Opportunistic DF-AF Selection Relaying with Optimal Relay Selection in Nakagami-m Fading Environments

0.24 MB·English

by  Tian Zhang

Opportunistic DF-AF Selection Relaying with
m
Optimal Relay Selection in Nakagami- Fading
Environments
Tian Zhang∗,§, Wei Chen∗, and Zhigang Cao∗
∗State Key Laboratory on Microwave and Digital Communications, Department of Electronic Engineering,
Tsinghua National Laboratory for Information Science and Technology (TNList), Tsinghua University, Beijing, China.
§School of Information Science and Engineering, Shandong University, Jinan, China.
Email: [email protected],{wchen, czg-dee}@tsinghua.edu.cn.
3
1
0
2

n Abstract—An opportunistic DF-AF selection relaying scheme notbeenextensivelystudiedyetduetothemathematicaldiffi-
a with maximal received signal-to-noise ratio (SNR) at the des- culty. Furthermore, when each relay utilizes DF-AF selection
J
tination is investigated in this paper. The outage probability
relaying protocol, how to choose a best one among them?
1 of the opportunistic DF-AF selection relaying scheme over
Nakagami-m fading channels is analyzed, and a closed-form In this paper, we study the opportunistic DF-AF selection

] solution is obtained. We perform asymptotic analysis of the relaying with optimal relay selection whereby the destination
T
outageprobabilityinhighSNRdomain.Thecodinggainandthe obtainsmaximalreceivedSNRincooperativenetworks.More-
I diversityorderareobtained.Forthepurposeofcomparison,the over,we carry out asymptotic outage behavior analysis of the
.
s asymptotic analysis of opportunisticAF scheme in Nakagami-m
opportunisticDF-AF selection relaying scheme in Nakagami-
c fadingchannelsisalsoperformedbyusingtheSqueezeTheorem.
[ m fading channels. In addition, the asymptotic performance
In addition, we prove that compared with the opportunistic DF

scheme and opportunistic AF scheme, the opportunistic DF-AF of opportunistic AF protocol in Nakagami-m fading channels
1
selection relaying scheme has better outage performance. is analyzed for comparison.
v
7 Index Terms—Cooperative diversity, opportunistic DF-AF The rest of the paper is structured as follows. Section II
selection relaying, outage probability, asymptotic analysis,
8 introducestheopportunisticDF-AFselectionrelayingscheme.
Nakagami-m fading.
0 Section III presents the asymptotic outage analysis of the
0
opportunistic DF-AF selection relaying. Next, in Section IV,
. I. INTRODUCTION
1 comparisons with the opportunistic DF scheme and oppor-
0 COPERATIVE diversity, which lets the single antenna tunisticAFschemeareperformed.InSectionV,thenumerical
3 equippedcommunicationterminalenjoytheperformance
resultsarepresented.Finally,themainresultsofthepaperare
1 gainfromspatial diversity,is an importantmodusoperandiof
summarized in Section VI.
:
v substantially improvingcoverageandperformancein wireless
i networks.Thebasic ideais thatbesidethe directtransmission II. DESCRIPTION OFOPPORTUNISTIC DF-AFSELECTION
X
from the source to the destination, some adjacent nodes RELAYING
r
a can be used to obtain the diversity by relaying the source
signal to the destination[1], [2]. Severalcooperativediversity
Relay 1
protocols including amplify-and-forward (AF), decode-and-
forward (DF), selection relaying and incremental relaying,
have been discussed in [2]-[4]. DF-AF selection relaying
protocol, where each relay can adaptively switch between DF h Relay 2 h
s,1 1,d
and AF according to its local signal-to-noiseratio (SNR), has
been developed and investigated in [5]-[8]. h h
Forthepurposeofimprovingthesystemspectralefficiency, s,2 ... 2,d Best-relay selection
Relay K
the opportunistic relaying scheme for cooperative networks
has been introduced [9], [10]. In such a scheme, a single h h
s,K K,d
relay is selected from a set of relay nodes. The opportunistic
DF protocol and opportunistic AF protocol have been well
studied in Rayleigh fadingchannels[11]-[15]. In contrast, the h
s,d
opportunisticrelayingoverNakagami-mfadingchannelshave Source Destination
ThisworkispartiallysupportedbytheNationalNatureScienceFoundation Fig.1. Wireless relaychannel
ofChinaunderGrantNo.60832008andNo.60902001.
