Opportunistic Adaptive Relaying in Cognitive Radio Networks

0.32 MB·English

by  Wael Jaafar

Opportunistic Adaptive Relaying in Cognitive Radio
Networks
Wael Jaafar Wessam Ajib David Haccoun
E´cole Polytechnique de Montre´al Universite´ du Que´bec a` Montre´al E´cole Polytechnique de Montre´al
Department of Electrical Engineering Department of Computer Science Department of Electrical Engineering
Montreal, Canada Montreal, Canada Montreal, Canada
Email: [email protected] Email: [email protected] Email: [email protected]
2
1
0 Abstract—Combining cognitive radio technology with user Cognitive Radio Networks (CRNs) to improve the secondary
2 cooperation could be advantageous to both primary and sec- outage performance while satisfying a primary outage prob-
n ondary transmissions. In this paper, we propose a first relaying ability threshold. By letting the “best” CR relay assist the
scheme for cognitive radio networks (called “Adaptive relaying
a secondary transmission, the secondary outage probability can
scheme 1”), where one relay node can assist the primary or
J the secondary transmission with the objective of improving the be considerably reduced. In [7], secondary transmissions are
3 outage probabilityof thesecondary transmission with respect to assisted by a group of CR relay nodes located at different
1 aprimaryoutageprobabilitythreshold.Upperboundexpressions positions. The outage probability was investigated when all
of the secondary outage probability using the proposed scheme the relays forward simultaneously their received signals. The
] are derived over Rayleigh fading channels. Numerical and
I systemachievesfulldiversitywhenthenumberofcooperating
N simulation results show that the secondary outage probability
using the proposed scheme is lower than that of other relaying relay nodesis adequately selected. In [8], we proposeda new
.
s schemes. Then, we extend the proposed scheme to the case relaying scheme for CRNs where a CR relay node is able to
c wheretherelay node hastheabilityto decode boththe primary assistsimultaneouslytheprimaryandsecondarytransmissions.
[ and secondary signals and also can assist simultaneously both
It has been shown that for certain relay’s position, assisting
transmissions. Simulations show the performance improvement
1 simultaneously both transmissions providesbetter outage per-
that can beobtaineddueto thisextension intermsof secondary
v outage probability. formance than assisting only the primary or the secondary
7
transmission. However,the proposedscheme is greedy on the
3
I. INTRODUCTION relay’s transmit power.
9
2 In order to overcome the problems related to the rigid Even though, the previous works have investigated the uti-
. allocation of spectrum bands to few licensed operators and lizationof user cooperationin CRNs for assisting the primary
1
0 the under-utilization of these bands, Cognitive Radio (CR) transmissions, the secondary transmissions or both, no work
2 technology has evolved in wireless communications for al- has investigated adaptive relaying schemes where the relay
1 lowing unlicensed secondary users (SUs) to access licensed node decides independently when and which communication
:
v parts of the spectrum without harmfully interfering with the to assist. Consequently, we propose in this paper a novel
i transmissionsofthelicensedprimaryusers(PUs)takingplace opportunistic adaptive relaying scheme, where the CR relay
X
in the same spectrum band [1]-[2]. In underlay spectrum node is able to decide when to cooperate or not, and in case
r
a sharing mode, SUs are allowed to transmit simultaneously ofcooperation,whomtocooperatewith(primarytransmission
with PUs if they tune their transmission parameters (such as or secondary transmission) depending on the channel states.
transmit power) to be harmless to primary transmissions. Weproposetoextendtheadaptiverelayingschemetothecase
Meanwhile, user cooperation has been recognized as an where the relay node can also cooperate simultaneously with
interestingtechniquethatallowstoachieveincreaseddiversity both transmissions.
order when one or several relay nodes assist the transmission The paper is organized as follows. Section II presents the
[3]-[4]. system model. In section III, we describe the two adaptive
Consequently, combining user cooperation and cognitive relaying schemes and we provide analytically the secondary
radio has recently attracted attention to improve both the outage probability for the first adaptive relaying scheme.
