The impact of ICI1 on the opportunistic relay selection in dual-hopcognitivenetworksi.e.,withoutconsideringthedirect channel,whichselectstherelaywiththemaximumend-to-end 1 The impact of
Trang 1jo u r n al ho m e p a g e :w w w e l s e v i e r c o m / l o c a t e / a e u e
Khuong Ho-Van∗
Telecommunications Engineering Department, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Str., District 10, Ho Chi Minh City, Viet Nam
a r t i c l e i n f o
Article history:
Received 8 February 2015
Accepted 7 August 2015
Keywords:
Opportunistic relay selection
Imperfect channel information
Cognitive radio
Performance saturation
a b s t r a c t
1 Introduction
Traditional static spectrum allocation is not flexible and
induceslowspectrumutilizationefficiency[1].Thisissueturned
withhighradiospectrumdemandofemergingwirelessservices
requires appropriate solutions to mitigate current spectrum
under-utilization.Cognitiveradiotechnology,which allows
sec-ondary/unlicensed users (SUs) to opportunistically access the
spectruminherentlyallotted toprimary/licensedusers (PUs),is
arightsolutiontothesecriticalissues[2].Nevertheless,inorder
toassuretransparentcommunicationofPUs,SUsmustlimittheir
transmitpowerforacceptableinterferenceatPUs,andthus,
reduc-ingthecommunicationcoverageofsecondarytransmitters.With
theadvantageofwide radiocoverage,relayingtechniqueshave
recentlybeenincorporatedintoSUstocomplementthedrawback
oftheshortradiorangeof SUs[3].Therelayingprocesscanbe
assistedbymultiplerelaysforhighperformancebut low
band-widthefficiencyduetotherequirementoforthogonalchannelsfor
differentrelaysinordertopreventmutualinterference.Assuch,
selectingasinglerelayamong allpossiblecandidatesaccording
∗ Corresponding author Tel.: +84 1229900719.
E-mail address: khuong.hovan@yahoo.ca
to a certain criterion is preferred tooptimize system resource utilization(e.g.,powerandbandwidth),incomparisonwith multi-relayassisted transmission whileremaining thesame diversity order[4].Furthermore,channelstateinformationisvery impor-tantin theprocessofsystemdesign optimization(e.g.,optimal signaldetection).However,itisinevitablethatthis information cannotbecollectedwithoutanyerror.Therefore,theimpactof imperfectchannelinformation(ICI)ontheoutageperformanceof relayselection criteriaincognitiverelayingnetworksshouldbe thoroughlyinvestigatedbeforepracticalimplementation
The impact of ICI1 on the opportunistic relay selection in dual-hopcognitivenetworks(i.e.,withoutconsideringthedirect channel),whichselectstherelaywiththemaximumend-to-end
1 The impact of ICI on cognitive radio networks was studied in different aspects; for example, dual-hop relaying with relay selection (e.g., [7,6,5]), direct trans-mission (i.e., no relay) [8], the amplify-and-forward relay selection (e.g., [10,9]), relay non-selection (e.g., [11,13,15,12,14]) Moreover, several relay selection crite-ria in cognitive radio networks are suggested without investigating the impact
of ICI in [16–18,27,28,26,29,23,30,24,31,38,32,35,36,34,25,33,37,39,44,43,42,40,41] The current paper concentrates on the opportunistic relay selection in decode-and-forward cooperative cognitive networks, and thus, the literature related to the aspects studied in [11,16–18,27,28,26,29,23,30,24,31,38,32,35, 36,34,25,33,37,44,43,42,40,7,6,8,10,9,13,15,12,14,39,41,5] should not be further surveyed.
http://dx.doi.org/10.1016/j.aeue.2015.08.004
1434-8411/© 2015 Elsevier GmbH All rights reserved.
