power allocation for a hybrid decode–amplify–forward cooperative communication system with two...

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE SYSTEMS JOURNAL 1

Power Allocation for a HybridDecode–Amplify–Forward Cooperative

Communication System With TwoSource–Destination Pairs Under Outage

Probability ConstraintHailin Xiao and Shan Ouyang

Abstract—We develop a two-source–destination-pair coopera-tive communication scheme that can achieve multiuser diver-sity and cooperative diversity. In this scheme, we use hybriddecode–amplify–forward (HDAF) protocol to improve system per-formance. From practical point of view, HDAF protocol performsbetter than amplify-and-forward and decode-and-forward pro-tocols by combining the merits of both. Meanwhile, we derivea closed-form expression of outage probability associated withHDAF protocol analyzed. Based on outage probability constraint,we investigate optimal power allocation that minimizes the totalpower. Numerical analysis is used to confirm the accuracy of thederived theory and to examine the performance of our proposedcooperative scheme, particularly as we analyze power savingsin using optimal power allocation compared with equal powerallocation, which is commonly assumed in previous studies. It isshown that significant power savings can be obtained by using theproposed power optimization method.

Index Terms—Cooperative diversity, hybrid decode–amplify–forward (HDAF), outage probability, power allocation.

I. INTRODUCTION

IN many wireless systems, the mobile terminals are unableto support multiple physical antennas due to limitations in

size, complexity, cost, or other constraints. Cooperative com-munication [1] is an alternative approach that exploits spatialdiversity in wireless systems without the need for multipleantennas implemented at the terminals. In its simple form, acooperative communication system is a relay system consist-ing of three nodes, i.e., a source, a relay, and a destination(source–relay–destination), where the relay assists the sourceby forwarding its signals to the destination. Various relay-ing strategies have been investigated in the literature [2]–[4],

Manuscript received March 31, 2013; revised September 23, 2013; acceptedOctober 31, 2013. This work was supported in part by the National NaturalScience Foundation of China under Grant 61261018 and Grant 61362007,by Guangxi Natural Science Foundation under Grant 2013GXNSFFA019004and Grant 2011GXNSFD018028, and by the opening project of Guangxi KeyLaboratory of Wireless Wideband Communication and Signal Processing underGrant 12111.

The authors are with the School of Information and Communication,Guilin University of Electronic Technology, Guilin 541004, China (e-mail:[email protected]; [email protected]).

Digital Object Identifier 10.1109/JSYST.2013.2296740

among which, amplify-and-forward (AF) and decode-and-forward (DF) have been the most widely adopted protocols.For AF, a disadvantage is the noise amplification, which isincurred by the relay’s action. Meanwhile, one notable ad-vantage is able to operate at all times, including when thesource–relay channel experiences outage. For DF, on one hand,this protocol can result in severe performance degradation ifthe relay wrongly decodes the signal. On the other hand, whenthe instantaneous source–relay channel is suitable for a cleandata extraction, DF can perform better since it regenerates andpasses on a clean set of signals. These observations motivatethe proposition of a new signal forwarding strategy that extractsmaximal benefit from AF and DF; this strategy is called hybriddecode–amplify–forward (HDAF). The intuition behind thisprotocol is that the relay will amplify the received signal andforward the amplified signal to the destination if it cannotdecode the signal correctly or the link between the relay andthe source is not good enough.

The available research on HDAF protocol has been proposed[5]–[9]. In [5], the relay has employed HDAF protocol toperform soft decoding and forward the reliability informationto destination. In [6], the symbol error probability of HDAFcooperative strategy has been analyzed. In [7], HDAF coopera-tive strategy is the best cooperative protocol when the qualityof relay–destination link is better than source–relay link. In[8], the performance of SNR-based HDAF relaying cooperativediversity networks has been analyzed, and the closed-formexpressions for the outage and bit error probability of the HDAFrelaying scheme have been derived. In [9], the incrementalHDAF relaying scheme has been proposed; simulation resultsand analysis have shown that the proposed scheme outperformsthe incremental DF relaying scheme. These works only concernthe performance of three-node scenario for HDAF cooperationcommunication, which provide a simple but effective meanfor source to leverage the processing and transmit power ofthe relay, as well as the spatial diversity of the relay channelin a wireless scenario. However, focusing on the worst casescenarios, the performance of HDAF modes is not differentfrom that of AF or DF and is pretty bad [10]. In [11] and [12],the authors have studied a multirelay HDAF scheme. However,the scheme in [11] and [12] requires many relay nodes to

1932-8184 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

http://www.ieee.org/publications_standards/publications/rights/index.html

mailto: [email protected]


2 IEEE SYSTEMS JOURNAL

process the received signal and forward it to the destination,and hence, it severely degrades spectral efficiency.

