IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.00,NO.00,2016 1 Security-Reliability Tradeoff Analysis of Artificial 1 Noise Aided Two-Way Opportunistic Relay Selection 2 XiaojinDing,StudentMember,IEEE,TiechengSong,Member,IEEE,YulongZou,SeniorMember,IEEE, 3 XiaoshuChen,andLajosHanzo,Fellow,IEEE 4 5 Abstract—Inthispaper,weinvestigatethephysical-layersecu- andfast-fadingeffectsofwirelesschannels.Therearetwopop- 39 6 rity of cooperative communications relying on multiple two-way ular relaying protocols, namely the amplify-and-forward (AF) 40 7 relays using the decode-and-forward (DF) protocol in the pres- [1],[2]aswellasthedecode-and-forward(DF)[3],[4].Inthe 41 8 ence of an eavesdropper, where the eavesdropper appears to tap 9 thetransmissionsofboththesourceandoftherelay.Thedesign case of AF relaying, the selected relay multiplies its received 42 10 tradeofftoberesolvedisthatthethroughputisimprovedbyin- signalsbyagainfactorandthenforwardthemtothedestination 43 11 vokingtwo-wayrelaying,butthesecrecyofwirelesstransmissions [1],[2].Bycontrast,theDFrelaydecodes itsreceived signals 44 12 maybedegraded,sincetheeavesdroppermayoverhearthesignals and then the selected relay forward its decoded signal to the 45 13 transmitted by both the source and relay nodes. We conceive an destination[3],[4].Additionally,in[5],bothAFandDFrelay- 46 14 artificialnoiseaidedtwo-wayopportunisticrelayselection(ANaT- 15 WORS) scheme for enhancing the security of the pair of source ing schemes are investigated. In general, closer to the source, 47 16 nodescommunicatingwiththeassistanceofmultipletwo-wayre- DFrelayinghasahighprobabilityofsuccessfuldecodingand 48 17 lays. Furthermore, we analyze both the outage probability and flawless retransmission from the relay to the destination from 49 18 interceptprobabilityoftheproposedANaTWORSscheme,where areduceddistance[6].Bycontrast,closetothedestinationthe 50 19 thesecurityandreliabilityarecharacterizedintermsoftheinter- DFrelayhasjustasbadreceptionasthedestinationitself,hence 51 20 ceptprobabilityandthesecurityoutageprobability.Forcompari- 21 son,wealsoprovidethesecurity–reliabilitytradeoff(SRT)analysis itofteninflictserrorpropagation.Fortunatelyinthevicinityof 52 22 ofboththetraditionaldirecttransmissionandoftheone-wayre- thedestinationAFrelyingtendstooutperformDFrelaying[6]. 53 23 layingschemes.ItisshownthattheproposedANaTWORSscheme Additionally, [7] also shows that adaptive DF outperforms AF 54 24 outperformsboththeconventionaldirecttransmission,aswellas intermsofitsframeerrorrate(FER). 55 25 theone-wayrelaymethodsintermsofitsSRT.Morespecifically, Atthetimeofwritingthispaper,physical-layersecurity[8], 56 26 in the low main-user-to-eavesdropper ratio (MUER) region, the 27 proposedANaTWORSschemeiscapableofguaranteeingsecure [9]incooperativerelaynetworksisreceivingagrowingresearch 57 28 transmissions, whereas no SRT gain is achieved by conventional attentionasbenefitofitscapabilityofprotectingwirelesscom- 58 29 one-wayrelaying.Infact,theone-wayrelayingschememayeven municationsagainsteavesdroppingattacks.In[10]and[11],the 59 30 beinferiortothetraditionaldirecttransmissionschemeinterms physical-layer security of MIMO-aided relaying networks has 60 31 ofitsSRT. beenexplored,demonstratingthatthesecrecycapacitycanin- 61 32 Index Terms—Artificial noise, opportunistic relay selection, deed be improved by using MIMO-aided relays. Additionally, 62 Q1 33 physical-layer security, security-reliability tradeoff (SRT), TekinandYener[12]proposedthecooperativejammingphilos- 63 34 two-wayrelay. ophy,andstudiedtheattainablesecrecyratewiththeobjectiveof 64 improvingthephysical-layersecurity.Asafurtherdevelopment, 65 35 I. INTRODUCTION Long et al. [13] investigated cooperative jamming schemes in 66 bidirectionalsecrecycommunications.In[14]and[15],beam- 67 36 COOPERATIVE relaying has attracted substantial re- formingtechniqueshavebeeninvestigatedandsignificantwire- 68 37 search interests from both the academic and industrial less secrecy capability improvements were demonstrated with 69 38 community,sinceitiscapableofmitigatingboththeshadowing theaidofbeamformingtechniques.Additionally,theimpactof 70 antennaselectiononsecuretwo-wayrelayingcommunications 71 Manuscript received January 21, 2016; revised May 9, 2016 and July 22, hasbeenanalyzedin[16]. 