Trang 2signal-to-noiseratio(SNR),isinvestigated in[45].Nevertheless,
thisworkdoesnotinvestigateICIonallfadingchannels
simulta-neously,thatis,ICIoninterferencechannels(i.e.,channelsfrom
SUstoPUs)whileperfectchannelinformation(PCI)on
transmis-sionchannels(i.e.,betweenSUs);orICIontransmissionchannels
butPCIoninterferencechannels.Also,[45]onlyconsiders
indepen-dentpartially-identical(i.p.i.)fadingdistributions(i.e.,relaysare
assumedtobecloselylocated).TheeffectofICIonthereactiverelay
selection,which selectstherelayamong allpossiblecandidates
(i.e.,allrelays areassumedtocorrectlydecodesource
informa-tion)withthelargestSNRtothedestination,andtheLth-worst
relayselection,whichselectstheLth-worstrelay,isinvestigated
in[46,47].However,both[46,47]arelimitedtothecaseofICIon
interferencechannelswhilePCIontransmissionchannels,andthe
i.p.i.fadingdistributionassumption.TheeffectofICIonthepartial
relayselection,whichsimplyselectstherelaywiththelargestSNR
fromthesource,isstudiedin[42,48–50].Nevertheless,for
analy-sissimplicity,theworksin[42,48–50]imposeseveralassumptions
suchasonlyICIoninterferencechannelswhilePCIontransmission
channels,i.p.i.fadingdistributions,anddual-hoprelaying
The opportunistic relay selection is proved to be
capacity-optimal[16],andhence,itisinterestingtopredictits
information-theoreticperformancelimit(i.e.,outageprobability).Motivatedby
theabove,thispaperthoroughlyanalyzesitsoutageperformance
Thecontributionsofthispaperaresummarizedbelow:
• Proposeanexactclosed-formoutageprobabilityexpressionfor
cooperativecognitivenetworkswithopportunisticrelay
selec-tion,neglectingallassumptionsof[45].Morespecifically,this
expressionisapplicabletoageneralscenario:ICIonall
chan-nelsconcurrently,i.n.i.fadingdistributions,maximumtransmit
powerconstraint,interferencepowerconstraint,theusageofthe
directchannel
• Derivetheperformancelimitofcooperativecognitivenetworks
withopportunisticrelayselection,whichprovesnodiversitygain
achievableinthepresenceofICI
• Perform numerouscomparisons betweendual-hop and
coop-erativecognitivenetworks withopportunistic relayselection,
whichdemonstrateasignificantgainofutilizingthedirect
chan-nelinrelayingcommunicationsatalmostnoexpenseofsystem
resources(e.g.,powerandbandwidth)
• Provide numerousresultsto haveuseful insightsinto system
performancesuchasperformancesaturationphenomenonand
considerableperformance deterioration due to ICI, significant
performanceimprovementwithrespecttotheincreaseinthe
numberofrelays
• Outline an interference probability2 expression to reflect the
effect of channel information imperfection on the quality of
serviceof primaryusers Illustrativeresultsare alsoprovided
to show that the interference probability is proportional to
thenumberofrelays,whichconflictswithoutageperformance
improvement of secondary users when the number of relays
increases,establishingtheperformancetrade-offbetweenthe
primarynetworkandthesecondarynetworkwithrespecttothe
numberofrelays
Therestofthecurrentpaperisstructuredasfollows.The
sys-temmodelunderconsiderationispresentedin Section 2.Exact
2 Interference probability is defined as the probability that the interference power
constraint is invalidated Some works proposed the interference probability
expres-sion for the partial relay selection (e.g., [42,48,50]) and the reactive relay selection
(e.g., [46]) To the best of the author’s knowledge, the interference probability
expression for the opportunistic relay selection have not been presented in open
andlimit outageanalysisframework fortheopportunisticrelay selectionincooperativecognitivenetworksaswellasindual-hop cognitivenetworksiselaboratelydescribedinSection3.The inter-ferenceprobabilityexpressionisoutlinedinSection4.Resultsand discussionsontheoutageperformanceofthesenetworksaswell
astheinterferenceprobabilityareprovidedinSection 5.Finally, thepaperisclosedwithusefulconclusionsinSection6
2 System model
Acooperativecognitivenetworkwithopportunisticrelay selec-tionisdemonstratedinFig.1.Cooperativerelayingisimplemented
inthesecondarynetworkinwhichinformationtransmissionfrom thesourceSstothedestinationSdishelpedbytheselectedrelaySb
inthegroupofKrelays,S={S1,S2, ,SK}.Weassumecognitive radiostooperateintheunderlaymechanism(e.g.,[16,19–22]),and hence,SsandSbinterferethePU,namelyPp,buttheinterference levelatPpmustbelowerthanthemaximuminterferencepower,
I,thatcanbetoleratedbyPp
Weinvestigatefrequency-flatandi.n.i.Rayleighfading chan-nels.Therefore,thechannelcoefficient,htr,betweenatransmitter andareceiver,wheretandrdenotetheindicesofthe transmit-terandthereceiver,respectively(thespecificvaluesoftandrwill
bespecifiedlater),canbemodelledasacircularsymmetric com-plexGaussianrandomvariablewithzeromeanand1/tr-variance, i.e.htr∼CN(0,1/tr).Sinceourworkinvestigatesi.n.i.fading distri-butions,alltr’s,∀{t,r},arenotnecessarilyequal.Therefore,itis moregeneralandpracticalthanmostexistingworksonrelay selec-tionwherei.p.i.(i.e.,tr’sarepartitionedintogroupsofidentical value.Forexample,sr’s,rd’s,rp’swithr∈{1, ,K}areassumed
tobeidenticalin[7,16,23,24,26,29,42,45–48])orindependentand identical(i.e.,tr’s,∀{t,r},areequalin[25,27,28,31])fading distri-butionsareassumedforsimplicityofperformanceanalysis
It is inevitablethat PCIis impossibly availableowing tothe limitationsofchannelestimationalgorithms.Assuch,inorderto support performance analysis,we should model channel infor-mation imperfection appropriately In this work, we apply the well-known channel information imperfection model used in
[8,10,13,39,42,45,46,48,49,51].Accordingtothis model, thereal channelcoefficient,htr,isrelatedtotheestimatedone, ˆhtras
ˆhtr=trhtr+
1−2
Phase 1
Phase 2
Primary receiver
Secondary network
Pp
Trang 3where εtr is the channel estimation error, t∈
s,1, ,K
,r∈
p,1, ,K,d
.Aselaboratelydiscussedin[8],allrandom
vari-ables {ˆhtr, htr, εtr} are modelledas CN(0,1/tr) Moreover,the
correlationcoefficient0≤tr≤1isaconstant,characterizingthe
averagequalityofchannelestimation
Asexposed inFig.1,cooperative relayingwithopportunistic
relayselectiontakesplaceintwophases.Inthefirstphase,Ss
trans-mitsthesignalvswithtransmitpowerPs(i.e.,Ps=Evs{|vs|2}where
EX{·}denotestheexpectationovertherandomvariableX).Acertain
secondarytransmitterSt,t∈
s,1, ,K
mustobeythe under-laymechanismononehand(i.e.,Pt|htp|2≤I),andthemaximum
transmitpowerPdesignedforit(i.e.,Pt≤P)ontheotherhand.For
maximumtransmissioncoverage,theupper-boundofthetransmit
powerischosen,i.e.Pt=min(I/|htp|2
,P).Duetotheunavailability
ofchannelinformation,thetransmitpowermustbesetwiththe
estimatedchannelinformation(e.g.,[8])asPt=min(I/|ˆhtp|2,P).
