Secure Cognitive Reactive Decode-and-Forward Relay Networks: With and Without Eavesdropper

Secure Cognitive Reactive Decode-and-Forward RelayNetworks: With and Without Eavesdropper

Dac-Binh Ha1 • Tung Thanh Vu1 •

Tran Trung Duy2 • Vo Nguyen Quoc Bao2

� Springer Science+Business Media New York 2015

Abstract In this paper, we study performances of cooperative relay networks in cognitive

radio with reactive multiple decode-and-forward (DF) relays. In particular, we first derive

exact and asymptotic expressions of outage probability for the considered scheme with K-

th best relay selection over Rayleigh fading channel. Next, in the presence of an eaves-

dropper and the same relay selection scheme, secrecy performance of the cognitive relay

network is also evaluated, in terms of average secrecy capacity. We then perform Monte-

Carlo simulations to verify the theoretical derivations. Our results have presented the

significance of using relay networks to enhance the system and secrecy performance of

cognitive reactive DF relay networks.

Keywords Underlay cognitive radio � Reactive relay selection � Physical-layer security �Channel capacity � Secrecy capacity

This paper has been presented in part as the best paper in Signal Processing and CommunicationsSymposium at the IEEE CHINACOM, Maoming, China, August 2014.

& Tran Trung [email protected]

Dac-Binh [email protected]

Tung Thanh [email protected]

Vo Nguyen Quoc [email protected]

1 Duy Tan University, Da Nang, Vietnam

2 Posts and Telecommunications Institute of Technology, Hochiminh city, Vietnam

123

Wireless Pers CommunDOI 10.1007/s11277-015-2924-y

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1 Introduction

With the ever increasing demand of mobile multimedia services, wireless systems have

encountered several practical constraints, e.g., bandwidth availability, multi-path signal

degradation, interference management. Among these affects, shortage of radio frequency

spectrum is the most critical issue. To cope with this problem, cognitive radio (CR) has

been proposed as an efficient sharing scheme among licensed and unlicensed users. By

allowing unlicensed users to concurrently occupy the radio spectrum, the utilization of

frequency spectrum is remarkably enhanced [1]. A key characteristic of spectrum sharing

networks is to guarantee the quality of service (QoS) of the licensed networks under an

acceptable interference constraint. To accomplish this, unlicensed users need to respect the

interference limit regulated by the licensed users. However, due to the limited transmit

power, the performance at the unlicensed receivers is drastically reduced, especially when

the channels experience heavy path-loss and severe shadowing effects [2, 3].

However, the CR has faced some practical challenges due to its deduced system per-

formance and secure performance as compared to non spectrum-sharing counterpart.

Recently, opportunistic relaying strategies which are based on equal-power multiple-relay

transmissions with local channel knowledge have been realized as a supreme mean to

enhance communication coverage [4]. As such, the extension of using relay in CR has

attracted great attention in the research community [5–8]. In [9], the authors evaluated the

performance of proactive relay networks, in terms of outage probability, error probability,

and ergodic capacity. In [10], the ergodic capacity of reactive multiple decode-and-forward

(DF) relays has been investigated. It is important to note that the published works [9, 10]

assumed that the system can select the best relay among the potential ones to assist the

source–destination communication. However, such scheduling may be not applicable in the

dense heterogeneous networks due to the load balance and imperfect channel state infor-

mation. Very recently, the authors in [11] proposed an incremental cooperative commu-

nication protocol with N-th best partial relay selection. In [12], by considering the N-th best

relay, the outage probability of reactive DF relays has been derived. However, this work is

limited to the case of identical fading channels and only exact outage probability.

Due to the broadcast nature in wireless network, the message can be overheard by

eavesdroppers. To protect transmission against severe privacy security risks from eaves-

droppers, Physical Layer Security has been considered as an attractive approach without

complex cryptographic deployments. In [13], Wyner first introduced the wiretap channel to

study the secrecy rate. Latter researches on the secrecy performance over different fading

channels were extended and analyzed [14–17]. Specifically, in [14, 15], the authors have

studied the main and eavesdropper links undergo independent Rayleigh fading and eval-

uated the secrecy capacity. More recently, [16] evaluated the secrecy performance over

diffused power fading channels while [17] investigated multiple antennas wiretap channels

in cognitive network.

To improve the secrecy performance of wireless network, antenna selection techniques

in multiple-input-multiple-output (MIMO) systems [18–20] have been studied to enhance

the secrecy performance. Besides antenna selection technique, relaying technique can be

used to improve the secrecy performance of wireless networks. For example, ergodic

secrecy capacity and the impact of large scale antenna arrays at either the source or the

destination were investigated in [21]. In [22], the authors have considered the security

enhancement in cooperative single carrier systems with multiple relays, multiple desti-

nations and multiple eavesdroppers in selective fading channels. For security improvement

D.-B. Ha et al.

123

of cognitive radio network, the relaying technique has been also exploited. In particular,

[23] introduced a selected pair of opportunistic cognitive relays to protect secure trans-

mission against eavesdroppers. In this paper, our contributions are summarized as follow:

• We consider the joint impact of peak interference power constraint of licensed user and

maximal transmit power of unlicensed user on the performance of CR networks with

reactive multiple DF relays and K-th best relay selections.

• We derive exact outage probability and ergodic capacity for the proposed protocol

without eavesdropper. Moreover, we consider a more general fading model in which all

links are assumed independent but non-identically distributed (i.n.i.d.).

• To provide more insights into the system performance, we also derive the asymptotic

outage probability where both diversity and coding gains are obtained. It has been

shown that the full diversity can be realized when the peak interference power is

proportional to the maximal transmit power.

• Finally, we also derive asymptotic secrecy capacity of the cooperative hop in the

presence of an eavesdropper when the primary user is far the secondary network. It has

been showed that secrecy performance is enhanced by increasing the number of relays.

2 System and Channel Models

The cognitive network consists of a secondary source (S), a secondary destination (D), M

secondary relays (R), a primary user (PU) and an eavesdropper (E). Let dsi; did; dsp; dip and

die denote distances of the S ! Ri, Ri ! D, S ! PU, Ri ! PU and Ri ! E links,

respectively, where i 2 1; 2; . . .;Mf g. We also denote hsi; hid; hsp; hip, and hie as channel

coefficients of the S ! Ri, Ri ! D, S ! PU, Ri ! PU, and Ri ! E links, respectively.

