A Cooperative Transmission Scheme for Improving the Secondary Access in Cognitive Radio Networks

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 11, NOVEMBER 2014 6219

A Cooperative Transmission Scheme for Improvingthe Secondary Access in Cognitive Radio Networks

Wael Jaafar, Student Member, IEEE, Wessam Ajib, Member, IEEE, and David Haccoun, Life Fellow, IEEE

Abstract—In this paper, we examine the problem of secondaryaccess blocking in cognitive radio networks when secondary trans-missions cause unacceptably high interference to primary trans-missions. In general, the access of secondary users (SUs) to alicensed spectrum band is only allowed when this access does notalter the performance of primary users that can be defined by theprimary QoS requirement. In this paper, we propose a cooperativescheme that allows SUs to increase their access to the spectrumband and access the spectrum even when the primary QoS isnot satisfied. Using relay selection and a proper power allocationmethod, we show that the secondary outage performance can besignificantly improved, whereas the primary outage performanceis either not altered or slightly improved. Moreover, closed-formexpressions of the primary and secondary outage probabilities arederived, and the achieved diversity order is calculated. Finally,analytical and simulation results illustrate the primary outageperformance and secondary outage performance of the proposedscheme and show its advantages compared with conventionalschemes.

Index Terms—Cognitive radio, relaying, decode-and-forward,relay selection, power allocation.

I. INTRODUCTION

COGNITIVE radio (CR) is a key technology for solvingthe spectrum under-utilization and spectrum congestion

issues [1]–[4]. By allowing unlicensed Secondary Users (SUs)to transmit on the licensed spectrum band of the PrimaryUsers (PUs) without disrupting the primary transmissions, thespectrum resources are better exploited. In underlay CognitiveRadio Networks (CRNs), the SUs may transmit at the sametime as the PUs as long as the induced interference is belowa predefined threshold (such as a Signal-to-Noise-Ratio-SNR-threshold, outage probability threshold, etc.) [4].

User cooperation has also been developed to provide spatialdiversity gain and reduce interference due to simultaneouscommunications [5]–[7]. In [6], several cooperative schemeshave been proposed such as fixed relaying, selection relayingand incremental relaying. These schemes provide an increaseddiversity gain at the expense of a reduced spectral efficiency.This shortcoming can be overcome by selecting only the “best”

Manuscript received November 8, 2013; revised April 19, 2014; acceptedJune 11, 2014. Date of publication June 20, 2014; date of current versionNovember 7, 2014. The associate editor coordinating the review of this paperand approving it for publication was H. Wymeersch.

W. Jaafar and D. Haccoun are with the Department of Electrical Engineering,École Polytechnique de Montréal, Montreal QC H3T 1J4, Canada (e-mail:[email protected]; [email protected]).

W. Ajib is with the Department of Computer Science, Université du Québecà Montréal, Montreal QC H2X 3YZ, Canada (e-mail: [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/TWC.2014.2332161

relay, among a set of relay nodes, to assist the transmission[8]. Hence, the cooperative scheme achieves full diversity whileavoiding complex synchronization among the relay nodes.

Integrating user cooperation to CRNs has recently attractedattention for enhancing the transmissions performances. Theauthors in [9] propose assisting the secondary transmissionsusing a group of co-located CR relay nodes. By “adequately”selecting the relay nodes, the maximal diversity gain can beachieved. In [10], a less-complex scheme has been proposedachieving the maximal diversity gain at high primary SNRand improving the secondary outage probability compared toconventional schemes. In [11], the authors show that by jointlyoptimizing spectrum sensing and the secondary access, the sec-ondary outage performance can be significantly improved. Thesame authors investigate an incremental cooperation schemefor secondary transmissions in [12] and derive closed-formexpressions of the secondary outage probability. Both schemesare then extended to multiple-relay CRNs and the relateddiversity-multiplexing tradeoff is obtained. The authors in [13]investigated the cooperative diversity gain in underlay CRNs interms of outage probability and diversity order. They showedthat diversity is lost for a fixed interference power constraintat the primary receiver. However, if the interference powerconstraint is proportional to the peak transmit power at thesecondary transmitters, then full diversity is achieved, whichis equal to the number of relay nodes +1 (by accounting thedirect transmission).

Other works propose cooperative schemes to assist the pri-mary transmissions, using either a cognitive relay node [14],[15] or the secondary transmitter [16]. They showed that cog-nitive relaying is efficient under certain network topologiesand nodes locations. It is to be noted that in this type ofnetworks, a limited information exchange between primary andsecondary systems is required in order to respect the primaryQoS constraint.

In [17]–[20], we have proposed cooperative schemes toassist either the primary transmission (as in [14]–[16]) or thesecondary one (as in [9]–[13]) or both simultaneously. In [17],the proposed scheme assists simultaneously PUs and SUswhenever the relay node is able to decode both primary andsecondary signals. Provided results show that the secondaryoutage performance improves at the expense of a higher relaytransmit power, while the primary QoS is maintained. Anextension to the multi-antenna relay with antenna selectionis studied in [18]. In [19], assisting the primary or secondarytransmission is activated using the incremental relaying tech-nique (acknowledgment-based cooperation as in [12]). Resultsshow that choosing first the best relay to assist the PUs before

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6220 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 11, NOVEMBER 2014

choosing the relay that would assist the SUs improves betterthe secondary outage performance while respecting a primaryoutage threshold. Moreover, by using an adequate powerallocation method, secondary access is allowed at low primarySNR. In [20], several relaying schemes are investigated whererelay nodes may help primary and/or secondary transmissionsin order to improve the secondary outage probability with re-spect to a primary outage threshold. Results provide a guidelineabout the impact of several parameters (such as relay selection,primary outage threshold, number of relays, distances betweennodes, etc. . .) on the secondary system’s outage performance.

In conventional CRNs, whenever the primary SNR is belowits cutoff value, the secondary transmissions are not allowed[10], [17], [20]. In [19], we proposed to circumvent this limi-tation by allowing the secondary user to transmit using a pre-determined minimal power value. Even though this techniqueimproves significantly the secondary outage probability at lowprimary SNR, it is complex to implement since such a pre-determined transmit power is difficult to determine as it de-pends on many factors such as the nodes’ locations and theavailability of the Channel State Information (CSI) at the trans-mitters. Moreover, it imposes the primary transmission to bealways processed over two time-slots rather than a single one,even when the quality of the primary direct channel is good.

Consequently, in this paper we propose a simple and efficientcooperative scheme for CRNs, where the “best” selected relaynode among a non co-located set of relays (unlike [10] whererelays are assumed to be co-located), assists the secondarytransmission when the primary SNR is above the cutoff value(as in [10], [17]), and assists the primary transmission whenit is below the cutoff value. We assume that the relays use theDecode-and-Forward (DF) cooperative technique [6]. Assistingthe primary transmission in our scheme is not aimed at improv-ing its performance but is rather used to provide more accessopportunities for secondary transmissions while realizing atworst, the same primary outage performance as it would be for anon-cooperative communication. This scenario holds assumingthat primary data is multimedia-like where the primary systemrequires a fixed data rate and a pre-defined outage probabilitythreshold [21]–[23].