ThereceivedsignalatSr,r∈
1, ,K,d
,canbeexpressedas
usr=hsrvs+nsrinwhichnsr∼CN(0,N0)istheadditivewhite
Gauss-iannoise(AWGN)atthesecondaryreceiverSr.Plugging(1)intousr,
oneobtains
usr= ˆhsr
srvs−
1−2
sr
whichgeneratesthesignal-to-noiseratio(SNR)atSrinthefirst
phaseas
sr= Evs{|ˆhsrvs/sr|2}
Evs,nsr{|nsr−
1−2
srεsrvs/sr|2}=ˇsr|ˆhsr|
2
BydenotingI=I/N0,P=P/N0,=I/P,x=|ˆhsp|2,theˇsrterm
in(3)canberepresentedinacompactformas
ˇsr= srPs
(1−2
sr)Ps+sr2
srN0
=
⎧
⎪
⎪
srI
sr2srx+(1−2sr)I ,x>
srP
(1−2sr)P+sr2sr
,x< (4)
Opportunisticrelayselectionoptsforarelay,namelySb,with
themaximumend-to-endSNR.Therefore,theSNRatSdthrough
therelayingchannelisexpressedas
sbd=max
whereR=
1,2, ,K
andkdistheSNRoftheSk−Sdchannel
Theexpressionofkdcanbeinferredinthesamemannerassr,i.e
where
ˇkd=
⎧
⎪
⎪
kdI
kd2
kdyk+(1−2
kd)I ,yk>
kdP
(1−2
kd)P+kd2
kd
,yk<
(7)
withyk=|ˆhkp|2.Itisnotedthatopportunisticrelayselectioncanbe
implementedinadistributedmannerusingthetimermethodin[4]
whereeachrelaySksetsitstimerwiththevaluethatisinversely
proportionaltomin(sk,kd)andtherelaywiththetimerthatruns
outfirstisselected
Inthesecondphase,theselectedrelaySbdecodesthesource
signalandre-encodesthedecodedinformationbeforeforwarding
toSd Then,Sd candecodethesourceinformationby
selection-combiningthereceivedsignalsinbothphases.Therefore,thetotal
SNRatS canberepresentedas =max( , ).Itisrecalled
thattheimplementationoftheselectioncombininginthispaper
issimplerthanthemaximumratiocombiningwithoutsignificant performancedegradation[52].Therefore,theselectioncombining
ispreferableinpracticalapplications.Moreover,sincebothsdand
sbd containa commontermx=|ˆhsp|2,theyarecorrelated Fur-thermore,thequantitiesmin(sk,kd)fordifferentk insidethe maximumoperatorin(5) arecorrelatedsincetheyalsocontain
x.TheseSNRcorrelations(i.e.,betweensdandsbd,andbetween min(sk,kd)andmin(si,id),∀(k,i))maketheperformance analy-sisinnextsectionscomplicatedbutaccurate.Itisalsonotedthatfor analysissimplicity,[45]assumedthatmin(sk,kd)isuncorrelated withmin(si,id),∀(k,i)whilethisdoesnothold
3 Outage performance analysis
Thissectionfirstlypresentsanexactoutageanalysisin coopera-tivecognitivenetworkswithopportunisticrelayselection,whichis thenusedtoinfersystemperformancelimits.Theproposed analy-sisframeworkisrelativelygeneral,andhence,basedonit,asimilar analysisindual-hopcognitivenetworkswithopportunisticrelay selection(e.g.[45])canbeperformedtoexposetheadvantageof utilizingthedirectchannelinrelayingcommunicationswithout time-consumingsimulations
