Energy aware cooperation strategy with uncoordinated group relays for delay-sensitive services

2104 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 5, JUNE 2014

Energy-Aware Cooperation Strategy WithUncoordinated Group Relays for

Delay-Sensitive ServicesA-Long Jin, Wei Song, Member, IEEE, Peijian Ju, and Dizhi Zhou

Abstract—Due to channel fading and user mobility in wirelessnetworks, quality-of-service (QoS) provisioning for multimediaservices requires great effort. It is even more challenging to sup-port the fast-growing multimedia services in a green manner. Asa promising technique, cooperative communications make use ofthe broadcasting nature of the wireless medium to facilitate datatransmission, and it can achieve energy saving. To support thedelay-sensitive multimedia services in an energy-efficient man-ner, we consider a new framework in this paper where multiplesource–destination pairs share a group of relays with an energyconstraint. We also propose an effective uncoordinated coopera-tion strategy, which is based on the backoff timer. The theoreticalperformance bounds of the proposed strategy are derived withrespect to the collision probability and the transmission successprobability. As shown in the numerical and simulation results, theproposed strategy outperforms a probability-based uncoordinatedstrategy in terms of average packet delay, delay outage probability,and energy consumption. Further, we investigate the scalabilityof our proposed strategy and find that it can be deployed in alarge-scale network.

Index Terms—Cooperative wireless networks, delay-sensitiveservices, energy efficiency, performance analysis, quality of service(QoS), scalability, uncoordinated cooperation strategy.

I. INTRODUCTION

W ITH rising energy costs and rigid environmentalstandards, green communications have attracted con-

siderable research attention in recent years, particularly for thefast-growing multimedia services in wireless networks [1], [2],since mobile devices are usually energy constrained. Due to thechallenging issues imposed in wireless networks [3], such aschannel fading and user mobility, QoS provisioning for delay-sensitive multimedia services is much more difficult than it isin wired networks. To deal with these challenges, attractivetechniques, such as multiple-input–multiple-output (MIMO)[4], [5] systems and cooperative communications [6]–[8], havebeen developed by exploiting spatial diversity [9]. Nonetheless,due to the size, cost, and energy limitations of mobile devices, itcan be infeasible to deploy multiple antennas in some wirelessterminals.

Manuscript received August 16, 2013; revised January 19, 2014; acceptedFebruary 27, 2014. Date of publication March 11, 2014; date of current versionJune 12, 2014. The review of this paper was coordinated by the Guest Editorsof the Special Section on Green Mobile Multimedia Communications.

The authors are with the Faculty of Computer Science, University ofNew Brunswick, Fredericton NB E3B 5A3, Canada (e-mail: [email protected];[email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2014.2310708

Fig. 1. Widely studied network model for cooperative communications.

To meet the ever increasing demands for multimedia servicesin future wireless networks, user cooperation [10] is studiedas a promising low-cost and energy-efficient technique forproviding spatial diversity. Taking advantage of the inherentbroadcasting nature of the wireless medium, the nodes withgood channel conditions can forward the overheard data tofacilitate the transmission of one source–destination (S–D)pair, which includes a single source (S) and a single des-tination (D). As shown in Fig. 1, the relay(s) that correctlyoverhear the packet from S can forward the data to D. Differentrelaying strategies can be used by the relays, such as amplify-and-forward, decode-and-forward (DF), and coded cooperation[6], [7] schemes. Based on this model, the number of relaysthat participate in each cooperation depends on the channelconditions and the cooperation strategy. It is often assumed thata collision occurs when two or more relays happen to transmitthe packet at the same time. Hence, the cooperation gain [11],[12] can vary considerably with the relay selection strategyand the medium access control protocol. It is vital to designan effective and efficient cooperation strategy to identify andcoordinate the optimal cooperating nodes.

In the centralized solutions such as [13] and [14], a cen-tral controller (e.g., the source node) needs to acquire theknowledge of the potential relays via additional handshakingmessages and then chooses the optimal relay. The messageexchange may induce an unacceptable delay for multimediaservices and high energy consumption. In contrast, a distributedsolution usually does not require such a priori information andcarries out relay selection in an uncoordinated fashion. Forexample, the relays that correctly receive the data from thesource can contend to forward the packet to the destination.

For the probability-based uncoordinated cooperation strate-gies [15]–[17], each relay that successfully overhears the dataindependently determines a forwarding probability. Althoughsuch strategies involve little signaling overhead, the collisionprobability can be potentially high when the number of avail-able relays is large. As a consequence, retransmissions will

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incur high energy consumption and long delay. Hence, suchcooperation strategies may not be able to accommodate greenmultimedia services. There is another class of uncoordinatedstrategies that make use of the relay’s local information to tune abackoff timer [18], [19]. A relay of higher transmission capabil-ity is prioritized with shorter backoff time. Such backoff-baseduncoordinated strategies can greatly reduce collisions and offera good match in support of green multimedia communications.

By extending the simple cooperation scenario in Fig. 1, weconsider a new framework where multiple S–D pairs share agroup of relays with an energy constraint. To satisfy the QoSrequirements of multimedia services in a green manner, we pro-pose an energy-aware uncoordinated cooperation strategy basedon the backoff timer. Moreover, its performance is evaluated an-alytically with respect to the theoretical bounds of the collisionprobability and the transmission success probability. Extensivesimulations are conducted to compare the performance of dif-ferent uncoordinated strategies and the analytical bounds. Thenumerical and simulation results demonstrate that our proposedstrategy is preferable for delay-sensitive multimedia servicesand achieves significant energy saving.