spectrum utilization and the transmission performances. User Section IV shows and discusses the numericaland simulation
cooperation has been applied for the primary transmission results and a conclusion closes the paper in section V.
when a cognitivesecondarytransmitter acts asa relay [5]. By
doing so, the primary outage probability is improved, while II. SYSTEMMODEL
SUs have more opportunities to access the licensed spec- We assume a CRN where one primary transmitter (PT)
trum bands and hence secondary transmission performances transmits data to a primary destination (PD) and a secondary
can be also improved. In [6], an adaptive user cooperation transmitter (ST) communicates with a secondary destination
schemewith best-relayselection is proposedin multiple-relay (SD) over the same frequency band (Fig. 1). We assume a
Y Axis
III. ADAPTIVE RELAYING SCHEMES
PT(0,1.82) PD(1,1.82) A. Description of adaptive relaying scheme 1
h
pp
This novel scheme aims to exploit efficiently the relay
hps position, the acquired information and the propagation en-
hpr hrp vironment conditions. We define by a0 = γpγ|sh|phss|s2|+21, ap =
γs|hss|2 , a = γr(s)|hrs|2 whereγ =P /N (a=pors)
γr(p)|hrs|2+1 s γp|hps|2+1 a a 0
hsr R(xr,yr) hrs andγr(i) isthetransmitpoweroftherelaynodewhenassisting
transmission i. We also define E ={a =max{a ,a ,a }}
i i p s 0
hsp theopportunismcondition(i=p,sor0).Atthefirstsub-slot,
hss X Axis R attempts to decode xp or xs and then, a relaying procedure
is chosen depending on the value of D defined by:
ST(0,0) SD(1,0)
1st sub-slot transmissions If A ∩ A¯ ∩(a >a ) ∪{A ∩E } ,then D =1,
p s p 0 s p
2nd sub-slot transmissions If A ∩ A¯ ∩(a >a ) ∪{A ∩E } ,then D =2,
s (cid:8)(cid:8) p s 0 (cid:9) p s (cid:9)
Interfering signals Otherwise D =0,
(cid:8)(cid:8) (cid:9) (cid:9)
(3)
Fig.1. TheCognitive RadioNetwork
where A¯ is the complement of A, and
1 γ |h |2
dasesciostdet-haendp-rfiomrawrayrdorsethceonsdeacroyndCaRryrterlaanysmniosdsieon(Rin) tohradtercaton Ap =(2log2 1+ γs|hpsr|p2r+1!≥Rp), (4)
increase the secondary access to the licensed spectrum bands 1 γ |h |2
Iwniththeresepxetecntstoiona,cweretaiansspurmimearthyaotutthaegereplraoybaibsilaibtylethtroesahsoslidst. As =(2log2 1+ γp|hsprs|2r+1!≥Rs). (5)
both transmissions. Thecomparisonof(a :i=p,sor0)indicateswhichrelaying
i
We assume that PT and ST transmit their signals x and would improve better the secondary outage probability.
p
x (where E{|x |2} = E{|x |2} = 1) with powers P The different cases are detailed below.
s p s p
and P respectively in order to achieve data rates R and 1) R assists the primary transmission (D = 1): This case
s p
R respectively. We assume also that R uses transmit power occurs either when (i) R succeeds to decode the primary
s
P ≤Pmax,wherePmaxisthemaximalrelaytransmitpower. signal but not the secondary signal and when relaying the
r r r
We assumethatthechannelsaresubmittedtoRayleighfading primary signal provides lower secondary outage probability
and path loss attenuationand are stationaryduringa time-slot than the repetition (i.e., ap > a0) or (ii) R succeeds to
(time slot =1st + 2nd sub-slots). decode both the primary and secondary signals and assisting
theprimarytransmissionprovidesthelowestP (i.e.,E ).
