [8]. In this paper, friendly jammers will be jointed, which can enhance the physical layer security in downlink NOMA wireless network. The main contributions of this paper are summarized as follows:(1)
Two physical layer security schemes are proposed, where friendly jammers are jointed in NOMA wireless network. Jammers transmit friendly artificial noise. A jammer selection policy is discussed based on the received jamming power at user.(2)
Using stochastic geometry tools, the downlink NOMA performance is analyzed in terms of outage probability and secrecy probability. In particular, the BSs and user positions are model Poisson point process (PPP) on a 2-D plane. The active jammer positions are model Poisson hole process.(3)
All the analytical results are validated by system-level simulations. Our proposed schemes provide a better security performance compared with the traditional scheme.The rest of the paper is organized as follows. In Section2, we introduce the system model. In Section 3, the outage probability performance of proposed schemes is investigated. In Section 4, the user secrecy probability performance of proposed schemes is investigated. In Section 5, numerical simulation and analysis are discussed to verify these results. A conclusion is drawn in Section 6.Notation: the expectation of functionfx with respect to x is denoted as Efx. Cumulative distribution function of fx is denoted as Ff. The Laplace transform of fx is denoted by Lfs. An exponential distributed random variable with mean 1 is denoted by x∼exp1. Let I1 be a set and I2 be a subset of I1; then, I1\I2 denotes the set of elements of I1 that do not belong to I2.


## 2. System Model

In this paper, we consider a dense multicell NOMA downlink wireless network in presence of eavesdroppers (EVEs) as shown in Figure1. All BSs users and EVEs are equipped with one antenna. The BS locations are distributed as an independent homogeneous PPP ΦB with density λB in two-dimensional plane. Without loss of generality, the analysis is performed in a typical cell denoted as BS0. Based on Slivnyak’s Theorem, due to stationarity of ΦB, the typical cell can reflect the averaged performance of the entire system. The system assumes a frequency reuse factor 1; hence, the same frequency resources are used in all cells. The radio resources are partitioned into a number of subbands. We assume the bandwidth of each subband is normalized to 1. The UE and EVE locations are distributed as an independent homogeneous PPP ΦU and ΦE with densities λU and λE, respectively. In this paper, the NOMA group includes two users. Existing results have shown that the NOMA group with more than two UEs may provide a better performance gain [18]. In order to process the SIC easily, two user NOMA networks are more practical in the reality system. UE1 and UE2 consist of a NOMA group. We assume λU≫λB so that a sufficient number of UEs can always be found to form the NOMA group in each cell. To enhance the security performance, friendly jammers are jointed in NOMA network. In the selective jammer scheme, a jammer is selected to be active if its interference power to the scheduler user is below a threshold. Actually, the threshold is the jammer exclusion zone around the scheduler user, i.e., ΦJS=jj∈ΦJ,PJRj,Ui−a<PJD−a,∀Ui∈ΦUs. ΦJS is the Poisson hole process of active jammer. ΦUs denotes the point process of scheduled users. ΦUs is an inhomogeneous PPP, for which the density is λUs. Rj,Ui−a is the distance between the jammer and scheduled users. D is the exclusion zone radius. PJ is denoted as the transmit power of the jammer. a is the pathloss exponent. Pb is the total power of BS on a subband in downlink NOMA. The allocated powers of UE1 and UE2 can be denoted as P1=εPb and P2=1−εPb, respectively, where ε∈0,0.5 is a NOMA power allocation parameter. UE1 is assumed to be with a better normalized channel gain. UE2 is assumed to be with a worse normalized channel gain. The two users are selected randomly in NOMA network. PJ denotes the power of jammer. BS-transmitted signals to UE1 and UE2 are expressed as x1 and x2, respectively. Since UE1 and UE2 form a NOMA group, x1 and x2 are encoded as the composite signal at the BS0 [12]:(1)x¯=P1x1+P2x2.Figure 1
NOMA wireless network with the selected jammer.The received signal atUEi,i∈1,2 can be expressed as(2)yi=hiri−ax¯+ni,where hi is the Rayleigh fading gain between BS0 and UEi, which follows an exponential distribution with mean 1. All hi are assumed to be i.i.d. ri is the distance between BS0 and UEi. ni is the additive noise.