72 2016;acceptedAugust12,2016.Dateofpublication;dateofcurrentversion. ThisworkwassupportedinpartbytheNationalNaturalScienceFoundation As a design alternative, relay selection schemes may also 73 ofChinaunderGrant61401223,Grant61522109,Grant61271207,andGrant be used for improving the physical-layer security of wireless 74 61372104;inpartbytheNaturalScienceFoundationofJiangsuProvinceunder communications.One-wayrelayinghasbeenanalyzedin[17]– 75 GrantBK20140887andGrantBK20150040;andinpartbytheKeyProjectof NaturalScienceResearchofHigherEducationInstitutionsofJiangsuProvince [24]. Specifically, hybrid relaying and jamming schemes are 76 underGrant15KJA510003.ThereviewofthispaperwascoordinatedbyProf. exploredin[17]–[22].In[17]–[19],jointAFrelayingandjam- 77 M.C.Gursoy. merselectionschemeshavebeeninvestigated.Additionally,hy- 78 X.Ding,T.Song,andX.ChenarewiththeNationalMobileCommunications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail: brid cooperative beamforming and cooperative jamming have 79 dxj@seu.edu.cn;songtc@seu.edu.cn;xchen@seu.edu.cn). beenproposedin[20]and[21].In[22],jointDFrelayingand 80 Y.ZouiswiththeSchoolofTelecommunicationsandInformationEngineer- cooperative jamming schemes have been investigated. More- 81 ing, Nanjing University of Posts and Telecommunications, Nanjing 210003, China(e-mail:yulong.zou@njupt.edu.cn). over, in [23], the AF- and DF-based optimal relay selection 82 L. Hanzo is with the Department of Electronics and Computer Sci- schemeshavebeenproposed.Theassociatedinterceptprobabil- 83 ence, University of Southampton, Southampton SO17 1BJ, U.K. (e-mail: itieshavealsobeenanalyzedinthecontextofbothAF-andDF- 84 lh@ecs.soton.ac.uk). DigitalObjectIdentifier10.1109/TVT.2016.2601112 basedone-wayrelayingschemes,whereaneavesdropperisonly 85 0018-9545©2016IEEE.Personaluseispermitted,butrepublication/redistributionrequiresIEEEpermission. Seehttp://www.ieee.org/publicationsstandards/publications/rights/index.htmlformoreinformation. 2 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.00,NO.00,2016 86 capableofwiretappingthetransmissionsoftherelays.Bycon- 87 trast, in [24], an eavesdropper was tapping the transmissions 88 of both the source and of the relays. Moreover, the security- 89 reliabilitytradeoff(SRT)hasbeenexploredinthecontextofthe 90 proposedopportunisticrelayselectionschemeinthehighmain- 91 user-to-eavesdropper ratio (MUER) region, where the MUER 92 is defined as the ratio of the average channel gain of the main 93 links(spanningfromthesourcetothedestination)tothatofthe 94 wiretap links (spanning from the source to the eavesdropper). 95 Additionally,two-wayrelayinghasbeenexploredin[25]–[31]. 96 Specifically, Mo et al. [25] investigated two-way AF relaying 97 schemesrelyingoneithertwoslotsorthreeslotsdemonstrated 98 that the three-slot scheme performs better than the two-slot 99 scheme, when the transmitted source powers approach zero. Fig.1. WirelessnetworkconsistingofapairofsourceS1,S2,andN relays 100 In[26],DFrelayinghasbeeninvokedforimprovingthewire- inthepresenceofaneavesdropperE. 101 less security of bidirectional communications, where a relay 102 is invoked for transmitting artificial noise in order to perturb 103 the eavesdropper’s reception both in the first and in the sec- thethirdtimeslot,therelayforwardtheencodedsignalstoS1 142 104 ondtransmissionslot.In[27],jointrelayandjammerselection andS2. 143 105 oftwo-wayrelaynetworkshavebeenproposed.In[28],Wang Second,wepresentthemathematicalSRTanalysisofthepro- 144 106 et al. explored hybrid cooperative beamforming and jamming posed ANaTWORS scheme in the presence of artificial noise 145 107 oftwo-wayrelaynetworks.In[29],securerelayandjammerse- imposed both on the relays and on the eavesdropper for trans- 146 108 lectionwasconceivedforthephysical-layersecurityimprove- mission over Rayleigh fading channels. Moreover, we assume 147 109 mentofawirelessnetworkhavingmultipleintermediatenodes that the teletraffic of S1 and S2 is different. Closed-form ex- 148 110 andeavesdroppers,wherethelinksbetweenthesourceandthe pressions are obtained both for the OP and for the intercept 149 111 eavesdropper are not considered. In [30], three different cat- probability(IP)ofbothS1andS2. 