Following Fig. 1, the received signals during the first sub- outsec p
Hence, when the relay is able to decode the primary signal
slot are expressed by:
and the best choice is to assist the primary transmission, then
y (1)= P h x + P h x +n , (1) D =1. Consequently, the received signals at PD and SD, on
a p pa p s sa s a
the second sub-slot, are respectively given by:
where a = p,s orpr (p, s and rpdenote primary, secondary
and relay node resp.), hba (b = p or s) is the channel gain y (2|D =1)= P(p)h x + P h x +n . (6)
between nodes b and a having variance σ2 = d−β , d is a r ra p s sa s a
ba ba ba q
thedistancebetweenbanda, β isthepath-lossexponent,and After normalizing the noise variancpes and combining the
where n is the additivewhite gaussian noise with zero mean signals received in the two sub-slots (given by (1) and (6))
a
andvarianceN receivedata.We assumeafixedP andthat with Maximum Ratio Combining (MRC) [5], the Signal-to-
0 p
P iscalculatedwithrespecttotheprimaryoutageprobability Interference-plus-Noise-Ratio(SINR) at PD is:
s
threshold denoted ε. Ps is given similarly to [6] by: γ |h |2 γ(p)|h |2
SINR (D =1)= p pp + r rp , (7)
P = 2Ppσp2pρ+, (2) p γs|hsp|2+1 γs|hsp|2+1
s Λ σ2
p sp while SINR at SD is given by:
s
awnhderγe ρ=+P=/mNa.x(S0T,ρc)a,lcρul=atees−P21γ−pΛεσapp2spsu−mi1n,gΛthpat=PT22Rreppe−at1s SINRs(D =1)= γpγ|hsp|hs|s2s|+2 1 + γr(pγ)|sh|hrss|s2|2+1. (8)
p p 0 s
the same signal overthe two sub-slots with the same transmit 2) R assists the secondary transmission (D = 2): This
power P . second case occurs when (i) R succeeds to decode only the
p
secondary signal and when relaying the secondary signal is where
beneficial to the secondary transmission (i.e., as >a0) or (ii) − Λp
Rsucceedstodecodebothsignalsandassisting thesecondary γ˜s2pΛ2p+γ˜r(pp)γ˜spΛp 1−e γ˜r(pp)
transmissionprovidesthelowestP (i.e.,E ).Inthiscase, !
Rassists thesecondarytransmissioonutasnecdD =2s.Thereceived λ1 = (γ˜ +Λ γ˜ )(γ˜(p)+Λ γ˜ ) ,
pp p sp rp p sp
SINR at PD and that at SD are expressed as (8) and (7) (12)
res3p)ecRtivdeoleys, wnohteraessiinsdtetxheestpraannsmdisssaiorensin(vDer=ted0.): When the γ˜p2p 1−e−γ˜Λppp −γ˜ppγ˜r(pp) 1−e−γ˜Λr(ppp)
relay is not able to decode the signals or when relaying is (cid:18) (cid:19) !
λ = ,
not beneficial to Poutsec, the relay does not participate in the 2 (γ˜pp+Λpγ˜sp)(γ˜r(pp)−γ˜pp)
transmissions. In this case, we assume that the primary and
∀ γ˜ 6=γ˜(p). (13)
secondary transmitters retransmit the same signals. Accord- pp rp
ingly, the received SINR at SD is given by (eq.(7), [8]) and Proof: See Appendix B.
that at PD by inverting indexes p and s in (eq.(7), [8]).
Lemma 2. An upper bound on the conditional secondary
B. Outage Probability Analysis outage probability is given by:
In this scheme, any of three cases can happen. We start by ln 1+ Λsγ˜ps
calAcunlautpinpgerthbeoupnrdoboanbitlhiteyporfoboacbciulritryenocfeoocfcuerarcehncoeneo.f D =1 Psec(out.|D =1) = 1−e−γ˜Λsss 1+ (cid:16) γ˜psγ˜ss (cid:17)
is given by:
  
× γ˜(p)+1 =ϕ× γ˜(p)+1 . (14)
rs rs
P (D =1) = γ˜ps × γ˜pre−γ˜Λppr−(1Λ−sΛ(p1+ΛsΛ)pγ˜)sr Proof: See Appendi(cid:16)x C. (cid:17) (cid:16) (cid:17)
γ˜ps+γ˜r(ps) γ˜pr +Λpγ˜sr By assisting the primary transmission, this relaying proce-
γ˜ps γ˜sre−γ˜Λssr dure aims to reduce the interference caused to the secondary
+ 1− transmission with respect to the primary outage threshold ε.