Consider a cooperative wireless network consisting of a Lemma1. TheoutageprobabilityoftheopportunisticDF-AF
sourcenode(S),adestinationnode(D)andK potentialrelays selection relaying scheme can be given by
R = (R ,R ,...,R ) as shown in Fig. 1. Instantaneous
1 2 K K
Γ(m ,α γ ) Γ(m ,α ∆)
SNRs of S →D, S →Ri and Ri →D channelsare denoted Pout = 1− 0 0 th 1i 1i 1
by γ0, γ1i and γ2i, where i=1,2,··· ,K. The effects of the (cid:20) Γ(m0) (cid:21)i=1" Γ(m1i)
Y
fading are captured by complex channel gains h , h and
s,d s,i Γ(m ,α γ ) Γ(m ,α ∆)
h respectively.Thefadingin eachchannelisassumedto be − 2i 2i th + 1− 1i 1i , (3)
i,d
Γ(m ) Γ(m )
independent, slow and Nakagami-m distributed with parame- 2i ! 1i !#
ters(m0,ω0),(m1i,ω1i),and(m2i,ω2i)respectively.Wehave where R is the transmission rate, ∆ = 22R −1 and γ is
γ0 = |hs,d|2SNR, γ1i = |hs,i|2SNR, and γ2i = |hi,d|2SNR, the SNR threshold at the destination. α = m0, α =tmh1i,
whIenreopSpNoRrtuisnitshtiectrDaFns-AmFit sSeNleRc.t1ion relaying, among the K- ianncdomα2pile=temγg2a2iim,mΓ(a·)fuinsctthioeng.amma funct0ion, aγn0d Γ(1·i,·) isγt1hie
relay set, where each relay uses DF-AF selection relaying
protocol,a“best”relaywillbeselectedforeachtransmission. Proof: Throughout this paper, we use X ∼ G(m) to
Suchacooperativetransmissionisdividedintotwostepswith denote that a random variable X has the p.d.f. given by
equaldurations.Inthefirststepthesourcenodebroadcastsits fX(y)= Γ(1m) mX mym−1e−mXy.First,itcanbederivedthat
signalto the destination nodeand the set of K-relaynodesas c.d.f. of Y ∼G(cid:16)(m)(cid:17)can be given by
well.Inthesecondstep,thebestrelayR isselectedaccording
b
to Γ m,my
Y
F (y)=1− . (4)
b=arg max ξ γ +(1−ξ ) γ1iγ2i , (1) Y (cid:16)Γ(m) (cid:17)
i 2i i
i=1,2,···,K(cid:26) γ1i+γ2i+1(cid:27) If the source-relay link is able to support R,
whereξi denotesthedecodingstateofRi,i.e.,ξi =1whenRi i.e., 12log2(1+γ1i) ≥ R,2 or equivalently, if
couldfullydecodethesourcemessage,otherwiseξi =0.And γ1i ≥ ∆ = 22R − 1, the relay could fully decode
the best relay Rb will use DF-AF selection relaying protocol the source message. Consequently, the instantaneous
to forward the received signal. Specifically, relay Rb uses DF equivalent end-to-end SNR per symbol at the destination is
tboerues-terda.nsSminictethceormecbeinivgedmseitghnoadlidfoξebs=no1t.aOfftehcetrwthiesedAivFerwsiitlyl γ = max γ0,maxi=1,2,···,K ξiγ2i+(1−ξi)γ1iγ+1iγγ22ii+1 ,
order analysis, we assume that the destination uses Selection where Pr(cid:16){ξi = 0} = Pnr{γ1i < ∆} = Fγ1io(∆(cid:17))
and Pr{ξ = 1} = 1 − Pr{ξ = 0}. The outage
i i
Combining (SC) to combine the signals received in the two
probability can be given by P = Pr{γ <γ } =
out th
stages for tractability unless otherwise specified.
Pr{γ <γ } K Pr ξ γ +(1−ξ ) γ1iγ2i <γ .
