Secrecy outage probability of a NOMA scheme and impact imperfect channel state information in underlay cooperative cognitive networks

senso s A icle Sec ecy Ou age P obabili y o a NOMA Scheme and Impac Impe ec Channel S a e In o ma ion in Unde lay Coope a i e Cogni i e Ne wo ks Tan-Phuoc Huynh 1,2 , Duy-Hung Ha 1, Cong T uong Thanh 1, Peppino Fazio 1and Mi osla Voznak 1,* 1Depa men o Telecommunica ions, VSB-Technical Uni e si y o Os a a, 17. lis opadu 2172/15, 708 00 Os a a, Czech Republic; [email p o ec ed] (T.-P.H.); duy[email p o ec ed] (D.-H.H.); [email p o ec ed] (C.T.T.); [email p o ec ed] (P.F.) 2Depa men o Compu e Ne wo ks and Da a Communica ions, Eas e n In e na ional Uni e si y (EIU), Nam Ky Khoi Nghia, Binh Duong 75000, Vie nam *Co espondence: mi osla [email p o ec ed]; Tel.: +420-603-565-965 Recei ed: 29 Decembe 2019; Accep ed: 3 Feb ua y 2020; Published: 7 Feb ua y 2020 Abs ac : Secu i y pe o mance and he impac o impe ec channel s a e in o ma ion (CSI) in unde lay coope a i e cogni i e ne wo ks (UCCN) is in es iga ed in his pape . In he p oposed scheme, elay R uses non-o hogonal mul iple access (NOMA) echnology o ans e messages e1 , e2 om he sou ce node S o Use 1 (U 1 ) and Use 2 (U 2 ), espec i ely. An ea esd oppe (E) is also p oposed o wi e ap he messages o U1 and U 2 . The ansmission’s secu i y pe o mance in he p oposed sys em was analyzed and pe o med o e Rayleigh ading channels. Th ough nume ical analysis, he esul s showed ha he p oposed sys em’s sec ecy pe o mance became mo e e icien when he ea esd oppe node E was a he away om he sou ce node S and he in e media e coope a i e elay R. The sec ecy pe o mance o U 1 was also compa ed o he sec ecy pe o mance o U2. Finally, he simula ion esul s ma ched he Mon e Ca lo simula ions well. Keywo ds: non-o hogonal mul iple access; physical laye secu i y (PLS); coope a i e communica ion; successi e in e e ence cancella ion (SIC); decode-and- o wa d (DF); cogni i e adio (CR); channel s a e in o ma ion; ou age p obabili y 1. In oduc ion The UCCN is known as he CR which is a p omising echnology and inno a i e solu ion o dealing wi h he adio spec um alloca ion and p ecise equi emen s issues [ 1 ]. CR pe mi s seconda y use s (SUs o unlicensed use s) o access he do man equency spec um wi hou causing in e up ion o he p ima y use s (PUs o licensed use ). Due o SUs being accep ed o he PUs a he same ime, he SUs ha e o keep hei ansmi powe s wi hin he accep able le els. Besides ha , wi h apidly ex ending wi eless senso ne wo ks (WSNs) in many a eas o indus y, he secu i y o in o ma ion ans e becomes a mo e se ious p oblem. Many esea che s in es iga ed PLS o help secu i y ansmission be ween he sou ce node and he des ina ion node o imp o e and enhance he sec ecy o WSNs. Recen ly, many solu ions and echnologies ha e been in es iga ed o he pu poses o speeding up mobile da a ansmission, ex ending wi eless communica ion ange, and assis ing use s in connec ing secu i y oge he . Examples o hese echnologies include ampli y-and- o wa d (AF), o hogonal mul iple access (OMA), and ene gy ha es ing [ 2 – 4 ]. NOMA echnology, howe