γ˜ps+γ˜r(ps) γ˜sr+Λsγ˜pr! For that purpose, R should control its transmit power P to
r
× 1−e(1−−ΛΛsp(1Λ+sΛ)γ˜ps)r −φi −γ˜1 − γ˜γ˜r(γ˜ss) ebvealausatleodwnausmpeorsicsiablllye.bTyhissolvvailnugePof P(ro,udt.e|nDote=d 1P)r(,pn=)umε., Iisf
(cid:18) (cid:19) ps ss ps! pri
γ˜ps 1+γ˜ps 1 + γ˜r(ss) Pr(,pn)um >Prmax, then relaying is not beneficial and D =0.
× γ˜ps+γ˜r(ps) (cid:18) γ˜ss (cid:19)eγ˜ps γ˜ssγ˜ps • D =2
Due to the similarity of the outage probability analysis of
× γ˜sre−γ˜Λssr−(1Λ−pΛ(p1Λ+sΛ)sγ˜)pr , (9) this relaying procedure to the first one, it is not given in
γ˜ +Λ γ˜ details. However, by inverting indexes p and s and indexes
sr s pr
pri and sec in equations (10)-(14), we obtain an accurate
whereγ˜ =γ σ2 ,γ˜(i) =γ(i)σ2 (a=p,s orr andb=p,s
ab a ab rb r rb outage probability analysis. The relay transmit power should
or r) and φi(x)= −x∞ ettdt. also be calculated such that Ppri(out.|D = 2) = ε. The
ByPfroololof:wSinegesAimpRpileanrdciaxlcAul.ations,wecanobtainP(D =2). relay transmit power is given by γr(,sn)um = ε/σϕr2′p−1, where
Finally, P(D =0)=1− 2 P(D =i). ϕ′ = 1−e−γ˜Λppp 1+ ln 1+γ˜sΛpγ˜ppγ˜psp .
i=1 (cid:18) (cid:18) (cid:0) (cid:1)(cid:19)(cid:19)
We next present the coPnditional primary and conditional Then, γr(s) =min γr(,sn)um,γrmax .
secondary outage probabilities for each case:
• D =0 (cid:16) (cid:17)
• D =1
The outage probability analysis of this case is presented in
The conditional primary outage probability is given by:
[8]. The conditional secondary outage probability is given by
(eq.(16), [8]), while P (out.|D = 0) is obtained by simply
P (out.|D =1) = P (SINR (D =1)<Λ ) pri
pri p p
inverting indexes p and s in (eq.(16), [8]).
= P(ω <Λ +Λ ω −ω ) (10)
p p 1 2 Finally,upperboundson the primaryandsecondaryoutage
where Λa = 22Ra − 1 (a = p or s), ω = γr(p)|hrp|2, probabilities are given by:
ω = γ |h |2 and ω = γ |h |2. We shall make use of
1 s sp 2 p pp 2
the following Lemma. P = P(D =i)P (out.|D =i), (15)
outc c
Lemma1. Theexactclosed-formexpressionoftheconditional Xi=0
primary outage probability is expressed by: where c = pri or sec. The obtained expressions are upper
bounds since some of the conditional outage probabilities
Ppri(out.|D =1)=λ1+λ2, (11) calculated are upper bounds.