The remainder of this paper is structured as follows. Therelated work is reviewed in Section II. Section III gives thesystem model and the problem formulation. In Section IV, wepropose a novel uncoordinated cooperation strategy and thenanalyze its performance bounds in Section V. Numerical andsimulation results are presented in Section VI, which validatesthe accuracy of the analysis and demonstrates the performanceimprovement with the proposed strategy. Section VII concludesthis paper.

II. RELATED WORK

In the literature, many studies on cooperative communica-tions focus on the network model shown in Fig. 1, where agroup of relays can overhear the transmission from S, andone or more relays can help forward the overheard data toD. The selection and coordination of the relays are essentialto the achievable performance. These centralized approachesusually require a global knowledge of the relays, and it isoften infeasible to acquire such information in an accurate andtimely manner. Hence, there has been substantial research ondistributed cooperation strategies to effectively identify andorganize the optimal relay(s).

For the probability-based strategies in [15] and [16], eachpotential relay independently decides a forwarding probabil-ity by considering a variety of factors, such as the distance,direction, local SNR [15], or the statistical information of thelocal environment [16]. As a collision occurs when more thanone relay happens to forward the overheard data at the sametime, probabilistic cooperation strategies need to minimize thecollision probability and maximize the transmission successprobability. However, when the number of relays builds up,determining the optimal forwarding probability for each relaybecomes a challenge. If the forwarding probability is under-estimated, the transmission success probability can be lowsince the relays are overconservative. On the other hand, if theforwarding probability is overvalued, the transmission successprobability can be low as well because of high collisions. As

a result, the transmission success probability is usually upperbounded at a low level. Frequent retransmissions not onlyresult in high energy consumption but also fail to guarantee thestringent QoS requirements of the delay-sensitive multimediaservices.

From this point of view, another class of distributed co-operation strategies based on the backoff timer seems morepromising because of its low collision probability and hightransmission success probability. In [18], a cross-layer dis-tributed strategy is proposed by extending the conventionalready-to-send/clear-to-send handshaking with a ready-to-helpmessage from the optimal relay. The relay selection is basedon the composite cooperative transmission rate (CCTR), whichinvolves the broadcast rate from the source and the data ratefrom the relay to the destination. To reduce collisions in relay-ing, the contention process is divided into intergroup contentionand intragroup contention. The relays are grouped according toCCTR and send out indication signals after different backofftime. The optimal relay of the highest CCTR waits for theshortest time and wins the contention. In [19], Bletsas et al.propose a simple cooperative diversity method based on thelocal measurements of the instantaneous conditions of thesource-to-relay and relay-to-destination channels. Two policiesare proposed to map the estimated channel conditions into abackoff timer value. The theoretical analysis of the collisionprobability also demonstrates the advantage of the two backoffpolicies.

Nevertheless, many existing cooperation strategies neglectthe energy consumption of relays, which may lead to unaccept-able performance in the energy-constrained scenario, particu-larly for the QoS-demanding multimedia services. Moreover,many studies focus on a single S–D pair served by a numberof dedicated relays. It becomes more complicated to considermultiple S–D pairs that share a group of relays, which is a morerealistic scenario in practice. The energy involved and the newcooperation scenario pose new challenges in the cooperationstrategy design. In addition, the scalability of the cooperationstrategies is another key issue that requires further investigation.

III. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

Consider a wireless network with M S–D pairs and Krelay nodes, as shown in Fig. 2. We assume that the relays areuniformly distributed in a given region and the relay distributionis time stationary. This assumption is generally valid for avariety of scenarios, e.g., under random direction mobility [20],[21]. The sources refer to the nodes that generate data traffic,whereas the destinations refer to the nodes that receive datatraffic. Relay nodes have no intrinsic traffic demands. Sincethe relays are shared by multiple S–D pairs, we considerthat the relays are energy constrained. When a relay runs outof energy, it is not eligible for future relaying. The sourcescan communicate with their destinations only through theseshared relays using a two-hop DF [6] protocol; other coop-erative communication protocols can be also considered in asimilar way.


Fig. 2. System model for cooperative transmission.

We assume that each node knows its own location, which canbe obtained either from a positioning technique based on signalstrength, time-of-arrival, or angle-of-arrival measurements withnearby nodes [22], [23], or through a GPS receiver, whichis becoming increasingly ubiquitous in mobile devices. Fur-ther, the relay nodes can obtain the locations of the sourcesand destinations from the piggybacked information within theoverheard packets. It should be noted that the sources do nothave knowledge of the locations of the relays, and one relaydoes not have the location information of the other relayseither. Moreover, we assume that the locations of all the nodesin the network do not change significantly during the shortcooperative transmission period, which is a typical assumptionthat generally holds.