In recent years, there is increasing interest in investigatingthe advantages of relaying in multisource multidestination net-works, which promise significant achievable rate improvementin shared-spectrum multiple access wireless networks [13].Therefore, the multisource multidestination generally achieveshigh cooperative diversity (cf., user cooperation diversity of[14]), where multiple sources transmit date to multiple desti-nations, being helped by multiple relays. As previous descrip-tion, multiple-relay strategy can result in very low spectralefficiency and high complexity. To reduce spectral efficiencyloss and complexity, we decrease the numbers of relays andrequire two users to share their individual antennas and workas relays for each other in this paper. Hence, the simplesttwo-source two-destination (two source–destination pairs) relaynetwork is modeled, where each source helps an indepen-dent source–destination pair by using HDAF. The achieveddiversity order for each source–destination pair is the sameas that using relay assistance (three nodes). Therefore, twosource–destination pairs can achieve higher cooperative diver-sity in fading environments when compared with three nodes,particularly in the high-SNR region. More importantly, the pro-posed simplest two-source–destination-pair relay network canbe implemented in distributed antennas belonging to multipleterminals (each with its own information to transmit) and canreduce the power consumption of terminals.

In general, the high quality of the source–relay links isnot guaranteed in deep fading channels. Thus, one may askwhether it is possible that the same diversity performancecan be achieved in general source–relay–destination channelconditions. In this case, diversity can be attained through thehelp of users in which, by letting only the user with the highestinstantaneous SNR at a given time or whose channel gainis near the “peak.” This diversity strategy called multiuserdiversity (MUD) [15], [16], which is an inherent diversity ina multiuser network [17]. The diversity gain arises from thefact in a system with many users. The channels at differentusers vary independently; there is likely to have a user withgood channel quality. In such a case, the channel resourceis always allocated to the user that can best exploit it at aparticular time. This is also known as selection diversity. Hence,in deep fading channels, the proposed two source–destinationpairs are efficient schemes for the combined use of cooperativediversity and MUD that reduces the probability of deep fades,thus reducing the total power.

Beyond the diversity considerations, power allocation is acritical design consideration to improve the performance ofcooperative communication due to limited transmission powerof mobile terminals [18]–[20]. In [18], optimal power allocationhas improved the system performance significantly when thechannel state information (CSI) is available at relays or desti-nations. In [19], optimal power allocation for DF cooperativediversity has been proposed to optimize resource allocations.Under the total power budget, joint relay selection and powerallocation for bidirectional relay networks have been presentedin [20]. Most works in the literature focus on finding powerallocation that minimizes outage probability subject to a total

power constraint. However, using outage probability minimiza-tion as an optimization criterion of power allocation is a difficulttask [21] due to the exact minimization of outage probability forany SNR should be known. It is of clear interest to minimize thetotal power for the proposed cooperative scheme under outageprobability constraint. This will be the subject of this paper.Moreover, some power allocation strategies primarily focuson the DF and AF cooperative communication systems. Forexample, in [22], the authors have proposed joint relay selectionand power minimization algorithm in a DF cooperative uplinkto minimize the total uplink transmit power. In [23], outageprobability and power allocation of AF relaying with channelestimation errors have been investigated; it has been shownthat significant power savings can be obtained. However, fewresearchers have used HDAF protocol to study power allocationproblem for a cooperative communication system under outageprobability constraint.

In this paper, we aim for optimal power allocation for anHDAF cooperative communication system with two source–destination pairs under outage probability constraint. We as-sume that instantaneous channel gains follow the quasi-staticRayleigh distribution. The instantaneous CSI of all channelsmay be available at the transmitter. Our contributions in thispaper are summarized in three points.

1) The simplest two-source–destination-pair relay networkis modeled, which cannot only achieve higher coop-erative diversity in fading environments when com-pared with three nodes, particularly in high-SNR region,but also reduce spectral efficiency loss and complexityover multisource multidestination with multiple relays.More importantly, the proposed simplest two-source–destination-pair relay network can be implemented indistributed antennas belonging to multiple terminals andcan reduce the power consumption of terminals. Evenif channels are in deep fading, the proposed two source–destination pairs are efficient schemes for the combineduse of cooperative diversity and MUD that reduces theprobability of deep fades, thus reducing the total power.

