A Cooperative Transmission Scheme for Improving the ... - IEEE Xplore

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

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A Cooperative Transmission Scheme for Improving the 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 secondary access blocking in cognitive radio networks when secondary transmissions cause unacceptably high interference to primary transmissions. In general, the access of secondary users (SUs) to a licensed spectrum band is only allowed when this access does not alter the performance of primary users that can be defined by the primary QoS requirement. In this paper, we propose a cooperative scheme that allows SUs to increase their access to the spectrum band and access the spectrum even when the primary QoS is not satisfied. Using relay selection and a proper power allocation method, we show that the secondary outage performance can be significantly improved, whereas the primary outage performance is either not altered or slightly improved. Moreover, closed-form expressions of the primary and secondary outage probabilities are derived, and the achieved diversity order is calculated. Finally, analytical and simulation results illustrate the primary outage performance and secondary outage performance of the proposed scheme and show its advantages compared with conventional schemes. Index Terms—Cognitive radio, relaying, decode-and-forward, relay selection, power allocation.

I. I NTRODUCTION

C

OGNITIVE radio (CR) is a key technology for solving the spectrum under-utilization and spectrum congestion issues [1]–[4]. By allowing unlicensed Secondary Users (SUs) to transmit on the licensed spectrum band of the Primary Users (PUs) without disrupting the primary transmissions, the spectrum resources are better exploited. In underlay Cognitive Radio Networks (CRNs), the SUs may transmit at the same time as the PUs as long as the induced interference is below a predefined threshold (such as a Signal-to-Noise-Ratio-SNRthreshold, outage probability threshold, etc.) [4]. User cooperation has also been developed to provide spatial diversity gain and reduce interference due to simultaneous communications [5]–[7]. In [6], several cooperative schemes have been proposed such as fixed relaying, selection relaying and incremental relaying. These schemes provide an increased diversity 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; accepted June 11, 2014. Date of publication June 20, 2014; date of current version November 7, 2014. The associate editor coordinating the review of this paper and 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 Québec à Montréal, Montreal QC H2X 3YZ, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at 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 while avoiding complex synchronization among the relay nodes. Integrating user cooperation to CRNs has recently attracted attention for enhancing the transmissions performances. The authors in [9] propose assisting the secondary transmissions using a group of co-located CR relay nodes. By “adequately” selecting the relay nodes, the maximal diversity gain can be achieved. In [10], a less-complex scheme has been proposed achieving the maximal diversity gain at high primary SNR and improving the secondary outage probability compared to conventional schemes. In [11], the authors show that by jointly optimizing spectrum sensing and the secondary access, the secondary outage performance can be significantly improved. The same authors investigate an incremental cooperation scheme for secondary transmissions in [12] and derive closed-form expressions of the secondary outage probability. Both schemes are then extended to multiple-relay CRNs and the related diversity-multiplexing tradeoff is obtained. The authors in [13] investigated the cooperative diversity gain in underlay CRNs in terms of outage probability and diversity order. They showed that diversity is lost for a fixed interference power constraint at the primary receiver. However, if the interference power constraint is proportional to the peak transmit power at the secondary transmitters, then full diversity is achieved, which is equal to the number of relay nodes +1 (by accounting the direct transmission). Other works propose cooperative schemes to assist the primary transmissions, using either a cognitive relay node [14], [15] or the secondary transmitter [16]. They showed that cognitive relaying is efficient under certain network topologies and nodes locations. It is to be noted that in this type of networks, a limited information exchange between primary and secondary systems is required in order to respect the primary QoS constraint. In [17]–[20], we have proposed cooperative schemes to assist either the primary transmission (as in [14]–[16]) or the secondary one (as in [9]–[13]) or both simultaneously. In [17], the proposed scheme assists simultaneously PUs and SUs whenever the relay node is able to decode both primary and secondary signals. Provided results show that the secondary outage performance improves at the expense of a higher relay transmit power, while the primary QoS is maintained. An extension to the multi-antenna relay with antenna selection is studied in [18]. In [19], assisting the primary or secondary transmission is activated using the incremental relaying technique (acknowledgment-based cooperation as in [12]). Results show that choosing first the best relay to assist the PUs before

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choosing the relay that would assist the SUs improves better the secondary outage performance while respecting a primary outage threshold. Moreover, by using an adequate power allocation method, secondary access is allowed at low primary SNR. In [20], several relaying schemes are investigated where relay nodes may help primary and/or secondary transmissions in order to improve the secondary outage probability with respect to a primary outage threshold. Results provide a guideline about the impact of several parameters (such as relay selection, primary outage threshold, number of relays, distances between nodes, etc. . .) on the secondary system’s outage performance. In conventional CRNs, whenever the primary SNR is below its cutoff value, the secondary transmissions are not allowed [10], [17], [20]. In [19], we proposed to circumvent this limitation by allowing the secondary user to transmit using a predetermined minimal power value. Even though this technique improves significantly the secondary outage probability at low primary SNR, it is complex to implement since such a predetermined transmit power is difficult to determine as it depends on many factors such as the nodes’ locations and the availability of the Channel State Information (CSI) at the transmitters. Moreover, it imposes the primary transmission to be always 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 efficient cooperative scheme for CRNs, where the “best” selected relay node among a non co-located set of relays (unlike [10] where relays are assumed to be co-located), assists the secondary transmission when the primary SNR is above the cutoff value (as in [10], [17]), and assists the primary transmission when it is below the cutoff value. We assume that the relays use the Decode-and-Forward (DF) cooperative technique [6]. Assisting the primary transmission in our scheme is not aimed at improving its performance but is rather used to provide more access opportunities for secondary transmissions while realizing at worst, the same primary outage performance as it would be for a non-cooperative communication. This scenario holds assuming that primary data is multimedia-like where the primary system requires a fixed data rate and a pre-defined outage probability threshold [21]–[23]. The main contributions of this paper can be summarized as follows: • We propose a novel cooperation scheme for CRNs that can assist either the primary or secondary transmission, aiming at substantially increasing the secondary access to the licensed spectrum band while preserving (or improving) the primary outage performance. First, the proposed scheme is similar to [14]–[20] by the fact that it assists at some point the primary transmission to guarantee more secondary access opportunities. It also assists the secondary transmissions similarly to some of the techniques presented in [9]–[13]. However, since we choose a particular type of primary communications, which works as multimedialike transmissions with a fixed data-rate and an outage QoS requirement, it is more likely that the secondary transmission would experience less primary interference than 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 of continuous primary transmissions. It is to be noted that if the primary transmission were continuous, the only effect would be a dramatically degraded secondary outage performance at high primary SNR. This case has already been studied in part by Zou et al. in [10]. • We investigate the power allocation issue at the cognitive radio transmitters (secondary transmitter and selected relay node) and we derive closed-form expressions of the primary and secondary outage probabilities. The diversity order analysis is then conducted for the proposed scheme. • We compare the outage probability performances of the proposed scheme to that of conventional schemes and we study the impact of several parameters on its outage performances. The rest of the paper is organized as follows. The next section presents the system model. In Section III, the proposed cooperative scheme is detailed. Section IV investigates the power allocation problem. In Section V, we derive closed-form expressions of the primary and secondary outage probabilities and presents the diversity order analysis. In Section VI, analytical and simulation results are presented and finally a conclusion closes the paper in Section VII. II. S YSTEM M ODEL We consider a CRN in which a secondary system consisting of a secondary transmitter (ST), a secondary receiver (SR) and a set of N cognitive relay nodes denoted = {R1 , . . . , RN } coexists with a primary system composed of a primary transmitter (PT) and a primary receiver (PR), as illustrated in Fig. 1. All nodes of the systems are equipped with a single antenna used for transmission and reception in a half-duplex mode. We assume that the data transmission is processed over successive time-slots, where each time-slot is divided into two sub-slots. The channels are assumed stationary during a time-slot and vary independently from one time-slot to another. Let γp , γsmax , and γrmax 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