100 100
Repetition scheme
R assists primary transmissions
R assists secondary transmissions
Adaptive relaying scheme 1 10−1
Outage Probability10−1 Simulation utage Probability1100−−32
Secondary 10−2 econdary O10−4
S
10−5
Adaptive relaying scheme 1
10−3 Adaptive relaying scheme 2
0 5 10 γp 1(d5B) 20 25 30 10−6 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
R (bits/sHz) (R=R/2)
p s p
Fig.2. Comparaisonofdifferent relaying schemes
Fig. 3. “Adaptive relaying scheme” versus “Adaptive relaying scheme 2”
(simulations only)
C. Extension to “Adaptive relaying scheme 2”
In this extension, we assume that R is equipped with
a SIC (Successive Interference Cancelation) receiver [9], x 10−3
daanepsfidneh=eCnci(eα1−=γir(αtp)s{γi)s|r(ahpisra)s=|b|h2lr+ems1|2at,ox{wdahe0ce,oraedpe,0abso,≤athpsα}si}gn≤(ails.=1.W0We,ped,esafilnsooer age probability10−3 223.5
cpess)sfaunldsEucc=ess{ivAepd∩ecBopd}in∪g {oAfsb∩otBhss}igtnhaelse,vewnhteoref aBisu=c- ndary out10−4 11.5
12log2 1+γi|hir|2 ≥Ri . We call this extension “Adap- Seco10−5 PT PD 0.5
ntive relay(cid:16)ing scheme 2(cid:17)”. Forothis scheme, we distinguish four 2 SD
1.5 ST 1.5
relaying procedures: 1 0.5 0 0.5 1
0 −0.5
If E∩C , then D =3, Y−axis X−axis
ps
If A ∩B¯ ∩(a >a ) ∪{E∩C }, then D =2,
s s s 0 s Fig.4. Secondary OutageProbability vs.Relayposition (simulations only)
If A ∩B¯ ∩(a >a ) ∪{E∩C }, then D =1,
(cid:8) p p p 0 (cid:9) p
Otherwise D =0.
(cid:8) (cid:9) outage performance since the proposed scheme chooses the
The relaying procedures for D = 0,1 or 2 are identical to most adequate relaying procedure. The “R assists secondary
thefirstscheme.WhenD =3,afractionoftherelaytransmit transmissions”and“Rassistsprimarytransmissions”schemes
powerαP(ps) isusedtosendx andtherest,i.e.,(1−α)P(ps) outperformsthenoncooperativescheme.WhenRassistsonly
r p r
is used to transmit x . SINRs at PD and at SD are then given the secondary transmissions, the performances are degraded
s
by(eq.(10),[8])and(eq.(11),[8])respectively.Theparameter by the fact that the relay transmit power is limited to Pmax.
r
α is calculated using (eq.(33), [8]) where γ(ps) =γmax. In Fig. 3, we compare the secondary outage probabilities
r r
of the two adaptive relaying schemes for different R values
p
IV. NUMERICAL AND SIMULATION RESULTS and where we assume R = Rp. For R ≤ 2.2bits/s/Hz,
s 2 p
We consider the CRN presented in Fig. 1 where the the second scheme outperforms the first one. Indeed, the
coordinates of PT, ST, PD and SD are given by (0,1.82), proposed second scheme offers more relaying possibilities
(0,0), (1,1.82) and (1,0) respectively (coordinates are in dis- for R and hence improves the secondary performance. For
tance units). We assume that R = 0.8bits/s/Hz, R = R ≥ 2.2bits/s/Hz, no secondary or relaying transmissions
p s p
0.2bits/s/Hz, ε = 0.1, β = 4 and γ = γmax = 20dB. are allowed due to the high primary outage probability re-
p r
We measure the average of the secondary outage probability quirement that blocks any interfering transmission.
calculated for different random positions of the relay node In Fig. 4, we present the secondary outage performance
in the plan of coordinates (X,Y) where 0.1 ≤ X ≤ 0.9 and usingthe“Adaptiverelayingscheme2” fordifferentpositions
0.1≤Y ≤1.7 unless otherwise is stated. of the relay node on the plan (X,Y) where −0.5 ≤ X ≤ 1.5
In Fig. 2, we compare the “Adaptive relaying scheme 1” and 0≤Y ≤2. When R is close to the secondary nodes, the
to other transmission schemes presented in the literature [6], secondary outage performance is improved. Indeed, when R
[8]. At low γ (γ ≤ 8dB), no secondary transmissions is close to the primary nodes, the cases D = 1 and D = 3
p p
are allowed. When γ is higher than the cutoff value, the are predominant and the outage probability gain comes from
p
“Adaptive relaying scheme 1” presents, as expected, the best the interference reduction. As R gets closer to the secondary
nodes, the cases D =2 and D =3 occur more often. Hence, Using (17),(18) and (20) in (16), we obtain (9).