2) Comparing the SNR threshold with the SNR ofsource–“relay” channel, we choose AF/DF to forwardsignals to destinations. This HDAF protocol can signif-icantly improve system performance according to dif-ferent channel conditions. At the same time, we deriveclosed-form expressions of outage probability associatedwith HDAF protocol analyzed.

3) Based on outage probability constraint, we investigateoptimal power allocation that minimizes the total power.Numerical analysis is used to confirm the accuracy ofthe derived theory and to examine the performance ofour proposed cooperative scheme. It is shown that theproposed power allocation outperforms equal power al-location significantly.

The remainder of this paper is organized as follows.Section II describes the system model. Section III presentsoutage probability analysis. Based on outage probability con-straint, we derive optimal power allocation in Section IV.


XIAO AND OUYANG: POWER ALLOCATION FOR A HDAF SYSTEM WITH TWO SOURCE–DESTINATION PAIRS 3

Fig. 1. Two-source–destination-pair cooperative communication systemmodel.

Section V provides numerical simulation results and discus-sions. Finally, conclusions are drawn in Section VI.

II. SYSTEM MODEL

Consider the two-source–destination-pair cooperative com-munication system in Fig. 1, in which sources s1 and s2transmit to destinations d1 and d2, respectively. This examplemight correspond to a snapshot of a wireless network in whicha higher level network protocol has allocated bandwidth totwo terminals for transmission to their intended destinationsor next hops, such as, in a cellular network, s1 and s2 arerespectively handsets and d1 = d2 might correspond to thebase station. As another example, i.e., in a wireless local areanetwork, cases d1 and d2 might respectively correspond to anad hoc configuration among the terminals. As stated earlier,full CSI is assumed, and all the channels are assumed thequasi-static Rayleigh distribution. The additive white Gaussiannoise (AWGN) at each receiver is represented as a zero-meancomplex Gaussian random variable with variance N0. Sourcestransmit symbols (not restricted to binary symbols) formed asa linear combination of new and previously amplified/decodedsymbols from each other.

In this paper, our focus is put on half-duplex relaying thatlends itself more easily to practical implementation by pre-venting the transmit chain of the relay terminal to interfer-ence. Thus, to ensure half-duplex operation, we further divideeach channel into orthogonal subchannels. Fig. 2 illustratesour channel allocation for two-terminal time-division duplex(TDD). Under above orthogonality constraints, we can nowconveniently, and without loss of generality, characterize ourchannel models using a time-division notation; frequency-division counterparts to this model are straightforward due tothe symmetry of the channel allocations. Specifically, usingsystem communication, we can provide the powerful benefitsof diversity without the need for physical arrays, although ata loss of spectral efficiency due to half-duplex operation andpossibly at the cost of additional received hardware.

For the system model considered here, we use a baseband-equivalent discrete-time channel model for the continuous-timechannel and consider N consecutive uses of the channel, whereN is large (i.e., to transmit a total of N symbols is in thetwo phases of duration time). We expect that some level ofsynchronization between the terminals for cooperative diversityto be effective, as suggested in Fig. 2, where we consider thescenario in which the terminals are block, carrier, and symbol

Fig. 2. (a) ODT. (b) OCT.

synchronization. Given some form of network block synchro-nization, carrier and symbol synchronization for network canbuild upon the same between the individual transmitters andreceivers. As shown in Fig. 2(a), orthogonal direct transmission(ODT) based on TDD is illustrated; s1 and s2 transmit onlyhalf of N symbol in two transmission phases, respectively.Due to ODT, there is no “relay” to cooperative transmission.In Fig. 2(b), we consider HDAF protocol that consists of twotransmission phases. During the first phase, sources s1 ands2 broadcast their messages x1 and x2 to each other anddestinations d1 and d2, respectively. In the phase, s1 acts asthe “source” (for notational convenience, it is described as“Tx”), and s2 serves as a “relay” (“Rx”) and vice versa. In thesecond phase, the “relay” retransmits the messages with HDAFprotocol. At the end of the second phase, each destinationcombines the two received signals with the maximal ratiocombining (MRC) technique.

For ODT, we model the channel as

ydi[n] =

√psihsidi

xi[n] + nsidi[n] (1)

for n = 1, . . . , N/2, where xi[n], i ∈ {1, 2}, is the sourcetransmitted signal, and ydi

[n] is the destination received sig-nal. The other terminal transmits for n = N/2 + 1, . . . , N , asdepicted in Fig. 2(a). Thus, each source utilizes only half of theavailable degrees of freedom of the channel.

