research article - hindawi · 2019. 11. 16. · research article physical layer security in...

Research ArticlePhysical Layer Security in Nonorthogonal Multiple AccessWireless Network with Jammer Selection

Langtao Hu Xin Zheng and Chunsheng Chen

Anqing Normal University AnQing 246133 China

Correspondence should be addressed to Langtao Hu 122634998qqcom

Received 1 April 2019 Accepted 22 October 2019 Published 16 November 2019

Academic Editor Salvatore Sorce

Copyright copy 2019 Langtao Hu et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

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

1 Introduction

e development of mobile internet and Internet of ingsbrings lots of challenging requirements to fth-generation(5G) networks such as increasing high data rate and lowlatency [1ndash3] e nonorthogonal multiple access has beenconsidered as key promising multiple access candidates for5G cellular networks NOMA allows serving multiple userssimultaneously using the same frequencytime resources atthe cost of increased intracell interference At the basestation side messages for multiple users are superposed bysuperposition coding e successive interference cancella-tion (SIC) technique is applied to extract the intendedmessage in the receiver side Security is always an importantissue for wireless networks since the broadcast nature ofwireless radio propagation makes it easily be overheard byeavesdroppers

11 RelatedWorks Recently NOMAhas received remarkableattention both in the world of academia and industry [4ndash6]Power-domain NOMA has been proposed for the 3GPP long-term evolution initiative in [4] e authors in [5] investigated

the performance of NOMA in a cellular downlink scenariowith randomly deployed users It was shown that NOMA canachieve superior ergodic sum rate performance than traditionalorthogonal multiple access (OMA) counter parts Challengesopportunities and future research trends for NOMA designare highlighted to provide some insight into the potentialfuture work of researchers in [6] e security performance ofthe NOMA networks can be improved by invoking the pro-tected zone and by generating noise at the BS as shown by Liuet al [7] e physical layer security of uplink nonorthogonalmultiple access is analyzed by Gerardo Gomez et al [8] Tao etal [9] proposed a new reliable physical layer network codingand cascade-computation decoding scheme e authors in[10] proposed an opportunistic multiple-jammer selectionscheme for enhancing the physical layer security e authorsin [11] studied the security-reliability tradeocent analysis forconventional single-hop networks under a single passiveeavesdropper attack e authors in [12] enhanced physicallayer security for downlink heterogeneous networks by usingfriendly jammers and full-duplex users Recently stochasticgeometry has been used to model some network such as large-scale HET wireless networks [10] massive MIMO-enabledHetNets [14] cognitive cellular wireless networks [15]

HindawiSecurity and Communication NetworksVolume 2019 Article ID 7869317 9 pageshttpsdoiorg10115520197869317

multitier millimeter wave cellular networks [16] and NOMAnetwork [17] It has been succeeded to develop tractablemodelsto characterize and better understand the performance of thesenetworks and these models have been shown to providetractable yet accurate performance bounds for these networks

12 Motivations and Contributions In this paper we in-vestigate the physical layer security of NOMA with friendlyjammers and multiple noncolluding eavesdroppers (EVEs)in large-scale networks with stochastic geometry For thesake of easy deployment all nodes in NOMA wirelessnetwork are equipped with single antenna and eaves-droppers are randomly distributed along the whole planee jammers are assumed to transmit friendly artificialnoise To enhance the physical layer security two schemesare proposed with jointing jammers in NOMA network Inorder to alleviate the interference from jammers to sched-uled users a jammer selection policy is discussed based onthe received jamming power at the user When the jammerpower is below a threshold the jammer around thescheduled user is active otherwise the jammer is idleUnlike the scheme in [7 8] the security performance of theNOMAnetworks can be improved by generating noise at theBS in [7] and physical layer security in uplink NOMA isdiscussed in [8] In this paper friendly jammers will bejointed which can enhance the physical layer security indownlink NOMA wireless network e main contributionsof this paper are summarized as follows

(1) Two physical layer security schemes are proposedwhere friendly jammers are jointed in NOMAwireless network Jammers transmit friendly artifi-cial noise A jammer selection policy is discussedbased on the received jamming power at user

(2) Using stochastic geometry tools the downlinkNOMA performance is analyzed in terms of outageprobability and secrecy probability In particular theBSs and user positions are model Poisson pointprocess (PPP) on a 2-D plane e active jammerpositions are model Poisson hole process

(3) All the analytical results are validated by system-levelsimulations Our proposed schemes provide a bettersecurity performance compared with the traditionalscheme

e rest of the paper is organized as follows In Section 2we introduce the system model In Section 3 the outageprobability performance of proposed schemes is in-vestigated In Section 4 the user secrecy probability per-formance of proposed schemes is investigated In Section 5numerical simulation and analysis are discussed to verifythese results A conclusion is drawn in Section 6

Notation the expectation of function f(x) with respectto x is denoted as E[f(x)] Cumulative distribution functionof f(x) is denoted as Ff( )e Laplace transform of f(x) isdenoted by Lf(s) An exponential distributed randomvariable with mean 1 is denoted by x sim exp(1) Let I1 be a setand I2 be a subset of I1 then I1I2 denotes the set of el-ements of I1 that do not belong to I2

2 System Model

In this paper we consider a dense multicell NOMAdownlink wireless network in presence of eavesdroppers(EVEs) as shown in Figure 1 All BSs users and EVEs areequipped with one antenna e BS locations are distrib-uted as an independent homogeneous PPP ΦB with densityλB in two-dimensional plane Without loss of generalitythe analysis is performed in a typical cell denoted as BS0Based on Slivnyakrsquos eorem due to stationarity of ΦB thetypical cell can reflect the averaged performance of theentire system e system assumes a frequency reuse factor1 hence the same frequency resources are used in all cellse radio resources are partitioned into a number ofsubbands We assume the bandwidth of each subband isnormalized to 1 e UE and EVE locations are distributedas an independent homogeneous PPP ΦU and ΦE withdensities λU and λE respectively In this paper the NOMAgroup includes two users Existing results have shown thatthe NOMA group with more than two UEs may provide abetter performance gain [18] In order to process the SICeasily two user NOMA networks are more practical in thereality system UE1 and UE2 consist of a NOMA group Weassume λU≫ λB so that a sufficient number of UEs canalways be found to form the NOMA group in each cell Toenhance the security performance friendly jammers arejointed in NOMA network In the selective jammer schemea jammer is selected to be active if its interference power tothe scheduler user is below a threshold Actually thethreshold is the jammer exclusion zone around thescheduler user ie ΦJS j | j isin ΦJ PJRminus a