e , is a p omising me hod and has a ac ed signi ican a en ion in ecen yea s [5–10]. NOMA echnology has g adually become one o he mos e icien solu ions in de eloping he i h-gene a ion mobile ne wo k (5G). In he NOMA echnique, he use s can sha e bo h ime and Senso s 2020,20, 895; doi:10.3390/s20030895 www.mdpi.com/jou nal/senso s Senso s 2020,20, 895 2 o 17 equency esou ces and only adjus hei powe alloca ion a ios. The use s wi h be e channel condi ions can se e as elays o enhance he sys em pe o mance by using SIC [ 9 ]. This echnology imp o es he limi a ion o o hogonal mul iple access (OMA). I mee s he needs o end use s in p o iding access o da a quickly and secu ely. NOMA and PLS a e he e o e e y impo an echniques in da a ans e . They assis in ansmi ing signals om he sou ce node o des ina ion node wi h high speed, e iciency, and da a con iden iali y. Se e al s udies ha e examined NOMA and PLS in wi eless sys ems [ 11 – 13 ]. In [ 11 ], he au ho s conside ed a coope a i e elaying sys em using he NOMA echnique o enhance he e iciency o he ansmi ed signal. The esea che s in [ 13 ] in es iga ed he e ec i eness o new schemes ha combined pa ial elay selec ion and NOMA in AF elaying sys ems o inc ease da a ansmission a es o 5G mobile ne wo ks. A conside able amoun o li e a u e has been published on PLS [ 14 – 16 ]. In [ 14 ], he au ho s analyzed he sec ecy pe o mance o coope a i e p o ocols wi h elay selec ion me hods in luenced by co-channel in e e ence. The au ho s in [ 15 ] inspec ed he impac o co ela ed ading on he sec ecy pe o mance o mul iple DF elaying ha uses he op imal elay selec ion me hod. Some esea che s ha e also combined he NOMA echnique wi h PLS [ 17 – 19 ]. In [ 17 ], he au ho s esol ed he p oblem o maximizing he minimum con iden ial in o ma ion a e in use s subjec o he sec ecy ou age cons ain and ins an aneous ansmi powe cons ain . Coope a i e NOMA sys ems wi h PLS in bo h AF and DF we e s udied by he au ho s in [18]. The applica ion o NOMA echniques and secu i y p inciples in unde lay cogni i e adio ne wo ks we e also sugges ed by some au ho s in [ 20 – 24 ]. In [ 20 ], he au ho s discussed a coope a i e ansmission scheme o a downlink NOMA in CR sys ems. This esea ch exploi ed maximum spa ial di e si y. The esea che s in [ 24 ] conside ed secu e communica ion in cogni i e DF elay ne wo ks in which a pai o cogni i e elays we e oppo unis ically selec ed o secu i y p o ec ion agains ea esd oppe s. Channel s a e in o ma ion (CSI) has a i al ole in wi eless communica ion sys ems. I desc ibes how a signal p opaga es om he sou ce node o he elay, such as sca e ing, ading, and powe decay o e dis ance. Du ing a ecei e ’s se -up pe iod, he CSI is e alua ed and ans e ed o ela ed nodes in he sys em h ough a media access con ol p o ocol. In [ 25 ], he au ho s esea ched he e ec o impe ec channel CSI on seconda y use s in an unde lay DF cogni i e ne wo k wi h mul iple p ima y ecei e s. In [ 26 ], scien is s s udied he e ec o impe ec CSI on a DF coope a i e unde lay cogni i e adio NOMA ne wo k in o de o de e mine he op imal powe alloca ion ac o s o di e en