3.1 Exactanalysis Theoutageprobabilityisdefinedastheprobabilitythate2e
isbelowathreshold0,i.e.PCC
o =Pr{e2e≤0}where0=22R−1 withRbeingtherequiredtransmissionrateandPr
X
denotesthe probabilityoftheeventX.Sincee2econtainstwocorrelated quan-tities,sdandsbd,PCC
o mustbeevaluatedintermsofconditional probabilities,i.e
PCCo =Pr
max (sd,sbd)≤0
=Ex
Pr
max (sd,sbd)≤0 x
=Ex
⎧
⎪
⎪Pr
sd≤0 x
Pr
sbd≤0 x
⎫
⎪
Since ˆhtr∼CN
0,1/tr
,theprobabilitydensityfunction(pdf) and the cumulative distribution function (cdf) of ˆhtr 2
are expressed as f ˆhtr 2(z) =tre−tr z and F ˆhtr 2(z) =1−e−tr z for
z≥0.Therefore,itimmediatelyfollowsthat
=Pr
ˇsd ˆhsd 2
≤0 x
=F ˆhsd 2
0
ˇsd
x
whereQsd=e−sd0ˇsd hasacommonformasQtr=e−tr 0ˇtr ,whichis furthersimplifiedafterusing(4)and(7)as
Qtr=e−ˇtrtr0 =
⎧
⎪
⎪
Atre−
tr2
tr0
I z ,z= ˆhtp 2
>
Btr ,z= ˆhtp 2
<
(10)
with
Atr =e(2tr −1) 0
Btr =e
−
1 − 2
tr +tr2 tr
P
0
(11)
Trang 4=Pr
max
k∈R (min (sk,kd))≤0 x
=
K
k=1
Pr
min (sk,kd)≤0 x
=
K
k=1
1ưPr
min (sk,kd)≥0 x
=
K
k=1
1ưPr
sk≥0 x
Pr
kd≥0 x
Since kd is independent of x, the conditional probability
Pr
kd≥0 x
becomes the unconditional one Pr
kd≥0
Therefore,(12)canbefurtherrewrittenas
=
K
k=1
1ưPr
sk≥0 x
Pr
kd≥0
Inserting(3)and(6)into(13)andaftersomebasic
manipula-tions,oneobtains
=
K
k=1
1ưPr
ˇsk ˆhsk 2
≥0
x
Pr
ˇkd ˆhkd 2
≥0
=
K
k=1
1ưPr
ˆhsk 2
≥ 0
ˇsk
x
Pr
ˆhkd 2
≥ 0
ˇkd
=
K
k=1
1ư
1ưF ˆhsk 2
0
ˇsk
x
Eyk
1ưF ˆhkd 2
0
ˇkd
yk
(14) Usingthegeneralnotationin(10)forbothQskandQkd,onecan
simplify(14)as
=
K
k=1
1ưQskEyk
Qkd
=
K
k=1
(1ưQkdQsk) (15)
In(15),Qkd=Eyk
Qkd
.Itsexactclosed-formrepresentationis obtainedbyusingthecompactformofQkdin(10)as
Qkd=
∞
Akdeưkd
2
kd 0
I ykkpeưkp ykdyk+
0
Bkdkpeưkp ykdyk
= Akdkp
whereAkd and Bkd aregiven in(11)withappropriate subscript
substitutions,and
Ck =1ưeưkp
Dkd =kd
2
kd0
(17)
Usingthefactthat
K
k=1
(1ưak)=1+ (ư1)K
k∈R
ak
+
Kư1
u=1
(ư1)u Kưu+1
s =1
Kưu+2
s =s +1
···
K
k∈A
ak, (18)
whereA=
R [s1], ,R [su]3
,toexpandtheproductin(15),one obtains
=1+ (ư1)K
k∈R
Qkd
k∈R
Qsk
+
Kư1
u=1
(ư1)u Kưu+1
s 1 =1
Kưu+2
s 2 =s 1 +1
···
K
s u =suư1+1
k∈A
Qkd
k∈A
Plugging(9)and(19)into(8)resultsinthesimplifiedformof
PCC
PCC
o =T∅+ (ư1)KT R
k∈R
Qkd
+
Kư1
u=1
(ư1)u Kưu+1
s 1 =1
Kưu+2
s 2 =s 1 +1
···
K
s u =suư1+1
T A
k∈A
whereW= {∅,A, R} and
T W=Ex (1ưQsd)
k∈W
Qsk
!
=Ex
k∈W
Qsk
!
ưEx
⎧
⎨
⎩
k∈{W,d}
Qsk
⎫
⎬
It is apparent that the derivation of the exact closed-form expressionofPCC
o iscompletedafteranalyticallyevaluating ˆT Gin
(21)whereGiseitherWor{W,d}.Towardsthisend,weuse(10)
andthenevaluatetheresultingintegralsas ˆ
T G=Ex
k∈G
Qsk
!