Remark: Let path 0 represent the direct link (S →D) and 0 th i=1 i 2i i γ1i+γ2i+1 th
path i represent the ith cascaded link (S →Ri →D) where AccordingtothQeTheorenmofTotalProbabilityandconditioonal
i = 1,··· ,K. For the ith cascaded link we introduce a ran- probability, we have
dom variable γi that will denote the equivalentinstantaneous K
SNR at the destination [15]. That is, let γi takes into account Pout = Pr{γ0 <γth} Pr{ξi =1}Pr{γ2i <γth}
boththefadingonS →Ri linkandthefadingontheRi →D Yi=1(cid:16)
γ γ
link. γi = γ2i when Ri uses DF, otherwise if AF is used by + Pr{ξi =0}Pr 1i 2i <γth|ξi =0
Ri, γi = γ1iγ+1iγγ22ii+1 [2]. Then we have K nγ1i+γ2i+1 o(cid:17)
γi =ξiγ2i+(1−ξi)γ +γ1iγγ2i+1. (2) (=a) Fγ0(γth) (1−Fγ1i(∆))Fγ2i(γth)
1i 2i iY=1h
Combining (1) and (2), it can be shown that the proposed
+ F (∆) . (5)
selectionmethodofthebestrelaygivesthemaximalequivalent γ1i
instantaneous SNR of S → R → D path. On the other (a)holdssincewhenξi=0,i.e.,γ <∆,wehave γ1γ2 <
b i 1i γ1+γ2+1
hand, as Selection Combining (SC) is used at the destina- γ <∆=γ ,i.e.,Pr γ1iγ2i <γ |ξ =0 =1.Using
tion. The received SNR at the destination can be given by 1i th γ1i+γ2i+1 th i
γ =max{γ ,γ }.Hencetheproposedselectionmethodofthe (4) and (13), we arrivenat (3). o
0 b Thefollowinglemmapresentsthe asympoticanalysis(high
bestrelay givesthe maximalreceivedSNR atthedestination.
SNR) of the outage.
III. OUTAGE ANALYSIS OFTHE OPPORTUNISTICDF-AF
Lemma 2.
SELECTIONRELAYING SCHEME
The outage probability can be given by the following m0γth m0 K
P ≃ ω0 SNR−m0 Θ , (6)
lemma. out (cid:16)m Γ(m(cid:17) ) i
0 0
i=1
Y
1The destination and the relay apply equal transmit power P unless
otherwise specified, andSNR=P/N0 with N0 being theAWGNvariance 2Themutualinformation betweenS andRi isgivenby 21log2(1+γ1i)
attherelayandthedestination. [15].
where ≃ denotes asymptotic equality, and IV. COMPARISON WITHTHE OPPORTUNISTICAF
RELAYING SCHEMEAND OPPORTUNISTIC DFRELAYING
1 m2iγth m2iSNR−m2i, m >m ; SCHEME
Θi =Proommmf:211iiiFΓΓΓ21(((irmmmst211,iii)))n(cid:16)(cid:16)(cid:16)ommtωωiω11c11ii2eii∆∆i (cid:17)(cid:17)th(cid:17)mma11tiiSSthNNeRR−−lommw11iie,,r gammm111miii a<=mmfu222niiic;.tion(7) FFirsγ×1t,γi+1ciγ.γ2dm2ii.+f1.i1−(oy1f)γn=1iγ+1m1iγγ2−2i2i−i+211αim2s1i2gi(ivmΓne(n1mib−1myi)12[Γ)1i(!7−em]−21(iα)1αi+2αn2−ij)2+yk+1
γ(a,b)≃(1/a)ba as b→0 [16]. It can be shown that n! j k 1i
n=0 j=0 k=0 (cid:20) (cid:18) (cid:19)(cid:18) (cid:19)
X X X
1− Γ(m0,α0γth) = γ(m0,α0γth) × α2ji−k2−1(1+y)j+k2+1y2n+2m2i2−j−k−1
Γ(m ) Γ(m )
0 0 × K 2 α α y(y+1) , (13)
1 m γ m0 j−k−1 1i 2i
≃ m Γ(m ) ω0 th SNR−m0. (8) (cid:16) p (cid:17)(cid:21)
0 0 (cid:18) 0 (cid:19) where Kv(·) denotes the vth order modified Bessel function
of the second kind. Consequently, the outage probability for
Similarly we obtain that
the opportunistic AF scheme is given by
Γ(m ,α ∆) 1 m ∆ m1i γ γ
1− 1i 1i ≃ 1i SNR−m1i (9) P = Pr max γ , max 1i 2i <γ
af 0 th
Γ(m1i) m1iΓ(m1i)(cid:18) ω1i (cid:19) (cid:26) (cid:18) i=1,2,···,K(cid:26)γ1i+γ2i+1(cid:27)(cid:19) (cid:27)
Γ(m ,α γ )
and = 1− 0 0 th F γ1iγ2i (y), (14)
(cid:20) Γ(m0) (cid:21) γ1i+γ2i+1
1−≃Γ(mΓ2(im,1α22ii)γth) m2iγth m2iSNR−m2i. (10) mwγ1hiiγn+e1{riγγeγ22i1i+iF,1γγ21<γii+1}iγ,γγ22iiiw+1[h1(ey8n)].STiNshRegreivf→oerne w∞bye, h(oa1bv3se)e.rPveDr{etγnhioat<te γ12γtγhii} =≤<
m2iΓ(m2i)(cid:18) ω2i (cid:19) Pr γ1iγ+1iγγ22ii+1 <γth ≤ Pr 12γi <γth . Using (4), it can
Using (8), (9), (10), and (3), the theorem can be obtained. benshown that o (cid:8) (cid:9)
Pr{γ <γ }
i th
Γ(m ,α γ )Γ(m ,α γ )
Corollary 1. The coding gain in high SNR, g,3 can be = 1− 1i 1i th 2i 2i th
Γ(m )Γ(m )
expressed as 1i 2i
Γ(m ,α γ ) Γ(m ,α γ )
1i 1i th 2i 2i th
m0γth m0 K = 1− Γ(m1i) !+ 1− Γ(m2i) !
