Outage Analysis of Selective Cooperation inUnderlay Cognitive Networks with Fixed Gain

Relays and Primary Interference ModelingSyed Imtiaz Hussain1, Mohamed-Slim Alouini2, Khalid Qaraqe1 and Mazen Hasna3

1Texas A&M University at Qatar, Doha, Qatar2King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

3 Qatar University, Doha, Qatar

E-Mails: {syed.hussain, khalid.qaraqe}@qatar.tamu.edu, slim.alouini@kaust.edu.sa, hasna@qu.edu.qa

Abstract—Selective cooperation is a well investigated techniquein non-cognitive networks for efficient spectrum utilization andperformance improvement. However, it is still a nascent topicfor underlay cognitive networks. Recently, it was investigatedfor underlay networks where the secondary nodes were able toadapt their transmit power to always satisfy the interferencethreshold to the primary users. This is a valid assumptionfor cellular networks but many non-cellular devices have fixedtransmit powers. In this situation, selective cooperation poses amore challenging problem and performs entirely differently. Inthis paper, we extend our previous work of selective cooperationbased on either hop’s signal to noise ratio (SNR) with fixed gainand fixed transmit power relays in an underlay cognitive network.This work lacked in considering the primary interference overthe cognitive network and presented a rather idealistic analysis.This paper deals with a more realistic system model and includesthe effects of primary interference on the secondary transmission.We first derive end-to-end signal to interference and noise ratio(SINR) expression and the related statistics for a dual-hop relaylink using asymptotic and approximate approaches. We thenderive the statistics of the selected relay link based on maximumend-to-end SINR among the relays satisfying the interferencethreshold to the primary user. Using this statistics, we deriveclosed form asymptotic and approximate expressions for theoutage probability of the system. Analytical results are verifiedthrough simulations. It is concluded that selective cooperationin underlay cognitive networks performs better only in low tomedium SNR regions.

Index Terms—cognitive radio, underlay networks, overlaynetworks, user cooperation, and relay selection etc.

I. INTRODUCTION

Underlay cognition allows secondary users to access the pri-mary spectrum by satisfying strict interference threshold at theprimary users. This is in contrast to overlay cognition whereinterference avoidance techniques enable simultaneous in-bandco-existence of the primary and secondary users. Alternatively,if the secondary devices are equipped with spectrum sensingcapability, they can exploit unused primary spectrum andmaintain out-of-band co-existence with the primary users.This approach is known as inter-weaved cognition [1]. Inthis paper, we concentrate on underlay cognitive networks.Strict interference threshold to the primary users forces thesecondary devices to operate with low transmit powers reduc-ing their operational area and making user cooperation a likelychoice to reach distant secondary nodes. In this situation, somesecondary devices volunteer to act like relays and forward the

source’s message to the intended destination either in amplify-and-forward (AF) or decode-and-forward (DF) mode [2]. Theuse of multiple relays, though, improves system performancebut consumes more bandwidth due to orthogonal channelsneeded for cooperating relays. This made way for selectivecooperation [3] which needs only two orthogonal channels.

Recent studies about selective cooperation in cognitivenetworks mainly assumed inter-weaved [4] and underlay ap-proach [5]-[8] with different forwarding protocols. However, ageneral assumption in [4]-[8] is that the secondary nodes arecapable of adapting their transmit power in order to alwayssatisfy the interference constraint. This is a valid assumptionfor cellular devices, but many non-cellular devices, such asWiFi routers, can transmit at fixed power to guarantee aparticular area of coverage. It may also be due to hardwarelimitations, for example sensor nodes. With fixed transmissionpower, secondary nodes may violate the interference thresholdwith certain probability and may be barred from transmission.Similarly, relay selection which is generally based on themaximum signal to noise ratio (SNR) offered by a relay maynot be an optimum criterion; because, a relay with highestSNR is more likely to breach the interference constraint.Hence, selective cooperation with fixed transmit power nodespresents a different problem and the system performance isexpected to be anomalous.