We assume that all of the channels follow a Rayleigh fading distribution. Hence, the

channel gains csi ¼ jhsij2; cid ¼ jhidj2; csp ¼ jhspj2, cip ¼ jhipj2, and cie ¼ jhiej2 follow

exponential distributions. To take path-loss into account, we model the parameters of

csi; cid; csp, cip, and cie as in [24]: ksi ¼ ðdsiÞb, kid ¼ ðdidÞb, ksp ¼ ðdspÞb, kip ¼ ðdipÞb, andkie ¼ ðdieÞb, where b denotes the path-loss exponent.

In cognitive underlay networks, the source and relay must adapt their transmit power so

that interference caused at PU is lower than a maximum interference level, denoted by Ith.

In addition, it is also assumed that their transmit power must be lower than a maximum

threshold, denoted by Pth. We assume that all of the nodes are equipped with a single

antenna and operate on half-duplex mode. Similar to the model proposed in [6], the

maximum transmit power of the source S and relay Ri are, respectively, given as PS ¼min Pth; Ith=csp

� �and PRi

¼ min Pth; Ith=cip� �

. Therefore, the instantaneous signal-to-noise

ratio (SNR) of the S ! Ri and Ri ! D links are, respectively, expressed as follow

Wsi ¼Mmin Pth; Ith=csp� �

N0

csi ¼ min �cP;�cIcsp

!

csi;

Wid ¼Mmin Pth; Ith=cip

� �

N0

cid ¼ min �cP;�cIcip

!

cid;

ð1Þ

where N0 denotes the variance of an additive complex Gaussian noise (it is assumed to be

the same at all receivers in the relays destination and eavesdropper). Also, we define

Secure Cognitive Reactive Decode-and-Forward Relay Networks...

123

quantities as follows: �cP ¼ Pth=N0 and �cI ¼ Ith=N0. Without loss of generality, we assume

that the ratio between �cP and cI is constant, i.e.,

�cI�cP

¼ Ith

Pth

¼ l: ð2Þ

The operation of the proposed protocol is realized by TDMA technique. In the first time

slot, the source S broadcasts its data to the relays. Then, the relays try to decode the

source’s signal from the received signal. Let us denote Q1 and Q2 as the set of the relays

decoding the signal successfully and unsuccessfully, respectively. We can assume that

Q1 ¼ Rj1 ;Rj2 ; . . .;RjN

� �and Q2 ¼ RjNþ1

;RjNþ2; . . .;RjM

� �, where N is the cardinality of Q1,

N 2 0; 1; 2; . . .;Mf g, and j1; j2; . . .; jM 2 1; 2; . . .;Mf g. In the considered cognitive radio

networks, we consider two cases as follow:

• (C1): The Kth-best relay is chosen among N successful relays (N�K) to forward the

source’s signal to the destination at the second time slot. The relay selection is realized

by the following strategy

Rb:Wbd ¼ Kth maxt¼1;2;...;N

Wjtd

� �; ð3Þ

where Rb denotes the Kth-best chosen relay.

• (C2): The system cannot choose a relay to forward the source’s signal to the destination

since N\K. Hence, in this case, the signal is dropped.

3 Performance Evaluation

3.1 System Performance of Cognitive Relay Networks Without Eavesdropper

3.1.1 Derivation of the CDF and PDF of the Instantaneous SNR by Kth-Best RelaySelection

We observe that among N successful relays of the set Q1, there are K � 1 relays whoseWjtd

is larger than Wbd and N � K relays whose Wjtd is smaller than Wbd, where

t 2 1; 2; . . .;Nf g= cjjc ¼ bf gf g. We, respectively, denote these sets as W1 ¼Rz1 ;Rz2 ; . . .;RzK�1f g and W2 ¼ RzKþ1

;RzKþ2; . . .;RzN

� �, where W1 � Q1,W2 � Q1 and

W1 [W2 ¼ Q1= Rbf g. Thus, from [25, Eq. (8)], we can write the CDF and PDF of

Wid; i 2 1; 2; . . .;Mf g, as follow

FWidðxÞ ¼ 1� exp � kid

�cPx

� �þ kidxkidxþ kipl�cP

exp � kid�cP

x� kipl

� �;

fWidðxÞ ¼ kid

�cPexp � kid

�cPx

� �exp � kid

�cPx� kipl

� �

� kidkipl�cPkidxþ kipl�cP� �2 �

k2idx

�cP kidxþ kipl�cP� �

" #

:

ð4Þ

Let us denote Y1 ¼ minðWz1d; . . .;WzK�1dÞ and Y2 ¼ maxðWzKþ1d; . . .;WzNdÞ, we can express

the CDFs of the RVs Y1 and Y2 as

D.-B. Ha et al.

123

FY1ðxÞ ¼ 1�YK�1

v¼1

exp � kzvd�cP

x

� �� kzvdxkzvdxþ kzvpl�cP

exp � kzvd�cP

x� kzvpl

� �� ;

FY2ðxÞ ¼YM

v¼Kþ1

1� exp � kzvd�cP

x

� �þ kzvdxkzvdxþ kzvpl�cP

exp � kzvd�cP

x� kzvpl

� �� :

ð5Þ

In addition, we can formulate the CDF of Wbd as follow

FWbdðxÞ ¼

X

c¼1

N

jc¼b

X

W1;W2

PrðWbd\x; Y2 �Wbd � Y1Þ; ð6Þ

which is equivalent to the following expression

FWbdðxÞ ¼

X

c¼1

N

jc¼b

Z x

0

kbd expð�kbdy=�cPÞ�cP

þ kbdkbpl�cPðkbdyþ kbpl�cPÞ2

� ðkbdÞ2y�cP kbdyþ kbpl�cP� �

!"

� exp � kbd�cP

y� kbpl

� ��ð1� FY1ðyÞÞFY2ðyÞdy: ð7Þ

Based on (7), the corresponding PDF is given by

fWbdxð Þ ¼ oFWbd

xð Þox

; ð8Þ

which is evaluated as

fWbdðxÞ ¼

X

c¼1

N

jc¼b

X

W1;W2

kbd exp �kbdx=�cPð Þ�cP

þ kbdkbpl�cPkbdxþ kbpl�cP� �2 �

ðkbdÞ2x�cP kbdxþ kbpl�cP� �

!"