jUiltPJDminus a1113966

forallUi isin ΦUs1113967 ΦJS is the Poisson hole process of active

jammer ΦUsdenotes the point process of scheduled users

ΦUsis an inhomogeneous PPP for which the density is λUs

Rminus a

jUiis the distance between the jammer and scheduled

users D is the exclusion zone radius PJ is denoted as thetransmit power of the jammer a is the pathloss exponentPb is the total power of BS on a subband in downlinkNOMA e allocated powers of UE1 and UE2 can bedenoted as P1 εPb and P2 (1 minus ε)Pb respectively whereε isin (0 05) is a NOMA power allocation parameter UE1 isassumed to be with a better normalized channel gain UE2is assumed to be with a worse normalized channel gain etwo users are selected randomly in NOMA network PJ

denotes the power of jammer BS-transmitted signals toUE1 and UE2 are expressed as x1 and x2 respectively SinceUE1 and UE2 form a NOMA group x1 and x2 are encodedas the composite signal at the BS0 [12]

x P1

1113968x1 +

P2

1113968x2 (1)

e received signal at UEi i isin 1 2 can be expressed as

yi

hirminus ai

1113969

x + ni (2)

where hi is the Rayleigh fading gain between BS0 and UEiwhich follows an exponential distribution with mean 1 Allhi are assumed to be iid ri is the distance between BS0 andUEi ni is the additive noise

2 Security and Communication Networks

3 NOMA User Outage Probability

We assume UE1 has a better channel condition At thereceiver side successive interference cancellation (SIC) isused to decode the intended message UE1 first decodes theUE2 signal x2 and removes it from the received compositesignal after that UE1 can further decode its signal x1 UE2decodes x2 directly by treating x1 as interference Weconsider the possible SIC error propagation which is causedby decoding unsuccessfully in the first step and thus error iscarried over to the next-level decoding Let β be the fractionof NOMA interference due to SIC error propagation Noisecan be safely neglected in a dense interference limitedwireless systeme signal to interference ratio (SIR) of UE1can be represented as SIRU1

((P1h1rminus a1 )(IB1

+ IJS1+ IW1

))where IB1

1113936jisinΦBBS0Pbg1jRminus a1j

denotes the cumulativedownlink intercell interference from the all other cells andIJS1

1113936yisinΦJSPjh1yRminus a1y

denotes cumulative downlink in-terference from the selected jammers IW1

βP2h1rminus a1 de-

notes the interference from SIC error propagation g1j is theRayleigh fading an exponential distribution with mean 1g1j sim exp(1) ΦBBS0 represents the set of all BSs excludingBS0

e achievable rate of UE1 on each subband in NOMAnetwork is given as

τ1 log 1 + SIRU11113872 1113873

log 1 +c1P1

βc1P2 + 11113888 1113889

(3)

where c1 ((h1rminus a1 )(IB1

+ IJS1)) is the UE1 channel gain

including pathloss and fast fading normalized by two kindsof interferences e signal to interference ratio of UE2 canbe represented as SIRU2

((P2rminus a2 h2)(IB2

+ IJS2+ P1r

minus a2 h2))

where IB2 1113936jisinΦBBS0Pbg2jRminus a

2jis the cumulative downlink

intercell interference from all the other cellsIJS2

1113936yisinΦJSPJh2yRminus a2y

denotes cumulative downlink in-terference from the selective jammers P1r

minus a2 h2 is the in-

terference from UE1e achievable rate of UE2 on each subband in NOMA

network is given as

τ2 log 1 + SIRU21113872 1113873

log 1 +c2P2

c2P1 + 11113888 1113889

(4)


+ IJS2)) We assume that two users

are randomly selected among all scheduled users Two usersare marked as UEn and UEm e normalized channel gainsof UEn and UEm are denoted as cn and cm respectively LetUE1 UEi | UEi isin UEn UEm1113864 1113865 ci max(cn cm)11138651113864 and U

E2 UEi | UEi isin UEn UEm1113864 1113865 ci min(cn cm)11138651113864 z max(x y) andϖ min(x y) e CDF of z and ϖ can berepresented as Fz(z) Fxy(z z) Fϖ(ϖ) Fx(ϖ) + Fy

(ϖ) minus Fxy(ϖϖ) [18]us CDFs of c1 and c2 can be derivedas follows

Fc1(C) Fcncm

(C C) Fc(C)2 (5)

Fc2(C) Fcn

(C) + Fcm(C) minus Fcncm

(C C)

2Fc(C) minus Fc(C)2

(6)

where Fc(C) 1 minus P(cgtC) and P(cgtC) denotes theprobability of cgtC According to (5) and (6) Fc1

(C) andFc2

(C) can be given as (7) and (8) respectively

Fc1(C) Fc(C)

2 (1 minus P(cgtC))

2 (7)

Fc2(C) 2Fc(C) minus Fc(C)

2

2(1 minus P(cgtC)) minus (1 minus P(cgtC))2

(8)

For a given normalized channel gain to UE1 or UE2 c

((hirminus ai )(IB + IJS)) and P(cgtC) can be derived as follows

P(cgtC) EriP(cgtC) | ri1113858 1113859

1113946ri gt 0

Phir

minus αi

IB + IJS

gtC | ri1113888 1113889f ri( 1113857dri

1113946ri gt 0

EIBIJSexp minus Cr

αi IB + IJS1113872 11138731113872 11138731113960 1113961f ri( 1113857dri

1113946ri gt 0

LIBCr

αi( 1113857LIJS

Crαi( 1113857f ri( 1113857dri

(9)

In (9) the second term follows from hi sim exp(1) [13]e Laplace transform of IB is given by

Signal to userSignal to EVEInterference to userInterference to EVE

UE1

UE2D

D

Base station

Scheduled user

EVE

Selected jammer

Idle jammer

Figure 1 NOMA wireless network with the selected jammer

Security and Communication Networks 3

LIB(s) EΦBg minus exp minus s 1113944

jisinΦBBS0gijR

minus aj PB

⎛⎝ ⎞⎠⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

exp minus 2πλB 1113946infin

ri

1 minus1

1 + svminus aPB

1113888 1113889vdv1113888 1113889

exp minus 2πλB sPB( 1113857δ

1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889

(10)

where δ 2ae Laplace transform of IJS is given by

LIJS(s) EΦJSh minus exp minus s 1113944

jisinΦJS

hijRminus aij PJ

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB UEiD( )