## 3. NOMA User Outage Probability

We assumeUE1 has a better channel condition. At the receiver side, successive interference cancellation (SIC) is used to decode the intended message. UE1 first decodes the UE2 signal x2 and removes it from the received composite signal; after that, UE1 can further decode its signal x1. UE2 decodes x2 directly by treating x1 as interference. We consider the possible SIC error propagation, which is caused by decoding unsuccessfully in the first step, and thus, error is carried over to the next-level decoding. Let β be the fraction of NOMA interference due to SIC error propagation. Noise can be safely neglected in a dense interference limited wireless system. The signal to interference ratio (SIR) of UE1 can be represented as SIRU1=P1h1r1−a/IB1+IJS1+IW1, where IB1=∑j∈ΦB\BS0Pbg1,jR1,j−a denotes the cumulative downlink intercell interference from the all other cells and IJS1=∑y∈ΦJSPjh1,yR1,y−a denotes cumulative downlink interference from the selected jammers. IW1=βP2h1r1−a denotes the interference from SIC error propagation. g1,j is the Rayleigh fading an exponential distribution with mean 1, g1,j∼exp1. ΦB\BS0 represents the set of all BSs excluding BS0.The achievable rate ofUE1 on each subband in NOMA network is given as(3)τ1=log1+SIRU1=log1+c1P1βc1P2+1,where c1=h1r1−a/IB1+IJS1 is the UE1 channel gain including pathloss and fast fading normalized by two kinds of interferences. The signal to interference ratio of UE2 can be represented as SIRU2=P2r2−ah2/IB2+IJS2+P1r2−ah2, where IB2=∑j∈ΦB\BS0Pbg2,jR2,j−a is the cumulative downlink intercell interference from all the other cells. IJS2=∑y∈ΦJSPJh2,yR2,y−a denotes cumulative downlink interference from the selective jammers. P1r2−ah2 is the interference from UE1.The achievable rate ofUE2 on each subband in NOMA network is given as(4)τ2=log1+SIRU2=log1+c2P2c2P1+1,where c2=h2r2−a/IB2+IJS2. We assume that two users are randomly selected among all scheduled users. Two users are marked as UEn and UEm. The normalized channel gains of UEn and UEm are denoted as cn and cm, respectively. Let UE1=UEiUEi∈UEn,UEm,ci=maxcn,cm, and UE2=UEiUEi∈UEn,UEm,ci=mincn,cm, z=maxx,y,andϖ=minx,y. The CDF of z and ϖ can be represented as Fzz=Fxyz,z;Fϖϖ=Fxϖ+Fyϖ−Fxyϖ,ϖ [18]. Thus, CDFs of c1 and c2 can be derived as follows:(5)Fc1C=FcncmC,C=FcC2,(6)Fc2C=FcnC+FcmC−Fcn,cmC,C=2FcC−FcC2,where FcC=1−Pc>C and Pc>C denotes the probability of c>C. According to (5) and (6), Fc1C and Fc2C can be given as (7) and (8), respectively:(7)Fc1C=FcC2=1−Pc>C2,(8)Fc2C=2FcC−FcC2=21−Pc>C−1−Pc>C2.For a given normalized channel gain toUE1 or UE2, c=hiri−a/IB+IJS and Pc>C can be derived as follows:(9)Pc>C=EriPc>Cri=∫ri>0Phiri−αIB+IJS>Crifridri=∫ri>0EIB,IJSexp−CriαIB+IJSfridri=∫ri>0LIBCriαLIJSCriαfridri.In (9), the second term follows fromhi∼exp1 [13].The Laplace transform ofIB is given by(10)LIBs=EΦB,g−exp−s∑j∈ΦB/BS0gi,jRj−aPB=exp−2πλB∫ri∞1−11+sv−aPBvdv=exp−2πλBsPBδ∫ri2/sPBδ∞11+uδdu,where δ=2/a.The Laplace transform of IJS is given by(11)LIJSs=EΦJS,h−exp−s∑j∈ΦJShi,jRi,j−aPJ=EΦJ∏j∈ΦJ\BUEi,DLhi,jsRi,j−aPJ=aEΦJexp−λJ∫j∈ΦJ\BUEi,D1−Lhi,jsPJx−adx≈bexp−2πλJD2−aPJsa−2−1F211,1−2a;2−2a;−sPJDa.In step (a),BUEi,D is a hole of radius D centered at UEi, ΦJ\BUEi,D denotes the active jammers location, and ΦJ is the jammer baseline PPP from which the hole is carved out. In step (b), we only discuss the hole around the UEi. The step (b) follows from the probability generating functional of PPP [13], where F21a,b;c;d is the Gauss hypergeometric function.When all jammers are active without jammer selection (NO JS scheme),δ=2/a. LINOJSs denotes the Laplace transform of interference from all jammers without selection to UEi in NO JS scheme. We can derive LINOJSs as [13](12)LINOJSs=exp−πλJsPJδsincδ.By plugging (10) and (11) into (9), Pc>C with jammer selection in NOMA network is given as(13)Pc>C=∫ri>0exp−2πλBsPBδ∫ri2/sPBδ∞11+uδdu×exp−2πλJD2−aPJsa−2−1×F211,1−2a;2−2a;−sPJDa×2πλBriexp−πλBri2dris=Criα.When a = 4,(14)Pc>C=∫ri>0exp−2πλBri2CPB1/2π2−arctan1CPB1/2×exp−πλJD−2PJCri4F211,0.5;1.5;−Cri4PJD4×2πλBriexp−πλBri2dri.The outage probability of UE1 with jammer selection in NOMA network can be evaluated as follows:(15)P1τ¯1,τ¯2=1−Pτ1>τ¯1,τ1⟶2>τ¯2=1−Pc1P1βc1P2>γ1,c1P2c1P1+1>γ2=1;ifγ1≥P1βP2orγ2≥P2P1,Fc1maxθ1,θ2;otherwise,where Pτ1>τ¯1,τ1⟶2>τ¯2 denotes the connection probability of UE1, γ1 and γ2 denote the SIRs of UE1 and UE2, respectively. γ1=2τ¯1−1andγ2=2τ¯2−1. τ¯1 and τ¯2 are the target rate thresholds for UE1 and UE2, respectively. τ1⟶2 is the rate of decoding UE2 signal x2 in the UE1 receiver, which must be greater than the QoS requirement of UE2. τ1⟶2>τ¯2 can ensure that UE1 is able to remove UE2’s signal from interference. θ1=γ1/p1−γ1βP2,andθ2=γ2/p2−γ2P1. Plugging maxθ1,θ2 into (7), we get Fc1maxθ1,θ2 in (15).The outage probability ofUE2 with jammer selection in NOMA network can be evaluated as follows:(16)P2τ2≤τ¯2=0;ifγ2≥P2P1.Fc2θ2;otherwise.Takingθ2 into (8), we can easily get Fc2θ2 as shown in (16).