=
∞
speưsp x
k∈G
Askeưsk
2
sk 0
I xdx
+
0
speưsp x
k∈G
Bskdx
=sp
k∈G
Ask
∞
e
ư
"
sp+0I
k∈G
sk 2 sk
# x
dx
k∈G
Bsk
0
speưsp xdx=sp
EGeưEG
k∈G
Ask+Cs
k∈G
Bsk, (22)
where{Ask,Bsk}andCsaregivenin(11)and(17)withappropriate subscriptsubstitutions,respectively,and
EG=sp+0
I
k∈G
Itisworthemphasizingthatalthoughtheopportunisticrelay selection in this paper is elaborately discussed (e.g., [45]), the derivationofitsexactclosed-formoutageprobabilityexpression
in(20)hasnotbeenreportedinanyopenliteratureforthe gen-eralcaseofi.n.i.fadingdistributions,cooperativerelaying,andICI
onallchannelsconcurrently.Oncontrary,[45]considersdual-hop relaying,i.p.i.fadingdistributions,andICIeitheroninterference channels or transmission channels.To the best of the author’s knowledge,(20)istotallynovelandrepresentedinavery conve-nientandcompactformfortheanalyticalevaluation.Furthermore,
Trang 5iseasilyextendedtothecorrespondinganalysisindual-hop
cog-nitive networks withopportunistic relay selection Indeed, the
outageprobability of dual-hop cognitivenetworks with
oppor-tunisticrelayselectionisgivenby
PDH
sbd≤0
ByfollowingthesameprocedureofderivingPCC
obtains
PDH
o = ˆT∅+ (ư1)KTˆR
k∈R
Qkd
+
Kư1
u=1
(ư1)u
Kưu+1
s 1 =1
Kưu+2
s 2 =s 1 +1
···
K
s u =suư1+1
ˆ
T A
k∈A
Itisinterestingtodiscoverfrom(20),(21),(25)thatT W < ˆT W
andPCC
o <PDH
o Inotherwords,cooperativerelayingunder
con-siderationin thispaperis alwaysbetterthandual-hoprelaying
in[45]atnosignificantcostofsystemresources(e.g.,powerand
bandwidth),and hence, the former shouldbe usedin practice
Itisalsonotedthat(25)accountsforthecorrelationamongthe
quantitiesmin(sk,kd)in sbdfor differentkand hasnotbeen
reportedinanyopenliteraturewhile[45]ignoresthiscorrelation
inperformancelimitanalysis
3.2 Performancelimitanalysis
Tohave insightsinto systemperformance limits,we should
investigatetheoutageperformance inthehighSNR regime,i.e
P→∞.SinceI=P,thisregimealsoimpliesI→∞.Therefore,
basedon(4)and(7),onecanapproximatethequantityQtrin(10)
as4
QtrP,I→∞
Using(26),wecanalsoapproximatethequantitiesin(9),(15),
(16)as
{Qkd,,}P,I→∞→ {Akd,1ưAsd,
K
k=1
(1ưAskAkd)} (27)
Substituting(27)into(20),weobtaintheoutageperformance
limit (i.e., in the high SNR regime) of cooperative cognitive
networkswithopportunisticrelayselectionas
PCCo =(1ưAsd)
K
k=1
Followingthesameprocedureofderiving(28),onecanachieve
theoutageperformancelimitofdual-hopcognitivenetworkswith
opportunisticrelayselection(i.e.,inthehighSNRregime)as
PDHo =
K
k=1
Itisobservedfrom(28)and(29)thattheperformancelimits
ofbothdual-hopandcooperativecognitivenetworkswith
oppor-tunisticrelayselectiondependonlyonconstantsAtr,which are
functionsofcorrelationcoefficientstr.Assuch,thesenetworks
experience performance saturation phenomenon at high SNRs
X, Y,
is the short-hand representation which denotes
(equivalently,nodiversitygaincanbeachievable)andtheir satu-rationlevelsonlydependonthequalityofchannelestimators(i.e.,
tr).Inotherwords,ICIcompletelydestroystheadvantageofthe relayselectionintermsofdiversitygain(i.e.,zerodiversityorder) ThisiscontrasttothecaseofPCI(i.e.,tr=1),wherethediversity orderisalwaysnon-zero.Indeed,insertingtr=1into(28)and(29)
resultsinzerooutageprobabilityandhence,thenon-zerodiversity orderisachievable.However,thesaturationlevelofcooperative relayingissmallerthanthatofdual-hoprelaying.Thiscanbeseen againfrom(28)and(29)thatPDHo /PCCo =1/(1ưAsd),andhence,the saturationlevelofcooperativerelayingis1/(1ưAsd)timessmaller thanthatofdual-hoprelaying.Theseresultsencourageutilizing thedirectchannelinrelayingcommunications
4 Interference probability
TheinterferencepowerItatthePUcaused bythesecondary transmitterStcanbeexpressedas
It=Pt|htp|2
=min
"
I
|ˆhtp|2,P
#
|htp|2
Due to channel information imperfection (i.e., htp /= ˆhtp), It
can exceed the maximum interference power I, violating the interferencepowerconstraintwhichisacriticalrequirementfor guaranteeingthequalityofserviceofPUs.Theprobabilitythatthe interferencepoweratthePUexceedsIisdefinedastheinterference probability,J.Fortheopportunisticrelayselectionunder consider-ation,therearetwocaseswhichcausetheinterferencepowerat thePUtoexceedI:
• Case1:Thiscasecorrespondsthefirstphaseofcooperative relay-ingprocessasshowninFig.1.Thesourcemodifiesitstransmit powerPsinaccuratelyandcausesaninterferencepowerIsin(30)
tobelargerthanI.