150 112 egories of relay and jammer selection have been considered, Finally,itisshownthatastheimpactofartificialnoiseonthe 151 113 where the channel coefficients between the legitimate nodes main link is reduced and on the wiretap link is increased, the 152 114 andtheeavesdroppersareusedbothforrelayselectionandfor SRT of the proposed ANaTWORS scheme is improved. Fur- 153 115 jammerselection.In[31],awirelessnetworkconsistingoftwo thermore,ourperformanceevaluationsrevealthattheproposed 154 116 source nodes is considered and multiple DF relay nodes are ANaOTWRS scheme consistently outperforms both the tradi- 155 117 involved in the presence of a single eavesdropper. The outage tionaldirecttransmissionregimeandtheone-waytransmission 156 118 probability(OP)hasbeenanalyzedforthetwo-wayDFscheme scheme[24]intermsofitsSRT. 157 119 relyingonthreetransmissionslots. The organization of this paper is as follows. In Section II, 158 120 Motivatedbytheaboveconsiderations,weinvestigateawire- webrieflycharacterizethephysical-layersecurityofatwo-way 159 121 lessnetworksupportingapairofsourcenodeswiththeaidofN wireless network. In Section III, the SRT analysis of the con- 160 122 two-wayDFrelaysinthepresenceofaneavesdropper.Incon- ventionaldirecttransmissionschemeaswellasoftheproposed 161 123 trastto[17]–[24],weexploreatwo-wayrelayingaidedwireless ANaOTWRS scheme communicating over a Rayleigh chan- 162 124 network.Furthermore,weproposeanartificialnoiseaidedtwo- nel is carried out. Our performance evaluations are detailed in 163 125 way opportunistic relay selection (ANaTWORS) scheme, and SectionIV.Finally,inSectionV,weconcludethepaper. 164 126 analyzetheSRTofthewirelessnetworkinvestigated.Duetothe 127 channelstateinformation(CSI)estimationerror,itisimpossible II. SYSTEMMODELANDRELAYSELECTION 165 128 toguaranteethatnointerferenceisreceivedattherelaynodes, 129 causedbythespeciallydesignedartificialnoise.Moreover,the A. SystemModel 166 130 impact of the artificial noise both on the relays and on the As shown in Fig. 1, we consider a wireless network con- 167 131 eavesdropperischaracterized,whichwillbetakenintoaccount sisting of a pair of source nodes, denoted by S1 and S2, plus 168 132 whenevaluatingthewirelessSRToftheproposedANaTWORS N two-way DF relays, denoted by Ri, i∈{1,...,N}, which 169 133 scheme.Againstthisbackground,themaincontributionsofthis communicate in the presence of an eavesdropper E, where 170 134 paperaresummarizedasfollows. E is assumed to be within the coverage area of S1, S2, and 171 135 First,weproposeanANaTWORSschemeforprotectingthe Ri. All nodes are equipped with a single antenna. We assume 172 136 ongoingtransmissionsagainsteavesdropping.Tobespecific,in that there is no direct link between S1 and S2 due to the path 173 137 thefirsttimeslot,S1 transmitsitssignalstotherelays,andS2 loss. Furthermore, in the spirit of [21], both the main and the 174 138 transmits artificial noise in order to protect the signals trans- wiretaplinksaremodeledbyRayleighfadingchannels,where 175 139 mittedbyS1 againsteavesdropping. Similarlytothefirsttime the main and wiretap links are represented by the solid and 176 140 slot, S2 transmits its signals to the relays in the second time dashed lines in Fig. 1, respectively. Let hs1i, hs2i, hs1e, and 177 141 slotundertheprotectionofartificialnoisetransmittedbyS1.In hs2e,i∈{1,...,N},representtheS1−Ri,S2−Ri,S1−E, 178 DINGetal.:SECURITY-RELIABILITYTRADEOFFANALYSISOFARTIFICIALNOISEAIDEDTWO-WAYOPPORTUNISTICRELAYSELECTION 3 179 and S2−E channel gains, respectively. We assume that the From (1), the achievable rate of the S1−Ri link can be 231 180 channelcoefficientshs1i,hs2i,hs1e,andhs2e aremutuallyinde- expressedas 232 181 pendentzero-meancomplexGaussianrandomvariables(RVs) (cid:3) (cid:4) 118832 woviethr,vwaeriaanscsuesmoeftσhas21tit,hσes2S2i1,σ−s21Re,iaannddσSs222e−,rResipelicntkivsealyre.Mreocirpe-- Cs1i = 31log2 1+ α|h|hs2si1|i2|γ2sγs+2 (2) 184 