More recently, selective cooperation in underlay cognitivenetworks with fixed transmit power secondary nodes wasstudied in [9]-[12] with different system settings and selectioncriteria. However, the analysis therein lacks in consideringthe effects of primary interference on the secondary networkmaking the system model somewhat unrealistic. In this paper,we extend the work of [11] and [12] by modeling the primaryinterference in the system and changing the selection criteriafrom either hop’s SNR to end-to-end signal to interferenceand noise ratio (SINR). We first derive the expression forend-to-end SINR with fixed gain relays and its cumulativedistribution function (CDF) using asymptotic and approximateapproaches. This statistics is later used to derive the distribu-tions of the selected relay SINR. Once the statistics of receivedSINR at the destination becomes available, we derive closedform asymptotic and approximate expressions for the outageprobability of the system. Asymptotic analysis is valid for anysystem parameters and provide accurate results in high SNR

2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC)

978-1-4673-2569-1/12/$31.00 ©2012 IEEE 1203

S

P

RL

Ri

R1

D

h11

h1i

h1L

h21

h2i

h2L

hSP hiP

hDP

R1 h12 h22

Fig. 1. System model: A multiple relay cognitive network in the presenceof a primary user.

region. However, approximate analysis is system dependentand works well under a certain set of system parameters.Simulation results are also presented to verify the analyticalresults.

The remainder of the paper is arranged as follows. Insection II, we describe the system model and introduce variousnotations used throughout. Section III presents the derivationsof some important distributions required for performance anal-ysis. In Section IV, we present simulation results and sectionV concludes the paper.

II. SYSTEM MODEL

We consider an underlay cognitive network operating neara primary user 𝑃 , as shown in Fig. 1. The secondary source 𝑆is transmitting its signal to a secondary destination 𝐷 with thehelp of 𝐿 secondary relays operating in AF mode with fixedgains. The direct link from the source to the destination doesnot exist. A traditional two time slot model is considered inwhich the source broadcasts its message to all the relays inthe first slot with fixed transmission power 𝐸𝑠. This broadcastcauses some interference to the primary transmission and itmust be below a defined threshold 𝜆 to exist simultaneouslywith the primary user. Otherwise, the source would refrainfrom transmission until this condition is met. Channel gainfrom the source to the 𝑖𝑡ℎ relay (𝑆 → 𝑅𝑖) is ℎ

1𝑖. The

interference channels are ℎ𝑆𝑃

, ℎ𝑖𝑃

and ℎ𝐷𝑃

for 𝑆 → 𝑃 ,𝑅𝑖 → 𝑃 and 𝐷 → 𝑃 links, respectively. The channelcoefficients remain the same in either direction; however,SNRs may be different due to the power available at thetransmitting node. In addition, we assume that each hop issubjected to additive white Gaussian noise (AWGN) with zeromean and variance 𝑁0. The signal received at the 𝑖𝑡ℎ relay is

𝑦𝑅𝑖(1) =

√𝐸𝑠ℎ1𝑖

𝑥𝑠(1)︸ ︷︷ ︸Secondary Signal

+√𝐸

𝑃ℎ

𝑖𝑃𝑥

𝑃(1)︸ ︷︷ ︸

Primary Interference

+𝑛1𝑖(1)︸ ︷︷ ︸

Noise

, (1)

where the numbers within the brackets represent the timeslot, 𝑥𝑠 and 𝑥

𝑃are the transmitted symbols with unit energy

from the source and the primary user, respectively, 𝐸𝑃is the

transmission power of the primary user and 𝑛1𝑖

is the noiseterm of the first hop.