use dis ances. In mos o he li e a u e epo ed abo e, he combina ion o NOMA and PLS in a UCCN in luenced by CSI was no p oposed. Mo i a ed and inspi ed by he abo e ideas, a coope a i e scheme is sugges ed in his pape . In his scheme, a p oposed UCCN using NOMA is equi ed o bo h decode and o wa d he messages e1 and e2 om node S o wo des ina ion nodes (U 1 and U 2 ) unde he e ec o CSI and an ea esd oppe . The sec ecy pe o mance o he communica ions e1 and e2 in he p oposed sys em we e hen examined and es ima ed in e ms o sec ecy ou age p obabili y o e Rayleigh ading channels o imp o e spec al e iciency and secu e communica ion. The main con ibu ions o he pape a e summa ized as ollows: - A s udy o he impac o impe ec CSI and he sec ecy pe o mance o a UCCN applying he NOMA echnique o imp o e sys em pe o mance in a 5G wi eless ne wo k. - Sec ecy ou age p obabili y (SOP) is pe o med o e Rayleigh ading channels and e i ied wi h Mon e Ca lo simula ions. - The esul s achie ed by he p oposed scheme demons a e he secu i y pe o mance o U 1 and U 2 . - The sec ecy pe o mance o he p oposed sys em imp o ed when he dis ance be ween he ea esd oppe node E and he sou ce and coope a i e elay inc eased. Senso s 2020,20, 895 3 o 17 The pape has i e sec ions. Sec ion 1in oduces he opic. Sec ion 2desc ibes he p oposed scheme’s sys em model. Sec ion 3p esen s he esul s o an analysis o he sec ecy ou age p obabili y a he sou ce nodes. Sec ion 4p esen s he simula ion esul s. Sec ion 5summa izes he conclusions. 2. Sys em Model Figu e 1illus a es he in luence o impe ec CSI in a UCCN using NOMA and PLS. The sys em model consis s o he sou ce nodes S ans e ing a supe imposed signal e1 and e2 o U 1 and U 2 , espec i ely, h ough elay node R. One ea esd oppe node E is p oposed o wi e ap he signals e1 , e2 o he links S-U 1 , S-U 2 . In addi ion, he sys em model also consis s o a node Pu which is known as he p ima y use ha ing he license. Due o he in e e ence cons ain a he Pu node in he UCCN, he elay R and sou ce S adjus hei ansmi ing powe s. In his model, we assume ha he in e media e elay node R ope a es in DF elaying me hod and applies he NOMA p inciple unde he in luence o impe ec CSIs and PLS in UCCN. In addi ion, he a iances o Ze o-mean Whi e Gaussian Noises (AWGNs) a e equal, gi en as N0 . In his wo k, he co esponding dis ances o he links S-Pu, R-Pu, S-R, S-E, R-E, R-Pu, R-U1, and R-U2in Figu e 1a e gi en as lSPu,lRPu,lSR,lSE,lRE,lRPu,l1, and l2. Rega ding he sys em channels, hi ep esen s he Rayleigh ading channel coe icien , i∈(hSR,hSE,hSPu,hRE,hRPu, 1, 2) . We assume ha he channels hi do no change du ing block ime T and a e independen ly and iden ically dis ibu ed be ween wo consecu i e block imes [10]. Finally, all o nodes in he sys em model ha e a single an enna o ansmi ing and ecei ing messages. Figu e 1. Sys em model o NOMA and PLS unde impe ec CSI in a UCCN. In p inciple, he e a e wo ime slo s in ol ed in each sys em communica ion p ocess, and a e gi en as ollows: A he i s ime slo , he sou ce node S ans e s he in o ma ion e S o he elay R and he ea esd oppe node E, which is gi en by