rocal,i.e.,wehave,hs1i =his1 andhs2i =his2.Forsimplicity, 111888567 wσnes2el2eags=asiunαmsse2oefσσs2et21h,iew=mhαearisen1iσσlim2m2nk,asσns2ad2nidσ=e2oαrfestp2hrieeσsm2wen,irtσets2tha1eep=alvineαkrsas1,geeσree2cs,hpaaenncd-- wtfirmohmeeresSlto1httesofaSarce2tovreriaq1uR/i3rie.adrifsoerscforommpltehtienfgacthtethsaitgtnharleetraonrtshmoigsosinoanl 222333534 188 tively.Moreover,letλme =σm2 /σe2,whichisreferredtoasthe Naturally,theartificialnoiseisspeciallydesignedtointerfere 236 189 MUER. withtheeavesdropper.However,itsperturbationimposedonthe 237 190 ThethermalnoiseofanynodeismodeledasacomplexGaus- eavesdropper may be imperfect due to CSI estimation errors, 238 191 sian random variable with a zero mean and a variance of N0, which is characterized by β. Hence, the signals received at E 239 192 denoted by ns1, ns2, ni, and ne, respectively. Following [31], fromS1canbeexp(cid:2)ressedas (cid:2) 240 193 theoperationofthetwo-wayDFschemerelyingonopportunis- y =h P /2x +h βP /2ω +n . (3) 194 ticrelayselectionissplitintothreetimeslots.Weassumethat s1e s1e s s1 s2e s s2 e 195 the nodes in the network are synchronized with each other. In From (3), the achievable rate of the S1−E link can be 241 196 thefirsttimeslot,S1 transmitsitssignal,denotedbyxs1 tothe formulatedas 242 119987 roeulsalyys.,IanntdhethseencoSn2dtrtaimnsemsiltost,thSe2atrrtainfiscmiailtsnoitissesiωgns2alsxims2ulttoanthee- Cs = 1log (cid:3)1+ |hs1e|2γs (cid:4). (4) 199 relays and S1 transmits artificial noise simultaneously. In the s1e 3 2 β|hs2e|2γs +2 200 thirdtimeslot,theselectedrelayforwardthesignalxr toboth 220012 SX1ORanodpSer2a,twiohne.rFeuwrtehehramvoerxe,rt=hexpsr1o⊕poxsesd2,raenlady⊕sedleecntoiotensctahne nodInest,heansdecSo1ndsitmimueltasnloeto,uSs2lytrtarnansmsmitistsitasrstiifignciaallsntooitshee. rSeilmay- 224434 203 becoordinatedbyrelyingonadistributedpattern(governedby ilarly, the signals received at Ri transmitted by S2 can be 245 204 atimer).Withoutlossofgenerality,weassumeE[|xsj|2]=1, expressedas (cid:2) (cid:2) 246 220056 E[F|ωusrjth|2e]rm=oNre0,,wje=al1s,o2a.ssumethatS1 andS2 havetoconvey ys2i =hs2i Ps/2xs2 +hs1i αPs/2ωs1 +ni. (5) 220078 dcoifmfepreanrits-orant,etthreafofince,-dweanyoteredlabyyinRgs1scahnedmRes(2O,rReSsp)eocftiv[2el4y].cFaonr Using(5),theachievabl(cid:3)erateoftheS2−Ri l(cid:4)inkisgivenby 247 209 besimplyextendedtoatwo-wayscenariorelyingonfourtime C = 1log 1+ |hs2i|2γs . (6) 210 slots. To be specific, S1 transmits its signals to the relays in s2i 3 2 α|hs1i|2γs +2 211 the first time slot, S2 transmits its signals to the relays in the 212 second time slot, and the selected relay forward the decoded Similarly,thesignalsreceivedatEfromS2canberepresented 248 213 signals to S2 and S1 in the third time slot and the fourth time as (cid:2) (cid:2) 249 214 slot,respectively. y =h P /2x +h βP /2ω +n , (7) s2e s2e s s2 s1e s s1 e whiletheachievablerateoftheS2−E linkis 250 215 B. Two-WayRelayingScheme (cid:3) (cid:4) 1 |h |2γ 216 In this section, we first consider the physical-layer security Cs = log 1+ s2e s . (8) 217 of the two-way relaying scheme. We then propose our ANaT- s2e 3 2 β|hs1e|2γs +2 218 WORSarrangement. 2) Decoding Set: In this section, we analyze the suc- 251 219 1) S1andS2Transmit: Inthefirsttimeslot,S1transmitsits cessful decoding set of the wireless network portrayed in 252 220 signaltotherelaysundertheprotectionofartificialnoisetrans- Fig. 1. As shown in [24], the resultant successful de- 253 221 mitted by S2. For the sake of a fair power consumption com- coding set of the ORS scheme is given by Ω, where 254 222222342 ptthhaeerittsrooatnnalswmtriatihtnpsbomowtihteprthsoewofdeiSrre1ocfatnStdr1aSnan2smdariSess2dioiesnncoaotnenddsttbrhayeinPOesRd/S2to.sAcPhsse,mmtheeunss-, Ωslaeyt=sa,n{ndφ∈,ΦD{n11,r,De2p,2r.,e..s..e,.n2,tsNDtn−h,e.1.n}.t.h,TDnh2oeNns−eum1c}pc,etyφsssfduuelbnsdeoettceoosdfittnhhgeeseNemtsproteyf- 222555576 225 tionedabove,itisimpossibletoguaranteethattheartificialnoise 222267 ptheerfuebctilqyuiltioesusinCtShIeensutilmlsaptiaocneeorfrothr,ehSe1nc−eRleiadcihnagnntoelas,cdeuretation tdheecordeilnagysxdse1fiannedd axss2thaorseedtehnaotteadrebcyapΩab1leanodf sΩu2c,cersessfpuelcly- 225598 tively. Consequently, the set of the relays that successfully 260 222232908 iRSn1itecirsafneqrubeanenceteixfirpeerdceesbisvyeedαda.asTthReis.iTghnealismrpecaecitvoefdthateRarititfiracniaslmniottiesdeobny dlΨaetce=oddΩaes1bΨ∩otΩ=h2.x{φs1,Φan1,dΦx2s,2..i.s,dΦenn,o.t.e.d,Φby2NΨ−1,}w,whihcehreiswfeorhmavue- 222666321 (cid:2) (cid:2) Forexample,thedecodingsetsofΩj andΨhavebeenshown 264 ys1i =hs1i Ps/2xs1 +hs2i αPs/2ωs2 +ni. (1) asTableI,wherewehaveN =3andj ∈{1,2}. 