LhijsR

minus aij PJ1113872 1113873⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠

(a) EΦJ

exp minus λJ1113946jisinΦJB UEiD( )

1 minus LhijsPJx

minus a1113872 1113873dx1113874 11138751113888 11138891113888 1113889

asymp(b)exp minus 2πλJD

2minus aPJs(a minus 2)

minus 12F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889

(11)

In step (a) B(UEi D) is a hole of radius D centered atUEiΦJB(UEi D) denotes the active jammers location andΦJ is the jammer baseline PPP from which the hole is carvedout In step (b) we only discuss the hole around the UEi estep (b) follows from the probability generating functional ofPPP [13] where 2F1(a b c d) is the Gauss hypergeometricfunction

When all jammers are active without jammer selection(NO JS scheme) δ (2a) LINOJS

(s) denotes the Laplacetransform of interference from all jammers without selectionto UEi in NO JS scheme We can derive LINOJS

(s) as [13]

LINOJS(s) exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ (12)

By plugging (10) and (11) into (9) P(cgtC) with jammerselection in NOMA network is given as

P(cgtC) 1113946ri gt 0


1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889

times exp minus 2πλJD2minus a

PJs(a minus 2)minus 1

times 2F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889

times 2πλBriexp minus πλBr2i1113872 1113873dri

11138681113868111386811138681113868sCrαi

(13)

When a 4


exp⎡⎣ minus 2πλBr2i CPB( 1113857

12

middotπ2

minus arctan1

CPB( 111385712

⎛⎝ ⎞⎠⎛⎝ ⎞⎠⎤⎦

times exp minus πλJDminus 2

PJCr4i 2F1 1 05 15 minus

Cr4i PJ

D41113888 11138891113888 1113889


(14)

e outage probability of UE1 with jammer selection inNOMA network can be evaluated as follows

P1 τ1 τ2( 1113857 1 minus P τ1 gt τ1 τ1⟶2 gt τ2( 1113857

1 minus Pc1P1

βc1P2gt c1

c1P2

c1P1 + 1gt c21113888 1113889

1 if c1 geP1

βP2or c2 ge

P2

P1

Fc1max θ1 θ2( 1113857( 1113857 otherwise

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(15)

where P(τ1 gt τ1 τ1⟶2 gt τ2) denotes the connection prob-ability of UE1 c1 and c2 denote the SIRs of UE1 and UE2respectively c1 2τ1 minus 1 and c2 2τ2 minus 1 τ1 and τ2 are thetarget rate thresholds for UE1 and UE2 respectively τ1⟶2 isthe rate of decoding UE2 signal x2 in the UE1 receiver whichmust be greater than the QoS requirement of UE2 τ1⟶2 gt τ2can ensure that UE1 is able to remove UE2rsquos signal frominterferenceθ1 (c1(p1 minus c1βP2)) and θ2 (c2(p2 minus c2P1)) Plug-ging max(θ1 θ2) into (7) we get Fc1

(max(θ1 θ2)) in (15)e outage probability of UE2 with jammer selection in

NOMA network can be evaluated as follows

P2 τ2 le τ2( 1113857

0 if c2 geP2

P1

Fc2θ2( 1113857 otherwise

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(16)

Taking θ2 into (8) we can easily getFc2(θ2) as shown in (16)

4 NOMA User Secrecy Probability

We investigate the secrecy probability of a randomly locatedNOMA user In this work the user secrecy probabilitycorresponds to the probability that a secret message for theschedule user cannot be decoded by any noncolludingeavesdroppers because UE1rsquos and UE2rsquos signals are derivedby eavesdroppers in the similar way Here we only discussthe secrecy performance of UE1 Hence the secrecy prob-ability can be expressed as


PSec cs( 1113857 P maxxisinΦe

SIR(x)lt cs1113888 1113889

P capxisinΦe

SIR(x) lt cs1113888 1113889

E 1113945xisinΦe

P SIR(x) lt cs | x( 1113857⎛⎝ ⎞⎠

EΦe1113945xisinΦe

1 minus exp minus Pminus 11 csr

axIE(x)1113872 11138731113872 1113873⎛⎝ ⎞⎠

exp minus 2πλe 1113946infin

0LIE(x) P

minus 11 csr

ax1113872 1113873rxdrx1113874 1113875

(17)

where SIR(x) of the typical EVE is given by

SIR(x) P1hxrminus a

x

IB⟶E + IJS⟶E

(18)

where cs is the target secrecy SIR hx is the Rayleigh fadinggain between BS0 and EVE and hx follows an exponentialdistribution with mean 1 rx is the distance between BS0 andEVE LIE

(s) LIB⟶E(s)LIJS⟶E

(s) where LIB⟶E(s) and

LIJS⟶E(s) denote the Laplace transform of IB⟶E and IJS⟶E

respectively IB⟶E is the interference from the other cell BSsto EVE IJS⟶E is the interference from the selective jammersto EVE e detailed derivation of LIJS⟶E

(s) is provided inAppendix A We can derive the following

LIE(s) LIB⟶E

(s)LIJS⟶E(s)

exp minusπs2Pδ

1λB

sinc(δ)1113888 1113889exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠

times 1113946infin

0H(v s)g(v)dv

(19)

Inserting (19) into (17) we can easily have the expressionof PSec(cs)

When all jammers are active without jammer selectionLIE

(s) is given by

LIE(s) LIB⟶E

(s)LIJ⟶E(s)

exp minus πλB

sP1( 1113857δ

sinc(δ)⎛⎝ ⎞⎠exp minus πλJ

sPJ1113872 1113873δ


(20)

5 Simulation Results and Discussion

In this section we present Monte Carlo simulations toevaluate the performance of the proposed scheme andanalytical results are illustrated and validated with extensivesimulations in NOMA network e default parameters arelisted in Table 1 unless otherwise stated

Our first proposed scheme is that all jammers areactive without jammer selection in NOMA networkwhich is marked as ldquoNO JS schemerdquo Our second proposed

scheme is that some jammers are active with jammerselection in NOMA network which is marked ldquoJSschemerdquo ere are no jammers in the traditional schemein NOMA network As expected our proposed schemesprovide a better security performance compared with thetraditional schemee JS scheme provides a good balancebetween the user outage probability and the user secrecyprobability Figure 2 shows UE1 outage probabilityP1(τ1 τ2) and UE2 outage probability P2(τ2 le τ2) versusdifferent target rates τ1 where τ2 is fixed to 01 bitsssubband