Each relay is equipped with fixed gain 𝑔 and amplifieswhatever is received including interference and noise. Hence,the signal received at the destination becomes

𝑦𝐷(2) = 𝑔ℎ

2𝑖𝑦𝑅𝑖(1) +

√𝐸

𝑃ℎ

𝐷𝑃𝑥

𝑃(2) + 𝑛

2𝑖(2), (2)

where ℎ2𝑖

is the channel coefficient on 𝑅𝑖 → 𝐷 link and 𝑛2𝑖

is the noise term of the second hop.Using (2), end-to-end SINR of the 𝑖𝑡ℎ relay link, 𝛾𝑖, can

be written as

𝛾𝑖 =𝛾

1𝑖𝛾

2𝑖

𝛾2𝑖(𝛾𝑃𝑅𝑖+ 1) + 𝐶(𝛾

𝑃𝐷+ 1)

, (3)

where 𝛾1𝑖 = 𝐸𝑠

𝑁0∣ℎ1𝑖 ∣2 is the first hop SNR, 𝛾2𝑖 = 𝐸𝑠

𝑁0∣ℎ2𝑖 ∣2

is the second hop SNR, 𝛾𝑃𝑅𝑖

=𝐸

𝑃

𝑁0∣ℎ

𝑖𝑃∣2 is the primary

interference at the 𝑖𝑡ℎ relay, 𝛾𝑃𝐷

=𝐸

𝑃

𝑁0∣ℎ

𝐷𝑃∣2 is the primary

interference at the secondary destination and 𝐶 = 𝐸𝑠

𝑔2𝑁0is a

constant term.We assume that all the channels are Rayleigh distributed;

hence, each SNR term in (3) is exponentially distributed withcorresponding average SNR parameter. Let 𝛼, 𝛽, 𝜎 and 𝜃 bethe average SNRs of the first hop, second hop, 𝑃 → 𝑅𝑖 linkand 𝑃 → 𝐷 link, respectively. The average SNR for 𝑆 → 𝑃link is denoted by 𝜇 and will be used later in the derivation.

III. RECEIVED SINR STATISTICS

To derive the CDF of 𝛾𝑖, we start with the outage probabilityof the relay link, which is defined by the probability of having𝛾𝑖 below a certain value 𝛾

𝑡ℎ,

𝑃 𝑖𝑜𝑢𝑡=Pr[𝛾𝑖<𝛾𝑡ℎ

]=Pr[𝛾1𝑖<𝛾𝑡ℎ

{(𝛾

𝑃𝑅𝑖+1)+

𝐶(𝛾𝑃𝐷

+1)

𝛾2𝑖

}].

(4)

This probability can be evaluated as follows

𝑃 𝑖𝑜𝑢𝑡=

∞∫0

∞∫0

∞∫0

Pr[𝛾

1𝑖<𝛾

𝑡ℎ

{(𝛾

𝑃𝑅𝑖+1)+

𝐶(𝛾𝑃𝐷

+1)

𝛾2𝑖

}∣∣∣𝛾2𝑖, 𝛾

𝑃𝑅𝑖, 𝛾

𝑃𝐷

]× 𝑝𝛾

2𝑖(𝑥) 𝑝𝛾

𝑃𝑅𝑖(𝑦) 𝑝𝛾

𝑃𝐷(𝑧) 𝑑𝑥 𝑑𝑦 𝑑𝑧,

=1

𝛽𝜎𝜃

∞∫0

∞∫0

∞∫0

[1− 𝑒−

𝛾𝑡ℎ𝛼 {(𝑦+1)+

𝐶(𝑧+1)𝑥 }

]𝑒−

𝑥𝛽 𝑒−

𝑦𝜎 𝑒−

𝑧𝜃 𝑑𝑥 𝑑𝑦 𝑑𝑧.

(5)

A. Asymptotic Approach

Solving (5) in the sequence of 𝑥, 𝑦 and 𝑧 integrals and using[13, Eq. (3.324.1)], we reach to a situation when

𝑃 𝑖𝑜𝑢𝑡 = 1− 2𝛼𝑒−

𝛾𝑡ℎ𝛼

𝜃(𝛼+ 𝜎𝛾𝑡ℎ)

∫ ∞

0

√𝛾

𝑡ℎ𝐶(𝑧 + 1)

𝛼𝛽

×𝐾1

(2

√𝛾

𝑡ℎ𝐶(𝑧 + 1)

𝛼𝛽

)𝑒−

𝑧𝜃 𝑑𝑧. (6)