of any relay node respectively. Without loss of generality, we assume that γsmax and γrmax are of the same order of magnitude as γp . In fact, when a secondary transmission occurs at the same time as the primary one, ST and the relay node lower their powers to meet the primary QoS constraint. All channels are modeled as Rayleigh fading channels. We denote by hkl the fading coefficient of the channel k–l (k is the transmitter and l is the receiver), having variance λkl = d−α kl , where dkl is the distance between nodes k and l and where α is the path-loss exponent. For simplicity of notations, we assume that k = p, s or i and l = p, s or i, where the indices p, s, and i designate primary node, secondary node and a relay node Ri ∈ respectively. All channels are assumed independent over time and are non-identically distributed (i.ni.d.). Moreover, we assume that the transmissions are corrupted by Additive White Gaussian Noise (AWGN) of unit energy. We assume also that the secondary system (including the relay nodes) is able to synchronize itself to the time-slotted primary transmissions. Synchronization methods are out of the scope of this paper, some of them are investigated in [24]– [28]. We assume that the relay nodes have a perfect knowledge of their channel states and of the statistics of the primary and secondary channel states. Meanwhile, we assume that ST knows only the statistics of the primary and secondary channel states. These assumptions favors the limitation of the overhead between primary and secondary systems. Finally, without loss of generality, a primary transmission (resp. a secondary transmission) is considered successful whenever the received Signal-to-Interference-plus-Noise-Ratio (SINR) is above a pre-defined primary threshold denoted by (p) (s) γth (resp. a secondary threshold γth ). III. P ROPOSED C OOPERATIVE S CHEME Each data transmission in our scheme is performed over two consecutive sub-slots. At the first sub-slot, PT broadcasts its signal using transmit power γp . Meanwhile, ST may broadcast (0) its signal using a transmit power γs that satisfies a primary outage threshold ε, set as the QoS parameter. The received signals by PR, SR and relay node Ri ∈ at the first sub-slot are expressed by: √ (0) yp (1) = γp hpp xp + γs hsp xs + np , (1) √ (0) (2) ys (1) = γs hss xs + γp hps xp + ns , and yi =

√ γp hpi xp +

(0)

γs hsi xs + ni ,

∀Ri ∈ R,

(3)

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where |x| is the magnitude of the complex coefficient x and ε is the outage probability threshold to be respected. According to (4), the value of the secondary broadcast power at the first (0) sub-slot, γs , is given by [10]: γs(0) = min (γsmax , max(0, ρ)) , (p) −(γth /γp λpp )

(p)

where ρ = (γp λpp /λsp γth )((e When ρ < 0, i.e., γp < γpcut , where

(5)

/(1 − ε)) − 1).

(p)

γpcut = −

γth , λpp ln(1 − ε)

(6)

the primary system does not satisfy its outage probability threshold ε over the first sub-slot. Hence, no secondary access is allowed. When the primary direct transmission at the first subslot satisfies ε, PT keeps silence during the second sub-slot. The primary transmission may then be considered as a multimedia communication requiring a fixed data-rate. Hence, if its QoS is satisfied at the first sub-slot, no further transmission is needed at the second sub-slot [21]–[23]. For the transmissions at the second sub-slot, the relay nodes attempt either to decode xs if γp > γpcut or to decode xp if γp ≤ γpcut . For simplicity, we denote by Ds (or Dp respectively) the set of relays able to successfully decode xs (or xp respectively). Then, we have (0)

γs |hsi |2 (s) ≥ γth , γp |hpi |2 + 1

∀i ∈ Ds .

(7)

Dp is defined similarly by inverting indices p and s in (7). Even though the Amplify-and-Forward (AF) cooperative technique could be used in our model, we prefer not to use it since in an interfered system, the gain provided by AF is smaller than that of DF [29]. Depending on the value of γp , the proposed scheme proceeds differently at the second sub-slot as described below: A. “High Primary Transmit Power” (γp > γpcut ) In this case, ST has access to the licensed spectrum band at the first sub-slot since the primary transmission satisfies its outage QoS. At the second sub-slot, if no relay is able to decode the secondary signal (Ds = ∅), ST retransmits xs using the transmit power γsmax since PT is silent. Using Optimum Combining (OC) [30], the secondary receiver decodes xs . Otherwise, if Ds = ∅, an adequately selected relay node i∗ ∈ Ds forwards xs at the second sub-slot using γrmax . Without loss of generality, the relay selection criterion is given by: i∗ = arg max |his |2 .

(8)

i∈Ds

where xp and xs are the unit energy signals transmitted by PT and ST respectively; nk is the AWGN received at node k (0) (k = p, s or i); and γs is calculated assuming that the primary transmission is performed over only one sub-slot. The primary outage probability, in this case, is defined as: γp |hpp |2 (p) Pout,p (1) = P < γth ≤ ε, (4) (0) γs |hsp |2 + 1

The use of this criterion is adopted since the secondary transmission in this case is processed in an interference-free environment [31]. The received SINR at PR, over the entire time-slot, is expressed by: SINRp =

γp |hpp |2 (0)

γs |hsp |2 + 1

.

(9)

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Fig. 2. Flow chart of the proposed scheme.

Meanwhile, the secondary receiver makes use of OC to combine the two received signals, resulting in a SINR given by: (0)

SINRs (Ds = ∅) =

γs |hss |2 + γsmax |hss |2 . γp |hps |2 + 1

(10)

relay nodes of its participation in the transmission. It has been shown in [20] that the use of this criterion outperforms other criteria used in the CRN. The use of any other criterion is out of the scope of this paper. Using OC at PR, the received SINR at PR is expressed by:

and

SINRp (Dp = ∅) = γp |hpp |2 +

(0)

γs |hss |2 SINRs (Ds = ∅) = + γrmax |hi∗ s |2 . γp |hps |2 + 1

(11)

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

j ∗ = arg max j∈Dp

|hjp |2 . λjs

(12)

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

(1)

γs |hsp |2 + 1

,

(13)

.