In Figure 2 ldquoanardquo (the dashed curves) and ldquosimrdquo (thecurves with circle marks) are the abbreviation of analysis andsimulation respectively ldquoUE1 NO JS anardquo denotes theanalytical result of UE1 outage probability using the firstproposed scheme where all jammers are active ldquoUE1 NO JSsimrdquo denotes the simulation result of UE1 outage proba-bility ldquoUE1 JS anardquo denotes the analytical result of UE1 inthe second proposed scheme where some selective jammersare active From Figure 2 we can observe that the analyticalresults match well with the simulation results which validatethe accuracy of the analysis

In Figure 2 all jammers are active in the first proposedscheme Jammers transmit artificial noise to legitimateNOMA users and the eavesdroppers While transmittingnoise to eavesdroppers the jammer also transmits artificialnoise to legitimate NOMA users in the proposed schemee noise is the interference for NOMA users When theinterference increases the SIR decreases Compared with thetraditional scheme without jointing the jammer the outageprobability increases in our proposed scheme with jointingjammers in NOMA network Compared to the first schemethe outage probability decreases for the selective jammerscheme In other words the user connective performanceimproves In Figure 2 we can see that P1(τ1 τ2) remainsconstant when τ1 le 004 bitssubbandis is due to the factthat UE1 needs to decode the signal intended to UE2 firstbefore it can decode the signal for itself When τ1 is below004 the outage is always remained by failing to decode UE2signal e result also can be explained by the definition ofoutage probability of UE1P1(τ1 τ2) 1 minus P1(τ1 gt τ1τ1⟶2 gt τ2) P1(τ1 τ2) is related to τ1 and τ2 If τ2 is fixedwhen τ1 is quite small τ1⟶2 gt τ2 can guarantee τ1 gt τ1 andP1(τ1 gt τ1 τ1⟶2 gt τ2) becomes P1(τ1⟶2 gt τ2) soP1(τ1 τ2) is not a function of τ1 and it remains constant

Table 1 Parameter assumptions

Parameter Meaning Default valueλB Density of BS 1km2

λJ Density of jammer 10km2

λE Density of eavesdropper 11km2

λU Density of user 100km2

PB Transmission power of BS 46 dBmPJ Transmission power of jammer 23 dBmε NOMA power allocation parameter 03α Pathloss exponent 4D Jammer exclusion circle radius 01 km


when τ1 is quite small When τ1 gt 004 the outage proba-bility reduces as τ1 increases P2(τ2 le τ2) remains constant asτ1 increases due to the fact that P2(τ2 le τ2) is not a functionof τ1

Figure 3 shows the outage probability of UE1 and UE2when τ1 is fixed to τ1 01 bitssubband We can observeP1(τ1 τ2) remains constant at first and then increases inthe same way as shown in Figure 2 When τ2 is smallP1(τ1 τ2) is only a function of τ1 which is not affected byτ2 As τ2 continues to increase both τ1 and τ2 will affectP1(τ1 τ2)

Figure 4 shows that outage probability of UE1 in threeschemes versus τ1 with different ε in NOMA network eallocation power of UE1 increases as ε increases we can seethat while ε increases in these schemes P1(τ1 τ2) does notnecessarily decrease is outcome can be explained thatmore transmit power allocated to UE1 also means less powerallocated to UE2 so it is difficult for UE1 to decode UE2signal x2 But the lower bound of outage probability of UE1can be improved which is related by successfully decodingUE2rsquos signal x2

Figure 5 shows that UE2 outage probability of threeschemes versus τ2 with different ε in NOMA network Wecan observe that the outage probability decreases whsen ε isdecreasing from 05 to 03 is is because more powerallocated to UE2 will result in a better outage performance ofUE2

Figure 6 shows the impact of imperfect SIC of threeschemes with different β From the SIR of UE1((c1P1)(βc1P2 + 1)) we can see SIR decreases as β in-creases When β 002 compared to perfect SIC β 0 theoutage probability of UE1 increases

Figure 7 shows that the UE1 secrecy probability of ourproposed scheme versus SIR threshold cs with different Dexclusion zone radii We can see that our proposedscheme has a better performance than the traditionalscheme in secrecy probability in NOMA network ldquoNO JSschemerdquo will obtain the highest secrecy probability Butthe outage probability of ldquoNO JS schemerdquo is the worstSecrecy probability of ldquoJS schemerdquo with small jammer

τ1 (bitsssubband)

τ2 is fixed to 01 bitsssubband

0

01

02

03

04

05

06

Out

age p

roba

bilit

y

UE1 NO JS anaUE1 NO JS simUE2 NO JS anaUE2 NO JS simUE1 traditional anaUE1 traditional sim

UE1 JS anaUE1 JS simUE2 traditional anaUE2 traditional simUE2 JS anaUE2 JS sim

0 01 02 03 04 05 06

Figure 2 Outage probability of NOMA when τ2 is fixed to 01 bitsssubband

τ2 (bitsssubband)

UE1 NO JS anaUE1 NO JS simUE2 NO JS anaUE2 NO JS anaUE1 traditional anaUE1 traditional sim


0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y



UE1 NO JS anaUE1 traditional anaUE1 JS ana


ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y

Figure 4 Outage probability of UE1 three schemes versus τ1 withdifferent ε in NOMA network


exclusion zone is better When the exclusion zone radiusincreases the small jammers transmit noise to interferethe eavesdropper so secrecy probability decrease Ourproposed jammer selection scheme provides a good bal-ance between the user outage probability and secrecyprobability

Figure 8 compares the connection probability per-formance of UE1 versus jammer density λJ We can ob-serve that simply deploying more jammers cannotenhance the connection probability When jammer den-sity λJ increases the connection probability of JS schemeincreases But the connection probability of NO JS scheme

decreases as λJ increases e connection probability oftraditional scheme without jointing jammer remainsconstant is is because the jammers whose interferenceon any scheduled user is stronger than a threshold areprevented from being active When λJ increases there aremore jammers around the eavesdropper but the in-terference level suffered by the legitimate user fromjammers is mitigated and the interference level remainslow in the jammer selection scheme When λJ 0 theperformance is the same between our proposed schemesand the traditional scheme

UE2 NO JS ε = 05 UE2 traditional ε = 05UE2 JS ε = 05

UE2 NO JS ε = 03UE2 traditional ε = 03UE2 JS ε = 03

τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y


Figure 5 Outage probability of UE2 in three schemes versus τ2with different ε in NOMA network