he ma h exp ession as es=pβ1Pse1+pβ2Pse2, (1) whe e Ps is he powe a sou ce node S, e1 , and e2 a e he messages o U 1 , U 2 , espec i ely, wi h E{|ej|2}= 1, j∈(1, 2) , ( E{e} being no a ed o he expec a ion p ocess o e ). The β1 and β2 a e he powe alloca ion coe icien s. Following he p inciple o he NOMA, we assume ha β1>β2 wi h β1+β2=1. Senso s 2020,20, 895 4 o 17 Because o he es ima ion e o s o channels hi , he e alua ed ading channel coe icien s a he nodes a e ep esen ed as ollows [25]: b hi=ρhi+q1−ρ2εi, (2) whe e b hi , hi , and εi a e modeled as he addi i e whi e Gaussian noise (AWGN) wi h he andom a iable i=|b hi|2 . The co ela ion coe icien ρ∈[0, 1] is desc ibed as he a e age quali y o he channel es ima ion. No a ion: The Cumula i e Dis ibu ion Func ion (CDF) and p obabili y densi y unc ion (pd ) o he andom a iable i is deno ed espec i ely as F i(x) = 1 −e−1 λix and i(x) = 1 λie−1 λix , whe e λi=l−β i , and βis a pa h-loss exponen . The ecei ed signal a R om sou ce node S o decode e1 unde impac impe ec CSIs is gi en as ollows: ye1 SR =hSRes+σR. (3a) Replace hSR om o mula (2), he signal ye1 SR is calcula ed as ye1 SR =pβ1Pse1bhSR−√1−ρ2εSR ρ+pβ2Pse2bhSR−√1−ρ2εSR ρ+nR =√β1Pse1bhSR ρ+√β2Pse2bhSR ρ−√β1Pse1√1−ρ2εSR ρ−√β2Pse2√1−ρ2εSR ρ+nR, (3b) whe e nRdeno es he AWGNs a he elay R wi h he same a iance N0. Because o applying NOMA echnology, hanks o he deploymen o SIC in NOMA p inciple, i s ly, he elay R decodes he signal e1 om o mula (3b) and emo es i , hen he signal e2 will be decoded wi hou he componen √β1Pse1bhSR ρ in o mula (3b). The e o e, he signal e2 ecei ed a R om sou ce S a e emo ing he signal e1is exp essed as ollows: ye2 SR =pβ2Pse2bhSR ρ−pβ1Pse1p1−ρ2εSR ρ−pβ2Pse2p1−ρ2εSR ρ+nR. (4) Simila ly, he node E also wi e aps he packe s e1 and e2 om S, espec i ely, and he ecei ed signals a node E a e ob ained as ollows: ye1 SE =pβ1Pse1bhSE ρ+pβ2Pse2bhSE ρ−pβ1Pse1p1−ρ2εSE ρ−pβ2Pse2p1−ρ2εSE ρ+nE(5) ye2 SE =pβ2Pse2bhSE ρ−pβ1Pse1p1−ρ2εSE ρ−pβ2Pse2p1−ρ2εSE ρ+nE, (6) whe e nEdeno es he AWGNs a he E wi h he same a iance N0. In he second ime slo , a e he ecei ed signals, he elay R sends hem o he sou ce nodes U 1 and U2. Hence, he ecei ed signals a he des ina ion node U1, U2a e gi en espec i ely as ye1 RU1=pβ1PRe1b h1 ρ+pβ2PRe2b h1 ρ−pβ1PRe1p1−ρ2ε1 ρ−pβ2PRe2p1−ρ2ε1 ρ+nU1(7) ye2 RU2=pβ2PRe2b h2 ρ−pβ1PRe1p1−ρ2ε2 ρ−pβ2PRe2p1−ρ2ε2 ρ+nU2, (8) whe e nU1 , nU2 deno e he AWGNs a he des ina ion U 1 , U 2 wi h he same a iance N0 , and PR is a ansmi powe o he elay R. Senso s 2020,20, 895 5 o 17 In he p oposed scheme, unde he in e e ence cons ain a he node Pu , he sou ce node S and elay node R ha e o adjus hei ansmi ing powe s so ha he in e e ence powe a he Pu mus be less han a h eshold alue, which is assumed as I h . The maximum powe s o nodes S and R a e gi en, espec i ely, PS=I h |d hSR|2=I h SR . (9a) PR=I h |d hRPu|2=I h RPu . (9b) Because he node E connec s o he elay R di ec ly, so i wi e aps he packe s e1 and e2 om elay R. The e o e, he ecei ed signals a E h ough he link R-E a e exp essed as ye1 RE =pβ1PRe1bhRE ρ+pβ2PRe2bhRE ρ−pβ1PRe1p1−ρ2εRE ρ−pβ2PRe2p1−ρ2εRE ρ+nE. (10) ye2 