If 𝛼 and 𝛽 are large, we can approximate the first ordermodified Bessel function of the second kind, 𝐾1(𝑥) ≈ 1

𝑥 for

1204

all 0 < 𝑥 ≪ 2 [14, Eq. (9.6.9)]. Hence, with 𝛾𝑡ℎ

= 𝛾, theCDF of 𝛾𝑖 can obtained as follows

𝑃𝑎𝑠𝑦𝑚

𝛾𝑖(𝛾) = 1− 𝛼𝑒−

𝛾𝛼

𝛼+ 𝜎𝛾. (7)

B. Approximate Approach

Similarly, if we solve (5) in the reverse order, we comeacross an integral

𝑃 𝑖𝑜𝑢𝑡 = 1− 𝛼2𝑒−

𝛾𝑡ℎ𝛼

𝛽(𝛼+ 𝜎𝛾𝑡ℎ)

∫ ∞

0

𝑥

𝛼𝑥+ 𝜃𝛾𝑡ℎ𝐶𝑒−(

𝛾𝑡ℎ

𝐶

𝛼𝑥 + 𝑥𝛽 )𝑑𝑥.

(8)

The above integral is difficult, if not impossible, to be solved inclosed form. However, the rational function inside the integralcan be approximated as follows

𝑥

𝛼𝑥+ 𝜃𝛾𝑡ℎ𝐶≈ 𝐴𝑒−𝐵𝑥, 𝛾

𝑡ℎ< 1, (9)

where 𝐴 = 1𝛼 and 𝐵 = ln(

𝛼+𝜃𝛾𝑡ℎ𝐶

𝛼 ).The validity condition for this expression, 𝛾

𝑡ℎ< 1, is very

likely to happen as the underlay network is already operatingwith low transmit power and can not afford to have largeoutage threshold. Replacing (9) in (8) and solving through [13,Eq. (3.324.1)] with 𝛾

𝑡ℎ= 𝛾, the CDF of 𝛾𝑖 can be obtained

as

𝑃𝑎𝑝𝑟𝑥

𝛾𝑖(𝛾)= 1− 2𝛼𝑒−

𝛾𝛼

(𝛼+𝜎𝛾)

√𝛾𝐶

𝛼𝛽(𝐵𝛽+1)𝐾1

(2

√𝛾𝐶(𝐵𝛽+1)

𝛼𝛽

).

(10)

C. Selective Cooperation

As mentioned earlier, the source transmission begins onlywhen it satisfies the interference threshold to the primary user.The probability of this event is

Pr[𝐸𝑠∣ℎ𝑆𝑃∣2 < 𝜆] = 1− 𝑒−𝜆

𝜇 . (11)

To analyze the selective cooperation, we assume a situationwhen the source is satisfying this condition and broadcastsits message to all the relays. Similarly, it is necessary for arelay as well to satisfy 𝜆 and become a candidate for selection.The probability with which a relay could meet the interferencethreshold is

𝑃𝜆 = Pr[𝑔2∣ℎ

𝑖𝑃∣2(𝐸𝑠∣ℎ1𝑖

∣2 + 𝐸𝑃∣ℎ

𝑖𝑃∣2) < 𝜆]. (12)

The value of 𝑃𝜆 is actually the CDF of 𝑔2∣ℎ𝑖𝑃∣2(𝐸𝑠∣ℎ1𝑖

∣2 +𝐸

𝑃∣ℎ

𝑖𝑃∣2) calculated at 𝜆 which can be derived using the same

technique as in (5). Similarly, with probability 𝑃𝜆 = 1− 𝑃𝜆,a relay could violate the interference threshold and will bedropped from the selection process irrespective of the SINR itis offering for the transmission. Let ℓ relays out of 𝐿 satisfythe interference constraint and the probability of this eventfollows a binomial distribution as given below

𝑝ℓ(ℓ;𝐿,𝑃𝜆) =

(𝐿

ℓ

)𝑃 ℓ𝜆𝑃

𝐿−ℓ𝜆 , ℓ = 0, 1, ⋅ ⋅ ⋅ , 𝐿. (13)