For cooperative diversity, HDAF cooperative transmissionis divided into two phases. During phase I, the sources sibroadcast the signals with the transmission power psi , and the“relays” sj , j ∈ {2, 1}, and destinations di receive the signals,respectively

ysj [n] =√psihsisjxi[n] + nsisj [n] (2)

ydi[n] =

√psihsidi

xi[n] + nsidi[n] (3)

for example, n = 1, . . . , N/4, where xi[n] is the sources trans-mitted signal, and ysj [n] and ydi

[n] are the “relays” and des-tinations received signals, respectively. In this paper, nsisj [n],nsjdi

[n], and nsidi[n] are the AWGN components, which are

random with N(0, N0), respectively. hsisj , hsjdi, and hsidi

denote the Rayleigh fading coefficients over si → sj , sj → di,and si → di links and are modeled as zero-mean complexGaussian fading coefficients with variance Ωsisj , Ωsjdi

, andΩsidi

, respectively.



During phase II, the “relays” sj help the sources si to forwardinformation using HDAF protocol. We model the receivedsignal as

ydi[n] =

√psjhsjdi

x′[n] + nsjdi[n] (4)

for n = N/4 + 1, . . . , N/2, where x′[n] is the “relays” trans-mitted signal, ydi

[n] is the destinations received signal. Notethat only half the degrees of freedom are allocated to eachsource terminal for transmission to its destination and a quarterof the degrees of freedom are available for communication toits relay, as depicted in Fig. 2(b).

The SNR of channel si → sj is γsisj = psi |hsisj |2/N0. Ifγsisj is below the SNR threshold γth, the “relays” choose AFto avoid error propagation; otherwise, DF protocol is adopted toavoid noise amplification. Defining Z represents the comparedresults at the “relays”

Z =

{1, γsisj < γth0, γsisj ≥ γth.

(5)

If AF protocol is performed, the destination received informa-tion is given by

yAFdi

[n] = βhsjdiysj [n] + nsjdi

[n] (6)

where β is the amplification factor and is defined as [24]

β =√psj/(psi |hsisj |2 +N0). (7)

If the “relays” use DF protocol, the received information at thedestinations is given by

yDFdi

[n] =√psjhsjdi

x[n] + nsjdi[n] (8)

where psj is the “relays” transmitted power, and x[n] representsthe re-encode signals at the “relays.”

At the end of the second phase, the destinations combine thereceived information at two phases with MRC technique. Then,the SNR of the source–relay–destination link, as denoted by γZ ,can be written as [25]

γZ =

(γsisjγsjdi

γsisj + γsjdi+ 1

)Z

(γsjdi)1−Z (9)

where γsidi= psi |hsidi

|2/N0 and γsjdi= psj |hsjdi

|2/N0 arethe SNRs of si → di and sj → di links, respectively.

III. OUTAGE PROBABILITY ANALYSIS

In a cooperative communication system, an outage eventoccurs at the destination when the mutual information fromthe source to the destination fails to achieve the target rateR. In this section, we first focus our attention on the exactoutage probability of adaptive HDAF relaying. We characterizethe performance of HDAF protocol and derive closed-formexpressions of outage probability in the high-SNR regime. As afunction of the fading coefficients viewed as random variables,the mutual information I for a protocol is a random variable.For a target rate R, Pr[I < R] denotes outage probability.

A. ODT

As shown in Fig. 2(a), the sources transmit over quasi-static Rayleigh fading channels. The maximum average mutualinformation between the input and output is given by

I = log(1 + γsidi). (10)

For ODT link, the outage probability is expressed as follows:

PODTout = Pr {log(1 + γsidi

) < R} =(2R − 1)N0

psiΩsidi

. (11)

When the outage probability satisfies the outage probabilityconstraint η, the total power in the ODT link is given by

pODT =(2R − 1)N0

ηΩsidi

. (12)

B. OCT

In the orthogonal cooperative transmission [OCT, as shownin Fig. 2(b)] path si−sj−di, the outage probability is given by

POCTout = Pr

{1

2log(1 + γsidi

+ γZ) < R

}. (13)

In order to calculate POCTout , we first derive the cumulative

distribution function (CDF) of γZ . Using the approximation[26], we have

γsisjγsjdi

γsisj + γsjdi+ 1

≈ min(γsisj , γsjdi). (14)

As the above system model description, all the channels areindependent distributed channels; the CDF of γZ is given by

FγZ(g(R))

=∑

Z∈{0,1}Pr{Z}Pr {γZ < g(R)}

=∑

Z∈{0,1}Pr(Z) Pr (γZ < g(R)|Z = 1)

× Pr (γZ < g(R)|Z = 0)