The main contributions of this paper can be summarized asfollows:

• We propose a novel cooperation scheme for CRNs that canassist either the primary or secondary transmission, aimingat substantially increasing the secondary access to the li-censed spectrum band while preserving (or improving) theprimary outage performance. First, the proposed scheme issimilar to [14]–[20] by the fact that it assists at some pointthe primary transmission to guarantee more secondaryaccess opportunities. It also assists the secondary trans-missions similarly to some of the techniques presentedin [9]–[13]. However, since we choose a particular typeof primary communications, which works as multimedia-like transmissions with a fixed data-rate and an outageQoS requirement, it is more likely that the secondarytransmission would experience less primary interferencethan in the case of continuous primary transmissions [9]–[13]. Hence, at high primary SNR, the secondary outage

Fig. 1. Primary and secondary systems transmissions.

performance is expected to be better than in the case ofcontinuous primary transmissions. It is to be noted thatif the primary transmission were continuous, the onlyeffect would be a dramatically degraded secondary outageperformance at high primary SNR. This case has alreadybeen studied in part by Zou et al. in [10].

• We investigate the power allocation issue at the cognitiveradio transmitters (secondary transmitter and selected re-lay node) and we derive closed-form expressions of theprimary and secondary outage probabilities. The diversityorder analysis is then conducted for the proposed scheme.

• We compare the outage probability performances of theproposed scheme to that of conventional schemes andwe study the impact of several parameters on its outageperformances.

The rest of the paper is organized as follows. The nextsection presents the system model. In Section III, the proposedcooperative scheme is detailed. Section IV investigates thepower allocation problem. In Section V, we derive closed-formexpressions of the primary and secondary outage probabilitiesand presents the diversity order analysis. In Section VI, analyti-cal and simulation results are presented and finally a conclusioncloses the paper in Section VII.

II. SYSTEM MODEL

We consider a CRN in which a secondary system consistingof a secondary transmitter (ST), a secondary receiver (SR) anda set of N cognitive relay nodes denoted � = {R1, . . . , RN}coexists with a primary system composed of a primary trans-mitter (PT) and a primary receiver (PR), as illustrated in Fig. 1.All nodes of the systems are equipped with a single antennaused for transmission and reception in a half-duplex mode. Weassume that the data transmission is processed over successivetime-slots, where each time-slot is divided into two sub-slots.The channels are assumed stationary during a time-slot and varyindependently from one time-slot to another.

Let γp, γmaxs , and γmax

r denote the transmit power of PT,maximal transmit power of ST and maximal transmit power

JAAFAR et al.: COOPERATIVE TRANSMISSION SCHEME FOR IMPROVING THE SECONDARY ACCESS IN CRNs 6221

of any relay node respectively. Without loss of generality, weassume that γmax

s and γmaxr are of the same order of magnitude

as γp. In fact, when a secondary transmission occurs at the sametime as the primary one, ST and the relay node lower theirpowers to meet the primary QoS constraint.

All channels are modeled as Rayleigh fading channels. Wedenote by hkl the fading coefficient of the channel k–l (k is thetransmitter and l is the receiver), having variance λkl = d−α

kl ,where dkl is the distance between nodes k and l and where α isthe path-loss exponent. For simplicity of notations, we assumethat k = p, s or i and l = p, s or i, where the indices p, s, andi designate primary node, secondary node and a relay nodeRi ∈ � respectively. All channels are assumed independentover time and are non-identically distributed (i.ni.d.). Moreover,we assume that the transmissions are corrupted by AdditiveWhite Gaussian Noise (AWGN) of unit energy.

We assume also that the secondary system (including therelay nodes) is able to synchronize itself to the time-slottedprimary transmissions. Synchronization methods are out of thescope of this paper, some of them are investigated in [24]–[28]. We assume that the relay nodes have a perfect knowledgeof their channel states and of the statistics of the primaryand secondary channel states. Meanwhile, we assume that STknows only the statistics of the primary and secondary channelstates. These assumptions favors the limitation of the overheadbetween primary and secondary systems.

Finally, without loss of generality, a primary transmis-sion (resp. a secondary transmission) is considered successfulwhenever the received Signal-to-Interference-plus-Noise-Ratio(SINR) is above a pre-defined primary threshold denoted byγ(p)th (resp. a secondary threshold γ

(s)th ).

III. PROPOSED COOPERATIVE SCHEME

Each data transmission in our scheme is performed over twoconsecutive sub-slots. At the first sub-slot, PT broadcasts itssignal using transmit power γp. Meanwhile, ST may broadcast

its signal using a transmit power γ(0)s that satisfies a primary

outage threshold ε, set as the QoS parameter. The receivedsignals by PR, SR and relay node Ri ∈ � at the first sub-slotare expressed by:

yp(1) =√γphppxp +

√γ(0)s hspxs + np, (1)

ys(1) =

√γ(0)s hssxs +

√γphpsxp + ns, (2)

and

yi =√γphpixp +

√γ(0)s hsixs + ni, ∀Ri ∈ R, (3)

where xp and xs are the unit energy signals transmitted byPT and ST respectively; nk is the AWGN received at node k

(k = p, s or i); and γ(0)s is calculated assuming that the primary

transmission is performed over only one sub-slot. The primaryoutage probability, in this case, is defined as:

Pout,p(1) = P

{γp|hpp|2

γ(0)s |hsp|2 + 1

< γ(p)th

}≤ ε, (4)

where |x| is the magnitude of the complex coefficient x and εis the outage probability threshold to be respected. Accordingto (4), the value of the secondary broadcast power at the firstsub-slot, γ(0)

s , is given by [10]:

γ(0)s = min (γmax

s ,max(0, ρ)) , (5)

where ρ = (γpλpp/λspγ(p)th )((e−(γ

(p)

th/γpλpp)/(1− ε))− 1).

When ρ < 0, i.e., γp < γcutp , where

γcutp = − γ

(p)th

λpp ln(1− ε), (6)

the primary system does not satisfy its outage probabilitythreshold ε over the first sub-slot. Hence, no secondary access isallowed. When the primary direct transmission at the first sub-slot satisfies ε, PT keeps silence during the second sub-slot. Theprimary transmission may then be considered as a multimediacommunication requiring a fixed data-rate. Hence, if its QoS issatisfied at the first sub-slot, no further transmission is neededat the second sub-slot [21]–[23].