From (13), the probability of having no relay meeting theinterference threshold is 𝑃𝐿

𝜆 . In this case, the system will be

in outage and no transmission will take place. With ℓ relays inthe selection set 𝒜, based on order statistics, the asymptoticCDF of the selected relay SINR, 𝛾𝑠 =max

𝑖∈𝒜𝛾𝑖 can be given

as

𝑃𝑎𝑠𝑦𝑚

𝛾𝑠(𝛾∣ℓ) =

[1− 𝛼𝑒−

𝛾𝛼

𝛼+ 𝜎𝛾

]ℓ. (14)

Finally, averaging (14) over (13) gives the unconditional CDFof selected relay SINR as follows

𝑃𝑎𝑠𝑦𝑚

𝛾𝑠(𝛾) =

𝐿∑ℓ=0

(𝐿

ℓ

)𝑃 ℓ𝜆𝑃

𝐿−ℓ𝜆

[1− 𝛼𝑒−

𝛾𝛼

𝛼+ 𝜎𝛾

]ℓ. (15)

Similarly, the approximate CDF of 𝛾𝑠 can be given as

𝑃𝑎𝑝𝑟𝑥

𝛾𝑠(𝛾) =

𝐿∑ℓ=0

(𝐿

ℓ

)𝑃 ℓ𝜆𝑃

𝐿−ℓ𝜆

[1− 2𝛼 𝑒−

𝛾𝛼

(𝛼+ 𝜎𝛾)

×√

𝛾𝐶

𝛼𝛽(𝐵𝛽+1)𝐾1

(2

√𝛾𝐶(𝐵𝛽+1)

𝛼𝛽

)]ℓ.

(16)

The above CDFs provide the basis for system’s performanceanalysis. The corresponding probability density functions(PDFs) can be obtained by differentiating (15) and (16) withrespect to 𝛾. Once this statistics is available, we can deriveclosed form expressions for various performance parameters,for example, bit error probability, average channel capacity,amount of fading (AoF), moment generating function (MGF)and the related moments of output SNR etc. However, dueto space limitations, we concentrate our discussion on outageprobability which is readily available from (15) and (16) byreplacing 𝛾 = 𝛾

𝑡ℎ.

IV. SIMULATION RESULTS

In the following, we present the simulation results anddiscuss the conditions under which the derived equationsprovide more accurate results or contrarily become inaccurate.

A. Parametric Setup

All the simulations are generated by varying average per hopSNR such that 𝛼 = 𝛽 = 𝛾 and 𝜎 = 𝜃 = 0.3𝛾. Transmit powerat the secondary source is half of the primary user i.e. 𝐸𝑃 =2𝐸𝑠. Relays are equipped with unit gain whereas noise ineach hop is also assumed to have unit variance. The maximumnumber of relays in the system is 4 and the maximum tolerableinterference level at the primary user is 𝜆 = 10. Secondaryoutage threshold 𝛾

𝑡ℎis also varied to elaborate the accuracy

region.

B. Discussion

Asymptotic analysis is depicted in Fig. 2 along with thesimulation results. Outage threshold is 0.5 in this case. It isimportant to explain the system behaviour in low SNR region,𝛾 < 8 dB, in spite of analytical inaccuracy. Initially, at lowSNR, generally all the relays satisfy the interference constraintand cardinality of the selection set 𝒜 is ℓ = 𝐿. The system

1205

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

SNR Per Hop (dB)

Outa

ge P

robabili

ty

SimulationAsymptotic Analysis

L = 1, 2, 3 and 4.

Start of asymptotic behaviour.