(14)

and SINRp (Dp = ∅) = γp |hpp |2 +

In this case, secondary transmissions over the first sub-slot are not allowed since the primary communication has not yet reached its outage threshold ε. If Dp = ∅, PT retransmits xp at the second sub-slot while ST may be allowed to transmit xs using a controlled power (1) value denoted γs (To be determined in the next section). Otherwise (if Dp = ∅), a selected relay node j ∗ ∈ Dp forwards xp while ST is allowed to transmit at the second sub-slot with a (2) controlled power value γs (To be derived at the next section). The criterion used to select j ∗ takes into account the primary interference caused to SR. It is given by:

γp |hpp |2

γj ∗ |hj ∗ p |2 (2)

γs |hsp |2 + 1

Meanwhile, SINR at SR can be written as: (1)

SINRs (Dp = ∅) =

γs |hss |2 , γp |hps |2 + 1

(15)

and (2)

SINRs (Dp = ∅) =

γs |hss |2 . γj ∗ |hj ∗ s |2 + 1

(16)

For clarity, the main steps of the proposed scheme are summarized in the flow chart of Fig. 2. In the next section, we investigate the power allocation issues associated with the proposed cooperative scheme. IV. P OWER A LLOCATION In the case of “High primary transmit power”, the transmit power of ST is given by (5) at the first sub-slot and is equal to γsmax at the second sub-slot, while the transmit power of i∗ is equal to γrmax . In the “Low primary transmit power” case, if Dp = ∅, then the transmit power of ST has to be adjusted in order to preserve the primary outage probability. The conditions in (17) and (18) 2 |h | γ p pp (p) < γth Pout,p (Dp = ∅) = P γp |hpp |2 + (1) γs |hsp |2 + 1 ≤ ε2

(17)


and 0 ≤ γs(1) ≤ γsmax

(18)

rep rep have to be satisfied, where ε2 = max(ε, Pout,p ) and Pout,p is the outage probability of the primary system when PT repeats the same signal over both sub-slots at the complete absence of secondary transmissions. Its expression is given by: (p) rep (19) = P 2γp |hpp |2 < γth . Pout,p rep Pout,p emphasizes our choice to improve the secondary performance while providing the same primary outage performance at the absence of secondary transmissions. To obtain (1) (p) γs , the cumulative probabilities P{2γp |hpp |2 < γth } and (1) (p) P{γp |hpp |2 + (γp |hpp |2 /(γs |hsp |2 + 1)) < γth } have to be derived. We denote by Xab the random variable (RV) Xab = γa |hab |2 . This RV has an exponential distribution with parameter 1/δab , where δab = γa λab , a = p, s or i and b = (p) (p) p, s or i. Consequently, P{2γp |hpp |2 < γth } = FXpp (γth /2) where FX (.) denotes the cumulative distribution function (cdf) of the random variable X. (1) (p) Lemma 1: P{γp |hpp |2 +(γp |hpp |2 /(γs |hsp |2 +1)) < γth } is expressed by (20) γp |hpp |2 (p) 2 < γth P γp |hpp | + (1) γs |hsp |2 + 1 (p) γth 1 1 (1) −x δpp − (1) (p) e1/δsp δsp (x−γ th ) dx, = e (20) δpp (p)

γth /2 (1) δsp

(1) γs λsp

= and the integral term is calculated where numerically. Proof: See Appendix A. (1) Since γs cannot be explicitly derived using Lemma 1 with respect to (17) and (18), we propose the use of a simple linear search algorithm, (A1), as presented below. It is to be noted that the speed of convergence of algorithm (A1) to the best value depends on the value of the power step st. In general, the al(1) gorithm provides a sub-optimal value of the transmit power γs .

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probability without degrading the primary outage performance. (2) The used values of γs and γj ∗ should respect the conditions (21) γj ∗ |hj ∗ p |2 (p) 2 < γth ≤ ε2 , Pout,p (Dp = ∅) = P γp |hpp | + (2) γs |hsp |2 + 1 (21) and (22) and (23): 0 ≤ γs(2) ≤ γsmax ,

(22)

0 ≤ γj ∗ ≤ γrmax .

(23)

and

Lemma 2: Pout,p (Dp = ∅) is derived as given in (24), shown at the bottom of the next page, and (25) • If δj ∗ p = δpp (See equation at bottom of the next page), • Otherwise,

(p) (p) γ (2) γ ∗p δ δ − δ th sp − δth j (p) Pout,p (Dp = ∅) = 1−e pp − , e j ∗ p ln 1+γth (2) δj ∗ p δpp δsp (25) (2) (2) where δsp = γs λsp and the function ψ(x) is defined as:

u 1 1 ∞ − δpp δj ∗ p xu

u , ∀x > 0. (26) ψ(x) = ln(x) + (2) u!u δ u=1 sp

Proof: See Appendix B. Due to the complexity of the expressions in Lemma 2, we (2) propose to use algorithm (A2) to obtain the best values of γs 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) (1) 2: γs ← γsmax (1) (p) 3: calculate P{γp |hpp |2 +(γp |hpp |2 /(γs |hsp |2 +1)) < γth } using (20) (1) (p) while P{γp |hpp |2 +(γp |hpp |2 /(γs |hsp |2 +1)) < γth } > ε2 (1) and γs > 0 do (1) (1) 4: γs ← γs − st (1) (p) 5: calculate P{γp |hpp |2 +(γp |hpp |2 /(γs |hsp |2 +1)) < γth } using (20) end while (1) 6: return max(0, γs )

1: st > 0 (power step) (2) 2: γs ← γsmax 3: γj ∗ ← 0 (2) 4: calculate P{γp |hpp |2 + (γj ∗ |hj∗p |2 /((γs |hsp |2 + 1)) < (p) γth } using (24) and (25) (2) (p) while P{γp |hpp |2 +(γj ∗ |hj∗p |2 /(γs |hsp |2 +1)) < γth } > ε2 (2) and γs > 0 and γj ∗ < γrmax do (2) (2) 5: γs ← γs − st 6: γj ∗ ← γj ∗ + st (2) 7: calculate P{γp |hpp |2 + (γj ∗ |hj∗p |2 /(γs |hsp |2 + 1)) < (p) γth } using (24) and (25) end while (2) 8: return max(0, γs ) 9: return min(γj ∗ , γrmax )

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

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

Transmit power algorithm (A1)

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calculated power value γj ∗ at ST (or γs at j ∗ ) is transmitted to j ∗ (or to ST) via a limited feedback channel. (2)

(t)

V. O UTAGE P ROBABILITY AND D IVERSITY O RDER A NALYSIS In this section, we analyze the outage probability performance of the proposed cooperative scheme and establish the outage probability expressions. We derive both the primary and secondary outage probability expressions, starting with the primary one. Then, we use the secondary outage probability expressions to derive the diversity order of the proposed scheme.