g = ω0 η . (11)
(cid:16)m0Γ(m(cid:17)0) i=1 i − 1− Γ(m1i,α1iγth) 1− Γ(m2i,α2iγth) .(15)
Y Γ(m ) Γ(m )
1i ! 2i !
ηi = m2iΓ1(m2i) mω2i2γith m2i if m1i > m2i. Otherwise, ηi = Combining (9), (10), and (15), it can be shown that
1 m1i∆(cid:16) m1i. (cid:17) 1 m γ mi
m1iΓ(m1i) ω1i Pr{γi <γth}≃ i th SNR−mi :=Li, (16)
Corollary(cid:16)2. The(cid:17)diversity order can be given by miΓ(mi)(cid:18) ωi (cid:19)
where m =min{m ,m }. Similarly, we get
i 1i 2i
logP
d = − lim out 1 1 2m γ mi
SNR→∞logSNR Pr γi <γth ≃ i th SNR−mi
2 m Γ(m ) ω
K (cid:26) (cid:27) i i (cid:18) i (cid:19)
:= U . (17)
= m + min{m ,m }. (12) i
0 2i 1i
Xi=1 Consequently, we have Li (cid:22) Pr γ1iγ+1iγγ22ii+1 <γth (cid:22) Ui,
Remark:Corollary2revealsthatthediversityorderdepends i.e., n o
not only on the number of the relays, K, but also the fading Li (cid:22)F γ1iγ2i (y)(cid:22)Ui, (18)
parameters of the channels. Meanwhile, the diversity order γ1i+γ2i+1
can be non-integer according to Corollary 2. where f (SNR) (cid:22) f (SNR) means 0 < lim f1(SNR) ≤ 1.
1 2 SNR→∞f2(SNR)
Using (8), (9), (10), (18), we have P ≃
af
ord3eWrhreesnpePcotiuvtely≃. gSNR−l, g and l are called coding gain and diversity (cid:16)mm00ωγΓ0t(hm(cid:17)0m)0SNR−m0 Ki=1Λi, Li (cid:22) Λi (cid:22) Ui. Then, we
Q
obtain the coding gain g = (cid:16)m0ωγ0th(cid:17)m0 K ηaf with V. NUMERICAL RESULTS
miΓ1(mi) mωiγith mi ≤ ηiafaf≤ miΓ1(mm0i)Γ(m20m)ωiiγQthi=m1i.iand the theInacthciusrsaeccytioofn,ocuormdpeuritveerdsimanuallayttiiocnaslarreesupletsrf.oIrnmtehdetosivmeurilfay-
diversity(cid:16)order d(cid:17)af =m0+ Ki=1min{m(cid:16)2i,m1i(cid:17)}. tions, we have set R=1 bit/sec/HZ, ω0 =ω1i =ω2i =1.