Fig. 2. Outage probability of the system with 𝐿 = 1, 2, 3, 4, and 𝛾𝑡ℎ = 0.5.

behaves normally in this region and we see a decrease in theoutage probability with increasing SNR. However, with furtherincrease in SNR, interference to the primary user becomesmore stronger and some relays may not be able to satisfy𝜆. In this situation, ℓ becomes less than 𝐿 causing reduceddiversity order or more outages in the system and creatinga unique minima in the curve which occurs roughly around5 dB for any number of relays. Analytical results, thoughinaccurate, also exhibit the same phenomenon. Asymptoticanalysis, as expected, becomes accurate in medium to highSNR range starting from 7 dB for 𝐿 = 4 to 9 dB for 𝐿 = 1.This outage probability trend is completely opposite to thetraditional underlay cognitive networks where the nodes canadapt their transmit power to always satisfy the interferenceconstraint. For those networks, ℓ will always be equal to 𝐿 andthe system operates on the same diversity order throughout.At very high SNR, none of the relays could satisfy 𝜆 makingℓ = 0 and the system goes in complete outage with probability1.

Fig. 3 shows that the asymptotic analysis becomes moreaccurate if 𝜆 is reduced to 0.1. The accuracy region now startsearlier as well, i.e. around 6 to 8 dB for 𝐿 = 4 to 𝐿 = 1,respectively.

Approximate results derived in (16) are verified in Fig. 4.As mentioned before, approximate analysis is only accurateif the outage threshold is set to a small value. Here, we set𝜆 = 0.01, no other system parameter is changed. It is evidentthat (16) provides very accurate results under this condition.

Another very important performance factor is the interfer-ence constraint 𝜆. If 𝜆 is small, it is difficult for the secondaryrelays to satisfy it with increasing SNR. However, if it isrelaxed or increased, secondary relays can still satisfy it inslightly higher SNR regions. In Fig. 5, we demonstrate theeffects of 𝜆 on the system performance and also on bothanalyses. We plot the curves in the regions where each scheme

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

SNR Per Hop (dB)

Outa

ge P

robabili

ty

SimulationAsymptotic Analysis

L=1, 2, 3 and 4.

Start of asymptotic behaviour.

Fig. 3. Outage probability of the system with 𝐿 = 1, 2, 3, 4, and 𝛾𝑡ℎ = 0.1.

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

SNR Per Hop (dB)

Outa

ge P

robabili

ty

SimulationApproximate Analysis

L = 1, 2, 3 and 4.

Fig. 4. Outage probability of the system with 𝐿 = 1, 2, 3, 4, and 𝛾𝑡ℎ = 0.01.

provides accurate results to highlight the effects of variationin 𝜆 only. For clarity of display, we plot the asymptoticanalysis for 𝐿 = 1 and approximate analysis for 𝐿 = 4.The first evident result is that both analyses are independentof 𝜆 and their accuracy region is not disturbed by choosingdifferent values of 𝜆. Secondly, an increase in 𝜆 from 10 to20 provides roughly a 2 dB gain in the outage probability.Furthermore, this gain is also independent of the number ofrelays in the system. Similarly, just for reference, if 𝜆 is madeextremely large, the system can operate on a very low outageprobability even at very high SNR. However, in practicalunderlay cognitive networks 𝜆 may not be very high to protectprimary transmission.

1206

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

SNR Per Hop (dB)

Outa

ge P

robabili

ty

SimulationAsymptotic/Approximate Analysis

Asymptotic AnalysisL = 1, γ

th= 0.01, λ = 10

Asymptotic AnalysisL = 1, γ

th = 0.01, λ = 20 Approximate Analysis

L = 4, γth

= 0.01, λ = 10

Approximate AnalysisL = 4, γ

th = 0.01, λ = 20

λ = 106

Fig. 5. Outage probability of the system with 𝜆 = 10 and 20 for bothanalyses.

In general, it can be easily concluded that if the secondarydevices have fixed transmission powers and gains, selectiverelaying behaves differently compared to the traditional un-derlay networks with variable transmit power nodes. It canalso be noticed that selective cooperation in this system isonly feasible in low SNR region.

V. CONCLUSION

In this paper, we analyzed selective cooperation in underlaycognitive networks with fixed gain and fixed transmit powerrelays including primary interference modeling. We deriveda new expression for the end-to-end SINR of a dual-hoprelay link and the corresponding CDFs using asymptoticand approximate approaches. Using these CDFs, we derivedclosed form expressions for the outage probability of selectivecooperation. We identified the regions in terms of SNR andother system parameters in which these analyses generateaccurate results. Simulation results validated the analyses andrevealed several performance tradeoffs.