For the transmissions at the second sub-slot, the relay nodesattempt either to decode xs if γp > γcut

p or to decode xp if γp ≤γcutp . For simplicity, we denote by Ds (or Dp respectively) the

set of relays able to successfully decode xs (or xp respectively).Then, we have

γ(0)s |hsi|2

γp|hpi|2 + 1≥ γ

(s)th , ∀i ∈ Ds. (7)

Dp is defined similarly by inverting indices p and s in (7). Eventhough the Amplify-and-Forward (AF) cooperative techniquecould be used in our model, we prefer not to use it since in aninterfered system, the gain provided by AF is smaller than thatof DF [29].

Depending on the value of γp, the proposed scheme proceedsdifferently at the second sub-slot as described below:

A. “High Primary Transmit Power” (γp > γcutp )

In this case, ST has access to the licensed spectrum bandat the first sub-slot since the primary transmission satisfies itsoutage QoS. At the second sub-slot, if no relay is able to decodethe secondary signal (Ds = ∅), ST retransmits xs using thetransmit power γmax

s since PT is silent.Using Optimum Combining (OC) [30], the secondary re-

ceiver decodes xs. Otherwise, if Ds = ∅, an adequately selectedrelay node i∗ ∈ Ds forwards xs at the second sub-slot usingγmaxr . Without loss of generality, the relay selection criterion is

given by:

i∗ = argmaxi∈Ds

|his|2. (8)

The use of this criterion is adopted since the secondary trans-mission in this case is processed in an interference-free envi-ronment [31].

The received SINR at PR, over the entire time-slot, is ex-pressed by:

SINRp =γp|hpp|2

γ(0)s |hsp|2 + 1

. (9)


Fig. 2. Flow chart of the proposed scheme.

Meanwhile, the secondary receiver makes use of OC to com-bine the two received signals, resulting in a SINR given by:

SINRs(Ds = ∅) = γ(0)s |hss|2

γp|hps|2 + 1+ γmax

s |hss|2. (10)

and

SINRs(Ds = ∅) = γ(0)s |hss|2


r |hi∗s|2. (11)

B. “Low Primary Transmit Power” (γp ≤ γcutp )

In this case, secondary transmissions over the first sub-slotare not allowed since the primary communication has not yetreached its outage threshold ε.

If Dp = ∅, PT retransmits xp at the second sub-slot whileST may be allowed to transmit xs using a controlled powervalue denoted γ

(1)s (To be determined in the next section).

Otherwise (if Dp = ∅), a selected relay node j∗ ∈ Dp forwardsxp while ST is allowed to transmit at the second sub-slot with a

controlled power value γ(2)s (To be derived at the next section).

The criterion used to select j∗ takes into account the primaryinterference caused to SR. It is given by:

j∗ = argmaxj∈Dp

|hjp|2λjs

. (12)

This criterion, first proposed in [10], allows to develop a spe-cific best-relay selection algorithm for centralized or distributedapproaches. In a centralized manner, PT maintains a look-uptable of the relays and their associated channel information(specifically |hjp|2 and λjs). Then, the best relay can be chosenby looking up into the table. In a distributed manner, each relaynode maintains a timer [8] and sets it in inverse proportion to theterm |hjp|2/λjs given in (12). Then, the relay with the smallestinitial timer value is selected. When the chosen relay’s timer isexpired, it broadcasts a control message to notify PT and the

relay nodes of its participation in the transmission. It has beenshown in [20] that the use of this criterion outperforms othercriteria used in the CRN. The use of any other criterion is outof the scope of this paper.

Using OC at PR, the received SINR at PR is expressed by:

SINRp(Dp = ∅) = γp|hpp|2 +γp|hpp|2

γ(1)s |hsp|2 + 1

, (13)

and

SINRp(Dp = ∅) = γp|hpp|2 +γj∗ |hj∗p|2

γ(2)s |hsp|2 + 1

. (14)

Meanwhile, SINR at SR can be written as:

SINRs(Dp = ∅) = γ(1)s |hss|2

γp|hps|2 + 1, (15)

and

SINRs(Dp = ∅) = γ(2)s |hss|2

γj∗ |hj∗s|2 + 1. (16)

For clarity, the main steps of the proposed scheme aresummarized in the flow chart of Fig. 2. In the next section,we investigate the power allocation issues associated with theproposed cooperative scheme.

IV. POWER ALLOCATION

In the case of “High primary transmit power”, the transmitpower of ST is given by (5) at the first sub-slot and is equalto γmax

s at the second sub-slot, while the transmit power of i∗

is equal to γmaxr . In the “Low primary transmit power” case,

if Dp = ∅, then the transmit power of ST has to be adjusted inorder to preserve the primary outage probability. The conditionsin (17) and (18)

Pout,p(Dp=∅)=P

{γp|hpp|2+

γp|hpp|2

γ(1)s |hsp|2+ 1

< γ(p)th

}

≤ ε2 (17)


and0 ≤ γ(1)

s ≤ γmaxs (18)

have to be satisfied, where ε2 = max(ε, P repout,p) and P rep

out,p isthe outage probability of the primary system when PT repeatsthe same signal over both sub-slots at the complete absence ofsecondary transmissions. Its expression is given by:

P repout,p = P

{2γp|hpp|2 < γ

(p)th

}. (19)

P repout,p emphasizes our choice to improve the secondary per-

formance while providing the same primary outage perfor-mance at the absence of secondary transmissions. To obtainγ(1)s , the cumulative probabilities P{2γp|hpp|2 < γ

(p)th } and

P{γp|hpp|2 + (γp|hpp|2/(γ(1)s |hsp|2 + 1)) < γ

(p)th } have to be

derived. We denote by Xab the random variable (RV) Xab =γa|hab|2. This RV has an exponential distribution withparameter 1/δab, where δab = γaλab, a = p, s or i and b =

p, s or i. Consequently, P{2γp|hpp|2 < γ(p)th } = FXpp

(γ(p)th /2)

where FX(.) denotes the cumulative distribution function (cdf)of the random variable X .

Lemma 1: P{γp|hpp|2+(γp|hpp|2/(γ(1)s |hsp|2+1)) < γ

(p)th }

is expressed by (20)

P

{γp|hpp|2 +

γp|hpp|2

γ(1)s |hsp|2 + 1

< γ(p)th

}

=e1/δ

(1)sp

δpp

γ(p)

th∫γ(p)

th/2

e−x

[1

δpp− 1

δ(1)sp (x−γ

(p)

th )

]dx, (20)

where δ(1)sp = γ

(1)s λsp and the integral term is calculated

numerically.Proof: See Appendix A. �

Since γ(1)s cannot be explicitly derived using Lemma 1 with

respect to (17) and (18), we propose the use of a simple linearsearch algorithm, (A1), as presented below. It is to be notedthat the speed of convergence of algorithm (A1) to the bestvalue depends on the value of the power step st. In general, the al-gorithm provides a sub-optimal value of the transmit power γ(1)

s .