� exp � kbd�cP

x� kbpl

� ��ð1� FY1ðxÞÞFY2ðxÞ: ð9Þ

Substituting (5) into (9), the PDF of Wbd is given as in (10).

fWbdðxÞ ¼

X

c¼1

N

jc¼b

X

W1;W2

kbd�cP

exp �kbd�cP

x

� �þkbdkbpl�cP exp � kbd

�cPx� kbpl

kbdxþ kbpl�cP� �2

2

4

�kbd�cP

kbdxexp � kbd�cPx� kbpl

kbdxþ kbpl�cP

3

5YK�1

v¼1

exp �kzvd�cP

x

� ��kzvdxexp � kzvd

�cPx� kzvpl

kzvpxþ kzvpl�cP

2

4

3

5

�YK�1

v¼1

exp �kzvd�cP

x

� ��kzvdxexp � kzvd

�cPx� kzvpl

kzvdxþ kzvpl�cP

2

4

3

5: ð10Þ

3.1.2 Exact Outage Probability of Non-homogeneous Networks

We assume that the relay Ri (the destination D) can decode the signal successfully if the

instantaneous SNR of the S ! Ri (Ri ! D) link exceeds a threshold cth. Therefore, theoutage probability of the proposed protocol can be calculated as follow


123

Pout ¼ Pr N\Kð Þ|fflfflfflfflfflffl{zfflfflfflfflfflffl}

Pout1

þPr Wbd\cth;N �Kð Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

Pout2

; ð11Þ

where Pout1 represents case C1 where the system cannot choose any relays to forward the

source’s signal to the destination, while Pout2 represents case C2 where the system can

choose the Kth-best relay for the cooperation but the transmission between the selected

relay and the destination is in outage. Considering the outage probability Pout1 , we can

formulate it as

Pout1 ¼

X

Q1;Q2

N\K

Pr Wsj1 � cth; . . .;WsjN � cth;WsjNþ1\cth; . . .;WsjM\cth

� �; ð12Þ

which can be rewritten by (13) at the top of next page,

Pout1 ¼

X

Q1;Q2

N\K

Pr csp\l; csj1 �qP; . . .; csjN �qP; csjNþ1\qP; . . .; csjM\qP

� �

þ Pr csp � l; csj1 �qIcsp; . . .; csjN �qIcsp; csjNþ1\qIcsp; . . .; csjM\qIcsp

� �

¼MX

Q1;Q2

N\K

ðV1 þ V2Þ;ð13Þ

where

V1 ¼M Pr csp\l; csj1 � qP; . . .; csjN �qP; csjNþ1\qP; . . .; csjM\qP

� �;

V2 ¼M Pr csp � l; csj1 �qIcsp; . . .; csjN �qIcsp; csjNþ1\qIcsp; csjM\qIcsp

� �;

with qP ¼ cth=cP and qI ¼ cth= lcPð Þ. With some manipulations, we can readily obtain V1

and V2 as

V1 ¼ 1� exp �kspl� �� YN

t¼1

exp �ksjtqP� � YM

t¼Nþ1

1� exp �ksjtqP� ��

; ð14Þ

V2 ¼Z þ1

lksp expð�kspxÞ

YN

t¼1

expð�ksjtqIxÞYM

t¼Nþ1

ð1� exp �ksjtqIx� �

Þ" #

dx: ð15Þ

Having expandedQM

t¼Nþ1 1� exp �ksjtqIx� ��

by the binomial identity, we have the

following expression for V2

V2 ¼ksp exp �kspl�

PNt¼1 ksjtqP

� �

ksp þPN

t¼1 ksjtqIþXM�N

v¼1

X

j1;...;jv¼Nþ1

M

j1\...\jv

ð�1ÞvkspqPksp þ

PNt¼1 ksjt þ

Pvl¼1 ksjl

� �qI

� exp �kspl�XN

t¼1

ksjt þXv

l¼1

ksjl

!cthcP

!

: ð16Þ

Collecting (14) and (16), the closed-form expression of the exact outage probability (13) is

given by

D.-B. Ha et al.

123

Pout1 ¼

X

Q1;Q2

N\K

ð1� expð�ksplÞÞYN

t¼1

exp �ksjtcth�cP

� � YM

t¼Nþ1

1� exp �ksjtcth�cP

� �� "

þkspl�cP exp �kspl�

PNt¼1 ksjt

cth�cP

kspl�cP þPN

t¼1 ksjtcth

þXM�N

v¼1

X

j1;...;jv¼Nþ1

M

j1\...\jv

ð�1Þvkspl�cPkspl�cP þ

PNt¼1 ksjt þ

Pvl¼1 ksjl

� �cth

� exp �kspl�XN

t¼1

ksjt þXv

l¼1

ksjl

!cth�cP

!#

:

ð17Þ

Note that in the derivation of (17), we used qP ¼M

cth=�cP and qI ¼M

cth= l�cPð Þ.Next, we calculate the term Pout

2 in (11). We first rewrite it as follow

Pout2 ¼

X

Q1;Q2

N�K

PrðWsj1 � cth; . . .;WsjN � cth;WsjNþ1\cth; . . .;WsjM\cthÞFWbd

ðcthÞ: ð18Þ

With the same manner as in the derivation of (17) and using (7), we can obtain the exact

expression of Pout2 as in (19).

Pout2 ¼

X

Q1;Q2

N�K

1�expð�ksplÞ� �YN

t¼1

exp �ksjtcth�cP

� � YM

t¼Nþ1

1�exp �ksjtcth�cP

� �� "

þ kspl�cPkspl�cPþ

PNt¼1ksjtcth

exp �kspl�XN

t¼1

ksjtcth�cP

!