For the data transmission between a transmitter located at xand a receiver located at y, the SNR of the received signal canbe written as

γxy =P0

N0hxygxy (1)

where P0 is the transmit power, N0 is the power of additivewhite Gaussian noise, and hxy denotes the small-scale channelfading that is exponentially distributed with unit mean. Thepath-loss effect is captured by gxy = ‖x− y‖−α, where ‖x−y‖ is the Euclidean distance, and α is the path-loss exponent.We assume that the receiver is able to decode correctly thereceived signal only when the instantaneous SNR is no less thana threshold T0 [15]. Therefore, the probability that a packet issuccessfully received is given by

Pxy = Pr{γxy ≥ T0} = exp

(− T0

P0/N0‖x− y‖α

). (2)

Since the location information of the sources and destinationsis available to the relays, the distances between them can becalculated. Thus, we can estimate the transmission successprobabilities from the M sources to the relay Ri by

PS,Ri= [PS1Ri

, PS2Ri, . . . , PSMRi

] , i = 1, 2, . . . ,K.

Similarly, the transmission success probabilities from the relayRi to the M destinations are given by

PRi,D = [PRiD1, PRiD2

, . . . , PRiDM] , i = 1, 2, . . . ,K.

B. Problem Formulation

To achieve a high transmission success probability, a cen-tralized relay selection protocol generally identifies the bestrelay(s) by exploiting the global view of the network. How-ever, additional overhead is usually incurred to exchange thechannel state information, which results in a large delay. Onthe other hand, distributed solutions often require an effectiveapproach to mitigating collisions among multiple potential re-lays. The probability-based uncoordinated strategies use a for-warding probability that is independently determined for eachrelay. Nonetheless, when the network scales up, it becomesmore difficult to figure out the optimal forwarding probability.Unfortunately, the transmission success probability of theseprobability-based strategies is upper bounded by 1/e ≈ 0.368[16], [24] due to high collisions, which also lead to a largedelay. In contrast, the backoff-based distributed strategies canhandle collisions more effectively and present better perfor-mance in terms of the transmission success probability anddelay.

In this paper, we propose a novel backoff-based uncoordi-nated cooperation strategy, in which each potential relay setsa backoff timer based on a variety of factors. Consideringthe group cooperation model in Section III-A, we need toeffectively address the energy constraint of the relays, whichare shared by multiple S–D pairs. The proposed cooperationstrategy should not only provide QoS guarantee to the delay-sensitive multimedia services but also perform well in a large-scale network. It is known that the real-time multimediaservices are sensitive to delay and delay jitter. In view ofthe time-varying nature of wireless networks, we considera statistical QoS guarantee for the delay. That is, the delayoutage probability defined in (3) is ensured bounded within anacceptable range, i.e.,

Pout = Pr{D ≥ Dmax} < ε (3)

where D is the packet delay, Dmax is the acceptable upperbound, and ε is a small probability that is allowed for QoSviolation.

IV. ENERGY-AWARE COOPERATION STRATEGY

A. Cooperation Criteria

For a backoff-based cooperation strategy, the determinationof the backoff timer is critical to reduce collisions because acollision may occur when the backoff timers of the first two ormore relays expire within an indistinguishable small interval.To improve the achievable performance, the backoff timer isoften based on the cooperation capability of the relay. Hence,we need to properly choose the metrics that characterize thecooperation capability, so that the backoff timers of the groupof relays can be appropriately scattered to decrease the collisionprobability.

First, we consider the distance between a relay and a des-tination, which can be estimated from the location informa-tion without incurring extra cost. This distance can capturethe transmission success probability of the relay-to-destination


Fig. 3. Effect of the energy constraint of the relays to relay selection. The solidlines indicate the cooperative transmissions without considering the energystatus, and the dashed lines indicate the cooperative transmissions with theenergy status taken into account.

channel according to (2). This is because we are interested inthe potential relays that have correctly overheard the packetfrom the source and thus only focus on the relay-to-destinationchannel condition. Denoting the distance between relay Ri anddestination Dj by dij , we define the cooperation capability ofRi for Dj with respect to the distance as

W dij =

{1 −

(dij

L

)2

, if dij ≤ L

0, if dij > L(4)

where L is the largest distance to the destination for a node tobe considered a potential relay. As such, a relay with a smallerdistance to the destination is characterized with a greater co-operation capability because of a higher transmission successprobability over the relay-to-destination channel.

Second, the energy status of the relay is also included inthe estimation of the cooperation capability since the sharedrelays are energy constrained. The example in Fig. 3 showsthe importance of incorporating the energy status into thecharacterization of the cooperation capability. As shown, relayR2 is the best relay for both S1–D1 and S2–D2 pairs if only thedistance to the destination is concerned. Consequently, R2 willrun out of energy quickly. The S1–D1 and S2–D2 pairs willneed to switch to relay R1. The performance of the S1–D1 pairwill remain almost the same, whereas the S2–D2 pair will sufferfrom performance degradation since R1 is far from S2 and D2.On the other hand, if both the distance and the energy statusare taken into account, R1 and R2 should serve S1–D1 andS2–D2, respectively. Thus, the relaying capacities are utilizedin a more balanced manner. Therefore, we further consider theenergy status of Ri to characterize its cooperation capability by

W ei = Ei/Ec (5)

where Ei is the energy level of Ri with an energy upper limitof Ec. Here, we assume that all the relays have the same energyupper limit and their energy levels are uniformly distributed.Therefore, W e follows a uniform distribution between 0 and 1,which is denoted U(0, 1). As shown, a relay of a higher energylevel thus has a greater cooperation capability.