Transmit power algorithm (A1)

1: st > 0 (power step)2: γ(1)

s ← γmaxs

3: calculate P{γp|hpp|2+(γp|hpp|2/(γ(1)s |hsp|2+1))<γ

(p)th }

using (20)while P{γp|hpp|2+(γp|hpp|2/(γ(1)

s |hsp|2+1)) < γ(p)th }

> ε2and γ

(1)s > 0 do

4: γ(1)s ← γ

(1)s − st

5: calculate P{γp|hpp|2+(γp|hpp|2/(γ(1)s |hsp|2+1))<γ

(p)th }

using (20)end while

6: return max(0, γ(1)s )

If Dp = ∅, the transmit powers of ST and j∗ should bejointly controlled in order to achieve the best secondary outage

probability without degrading the primary outage performance.The used values of γ(2)

s and γj∗ should respect the conditions(21)

Pout,p(Dp = ∅)=P

{γp|hpp|2+

γj∗ |hj∗p|2

γ(2)s |hsp|2 + 1

<γ(p)th

}≤ ε2,

(21)

and (22) and (23):

0 ≤ γ(2)s ≤ γmax

s , (22)

and

0 ≤ γj∗ ≤ γmaxr . (23)

Lemma 2: Pout,p(Dp = ∅) is derived as given in (24), shownat the bottom of the next page, and (25)

• If δj∗p = δpp (See equation at bottom of the next page),• Otherwise,

Pout,p(Dp =∅)=1−e−

γ(p)

thδpp − δj∗p

δppδ(2)sp

e−

γ(p)

thδj∗p ln

(1+γ

(p)th

δ(2)sp

δj∗p

),

(25)

where δ(2)sp = γ

(2)s λsp and the function ψ(x) is defined as:

ψ(x) = ln(x) +

∞∑u=1

(1

δpp− 1

δj∗p

)u(δ(2)sp

)u xu

u!u, ∀x > 0. (26)

Proof: See Appendix B. �Due to the complexity of the expressions in Lemma 2, we

propose to use algorithm (A2) to obtain the best values of γ(2)s

and γj∗ with respect to (21)–(23) (without loss of generality,(A2) provides sub-optimal values). (A2) is provided below.

Transmit power algorithm (A2)

1: st > 0 (power step)2: γ(2)

s ← γmaxs

3: γj∗ ← 0

4: calculate P{γp|hpp|2 + (γj∗ |hj∗p|2/((γ(2)s |hsp|2 + 1)) <

γ(p)th } using (24) and (25)

while P{γp|hpp|2+(γj∗ |hj∗p|2/(γ(2)s |hsp|2+1))<γ

(p)th }

> ε2and γ

(2)s > 0 and γj∗ < γmax

r do5: γ(2)

s ← γ(2)s − st

6: γj∗ ← γj∗ + st

7: calculate P{γp|hpp|2 + (γj∗ |hj∗p|2/(γ(2)s |hsp|2 + 1)) <

γ(p)th } using (24) and (25)

end while8: return max(0, γ

(2)s )

9: return min(γj∗ , γmaxr )

This procedure can be handled by either ST (assuming that itknows λj∗p) or by j∗ (assuming that it knows λsp). Then, the


calculated power value γj∗ at ST (or γ(2)s at j∗) is transmitted

to j∗ (or to ST) via a limited feedback channel.

V. OUTAGE PROBABILITY AND DIVERSITY

ORDER ANALYSIS

In this section, we analyze the outage probability perfor-mance of the proposed cooperative scheme and establish theoutage probability expressions. We derive both the primaryand secondary outage probability expressions, starting with theprimary one. Then, we use the secondary outage probability ex-pressions to derive the diversity order of the proposed scheme.

A. Primary Outage Probability

• If γp > γcutp , the primary outage probability, denoted

Pout,p, is written as:

Pout,p = Pout,p(1). (27)

• Otherwise,

Pout,p =

2N−1∑m=0

P

{Dp = D(m)

p

}Pp

{out.|Dp = D(m)

p

},

(28)

where D(m)p are subsets of � such that D(m)

p ⊂ P(�) (with

P(�) the power set of �), D(0)p = ∅, Pp{out.|Dp = D

(m)p } is

the primary outage probability conditioned on Dp = D(m)p , and

2N is the number of all possible decoding sets.To simplify the notations, we define the RVs Yabc=γa|hac|2/

(γb|hbc|2 + 1) and Y(t)sbc = γ

(t)s |hsc|2/(γb|hbc|2 + 1), having

cumulative distribution functions (cdfs) expressed by [10]:

FYabc(x) = 1− δace

− xδac

δac + xδbc, ∀x ≥ 0, (29)

FY

(t)

sbc

(x) = 1− δ(t)sc e

− x

δ(t)sc

δ(t)sc + xδbc

, ∀x ≥ 0, (30)

where δ(t)sc = γ

(t)s λsc, a, b, and c can be independently equal to

p, s or i and t = 0, 1 or 2.Using (29), Pout,p(1) can be given by [10]:

Pout,p(1) =P

{γp|hpp|2

γ(0)s |hsp|2 + 1

< γ(p)th

}

=1− δppe−

γ(p)

thδpp

δpp + γ(p)th δ

(0)sp

. (31)

From (31), we see that if γ(0)s = ρ, then Pout,p(1) = ε. The

probability of occurrence of Dp = D(m)p (m = 0, . . . , 2N − 1),

given in (28), is expressed by:

P

{Dp=D(m)

p

}=

∏j∈D(m)

p

(1−FXpj

(γ(p)th

)) ∏i∈D̄(m)

p

FXpi

(γ(p)th

),

(32)

where D̄(m)p = � \D(m)

p is the complementary set of D(m)p .

Pp{out.|Dp = ∅} is given by (20) and the primary outage

probability conditioned on Dp = D(m)p (m = 1, . . . , 2N − 1)

is written as:

Pp

{out.|Dp=D(m)

p

}=

Card(D

(m)p

)∑j=1

P{j∗=j}Pout,p(Dp =∅),

(33)

where Card(.) is the cardinality function and the probabilityPout,p(Dp = ∅) is expressed by (24) and (25). Meanwhile, theprobability to select relay node j to assist the primary system,denoted P{j∗ = j}, is given by (34), shown at the bottom of thepage, where Za = Xap/λas is an exponential random variablewith parameter λas/λap, and fZa

and FZadenote its pdf and

cdf respectively (a = k or a = j).For independent and identically distributed (i.i.d.) channels

(i.e., co-located relay nodes), λkp = λp and λks = λs, ∀k ∈Dp. Then, P{j∗ = j} can be given by (35), shown at the bottomof the page.