RE =pβ2PRe2bhRE ρ−pβ1PRe1p1−ρ2εRE ρ−pβ2PRe2p1−ρ2εRE ρ+nE. (11) We de ine he ecei ed Signal- o-In e e ence and Noise Ra ios (SINRs) as γ= E|signal|2/ E|o e all noise|2. Fi s ly, we calcula e he ecei ed Signal- o-In e e ence and Noise Ra ios (SINRs) o decoding he in o ma ion signal e1. Thus, om o mula (3b), he SINR a he elay R wi h he link S-R is ob ained as ollows: γe1 SR = β1PS|d hSR|2 ρ2 β2PS|d hSR|2 ρ2+β1PS(1−ρ2)λSR ρ2+β2PS(1−ρ2)λSR ρ2+N0 =β1PS SR β2PS SR+PS(1−ρ2)λSR(β1+β2)+ρ2N0. (12a) Replacing PS=I h SR in (9a), and se ing P=I h N0,γe1 SR is ew i en as γe1 SR =Pβ1 SR Pβ2 SR +P(1−ρ2)λSR +ρ2 SPu , (12b) Simila ly, wi h he o mula in (7), we also calcula e γe1 RU1 , and his is achie ed by ma hema ical exp ession as γe1 RU1=Pβ1 1 Pβ2 1+P(1−ρ2)λ1+ρ2 RPu , (13) whe e P=I h N0. Applying o mulas (5) and (10), he ecei ed SINRs a he ea esd oppe node E wi h he link S-E and R-E a e gi en, espec i ely, as ollows: γe1 SE =β1Ps SE β2Ps SE +Ps(1−ρ2)λSE +ρ2N0 =Pβ1 SE Pβ2 SE +P(1−ρ2)λSE +ρ2 SPu . (14) γe1 RE =Pβ1 RE Pβ2 RE +P(1−ρ2)λRE +ρ2 RPu . (15) Senso s 2020,20, 895 6 o 17 In he second, simila o decoding he in o ma ion signal e1 , we ind he ecei ed SINRs o decoding he in o ma ion signal e2as ollows. We apply o mulas (4) and (6), he ecei ed SINRs a he nodes R wi h he link S-R, and a he ea esd oppe node E wi h he link S-E a e exp essed, espec i ely, as ollows: γe2 SR =β2Ps SR β1Ps(1−ρ2)λSR +β2Ps(1−ρ2)λSR +ρ2N0 =Pβ2 SR P(1−ρ2)λSR +ρ2 SPu .(16) γe2 SE =β2Ps SE Ps(1−ρ2)λSE +ρ2N0 =Pβ2 SE P(1−ρ2)λSE +ρ2 SPu .(17) Simila ly, wi h o mulas (8) and (12), he ecei ed SINRs a he nodes U 2 and E om elay R a e in e ed, espec i ely, as ollows: γe2 RU2=Pβ2 2 P(1−ρ2)λ2+ρ2 RPu . (18) γe2 RE =Pβ2 RE P(1−ρ2)λRE +ρ2 RPu . (19) Applying he Shannon capaci y o mula, he achie able a es o he links X–Y a e o mula ed as Rej XY =1 2log2(1+γej XY ). (20) whe e he a io 1/2 ep esen s he ac ha da a ansmission is spli in o wo ime slo s, X∈{S,R} , and Y∈{E,U1,U2} . The sec ecy capaci y o he UCCN sys ems wi h DF-based NOMA o he S-U j communica ion can be exp essed as SCj=hSCej Uj−SCej Ei+, (21) whe e [x]+=max (0, x) ; SCei SR and SCej RUj a e he sec ecy capaci ies om he sou ce node S o he elay R and om he elay R o he des ina ion Uia e gi en, espec i ely, as SCej SR =max(0, Rej SR −Rej SE). (22) SCej RUi=max(0, Rej RUi−Rej RE). (23) 3. Sec ecy Ou age P obabili y Analysis In his sec ion, he sec ecy ou age p obabili y o ea esd opping he signals o U 1 and U 2 in he p oposed scheme a e analyzed. We assume ha a node success ully and sa ely decodes he ecei ed packe i i s achie able sec ecy capaci y is la ge han a h eshold sec ecy capaci y SC h. 3.1. Sec ecy Ou age P obabili y o U1. The sec ecy ou age p obabili y o U 1 occu ing when U 1 does no ecei e a signal sa ely om he sou ce node S unde he malicious a emp o he ea esd oppe E is exp essed as ollows: OPU1=P [min(SCe1 SR,SCe1 RU1)<SC h] =1−P [SCe1 SR ≥SC h,SCe1 RU1≥SC h].