265 4 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.00,NO.00,2016 TABLEI ANaTWORSscheme,whichcanbegivenby 283 DECODINGSETSOFΩj ANDΨ,WHENN =3ANDWHENj∈{1,2} o= argmax[min(C (i),C (i))] i∈Φn (cid:7) (cid:5) is1 is2 (cid:6)(cid:8) = argmax min |h |2,|h |2 (17) i∈Φn is1 is2 where o denotes the selected optimal relay. Moreover, from a 284 morepracticalpointofview,theCSIs|his1|2and|his2|2canbe 285 estimatedinpracticalwirelesscommunications,usingchannel 286 estimationschemes[32]. 287 5) ConditionofInterceptEvent: IntheΦ=φcase,aneaves- 288 dropper can successfully wiretap the signal transmitted by S1, 289 whenCss1e >Rs1. 290 In the Φ=Φn and Css1e >Rs1 case, an eavesdropper can 291 successfullywiretapthesignaltransmittedbyS1. 292 In the Φ=Φn and Css1e Rs2, the signal received at E can be 295 266 Asmentionedabove,theeventofΦ=φcanbecharacterized rewrittenas 296 (cid:2) 267 as y =h P x +n . (18) oe oe s s1 e C R andC >R , i∈Φ oe 3 2 oe s s1i s1 s2i s2 n Cs1j Rs2 andCoe >Rs1. 300 270 3) RelayTransmits: Withoutlossofgenerality,hereweas- Similarly,wecanformulatetheconditionofaneavesdropper 301 271 sumethatRiisselectedfromthesetΦn.Thentheselectedrelay successfullywiretappingthesignaltransmittedbyS2as 302 272 Ri broadcaststheencodedsignalxr toS1 andS2.Thesignals IntheΦ=φcase,aneavesdroppercansuccessfullywiretap 303 273 receivedatS1froyms1R(ii)c=anhbies1w(cid:2)riPttsexnra+s ns1. (11) tshuecIcnseitgshsnefauΦllltyr=awnΦsimrneitatatnpeddtChbesys2seSig>2n,apRlrotsr2vasindcseemdnaittrhtieaodt,Cabnyss2eSea2v>.esRdrso2.ppercan 333000465 274 ThesourceS1mayinvokesuccessiveinterferencecancelation casIen,athneeaΦve=sdrΦonp,peCrscs2aenwirRetsa1p, tahnedsiCgnoeal>traRnss2- 330078 275 (SIC),thus,(18)canbewrittenas (cid:2) mittedbyS1. 309 y (i)=h P x +n . (12) s1 is1 s s2 s1 III. SECURITY–RELIABILITYTRADEOFFANALYSIS 310 276 TheachievablerateoftheRi −S1linkcanbeexpressedas OVERRAYLEIGHFADINGCHANNELS 311 (cid:5) (cid:6) C = 1log 1+|h |2γ . (13) Inthissection,weanalyzeboththeOPandIPoftheproposed 312 is1 3 2 is1 s ANaTWORSschemesoverRayleighfadingchannels. 313 277 Similarly, S2 can also invoke SIC, thus the signals received 278 atS2fromRi canbewrittenas A. SRTAnalysisoftheProposedANaTWORSScheme 314 (cid:2) y (i)=h P x +n . (14) 1) SRTAnalysisofS1: IntheANaTWORSscheme,arelay 315 s2 is2 s s1 s2 willonly be chosen fromthe set Φn.Withthe aid of Shannon 316 279 TheachievablerateoftheRi −S2linkcanbeobtainedas [33]andthelawoftotalprobability[34],theOPoftheS1 →S2 317 (cid:5) (cid:6) linkrelyingontheANaTWORSschemecanbeformulatedas 318 1 C = log 1+|h |2γ . (15) is2 3 2 is2 s Psingle = Pr(C Δ1 ×⎝1−exp⎝−j∈An(m) σΔj2s12 + σΔj2s11 − σΔi2s11 − σΔi2s12⎠⎠⎠⎠. (cid:3) (cid:4)(cid:4) (24) |h |2 ×Pr (cid:3)α|hs1i|s(cid:3)22γis +(cid:3)2 >Δ2 (cid:4) ISnubosutrituAtNinagT(W23O)RanSds(c2h4e)minet,oa(n22e)a,vPesosduintrgsole1pcpaenr bcaenobotvaeirnheeda.r 333301 2(cid:9)N−1 (cid:10) |h |2 thesignalstransmittedbyS1,S2,andRi.Usingthelawoftotal 332 + Pr α|h |s21γi +2 >Δ1 probability[34]andthedefinitionofaninterceptevent,wecan 333 n=1(cid:3) i∈Φn s2i (cid:4)s(cid:4) expresstheIPoftheS1 →E linkas 334 (cid:15) (cid:16) ×Pr α|h|h|s22γi|2+2 >Δ2 Pisnitngsl1e = Pr Css1e >Rs1,D=φ (cid:3) s1i (cid:3)s (cid:4) 2(cid:9)N−1 (cid:15) (cid:16) × (cid:10) 1−Pr α|h|hs|21jγ|2+2 >Δ1 + n=1 Pr Css1e >Rs1,Φ=Φn j∈Φ¯(cid:3)n s2j s(cid:4)(cid:4) +2(cid:9)N−1Pr(cid:15)Cs R ,C >R ,Φ=Φ (cid:16). |h |2 s1e s1 s2e s2 oe s1 n ×Pr s2j >Δ n=1 (cid:5) α|hs1j|2γs +(cid:6)2(cid:6) 2 (25) ×Pr |hos2|2 <Δ1 (22) Using(4),(8),and(19),(25)canbeexpressedas 335 (cid:3) (cid:3) (cid:4) (cid:10)N |h |2 332243 (w2h3e·Rres2 −w1)e/γs.have Δ1 =(23·Rs1 −1)/γs, and Δ2 = Pisnitngsl1e = i=1 1−Pr α|hs2i|s21γis +2 >Δ1 (cid:3) (cid:4)(cid:4) 332256 