Pout,p(Dp = ∅) = 1− e−

γ(p)

thδpp − δj∗p

δppδ(2)sp

e− 1

δ(2)sp

− 1δpp

(γ(p)

th+

δj∗p

δ(2)sp

) [ψ(δj∗p + γ

(p)th δ(2)sp

)− ψ(δj∗p)

]. (24)

P{j∗ = j} = P

⎧⎨⎩ ⋂

k∈Dp\{j}

|hkp|2λks

≤ |hjp|2λjs

⎫⎬⎭ = P

⎧⎨⎩ ⋂

k∈Dp\{j}Zk ≤ Zj

⎫⎬⎭ =

+∞∫0

fZj(x)

∏k∈Dp\{j}

FZk(x)dx. (34)

P{j∗ = j} =λs

λp

+∞∫0

e−x λs

λp

(1− e

−x λsλp

)Card(Dp)−1

dx =

⎡⎢⎣(1− e

−x λsλp

)Card(Dp)

Card(Dp)

⎤⎥⎦+∞

0

=1

Card(Dp). (35)


By substituting (31)–(35) into (27) and (28), we obtain theclosed-form expression of the primary outage probability.

B. Secondary Outage Probability

• If γp > γcutp , the secondary outage probability, Pout,s, is

given by:

Pout,s =

2N−1∑n=0

P

{Ds = D(n)

s

}Ps

{out.|Ds = D(n)

s

}. (36)

• Otherwise,

Pout,s =

2N−1∑m=0

P

{Dp = D(m)

p

}Ps

{out.|Dp = D(m)

p

},

(37)

where D(n)s are subsets of � such that D(n)

s ⊂ P(�), D(0)s =

∅, and Ps{out.|Ds = D(n)s } and Ps{out.|Dp = D

(m)p } are the

conditional secondary outage probabilities. P{Dp = D(m)p } is

given by (32) and similarly, the expression of P{Ds = D(n)s }

is expressed by:

P

{Ds=D(n)

s

}=

∏i∈D(n)

s

(1−F

Y(0)spi

(γ(s)th

)) ∏j∈D̄(n)

s

FY

(0)spj

(γ(s)th

),

(38)where D̄

(n)s is the complementary set of D(n)

s .Lemma 3: The secondary outage probability conditioned on

Ds = ∅ can be given by (39), shown at the bottom of the page,where the integral is numerically evaluated.

Proof: Similarly to Lemma 1, the proof can be derived asin Appendix A. �

Meanwhile, the secondary outage probability when Dp = ∅can be expressed by:

Ps{out.|Dp = ∅} =P

{γ(1)s |hss|2

γp|hps|2 + 1< γ

(s)th

}

=FY

(0)sps

(γ(s)th

). (40)

As in (33), the conditional secondary outage probabilities (forn = 1, . . . , 2N − 1 and m = 1, . . . , 2N − 1) are respectivelygiven by (41) and (42), shown at the bottom of the page, whereP{j∗ = j} is given by (34) and (35), and P{i∗ = i} is theprobability to select relay node i to assist the secondary system.It is expressed similarly to (34) by:

P{i∗ = i} =P

⎧⎨⎩ ⋂

k∈Ds\{i}Xks ≤ Xis

⎫⎬⎭

=

+∞∫0

fXis(x)

∏k∈Ds\{i}

FXks(x)dx. (43)

For i.i.d. channels, i.e., λks = λs, ∀k ∈ Ds, P{i∗ = i} is ex-pressed similarly to (35) by:

P{i∗ = i} =1

Card(Ds). (44)

Lemma 4: The secondary outage probability conditioned onDs = ∅ can be given by (45) and (46),

• If δ(0)ss = δi∗s,

P

{SINRs(Ds = ∅) < γ

(s)th

}

= 1− e−

γ(s)

thδi∗s − δ

(0)ss

δi∗sδpse− 1

δps− 1

δi∗s

(γ(s)

th+

δ(0)ssδps

)

×[ψ′(δ(0)ss + γ

(s)th δps

)− ψ′

(δ(0)ss

)]. (45)

• Otherwise,

P

{SINRs(Ds = ∅) < γ

(s)th

}

= 1− e−

γ(s)

thδi∗s − δ

(0)ss

δi∗sδpse−

γ(s)

th

δ(0)ss ln

(1 + γ

(s)th

δps

δ(0)ss

), (46)

Ps{out.|Ds = ∅} = P

{γ(0)s |hss|2


s |hss|2 < γ(s)th

}=

e1/δps

λss

γ(s)

thγmaxs∫

γ(s)

th

γ(0)s +γmax

s

e−x

[1

λss− γ

(0)s

(xγmaxs −γ

(s)

th )δps

]dx, (39)

Ps

{out.|Ds = D(n)

s

}=

Card(D

(n)s

)∑i=1

P{i∗ = i}P{

SINRs(Ds = ∅) < γ(s)th

}, ∀n = 1, . . . , 2N − 1, (41)

Ps

{out.|Dp = D(m)

p

}=

Card(D

(m)p

)∑j=1

P{j∗ = j}P{

SINRs(Dp = ∅) < γ(s)th

}, ∀m = 1, . . . , 2N − 1, (42)


where the function ψ′(x) is defined as:

ψ′(x) = ln(x) +∞∑

u=1

(1

δi∗s− 1

δ(0)ss

)uδups

xu

u!u, ∀x > 0. (47)

Proof: Similarly to Lemma 2, the proof can be derived asin Appendix B. �

Finally, P{SINRs(Dp = ∅) < γ(s)th } is expressed by:

P

{SINRs(Dp = ∅) < γ

(s)th

}= F

Y(2)

sj∗s

(γ(s)th

). (48)

By substituting the expressions of Lemma 3, Lemma 4, (38),(40)–(44), and (48) into (36) and (37), we obtain the closed-form expression of the secondary outage probability.

C. Diversity Order Analysis

We focus here on the diversity order analysis of the sec-ondary system using the proposed cooperation scheme. Accord-ing to [32], the diversity gain is defined as

d = − limγ→+∞

ln (Pout,s(γ)) / ln(γ), (49)

where γ is the SNR of the intended transmission as we as-sumed unitary energy AWGN noise. In our scheme, we assumethat γmax

s = γmaxr = γp. To calculate the diversity order d,

γ → +∞ requires that γ(t)s → +∞, ∀t = 0, 1, 2, and γi∗ →

+∞. That means γmaxs → +∞, γmax

r → +∞, and γp → +∞.Hence, we propose the use of a new secondary outage probabil-ity expression, defined by substituting γ

(0)s , γmax

s , γp, γi∗ , andγmaxr by γ in the expression of Pout,s given in (36).Using (36) and by applying the Jensen’s inequality, we

obtain (50).

ln (Pout,s(γ))

= ln

⎡⎣2N−1∑

n=0

P

{Ds = D(n)

s

}Ps

{out.|Ds = D(n)

s

}⎤⎦

≥ 1

2N

2N−1∑n=0

ln[P

{Ds = D(n)

s

}Ps

{out.|Ds = D(n)

s

}]︸︷︷︸

Δ=G(n)