(24) Senso s 2020,20, 895 7 o 17 Replacing SCe1 SR =max( 0, Re1 SR −Re1 SE) a o mula (22) and SCe1 RU1=max( 0, Re1 RU1−Re1 RE) a (23) in o mula (24), he OPU1is ew i en as ollows: OPU1=1−P Re1 SR −Re1 SE ≥SC h | {z } P 1.1 ×P hRe1 RU1−Re1 RE ≥SC hi | {z } P 1.2 (25) P oposi ion 1. The p obabili y o he P 1.1, and P 1.2 in (25) is gi en as P 1.1 =           0a≤θb (1/λSPu)e−ψ11/λSR (1/λSPu)+(ψ2/λSR)−(1/λSRλSPu)I1a>θb. (26) whe e ψ11 =φcλSE (a−φb);ψ2=φρ2 (a−φb) I1= ∞ Z0 ∞ Z (ψ11+ψ2x) e−1 λSPu x+1 λSR ye−1 λSE ζ1dxdy , ζ1=cλSE +ρ2xay −φby +cλSR +ρ2x [φb+ (φ+1)a] [by +cλSR +ρ2x]−aby , P oo : See Appendix A. P 1.2 =           0a≤θb (1/λRPu)e−ψ12/λ1 (1/λRPu)+ψ2/λ1−(1/λ1λRPu)I2a>θb (27) whe e ψ12 =φcλ1 (a−φb);ψ2=φρ2 (a−φb) I2= ∞ Z0 ∞ Z (ψ12+ψ2x) e−1 λRPu x+1 λ1ye−1 λRE ζ2dxdy , ζ2=cλRE +ρ2xay −φby +cλ1+ρ2x [φb+ (φ+1)a] [by +cλ1+ρ2x]−aby , P oo : See Appendix B. F om o mulas in (26) and (27), he sec ecy ou age p obabili y o he U1is ob ained as OPU1=                    1a≤φb 1−  (1/λSPu)e−ψ11/λSR (1/λSPu)+(ψ2/λSR)−(1/λSRλSPu)×I1 ×1/λRPue−ψ12/λ1 1/λRPu+ψ2/λ1−(1/λ1λRPu)×I2  a>φb (28) Senso s 2020,20, 895 8 o 17 3.2. Sec ecy Ou age P obabili y o U2 Simila o U1, he SOP o U2can be exp essed as OPU2=P hmin SCe2 SR,SCe2 RU2<SC hi=1−P hSCe2 SR ≥SC h,SCe2 RU2≥SC hi. (29) P oposi ion 2. The sec ecy ou age p obabili y o U2in (26) is gi en as OPU2=1−1−1 λSPuλSE ×I3×1−1 λRPuλRE I4(30) whe e ζ3=φ(cλSR+ρ2x) b+(φ+1)(cλSR+ρ2x) (cλSE+ρ2x)y, ζ4=φ(cλ2+ρ2x) b+(φ+1)(cλ2+ρ2x) (cλRE+ρ2x)y, I3= ∞ Z0 ∞ Z0e−1 λSPu x+1 λSE y×1−e−ζ3 λSR dxdy, I4= ∞ Z0 ∞ Z0e−1 λRPu x+1 λRE y×1−e−ζ4 λ2dxdy. P oo : See Appendix C. The in eg als I1 and I2 in (28) and I3 and I4 in (30) a e complex in eg als and a e di icul o esol e p ac ically. In his pape , howe e , he alue o I1 , I2 , I3 and I4 can be ound using nume ical me hods. 4. Simula ion Resul s In his sec ion, he sec ecy pe o mance o a NOMA scheme and he impac o impe ec CSI in a UCCN we e examined, analyzed, and e alua ed. The heo e ical esul s o he analyses we e e i ied wi h Mon e Ca lo simula ions. The coo dina es o S, R, U 1 , U 2 , Pu, and E we e se o S( 0, 0 ) , R(xR, 0 ), U1xU1,yU1=(1, 0) , U2xU2,yU2=(0.75, −0.5) , Pu (xPu,yPu ) , E(xE,yE) , espec i ely, in he wo-dimensional plane and sa is ying (xi>0) . Hence, lSR =xR , lRU1=xU1−xR , lRU2=qy2 U2+xU2−xR)2 , lRPu =qy2 Pu +(xPu −xR)2 , lRE =qy2 E+(xE−xR)2 , lSE =qy2 E+x2 E , and lSPu =qx2 Pu +y2 Pu . We assume ha he a ge sec ecy capaci y SC h = 0.5 (bi /s/Hz) and he exponen βis se o a cons an β=3. Figu es 2and 3g aph he SOP o he wo Use s U 1 and U 2 ia SNR (dB) wi h SC h = 0.5 (bi /s/Hz). The elay R, Pu, U 1 , U 2 , and ea esd oppe E a e loca ed in posi ions R (xR, 0)=(0.5, 0) , Pu (xPu,yPu)=(0.5, −1) , U1xU1,yU1=(1, 0) , U2xU2,yU2=(0.75, −0.5) , E(xE,yE)=(0.5, 1) , espec i ely. F om he esul s in Figu e 2, we can see he e ec o he ea esd opping node E o he SOP when SNR is changed om 0 dB o 20 dB. Wi h ρ= 0.95, he SOP alues o Use U 1 a e g ea e han Use U 2 when SNR < 2.5 dB. Ne e heless, when he SNR inc eases om 2.5 dB o 30 dB, he SOP o Use U 2 is be e han Use U 1 , and bo h also inc ease when he SNR inc eases as a esul o la ge ansmi ing powe . Besides ha , i is no ed ha impe ec CSI deg ades he SOP o he signal. Senso s 2020,20, 895 9 o 17 SNR(dB) 0 5 10 15 20 25 30 Sec ecy Ou age P obabili