Based on the two metrics in (4) and (5), the overall coopera-tion capability of relay Ri for destination Dj is defined as

Wij = θ ·W ei + (1 − θ) ·W d

ij (6)

TABLE IENERGY-AWARE COOPERATION STRATEGY

where θ ∈ [0, 1] is a weighting parameter to the tradeoff be-tween the importance of the energy status and that of thedistance metric. As shown, Wij ∈ [0, 1].

B. Distributed Cooperation Strategy

Table I shows the proposed energy-aware cooperation strat-egy in detail. Based on the cooperation capabilities of therelays, the optimal relay for the Sj–Dj pair is defined as

Ri = arg maxi∈{1,...,K}

{1Aj

(i) ·Wij

}where Aj is the set of relays that correctly overhear the datapacket from Sj , and

1Aj(i) =

{1, if Ri ∈ Aj

0, if Ri /∈ Aj .

To ensure that the optimal relay has the fastest access to thechannel, the relay Ri sets an initial backoff time inverselyproportional to its cooperation capability for the Sj–Dj pair as

Tij = 1 −Wij (7)

in which the maximum backoff time is taken to be one unit time.As such, the optimal relay of the highest cooperation capability


sets the smallest backoff time. If the first two or more relaystime out within an indistinguishable small interval c, a collisionhappens [19].

To account for the energy consumption of packet forwardingof Ri for any S–D pair, we update the cooperation capabilityof Ri for all S–D pairs as follows:

Wir = Wir − θ · η, r = 1, 2, . . . ,M (8)

where η is the update step length. This is to yield the forward-ing opportunities to other relays and thus balance the energyconsumption.

A problem occurs when a collision happens among therelays. If all the relays involved in the collision update their co-operation capabilities according to (8), a collision will happenagain in the succeeding transmission. Therefore, we need to pe-nalize these relays by updating their cooperation capabilities to

Wij = Wij − (1 − θ) ·W dij · η, i = c1, c2, . . . , cn (9)

where c1, c2, . . . , cn are the indexes of relays Rc1 , . . . , Rcn

that collide when forwarding the packet for the Sj–Dj pair.As a higher W d

ij implies a lower energy level when a collisionhappens, the corresponding relay is punished more to achievethe energy balance and to avoid further collisions.

V. PERFORMANCE ANALYSIS

To satisfy the delay requirements of multimedia services,minimizing the collision probability to maximize the trans-mission success probability is essential. Here, we analyze theperformance bounds of the proposed cooperation strategy interms of the collision probability and the transmission suc-cess probability. Here, we focus on one S–D pair since theachievable performance of all S–D pairs is the same, given thehomogeneous setting of S–D pairs in the system model.

A. Upper Bound of Collision Probability

Lemma 1: If the relays are uniformly distributed, the proba-bility density function (pdf) of their distance d to the destinationD within L is given by

f(d) =

{2dL2 , if d ≤ L0, otherwise.

(10)

Proof: Consider the polar coordinate system where D isthe origin and an arbitrary relay is located at (d, ϕ). The corre-sponding location of the relay in the Cartesian coordinate sys-tem is then (x, y), where x = d · cos(ϕ), and y = d · sin(ϕ).For the relays uniformly distributed within the circle of radiusL and centered at D, the joint pdf of their locations (x, y) isgiven by

fX,Y (x, y) =

{1

πL2 , if√

x2 + y2 ≤ L0, otherwise.

Since d =√x2 + y2, according to the Jacobian matrix, we can

obtain the pdf of d as shown in (10). �

Lemma 2: If the pdf of the distance of a relay to thedestination follows (10), the general cooperation capabilityconcerning the distance, i.e., W d defined in (4), follows auniform distribution between 0 and 1.

Proof: The cumulative distribution function (cdf) of W d

is given by

Pr{W d ≤ w} (4)= Pr

{1 − (d/L)2 ≤ w

}= 1 − Pr{d ≤ L

√1 − w}

Lemma 1= 1 −

L√1−w∫

0

f(x)dx

= 1 − d2

L2

∣∣∣∣L√1−w

0

= w.

Therefore, W d ∼ U(0, 1). �Theorem 1: Since W e ∼ U(0, 1) and W d ∼ U(0, 1), the

overall cooperation capability defined in (6) with θ ∈ (0, 0.2]concerning both the distance and the energy status follows adistribution with a pdf:

fW (w) =

⎧⎪⎪⎨⎪⎪⎩w

θ(1−θ) , if 0 ≤ w ≤ θ1

1−θ , if θ < w ≤ 1 − θ1−w

θ(1−θ) , if 1 − θ < w ≤ 10, otherwise.

(11)

Proof: Given two continuous random variables U and V ,if V = aU , the pdfs of U and V are related according to

fV (x) =

(1a

)fU

(xa

)where fU (·) and fV (·) are the pdfs of U and V , respectively.Since W e ∼ U(0, 1) and W d ∼ U(0, 1) (Lemma 2), we have

X = θ ·W e ∼ U(0, θ) Y = (1 − θ) ·W d ∼ U(0, 1 − θ).