UE1 NO JS β = 0UE1 traditional β = 0UE1 JS β = 0


τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y


Figure 6e impact of imperfect SIC of three schemes on NOMAwith different β

SIR threshold γs (dB)

0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty

Traditional schemeProposed NO JS scheme

Proposed JS schemeD = 01kmProposed JS schemeD = 015km

ndash10 ndash8 ndash6 ndash4 ndash2 0 2 4 6 8 10

Figure 7 e UE1 secrecy probability versus SIR threshold cs

Density λJ (jammerkm2)

015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty

Proposed NO JS schemeProposed JS schemeTraditional scheme

100 20 30 40 50 60

Figure 8 e connection probability performance of UE1 versusjammer density λJ in three schemes


6 Conclusion

is paper analyzes the outage and secrecy performances ofNOMA network using stochastic geometry theory eanalytical expressions of outage and secrecy probabilities arederived Compared with the ldquoNO JS schemerdquo and traditionalscheme (without jointing jammer) the jammer selectionscheme provides a good balance between the user outageprobability and secrecy probability Simulation results showthat the expressions can provide sufficient precision toevaluate the system performance We can optimize jammerselection exclusion zone radius and NOMApower allocationto realize a secrecy transmission in future study

Appendix

A Derivation of LIJS⟶E(s)

To derive the LIJS⟶ E(s) we use the approach in [20] (see

Figure 9)Point-p is the closest hole location to the EVE as in [20]

V is the distance between the jammer and EVE Y and v havea cosine-law relation D2 y2 + v2 minus 2yvcos(θ) LIJS⟶ E

(s)

can be given as

LIJS⟶E(s) EΦJSh minus exp minus s 1113944

jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ


times Ep exp λJ 1113946

B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv

(A1)In step copy Rej y denotes the distance between selective

jammers with EVE e final step follows from the proba-bility-generating functional of PPP [13 19] and cosine-law

D2 y2 + v2 minus 2yvcos(θ) and some geometry derivation[20]

H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1

dy⎛⎝ ⎞⎠ vgtD

exp πλJ(D minus v)22F1 1 1 minus2a

1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889

times exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1

dy⎛⎝ ⎞⎠ vleD

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where

λJe(y) λJarccosy2 + v2 minus D2

2yv1113888 1113889 (A3)

g(v) 2πλUsrx v( 1113857vexp minus 2π 1113946

v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)

λUsrx v( 1113857 λB 1 minus exp minus π rx + y( 1113857

2λB1113872 11138731113872 1113873 (A5)

is completes the proof

Data Availability

e data that support the findings of this study are availablefrom the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported by the Natural Science Foundationof China (Grant nos 61801006 and 61603003) Key Labo-ratory of Intelligent Perception and Computing of AnhuiProvince Anqing Normal University China Key Project onAnhui Provincial Natural Science Study by Colleges andUniversities (Grant nos KJ2017A356 and KJ2018A0361)and Natural Science Foundation of Anhui Province (Grantnos 1608085 and 1908085MF194)

Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)

Figure 9 Illustration of the closest jammer hole to the eavesdropper (a) VleD (b) vltD


References

[1] B Dai Z Ma Y Luo X Liu Z Zhuang and M XiaoldquoEnhancing physical layer security in internet of things viafeedback a general frameworkrdquo IEEE Internet of 4ingsJournal p 1 2019

[2] Z Wang R F Schaefer M Skoglund M Xiao andH V Poor ldquoStrong secrecy for interference channels based onchannel resolvabilityrdquo IEEE Transactions on Information4eory vol 64 no 7 pp 5110ndash5130 2018

[3] B Dai Z Ma M Xiao X Tang and P Fan ldquoSecure com-munication over finite state multiple-access wiretap channelwith delayed feedbackrdquo IEEE Journal on Selected Areas inCommunications vol 36 no 4 pp 723ndash736 2018

[4] J Chen Y Liang and M S Alouini ldquoPhysical layer securityfor cooperative NOMA systemsrdquo IEEE Transactions on Ve-hicular Technology vol 67 no 5 pp 4645ndash4649 2018

[5] Z Ding Z Yang P Fan and H V Poor ldquoOn the perfor-mance of non-orthogonal multiple access in 5G systems withrandomly deployed usersrdquo IEEE Signal Processing Lettersvol 21 no 12 pp 1501ndash1505 2014

[6] L Dai B Wang Y Yuan S Han C-l I and Z Wang ldquoNon-orthogonal multiple access for 5G solutions challengesopportunities and future research trendsrdquo IEEE Communi-cations Magazine vol 53 no 9 pp 74ndash81 2015

[7] Y Liu Z Qin M Elkashlan Y Gao and L Hanzo ldquoEn-hancing the physical layer security of non-orthogonal mul-tiple access in large-scale networksrdquo IEEE Transactions onWireless Communications vol 16 no 3 pp 1656ndash1672 2017

[8] G Gomez F J Martin-Vega F Javier Lopez-Martinez Y Liuand M Elkashlan ldquoPhysical layer security in uplink NOMAmulti-antenna systems with randomly distributed eaves-droppersrdquo IEEE Access vol 7 pp 70422ndash70435 2019

[9] Y Tao Y Lei Y J Guo et al ldquoA non-orthogonal multiple-access scheme using reliable physical-layer network codingand cascade-computation decodingrdquo IEEE Transactions onWireless Communications vol 16 no 3 pp 1633ndash1645 2017

[10] C Wang and H M Wang ldquoOpportunistic jamming forenhancing security stochastic geometry modeling and anal-ysisrdquo IEEE Transactions on Vehicular Technology vol 65no 12 pp 10213ndash10217 2016

[11] A H Abdel-Malek A M Salhab S A Zummo et al ldquoPowerallocation and cooperative jamming for enhancing physicallayer security in opportunistic relay networks in the presenceof interferencerdquo Transactions on Emerging Telecommunica-tions Technologies vol 28 no 11 p e3178 2017

[12] W Tang S Feng Y Ding et al ldquoPhysical layer security inheterogeneous networks with jammer selection and full-du-plex usersrdquo IEEE Transactions on Wireless Communicationsvol 16 no 12 pp 7982ndash7995 2017

[13] H S Jo Y J Sang P Xia et al ldquoHeterogeneous cellularnetworks with flexible cell association a comprehensivedownlink SINR analysisrdquo IEEE Transactions on WirelessCommunications vol 11 no 10 pp 3484ndash3495 2011