y(SOP) 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 Simula ion Theo y-Use U1 Theo y-Use U2 Figu e 2. The SOP o U1and U2 e sus SNR (dB). SNR(dB) 0 5 10 15 20 25 30 Sec ecy Ou age P obabili y(SOP) 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 Simula ion Theo y-Use U1 Theo y-Use U2 ρ=0.9 ρ=0.95 Figu e 3. The SOP o U1and U2 e sus SNR (dB) when ρ=0.9 and ρ=0.95. In Figu e 3, we obse e he ob ious a ec ion o he channel es ima ion coe icien ρ o he SOP. The SOP o he wo use s in case ρ= 0.95 ou pe o ms he SOP in case ρ= 0.9. I means ha he sys em has been impac ed by impe ec CSI. We also can see ha he sec ecy pe o mance o he wo Senso s 2020,20, 895 16 o 17 OPU2=1−P Re2 SR −Re2 SE ≥SC h | {z } Ω2.1 ×P hRe2 RU2−Re2 RE ≥SC hi | {z } Ω2.2 (A18) Fi s ly, we calcula e he p obabili y o Ω2.1 as ollows: Ω2.1 =P Re2 SR −Re2 SE ≥SC h=1−P Re2 SR <SC h +Re2 SE =1−P 1 2log21+γe2 SR<SC h +1 2log21+γe2 SE =1−P " SR <φcλSR +ρ2 SPu b+(φ+1)cλSR +ρ2 SPu (cλSE +ρ2 SPu) SE#(A19) Applying he pd o he andom a iables SPu and SE, (A19) is w i en as Ω2.1 =1− ∞ Z0 ∞ Z0"P " SR <φcλSE +ρ2x b+(φ+1)cλSR +ρ2x (cλSE +ρ2x)y#× SPu (x) SE (y)#dxdy =1−1 λSPuλSE ∞ Z0 ∞ Z0 e−1 λSPu x+1 λSE y× 1−e−1 λSR φ(cλSR+ρ2x) b+(φ+1)(cλSR+ρ2x) (cλSE+ρ2x)y  dxdy (A20) Ω2.2 is calcula ed simila ly as (A20) and is gi en as Ω2.2 =1−1 λRPuλRE ∞ Z0 ∞ Z0   e−1 λRPu x+1 λRE y×  1−e−1 λ2 φ(cλ2+ρ2x) b+(φ+1)(cλ2+ρ2x) (cλRE+ρ2x)y!    dxdy (A21) Finally, wi h o mulas (A20) and (A21), he sec ecy ou age p obabili y o U 2 is ob ained by he exp ession as (30). Re e ences 1. Liu, X.; Zhang, X. NOMA-based Resou ce Alloca ion o Clus e -based Cogni i e Indus ial In e ne o Things. IEEE T ans. Ind. In .2019. [C ossRe ] 2. Liu, X.; Jia, M.; Zhang, X.; Lu, W. A No el Mul ichannel In e ne o Things Based on Dynamic Spec um Sha ing in 5G Communica ion. IEEE In e ne Things J. 2019,6, 5962–5970. [C ossRe ] 3. Gelenbe, E.; Zhang, Y. Pe o mance Op imiza ion Wi h Ene gy Packe s. IEEE Sys . J. 2019 ,13, 3770–3780. [C ossRe ] 4. Gelenbe, E.; Abdel ahman, O.-H. An Ene gy Packe Ne wo k model o mobile ne wo ks wi h ene gy ha es ing. Nonlinea Theo y App. IEICE 2018,9, 322–336. [C ossRe ] 5. Anwa , A.; See , B.-C.; Ding, Z. Non-O hogonal Mul iple Access o Ubiqui ous Wi eless Senso Ne wo ks. Senso s 2018,18, 516. [C ossRe ] [PubMed] 6. Rauniya , A.; Engels ad, P.; Øs e bø, O.-N. RF Ene gy Ha es ing and In o ma ion T ansmission Based on NOMA o Wi eless Powe ed IoT Relay Sys ems. Senso s 2018,18, 3254. [C ossRe ] 7. Yang, Z.; Ding, Z.; Fan, P.; Ka agiannidis, G.-K. On he Pe o mance o Non-o hogonal Mul iple Access Sys ems Wi h Pa ial Channel In o ma ion. IEEE T ans. Commun. 2016,64, 654–667. [C ossRe ] 8. Yang, Z.; Ding, Z.; Fan, P.; Al-Dhahi , N. The Impac o Powe Alloca ion on Coope a i e Non-o hogonal Mul iple Access Ne wo ks Wi h SWIPT. IEEE T ans. Wi eless Commun. 2017,16, 4332–4343. [C ossRe ] 9. T an, T.-N.; Voznak, M. Mul i-Poin s Coope a i e Relay in NOMA Sys em wi h N-1 DF Relaying Nodes in HD/FD Mode o N Use Equipmen s wi h Ene gy Ha es ing. Elec onics 2019,8, 167. [C ossRe ] 10. Zhang, Y.; Wang, X.; Wang, D.; Zhao, Q. A Range-Di ision Use Relay Selec ion Scheme and Pe o mance Analysis in NOMA-based Coope a i e Oppo unis ic Mul icas Sys ems. Elec onic 2019,8, 554. [C ossRe ] 11. Ding, Z.; Peng, M.; Poo , H.