=∑

Z∈{0,1}

{Pr

{γsisj < γth

}}Z {Pr

{γsisj ≥ γth

}}1−Z

×{Pr

{γsjdi

< g(R)}}1−Z

×{1− Pr

{γsisj > g(R)|γsisj < γth

}× Pr

{γsjdi

> g(R)}}Z

(15)

where g(R) = 22R − 1, Pr{Z} and Pr{γZ < g(R)} denotethe probability density function of Z and the conditional dis-tribution probability function of γZ , respectively. The condi-tion outage probability Pr{γsisj > g(R)|γsisj < γth} can beexpressed as

Pr{γsisj > g(R)|γsisj < γth

}=

{0, γth ≤ g(R)exp(−γth/γsisj

)−exp(−g(R)/γsisj)

1−exp(−γth/γsisj) , γth > g(R).

(16)



Substituting (16) into (15), we can obtain

FγZ(g(R))

=

⎧⎨⎩

g(R)N0

(1

psiΩsisj

+ 1psj

Ωsjdi

), γth ≤ g(R)

2γthN0−g(R)N0

psiΩsisj

+ g(R)N0

psjΩsjdi

, γth > g(R).(17)

The outage probability (13) can be rewritten as

POCTout = Pr {γsidi

+ γZ < g(R)}

=

g(R)∫0

Pr {γZ < g(R)− γsidi} pγsidi

(γsidi)d γsidi

.

(18)

Changing the variable γ′ = 1− γsidi/g(R), we obtain

POCTout =

g(R)N0

psiΩsidi

×1∫

0

Pr {γz < g(R)γ′}

× exp

(−N0g(R)(1− γ′)

psiΩsidi

)d γ′. (19)

At high SNR, all the “relays” can decode the sources’ messages[27]. In this paper, we deal with the high-SNR regime; there-fore, (19) can be simplified as

POCTout =

g(R)N0

psiΩsidi

1∫0

FγZ(g(R)γ′) d γ′

=

⎧⎨⎩

[g(R)N0]2

2psiΩsidi

(1

psiΩsisj

+ 1psj

Ωsjdi

), γth ≤ g(R)

g(R)(N0)2

2psiΩsidi

(2γth−g(R)psi

Ωsisj+ g(R)

psjΩsjdi

), γth > g(R).

(20)

IV. OPTIMAL POWER ALLOCATION

At any given time instant, a single source experiencing deepfades will then have to expend large amount of power in order tomeet the quality-of-service constraints. The proposed coopera-tive scheme can achieve MUD and cooperative diversity thatreduces the probability of deep fades, thus reducing the totalpower. In this section, the objective of power allocation is tominimize the total power while satisfying the outage probabilityconstraint (called optimal power allocation); the consideredoptimization problem is formulated as

min pOCT = psi + psj (i, j ∈ {1, 2}, i = j)

Subject to POCTout ≤ η. (21)

Using the Lagrange function, the optimization problem (21)(also called objective function) can be represented as

L(psi , psj , λ) = psi + psj + λ(POCTout − η

)(22)

where λ is the Lagrangian parameter (λ ≥ 0). According tothe Karush–Kuhn–Tucker conditions [28], we first prove thatthe objective function (22) is a continuous function and is a

concavity in psi or psj . The second derivative of the objectivefunction L(psi , psj , λ) is given by

∂L(psi , psj , λ)

∂p2sj= 2λ

K

psi

a

(psj )3> 0. (23)

From (23), the objective function is a continuous function andis a concavity in psi or psj . Hence, the optimal solutions ofthe objective function must exist. The corresponding optimalsolutions need to satisfy the following equations:

∂L(psi , psj , λ)

∂psi=1− λ

[K

(psi)2

(b

psi+

a

psj

)+

K

p3si

]= 0

(24)∂L(psi , psj , λ)

∂psj=1− λ

K

psi

a

(psj )2= 0 (25)

λ(POCTout − η

)=0 (26)

where K=[g(R)N0]2/2Ωsidi

Ωsisj , a=Ωsisj/Ωsjdi, and b =

(2γth − g(R))/g(R). The solutions for the transmission powerat sources and “relays” can be obtained as follows:⎧⎨⎩

psi =12η

√2ηK(a+ 2 +

√a2 + 8a)

psj =a√

2ηK(a+2+√a2+8a)

aη+η√a2+8a

γth ≤ g(R) (27)

⎧⎨⎩

psi =12η

√2ηK(a+ 2b+

√a2 + 8ab)

psj =a√

2ηK(a+2b+√a2+8ab)

aη+η√a2+8ab

γth > g(R). (28)

In (27), it is shown that optimal transmission power values ofsources and “relays” are unrelated to γth (γth ≤ g(R)). In thiscase, cooperative communication is not an optimal communica-tion mode for the two-source–destination-pair system. Hence,if ODT consumes less power than OCT, the sources transmitinformation through the ODT path; otherwise, the OCT path isdeployed.