=1 −

¯ p(m) D

(28) (m) Dp

where are subsets of such that ⊂ P() (with (0) (m) P() the power set of ), Dp = ∅, Pp {out.|Dp = Dp } is (m) the primary outage probability conditioned on Dp = Dp , and 2N is the number of all possible decoding sets. To simplify the notations, we define the RVs Yabc = γa |hac |2 / (t) (t) (γb |hbc |2 + 1) and Ysbc = γs |hsc |2 /(γb |hbc |2 + 1), having cumulative distribution functions (cdfs) expressed by [10]:

(t)

FY (t) (x) = 1 − sbc

δsc e (t)

,

δsc + xδbc

(29)

∀x ≥ 0,

(30)

Pout,p (Dp = ∅) = 1 − e

∗

P{j = j} = P

⎧ ⎨ ⎩

k∈Dp \{j}

−

δj ∗ p

e (2)

1 − (2) δsp

(m)

(33)

1 − δpp

δ ∗ (p) γth + j(2)p δsp

δpp δsp

⎫ ⎧ ⎨ |hkp |2 |hjp |2 ⎬ ≤ =P ⎩ λks λjs ⎭

(m) Dp

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

(p) γ − δth pp

(m)

¯p i∈D

j=1

x

∀x ≥ 0,

(31)

=\ is the complementary set of Dp . where Pp {out.|Dp = ∅} is given by (20) and the primary outage (m) probability conditioned on Dp = Dp (m = 1, . . . , 2N − 1) is written as: (m) Dp Card (m) = P{j ∗= j}Pout,p (Dp = ∅), Pp out.|Dp = Dp

m=0

x − (t) δsc

.

(32)

(27)

δac e− δac FYabc (x) = 1 − , δac + xδbc

(p) (0)

δpp + γth δsp

(m)

P Dp = Dp(m) Pp out.|Dp = Dp(m) ,

(m) Dp

(p) th δpp

γ

j∈Dp

• Otherwise, N 2 −1

−

(0)

• If γp > γpcut , the primary outage probability, denoted Pout,p , is written as:

Pout,p =

δpp e

From (31), we see that if γs = ρ, then Pout,p (1) = ε. The (m) probability of occurrence of Dp = Dp (m = 0, . . . , 2N − 1), given in (28), is expressed by:

(p) (p) P Dp = Dp(m) = FXpi γth , 1−FXpj γth

A. Primary Outage Probability

Pout,p = Pout,p (1).

(t)

where δsc = γs 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]: γp |hpp |2 (p) Pout,p (1) = P < γth (0) γs |hsp |2 + 1

k∈Dp \{j}

(p) (2) − ψ(δj ∗ p ) . ψ δj ∗ p + γth δsp

Zk ≤ Zj

⎫ ⎬ ⎭

+∞ fZj (x) = 0

FZk (x)dx.

(34)

k∈Dp \{j}

⎤+∞ ⎡ λs Card(Dp ) −x λ +∞ p

1 − e Card(Dp )−1 λs 1 ⎥ ⎢ −x λs −x λs . P{j ∗ = j} = e λp 1 − e λp dx = ⎣ = ⎦ λp Card(Dp ) Card(Dp ) 0

(24)

0

(35)


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

As in (33), the conditional secondary outage probabilities (for n = 1, . . . , 2N − 1 and m = 1, . . . , 2N − 1) are respectively given by (41) and (42), shown at the bottom of the page, where P{j ∗ = j} is given by (34) and (35), and P{i∗ = i} is the probability to select relay node i to assist the secondary system. It is expressed similarly to (34) by: ⎧ ⎫ ⎨ ⎬ Xks ≤ Xis P{i∗ = i} = P ⎩ ⎭

B. Secondary Outage Probability • If γp > γpcut , the secondary outage probability, Pout,s , is given by: Pout,s =

N 2 −1

P Ds = Ds(n) Ps out.|Ds = Ds(n) . (36)

k∈Ds \{i}

n=0

+∞ = fXis (x)

• Otherwise, Pout,s =

N 2 −1

(37)

spi

(n)

(n)

P{i∗ = i} =

(0)

spj

(0) δ (s) (0) 1 − δps − δ 1∗ γth + δss δss ps i s =1−e − e δi∗ s δps

(s) (0) (0) . (45) × ψ δss + γth δps − ψ δss (s) − δ th i∗ s γ

• Otherwise, (s) P SINRs (Ds = ∅) < γth γ

=1−e

(s)

− δ th ∗

i s

sps

Ps {out.|Ds = ∅} = P

(44)

• If δss = δi∗ s , (s) P SINRs (Ds = ∅) < γth

(38) ¯ s(n) is the complementary set of Ds(n) . where D 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 as in Appendix A. Meanwhile, the secondary outage probability when Dp = ∅ can be expressed by: (1) γs |hss |2 (s) < γth Ps {out.|Dp = ∅} = P γp |hps |2 + 1

(s) = FY (0) γth . (40)

(0) γs |hss |2 γp |hps |2 + 1

1 . Card(Ds )

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

¯s j∈D

(43)

(0)

where Ds are subsets of such that Ds ⊂ P(), Ds = (n) (m) ∅, and Ps {out.|Ds = Ds } and Ps {out.|Dp = Dp } are the (m) conditional secondary outage probabilities. P{Dp = Dp } is (n) given by (32) and similarly, the expression of P{Ds = Ds } is expressed by:

(s) (s) 1−FY (0) γth FY (0) γth , P Ds = Ds(n) = i∈Ds

FXks (x)dx.