þXM�N

v¼1

X

j1;...;jv¼Nþ1

M

j1\...\jv

ð�1Þvkspl�cP exp �kspl�PN

t¼1ksjt þPv

l¼1ksjl� �

cth=�cP� �

kspl�cPþPN

t¼1ksjt þPv

l¼1ksjl� �

cth

#

X

c¼1

N

jt¼b

X

W1;W2

Z cth

0

kbd�cP

exp �kbd�cP

y

� �þkbdkbpl�cP expð�kbdy=�cP�kbplÞ

ðkbdyþkbpl�cPÞ

2"

�kbd�cP

kbdyexp �kbdy=�cP�kbpl� �

kbdyþkbpl�cP

#YK�1

v¼1

exp �kzvd�cP

y

� ��kzvdyexp �kzvdy=�cP�kzvpl

� �

kzvdyþkzvpl�cP

� �

YN

v¼Kþ1

1�exp �kzvd�cP

y

� �þkzvdyexp �kzvdy=�cP�kzvpl

� �

kzvdyþkzvpl�cP

� �!

dy:

ð19Þ


123

3.1.3 Exact Outage Probability of Homogeneous Networks

In these networks, we assume that ksi ¼ ks, kid ¼ kd, and kip ¼ kp for all i, so that (13) can

be rewritten as follow

PH;out1 ¼

XK�1

N¼0

M

N

� �ðVH

1 þ VH2 Þ; ð20Þ

where

VH1 ¼ 1� exp �kspl

� �� exp �NksqPð Þ 1� exp �ksqPð Þð ÞM�N ;

and

VH2 ¼

Z þ1

lksp expð�kspxÞ expð�NksqIxÞð1� exp �ksqIxð ÞÞM�N �

dx: ð21Þ

Similar to the derivation of Pout1 in non-homogeneous networks, P

H;out1 can be obtained as

PH;out1 ¼

XK�1

N¼0

M

N

� �ð1� expð�ksplÞÞ exp

�Nkscth�cP

� �1� exp

�kscth�cP

� �� M�N"

þXM�N

t¼0

M � N

t

� �kspl�cP

kspl�cP þ ðN þ tÞkscthexp �kspl� ðN þ tÞkscth

�cP

� �#

:

ð22Þ

In these networks, by using the K-th best order statistics, Pr W2jc\cth� �

is given by

FWbdðxÞ ¼

XK

t¼1

N

t � 1

� �ðFWzt d

ðxÞÞN�tþ1ð1� FWzt dðxÞÞt�1: ð23Þ

By using the results obtained in (4) and (23), we can express PH;out2 by (24).

PH;out2 ¼

XM

N¼K

M

N

� �"

ð1� expð�ksplÞÞ expð�Nkscth=�cPÞð1� expð�kscth=�cPÞÞM�N :

þXM�N

t¼0

�1ð Þt M � N

t

� �kspl�cP

kspl�cP þ N þ tð Þkscthexp � ksplþ N þ tð Þkscth=�cP

� �� #

XK

t¼1

N

t � 1

� �1� expð�kd

cth�cPÞ þ kdcth

kdcth þ kpl�cPexpð�kp

cth�cP

� kplÞ� �N�tþ1

exp �kdcth�cP

� �þ kdcthkdcth þ kpl�cP

exp �kdcth�cP

� kpl

� �� t�1

:

ð24Þ

Finally, by adding either Pout1 and Pout

2 or PH;out1 and P

H;out2 , we obtain a closed-form

expression for the outage probability. To see an asymptotic outage diversity gain, we will

make an asymptotic outage probability analysis next.

D.-B. Ha et al.

123

3.1.4 Asymptotic Outage Probability

We shall derive the expressions of Pout in the high qP region. By choosing only first two

terms of Maclaurin expansion series for g(x) a function of x, we have

gðxÞ x!0�g 0ð Þ þ og

oxjx¼0

x. Applying this result for expð�xÞ, we obtain expð�xÞ x!0

�1� x

and 1� expð�xÞ x!0�1. Thus, at a very high �cP value, i.e., �cP ! þ1 (or qP ! 0), we can,

respectively, obtain asymptotic (25) and (26) from (14) and (15) as follows

V1 �qp!0

1� exp �kspl� �� YM

t¼Nþ1

ksjt

!

qM�NP ; ð25Þ

V2 �qp!0

kspYM

t¼Nþ1

ksjt

!qPl

� �M�NZ þ1

lxM�N exp �kspx

� �dx

¼YM

t¼Nþ1

ksjt

!

C M � N þ 1; kspl� � qP

kspl

� �M�N

;

ð26Þ

where Cða; xÞ ¼Rþ1x

xa�1 exp �xð Þdx denotes the incomplete gamma function [26]. Sim-

ilarly, an asymptotic CDF of Wid is given by

FWidðxÞ �

qp!0

kid þkid expð�kipuÞ

kipl

� �x

�cP; ð27Þ

which results in the asymptotic PDF of Wid in the following form

fWidðxÞ �

qp!0

kid þkid exp �kipu

� �

kipl

� �1

�cP: ð28Þ

Now using Eqs. (27) and (28), we can first obtain

Pr Wbd\cthð Þ �qp!0X

c¼1

N

jc¼b

X

W1;W2

kbd þkbd expð�kbpuÞ

kbpl

� �1

�cP

� �N�Kþ1

�YN

v¼Kþ1

kzvd þkzvd exp �kzvpl

� �

kzvpu

� �Z cth

0

xN�Kdx;

ð29Þ

which becomes

PrðWbd\cthÞ �qp!0X

c¼1

N

jc¼b

kbd þkbd expð�kbplÞ

kbpl

� �

�X

W1;W2

YN

v¼Kþ1

kzvd þkzvd expð�kzvplÞ

kzvpl

� �qN�Kþ1P

N � K þ 1:

ð30Þ

Theorem 1 Using Eqs. (25) and (26), and (30), asymptotic outage probabilities for non-

homogeneous and homogeneous networks are, respectively, given by


123

~Pout ��cp!1

ðD1 þ D2Þcth�cP

� �M�Kþ1

;

~PH;out ��cp!1

ðD3 þ D4Þcth�cP

� �M�Kþ1

;

ð31Þ

where we define

D1 ¼MX

Q1;Q2

N\K

XM

t¼K

ksjt

!

qPð ÞM�Kþ11� expð�ksplÞ þ

CðM � K þ 2; ksplÞðksplÞM�Kþ1

!

;

D2 ¼MX

Q1;Q2

N �K

XM

t¼Nþ1

ksjt

!

qPð ÞM�Kþ11� expð�ksplÞ þ

C M � N þ 1; kspl� �

kspl� �M�N

!