Then, for W = θ ·W e + (1 − θ) ·W d = X + Y , we have

fW (w) =

∞∫−∞

fX(w − y)fY (y) dy

=1

1 − θ

1−θ∫0

fX(w − y) dy.

Only when 0≤w−y≤θ, i.e., w−θ≤y≤w, fX(w−y)=1/θ,and the given integral is not zero. Therefore, we have

fW (w) =1

1 − θ

w∫0

1θdy =

w

θ(1 − θ), if 0 ≤ w ≤ θ

fW (w) =1

1 − θ

w∫w−θ

1θdy =

11 − θ

, if θ < w ≤ 1 − θ

fW (w) =1

1 − θ

1−θ∫w−θ

1θdy =

1 − w

θ(1 − θ), if 1 − θ < w ≤ 1

which conclude the proof. �


According to Theorem 1, for θ ∈ (0, 0.2], it can be easilyshown that the backoff time as defined by (7) follows a dis-tribution with a pdf, given by

fT (t) =

⎧⎪⎪⎨⎪⎪⎩t

θ(1−θ) , if 0 ≤ t ≤ θ1

1−θ , if θ < t ≤ 1 − θ1−t

θ(1−θ) , if 1 − θ < t ≤ 10, otherwise.

(12)

Assume that N relays (Ri1 , . . . , RiN ) correctly overhear thetransmitted packet from one particular source. Let T1 < T2 <· · · < TN denote the order statistics of the backoff time of theN relays. According to [19], the collision probability Pc isgiven by

Pc = Pr{T2 < T1 + c} = 1 − Ic (13)

Ic =N(N − 1)

1∫c

fT (t) [1 − FT (t)]N−2 FT (t− c) dt (14)

where fT (t) is the pdf of the backoff time, and FT (t) isthe corresponding cdf. Here, c is an indistinguishable smallinterval, and a collision happens when the backoff timers of thefirst two or more relays time out within c. As one example, thedistributed coordination function of IEEE 802.11 can choosea maximum backoff time of 1024 time slots [25]. Then, theinterval c can be considered one time slot. Provided that themaximum backoff time is taken to be one unit time, the intervalc can be on the order of 10−3.

When θ = 0, we have W = W d according to (6). Based onLemma 2, this means that the cooperation capability W followsa uniform distribution between 0 and 1. Thus, the backoff timedefined in (7) is also uniformly distributed with fT (t) = 1 andFT (t) = t for 0 ≤ t ≤ 1. From (14), we can easily obtain

Ic = (1 − c)N . (15)

For 0 < θ ≤ c, we have

Ic =N(N − 1)(1 − θ)N

{(1 − 3

2θ

)N−1 (1 − θ − c

N − 1− 1 − 3θ/2

N

)

+

(θ

2

)N−1 (2c− c2/θ

2N − 2− 2c

2N − 1

)}. (16)

For θ > c, because a closed-form Ic is not tractable, we derivethe following lower bound in Appendix A:

Ic <N(N − 1)(1 − θ)N

{(1 − 3

2θ

)N−2

(θ − c)3(

18θ

+c

24θ2

)

+

(1 − 3

2θ

)N−1 (1 − θ − c

N − 1− 1 − 3θ/2

N

)

+

(θ

2

)N−1 (2c− c2/θ

2N − 2− 2c

2N − 1

)}. (17)

Defining the right-hand side terms in (15)–(17) as ILc , we haveIc ≥ ILc and

Pc = 1 − Ic ≤ 1 − ILcΔ= PU

c (18)

where PUc denotes an upper bound of the collision probability.

B. Lower Bound of Transmission Success Probability

When the traffic load is high, most of the relays will runout of energy quickly, and the distribution of their cooperationcapabilities will no longer follow (11). Thus, it is hard totheoretically derive a lower or upper bound for the transmissionsuccess probability. Therefore, we focus on a normal traffic loadwhen analyzing the lower bound of the transmission successprobability here and its upper bound in Section V-C. In thiscircumstance, the energy constraint can be relaxed by settingθ = 0. Then, the cooperation capability is only determined bythe distance metric and follows a uniform distribution between0 and 1.

A relay Ri participates in the cooperative relaying for theSj–Dj pair only if Ri correctly receives the packet from Sj

and its cooperation capability Wij is the maximum amongthe N relays (Ri, Ri1 , . . . , RiN−1

) that overhear this packetsuccessfully. With the largest Wij , Ri sets the shortest backofftime and becomes the first to forward the packet. We have thefollowing occurrence probability:

Pij =PSjRi·N−1∏r=1

Pr{Wij > Wirj}

=PSjRi· (Wij)

N−1. (19)

Moreover, the probability that at least one relay successfullyoverhears and forwards the packet for Sj is given by

Qj = 1 −K∏r=1

(1 − PSjRr). (20)

Hence, the probability that Ri transmits the packet for Sj in thelong term is given by

Pij = Qj ·Pij∑Kr=1 Prj

. (21)

Finally, we have the transmission success probability for theSj–Dj pair, i.e.,

P (j)suc =

K∑r=1

Prj · PRrDj· (1 − Pc)

≥(1 − PU

c

)·

K∑r=1

Prj · PRrDj

Δ= PL

suc (22)

where PLsuc denotes the lower bound of the transmission success

probability.