+ ln(2N )

=1

2N

2N−1∑n=0

G(n) + ln(2N ). (50)

Using (38) and (39) and by substituting γ(0)s , γmax

s , and γpby γ in the expression of G(0), we obtain:

G(0) = ln

⎡⎢⎣ N∏j=1

⎛⎜⎝1− λsje

−γ(s)

thγλsj

λsj + γ(s)th λpj

⎞⎟⎠⎤⎥⎦

+ ln

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣e

1γλps

λss

γ(s)

thγ∫

γ(s)

th2γ

e−x

[1

λss− 1

λps(xγ−γ(s)

th )

]dx

︸︷︷︸Δ=η

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

N∑j=1

ln

⎡⎢⎣1− λsje

−γ(s)

thγλsj

λsj + γ(s)th λpj

⎤⎥⎦+ ln(η). (51)

Using the integral bounds, the expression η can be easily lower-bounded by:

η ≥ γ(s)th

2γλsse

1γλps

−γ(s)

thγ

(1

λss+ 2

γ(s)

thλps

). (52)

Using (52) and by applying the limit γ → +∞ to−G(0)/ ln(γ), we get (53) [33]

− limγ→+∞

G(0)/ ln(γ)

≤ − limγ→+∞

N∑j=1

ln

⎡⎢⎣1− λsje

−γ(s)

thγλsj

λsj+γ(s)

thλpj

⎤⎥⎦

ln(γ)︸︷︷︸=0

− limγ→+∞

ln

⎡⎢⎣ γ

(s)

th

2γλsse

1γλps

−γ(s)

thγ

(1

λss+ 2

γ(s)

thλps

)⎤⎥⎦

ln(γ)

= − limγ→+∞

ln

(γ(s)

th

2γλss

)ln(γ)︸︷︷︸

=−1

− limγ→+∞

1γλps

− γ(s)

th

γ

(1

λss+ 2

γ(s)

thλps

)ln(γ)︸︷︷︸

=0

= 1. (53)

By following the same approach as for G(0), G(n), ∀n =1, . . . , 2N − 1, can be expressed by:

G(n) =∑

i∈D(n)s

ln

⎛⎜⎝ λsie

−γ(s)

thγλsi

λsi + γ(s)th λpi

⎞⎟⎠

+∑

j∈D̄(n)s

ln

⎛⎜⎝1− λsje

−γ(s)

thγλsj

λsj + γ(s)th λpj

⎞⎟⎠

+ ln[Ps

{out.|Ds = D(n)

s

}], (54)


where Ps{out.|Ds = D(n)s } is given by (41). To simplify the

calculations, we assume co-located relay nodes (i.e., i.i.d.channels), then using the Jensen’s inequality, ln[Ps{out.|Ds =

D(n)s }] can be given by (55).

ln[Ps

{out.|Ds = D(n)

s

}]

= ln

⎡⎢⎣Card

(D

(n)s

)∑i=1

1

Card(D

(n)s

)P{SINR(Ds = ∅) < γ(s)th

}⎤⎥⎦

≥ ln(

Card(D(n)

s

))−

Card(D

(n)s

)∑i=1

ln(

Card(D

(n)s

))Card

(D

(n)s

)︸︷︷︸

=0

+1

Card(D

(n)s

)

×Card

(D

(n)s

)∑i=1

ln(P

{SINR(Ds = ∅) < γ

(s)th

}).

(55)

By substituting γ(0)s , γi∗ , and γp by γ in the expression

of P{SINR(Ds = ∅) < γ(s)th } given by (45) and (46), and

by applying the limit γ → +∞ to ln(P{SINR(Ds = ∅) <γ(s)th })/ ln(γ), we obtain (∀δ(0)ss and ∀δi∗s) [33]:

limγ→+∞

ln(P

{SINR(Ds = ∅) < γ

(s)th

})/ ln(γ) = −1. (56)

Consequently, by combining (55) and (56) in (54) and applyingthe limit γ → +∞ to −G(n)/ ln(γ), ∀n = 1, . . . , 2N − 1, weobtain (57), shown at the bottom of the page.

Finally, using (50), (53), and (57) in (49), the diversity orderof the proposed scheme can be given by:

d ≤ 1

2N

2N−1∑n=0

(+1) + limγ→+∞

− ln(2N )

ln(γ)︸︷︷︸=0

= 1. (58)

According to (58), using a large number of relay nodes N toassist the secondary transmission does not increase the diversity

order. This is due to the fact that at high γp, the secondarycommunication is not interfered by the primary transmissionsat the second sub-slot of a time-slot and the transmit powersof secondary transmitters are of the same order of magnitudeas γp. Consequently, retransmitting the secondary signal bythe chosen relay i∗, using transmit power γmax

r = γp, doesnot provide any additional diversity gain compared to the casewhere the signal is retransmitted by ST using the transmitpower γmax

s = γp.

VI. ANALYTICAL AND SIMULATION RESULTS

In this section, we evaluate the primary and secondary outageprobabilities of the proposed scheme, analytically using (27),(28) and (36), (37) respectively, and by simulation using Monte-Carlo method.

We consider the primary and secondary systems illustratedin Fig. 1. We assume that the normalized physical distancebetween the primary and secondary systems is d0 = 2dpp andthat d1 = dpp = dss = 1 distance unit. We assume a path-loss exponent value α = 4, the threshold ε = 0.5% (unlessotherwise stated) and that the primary and secondary SNRthresholds values are equal to γ

(p)th = 4.77 dB and γ

(s)th = 0 dB

respectively. We assume also that γmaxs = γmax

r = γp. Theoutage probabilities Pout,p and Pout,s are evaluated averagedover several relay nodes’ positions located within the areaPT-PR-SR-ST.

Performances of our proposed scheme are compared to thoseof a non-cooperative and a conventional relaying schemes. Inthe non-cooperative scheme, the primary system uses repetitionover the two sub-slots whenever γp ≤ γcut

p and transmits itssignal over the first sub-slot only when γp > γcut

p . Meanwhile,the secondary transmission is processed using repetition, whereST transmits with power γ(0)

s given in (5) at the first sub-slot,and with power γmax

s at the second sub-slot (if γp > γcutp ) or

with power γ(1)s (if γp ≤ γcut

p ). In the conventional relayingscheme, the primary transmission uses also repetition and STtransmits using γ

(1)s whenever γp ≤ γcut

p . However, when γp >γcutp , the secondary transmission is assisted by the “best” relay

node i∗ selected according to (8).Fig. 3 shows the primary and secondary outage probabilities

versus γp (expressed in dB) of the non-cooperative, conven-tional relaying and our proposed schemes. The primary outageprobability, Pout,p, of both non-cooperative and conventional