## 4. NOMA User Secrecy Probability

We investigate the secrecy probability of a randomly located NOMA user. In this work, the user secrecy probability corresponds to the probability that a secret message for the schedule user cannot be decoded by any noncolluding eavesdroppers, becauseUE1’s and UE2’s signals are derived by eavesdroppers in the similar way. Here, we only discuss the secrecy performance of UE1. Hence, the secrecy probability can be expressed as(17)PSecγs=Pmaxx∈ΦeSIRx<γs=P∩x∈ΦeSIRx<γs=E∏x∈ΦePSIRx<γsx=EΦe∏x∈Φe1−exp−P1−1γsrxaIEx=exp−2πλe∫0∞LIExP1−1γsrxarxdrx,where SIRx of the typical EVE is given by(18)SIRx=P1hxrx−aIB⟶E+IJS⟶E,where γs is the target secrecy SIR, hx is the Rayleigh fading gain between BS0 and EVE, and hx follows an exponential distribution with mean 1. rx is the distance between BS0 and EVE. LIEs=LIB⟶EsLIJS⟶Es, where LIB⟶Es and LIJS⟶Es denote the Laplace transform of IB⟶E and IJS⟶E, respectively. IB⟶E is the interference from the other cell BSs to EVE. IJS⟶E is the interference from the selective jammers to EVE. The detailed derivation of LIJS⟶Es is provided in Appendix A. We can derive the following:(19)LIEs=LIB⟶EsLIJS⟶Es=exp−πs2P1δλBsincδexp−πλJsPJδsincδ×∫0∞Hv,sgvdv.Inserting (19) into (17), we can easily have the expression of PSecγs.When all jammers are active without jammer selection,LIEs is given by(20)LIEs=LIB⟶EsLIJ⟶Es=exp−πλBsP1δsincδexp−πλJsPJδsincδ.