�X

c¼1

N

jc¼b

kbd þkbd exp �kbpuð Þ

kbpu

� �

N � K þ 1

X

W1;W2

YN

v¼Kþ1

kzvd þkzvd expð�kzvpuÞ

kzvpl

� �;

D3 ¼MM

K � 1

� �� 1� exp �kspl

� �� ksð ÞM�Kþ1 þ CðM � K þ 2; ksplÞ ks=kspl

� �M�Kþ1h i

;

D4 ¼MXM

N¼k

ð1� expð�ksplÞÞ ksð ÞM�N þ CðM � N þ 1; ksplÞ ks=kspl� �M�N

h i:

From (31), we can see that the outage diversity gain is Gd ¼ M � K þ 1.

Proof A proof of this theorem is provided in ‘‘Appendix’’.

Note that from Theorem 1, Gd is in the range of [1, M].

3.1.5 Ergodic Channel Capacity

The channel capacity of the proposed protocol can be expressed as

C Wbdð Þ ¼0; if N\K;

1

2log2ð1þWbdÞ; if N�K:

(

ð32Þ

From (32), the average channel capacity can be formulated as

Cavg ¼1

2 logð2ÞX

Q1;Q2

N�K

PrðWsj1 � cth; . . .;WsjN � cth;WsjNþ1\cth; . . .;WsjM\cthÞ

�Z 1

0

logð1þ xÞfWbdðxÞdx:

ð33Þ

Combining results obtained in (10) and (19), the exact expression of (33) is given by (34)

(see the top of next page).

D.-B. Ha et al.

123

Cavg ¼1

2 logð2ÞX

Q1;Q2

N�K

1� expð�ksplÞ� �YN

t¼1

exp �ksjtcth�cP

� � YM

t¼Nþ1


� �� "

þ kspl�cPkspl�cP þ

PNt¼1 ksjtcth

exp �kspl�XN

t¼1

ksjtcth�cP

!

þXM�N

v¼1

X

j1;...;jv¼Nþ1

M

j1\...\jv


t¼1 ksjt þPv

l¼1 ksjl� �

cth=�cP� �

kspl�cP þPN

t¼1 ksjt þPv

l¼1 ksjl� �

cth

#

�X

c¼1

N

jt¼b

X

W1;W2

Z 1

0

logð1þ xÞ kbd�cP

exp � kbd�cP

x

� �þkbdkbpl�cP exp � kbd

�cPx� kbpl

kbdxþ kbpl�cP� �2

2

4

� kbd�cP

kbdx exp � kbd�cPx� kbpl

kbdxþ kbpl�cP

3

5YK�1

v¼1

exp � kzvd�cP

x

� ��kzvdx exp � kzvd

�cPx� kzvdl

kzvdxþ kzvdl�cP

2

4

3

5

YK�1

v¼1

exp � kzvd�cP

x

� ��kzvdx exp � kzvd

�cPx� kzvpl

kzvdxþ kzvpl�cP

2

4

3

5dx:

ð34Þ

3.2 Secrecy Performance of Cognitive Relay Network with Eavesdropper

In the considered network, we assume that an eavesdropper E appears and attempts to

overhear the data transmitted from the relays. We assume that the eavesdropper is far the

source and hence it cannot listen the data transmission from this node.

Similar as above, we can express the channel capacity of the data link between the

selected relay Rb to the destination D as

Cbd ¼1

2log2ð1þWbdÞ: ð35Þ

For the eavesdropper link, the channel capacity from Rb to E can be given as

Cbe ¼1

2log2ð1þWbeÞ; ð36Þ

where wbe ¼ min cP; cI=cbp� �

cbe.Combining (35) and (36), the secrecy capacity can be defined as [27]:

CSec ¼ maxðCbd � Cbe; 0Þ

¼ max1

2log2

1þWbd

1þWbe

� �; 0

� �:

ð37Þ

Moreover, as discussed above, the considered system can select a relay for the cooperation

as Pr N�Kð Þ. Hence, the average secrecy capacity can be given as

CavgSec ¼ Pr N�Kð ÞE CSecf g; ð38Þ


123

where Eð:Þ is the expected operator.

Since it is difficult to obtain the exact expression of the average secrecy rate CavgSec , we

attempt to obtain an asymptotic one in case that the primary user is far the secondary

network. Indeed, in this case, we have the approximations as follows: wbd � cPcbd and

wbe � cPcbe, and the secrecy capacity in (37) can be approximated by

CSec � max1

2 log 2ð Þ log1þ cPcbd1þ cPcbe

� �; 0

� �: ð39Þ

Before calculating the average secrecy rate, we must find the CDF of the random variable

Z, i.e., Z ¼ 1þcPcbd1þcPcbe

. Indeed, the CDF FZ zð Þ, z� 1, can be formulated as

FZ zð Þ ¼ Pr Z\zð Þ ¼ Pr cbd\z� 1

cPþ zcbe

� �

¼Z þ1

0

Fbd

z� 1

cPþ zy

� �fcbe yð Þdy:

ð40Þ

Here, we again consider two cases: non-homogeneous network and homogeneous network.

3.2.1 Non-homogeneous Networks

In non-homogeneous networks, the CDF FbdðxÞ in (40) can be calculated similarly to (7) as

Fbd xð Þ ¼X

c¼1

N

jc¼b

Z x

0

kbd exp �kbdyð Þ 1� FT1 yð Þð ÞFT2 yð Þdy; ð41Þ

where T1 ¼ min cz1d; . . .; czK�1d

� �, T2 ¼ max czKþ1d

; . . .; czNd� �

, and their CDFs can be

respectively expressed by

FT1 yð Þ ¼ 1� exp �XK�1

v¼1

kzvdy

!

;

FT2 yð Þ ¼YM

v¼Kþ1

1� exp �kzvdyð Þð Þ

¼ 1þXM�K

j¼1

�1ð ÞjX

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

exp �Xj

k¼1

kzik dy

!

:

ð42Þ

Substituting (42) into (41), and after some manipulation, we can obtain

Fbd xð Þ ¼X

c¼1

N

jc¼b

kbdx1

1� exp �x1xð Þð Þ

þX

c¼1

N

jc¼b

XM�K

j¼1

�1ð ÞjX

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

kbdx2

1� exp �x2xð Þð Þ;ð43Þ

where x1 ¼ kbd þPK�1

v¼1

kzvd and x2 ¼ x1 þPj

k¼1

kzik d .

D.-B. Ha et al.