expBraessesdedaosn Appendix A, Pr(α|h|sh2si|12iγ|2s+2 >Δ1) can be ×Pr α|h|h|s22γi|2+2 >Δ2 (cid:3) (cid:4) (cid:3) (cid:4) (cid:3) s1i s (cid:4) Pr α|hs|2hi|s21γi|s2+2 >Δ1 =Δ1αγsσσss2212ii +σs21i exp −2σΔs21i1 . ×Pr β|hs|2hes|21eγ|s2+2 >Δ1 (23) (cid:17) (cid:3) (cid:3) (cid:4) 327 According to Appendix B, Pr(|hos2|2 <Δ1)) can be +2(cid:9)N−1 (cid:10) Pr |hs1i|2 >Δ 328 expressedas α|h |2γ +2 1 (cid:3)(cid:3) (cid:3) (cid:4)(cid:4) n=1(cid:3) i∈Φn s2i (cid:4)s(cid:4) (cid:5) (cid:6) (cid:9) Δ |h |2 Pr |h |2<Δ = 1−exp − 1 ×Pr s2i >Δ +2|Φ(cid:9)n|o−s12−1(−1)|1An(m)i|∈⎛⎝Φnσi2s1 (cid:9) (cid:3)σ12σi2s+2 σ12 (cid:4)+1⎞⎠−1 × (cid:10) (cid:3)α1|h−s1iP|2rγ(cid:3)s +α|2h|h|s21γi|22+2 >Δ1(cid:4) (cid:3)m=1 (cid:3) (cid:4)(cid:4) j∈An(m) js2 js1 j∈Φ¯(cid:3)n s2i s(cid:4)(cid:4) Δ |h |2 × 1−exp − 1 ×Pr s2i >Δ −2|Φ(cid:9)n|−1−1⎛⎝(−1σ)|i2As2n(m)|⎛⎝σ2 (cid:9) (cid:3) 1 + 1 (cid:4)+1⎞⎠−1 ×Pr(cid:3)α|hs|1his|21eγ|s2+2 >Δ2(cid:4)(cid:18) is1 σ2 σ2 β|h |2γ +2 1 m=1 j∈An(m) js2 js1 s2e s ×⎛⎝σi2s2j∈A(cid:9)n(m)(cid:3)σj12s2 + σj12s1(cid:4)+ σσii22ss21 +1⎞⎠−1 +2n(cid:9)N=−11(cid:17)i(cid:10)∈Φn (cid:3)Pr(cid:3)α|hs|2hi|s21γi|s2+2 >Δ1(cid:4) 6 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.00,NO.00,2016 (cid:3) (cid:4)(cid:4) 336 ×Pr (cid:3)α|hs|1hi|s22γi|(cid:3)s2+2 >Δ2 (cid:4) andC3)lPeiSasnirtRnlgsyTl1e,.Panosuiantlgsyle2siasndofPSisn1itngsal2encdanS2b:eoTbhteaiInPedansidmOilaPrloyftothPeospuintagsile1r 333444567 × (cid:10) 1−Pr |hs1i|2 >Δ of sources is defined as the average IP and OP of S1 and S2, 348 α|h |2γ +2 1 respectively: 349 j∈Φ¯(cid:3)n s2i s(cid:4)(cid:4) Psingle +Psingle |h |2 Psingle = ints1 ints2 (31) ×Pr s2i >Δ int 2 α|h |2γ +2 2 (cid:3) s1i s (cid:4) and 350 |h |2 |h |2 Psingle +Psingle ×Pr β|h s|21eγ +2 <Δ1,β|h s|22eγ +2 >Δ2 Posuintgle = outs1 2 outs2 . (32) (cid:5) s2e s (cid:6)(cid:8) s1e s ×Pr |h |2 >Δ . (26) IV. PERFORMANCEEVALUATION 351 oe 1 Forcomparison,theSRTanalysisoftheconventionaldirect 352 337 Accord(cid:3)ingtoAppendixC, (cid:4) transmissionschemeoperatingwithoutrelaysisalsoprovided. 353 |h |2 |h |2 The total IP and OP of S1 and S2 with the traditional direct 354 Pr β|h s|21eγ +2 <Δ1,β|h s|22eγ +2 >Δ2 transmissionschemeisdefinedas 355 s2e s s1e s Pdirect+Pdirect Pdirect = ints1 ints2 (33) 338 canobtainedas int 2 (cid:3) (cid:4) Pr |hs1e|2 <Δ , |hs2e|2 >Δ and 356 β|h |2γ +2 1 β|h |2γ +2 2 Pdirect +Pdirect s2e s s1e s Pdirect = outs1 outs2, (34) (cid:19) (cid:20) (cid:19) (cid:20) out 2 Δ γ βσ2 2Δ 334309 lateAdPccaros(cid:5)r|d=hing|12to−>AΔΔpp2(cid:6)γesn=βd2iσxs(cid:9)s21De,+s⎡⎣2Peσ⎛⎝rs(22|1he+oe|e22|xD>(cid:9)pn|−Δ1−−11)σ(−cs22ae12n)|bA.en(fmor)(m|2u7-) aPs(re2proesd2euipRrcteetsscgic12tvitve=−ivleyen11.ly)M−/,bγoyeswrx.ehpoPNe(vir−dneoeitrrtie,σsincn1sΛ2wt1g1=se2P)htiedhn,aixtaravesptnce1t(d,−σΛPs21Pσ2oΛdss2=uii1d1n1rte,eitrsce()s2tc2σ,2t=,2s2R1Pes1P,i1dn−oitd−ruaeisrtcne2etsc1dx1t=),p/σ(γe−as2xs2npeσad(sΛn2−2ad2srP2eσΛ)Λos2d,u22i2trtereh=esc)e2t-, 333335556678901 ⎛⎝ oσei2s2σi2s1 1 (cid:9)i∈Dn(cid:3) 1 + m1=(cid:4)1 +1⎞⎠−1⎞⎟⎠ erreexsspIpuneelcttcsthteiidfvsoesrlevycat.htliueoenst,rawodefitpiotrhneesaelnRdtVibrseoctht|hotsru2asrn1ns|2mu,mis|eshrisoic1nea,|l2aa,nsadwnsdeimll|uhalsas2teifo|o2nr, 333366662354 σi2s2 +σi2s1 j∈An(m) σj2s2 σj2s1 the ORS [24] and for the ANaTWORS schemes in terms of 366 (cid:19) (cid:20)(cid:24) their SRTs. Moreover, the analytic IP versus OP results of the 367 ×exp −Δ1 . (28) directtransmissionandANaTWORSschemesareobtainedby 368 σ2 plotting(33),(34),(31),and(32),respectively.Itispointedthat 369 ie theIPversusOPresultsoftheORSschemearecalculatedfrom 370 341 Substituting(27)and(28)into(26),Pisnitngsl1ecanbeobtained. (27) and (19) of [24], where α is rewritten as (24Rd −1)/γs. 371 342 2) SRTAnalysisofS2: SimilarlytoS1,theOPofS2canbe Throughout this performance evaluation, we assumed αs1i = 372 343 expressedas αs2i =αs1e =αs2e =αs1s2 =1. 