## 5. Simulation Results and Discussion

In this section, we present Monte Carlo simulations to evaluate the performance of the proposed scheme, and analytical results are illustrated and validated with extensive simulations in NOMA network. The default parameters are listed in Table1 unless otherwise stated.Table 1
Parameter assumptions.
Parameter
Meaning
Default value
λ
B
Density of BS
1
/
km
2
λ
J
Density of jammer
10
/
km
2
λ
E
Density of eavesdropper
11
/
km
2
λ
U
Density of user
100
/
km
2
P
B
Transmission power of BS
46 dBm
P
J
Transmission power of jammer
23 dBm
ε
NOMA power allocation parameter
0.3
α
Pathloss exponent
4
D
Jammer exclusion circle radius
0.1
kmOur first proposed scheme is that all jammers are active without jammer selection in NOMA network, which is marked as “NO JS scheme.” Our second proposed scheme is that some jammers are active with jammer selection in NOMA network, which is marked “JS scheme.” There are no jammers in the traditional scheme in NOMA network. As expected, our proposed schemes provide a better security performance compared with the traditional scheme. The JS scheme provides a good balance between the user outage probability and the user secrecy probability. Figure2 shows UE1 outage probability P1τ¯1,τ¯2 and UE2 outage probability P2τ2≤τ¯2 versus different target rates τ¯1, where τ¯2 is fixed to 0.1 bits/s/subband.Figure 2
Outage probability of NOMA whenτ¯2 is fixed to 0.1 bits/s/subband.In Figure2, “ana” (the dashed curves) and “sim” (the curves with circle marks) are the abbreviation of analysis and simulation, respectively. “UE1 NO JS ana” denotes the analytical result of UE1 outage probability using the first proposed scheme, where all jammers are active. “UE1 NO JS sim” denotes the simulation result of UE1 outage probability. “UE1 JS ana” denotes the analytical result of UE1 in the second proposed scheme, where some selective jammers are active. From Figure 2, we can observe that the analytical results match well with the simulation results, which validate the accuracy of the analysis.In Figure2, all jammers are active in the first proposed scheme. Jammers transmit artificial noise to legitimate NOMA users and the eavesdroppers. While transmitting noise to eavesdroppers, the jammer also transmits artificial noise to legitimate NOMA users in the proposed scheme. The noise is the interference for NOMA users. When the interference increases, the SIR decreases. Compared with the traditional scheme without jointing the jammer, the outage probability increases in our proposed scheme with jointing jammers in NOMA network. Compared to the first scheme, the outage probability decreases for the selective jammer scheme. In other words, the user connective performance improves. In Figure 2, we can see that P1τ¯1,τ¯2 remains constant when τ¯1≤0.04 bit/s/subband. This is due to the fact that UE1 needs to decode the signal intended to UE2 first before it can decode the signal for itself. When τ¯1 is below 0.04, the outage is always remained by failing to decode UE2 signal. The result also can be explained by the definition of outage probability of UE1P1τ¯1,τ¯2=1−P1τ1>τ¯1,τ1⟶2>τ¯2; P1τ¯1,τ¯2 is related to τ¯1 and τ¯2. If τ¯2 is fixed, when τ¯1 is quite small, τ1⟶2>τ¯2 can guarantee τ1>τ¯1 and P1τ1>τ¯1,τ1⟶2>τ¯2 becomes P1τ1⟶2>τ¯2, so P1τ¯1,τ¯2 is not a function of τ¯1 and it remains constant when τ¯1 is quite small. When τ¯1>0.04, the outage probability reduces as τ¯1 increases. P2τ2≤τ¯2 remains constant as τ¯1 increases due to the fact that P2τ2≤τ¯2 is not a function of τ¯1.Figure3 shows the outage probability of UE1 and UE2 when τ1 is fixed to τ1=0.1 bit/s/subband. We can observe P1τ¯1,τ¯2 remains constant at first and then increases in the same way as shown in Figure 2. When τ¯2 is small, P1τ¯1,τ¯2 is only a function of τ¯1, which is not affected by τ¯2. As τ¯2 continues to increase, both τ¯1 and τ¯2 will affect P1τ¯1,τ¯2.Figure 3