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

m=0 (n)

k∈Ds \{i}

0

P Dp = Dp(m) Ps out.|Dp = Dp(m) ,

(n)

6225

(s)

+ γsmax |hss |2 < γth

=

e1/δps λss

(s) γ (0) − th δss (0) (s) δps − e δss ln 1 + γth (0) , δi∗ s δps δss

(s) γ th max γs

−x

e

1 λss

−

(

(0) γs max −γ (s) δ xγs ps th

)

(46)

dx,

(39)

(s) γ th (0) max γs +γs

Ps out.|Ds = Ds(n) =

(n)

Card Ds

(s) P{i∗ = i}P SINRs (Ds = ∅) < γth ,

∀n = 1, . . . , 2N − 1,

(41)

i=1

Ps out.|Dp = Dp(m) =

(m)

Card Dp

j=1

(s) P{j ∗ = j}P SINRs (Dp = ∅) < γth ,

∀m = 1, . . . , 2N − 1,

(42)

6226


⎤

⎡

where the function ψ (x) is defined as:

u 1 1 ∞ − δi∗ s (0) xu δss , ψ (x) = ln(x) + u δps u!u u=1

⎥ ⎢ (s) ⎢ ⎥ γ ⎥ ⎢ th ⎥ ⎢ γλ1 γ −x 1 − 1 λss (s) ⎥ ⎢ e ps λps (xγ−γ th ) dx⎥ e + ln ⎢ ⎥ ⎢ λss ⎥ ⎢ (s) ⎥ ⎢ γ th ⎥ ⎢ 2γ ⎣# $% &⎦

∀x > 0. (47)

Proof: Similarly to Lemma 2, the proof can be derived as in Appendix B. (s) Finally, P{SINRs (Dp = ∅) < γth } is expressed by:

(s) (s) (48) P SINRs (Dp = ∅) < γth = FY (2) γth . sj ∗ s

Δ

=η

⎡ =

N

γ

⎢ ln ⎣1 −

λsj e

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

We focus here on the diversity order analysis of the secondary system using the proposed cooperation scheme. According to [32], the diversity gain is defined as d = − lim ln (Pout,s (γ)) / ln(γ), γ→+∞

(49)

where γ is the SNR of the intended transmission as we assumed unitary energy AWGN noise. In our scheme, we assume that γsmax = γrmax = γp . To calculate the diversity order d, (t) γ → +∞ requires that γs → +∞, ∀t = 0, 1, 2, and γi∗ → max → +∞, γrmax → +∞, and γp → +∞. +∞. That means γs Hence, we propose the use of a new secondary outage probabil(0) ity expression, defined by substituting γs , γsmax , γp , γi∗ , and max by γ in the expression of Pout,s given in (36). γr Using (36) and by applying the Jensen’s inequality, we obtain (50).

γλps − γ η ≥ th e 2γλss

1 2N

n=0

γ

1 λss

th γ

+ γ

2 (s) λ th ps

.

(52)

Using (52) and by applying the limit γ → +∞ to −G(0)/ ln(γ), we get (53) [33] − lim G(0)/ ln(γ) γ→+∞ ⎡ N j=1

⎢ ln ⎣1 −

≤ − lim γ→+∞ #

%$λsj e

(s)

λsj +γth λpj

1 γλps

(s)

γth 2γλss

⎥ ⎦ &

−

− lim

⎤

(s) γ th γλsj

ln(γ)

(s) ⎢ γth ln ⎣ 2γλ e ss

γ→+∞

−

=0

⎡

γ

(s)

⎤ 1 λss

th γ

+

2 (s) γ λ th ps

⎥ ⎦

ln(γ)

=−1

n=0

≥

1

ln = − lim γ→+∞ ln(γ) # $% &

ln (Pout,s (γ)) ⎡ ⎤ N 2 −1 = ln ⎣ P Ds = Ds(n) Ps out.|Ds = Ds(n) ⎦ N −1 2

(51)

Using the integral bounds, the expression η can be easily lowerbounded by: (s) (s)

C. Diversity Order Analysis

⎥ ⎦ + ln(η).

sj

(s) γth λpj

λsj +

j=1

⎤

(s)

th − γλ

ln P Ds = Ds(n) Ps out.|Ds = Ds(n) # $% &

− lim γ→+∞ #

1 γλps

−

(s)

γth γ

1 λss

+

2 (s) γth λps

ln(γ)

%$= 1.

(53)

&

=0

Δ

=G(n) N

+ ln(2 ) 2 −1 1 G(n) + ln(2N ). 2N n=0 N

=

(50) (0)

Using (38) and (39) and by substituting γs , γsmax , and γp by γ in the expression of G(0), we obtain: ⎛

⎡

⎢ ⎜ G(0) = ln ⎣ ⎝1 − N

j=1

λsj e

γ

⎞⎤

(s)

⎟⎥ ⎠⎦

(s) th − γλ sj

λsj + γth λpj

By following the same approach as for G(0), G(n), ∀n = 1, . . . , 2N − 1, can be expressed by: ⎞ ⎛ (s) γ th − γλ ⎜ λsi e si ⎟ ln ⎝ G(n) = ⎠ (s) λsi + γth λpi (n) i∈Ds

⎛ +

(n)

¯s j∈D

⎜ ln ⎝1 −

γ

λsj e λsj +

(s)

th − γλ

sj

(s) γth λpj

+ ln Ps out.|Ds = Ds(n) ,

⎞ ⎟ ⎠

(54)


(n)

where Ps {out.|Ds = Ds } 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 = (n) Ds }] can be given by (55). ln Ps out.|Ds = Ds(n) ⎡ ⎢ = ln ⎣

(n)

Card Ds

i=1

order. This is due to the fact that at high γp , the secondary communication is not interfered by the primary transmissions at the second sub-slot of a time-slot and the transmit powers of secondary transmitters are of the same order of magnitude as γp . Consequently, retransmitting the secondary signal by the chosen relay i∗ , using transmit power γrmax = γp , does not provide any additional diversity gain compared to the case where the signal is retransmitted by ST using the transmit power γsmax = γp .

⎤

1 (s) ⎥ P SINR(Ds = ∅) < γth

⎦ (n) Card Ds

≥ ln Card Ds(n) − #

VI. A NALYTICAL AND S IMULATION R ESULTS

(n)

(n) ln Card Ds

(n) Card Ds i=1 $% &

Card Ds

In this section, we evaluate the primary and secondary outage probabilities of the proposed scheme, analytically using (27), (28) and (36), (37) respectively, and by simulation using MonteCarlo method. We consider the primary and secondary systems illustrated in Fig. 1. We assume that the normalized physical distance between the primary and secondary systems is d0 = 2dpp and that d1 = dpp = dss = 1 distance unit. We assume a pathloss exponent value α = 4, the threshold ε = 0.5% (unless otherwise stated) and that the primary and secondary SNR (p) (s) thresholds values are equal to γth = 4.77 dB and γth = 0 dB respectively. We assume also that γsmax = γrmax = γp . The outage probabilities Pout,p and Pout,s are evaluated averaged over several relay nodes’ positions located within the area PT-PR-SR-ST. Performances of our proposed scheme are compared to those of a non-cooperative and a conventional relaying schemes. In the non-cooperative scheme, the primary system uses repetition over the two sub-slots whenever γp ≤ γpcut and transmits its signal over the first sub-slot only when γp > γpcut . Meanwhile, the secondary transmission is processed using repetition, where (0) ST transmits with power γs given in (5) at the first sub-slot, max at the second sub-slot (if γp > γpcut ) or and with power γs

=0

+

1

(n) Card Ds (n)

Card Ds

×

(s) . ln P SINR(Ds = ∅) < γth

i=1

(55) (0)