− limγ→+∞

G(n)/ ln(γ) ≤ − limγ→+∞

∑i∈D(n)

s

ln

⎛⎝ λsie

−γ(s)

thγλsi

λsi+γ(s)

thλpi

⎞⎠

ln(γ)︸︷︷︸=0

− limγ→+∞

∑j∈D̄(n)

s

ln

⎛⎜⎝1− λsje

−γ(s)

thγλsj

λsj+γ(s)

thλpj

⎞⎟⎠

ln(γ)︸︷︷︸=0

− limγ→+∞

1

Card(D

(n)s

) Card(D

(n)s

)∑i=1

(−1) = 1 (57)


Fig. 3. Outage probability versus γp, γ(p)th

= 4.77 dB, γ(s)th

= 0 dB, ε =

0.5%, and N = 2.

relaying schemes are the same, while that of the proposedscheme is better for γp ≤ γcut

p ≈ 27 dB. At γp = 12.2 dB,Pout,p of the proposed scheme is about 22% smaller thanthat of conventional schemes. Indeed, both non-cooperativeand conventional relaying schemes use repetitions for γp ≤γcutp while the proposed scheme uses best relay selection and

accurate power allocation to assist PUs. The non-cooperativeand conventional relaying schemes present the same worstPout,s performance since both schemes do not allow frequentsecondary access when γp ≤ γcut

p . Indeed, secondary accessis allowed only when (γcut

p /2) < γp ≤ γcutp , i.e., P rep

out,p > ε.The proposed scheme provides the best Pout,s performancesince it allows secondary access for any γp value. The realizedimprovement by the proposed scheme is substantial. It can beseen that at γp = 12.2 dB, Pout,s of the proposed scheme isabout 65% smaller than that of conventional schemes. From theslopes of Pout,s performances, we see that all schemes have thesame diversity order d = 1 at high γp. This is expected since athigh γp, no primary transmissions occur at the second sub-slotof a time-slot, and hence ST or i∗ transmit their signals with themaximal power allowed that is equal to γp.

The presented analytical and simulation results do agree, thatmeans (27), (28) and (36), (37) are accurate expressions ofPout,p and Pout,s respectively.

Fig. 4(a) and (b) illustrate the primary and secondary outageprobabilities versus γp for the proposed scheme with differentnumber of relay nodes N .

Fig. 4(a) validates the fact that the proposed scheme protectsthe primary outage performance for any γp value. As N in-creases, Pout,p becomes slightly better for γp ≤ γcut

p . At γp =12.2 dB, Pout,p of our proposed scheme (N = 3) improves byabout 46% over the non-cooperative scheme (N = 0). Indeed,since the best relay j∗ that assists PUs is chosen based onthe instantaneous CSI between the relays in D

(m)p and PR,

while the power allocated to j∗ is based on the average CSI,then Pout,p is expected to be better than that of the non-cooperative case.

Fig. 4. Impact of the number of relays N on the primary and secondary

outage probabilities versus γp, γ(p)th

= 4.77 dB, γ(s)th

= 0 dB, and ε = 0.5%.(a) Primary outage probability of the proposed scheme. (b) Secondary outageprobability of the proposed scheme.

In Fig. 4(b), Pout,s of the proposed scheme improves sub-stantially as N increases. At γp = 12.2 dB and for our proposedscheme (N = 3), Pout,s improves by about 73% over the non-cooperative scheme (N = 0). Indeed, a larger number of relaysmeans that the decoding sets may contain more nodes thatcould assist either the primary or the secondary transmission.Consequently, the relay selection criteria are more efficient andallow to obtain the best outage results.

Fig. 5 presents the primary and secondary outage probabil-ities of the proposed scheme for different ε values. For any ε,Pout,p decreases in the same manner until it reaches γcut

p , thenPout,p becomes equal to ε. However, Pout,s improves whenε increases. Indeed, a softer primary constraint would allowmore secondary access opportunities. Moreover, the cutoffpoint moves towards a lower value with increasing ε. This resultcould be seen directly in the cutoff expression given by (6).


Fig. 5. Outage probability of the proposed scheme versus γp for different ε

values, γ(p)th

= 4.77 dB, γ(s)th

= 0 dB, and N = 2.

VII. CONCLUSION

In this paper, we have proposed and analyzed a novelcooperative scheme for cognitive radio networks that allowssecondary users to access the licensed spectrum more oftenthan conventional cooperative schemes. By using adequaterelay selection criteria and power allocation method, the sec-ondary outage probability can be significantly improved whilepreserving (or improving) the primary outage performance.We have derived closed-form expressions of the primary andsecondary outage probabilities and we calculated the achieveddiversity order. The provided analytical and simulation resultsshow the advantage of using the relay nodes to either assistthe primary or secondary transmission compared to conven-tional schemes. Indeed, by adaptively using the relay nodes,the primary outage performance improves modestly while thesecondary outage probability drops substantially compared toconventional schemes at low primary SNR.

APPENDIX APROOF OF LEMMA 1

We have Xpp = γp|hpp|2 and X(1)sp = γ

(1)s |hsp|2 exponential

RVs with parameters 1/δpp and 1/δ(1)sp respectively. Then,

P{Xpp + (Xpp/X(1)sp + 1) < γ

(p)th } can be given by:

P

{Xpp +

Xpp

X(1)sp + 1

< γ(p)th

}

= P

{X(1)

sp

(1− γ

(p)th

Xpp

)<

γ(p)th

Xpp− 2

}. (59)

After some manipulations, (59) becomes:

=

γ(p)

th∫γ(p)

th2

fXpp(x)

+∞∫γ(p)

th/x−2

1−γ(p)

th/x

fX

(1)sp

(y)dy dx

=

γ(p)

th∫γ(p)

th2

fXpp(x)

(1− F

X(1)sp

(γ(p)th /x− 2

1− γ(p)th /x

))dx

=

γ(p)

th∫γ(p)

th2

1

δppe− x

δpp+ 1

δ(1)sp

+ 1

δ(1)sp (1−γ

(p)

th/x) dx

=e

1

δ(1)sp

δpp

γ(p)

th∫γ(p)

th2

e−x

[1

δpp− 1

δ(1)sp (x−γ

(p)

th )

]dx. (60)

This completes the proof of Lemma 1.