V. NUMERICAL SIMULATION RESULTS

In this section, we evaluate the performance of the proposedoptimal power allocation through numerical simulation results.Numerical simulations have been performed over quasi-staticRayleigh fading channels with AWGN. Note that psi and psjare respectively denoted as sources and “relays” transmissionpower in all numerical simulations (as previous description)unless stated otherwise.

Fig. 3 presents outage probability versus sources and “relays”transmission power in two cases: I) γth ≤ g(R) (ODT); andII) γth > g(R) (OCT). We set Ωsidi

= 1, Ωsisj = 10, Ωsjdi=

5, and R = 1 bit/s/Hz. It is shown that outage probabilitydecreases as sources and “relays” transmission power increase.As expected, there is a tradeoff between transmission power andoutage probability so that we can choose ODT/OCT to adaptdifferent channel conditions. The numerical simulation resultsof the outage probability are 0.01 at γth = 5, psj = 17.2 dB,and psi = 8.1 dB. There is agreement between the numericalsimulation results and the analytical values. In addition, theoutage probability of case I is much smaller than that of case II



Fig. 3. Sources transmission power and “relays” transmission power versusoutage probability.

Fig. 4. Outage probability versus the total power under different transmissionprotocols.

Fig. 5. Power saving comparison between equal power allocation and optimalpower allocation under different outage probabilities.

Fig. 6. Power saving comparison between equal power allocation and optimalpower allocation under different achievable rates.

Fig. 7. Total power versus SNR threshold for different channel fadingcoefficients.

under the same condition because the SNR of the si → sjlink is above the SNR threshold γth, and the “relays” performAF protocol to forward information; AF protocol requiresless power to forward signals as it does not require complexdecoding at the “relays.”

In order to compare HDAF protocol that can obtain anexcellent performance with both AF and DF protocols, wepresent performance analysis in Fig. 4. It is shown that HDAFconsumes less the total power than AF and DF. For the two-source–destination pair system, the numerical simulation re-sults of the required total power are 15.7, 16.8, and 18.6 dB forHDAF, DF, and AF at γth = 5 and POCT

out = 0.02, respectively.For a single-source single-destination system, the numericalsimulation results of the required total power are 19.8, 21.5, and25.6 dB for HDAF, DF, and AF at γth = 5 and POCT

out = 0.02,respectively. Hence, it is observed that the MUD gain anddiversity gain can be obtained in the form of improved outageperformance, thus reducing the total power.



It is interesting to study how much power savings can beobtained through the proposed optimal power allocation. InFig. 5, we compare power savings between equal power alloca-tion and optimal power allocation under different outage prob-abilities. It can be observed that the proposed optimal powerallocation always outperforms equal power allocation under thesame outage probability. When outage probability constraintis relaxed, the total power is also decreased. Compared withequal power allocation, optimal power allocation can save thetotal power about 1.3 dBm in case I and 3.7 dBm in case II,respectively.

In Fig. 6, we compare power savings between optimalpower allocation and equal power allocation as achievable rateschange from 0.5 to 1.5 bit/s/Hz. Here, equal power allocationand optimal power allocation are 14, 14, 17.2, and 8.1 dBmat γth = 5, POCT

out = 0.01, and R = 1 bit/s/Hz, respectively. Inother words, the total power is saved about 3 dBm by adoptingoptimal power allocation.

Setting different SNR thresholds is a significant impact onsystem performance. Fig. 7 plots the total power versus differ-ent SNR thresholds under different channel fading coefficients.Four types of different channel conditions are considered. Itis observed that the total power is fixed in case I. There isagreement between numerical simulation results and analyticalvalues in (27). Moreover, the total power will significantlyincrease as the SNR increases in case II. To improve the channelquality of si → sj , sj → di, and si → di links, the total powerwill approximately save 1.1, 2.4, and 5.1 dBm at γth = 5,POCTout = 0.02, and R = 1 bit/s/Hz, respectively.