• Case2:Thiscase happenswhenthesourcedoesnotinterfere withthePUinthefirstphase.However,whentheselectedrelay
Sbisactiveinthesecondphase,itadjustsitstransmitpowerPb
incorrectlyandcausesaninterferencepowerIbin(30)tobelarger thanI.
Basedonthetotalprobabilitylaw,theinterferenceprobability
isgivenby
J=Pr
Is>I
+Pr
Is≤I,Ib>I
=Pr
Is>I
+
K
b=1
Pr
Is≤I,Ib>I Sb is selected
Pr
Sb is selected
, (31) where the event {Sb is selected} is min(sb,bd)> min(sk,kd),∀k∈R\b.
Substituting{Is,Ib}in(30),{sb,sk}in(3),and{bd,kd}in
(6)into(31)resultsinanexpressionwithmanycorrelatedrandom variables.Therefore,itisimpossibletoobtainanapproximate/exact closed-formexpressionofJ.Consequently,weborrowsimulations
inthenextsectiontoinvestigatetheeffectofimperfectchannel informationontheprimarynetwork
5 Results and discussion
Thissectionprovidesnumerousresultstocorroboratethe valid-ityoftheproposedanalyticalexpressions,investigatetheimpact
ofICIontheoutagebehaviorofcooperativecognitivenetworks withopportunisticrelayselectionandontheinterference proba-bility,andhighlighttheadvantageofthedirectchannelinrelaying
Trang 6Fig 2.Outage probability versusP.
communications.Thefadingpowerofthet−rchannelisassumed
as1/tr=d−˛tr wheredtristhedistancebetweenthetransmittert
andthereceiverrwhile˛isthepath-lossexponent.Withoutlossof
generality,wechoose˛=3andfixedusercoordinates:Ssat(0,0),
Sdat(1,0),Ppat(0.6,0.7),
Sk
5 k=1at{(0.4612,−0.1765),(0.4867,
−0.1373),(0.5182,0.0621),(0.5282,0.1780),(0.4686,−0.0431)}.In
thesequel,‘Ana.’,‘Sim.’,‘CC’,and‘DH’standfor‘Analysis’,
‘Simula-tion’,‘CooperativeRelaying’,and‘Dual-hopRelaying’,respectively;
three groups of relays are considered: K=1 for {S1}, K=3 for
Sk
3
k=1,K=5for
Sk
5 k=1
Fig 2 demonstrates the outage behavior of the
oppor-tunistic relay selection in both dual-hop and cooperative
cognitive networks with respect to the variation of P=P/N0
for =0.2 and R=1bit/s/Hz Two availability levels of
channel information are illustrated: PCI (i.e., tr=1, ∀{t,
r}) and ICI with randomly selected and mutually
dif-ferent correlation coefficients (sd=0.9144, sp=0.9231,
kd
5
k=1={0.9037,0.9107,0.9681,0.9007,0.9749},
kp
5
{0.9095, 0.9438, 0.9040, 0.9556, 0.9345},
sk
5
{0.9168,0.9627,0.9094,0.9662,0.9528}) It is observed that
theexact analysis(i.e.,(20)and (25))perfectlyagrees withthe
simulationforthewholerangeofPwhiletheperformancelimit
analysis(i.e.,(28)and(29))isinaperfectagreementwiththe
sim-ulationatlargevaluesofP(e.g.,P≥30dB),verifyingthevalidity
oftheproposedexpressions5.Inaddition,inthecaseofICI,both
cooperativeanddual-hopcognitivenetworkswithopportunistic
relayselectionsuffertheerrorfloorphenomenoninthehighSNR
regime, which is already discussed and analytically proved in
Section3.2.Inotherwords,opportunisticrelayselectiondoesnot
contributeanydiversitygaininthecaseofICI,whichiscontrastto
thecaseofPCIwherethediversityorderisalwaysnon-zero6.Tobe
morespecific,inthecaseofPCI,bothnetworksobtainanon-zero
5 As discussed in Section 3.2, PCI makes zero outage probability in the high SNR
regime and hence, no performance limit for this case is shown in Fig 2.
6 To see no error floor even at very low outage probabilities, we extend the plot
of Fig 2 for the case of PCI at high SNRs The results are illustrated in Fig 3 It is seen
that both cooperative and dual-hop cognitive networks with opportunistic relay
selection do not experience performance saturation phenomenon and the former
is superior to the latter, especially at high SNRs This comes from the fact that the
former has a higher diversity order than the latter It is also noted that for PCI, [16]
proposed the exact and asymptotic outage analysis in dual-hop cognitive networks
with opportunistic relay selection but assumed the statistical independence of terms
in More specifically, [16] assumed that min( , ) is uncorrelated with
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
P (dB)
Sim.: K=1 & DH Exact Ana.: K=1 & DH Sim.: K=1 & CC Exact Ana.: K=1 & CC Sim.: K=3 & DH Exact Ana.: K=3 & DH Sim.: K=3 & CC Exact Ana.: K=3 & CC Sim.: K=5 & DH Exact Ana.: K=5 & DH Sim.: K=5 & CC Exact Ana.: K=5 & CC
Fig 3. Outage probability versusPfor perfect channel information.