C. Upper Bound of Transmission Success Probability

In Section V-B, the energy constraint is relaxed to derive thelower bound of the transmission success probability. To obtainthe upper bound, we assume no collisions among the relays indata forwarding. The upper bound of the transmission successprobability for an arbitrary Sj-Dj pair is then given by

PUsuc = PSjR(1)

· PR(1)Dj+(1 − PSjR(1)

)· PSjR(2)

· PR(2)Dj

+ · · ·+K−1∏r=1

(1 − PSjR(r)

)· PSjR(K)

· PR(K)Dj(23)

where PR(1)Dj> PR(2)Dj

> · · · > PR(K)Dj. The first term in

(23) represents the case that the best relay R(1) has correctlyreceived the packet from Sj with probability PSjR(1)

, and itsforwarding over the relay-to-destination channel to Dj suc-ceeds with a probability PR(1)Dj

. The second term in (23)indicates that the best relay R(1) fails to receive the packet fromSj with a probability (1 − PSjR(1)

), whereas the second bestrelay R(2) successfully receives and forwards the packet to Dj

with a probability PSjR(2)· PR(2)Dj

. The other terms in (23)can be interpreted in a similar way.

In addition, a relaxed upper bound of the transmission suc-cess probability can be obtained as

P̃Usuc = Qj · max

r∈{1,2,...,K}{PRrDj

} > PUsuc (24)

where Qj is given by (20). Here, P̃Usuc is derived by considering

the maximum success probability over the relay-to-destinationchannel when at least one relay forwards the packet.

VI. NUMERICAL EVALUATION

Here, numerical and simulation results are presented todemonstrate the effectiveness of our proposed cooperationstrategy and the analytical bounds. For comparison purposes,we consider an uncoordinated probability-based algorithm, inwhich each potential relay Ri chooses its forwarding probabil-ity according to

Pτi =

[1 +

P0

N0T0L2· ln (PRiD)

]N−1

(25)

where N is the number of relays that correctly overhear thepacket from the source. Here, Pτi is the probability that Ri

is the relay with the maximum transmission success proba-bility over the relay-to-destination channel (with α = 2). Thederivation of (25) is given in Appendix B. In the simulation, wefurther minimize collisions by normalizing Pτi to

P (i)τ =

Pτi∑Nr=1 Pτr

. (26)

In practice, it is not appropriate for a distributed approach toallow a relay to obtain the forwarding probabilities of otherrelays. Thus, the real performance of the probability-basedalgorithm can be worse.

In the following experiments, we assume that the nodes areuniformly distributed in a 40 m × 200 m area, as shown by the

Fig. 4. Nodes topology for analysis and simulation.

TABLE IISYSTEM PARAMETERS

example in Fig. 4. The maximum distance of potential relaysto a destination is L = 55 m since the transmission successprobability over the relay-to-destination channel is lower than0.25 when L > 55 m. Assume that all the relays are fullycharged at the beginning, and each relay can transmit up to 104

packets. More system parameters are given in Table II.

A. Collision Probability

Fig. 5 shows the analytical bounds and simulation results ofthe collision probability. As shown, when the collision intervalc increases, the collision probability increases accordingly.Further, when the number of relays K increases, the collisionprobability increases as well. We also find that the analyticalupper bound of the collision probability works well for theproposed strategy. Moreover, it is observed that the collisionprobability of the proposed strategy is smaller than 10%, evenwhen the collision interval and the number of relays are large.In contrast, the probability-based algorithm has a collisionprobability greater than 18%, which is much higher than thatof the proposed strategy. It should be noted that the collisionprobability of the probability-based algorithm has been mini-mized by normalizing the forwarding probability of each relay,which makes the approach not purely distributed.


Fig. 5. Collision probability Pc versus total number of relay nodes.

Fig. 6. Transmission success probability versus total number of relay nodes.

B. Transmission Success Probability

Fig. 6 compares the transmission success probability ofdifferent strategies with the analytical bounds. We can seethat the transmission success probability of the probability-based algorithm is bounded by 1/e ≈ 0.368, which verifiesthe conclusions in [16] and [24]. In contrast, our proposedbackoff-based strategy can easily achieve a transmission suc-cess probability higher than 0.6 because of the reduced collisionprobability. Moreover, we find that the upper bound and thelower bound of the transmission success probability both workwell. The proposed strategy approaches the upper bound in anormal traffic load.

Furthermore, it is shown in Fig. 6 that the transmissionsuccess probability of the proposed strategy increases with agreater number of relays, whereas that of the probability-basedalgorithm remains almost the same. This seems counterintuitivesince Fig. 5 shows the collision probability of both algorithmsincreases with the number of relays. This is because the op-portunity of finding a good relay increases with more potentialrelays. Thus, packet loss caused by poor channel conditions canbe reduced.

Fig. 7. Average packet delay D versus the packet transmission time.

Fig. 8. Delay outage probability Pout versus packet transmission time.