VI. CONCLUSION

In this paper, we have developed a two-source–destination-pair cooperative communication system and derived closed-form expressions of outage probability associated with HDAFprotocol analyzed. Based on outage probability constraint, wehave investigated optimal power allocation that minimized thetotal power. Numerical results have shown that the proposedpower allocation outperformed equal power allocation. Ourresults in this paper offer important analytical tools and fully ex-ploit the potential of HDAF-based multiple source–destinationpairs. More importantly, we have presented a multisourcemultirelay TDD cooperative communication system, which wehope will benefit future research in this area.

REFERENCES

[1] J. N. Laneman, D. N. Tse, and G. W. Wornell, “Cooperative diversity inwireless networks: Efficient protocols and outage behavior,” IEEE Trans.Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[2] I. Krikidis, J. Thompson, S. McLaughlin, and N. Goertz, “Optimizationissues for cooperative amplify-and-forward systems over block-fadingchannels,” IEEE Trans. Veh. Technol., vol. 57, no. 5, pp. 2868–2884,Sep. 2008.

[3] P. E. Elia, K. Vinodh, M. Anand, and P. V. Kumar, “D-MG tradeoffand optimal codes for a class of AF and DF cooperative communica-tion protocols,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3161–3185,Jul. 2009.

[4] S. Lee, W. Su, S. Batalama, and J. D. Matyjas, “Cooperative decode-and-forward ARQ relaying: Performance analysis and power optimization,”IEEE Trans. Wireless Commun., vol. 9, no. 8, pp. 2632–2642, Aug. 2010.

[5] X. Bao and J. Li, “Efficient message relaying for wireless user coop-eration: Decode–amplify–forward (DAF) and hybrid DAF and coded-cooperation,” IEEE Trans. Wireless Commun., vol. 6, no. 11, pp. 3975–3984, Nov. 2007.

[6] T. Q. Duong and H. J. Zepernick, “On the performance gain of hy-brid decode–amplify–forward cooperative communications,” EURASIPJ. Wireless Commun. Netw., vol. 2009, Article ID 479463, 10 pp.,2009.

[7] W. Su and X. Liu, “On optimum selection relaying protocols in cooper-ative wireless networks,” IEEE Trans. Wireless Commun., vol. 58, no. 1,pp. 52–57, Jan. 2010.

[8] H. Chen, J. Liu, C. Zhai, and L. Zheng, “Performance analysis ofSNR-based hybrid decode–amplify–forward cooperative diversity net-works over Rayleigh fading channels,” in Proc. IEEE WCNCW, Sydney,Australia, Apr. 2010, pp. 1–6.

[9] J. Jia, Z. Bai, J. Cui, and K. Kwak, “Performance analysis of hybrid DAFbased incremental relaying cooperative,” in Proc. IEEE 23rd Int. Symp.PIMRC, Sydney, Australia, Sep. 2012, pp. 1824–1828.

[10] T. T. Duy and H. Y. Kong, “Performance analysis of hybriddecode–amplify–forward incremental relaying cooperative diversity pro-tocol using SNR-based relay selection,” J. Commun. Netw., vol. 14, no. 6,pp. 703–709, Dec. 2012.

[11] T. Liu, L. Song, Y. Li, Q. Huo, and B. Jiao, “Performance analysisof hybrid relay selection in cooperative wireless systems,” IEEE Trans.Commun., vol. 60, no. 3, pp. 779–788, Mar. 2013.

[12] M. Abouelseoud and A. Nosratinia, “Heterogeneous relay selection,”IEEE Trans. Wireless Commun., vol. 12, no. 4, pp. 1735–1743, Apr. 2013.

[13] F. Chen, W. Su, S. Batalama, and J. D. Matyjas, “Joint power optimizationfor multi-source multi-destination relay networks,” IEEE Trans. SignalProcess., vol. 59, no. 5, pp. 2370–2381, May 2011.

[14] S. S. Ikki and M. H. Ahmed, “Performance analysis of cooperative diver-sity with incremental best relay technique over Rayleigh fading channels,”IEEE Trans. Commun., vol. 59, no. 8, pp. 2152–2161, Aug. 2011.

[15] H. Wang, S. Yang, J. Lin, and Y. Zhong, “Single relay selection withfeedback and power allocation in multisource multidestination coopera-tive networks,” IEEE Signal Process. Lett., vol. 17, no. 12, pp. 997–1000,Dec. 2010.

[16] R. Youssef and A. Graell i Amat, “Distributed serially concatenated codesfor multi-source cooperative relay networks,” IEEE Trans. Wireless Com-mun., vol. 10, no. 1, pp. 253–263, Jan. 2011.

[17] H. Ding, J. Ge, D. B. da Costa, and Z. Jiang, “A new efficient lowcomplexity scheme for multi-source multi-relay cooperative networks,”IEEE Trans. Veh. Technol., vol. 60, no. 2, pp. 716–722, Feb. 2011.