diversityorderandtheachievablediversityorderofcooperative relayingislargerthanthatofdual-hoprelaying(i.e.,theoutage probabilitycurveoftheformerhasalargerslopethanthatofthe latter).Also,thesaturationleveloftheformerisconsiderablylower thanthat ofthelatter.Briefly, theformer issignificantly better than thelatterfor anysystemparameters underconsideration This observation shows the importance of utilizing the direct channelinrelayingcommunicationswithoutanyadditionalcost
ofsystemresources(e.g.,bandwidthandpower).Moreover,both networksaredrasticallydegradedbyICI,especiallyathighSNRs Nevertheless, their performance can be considerably improved withtheincreaseinthenumberofrelayssincethemorerelaysare available,thehigherchanceofselectingthebestrelayis
InthealmostsamecontextasFig.2exceptP=20dB,Fig.4
investigatestheimpactoftheoutagethreshold0(ortherequired transmission rate R) onthe outage performance of the oppor-tunisticrelayselectioninbothdual-hopandcooperativecognitive networks It is seen that the simulation perfectly matches the analysis,verifyingtheaccuracyoftheproposedexpressions Addi-tionally,theoutageperformanceofbothnetworksissignificantly deterioratedwithrespecttotheincreaseintheoutagethreshold
0=22R−1.Thismakessensebecausegivenoperationconditions, themorestringentthesystemperformancerequirement(i.e.,the largeroutagethreshold),thehigheroutageprobabilitythesystem suffers.Also,theperformanceoftheopportunisticrelayselection
isconsiderablyenhancedwithbetterqualityofchannel estima-tion(i.e.,fromICItoPCI),whichexposestheimportanceofchannel estimationincognitiveradionetworks.Moreover,similartoFig.2, increasing the number of involved relays can further improve systemperformance.Foralloperationparametersunder consider-ation,cooperativerelayingisalwaysbetterthandual-hoprelaying, whichisalreadyprovedinSection3
InthealmostsamecontextasFig.2exceptP=20dB,Fig.5
investigatestheeffectoftheproportionalfactorontheoutage performanceofbothdual-hopandcooperativecognitivenetworks
min( si , id ),∀(k, i) while this does not hold since both contain a common term
x = ˆh 2 , as discussed in Section 2.
Trang 70.5 1 1.5 2
10−4
10−3
10−2
10−1
100
R (bits/s/Hz)
Sim.: PCI Ana.: PCI Sim.: ICI Ana.: ICI
Color codes blue: K=1 & DH magenta: K=1 & CC green: K=3 & DH red: K=3 & CC cyan: K=5 & DH black: K=5 & CC
Fig 4. Outage probability versus R.
withopportunisticrelayselection.Itisseenthatthesimulationand
theanalysisareinanexcellentagreement,againconfirmingthe
validityoftheproposedexpressions.Additionally,theoutage
per-formanceofbothnetworksissignificantlyimprovedwithrespectto
theincreasein.Thisisreasonablebecausetheincreasein=I/P
isequivalenttotheincreaseinIandthus,inducingthePUmore
tolerablewiththeinterferencefromSUs.Therefore,SUscan
oper-atewithhightransmitpowers,eventuallymitigatingtheiroutage
probability.Moreover,theoutageperformanceofthe
opportunis-ticrelayselectionisconsiderablyenhancedwithbetterqualityof
channelestimationandthehighernumberofinvolvedrelays,
espe-ciallyathighSNRs.Furthermore,takingtheadvantageofthedirect
10−4
10−3
10−2
10−1
100
μ
Sim.: PCI Ana.: PCI Sim.: ICI Ana.: ICI Color codes
blue: K=1 & DH magenta: K=1 & CC green: K=3 & DH red: K=3 & CC cyan: K=5 & DH black: K=5 & CC
Fig 5. Outage probability versus .
10−6
10−5
10−4
10−3
10−2
10−1
100
ρ
Sim.: K=1 & DH Exact Ana.: K=1 & DH Sim.: K=1 & CC Exact Ana.: K=1 & CC Sim.: K=3 & DH Exact Ana.: K=3 & DH Sim.: K=3 & CC Exact Ana.: K=3 & CC Sim.: K=5 & DH Exact Ana.: K=5 & DH Sim.: K=5 & CC Exact Ana.: K=5 & CC
Fig 6. Outage probability versus .