373 We first consider the effect of different MUERs. Fig. 2 de- 374 2(cid:9)N−1 Psingle =Pr(Φ=φ)+ Pr(C R ,D=φ(cid:16) serve from Fig. 2 that as the MUER decreases, all the IPs of 379 ints2 s2e s2 the direct transmission, of the ORS and of the ANaTWORS 380 2(cid:9)N−1 (cid:15) (cid:16) schemes are increased, which can be explained by observing 381 + Pr Css2e >Rs2,Φ=Φn that upon decreasing the MUER, an eavesdropper can achieve 382 n=1 a higher achievable rate. Moreover, Fig. 2 also illustrates that 383 2(cid:9)N−1 (cid:15) (cid:16) the proposed ANaTWORS scheme generally has a lower IP 384 + Pr Css2e Rs1,Coe >Rs2,Φ=Φn . than the traditional direct transmission and ORS regime for 385 n=1 MUER=3 dB and MUER=0 dB. Additionally, the dif- 386 (30) ferencebetweentheanalyticandsimulatedIPversusOPcurves 387 DINGetal.:SECURITY-RELIABILITYTRADEOFFANALYSISOFARTIFICIALNOISEAIDEDTWO-WAYOPPORTUNISTICRELAYSELECTION 7 Fig. 2. IP versus OP of the direct transmission, ORS, and ANaTWORS Fig. 4. IP versus OP of the direct transmission, ORS, OSJ-MMISR, and schemes for different MUERs λme and for N =8, which were calculated ANaTWORS schemes for different α and β associated with an MUER of from[24,(33),(34)and[27]],[(24),(19)],and(31)and(32). λme = 0dB,N =8,whichwerecalculatedfrom[24,(33),(34)and[27]], [(24),(19)],and(31)and(32). Fig. 4 illustrates the IP versus OP of both the direct trans- 401 mission, as well as of the ORS, of the optimal selection 402 withjammingwithmax–mininstantaneoussecrecyrate(OSJ- 403 MMISR) [30] and of the ANaTWORS schemes for differ- 404 ent self-interference and interference factors, where (β,α)= 405 (0.95,0.06)and(β,α)=(0.99,0.02)areconsidered.Observe 406 fromFig.4thatastheartificialnoiseparametersof(0.95,0.06) 407 are changed to (0.99,0.02), the IP versus OP performance 408 of the ANaTWORS scheme improves. Furthermore, Fig. 4 409 alsoillustratesthattheproposedANaTWORSschemeoutper- 410 forms the direct transmission, the ORS and the OSJ-MMISR 411 schemes in terms of its IP versus OP tradeoff for both the 412 (β,α)=(0.95,0.06)and(β,α)=(0.99,0.02)cases,sincethe 413 CSI of the eavesdropper links cannot be readily acquired, the 414 CSIsofthewiretaplinksarenottakenintoaccountinthepro- 415 posedANaTWORSscheme.Forthesakeofafaircomparison, 416 the CSIs of the wiretap links in the OSJ-MMISR scheme [30] 417 Fig. 3. IP versus OP of the direct transmission, ORS and ANaTWORS arenotconsideredeither. 418 schemesfordifferentnumberofrelaysassociatedwithanMUERofλme = Fig.5showstheIPversusOPofthedirecttransmission,ofthe 419 0 dB,whichwerecalculatedfrom[24,(33),(34)and[27]],[(24),(19)],and ORSandoftheANaTWORSschemesfordifferenttele-traffic 420 (31)and(32). ratiosofS1 andS2,namely,forRs1/Rs2 =0.5,Rs1/Rs2 =1, 421 and Rs1/Rs2 =2. Observe from Fig. 5 that the ANaTWORS 422 388 of the ANaTWORS scheme is negligible, demonstrating the scheme performs best for Rs1/Rs2 =1. Moreover, the dif- 423 389 accuracyofourSRTanalysis. ference remains modest for asymmetric traffic ratios of both 424 390 InFig.3,weshowtheIPverusOPperformanceofboththedi- Rs1/Rs2 =0.5 and Rs1/Rs2 =2. This is due to the fact that 425 391 recttransmission,aswellasoftheORSandoftheANaTWORS for a fixed power allocation case, some of the power will be 426 392 schemefordifferentnumberofrelaysN.Wecanobservefrom wasted,whentheinstantaneouschannelgainissufficientlyhigh 427 393 Fig. 3 that as the number of relays N increases from N =4 andthetrafficdemandislow.Additionally,nobeneficialrelia- 428 394 to 8, the IP of all schemes is reduced at a specific OP, which bilityimprovementisachieved,despitedegradingthesecurity. 429 395 meansthatincreasingthenumberofrelaysimprovesthesecurity This is interesting, hence we will adopt an adaptive power al- 430 396 versus reliability tradeoff of wireless transmissions. Addition- location scheme for improving the security of wireless trans- 431 397 ally, Fig. 3 also demonstrates that IP versus OP performance missions in our future research. Finally, Fig. 5 also illustrates 432 398 oftheproposedANaTWORSschemeisbetterthanthatofthe thattheproposedANaTWORSschemeperformsbetterthanthe 433 399 directtransmissionandoftheORSschemesforalltheN values directtransmissionandORSschemesforallthreetraffic-ratios 434 400 considered. considered. 