By substituting γs , γi∗ , and γp by γ in the expression (s) of P{SINR(Ds = ∅) < γth } given by (45) and (46), and by applying the limit γ → +∞ to ln(P{SINR(Ds = ∅) < (s) (0) γth })/ ln(γ), we obtain (∀δss and ∀δi∗ s ) [33]:

(s) / ln(γ) = −1. (56) lim ln P SINR(Ds = ∅) < γth γ→+∞

Consequently, by combining (55) and (56) in (54) and applying the limit γ → +∞ to −G(n)/ ln(γ), ∀n = 1, . . . , 2N − 1, we obtain (57), shown at the bottom of the page. Finally, using (50), (53), and (57) in (49), the diversity order of the proposed scheme can be given by: 2 −1 1 ln(2N ) d≤ N (+1) + lim − = 1. γ→+∞ 2 n=0 ln(γ) # $% &

(1)

with power γs (if γp ≤ γpcut ). In the conventional relaying scheme, the primary transmission uses also repetition and ST (1) transmits using γs whenever γp ≤ γpcut . However, when γp > cut γp , 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, conventional relaying and our proposed schemes. The primary outage probability, Pout,p , of both non-cooperative and conventional

N

(58)

=0

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

-

⎛ ln ⎝

(n)

− lim G(n)/ ln(γ) ≤ − lim γ→+∞ γ→+∞ #

i∈Ds

(s) − th γλ si λsi e (s) λsi +γth λpi

γ→+∞

γ

ln(γ) $% =0

− lim

6227

1

(n) Card Ds

⎛

⎞

-

⎠ &

(n)

− lim γ→+∞ #

¯ s(n) j∈D

⎜ ln ⎝1 −

λsj e

−

(s) th γλsj γ

(s)

λsj +γth λpj

ln(γ)

%$⎞ ⎟ ⎠ &

=0

Card Ds

i=1

(−1) = 1

(57)

6228


(p)

(s)

Fig. 3. Outage probability versus γp , γth = 4.77 dB, γth = 0 dB, ε = 0.5%, and N = 2.

relaying schemes are the same, while that of the proposed scheme is better for γp ≤ γpcut ≈ 27 dB. At γp = 12.2 dB, Pout,p of the proposed scheme is about 22% smaller than that of conventional schemes. Indeed, both non-cooperative and conventional relaying schemes use repetitions for γp ≤ γpcut while the proposed scheme uses best relay selection and accurate power allocation to assist PUs. The non-cooperative and conventional relaying schemes present the same worst Pout,s performance since both schemes do not allow frequent secondary access when γp ≤ γpcut . Indeed, secondary access rep > ε. is allowed only when (γpcut /2) < γp ≤ γpcut , i.e., Pout,p The proposed scheme provides the best Pout,s performance since it allows secondary access for any γp value. The realized improvement by the proposed scheme is substantial. It can be seen that at γp = 12.2 dB, Pout,s of the proposed scheme is about 65% smaller than that of conventional schemes. From the slopes of Pout,s performances, we see that all schemes have the same diversity order d = 1 at high γp . This is expected since at high γp , no primary transmissions occur at the second sub-slot of a time-slot, and hence ST or i∗ transmit their signals with the maximal power allowed that is equal to γp . The presented analytical and simulation results do agree, that means (27), (28) and (36), (37) are accurate expressions of Pout,p and Pout,s respectively. Fig. 4(a) and (b) illustrate the primary and secondary outage probabilities versus γp for the proposed scheme with different number of relay nodes N . Fig. 4(a) validates the fact that the proposed scheme protects the primary outage performance for any γp value. As N increases, Pout,p becomes slightly better for γp ≤ γpcut . At γp = 12.2 dB, Pout,p of our proposed scheme (N = 3) improves by about 46% over the non-cooperative scheme (N = 0). Indeed, since the best relay j ∗ that assists PUs is chosen based on (m) the instantaneous CSI between the relays in Dp 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 noncooperative case.

Fig. 4. Impact of the number of relays N on the primary and secondary (p) (s) outage probabilities versus γp , γth = 4.77 dB, γth = 0 dB, and ε = 0.5%. (a) Primary outage probability of the proposed scheme. (b) Secondary outage probability of the proposed scheme.

In Fig. 4(b), Pout,s of the proposed scheme improves substantially as N increases. At γp = 12.2 dB and for our proposed scheme (N = 3), Pout,s improves by about 73% over the noncooperative scheme (N = 0). Indeed, a larger number of relays means that the decoding sets may contain more nodes that could assist either the primary or the secondary transmission. Consequently, the relay selection criteria are more efficient and allow to obtain the best outage results. Fig. 5 presents the primary and secondary outage probabilities of the proposed scheme for different ε values. For any ε, Pout,p decreases in the same manner until it reaches γpcut , then Pout,p becomes equal to ε. However, Pout,s improves when ε increases. Indeed, a softer primary constraint would allow more secondary access opportunities. Moreover, the cutoff point moves towards a lower value with increasing ε. This result could be seen directly in the cutoff expression given by (6).


6229

(p)

γth

fXpp (x) 1 − FX (1)

=

dx

(p)

1 − γth /x

sp

γ

(p)

γth /x − 2

(p) th 2 (p)

γth

+ (1) (1) (p) 1 − δpp + δsp δsp (1−γ /x) th dx e δpp x

= γ

(p) th 2

=

e δpp

1

(p)

γth

1 (1) δsp

1

−x

e

1 δpp

−

1 (1) (p) δsp x−γ th

(

) dx.

(60)

(p) γ th 2

This completes the proof of Lemma 1. Fig. 5. Outage probability of the proposed scheme versus γp for different ε (p) (s) values, γth = 4.77 dB, γth = 0 dB, and N = 2.

A PPENDIX B P ROOF OF L EMMA 2 (2)

VII. C ONCLUSION In this paper, we have proposed and analyzed a novel cooperative scheme for cognitive radio networks that allows secondary users to access the licensed spectrum more often than conventional cooperative schemes. By using adequate relay selection criteria and power allocation method, the secondary outage probability can be significantly improved while preserving (or improving) the primary outage performance. We have derived closed-form expressions of the primary and secondary outage probabilities and we calculated the achieved diversity order. The provided analytical and simulation results show the advantage of using the relay nodes to either assist the primary or secondary transmission compared to conventional schemes. Indeed, by adaptively using the relay nodes, the primary outage performance improves modestly while the secondary outage probability drops substantially compared to conventional schemes at low primary SNR.