the outage performance gain is issued from the interference
APPENDIX B
reduction (D =3) and cooperation (D =2). Moreover,when
PROOF OFLEMMA.1
R is in the middle zone, the secondary outage probability
From (10), ω, ω and ω are exponential random variables
decreases. In this zone, the condition of the channels linked 1 2
with parameters 1/γ˜ , 1/γ˜ and 1/γ˜ respectively. Thus,
to the relay node favors successful decoding and efficient rp sp pp
the pdfs of ω and φ=ω −Λ ω are:
forwarding of the signals. 2 p 1
− φ
V. CONCLUSION f (ω)= e−γ˜ωrp ,ω ≥0; f (φ)= γ˜ppe+Λγ˜pppγ˜sp, φ≥0
In this paper, we proposed adaptive relaying schemes for ω γ˜ φ  φ
cognitiveradionetworks,wherea relaynodeis abletodecide rp  γ˜pepΛ+pΛγ˜pspγ˜sp, φ≤0.
assisting the primary, the secondary or both transmissions
Finally, we obtain the conditionalprimary outage probability:
depending on the channels condition. We showed by analysis
and by simulation that the first adaptive relaying scheme, Λp 0 Λpγ˜speΛpzγ˜sp
P(z <Λ ) = f (z)dz = dz
where the relay may help the primary or the secondary p z β β
Z−∞ Z−∞ 1 2
tiprnrainmtesamrmryisssoiouoftna,gseoecuoptpnroedbrafaroybrimloitsuyttahtgheerenspohrnoolbadad.baTiplhittieyvn,e,wraeiltsaheycironengsdpsecscchthetemomeaes + Λp Λpγ˜spe−γ˜r(zpp) + γ˜pp(cid:18)e−γ˜r(zpp) −e−γ˜pzp(cid:19)dz
hasbeenproposedconsideringthattherelaymayhelpsimulta- Z0 β1β2 β1 γ˜r(pp)−γ˜pp
neouslybothtransmissions.Simulationsshowtheperformance = λ +λ , (cid:16) (cid:17) (21)
1 2
improvementofthesecondscheme,speciallyatlowdatarates.
where z = ω+φ, f (z) is its pdf, β = γ˜ +Λ γ˜ , β =
z 1 pp p sp 2
APPENDIX A γ˜(p)+Λ γ˜ ;λ andλ aregivenby(12)and(13)respectively.
rp p sp 1 2
PROOF OFEQ.(9) This completes the proof of Lemma.1.
Due to the independencybetween events, we have:
APPENDIX C
P(D =1) = P A ∩A¯ P (a >a ) PROOF OFLEMMA.2
p s p 0
Using (19) for X (b=p or r), we obtain:
+ P(A |A )P(A )P(E ) sb
(cid:0) p s (cid:1) s p
= P(γ |h |2 ≥max{Λ (1+γ |h |2), P (X +X <Λ )= (22)
p pr p s sr sp sr s
+ Pγs(|γΛhss|rh|2 −|21≥})ΛPp((γ1r(p+)|Λhrss)|)2P≤(aγp|>hpas|2)) = Z0Λs (cid:16)1γ˜+ssγ˜+sγ˜ssx+sγγ˜˜xr(rγ˜(pspsr()ps))(cid:17) e−γ˜xss − γ˜ss+γ˜s(sΛes−−γ˜Λsssx)γ˜ps!dx.
p pr p 0
1−ΛpΛs 1+ γ˜ssγ˜r(ps)
P(γpγ|hsp|hr|s2r|+2 1 ≥Λs)P(ap >as). (16) iSnin(c2e2),(cid:16)wγ˜esγ˜sos+sb+xtaγx˜iγr˜(npsr(p)s()1(cid:17)4)≤.Thγ˜r(iγ˜psss)s+co1m, pthleetnesutshinegprtohoisfuopfpLeermbmoua.n2d.