[14] A He L Wang M Elkashlan et al ldquoSpectrum and energyefficiency in massive MIMO enabled HetNets a stochasticgeometry approachrdquo IEEE Communications Letters vol 19no 12 pp 2294ndash2297 2015

[15] H Elsawy E Hossain and M Haenggi ldquoStochastic geometryfor modeling analysis and design of multi-tier and cognitivecellular wireless networks a surveyrdquo IEEE CommunicationsSurveys Tutorials vol 15 no 3 pp 996ndash1019 2013

[16] M D Renzo ldquoStochastic geometry modeling and analysis ofmulti-tier millimeter wave cellular networksrdquo IEEE

Transactions on Wireless Communications vol 14 no 9pp 5038ndash5057 2015

[17] Y Sun Z Ding X Dai et al ldquoOn the performance of networkNOMA in uplink CoMP systems a stochastic geometry ap-proachrdquo 2018 httparxivorgabs180300168

[18] Z Zhang H Sun and R Q Hu ldquoDownlink and uplink non-orthogonal multiple access in a dense wireless networkrdquo IEEEJournal on Selected Areas in Communications vol 35 no 12pp 2771ndash2784 2017

[19] M Haenggi Wireless Security and Cryptography Specifica-tions and Implementations Cambridge University PressCambridge UK 2012

[20] Z Yazdanshenasan H S Dhillon M Afshang andP H J Chong ldquoPoisson hole process theory and applicationsto wireless networksrdquo IEEE Transactions on Wireless Com-munications vol 15 no 11 pp 7531ndash7546 2016


International Journal of

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Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Journal of



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SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Submit your manuscripts atwwwhindawicom

multitier millimeter wave cellular networks [16] and NOMAnetwork [17] It has been succeeded to develop tractablemodelsto characterize and better understand the performance of thesenetworks and these models have been shown to providetractable yet accurate performance bounds for these networks

12 Motivations and Contributions In this paper we in-vestigate the physical layer security of NOMA with friendlyjammers and multiple noncolluding eavesdroppers (EVEs)in large-scale networks with stochastic geometry For thesake of easy deployment all nodes in NOMA wirelessnetwork are equipped with single antenna and eaves-droppers are randomly distributed along the whole planee jammers are assumed to transmit friendly artificialnoise To enhance the physical layer security two schemesare proposed with jointing jammers in NOMA network Inorder to alleviate the interference from jammers to sched-uled users a jammer selection policy is discussed based onthe received jamming power at the user When the jammerpower is below a threshold the jammer around thescheduled user is active otherwise the jammer is idleUnlike the scheme in [7 8] the security performance of theNOMAnetworks can be improved by generating noise at theBS in [7] and physical layer security in uplink NOMA isdiscussed in [8] In this paper friendly jammers will bejointed which can enhance the physical layer security indownlink NOMA wireless network e main contributionsof this paper are summarized as follows

(1) Two physical layer security schemes are proposedwhere friendly jammers are jointed in NOMAwireless network Jammers transmit friendly artifi-cial noise A jammer selection policy is discussedbased on the received jamming power at user

(2) Using stochastic geometry tools the downlinkNOMA performance is analyzed in terms of outageprobability and secrecy probability In particular theBSs and user positions are model Poisson pointprocess (PPP) on a 2-D plane e active jammerpositions are model Poisson hole process

(3) All the analytical results are validated by system-levelsimulations Our proposed schemes provide a bettersecurity performance compared with the traditionalscheme

e rest of the paper is organized as follows In Section 2we introduce the system model In Section 3 the outageprobability performance of proposed schemes is in-vestigated In Section 4 the user secrecy probability per-formance of proposed schemes is investigated In Section 5numerical simulation and analysis are discussed to verifythese results A conclusion is drawn in Section 6

Notation the expectation of function f(x) with respectto x is denoted as E[f(x)] Cumulative distribution functionof f(x) is denoted as Ff( )e Laplace transform of f(x) isdenoted by Lf(s) An exponential distributed randomvariable with mean 1 is denoted by x sim exp(1) Let I1 be a setand I2 be a subset of I1 then I1I2 denotes the set of el-ements of I1 that do not belong to I2

2 System Model

In this paper we consider a dense multicell NOMAdownlink wireless network in presence of eavesdroppers(EVEs) as shown in Figure 1 All BSs users and EVEs areequipped with one antenna e BS locations are distrib-uted as an independent homogeneous PPP ΦB with densityλB in two-dimensional plane Without loss of generalitythe analysis is performed in a typical cell denoted as BS0Based on Slivnyakrsquos eorem due to stationarity of ΦB thetypical cell can reflect the averaged performance of theentire system e system assumes a frequency reuse factor1 hence the same frequency resources are used in all cellse radio resources are partitioned into a number ofsubbands We assume the bandwidth of each subband isnormalized to 1 e UE and EVE locations are distributedas an independent homogeneous PPP ΦU and ΦE withdensities λU and λE respectively In this paper the NOMAgroup includes two users Existing results have shown thatthe NOMA group with more than two UEs may provide abetter performance gain [18] In order to process the SICeasily two user NOMA networks are more practical in thereality system UE1 and UE2 consist of a NOMA group Weassume λU≫ λB so that a sufficient number of UEs canalways be found to form the NOMA group in each cell Toenhance the security performance friendly jammers arejointed in NOMA network In the selective jammer schemea jammer is selected to be active if its interference power tothe scheduler user is below a threshold Actually thethreshold is the jammer exclusion zone around thescheduler user ie ΦJS j | j isin ΦJ PJRminus a

jUiltPJDminus a1113966

forallUi isin ΦUs1113967 ΦJS is the Poisson hole process of active

jammer ΦUsdenotes the point process of scheduled users

ΦUsis an inhomogeneous PPP for which the density is λUs

Rminus a

jUiis the distance between the jammer and scheduled

users D is the exclusion zone radius PJ is denoted as thetransmit power of the jammer a is the pathloss exponentPb is the total power of BS on a subband in downlinkNOMA e allocated powers of UE1 and UE2 can bedenoted as P1 εPb and P2 (1 minus ε)Pb respectively whereε isin (0 05) is a NOMA power allocation parameter UE1 isassumed to be with a better normalized channel gain UE2is assumed to be with a worse normalized channel gain etwo users are selected randomly in NOMA network PJ

denotes the power of jammer BS-transmitted signals toUE1 and UE2 are expressed as x1 and x2 respectively SinceUE1 and UE2 form a NOMA group x1 and x2 are encodedas the composite signal at the BS0 [12]

x P1

1113968x1 +

P2

1113968x2 (1)

e received signal at UEi i isin 1 2 can be expressed as

yi

hirminus ai

1113969

x + ni (2)

where hi is the Rayleigh fading gain between BS0 and UEiwhich follows an exponential distribution with mean 1 Allhi are assumed to be iid ri is the distance between BS0 andUEi ni is the additive noise