Remark 1: It is difficult to perform the asymptotic analysis
(SNR → ∞) directly based Pon (14). The difficulty is that the 100
c.d.f. of the the equivalent relay path SNR γ1iγ2i is very
γ1i+γ2i+1
complicated.Inthispaper,we solvethe difficultybybounding
10-1
thetheequivalentrelaypathSNRwithsimplelowerandupper
boundsinhighSNR.Specifically, 1γ ≤ γ1iγ2i <γ .Then
we have the simple lower and up2peir boγu1in+dγs2io+f1the ci.d.f. of bility10-2 K=2
the theequivalentrelay pathSNR.Moreover, thelower bound a
b
andtheupperboundhavethesameSNRorder.Consequently, pro10-3 Theoretical results for opportunistic DF-AF, and
we obtain the asymptotic behavior of the outage probability. e opportunistic DF with K=3
g Theoretical results for opportunistic AF with K=3
haRveemthaerksa2m:eThdeivoeprspiotyrtuonrdisetri,ciD.e.F,-dAF=adnd o.pHpoowrteuvneirs,tiwchAeFn Outa10-4 SSiimmuullaattiioonn rreessuullttss ffoorr ooppppoorrttuunniissttiicc DDFF- AwFit h w Kit=h3 K=3 K=3
af Simulation results for opportunistic AF with K=3
∆ = γ , we have g ≤ g . That is to say, the opportunistic Theoretical results for opportunistic DF-AF, and
th af opportunistic DF with K=2
DF-AFhaslower outagethanopportunisticAFin highSNR. 10-5 Theoretical results for opportunistic AF with K=2
Simulation results for opportunistic DF-AF with K=2
WhenSCisappliedatthedestination,theoutageprobability Simulation results for opportunistic DF with K=2
Simulation results for opportunistic AF with K=2
for opportunistic DF scheme is the same as opportunistic 10-6
DF-AF.4 The opportunistic DF scheme has the same outage 0 5 10 15 20
SNR (dB)
behavior as the opportunistic DF-AF scheme in this case.5
However, if Maximal Ratio Combining (MRC) is used, the Fig.2. Outageprobability inRayleigh channels withK relays
outage probability for opportunistic DF-AF is given by
′
Pout =Pr γ0+ max {γi}<γth 104
( i=1,2,···,K )
= Pr max γ +γ <γ 102
0 i th
(i=1,2,···,K(cid:26) (cid:27) )
= K Pr{ξi =1}Pr{γ0+γ2i <γth}+Pr{ξi =0} ability100 m0=0.5,m1=[1 1 2],
iPY=r1(cid:16)γ0+ γ1iγ+1iγγ22ii+1 <γth|ξi =0 . (19) ge prob10-2 DADFFF,-- AAcFFom ,& sp iDmutFua,lt aicotoinomnputation m2=[1 1 1]
Incontrast,ntheoutageprobabilityforopportunois(cid:17)ticDFcanbe Outa10-4 DAFF,,ssiimmuullaattiioonn
derived as DF-AF & DF, computation m=1.5,m=[1 2 2],
AF , computation 0m=[11 2 1]
DF-AF, simulation 2
′ 10-6 DF, simulation
P =Pr γ + max {ξ γ }<γ
df 0 i 2i th AF, simulation
( i=1,2,···,K ) DF-AF & DF, asympotic
K 10-8 DF-AF & DF, asympotic
0 5 10 15 20
= Pr{ξi =1}Pr{γ0+γ2i <γth}+Pr{ξi =0} SNR (dB)
iY=1(cid:16)
Fig.3. Outageprobability inNakagami-mchannels with3relays
Pr γ <γ |ξ =0 (20)
0 th i
n o(cid:17)
Since Pr γ < γ |ξ = 0 > Pr γ + γ1iγ2i < Fig. 2 compares the outage probability obtained via sim-
0 th i 0 γ1i+γ2i+1 ulations and theoretical evaluation with different number of
γ |ξ = n0 , we have P′ <oP′ . Onnthe other hand, the
th i out df potential cooperating relays (K) in Rayleigh fading environ-
outage for oopportunistic AF with MRC is ment (m = m = m = 1). Fig. 3 compares the outage
0 1i 2i
probability with general Nakagami-m fading parameters in
Pa′f =Pr(γ0+i=1m,2a,·x··,K(cid:26)γ1iγ+1iγγ22ii+1(cid:27)<γth) (21) KAs=a 3berneclahymsasrcke,nwareioa,lmso0s=ho0w.5t,hme1ou=ta[g1e1p2ro],bmab2il=ity[1of1t1h]e.