C. Average Delay and Delay Outage Probability

Fig. 7 shows the average packet transfer delay of the twoalgorithms against the packet transmission time. The packettransfer delay represents the time duration from a packet gener-ation to successful transmission, whereas the packet transmis-sion time is given by the packet length over the transmissionrate. Here, the maximum backoff time is taken to be one unittime. As shown, the average packet delay of the proposedalgorithm is much smaller than that of the probability-basedalgorithm, although the proposed algorithm requires extra back-off time. This is because the collision probability of the pro-posed backoff-based algorithm is much lower than that of theprobability-based algorithm, as shown in Fig. 5. As a result,the transmission success probability is improved significantly,as shown in Fig. 6. Thus, the average packet transfer delayis reduced accordingly. In addition, we find that the averagepacket delay of the backoff-based algorithm increases slowerthan that of the probability-based algorithm, which implies thatour proposed algorithm can achieve more gain for a largerpacket length.

Fig. 8 compares the delay outage probability (in log scale)of the two algorithms with respect to the packet transmission


Fig. 9. Average energy cost for a packet versus total number of relay nodes.

time. It can be seen that the backoff-based algorithm has adelay outage probability smaller than 0.01. On the other hand,the delay outage probability of the probability-based algorithmincreases faster from 0.12 to 0.21, when the packet transmissiontime increases from 1 to 1.5. Therefore, our proposed algorithmis preferable for the real-time delay-sensitive services.

D. Energy Saving and Energy Balance

To further investigate the energy consumption of the twoalgorithms, Fig. 9 shows the average energy cost of the relaysfor a packet with respect to the total number of relays K.Here, the unit of energy cost is the energy consumption of onetransmission attempt for a packet with a transmission time ofone time unit. As shown in Fig. 9, our proposed backoff-basedalgorithm can save around 50% of energy on average, comparedwith the probability-based algorithm. This energy saving is dueto the low collision probability and high transmission successprobability of the backoff-based algorithm.

In Fig. 10, we show the variations of the transmission successprobability with the traffic demand of an S–D pair. Here, thetraffic demand is the number of packets transmitted for an S–Dpair, excluding the retransmitted packets. It is assumed in thesimulation that all M S–D pairs have the same traffic demand.As shown, when the traffic demand is low, the highest transmis-sion success probability is achieved at θ = 0. Given a low trafficdemand, no relay runs out of energy to satisfy the demand, andthe relays with the best channel conditions are always availableto forward the packets. Hence, the energy constraint does nottake effect, and it is not necessary to consider energy balance inrelay selection.

On the other hand, the situation becomes different with ahigh traffic demand. As shown in Fig. 10, when the trafficdemand is greater than 1.8 × 104, the transmission successprobability with θ = 0 is no longer higher than that of θ = 0.1.This is because the energy constraint is not addressed withθ = 0, and consequently, the best relay candidates may run outof energy very quickly. In contrast, we can take advantage ofenergy balance by setting θ = 0.1 for relay selection and thusextend the survival time of the relays. As a result, the averagetransmission success probability can be improved. Moreover, itis observed in Fig. 10 that the transmission success probability

Fig. 10. Transmission success probability Psuc versus traffic demand.

with θ = 0.2 is always worse than that of θ = 0 and θ = 0.1.This implies that the weight θ = 0.2 overvalues the importanceof energy status but underestimates that of the relay’s distanceto the destination. Consequently, the relay selection becomeskind of “blind” to the transmission success probability over therelay-to-destination channel. Therefore, it is usually assumedthat θ ≤ 0.2.

E. Scalability

To study the scalability of the proposed algorithm, we varythe total number of relays K and the total number of S–Dpairs M in the simulation. Given a fixed number of S–Dpairs, M = 5, Fig. 11(a) shows that the transmission successprobability first increases with the number of relays and thendecreases when K ≥ 50. On one hand, more good relaysbecome available for an S–D pair when the total number ofrelays is larger. On the other hand, the collision probability alsoincreases correspondingly. At the beginning, the advantage ofhaving more good relays dominates the side effect of collisions.On the contrary, when the number of relays further grows, thecollision probability becomes very high, and the transmissionsuccess probability decreases. For example, the collision prob-ability with K = 300 is 20.86%, which is much higher than10.34% with K = 100. For the relaying area considered in thesimulation, K = 500 is an extremely high and rare density inpractice. Even so, we still find that the transmission successprobability is above 60% and much larger than that of theprobability-based algorithm.

Fig. 11(b) shows the transmission success probability versusthe number of S–D pairs M given a fixed number of relaysK = 100. The two scenarios in comparison have differenttraffic loads, which are the total number of packets transmittedfor each S–D pair, including the retransmitted packets. It isobserved that the transmission success probability is above 50%with a reasonable number of S–D pairs (M ≤ 30) when thetraffic load is normal. This verifies that our proposed algorithmcan be deployed in a large-scale network. Moreover, it is seenthat the transmission success probability decreases with a largernumber of S–D pairs. When more S–D pairs share a groupof common relays, the relays with better channel conditionsto the destinations will run out of energy quickly. As a result,


Fig. 11. Scalability of the proposed cooperation strategy. (a) Psuc versus K.(b) Psuc versus M .

the transmission success probability goes down but decreasesslower with a lower traffic load. Hence, to guarantee the QoSrequirements, the amount of traffic that enters the networkshould be regulated by controlling the number of S–D pairsand/or their admissible traffic loads. In addition, we find thatthe Jain’s fairness index of the transmission success probabilityamong the M S–D pairs is almost 1, which implies that thegroup of relays are evenly shared by all S–D pairs with theproposed backoff-based algorithm.