Outage probability of NOMA whenτ¯1 is fixed to 0.1 bits/s/subband.Figure4 shows that outage probability of UE1 in three schemes versus τ¯1 with different ε in NOMA network. The allocation power of UE1 increases as ε increases; we can see that while ε increases in these schemes; P1τ¯1,τ¯2 does not necessarily decrease. This outcome can be explained that more transmit power allocated to UE1 also means less power allocated to UE2, so it is difficult for UE1 to decode UE2 signal x2. But the lower bound of outage probability of UE1 can be improved, which is related by successfully decoding UE2’s signal x2.Figure 4
Outage probability ofUE1 three schemes versus τ¯1 with different ε in NOMA network.Figure5 shows that UE2 outage probability of three schemes versus τ¯2 with different ε in NOMA network. We can observe that the outage probability decreases whsen ε is decreasing from 0.5 to 0.3. This is because more power allocated to UE2 will result in a better outage performance of UE2.Figure 5
Outage probability ofUE2 in three schemes versus τ¯2 with different ε in NOMA network.Figure6 shows the impact of imperfect SIC of three schemes with different β. From the SIR of UE1, c1P1/βc1P2+1, we can see SIR decreases as β increases. When β=0.02, compared to perfect SIC β=0, the outage probability of UE1 increases.Figure 6
The impact of imperfect SIC of three schemes on NOMA with differentβ.Figure7 shows that the UE1 secrecy probability of our proposed scheme versus SIR threshold γs with different D exclusion zone radii. We can see that our proposed scheme has a better performance than the traditional scheme in secrecy probability in NOMA network. “NO JS scheme” will obtain the highest secrecy probability. But the outage probability of “NO JS scheme” is the worst. Secrecy probability of “JS scheme” with small jammer exclusion zone is better. When the exclusion zone radius increases, the small jammers transmit noise to interfere the eavesdropper, so secrecy probability decrease. Our proposed jammer selection scheme provides a good balance between the user outage probability and secrecy probability.Figure 7
The UE1 secrecy probability versus SIR thresholdγs.Figure8 compares the connection probability performance of UE1 versus jammer density λJ. We can observe that simply deploying more jammers cannot enhance the connection probability. When jammer density λJ increases, the connection probability of JS scheme increases. But the connection probability of NO JS scheme decreases, as λJ increases. The connection probability of traditional scheme without jointing jammer remains constant. This is because the jammers whose interference on any scheduled user is stronger than a threshold are prevented from being active. When λJ increases, there are more jammers around the eavesdropper, but the interference level suffered by the legitimate user from jammers is mitigated, and the interference level remains low in the jammer selection scheme. When λJ=0, the performance is the same between our proposed schemes and the traditional scheme.Figure 8
The connection probability performance ofUE1 versus jammer density λJ in three schemes.


## 6. Conclusion

This paper analyzes the outage and secrecy performances of NOMA network using stochastic geometry theory. The analytical expressions of outage and secrecy probabilities are derived. Compared with the “NO JS scheme” and traditional scheme (without jointing jammer), the jammer selection scheme provides a good balance between the user outage probability and secrecy probability. Simulation results show that the expressions can provide sufficient precision to evaluate the system performance. We can optimize jammer selection exclusion zone radius and NOMA power allocation to realize a secrecy transmission in future study.



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