-V. Coope a i e Non-O hogonal Mul iple Access in 5G Sys ems. IEEE Commun. Le . 2015,19, 1462–1465. [C ossRe ] Senso s 2020,20, 895 17 o 17 12. Jiao, R.; Dai, L.; Zhang, J.; MacKenzie, R.; Hao, M. On he Pe o mance o NOMA-Based Coope a i e Relaying Sys ems o e Rician Fading Channels. IEEE T ans. Veh. Technol. 2017. [C ossRe ] 13. Lee, S.; da Cos a, D.-B.; Vien, Q.; Duong, T.-Q.; de Sousa, R.-T. Non-o hogonal mul iple access schemes wi h pa ial elay selec ion. IET Commun. 2017,11, 846–854. [C ossRe ] 14. Duy, T.-T.; Duong, T.-Q.; Thanh, T.-L.; Bao, V.N.-Q. Sec ecy pe o mance analysis wi h elay selec ion me hods unde impac o co-channel in e e ence. IET Commun. 2015,9, 1427–1435. [C ossRe ] 15. Fan, L.; Lei, X.; Yang, N.; Duong, T.-Q.; Ka agiannidis, G.-K. Sec ecy Coope a i e Ne wo ks Wi h Ou da ed Relay Selec ion O e Co ela ed Fading Channels. IEEE T ans. Veh. Technol. 2017 ,66, 7599–7603. [C ossRe ] 16. Hu, H.; Gao, Z.; Liao, X.; Leung, V.C.M. Secu e Communica ions in CIoT Ne wo ks wi h a Wi eless Ene gy Ha es ing Un us ed Relay. Senso s 2017,17, 2023. [C ossRe ] 17. He, B.; Liu, A.; Yang, N.; Lau, V.K. On he Design o Secu e Non-O hogonal Mul iple Access Sys ems. IEEE J. Sel. A eas Commun. 2017,35, 2196–2206. [C ossRe ] 18. Chen, J.; Yang, L.; Alouini, M.S. Physical Laye Secu i y o Coope a i e NOMA Sys ems. IEEE T ans. Veh. Technol. 2018,67, 4645–4649. [C ossRe ] 19. Do, D.T.; Van Nguyen, M.S.; Hoang, T.A.; Voznak, M. NOMA-Assis ed Mul iple Access Scheme o IoT Deploymen : Relay Selec ion Model and Sec ecy Pe o mance Imp o emen . Senso s 2019 ,19, 736. [C ossRe ] 20. Liu, X.; Wang, Y.; Liu, S.; Meng, J. Spec um Resou ce Op imiza ion o NOMA-Based Cogni i e Radio in 5G Communica ions. IEEE Access 2018,6, 24904–24911. [C ossRe ] 21. L , L.; Chen, J.; Ni, Q. Coope a i e Non-O hogonal Mul iple Access in Cogni i e Radio. IEEE Commun. Le . 2016,20, 2059–2062. [C ossRe ] 22. Lee, S.; Duong, T.Q.; Bene ides daCos a, D.; Ha, D.B.; Nguyen, S.Q. Unde lay cogni i e adio ne wo ks wi h coope a i e non-o hogonal mul iple access. IET Commun. 2018,12, 359–366. [C ossRe ] 23. L , L.; Chen, J.; Ni, Q.; Ding, Z. Design o Coope a i e Non-O hogonal Mul icas Cogni i e Mul iple Access o 5G Sys ems: Use Scheduling and Pe o mance Analysis. IEEE T ans. Commun. 2017 ,65, 2641–2656. [C ossRe ] 24. Liu, Y.; Wang, L.; Duy, T.T.; Elkashlan, M.; Duong, T.Q. Relay Selec ion o Secu i y Enhancemen in 251 Cogni i e Relay Ne wo ks. IEEE Wi el. Commun. Le . 2015,4, 46–49. [C ossRe ] 25. Son, P.N. Join impac s o Ha dwa e impai men s, Impe ec CSIs, and In e e ence cons ain s on Unde lay Coope a i e Cogni i e Ne wo ks wi h eac i e elay selec ion. Telecommun. Sys . 2019 ,71, 65–76. [C ossRe ] 26. A zykulo , S.; Tsi sis, T.A.; Nau yzbaye , G.; Abdallah, M. Ou age Pe o mance o Coope a i e Unde lay CR-NOMA Wi h Impe ec CSI. IEEE Commun. Le . 2019,23, 176–179. [C ossRe ] c 2020 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).