VII. CONCLUSION

In this paper, we study the uncoordinated cooperative com-munications between multiple S–D pairs that share a group ofenergy-constrained relays. A novel cooperation strategy is pro-posed based on backoff timers. It makes use of the cooperativecapability, which is characterized by the distance informationand the energy status of the relay. Thus, the relay of a highercooperative capability ends up with a shorter backoff time. Thebest relay times out first and wins the contention. However, acollision still happens if the backoff timers of the first two ormore relays expire within an indistinguishable time interval.Hence, we also derive the theoretical performance bounds forthe proposed strategy with respect to the collision probabilityand the transmission success probability.

As shown in the numerical results, our proposed strategy canachieve a much lower collision probability and, thus, a highertransmission success probability, compared with a probability-based reference strategy. We find that the transmission successprobability can approach the upper bound in a normal trafficload, which verifies that our algorithm can effectively andefficiently identify the optimal relay in an uncoordinatedmanner. Moreover, our algorithm also outperforms theprobability-based strategy in terms of average packet delay,delay outage probability, as well as the energy consumption.By adjusting the weighting parameter θ, we can achieve goodperformance in the high-traffic-load condition through energybalance. Therefore, it is safe to conclude that our proposedalgorithm can serve as an energy-efficient cooperation strategyfor delay-sensitive multimedia services, and it is a scalablesolution for a large-scale network.

APPENDIX APROOF OF (17)

According to (14), when θ > c, we have

Ic = N(N − 1)(Ic1 + Ic2 + Ic3) (27)

where Ic1 , Ic2 , and Ic3 are given by

Ic1 =

θ∫c

t

θ(1 − θ)

[1 − t2/2

θ(1 − θ)

]N−2(t− c)2/2θ(1 − θ)

dt (28)

Ic2 =

1−θ∫θ

11 − θ

[1 − t− θ/2

1 − θ

]N−2t− c− θ/2

1 − θdt (29)

Ic3 =

1∫1−θ

1 − t

θ(1 − θ)

[(1 − t)2

2θ(1 − θ)

]N−2 [1 − (1 − t+ c)2

2θ(1 − θ)

]dt.

(30)

As a closed-form expression is not tractable for Ic1 , we taket ≤ θ and have

Ic1 ≥θ∫

c

t

θ(1−θ)

[1− θ2/2

θ(1−θ)

]N−2(t−c)2/2θ(1−θ)

dt

=

(1

1−θ

)N (1− 3

2θ

)N−2

(θ−c)3(

18θ

+c

24θ2

). (31)

The closed-form expressions of Ic2 and Ic3 can be obtained as

Ic2 =

(1

1 − θ

)N{

1 − θ − c

N − 1

[(1 − 3

2θ

)N−1

−(θ

2

)N−1]

− 1N

[(1 − 3

2θ

)N

−(θ

2

)N]}

(32)

Ic3 =

(θ/2

1 − θ

)N (2θ

)×[

2(1 − θ)− c2/θ

2N − 2− 2c

2N − 1− θ

2N

]. (33)

The last three equations conclude the proof to (17).


APPENDIX BPROOF OF (25)

According to (2), we obtain the transmission success proba-bility over the relay-to-destination channel with α = 2 as

PRD = e−φd2

(34)

where φ = T0N0/P0. Given the pdf of d in (10), we derive thecdf of PRD by

Pr{PRD ≤ p}=Pr{e−φd2 ≤ p}=1 − Pr

{d ≤

√− ln p

φ

}

= 1 −

√− 1

φ lnp∫0

f(x) dx = 1 − d2

L2

∣∣∣∣√

− 1φ lnp

0

= 1 +P0

N0T0L2ln p.

Thus, it is easy to show that the probability that a relay has themaximum transmission success probability over the relay-to-destination channel among N candidates is given by (25).

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A-Long Jin received the B.Eng. degree fromNanjing University of Posts and Telecommunica-tions, Nanjing, China, in 2012. He is currently work-ing toward the M.S. degree with the University ofNew Brunswick, Fredericton, NB, Canada.

His main research interests include cooper-ative wireless networks, machine learning, andoptimization.

Wei Song (M’09) received the Ph.D. degree fromthe University of Waterloo, Waterloo, ON, Canada,in 2007.

Since July 2009, she has been an Assistant Profes-sor with the Faculty of Computer Science, Univer-sity of New Brunswick, Fredericton, NB, Canada.Her current research interests include the hetero-geneous interworking of wireless networks, co-operative wireless networks, mobile hotspots, andmultimedia quality-of-service provisioning.

Peijian Ju received the B.Eng. and M.Eng. degreesfrom Huazhong University of Science and Technol-ogy, Wuhan, China, in 2009 and 2011, respectively.He is currently working toward the Ph.D. degree withthe University of New Brunswick, Fredericton, NB,Canada.

His research interests include the physical layerand medium access control layer of cooperativewireless networks.

Dizhi Zhou received the M.S. degree from ChineseAcademy of Sciences, Beijing, China, in 2010. Heis currently working toward the Ph.D. degree withthe University of New Brunswick, Fredericton, NB,Canada.

His research interests include cooperative wire-less networks, multipath transmission, and networksimulation.

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Energy aware cooperation strategy with uncoordinated group relays for delay-sensitive services

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