APPENDIX BPROOF OF LEMMA 2

We have Xj∗p = γj∗ |hj∗p|2 and X(2)sp = γ

(2)s |hsp|2 are ex-

ponentially distributed RVs with parameters 1/δj∗p and 1/δ(2)sp

respectively. Hence, Pout,p(Dp = ∅) is expressed as:

P

{Xpp +

Xj∗p

X(2)sp + 1

< γ(p)th

}

= P

{Xj∗p

X(2)sp + 1

< γ(p)th −Xpp

}

=

γ(p)

th∫0

fXpp(x)F Xj∗p

X(2)sp +1

(γ(p)th − x

)dx. (61)

Using [20, eq. (9)] in (61),

=

γ(p)

th∫0

fXpp(x)

⎛⎜⎝1− δj∗pe

−γ(p)

th−x

δj∗p

δj∗p +(γ(p)th − x

)δ(2)sp

⎞⎟⎠ dx

=FXpp

(γ(p)th

)− δj∗p

δppe−

γ(p)

thδj∗p

×γ(p)

th∫0

e−x

(1

δpp− 1

δj∗p

)δj∗p +

(γ(p)th − x

)δ(2)sp

dx

︸︷︷︸Δ=f1

=1− e−

γ(p)

thδpp − δj∗p

δppe−

γ(p)

thδj∗p f1. (62)

If δj∗p = δpp, we substitute y = δj∗p + (γ(p)th − x)δ

(2)sp , and

hence f1 is written as:

f1 =1

δ(2)sp

e−δ

(γ(p)

th+

δj∗p

δ(2)sp

)δj∗p+γ

(p)

thδ(2)sp∫

δj∗p

e

δy

δ(2)sp

ydy, (63)


where δ = (1/δpp)− (1/δj∗p). Using [34, 5.4.19-eq.(502)] in(63), we obtain:

f1=1

δ(2)sp

e−δ

(γ(p)

th+

δj∗p

δ(2)sp

)[ψ(y)]

δj∗p+γ(p)

thδ(2)sp

δj∗p

=1

δ(2)sp

e−δ

(γ(p)

th+

δj∗p

δ(2)sp

)[ψ(δj∗p+γ

(p)th δ(2)sp

)−ψ (δj∗p)

]. (64)

By replacing (64) into (62), we obtain (24). If δj∗p = δpp, f1becomes:

f1 =

γ(p)

th∫0

1

δj∗p +(γ(p)th − x

)δ(2)sp

dx

=

δj∗p+γ(p)

thδ(2)sp∫

δj∗p

dy

δ(2)sp y

=

ln

(1 + γ

(p)th

δ(2)sp

δj∗p

)δ(2)sp

, (65)

where y = δj∗p + (γ(p)th − x)δ

(2)sp . By substituting (65) into

(62), we obtain (25). This completes the proof of Lemma 2.

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Wael Jaafar (S’14) received the B.Eng. degreefrom École Supérieure des Communications deTunis (SUPCOM), Tunis, Tunisia, in 2007 and theMA.Sc. degree in electrical engineering from ÉcolePolytechnique de Montréal, Montreal, QC, Canada,in 2009. He is currently working toward the Ph.D.degree with the Department of Electrical Engineer-ing, École Polytechnique de Montréal. He rankedin the top 10% in B.Eng. studies and received Ex-cellency scholarships during his MA.Sc. and Ph.D.studies. Between February 2007 and September

2007, he was a Research Intern with the Department of Computer Science,Université du Québec à Montréal, Montreal, QC, Canada, and between March2012 and June 2012, he was a Visiting Researcher with Keio University, Tokyo,Japan. His research interests include multiple-input–multiple-output communi-cations, wireless communication networks, cooperative communications, andcognitive radio networks.


Wessam Ajib (M’05) received the EngineerDiploma in physical instruments from InstitutNational Polytechnique de Grenoble, Grenoble,France, in 1996 and the Diplôme d’ÉtudesApprofondies degree in digital communicationsystems and the Ph.D. degree in computer sciencesand computer networks from École NationaleSupérieure des Télécommunications, Paris, France,in 1997 and 2000, respectively. From October 2000to June 2004, he was an Architect and a RadioNetwork Designer with Nortel Networks, Ottawa,

ON, Canada, where he had conducted many projects and introduced differentinnovative solutions for the third generation of wireless cellular networks. FromJune 2004 to June 2005, he was a Postdoctoral Fellow with the Departmentof Electrical Engineering, École Polytechnique de Montréal, Montreal, QC,Canada. Since June 2005, he has been with the Department of ComputerScience, Université du Québec à Montréal, Montreal, QC, Canada, where heis currently an Assistant Professor of computer networks. He is the author orcoauthor of many journal and conference papers. His research interests includewireless communications and wireless networks, multiple- and medium-accesscontrol design, traffic scheduling, multiple-input–multiple-output systems, andcooperative communications.

David Haccoun (S’62–M’67–SM’84–F’93–LF’03)received the Engineer and B.A.Sc. degrees (MagnaCum Laude) in engineering physics from ÉcolePolytechnique de Montréal, Montreal, QC, Canada;the S.M. degree in electrical engineering from theMassachusetts Institute of Technology, Cambridge,MA, USA; and the Ph.D. degree in electrical en-gineering from McGill University, Montreal, QC,Canada. Since 1980, he has been a Professor of elec-trical engineering with the Department of ElectricalEngineering, École Polytechnique de Montréal. He

is a coholder of a U.S. patent on an error-control technique. He is a coauthorof the books The Communications Handbook (Boca Raton, FL, USA: CRCPress, 1997; Piscataway, NJ, USA: IEEE Press, 2001), The Encyclopediaof Telecommunications (Hoboken, NJ, USA: J. Wiley, 2003), and DigitalCommunications by Satellite (Hoboken, NJ, USA: J. Wiley, 1981). A Japanesetranslation of that book was published in 1984. He is the author or coauthorof over 350 journal papers and conference papers in his areas of interest,including communication theory, the theory and applications of error-controlcoding using convolutional codes, and wireless and mobile communications.He is a Fellow of the Engineering Institute of Canada (2006) and a Member ofthe Order of Engineers of Quebec, Sigma Xi, and the American Association forthe Advancement of Sciences. He was the Managing Guest Editor of a SpecialIssue on network coding and its applications to wireless communicationsin Elsevier Physical Communication in 2011–2012. He is a member of theSteering Committee of the IEEE WIRELESS COMMUNICATIONS LETTERS

and is serving as a member of the IEEE 2013 Fellows Committee. He was aMember of the Board of Directors of the Communications Research Centre,Ottawa, ON, Canada, and was a Member of the Board of Directors of theTelecommunications Engineering Management Institute of Canada. He wasthe Treasurer of the 1982 IEEE International Symposium on InformationTheory, St Jovite, Canada; a Cochair of the 2006 IEEE Vehicular TechnologyConference (VTC)-Fall, Montreal, QC, Canada; and the Invited Speakers Chairof the 2012 IEEE VTC-Fall, Quebec, QC, Canada. He has been elected as aMember of the Board of Governors of the IEEE Vehicular Technology Society(VTS, 2009–2011 and 2013–2015). He is a Distinguished Lecturer of the VTS(2011–present), the Chair of the VTS Awards Committee (2011–present), anda Member of the IEEE Fellow Committee (2012–2013). He was the recipientof the Best Paper Award from the IEEE PIMRC in 2008 and the IEEE CanadaFessenden Award in Communications in 2012.

Documents

A Cooperative Transmission Scheme for Improving the Secondary Access in Cognitive Radio Networks