435 8 IEEETRANSACTIONSONVEHICULARTECHNOLOGY,VOL.00,NO.00,2016 specially designed artificial noise was projected onto the null 450 space of Ri, hence resulting in a certain amount of interfer- 451 enceimposedontherelays.Hence,theself-interferenceandthe 452 interference factors were taken into account for characterizing 453 thewirelessSRTsoftheproposedANaTWORS,wherethese- 454 curity and reliability are quantified in terms of the IP and OP, 455 respectively.ItwasalsoillustratedthattheANaTWORSscheme 456 outperforms both the conventional direct transmission and the 457 ORS schemes in terms of its (IP x OP) product. Furthermore, 458 asthenumberofrelaysincreases,theSRToftheANaTWORS 459 schemeimproves. 460 Here, we only explored the allocation of a fixed power to 461 thesourcenodesandrelaysnodes.Inourfuturework,wewill 462 adopt an adaptive power allocation scheme in this scenario. 463 Specifically,thepowercanbedynamicallyallocatedaccording 464 tothenearinstantaneouschannelgainandthetrafficdemands 465 ofusers. 466 Fig. 5. IP versus OP of the direct transmission, ORS and ANaTWORS schemesfordifferenttrafficassociatedwithanMUERofλme =0dB,N =8, whichwerecalculatedfrom[24,(33),(34)and[27]],[(24),(19)],and(31)and APPENDIXA 467 (32). Upon introducing the notation of X1 =|hs1i|2 and X2 = 468 |hs2i|2, noting that RVs |hs1i|2 and |hs2i|2 are exponentially 469 distributed and independent of each other. Thus, the proba- 470 bility density functions (PDFs) of X1 and X2 are fX1(x1)= 471 σ21 exp(−σx21 )andfX2(x2)= σ21 exp(−σx22 ),respectively. 472 s1i s1i s2i s2i Hence,Pr(α|h|sh2si|12iγ|2s+2 <Δ1)canbeexpressedas 473 (cid:3) (cid:4) |h |2 Pr s1i <Δ α|h |2γ +2 1 s2i s =Pr[x <(x αγ Δ +2Δ )] 1 2 s 1 1 (cid:3) (cid:4)(cid:3) (cid:3) (cid:4)(cid:4) (cid:25) ∞ 1 x 2Δ +Δ αγ x = exp − 2 1−exp − 1 1 s 2 dx σ2 σ2 σ2 2 0 s2i s2i s1i (cid:3) (cid:4) σ2 2Δ =1− s1i exp − 1 (A.1) Δ αγ σ2 +σ2 σ2 1 s s2i s1i s1i Fwiigth.6λ.meIP=x0OdBPoanfdthNed=ire8c,twtrhaincshmwisesrieonc,aOlcRulSateadndfrAomNa[T24W,O(3R3S),s(3ch4e)maneds whereσs21i andσs22i aretheexpectedvaluesofRVs|hs1i|2 and 474 [27]],[(24),(19)],and(31)and(32). |hs2i|2,respectively. 475 436 Fig.6illustratesthe(IPxOP)productofthedirecttransmis- APPENDIXB 476 437 sion,oftheORS,andoftheANaTWORSschemesfordifferent Using the law of total probability [34], the term 477 443389 SthNeRscsh.eOmbessercvaenferxohmibiFtiagn.(6IPthxaOt uPp)opneaikn,cbreuatstihnegmthaexiSmNuRm,(aIlPl Pr(|hos2(cid:5)|2 <Δ1)canb(cid:6)erewrittenas 478 440 xOP)productoftheproposedANaTWORSschemeissmallest Pr |h |2 <Δ 441 ofthethreeschemes,whichdemonstratesitssuperiority. (cid:9) os(cid:19)2 1 (cid:5) (cid:6) = Pr |h |2 <Δ , max min |h |2,|h |2 442 V. CONCLUSION i∈Φn (cid:5) is2 1(cid:6)j(cid:6)∈Φn−{i} js2 js1 443 In this paper, we proposed an ANaTWORS scheme for a 444 wirelessnetworkconsistingofthepairofsourcenodesS1 and Δ2)canbeobtained(cid:4)as 516 m=1 j∈An(m) |h |2 |h |2 (cid:3) (cid:4) (cid:4) Pr s1e <Δ , s2e >Δ × 1 + 1 + σi2s2 +1 −1 β|hs2e|2γs +2 1 β|hs1e|2γs +2 2 σ2 σ2 σ2 (cid:25) (cid:25) ⎛ js2 ⎛js1 (cid:3)is1 (cid:4) ⎞⎞⎞ = ∞ (x2−2Δ2)/Δ2βγs f (x ,x )dx dx (cid:9) X1X2 1 2 1 2 ×⎝1−exp⎝− Δ1 + Δ1 − Δ1 − Δ1⎠⎠⎠. (cid:25)2Δ2 0 (cid:3)(cid:25) (cid:4) j∈An(m) σj2s2 σj2s1 σi2s1 σi2s2 = ∞ f (x ) (x2−2Δ2)/Δ2βγs f (x )dx dx (B.8) 2Δ2 X2 2 0 X1 1 1 2 (cid:19) (cid:20) (cid:19) (cid:20) Δ γ βσ2 2Δ 504 Using(B.5)and(B.8),Υ0+Υ1canbeexpressedas = 1− Δ γ β2σs2 +s2eσ2 exp −σ2 2 . (C.1) (cid:3) (cid:4) 2 s s1e s2e s2e Υ +Υ =1−exp − Δ1 APPENDIXD 517 0 1 σ2 +2|Φ(cid:9)n|−1−1(−1)|An(m)|⎛⎝σi2s2 (cid:9) (cid:3) 1 + 1 (cid:4)+1⎞⎠−1 beUwsriinttg(cid:5)enthaeslaw of(cid:6)total probability [34], Pr(|hoe|2 >Δ) can 551189 is1 σ2 σ2 Pr |h |2 >Δ m=1 j∈An(m) js2 js1 oe (cid:3) (cid:3) (cid:4)(cid:4) (cid:9) (cid:19) (cid:5) (cid:6) ×−2|Φ1(cid:9)n−|−1−ex1⎛⎝p(−−1σ)Δ|i2As12n(m)|⎛⎝σ2 (cid:9) (cid:3) 1 + 1 (cid:4)+1⎞⎠−1 = i<∈Φmn Pinr(cid:5)|h|hisie2||22,>|hiΔs11|2,j(cid:6)∈(cid:6)Φmna−x{i}min |hjs2|2,|hjs1|2 ×⎛⎝σm2=1 (cid:9) (cid:3) 1 + 1is1j(cid:4)∈A+n(σmi2)s2 +σj21s⎞⎠2 −1σj2s1 = i(cid:9)∈Φn Pr(cid:5)(cid:5)|hie|2 >Δ1(cid:6)(cid:6)P(cid:6)r(cid:19)j∈mΦna−x{i}min(cid:5)|hjs2|2,|hjs1|2(cid:6) ⎛is2j∈An⎛(m) σj2s2 (cid:3)σj2s1 σi2s1(cid:4) ⎞⎞⎞

Security-Reliability Tradeoff Analysis of Artificial Noise Aided Two-Way Opportunistic Relay Selection

Similar Security-Reliability Tradeoff Analysis of Artificial Noise Aided Two-Way Opportunistic Relay Selection