[18] K. T. Phan, T. Le-Ngoc, S. A. Vorobyov, and C. Tellambura, “Powerallocation in wireless multi-user relay networks,” IEEE Trans. WirelessCommun., vol. 8, no. 5, pp. 2535–2545, May 2009.

[19] Y. R. Tsai and L. C. Lin, “Optimal power allocation for decode-and-forward cooperative diversity under an outage performance constraint,”IEEE Commun. Lett., vol. 14, no. 10, pp. 945–947, Oct. 2010.

[20] S. Talwar, Y. Jing, and S. Shahbazpanahi, “Joint relay selection andpower allocation for two-way relay networks,” IEEE Signal Process. Lett.,vol. 18, no. 2, pp. 91–94, Feb. 2011.

[21] W. Hachem, P. Bianchi, and P. Ciblat, “Outage probability-based powerand time optimization for relay networks,” IEEE Trans. Signal Process.,vol. 57, no. 2, pp. 764–782, Feb. 2009.

[22] K. Vardhe, D. Reynolds, and B. D. Woerner, “Joint power allocation andrelay selection for multiuser cooperative communication,” IEEE Trans.Wireless Commun., vol. 9, no. 4, pp. 1255–1260, Apr. 2009.

[23] F. S. Tabataba, P. Sadeghi, and M. R. Pakravan, “Outage probability andpower allocation of amplify and forward relaying with channel estimationerrors,” IEEE Trans. Wireless Commun., vol. 10, no. 41, pp. 124–134,Jan. 2011.

[24] S. Ren and M. V. D. Schaar, “Distributed power allocation in multi-usermulti-channel cellular relay networks,” IEEE Trans. Wireless Commun.,vol. 9, no. 6, pp. 1952–1964, Jun. 2010.

[25] T. Liu, L. Song, B. Jiao, and Y. Zhao, “A threshold-based hybrid relayselection scheme,” in Proc. IEEE WCNCW, Sydney, Australia, Apr. 2010,pp. 1–5.

[26] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple cooperativediversity method based on network path selection,” IEEE J. Sel. AreasCommun., vol. 24, no. 3, pp. 659–672, Mar. 2006.

[27] R. H. Gohary and T. N. Davidson, “On rate-optimal MIMO signaling withmean and covariance feedback,” IEEE Trans. Wireless Commun., vol. 8,no. 2, pp. 912–921, Feb. 2009.

[28] I. Krikidis, J. S. Thompson, and S. Mclaughlin, “Relay selection forsecure cooperative networks with jamming,” IEEE Trans. WirelessCommun., vol. 8, no. 10, pp. 5003–5011, Oct. 2009.



Hailin Xiao received the B.S. degree from WuhanUniversity, Wuhan, China, in 1998; the M.S. degreefrom Guangxi Normal University, Guilin, China, in2004; and the Ph.D. degree from the Universityof Electronic Science and Technology of China,Chengdu, China, in 2007.

He is currently a Professor with the School ofInformation and Communications, Guilin Universityof Electronic Technology, Guilin. He was a ResearchFellow with the Joint Research Institute for Signaland Image Processing, School of Engineering and

Physical Sciences, Heriot-Watt University, Edinburgh, U.K., from January 2011to February 2012. His research interests include multiple-input–multiple-outputwireless communications, cooperative communications, and smart antennatechniques.

Shan Ouyang received the B.S. degree in electronicengineering from Guilin University of ElectronicTechnology (GUET), Guilin, China, in 1986 and theM.S. and Ph.D. degrees in electronic engineeringfrom Xidian University, Xi’an, China, in 1992 and2000, respectively.

He is currently a Professor with the Schoolof Information and Communications, GUET. FromJune 2001 to May 2002, he was a Research Asso-ciate with the Department of Electronic Engineer-ing, The Chinese University of Hong Kong, Shatin,

Hong Kong. From January 2003 to January 2004, he was a Research Fellowwith the Department of Electronic Engineering, University of California,Riverside, CA, USA. His research interests are mainly in the areas of signalprocessing for communications and radar, adaptive filtering, and neural networklearning theory and applications.

Dr. Ouyang received the Outstanding Youth Award of the Ministry ofElectronic Industry and Guangxi Province Outstanding Teacher Award, China,in 1995 and 1997, respectively. He received the National Excellent DoctoralDissertation of China in 2002.

power allocation for a hybrid decode–amplify–forward cooperative communication system with two...

Documents