123

Plugging (40), (43) and fcbe yð Þ ¼ kbe exp �kbeð Þ together, the CDF FZ zð Þ can be given as

FZ zð Þ ¼X

c¼1

N

jc¼b

kbdx1

� kbdx1

:kbe exp x1=cPð Þ

kbe þ x1zexp �x1z

cP

� ��

þX

c¼1

N

jc¼b

XM�K

j¼1

�1ð ÞjX

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

kbdx2

� kbdx2

:kbe exp x2=cPð Þ

kbe þ x1zexp �x2z

cP

� �� :

ð44Þ

Moreover, the average secrecy capacity can be expressed under the following expression:

CavgSec �

Pr N�Kð Þ2 log 2ð Þ

Z þ1

1

log zð ÞfZ zð Þdz

� Pr N�Kð Þ2 log 2ð Þ

Z þ1

1

1� FZ zð Þz

dz:

ð45Þ

Substituting (44) into (45), we can rewrite CavgSec as follow

CavgSec �

Pr N �Kð Þ2 log 2ð Þ

�

P

c¼1

N

jc¼b

x1 exp kbd=x1ð Þkbd

Z þ1

1

1

z� 1

kbex1=kbd þ z

� �exp � kbd

x1

z

� �dz

þP

c¼1

N

jc¼b

PM�K

j¼1

�1ð ÞjP

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

x2 exp kbd=x2ð Þkbd

�Rþ11

1

z� 1

kbex2=kbd þ z

� �exp � kbd

x2

z

� �dz

8>>>>>>>>>>><

>>>>>>>>>>>:

9>>>>>>>>>>>=

>>>>>>>>>>>;

:

ð46Þ

Applying the following integral

Z þ1

1

exp �axð Þbþ x

dx ¼ exp abð ÞE1 1þ bð Það Þ;

for the corresponding integral in (46), we finally obtain

CavgSec � Pr N�Kð Þ

2 log 2ð Þ

�

P

c¼1

N

jc¼b

kbdx1

expx1

cP

� �E1

x1

cP

� �� exp

kbecP

� �E1 1þ kbe

x1

� �x1

cP

� ��

þP

c¼1

N

jc¼b

PM�K

j¼1

�1ð ÞjP

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

kbdx2

expx2

cP

� �E1

x2

cP

� �� exp

kbecP

� �E1 1þ kbe

x2

� �x2

cP

� ��

8>>>>>>>>>>><

>>>>>>>>>>>:

9>>>>>>>>>>>=

>>>>>>>>>>>;

;

ð47Þ

where a and b are positive numbers, and E1ð:Þ is the exponential integral function [26].


123

Then, by using the results Pr N�Kð Þ in (19), we can obtain an asymptotic expression of

CavgSec when the primary user is far the secondary system, as presented in (48).

CavgSec �

1

2 log 2ð ÞX

Q1;Q2

N�K

1� expð�ksplÞ� �YN

t¼1

exp �ksjtcth�cP

� � YM

t¼Nþ1


� �� "

þ kspl�cP

kspl�cP þPN

t¼1

ksjtcth

exp �kspl�XN

t¼1

ksjtcth�cP

!

þXM�N

v¼1

X

j1;...;jv¼Nþ1

M

j1\...\jv


t¼1 ksjt þPv

l¼1 ksjl� �

cth=�cP� �

kspl�cP þPN

t¼1 ksjt þPv

l¼1 ksjl� �

cth

3

775

�

P

c¼1

N

jc¼b

kbdx1

expx1

cP

� �E1

x1

cP

� �� exp

kbecP

� �E1 1þ kbe

x1

� �x1

cP

� ��

þP

c¼1

N

jc¼b

PM�K

j¼1

�1ð ÞjP

i1¼...¼ij¼Kþ1

M

i1 [ ...[ ij

kbdx2

expx2

cP

� �E1

x2

cP

� �� exp

kbecP

� �E1 1þ kbe

x2

� �x2

cP

� ��

8>>>>>>>>>>><

>>>>>>>>>>>:

9>>>>>>>>>>>=

>>>>>>>>>>>;

:

ð48Þ

3.2.2 Homogeneous Networks

In these networks, with ksi ¼ ks, kid ¼ kd, kip ¼ kp and kie ¼ ke for all i, with the same

manner, the approximate expression of E Csecf g is given as

E Csecf g � 1

2 log2

�

PK

j¼1

PN�Kþ1

i¼0

�1ð ÞiN

j� 1

� �N � jþ 1

i

� �exp iþ j� 1ð Þkd

cP

� �

E1 iþ j� 1ð ÞkdcP

� �� exp

kecP

� �E1 iþ j� 1ð Þ 1þ ke

iþ j� 1ð Þkd

� �kdcP

� ��

8>>><

>>>:

9>>>=

>>>;

:

ð49Þ

Moreover, from (24), we can obtain the probability Pr N�Kð Þ. Hence, the approximate

expression of the average secrecy capacity in the i.i.d. network can be given as in (50).

D.-B. Ha et al.

123

CavgSec �

1

2log2

XM

N¼K

M

N

� ��ð1� expð�ksplÞÞexpð�Nkscth=�cPÞð1� expð�kscth=�cPÞÞM�N :

þXM�N

t¼0

�1ð Þt M�N

t

� �kspl�cP

kspl�cPþ Nþ tð Þkscthexp � ksplþ Nþ tð Þkscth=�cP

� �� #

�

PK

j¼1

PN�Kþ1

i¼0

�1ð ÞiN

j�1

� �N� jþ1

i

� �exp iþ j�1ð Þkbd

cP

� �

E1 iþ j�1ð ÞkbdcP

� �� exp

kbecP

� �E1 iþ j�1ð Þ 1þ kbe

iþ j�1ð Þkbd

� �kbdcP

� ��

8>>><

>>>:

9>>>=

>>>;

:

ð50Þ

3.3 Performance Comparison

In this subsection, we compare the performance of our scheme with that of proactive relay

selection protocols. At first, we consider the amplify-and-forward relaying protocol using

partial relay selection (denoted by AF-PRS), which was proposed in [3]. In the AF-PRS

scheme, the K-th best relay is selected by [3, eq. (1)]:

Rb: csb ¼ Kth maxm¼1;2;...;M

csmð Þ: ð51Þ

By using [3, eq. (6)] and (1), the outage probability of this scheme can be calculated by