+ IJS1+ IW1

))where IB1





βP2h1rminus a1 de-



τ1 log 1 + SIRU11113872 1113873

log 1 +c1P1

βc1P2 + 11113888 1113889

(3)





+ IJS2+ P1r

minus a2 h2))








network is given as

τ2 log 1 + SIRU21113872 1113873

log 1 +c2P2

c2P1 + 11113888 1113889

(4)






Fc1(C) Fcncm

(C C) Fc(C)2 (5)

Fc2(C) Fcn


(C C)

2Fc(C) minus Fc(C)2

(6)


(C) andFc2


Fc1(C) Fc(C)

2 (1 minus P(cgtC))

2 (7)


2


(8)




1113946ri gt 0

Phir

minus αi

IB + IJS

gtC | ri1113888 1113889f ri( 1113857dri

1113946ri gt 0

EIBIJSexp minus Cr

αi IB + IJS1113872 11138731113872 11138731113960 1113961f ri( 1113857dri

1113946ri gt 0

LIBCr

αi( 1113857LIJS

Crαi( 1113857f ri( 1113857dri

(9)



UE1

UE2D

D

Base station

Scheduled user

EVE

Selected jammer

Idle jammer




jisinΦBBS0gijR

minus aj PB

⎛⎝ ⎞⎠⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦


ri

1 minus1

1 + svminus aPB

1113888 1113889vdv1113888 1113889


1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889

(10)



jisinΦJS

hijRminus aij PJ

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB UEiD( )

LhijsR

minus aij PJ1113872 1113873⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠

(a) EΦJ


1 minus LhijsPJx

minus a1113872 1113873dx1113874 11138751113888 11138891113888 1113889



minus 12F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889

(11)




(s) as [13]


sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ (12)




1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889



times 2F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889


11138681113868111386811138681113868sCrαi

(13)

When a 4



12

middotπ2

minus arctan1

CPB( 111385712

⎛⎝ ⎞⎠⎛⎝ ⎞⎠⎤⎦



Cr4i PJ

D41113888 11138891113888 1113889


(14)



1 minus Pc1P1

βc1P2gt c1

c1P2

c1P1 + 1gt c21113888 1113889

1 if c1 geP1

βP2or c2 ge

P2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(15)




P2 τ2 le τ2( 1113857

0 if c2 geP2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(16)






SIR(x)lt cs1113888 1113889

P capxisinΦe

SIR(x) lt cs1113888 1113889

E 1113945xisinΦe

P SIR(x) lt cs | x( 1113857⎛⎝ ⎞⎠

EΦe1113945xisinΦe


axIE(x)1113872 11138731113872 1113873⎛⎝ ⎞⎠


0LIE(x) P

minus 11 csr

ax1113872 1113873rxdrx1113874 1113875

(17)


SIR(x) P1hxrminus a

x

IB⟶E + IJS⟶E

(18)







LIE(s) LIB⟶E

(s)LIJS⟶E(s)

exp minusπs2Pδ

1λB


sPJ1113872 1113873δ


times 1113946infin

0H(v s)g(v)dv

(19)



(s) is given by

LIE(s) LIB⟶E

(s)LIJ⟶E(s)

exp minus πλB

sP1( 1113857δ


sPJ1113872 1113873δ


(20)




















τ1 (bitsssubband)


0

01

02

03

04

05

06

Out

age p

roba

bilit

y



0 01 02 03 04 05 06


τ2 (bitsssubband)



0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y





ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y








τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





+ IJS1+ IW1

))where IB1





βP2h1rminus a1 de-



τ1 log 1 + SIRU11113872 1113873

log 1 +c1P1

βc1P2 + 11113888 1113889

(3)





+ IJS2+ P1r

minus a2 h2))








network is given as

τ2 log 1 + SIRU21113872 1113873

log 1 +c2P2

c2P1 + 11113888 1113889

(4)






Fc1(C) Fcncm

(C C) Fc(C)2 (5)

Fc2(C) Fcn


(C C)

2Fc(C) minus Fc(C)2

(6)


(C) andFc2


Fc1(C) Fc(C)

2 (1 minus P(cgtC))

2 (7)


2


(8)




1113946ri gt 0

Phir

minus αi

IB + IJS

gtC | ri1113888 1113889f ri( 1113857dri

1113946ri gt 0

EIBIJSexp minus Cr

αi IB + IJS1113872 11138731113872 11138731113960 1113961f ri( 1113857dri

1113946ri gt 0

LIBCr

αi( 1113857LIJS

Crαi( 1113857f ri( 1113857dri

(9)



UE1

UE2D

D

Base station

Scheduled user

EVE

Selected jammer

Idle jammer




jisinΦBBS0gijR

minus aj PB

⎛⎝ ⎞⎠⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦


ri

1 minus1

1 + svminus aPB

1113888 1113889vdv1113888 1113889


1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889

(10)



jisinΦJS

hijRminus aij PJ

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB UEiD( )

LhijsR

minus aij PJ1113872 1113873⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠

(a) EΦJ


1 minus LhijsPJx

minus a1113872 1113873dx1113874 11138751113888 11138891113888 1113889



minus 12F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889

(11)




(s) as [13]


sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ (12)




1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889



times 2F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889


11138681113868111386811138681113868sCrαi

(13)

When a 4



12

middotπ2

minus arctan1

CPB( 111385712

⎛⎝ ⎞⎠⎛⎝ ⎞⎠⎤⎦



Cr4i PJ

D41113888 11138891113888 1113889


(14)



1 minus Pc1P1

βc1P2gt c1

c1P2

c1P1 + 1gt c21113888 1113889

1 if c1 geP1

βP2or c2 ge

P2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(15)




P2 τ2 le τ2( 1113857

0 if c2 geP2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(16)






SIR(x)lt cs1113888 1113889

P capxisinΦe

SIR(x) lt cs1113888 1113889

E 1113945xisinΦe

P SIR(x) lt cs | x( 1113857⎛⎝ ⎞⎠

EΦe1113945xisinΦe


axIE(x)1113872 11138731113872 1113873⎛⎝ ⎞⎠


0LIE(x) P

minus 11 csr

ax1113872 1113873rxdrx1113874 1113875

(17)