channelalwaysimprovesthesystemperformanceforalloperation parametersunderconsideration
Itisrecalledthatthecorrelationcoefficienttrcontrolsthe qual-ityofthechannelestimatorandthelargertr,themoreaccurate theestimatedchannelinformation.Consequently,inorderto inves-tigatetheeffectofICIontheoutageperformanceofcooperative cognitivenetworkswithopportunisticrelayselection,weshould investigatetheoutageprobabilitywithrespecttotr.Withoutloss
ofgenerality,weassumealltr’stobeequal,i.e.tr=,∀{t,r}in
Fig.6,whichdemonstratestheoutageprobabilityasafunctionof forP=20dB,=0.2,R=1bit/s/Hz.Itisobservedthatthe simula-tionexcellentlymatchestheanalysis,againvalidatingtheaccuracy
oftheproposedexpressions.Inaddition,ICIsignificantlydegrades theperformanceofcognitiveradionetworks.Morespecifically,the systemisalwaysinoutageas<0.5,andaslightimprovementof estimatedchannelinformationaccuracy(e.g.,=0.9→1.0) signifi-cantlyreducestheoutageprobability(e.g.,PCC
o isreducedmorethan
104timesforK=5).However,theperformancedegradationdueto ICIcanbecomplementedbyincreasingthenumber ofinvolved relays.Moreover,cooperativecognitivenetworksaremorerobust
toICIanddrasticallyoutperformsdual-hopcounterpartforany systemparameters
10−3
10−2
10−1
100
I (dB)
K=1 K=3 K=5
Fig 7.Interference probability versusI.
Trang 8variationofI=I/N0forP=10dB,R=1bit/s/Hz,andICIwith
ran-domly selected and mutually different correlation coefficients
(
kd
5
k=1={0.9037,0.9107,0.9681,0.9007,0.9749},
kp
5
k=1={0.9095,0.9438,0.9040,0.9556,0.9345},
sk
5
{0.9168,0.9627,0.9094,0.9662,0.9528}, sd=0.9144, sp=
0.9231).Itisrecalledfrom(31)thatbothdual-hopandcooperative
relaying schemes results in the same interference probability
since (31) is independent of the direct channel Therefore, the
interferenceprobabilityinthisfigurerepresentsforbothschemes
ItisseenthattheincreaseofIreducestheinterferenceprobability
ThisisreasonableinthesensethatthelargerI,themore
inter-ferencepowerthePUcantolerate.Therefore,givenothersystem
parameters,theprobabilitythattheinterferencepowerexceedsI
decreases.However,theinterferenceprobabilityisproportionalto
thenumberoftherelays.Inotherwords,thequalityofservicein
theprimarynetworkisdegradedwithrespecttotheincreaseinthe
numberoftherelays.Thisconflictswiththeoutageperformance
trendinthesecondarynetworkwheretheoutageperformanceis
improvedwithrespecttotheincreaseinthenumberoftherelays
Asaresult,thereisaperformancetrade-offbetweentheprimary
networkandthesecondarynetworkwithrespecttothenumber
ofrelaysundertheconditionofimperfectchannelinformationon
allchannelsconcurrently
6 Conclusions
Thispaperproposesanexactandlimitoutageanalysis
frame-workforcooperativecognitivenetworkswithopportunisticrelay
selectionunderageneralscenario:imperfectchannelinformation
forallchannelsconcurrently,i.n.i.Rayleighfadingchannels,and
bothmaximumtransmitpowerconstraintandinterferencepower
constraint.Thisframeworkisstraightforwardlyextended tothe
correspondinganalysisindual-hopcognitivenetworkswith
oppor-tunisticrelayselectionforcomparisonconvenienceandemphasis
oftheimportanceofthedirectchannelwithouttime-consuming
simulations.Numerousresultsdemonstratethat(i)channel
infor-mationimperfectionsignificantlyimpactstheoutageperformance,
especially forhighSNRsand smallnumberof relays;(ii)
relay-ingcognitivenetworksexperienceperformancesaturationathigh
SNRsandthesaturationlevelonlydependsonthequalityof
chan-nelestimator;(iii)theopportunisticrelayselectioninthecaseof
imperfectchannelinformationdoesnotbringanydiversitygainfor
bothcooperativeanddual-hopcognitivenetworks;(iv)increasing
thenumberofrelays candramaticallyimprovetheoutage
per-formanceirrespectiveofchannelinformationimperfectiondegree
butalsodegradethequalityofserviceofprimaryusers;(v)the
outageperformanceofrelayingcognitivenetworksisconsiderably
enhancedwithtakingadvantageofthedirectchannelwithoutany
significantcostofsystemresources(e.g.,powerandbandwidth)
Acknowledgement
Thisresearchis funded by VietnamNationalFoundation for
Scienceand Technology Development (NAFOSTED) under grant
number102.04-2014.42
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...chan-nelestimator;(iii)theopportunisticrelayselectioninthecaseof
imperfectchannelinformationdoesnotbringanydiversitygainfor
bothcooperativeanddual-hopcognitivenetworks;(iv)increasing
thenumberofrelays candramaticallyimprovetheoutage... qual-ityofthechannelestimatorandthelargertr,themoreaccurate theestimatedchannelinformation.Consequently,inorderto inves-tigatetheeffectofICIontheoutageperformanceofcooperative cognitivenetworkswithopportunisticrelayselection,weshould...
frame-workforcooperativecognitivenetworkswithopportunisticrelay
selectionunderageneralscenario:imperfectchannelinformation
forallchannelsconcurrently,i.n.i.Rayleighfadingchannels,and