PAF�PRSout ¼ Pr

WsbWbd

Wsb þWbd þ 1\cth

� �: ð52Þ

Moreover, the outage probability of the DF protocol using the K-th partial relay selection

above [28] (denoted by DF-PRS) can be given by

PDF�PRSout ¼ Pr min Wsb;Wbdð Þ\cthð Þ: ð53Þ

Next, we introduce the opportunistic relay selection scheme (denoted by DF-ORS), in

which the K-th best relay is selected as [29, eq. (6)]:

Rc: min Wsc;Wcdð Þ ¼ Kth maxm¼1;2;...;M

min Wsm;Wmdð Þð Þ: ð54Þ

Then, the outage probability of the DF-ORS scheme is computed as

PDF�ORSout ¼ Pr min Wsc;Wcdð Þ\cthð Þ: ð55Þ

4 Numerical Results

In this section, we present Monte Carlo simulations to verify our derivations. In a two-

dimensional Oxy, we assume that the co-ordinates of the source, the destination, the relay,

the primary user and the eavesdropper are (0, 0), (1, 0), xRi; 0ð Þ, xP; yPð Þ and xE; yEð Þ,

respectively. Hence, the distances are calculated as dsi ¼ xR, did ¼ 1� xR,


123

dsp ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2P þ y2P

p, dip ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixR � xPð Þ2 þ y2P

qand die ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixR � xEð Þ2 þ y2E

q. In all of the sim-

ulations, we assume the path-loss exponential b equals 3 and the ratio l between Ith and Pth

equals 1.

In Fig. 1, we present the outage probability as a function of �cP in dB. In this simulation,

the number of relays M equals to 3, the co-ordinates xRiof relays are 0.2, 0.4 and 0.6, and

the positions of the primary user are (0.5, 0.5). It can be seen from this figure that the

outage performance is best when the system can select the best relay to help the source

forward the data to the destination. Figure 2 illustrates the outage probability as a function

of �cP in dB in the i.i.d. network with xRi¼ 0:4, xP ¼ yP ¼ 0:4 and K ¼ 1. It can be

observed that the outage performance is better when increasing the number of relays M.

From Figs. 1 and 2, we can see that the simulation results (Ex) match very well with the

theoretical results (An and As), which validates our derivations. Moreover, it is also seen

that the diversity order obtained equals to M � K þ 1.

Figure 3 compares the outage performance of the proposed protocol with that of the

AF-PRS, DF-PRS and the DF-ORS protocols in the i.i.d. network when xRi¼ 0:5,

xP ¼ 0, yP ¼ 0:5, cth ¼ 1:5, M ¼ 4 and K ¼ 2. It is seen that the proposed protocol out-

performs two partial relay selection protocols, i.e., AF-PRS and DF-PRS, because it

obtains higher diversity gain. Moreover, we can observe from this figure that the DF-ORS

protocol provides the best performance, but it has the same diversity slope with our

scheme.

0 2 4 6 8 10 12 14 16 18 2010−6

10−5

10−4

10−3

10−2

10−1

100

101

γP [dB]

Out

age

Pro

babi

lity

Ex [K=3]An [K=3]As [K=3]Ex [K=2]An [K=2]As [K=2]Ex [K=1]An [K=1]As [K=1]

Fig. 1 The outage probability as a function of �cP in dB when xRi2 0:2; 0:4; 0:6f g, xP ¼ yP ¼ 0:5, cth ¼ 1

and M ¼ 3

D.-B. Ha et al.

123

In Fig. 4, we investigate the impact of the position of the primary user on the average

channel capacity. In this figure, we fix the parameters as follows: M ¼ 2, and xRi2

0:4; 0:6f g and K ¼ 1. It can be seen that the performance of the considered scheme

significantly enhances when the primary user is far the secondary network (xP and yP are

high).

In Figs. 5, 6 and 7, we present the average secrecy capacity of the proposed scheme

when there exists the eavesdropper in the network. In Fig. 5, we place the the primary user

at different positions and observe the impact of the primary user’s position on the secrecy

performance. In particular, we change the values of xP and yP (xP ¼ yP) from 0.2 to 5,

while fixing the parameters M, cth, yE, xE and cP by 4, 0.75, 1, 0.5 and 5 dB, respectively.

Similar to the results presented in Fig. 1, the secrecy performance of the proposed scheme

is better when the system can select the better relay for the cooperation. Furthermore, the

secrecy capacity increases with the increasing of xP and yP. However, the secrecy capacity

converges to a positive constant at the high xP (yP) value. It is because that the impact of

the primary network on the performance of the secondary network can be relaxed when

the distance between two networks is high. In Figs. 6 and 7, we verify our derivations by

placing the primary user far the secondary network. We can observe from these fig-

ures that the simulation (Ex) and theoretical (As) results are in a good agreement.

Moreover, it can be observed from Fig. 7 that the secrecy performance significantly

enhances when the distance between the relays and the eavesdropper increases (yEincreases).

0 5 10 15 20 2510

−6

10−5

10−4

10−3

10−2

10−1

100

101

γP [dB]

Out

age

Pro

babi

lity

Ex [M=1]An [M=1]As [M=1]Ex [M=2]An [M=2]As [M=2]Ex [M=3]An [M=3]As [M=3]

Fig. 2 The outage probability as a function of �cP in dB when xRi¼ 0:4, xP ¼ yP ¼ 0:4, cth ¼ 1 and K ¼ 1


123

0 5 10 1510−4

10−3

10−2

10−1

100

γP [dB]

Out

age

Pro

babi

lity

Ex [AF−PRS]Ex [DF−PRS]Ex [DF−ORS]Ex [Proposed Protocol]An

Fig. 3 The outage probability as a function of �cP in dB when xRi¼ 0:5, xP ¼ 0, yP ¼ 0:5, cth ¼ 1:5, M ¼ 4

and K ¼ 2

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

γP [dB]

Erg

odic

Cap

acity

Ex [PU=[0.2 0.2]]An [PU=[0.2 0.2]]Ex [PU=[0.4 0.4]]An [PU=[0.4 0.4]]Ex [PU=[0.6 0.6]]An [PU=[0.6 0.6]]Ex [PU=[0.8 0.8]]An [PU=[0.8 0.8]]

Fig. 4 The average capacity as a function of �cP in dB when xRi2 0:4; 0:6f g, M ¼ 2 and K ¼ 1

D.-B. Ha et al.