Sinceγa|hab|2andγc|hcb|2areexponentialdistributedrandom REFERENCES
variableswithparameters1/γ˜ and1/γ˜ respectively(a=p
ab cb [1] J.MitolaandG.Q.J.Maguire,“Cognitiveradio:makingsoftwareradios
or s, c=p or s, and b=p,s or r), then ∀x∈R:
morepersonal,”IEEEPersonalCommun.,vol.6,no.4,pp.13–18,aug.
1999.
γ˜
P(γ |h |2 ≤γ |h |2) = cb , (17) [2] S.Haykin,“Cognitiveradio:brain-empoweredwirelesscommunications,”
a ab c cb
γ˜ab+γ˜cb IEEEJ.Select. AreasCommun.,vol.23,no.2,pp.201–220,feb.2005.
− x [3] J.Laneman, D.Tse, and G.Wornell, “Cooperative diversity inwireless
P(γ |h |2 ≥(γ |h |2+1)x) = γ˜abe γ˜ab , (18) networks: Efficient protocols and outage behavior,” IEEE Trans. Inf.
a ab c cb γ˜ +xγ˜ Theory,vol.50,no.12,pp.3062–3080,Dec.2004.
ab cb
[4] W.Jaafar, W.Ajib,andD.Haccoun, “Ontheperformance ofmulti-hop
andtheprobabilitydensityfunction(pdf)ofX = γa|has|2 wirelessrelaynetworks,”WirelessCommunicationsandMobileComput-
ab γb|hbs|2+1 ing,Dec.2011,[Online]Available: http://www.wileyonlinelibrary.com.
(a=s or r; b=p or r) is given by:
[5] Y.Han,A.Pandharipande,andS.Ting,“Cooperativedecode-and-forward
f (x)= e−γ˜axs 1+ γ˜asγ˜bs , x≥0. (19) rveolla.y8in,gnofo.r1s0e,cpopn.d4ar9y45sp–e4c9tr5u0m,oacctcoebses,r”2I0E0E9E. Trans.WirelessCommun.,
Xab γ˜ +xγ˜ γ˜ +xγ˜ [6] Y. Zou, J. Zhu, B. Zheng, and Y.-D. Yao, “An adaptive cooperation
as bs (cid:18) as bs(cid:19) diversity scheme with best-relay selection in cognitive radio networks,”
Since 1+γ˜sγ˜sr(γ˜+ssr()sys+)γ˜γ˜yr(pγ˜pssp)s ≤ 1+γ˜sγ˜sps, ∀y ≥0 and using (19), we get: [[87]] WInKEe..tEwLJEaoeareTfkrasaar,n,”ndsWi.nA.SIi.AEgYnjEiaebEnl,ePGarn,rlood“cbOeDasul.st.TaH,gevaleeoccclp.ooem5ur8fnmo,,runm“noA.a.nC1nc0ooe,nvefop.l,fp,.rcde5ole4agcy3n.-8i2atii0–vd05ee64d,w45ptirr,pae.onlecs1smt–.s5i2sr.0sei1loa0ny.
P(ap >as)≤−φi − 1 − γ˜r(ss) 1+γ˜ps eγ˜p1s+γ˜sγ˜sr(γs˜s)ps. sCcohnefm.,edeicn.2c0o1g1n.it[iOvenlirnaed]i.oAnveatiwlaobrlek:s,h”ttpin://aIrExEivE.orGg/laobbsa/1l1T0e9l.e2c8o4m3mv1un.
γ˜ps γ˜ssγ˜ps!(cid:18) γ˜ss (cid:19) [9] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.
(20) CambridgeUniversity Press,,2005.