(p)

γth

=

fXpp (x)F 0

Using [20, eq. (9)] in (61), ⎛ (p) γth ⎜ fXpp (x) ⎝1 − =

(1)

(1)

We have Xpp = γp |hpp |2 and Xsp = γs |hsp |2 exponential (1) RVs with parameters 1/δpp and 1/δsp respectively. Then, (1) (p) P {Xpp + (Xpp /Xsp + 1) < γth } can be given by: Xpp (p) P Xpp + (1) < γth Xsp + 1

(p) (p) γth γth (1) = P Xsp 1 − − 2 . (59) < Xpp Xpp After some manipulations, (59) becomes: (p)

γth

=

+∞ fXpp (x)

γ

(p) th 2

fX (1) (y)dy dx sp

(p) /x−2 th (p) 1−γ /x th γ

= FXpp

(p) γth

(p)

γth

× 0

#

Xj ∗ p (2) Xsp +1

e

(p) γth − x dx.

−

γ

(p) −x th δj ∗ p

(61)

⎞

δj ∗ p e ⎟

⎠ dx (p) (2) δj ∗ p + γth − x δsp

0

A PPENDIX A P ROOF OF L EMMA 1

(2)

We have Xj ∗ p = γj ∗ |hj ∗ p |2 and Xsp = γs |hsp |2 are ex(2) ponentially distributed RVs with parameters 1/δj ∗ p and 1/δsp respectively. Hence, Pout,p (Dp = ∅) is expressed as: Xj ∗ p (p) < γth P Xpp + (2) Xsp + 1 Xj ∗ p (p) =P < γth − Xpp (2) Xsp + 1

γ

(p)

δj ∗ p − δjth∗ p e − δpp

−x

1 δpp

−δ

1 j∗ p

dx (p) (2) δj ∗ p + γth − x δsp $% & Δ

=f1

=1 − e

−

(p) th δpp

γ

γ

(p)

δj ∗ p − δjth∗ p − e f1 . δpp

(62) (p)

(2)

If δj ∗ p = δpp , we substitute y = δj ∗ p + (γth − x)δsp , and hence f1 is written as: (p) (2) δy δj ∗ p +γth δsp δj ∗ p (p) (2) −δ γth + (2) e δsp 1 δsp dy, (63) f1 = (2) e y δsp δj ∗ p

6230


where δ = (1/δpp ) − (1/δj ∗ p ). Using [34, 5.4.19-eq.(502)] in (63), we obtain: f1 =

(p)

−δ

1

e (2)

δsp

γth +

(p)

=

1 (2) δsp

−δ γth +

e

δj ∗ p (2) δsp

δ

∗

[ψ(y)]δjj ∗ pp

(p) (2)

+γth δsp

(2) δsp (p) (2) −ψ (δj ∗ p ) . (64) ψ δj ∗ p +γth δsp

δj ∗ p

By replacing (64) into (62), we obtain (24). If δj ∗ p = δpp , f1 becomes: (p)

γth

1

dx (2) − x δsp 0 (2) (p) (2) (p) δsp δj ∗ p +γth δsp ln 1 + γth δj ∗ p dy = = , (2) (2) δsp y δsp

f1 =

δj ∗ p +

(p) γth

(65)

δj ∗ p

(p)

(2)

where y = δj ∗ p + (γth − x)δsp . By substituting (65) into (62), we obtain (25). This completes the proof of Lemma 2. R EFERENCES [1] J. Mitola and G. J. Maguire, “Cognitive radio: Making software radios more personal,” IEEE Pers. Commun., vol. 6, no. 4, pp. 13–18, Aug. 1999. [2] T. Weiss and F. Jondral, “Spectrum pooling: An innovative strategy for the enhancement of spectrum efficiency,” IEEE Commun. Mag., vol. 42, no. 3, pp. S8–S14, Mar. 2004. [3] G. Ganesan and Y. G. Li, “Cooperative spectrum sensing in cognitive radio, part i: Two user networks,” IEEE Trans. Wireless Commun., vol. 6, no. 6, pp. 2204–2213, Jun. 2007. [4] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005. [5] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity. part i. system description, part ii. Implementation aspects and performance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–1948, Nov. 2003. [6] J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. [7] W. Jaafar, W. Ajib, and D. Haccoun, “On the performance of multi-hop wireless relay networks,” Wireless Commun. Mobile Comput., vol. 14, no. 1, pp. 145–160, Jan. 2014. [8] A. Bletsas, A. Khisti, D. Reed, and A. Lippman, “A simple cooperative diversity method based on network path selection,” IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp. 659–672, Mar. 2006. [9] K. Lee and A. Yener, “Outage performance of cognitive wireless relay networks,” in Proc. IEEE GLOBECOM, Dec. 2006, pp. 1–5. [10] Y. Zou, J. Zhu, B. Zheng, and Y.-D. Yao, “An adaptive cooperation diversity scheme with best-relay selection in cognitive radio networks,” IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5438–5445, Oct. 2010. [11] Y. Zou, Y.-D. Yao, and B. Zheng, “Cooperative relay techniques for cognitive radio systems: Spectrum sensing and secondary user transmissions,” IEEE Commun. Mag., vol. 50, no. 4, pp. 98–103, Apr. 2012. [12] Y. Zou, Y.-D. Yao, and B. Zheng, “Diversity-multiplexing tradeoff in selective cooperation for cognitive radio,” IEEE Trans. Commun., vol. 60, no. 9, pp. 2467–2481, Sep. 2012. [13] J. Hong, B. Hong, T.-W. Ban, and W. Choi, “On the cooperative diversity gain in underlay cognitive radio systems,” IEEE Trans. Commun., vol. 60, no. 1, pp. 209–219, Jan. 2012. [14] O. Simeone, Y. Bar-Ness, and U. Spagnolini, “Stable throughput of cognitive radios with and without relaying capability,” IEEE Trans. Commun., vol. 55, no. 12, pp. 2351–2360, Dec. 2007. [15] O. Simeone, J. Gambini, Y. Bar-Ness, and U. Spagnolini, “Cooperation and cognitive radio,” in Proc. IEEE ICC, Jun. 2007, pp. 6511–6515.