SIR(x) P1hxrminus a

x

IB⟶E + IJS⟶E

(18)







LIE(s) LIB⟶E

(s)LIJS⟶E(s)

exp minusπs2Pδ

1λB


sPJ1113872 1113873δ


times 1113946infin

0H(v s)g(v)dv

(19)



(s) is given by

LIE(s) LIB⟶E

(s)LIJ⟶E(s)

exp minus πλB

sP1( 1113857δ


sPJ1113872 1113873δ


(20)




















τ1 (bitsssubband)


0

01

02

03

04

05

06

Out

age p

roba

bilit

y



0 01 02 03 04 05 06


τ2 (bitsssubband)



0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y





ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y








τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



jisinΦBBS0gijR

minus aj PB

⎛⎝ ⎞⎠⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦


ri

1 minus1

1 + svminus aPB

1113888 1113889vdv1113888 1113889


1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889

(10)



jisinΦJS

hijRminus aij PJ

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB UEiD( )

LhijsR

minus aij PJ1113872 1113873⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠

(a) EΦJ


1 minus LhijsPJx

minus a1113872 1113873dx1113874 11138751113888 11138891113888 1113889



minus 12F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889

(11)




(s) as [13]


sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ (12)




1113946infin

r2i sPB( )

δ

11 + uδ du1113888 1113889



times 2F11113872

middot 1 1 minus2a

2 minus2a

minussPJ

Da11138891113888 1113889


11138681113868111386811138681113868sCrαi

(13)

When a 4



12

middotπ2

minus arctan1

CPB( 111385712

⎛⎝ ⎞⎠⎛⎝ ⎞⎠⎤⎦



Cr4i PJ

D41113888 11138891113888 1113889


(14)



1 minus Pc1P1

βc1P2gt c1

c1P2

c1P1 + 1gt c21113888 1113889

1 if c1 geP1

βP2or c2 ge

P2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(15)




P2 τ2 le τ2( 1113857

0 if c2 geP2

P1


⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(16)






SIR(x)lt cs1113888 1113889

P capxisinΦe

SIR(x) lt cs1113888 1113889

E 1113945xisinΦe

P SIR(x) lt cs | x( 1113857⎛⎝ ⎞⎠

EΦe1113945xisinΦe


axIE(x)1113872 11138731113872 1113873⎛⎝ ⎞⎠


0LIE(x) P

minus 11 csr

ax1113872 1113873rxdrx1113874 1113875

(17)


SIR(x) P1hxrminus a

x

IB⟶E + IJS⟶E

(18)







LIE(s) LIB⟶E

(s)LIJS⟶E(s)

exp minusπs2Pδ

1λB


sPJ1113872 1113873δ


times 1113946infin

0H(v s)g(v)dv

(19)



(s) is given by

LIE(s) LIB⟶E

(s)LIJ⟶E(s)

exp minus πλB

sP1( 1113857δ


sPJ1113872 1113873δ


(20)




















τ1 (bitsssubband)


0

01

02

03

04

05

06

Out

age p

roba

bilit

y



0 01 02 03 04 05 06


τ2 (bitsssubband)



0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y





ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y








τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



SIR(x)lt cs1113888 1113889

P capxisinΦe

SIR(x) lt cs1113888 1113889

E 1113945xisinΦe

P SIR(x) lt cs | x( 1113857⎛⎝ ⎞⎠

EΦe1113945xisinΦe


axIE(x)1113872 11138731113872 1113873⎛⎝ ⎞⎠


0LIE(x) P

minus 11 csr

ax1113872 1113873rxdrx1113874 1113875

(17)


SIR(x) P1hxrminus a

x

IB⟶E + IJS⟶E

(18)







LIE(s) LIB⟶E

(s)LIJS⟶E(s)

exp minusπs2Pδ

1λB


sPJ1113872 1113873δ


times 1113946infin

0H(v s)g(v)dv

(19)



(s) is given by

LIE(s) LIB⟶E

(s)LIJ⟶E(s)

exp minus πλB

sP1( 1113857δ


sPJ1113872 1113873δ


(20)




















τ1 (bitsssubband)


0

01

02

03

04

05

06

Out

age p

roba

bilit

y



0 01 02 03 04 05 06


τ2 (bitsssubband)



0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y





ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y








τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








τ1 (bitsssubband)


0

01

02

03

04

05

06

Out

age p

roba

bilit

y



0 01 02 03 04 05 06


τ2 (bitsssubband)



0 01 02 03 04 05 07060

02

04

06

08

1

Out

age p

roba

bilit

y





ε = 05

ε = 03

τ1 (bitsssubband)0 01 02 03 04 05 06


0

01

02

03

04

05

06

Out

age p

roba

bilit

y








τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







τ2 (bitsssubband)0 01 02 03 04 05 0706

0

02

04

06

08

1

Out

age p

roba

bilit

y





τ1 (bitsssubband)0 01 02 03 04 05 06

0

01

02

03

04

05

06

Out

age p

roba

bilit

y




0

01

02

03

04

05

06

07

08

Secr

ecy

prob

abili

ty






015

0152

0154

0156

0158

016

0162

0164

Con

nect

ion

prob

abili

ty


100 20 30 40 50 60



6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


6 Conclusion


Appendix





(s)

can be given as


jisinΦJS

PJhejRminus aej

⎛⎝ ⎞⎠⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

EΦJ1113945

jisinΦJB(pD)

LhejsPJR

minus aej1113872 1113873⎛⎜⎝ ⎞⎟⎠

(c) exp minus πλJ

sPJ1113872 1113873δ



B(pD)

1 minus LhejsPJy

minus a1113872 11138731113874 1113875dy

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎠

exp minus πλJ

sPJ1113872 1113873δ

sinc(δ)⎛⎝ ⎞⎠ times 1113946

infin

0H(v s)g(v)dv




H(v s)

exp 1113946v+D

vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1



1 +2a

minus (D minus v)a

sPJ

1113888 11138891113888 1113889


vminus D2yλJe 1 +

ya

sPJ

1113888 1113889

minus 1


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(A2)

where


2yv1113888 1113889 (A3)


v

0λUs

rx v( 1113857ydy1113874 1113875

(A4)


2λB1113872 11138731113872 1113873 (A5)


Data Availability




Acknowledgments


Dpy

θ

EVE

v

(a)

Dp

yθ

EVE

v

(b)



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


research article - hindawi · 2019. 11. 16. · research article physical layer security in...

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