ACKNOWLEDGEMENT

This publication was made possible by NPRP grant no. 08-055-2-011 from the Qatar National Research Fund (a memberof Qatar Foundation). The statements made herein are solelythe responsibility of the authors.

REFERENCES

[1] S. Haykin, “Cognitive radio: Brain-empowered wireless communica-tions, IEEE J. Sel. Areas Commun., Vol. 23, No. 2, pp. 201-220, 2005.

[2] J. N. Laneman, D. N. C. Tse and G. W. Wornell, “Cooperative diversityin wireless networks: efficient protocols and outage behaviour”, IEEETrans. on Info. Theory, Vol. 50, No. 12, pp. 3062-3080, Dec. 2004.

[3] A. Bletsas, H. Shin, M. Z. Win and A. Lippman, “A simple cooperativediversity method based on netwrok path selection”, IEEE J. Sel. AreasCommun., Vol. 24, No. 3, pp.659-672, Mar. 2006.

[4] J. Jia, J. Zhang and Q. Zhang, “Cooperative relay for cognitive radionetworks”, in proc. IEEE International Conference on Computer Com-munications (INFOCOM), pp. 2304-2312, Rio de Janeiro, Brazil, Apr.2009.

[5] L. Li, X. Zhou, H. Xu, G. Y. Li, D. Wang and A. Soong, “Simplifiedrelay selection and power allocation in cooperative cognitive radiosystems”, IEEE Trans. on Wireless Comm., Vol. 10, No. 1, pp. 33-36,Jan. 2011.

[6] L. Ruan and V. K. N. Lau, “Decentralized dynamic hop selection andpower control in cognitive multi-hop relay systems”, IEEE Trans. onWireless. Comm. , Vol. 9, No. 10, pp. 3024-3030, Oct. 2010.

[7] J. Lee, H. Wang, J. G. Andrews and D. Hong, “Outage probability ofcognitive relay networks with interference constraints”, IEEE Trans. onWireless Comm., Vol. 10, No. 2, pp. 390-395, Feb. 2011.

[8] Y. Zou, J. Zhu, B. Zheng and Y. -D. Yao, “An adaptive cooperationdiversity scheme with best-relay selection in cognitive radio networks”,IEEE Tran. on Sig. Pross., Vol. 58, No. 10, pp. 5438-5445, Oct. 2010.

[9] S. I. Hussain, M. M. Abdallah, M.-S. Alouini, M. O. Hasna, and K.Qaraqe, “Performance analysis of selective cooperation in underlay cog-nitive networks over Rayleigh channels”, in proc. IEEE Int. Workshopon Sig. Proc. Advances in Wireless Comm. (SPAWC), pp. 111-115, SanFrancisco, USA, Jun. 2011.

[10] S. I. Hussain, M. M. Abdallah, M.-S. Alouini, M. O. Hasna, K.Qaraqe, “Best relay selection using SNR and interference quotient forunderlay cognitive networks, in proc. IEEE International Conference onCommunications (ICC), pp. 5713-5715, Ottawa, Canada, Jun. 2012.

[11] S. I. Hussain, M.-S. Alouini, M. O. Hasna and K. Qaraqe, “Partial relayselection in underlay cognitive networks with fixed gain relays”, in proc.IEEE Vehicular Technology Conference (VTC), Spring 2012, Yokohama,Japan.

[12] S. I. Hussain, M.-S. Alouini, K. Qaraqe and M. O. Hasna, “Reactiverelay selection in underlay cognitive networks with fixed gain relays,in proc. IEEE International Conference on Communications (ICC), pp.1809-1813, Ottawa, Canada, Jun. 2012.

[13] I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series andProducts”, 5𝑡ℎ Ed., New York: Academic, 1994.

[14] M. Abramovitz and I.A. Stegun, “Handbook of Mathematical Functionswith Formulas, Graphs and Mathematical Tables”, 9𝑡ℎ Ed., New York:Dover, 1972.

1207