Since γ1iγ2i <γ , then P′ <P′ . best-relay selection adaptive DF scheme [15] as well as the
γ1i+γ2i+1 2i out af outage probability of the opportunistic AF schem. Observe
4Theoutageprobability foropportunistic DFisalsogiven by(3). that simulation curves match in high accuracy with analytical
5Thediversity orderandcodinggainarethesameconsequently. ones. When SC is utilized, opportunistic DF-AF scheme has
8
thesameoutageprobabilityasthebest-relayselectionadaptive
DF scheme, which has better outage performance than the
7
opportunistic AF scheme. The asymptotic outage coincides
with the exactoutage in high SNR region.We can notice that
6
both the number of potential cooperating relays (K) and the
er
fading parameters have a strong impact of the performance ord5
enhancement.We willanalyzetheimpactofthe relaynumber y
sit
and the fading parameter respectively in the following. er4
v
Di
100 3
10-1 2
1
bility10-2 KK==23 1 2 3 K4 5 6 7
e proba10-3 KKK===456 Fig.5. Diversity orderwithdifferent K
g K=7
a
ut10-4
O
20
10-5
er15
d
10-6 or
0 5 10 15 20 y 10
SNR(dB) sit
er
Fig.4. Outageprobability withK relays Div 5
0
Fig. 4 illustrates the theoretical results for the outage prob- 8
6 8
ability of opportunistic DF-AF scheme with different number 4 6
of relays, K. In the computation, we set m0 = 0.8 and 2 2 4
m1i = m2i = 1. When m1i = m2i = 1, the diversity g 0 0 g
order is d = m + K (See Fig. 5). From Fig. 4, we can 2 1
0
clearly find thatthe numberof relaysimpactsthe slope of the
Fig.6. Diversityorderwithdifferent fading parameters
curves. When there are more relays, the outage probability
decreases more faster. In addition, the slopes of the curves in
high SNR in Fig. 4 are concordant with the diversity order
illustrated in Fig. 5. Fig. 6 shows the diversity order with scheme outperforms the other two schemes. The advantages
differentchannelfadingparameters.We consider2symmetric are obvious when α = 0.2,...,0.7, and the opportunistic
relays, i.e., m =[g g ],m =[g g ]. Thefadingparameter DF-AF scheme has almost the same performance as the
1 1 1 2 2 2
for the direct channel from the source to the destination is opportunisticDFschemewhenα=0.8,0.9.Inaddition,from
m = 0.5. It can be observed that the diversity order is the curve for the opportunistic DF-AF scheme, we can notice
0
determined by the worse one in the source-relay channel (g ) that with the increase of α, the outage decreases at first and
1
and relay-destination channel (g ). then increases. This can be explained as follows: When the
2
To further demonstrate the advantages of the opportunistic source power increases, the relay has larger probability to
DF-AF scheme, we show the outageperformanceof the three correctly decode the source message, and then DF will be
schemes when MRC is used in Fig. 7. The fading parameters utilized with larger probability. Thus, the curves of the DF-
are set as m = 0.5,m = [1 1 2],m = [1 1 1]. Notice AF scheme and DF scheme approach while we increase α.
0 1 2
that the opportunistic DF-AF scheme has the best outage The equivalent SNR of the relay path is given by (2). When
performance,whichverifiestheproposedtheoreticalanalysis. the source power is low (i.e., α is small), the relay could not
InFig.8, weconsiderdifferentpowerallocationsbetweenthe decode the source messages with high probability, equivalent
sourceandtherelay.Defineα=P /(P +P )asthepoweral- SNR of the relay path is approximated by γ1iγ2i . In this
s s r γ1i+γ2i+1
locationcoefficient,wherePs andPr arethetransmitpowerat case, the increase α will result in the increases of γ1i and
the source andthe relay,respectively.In the simulation,MRC decreaseofγ2i.Observethatγ1iincreasefromasmallnumber
is applied at the destination, and we set the AWGN variance and γ decreases from a large number, i.e., γ and γ
2i 1i 2i
N =1.FromFig.8,wecanseethattheopportunisticDF-AF approacheachother.Consequently, γ1iγ2i increases.Thus,
0 γ1i+γ2i+1
100 The coding gain and diversity order are derived whereby the
asymptotic analysis in high SNR. We find that the diversity
orderdependsonnotonlytherelaynumberbutalsothefading
10-1 parameters.Moreover,we provethatthe opportunisticDF-AF
y selection relaying scheme outperforms both the opportunistic
bilit DF scheme and opportunistic AF scheme in terms of the
a
b outage performance. Finally, the numerical results verify our
o
pr10-2 analysis. In addition, simulations demonstrate that the power
e Opportunistic DF-AF
g allocationbetweenthesourceandtherelayplaysanimportant
a Opportunistic DF
ut Opportunistic AF role on the performance. We will investigate the the power
O
10-3 allocation to further improve the performance in the future
works.
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10-4 [1] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity-
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