[16] Y. Han, A. Pandharipande, and S. Ting, “Cooperative decode-and-forward relaying for secondary spectrum access,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 4945–4950, Oct. 2009. [17] W. Jaafar, W. Ajib, and D. Haccoun, “A novel relay-aided transmission scheme in cognitive radio networks,” in Proc. IEEE GLOBECOM, Dec. 2011, pp. 1–6. [18] W. Jaafar, W. Ajib, and D. Haccoun, “Adaptive relaying scheme for cognitive radio networks,” IET Commun., vol. 7, no. 11, pp. 1151–1162, Jul. 2013. [19] W. Jaafar, W. Ajib, and D. Haccoun, “Incremental relaying transmissions with relay selection in cognitive radio networks,” in Proc. IEEE GLOBECOM, Dec. 2012, pp. 1–6. [20] Z. Mlika, W. Ajib, W. Jaafar, and D. Haccoun, “On the performance of relay selection in cognitive radio networks,” in Proc. IEEE VTC-Fall, Sep. 2012, pp. 1–5. [21] S. Weber and G. de Veciana, “Rate adaptive multimedia streams: Optimization and admission control,” IEEE/ACM Trans. Net., vol. 13, no. 6, pp. 1275–1288, Dec. 2005. [22] M. van der Schaar and N. S. Shankar, “Cross-layer wireless multimedia transmission: Challenges, principles, new paradigms,” IEEE Trans. Wireless Commun., vol. 12, no. 4, pp. 50–58, Aug. 2005. [23] W. Sheng, C. Wai-Yip, and S. Blostein, “Rateless code based multimedia multicasting with outage probability constraints,” in Proc. 25th QBSC, 2010, pp. 134–138. [24] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitive MAC for opportunistic spectrum access in Ad Hoc networks: A POMDP framework,” IEEE J. Sel. Areas Commun., vol. 25, no. 3, pp. 589–600, Apr. 2007. [25] Q. Zhao and A. Swami, “A survey of dynamic spectrum access: Signal processing and networking perspectives,” in Proc. IEEE ICASSP, 2007, vol. 4, pp. IV-1349–IV-1352. [26] S. He, L. Jiang, and C. He, “A novel secondary user assisted relay mechanism in cognitive radio networks with multiple primary users,” in Proc. IEEE GLOBECOM, 2012, pp. 1254–1259. [27] L. Giupponi and C. Ibars, “Distributed cooperation among cognitive radios with complete and incomplete information,” EURASIP J. Adv. Signal Process., vol. 2009, no. 1, pp. 1–13, Jun. 2009. [28] T. W. Hassen, “Synchronization in Cognitive Overlay Systems,” M.S. thesis, Dept. Elect. Eng., Aalto Univ., Espoo, Finland, 2012, 1st ed. [29] C. Zhong, S. Jin, and K.-K. Wong, “Dual-hop systems with noisy relay and interference-limited destination,” IEEE Trans. Commun., vol. 58, no. 3, pp. 764–768, Mar. 2010. [30] J. Winters, “Optimum Combining in digital mobile radio with cochannel interference,” IEEE J. Sel. Areas Commun., vol. 2, no. 4, pp. 528–539, Jul. 1984. [31] A. Bletsas, A. Lippnian, and D. Reed, “A simple distributed method for relay selection in cooperative diversity wireless networks, based on reciprocity and channel measurements,” in Proc. IEEE 61st VTC-Spring, 2005, vol. 3, pp. 1484–1488. [32] L. Zheng and D. Tse, “Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels,” IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1073–1096, May 2003. [33] Wolfram Alpha LLC, Wolframalpha Computational Knowledge Engine, Dec. 2013. [Online]. Available: http://www.wolframalpha.com [34] D. Zwillinger, Standard Mathematical Tables and Formulae, 31st ed. London, U.K.: Chapman & Hall, 2003.

Wael Jaafar (S’14) received the B.Eng. degree from École Supérieure des Communications de Tunis (SUPCOM), Tunis, Tunisia, in 2007 and the MA.Sc. degree in electrical engineering from École Polytechnique de Montréal, Montreal, QC, Canada, in 2009. He is currently working toward the Ph.D. degree with the Department of Electrical Engineering, École Polytechnique de Montréal. He ranked in the top 10% in B.Eng. studies and received Excellency 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 March 2012 and June 2012, he was a Visiting Researcher with Keio University, Tokyo, Japan. His research interests include multiple-input–multiple-output communications, wireless communication networks, cooperative communications, and cognitive radio networks.


Wessam Ajib (M’05) received the Engineer Diploma in physical instruments from Institut National Polytechnique de Grenoble, Grenoble, France, in 1996 and the Diplôme d’Études Approfondies degree in digital communication systems and the Ph.D. degree in computer sciences and computer networks from École Nationale Supérieure des Télécommunications, Paris, France, in 1997 and 2000, respectively. From October 2000 to June 2004, he was an Architect and a Radio Network Designer with Nortel Networks, Ottawa, ON, Canada, where he had conducted many projects and introduced different innovative solutions for the third generation of wireless cellular networks. From June 2004 to June 2005, he was a Postdoctoral Fellow with the Department of Electrical Engineering, École Polytechnique de Montréal, Montreal, QC, Canada. Since June 2005, he has been with the Department of Computer Science, Université du Québec à Montréal, Montreal, QC, Canada, where he is currently an Assistant Professor of computer networks. He is the author or coauthor of many journal and conference papers. His research interests include wireless communications and wireless networks, multiple- and medium-access control design, traffic scheduling, multiple-input–multiple-output systems, and cooperative communications.

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David Haccoun (S’62–M’67–SM’84–F’93–LF’03) received the Engineer and B.A.Sc. degrees (Magna Cum Laude) in engineering physics from École Polytechnique de Montréal, Montreal, QC, Canada; the S.M. degree in electrical engineering from the Massachusetts Institute of Technology, Cambridge, MA, USA; and the Ph.D. degree in electrical engineering from McGill University, Montreal, QC, Canada. Since 1980, he has been a Professor of electrical engineering with the Department of Electrical Engineering, École Polytechnique de Montréal. He is a coholder of a U.S. patent on an error-control technique. He is a coauthor of the books The Communications Handbook (Boca Raton, FL, USA: CRC Press, 1997; Piscataway, NJ, USA: IEEE Press, 2001), The Encyclopedia of Telecommunications (Hoboken, NJ, USA: J. Wiley, 2003), and Digital Communications by Satellite (Hoboken, NJ, USA: J. Wiley, 1981). A Japanese translation of that book was published in 1984. He is the author or coauthor of over 350 journal papers and conference papers in his areas of interest, including communication theory, the theory and applications of error-control coding using convolutional codes, and wireless and mobile communications. He is a Fellow of the Engineering Institute of Canada (2006) and a Member of the Order of Engineers of Quebec, Sigma Xi, and the American Association for the Advancement of Sciences. He was the Managing Guest Editor of a Special Issue on network coding and its applications to wireless communications in Elsevier Physical Communication in 2011–2012. He is a member of the Steering Committee of the IEEE W IRELESS C OMMUNICATIONS L ETTERS and is serving as a member of the IEEE 2013 Fellows Committee. He was a Member of the Board of Directors of the Communications Research Centre, Ottawa, ON, Canada, and was a Member of the Board of Directors of the Telecommunications Engineering Management Institute of Canada. He was the Treasurer of the 1982 IEEE International Symposium on Information Theory, St Jovite, Canada; a Cochair of the 2006 IEEE Vehicular Technology Conference (VTC)-Fall, Montreal, QC, Canada; and the Invited Speakers Chair of the 2012 IEEE VTC-Fall, Quebec, QC, Canada. He has been elected as a Member 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), and a Member of the IEEE Fellow Committee (2012–2013). He was the recipient of the Best Paper Award from the IEEE PIMRC in 2008 and the IEEE Canada Fessenden Award in Communications in 2012.