123

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

xP

(yP

)

Sec

recy

Cap

acity Ex [K=1]

Ex [K=2]Ex [K=4]

Fig. 5 The secrecy capacity as a function of xPðyPÞ when xRi2 0:2; 0:4; 0:6; 0:8f g, M ¼ 4, cth ¼ 0:75,

yE ¼ 1, xE ¼ 0:5 and cP ¼ 5dB

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

γP [dB]

Sec

recy

Cap

acity Ex [K=1]

Ex [K=2]Ex [K=3]As

Fig. 6 The secrecy capacity as a function of �cP in dB when xRi2 0:3; 0:5; 0:7f g, M ¼ 3, cth ¼ 0:75,

yE ¼ 1, xE ¼ 0:5 and xP ¼ yP ¼ 20


123

5 Conclusions

In this paper, the system performance and the secrecy performance of the cooperative relay

networks with K-th best reactive DF relay selection strategy were evaluated. In particular,

we derived the exact expressions for outage probability and ergodic capacity in homo-

geneous and non-homogeneous networks. Furthermore, with the presence of the eaves-

dropper in the considered network, the secrecy performance of the cooperative hop has

been evaluated, in terms of the average secrecy capacity. Finally, computer simulations

have been provided to validate our analysis. The results presented that the performances of

CR significantly depend on the number of relays, the K-best relay selection as well as the

position of the primary user and eavesdropper.

Acknowledgments This research is funded by Vietnam National Foundation for Science and TechnologyDevelopment (NAFOSTED) under Grant Number 102.04-2013.13.

Appendix: A Detailed Derivation of (31)

Using Eqs. (25), (26), and (30), the corresponding asymptotic outage probability of (17) is

given by

~Pout1 �

qp!0 X

Q1;Q2

N\K

YM

t¼K

ksjt ðqPÞM�Kþ1

� 1� expð�ksplÞ þCðM � K þ 2; ksplÞ

ðksplÞM�Kþ1

!

:

ð56Þ

Using again Eqs. (56) and (30) for (19), we get (57) as

0 2 4 6 8 10 12 14 16 18 200.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

γP [dB]

Sec

recy

Cap

acity

Ex [yE

=0.2]Ex [y

E=0.5]

Ex [yE

=1]As

Fig. 7 The secrecy capacity as a function of �cP in dB when xR ¼ 0:5, M ¼ 4, K ¼ 2, cth ¼ 0:5, xE ¼ 1 andxP ¼ yP ¼ 15

D.-B. Ha et al.

123

~Pout2 �

qp!0 X

Q1;Q2

N �K

YM

t¼Nþ1

ksjt 1� exp �kspl� �

þC M � N þ 1; kspl� �

kspl� �M�N

!

�X

c¼1

N

jt¼b

1

N � K þ 1kbd þ

kbd exp �kbpl� �

kbpl

� �

�X

W1;W2

YN

v¼Kþ1

kzvd þkzvd expð�kzvplÞ

kzvpl

� �qM�Kþ1P :

ð57Þ

Thus, combining (56) and (57), we can obtain ~Pout. Similarly, an asymptotic expression for~PH;out in the homogeneous networks can be readily computed as ~PH;out in (31).

References

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Dac-Binh Ha received the B.S. degree in Radio Technique, the M.Sc.and Ph.D. degree in Communication and Information System fromHuazhong University of Science and Technology (HUST), China in1997, 2006, and 2009, respectively. He is currently the dean of Facultyof Electrical and Electronics Engineering, Duy Tan University, DaNang, Vietnam. During 1997–2001, he worked for Center of TelecomTechnology, Vietnam. From 2001 to 2003, he joined the Faculty ofElectrical and Electronics Telecommunications Engineering of Ho ChiMinh City University of Transport, Vietnam. He is the recipient of theChinese Government Distinguished International Students Scholarship.His research interests are secrecy physical layer communications,MIMO systems, combining techniques, cooperative communications,cognitive radio, and image processing. Dr. Ha is a member of theInstitute of Electrical and Electronics Engineers (IEEE). He is arecipient of the Best Paper Award at the 2014 IEEE InternationalConference on Computing, Management and Telecommunications.

D.-B. Ha et al.

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http://dx.doi.org/10.1109/TVT.2014.2358624

http://dx.doi.org/10.1109/TVT.2014.2358624

Tung Thanh Vu received the B.Sc. degree in Telecommunicationsand Networking from the Ho Chi Minh City University of Science in2012. He is pursuing his M.Sc. degree in Telecommunications Engi-neering at the Ho Chi Minh City University of Technology. His currentresearch interests include cognitive ratio networks, cooperative net-works, physical layer security, interference alignment and optimizationdesign.

Tran Trung Duy was born in Nha Trang city, Vietnam, in 1984. Hereceived the B.E. degree in Electronics and TelecommunicationsEngineering from the French-Vietnamese training program for excel-lent engineers (PFIEV), Ho Chi Minh City University of Technology,Vietnam in 2007. In 2013, he received the Ph.D. degree in electricalengineering from University of Ulsan, South Korea. In 2013, he joinedthe Department of Telecommunications, Posts and Telecommunica-tions Institute of Technology (PTIT), as a lecturer. His major researchinterests are cooperative communications, cognitive radio, and physi-cal layer security.

Vo Nguyen Quoc Bao was born in Khanh Hoa, Vietnam, in 1979. Hereceived the B.E. and M.Eng. degree in electrical engineering from HoChi Minh City University of Technology (HCMUT), Vietnam, in 2002and 2005, respectively, and Ph.D. degree in electrical engineering fromUniversity of Ulsan, South Korea, in 2010. In 2002, he joined theDepartment of Electrical Engineering, Posts and TelecommunicationsInstitute of Technology (PTIT), as a lecturer. Since February 2010, hehas been with the Department of Telecommunications, PTIT, where heis currently an Assistant Professor. His major research interests aremodulation and coding techniques, MIMO system, combining tech-nique, cooperative communications and cognitive radio. Dr. Bao is aMember of Korea Information and Communications Society (KICS),The Institute of Electronics, Information and Communication Engi-neers (IEICE) and the Institute of Electrical and Electronics Engineers(IEEE).


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Secure Cognitive Reactive Decode-and-Forward Relay Networks: With and Without Eavesdropper

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