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Cooperative Beamforming and User Selection for Improving theSecurity of Relay-aided Systems
Hoang, T. M., Duong, T. Q., A. Suraweera, H., Tellambura, C., & Poor, H. V. (2015). Cooperative Beamformingand User Selection for Improving the Security of Relay-aided Systems. IEEE Transactions on Communications,63(12), 5039 - 5051. https://doi.org/10.1109/TCOMM.2015.2494012
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Download date:16. Aug. 2019
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Cooperative Beamforming and User Selection forImproving the Security of Relay-aided Systems
Tiep M. Hoang, Trung Q. Duong, Senior Member, IEEE, Himal A. Suraweera, Senior Member, IEEE, ChinthaTellambura, Fellow, IEEE, and H. Vincent Poor, Fellow, IEEE
Abstract—A relay network in which a source wishes to conveya confidential message to a legitimate destination with the assis-tance of trusted relays is considered. In particular, cooperativebeamforming and user selection techniques are applied to protectthe confidential message. The secrecy rate (SR) and secrecyoutage probability (SOP) of the network are investigated first,and a tight upper bound for the SR and an exact formula for theSOP are derived. Next, asymptotic approximations for the SR andSOP in the high signal-to-noise ratio (SNR) regime are derived fortwo different schemes: i) cooperative beamforming and ii) multi-user selection. Further, a new concept of cooperative diversitygain, namely, adapted cooperative diversity gain (ACDG), whichcan be used to evaluate security level of a cooperative relayingnetwork, is investigated. It is shown that the ACDG of cooperativebeamforming is equal to the conventional cooperative diversitygain of traditional multiple-input single-output networks, whilethe ACDG of the multiuser scenario is equal to that of traditionalsingle-input multiple-output networks.
Index terms—Physical layer security, decode-and-forwardrelays, cooperative diversity, cooperative beamforming, largescale relaying.
I. INTRODUCTION
The broadcasting aspect of wireless networks makes themvulnerable to malicious attacks of adversaries. In order tothwart such attacks, wireless security has traditionally reliedon data encryption and decryption algorithms at many layersof the open systems interconnection (OSI) reference model,e.g., [1], [2]. Alternatively, an information-theoretic approachto physical layer security (PLS) exploits the random fadingof wireless channels. Although PLS was first introduced by
Manuscript received April 22, 2015; revised July 27, 2015; acceptedOctober 6, 2015. The editor coordinating the review of this paper andapproving it for publication was Dr. Jinhong Yuan.
This work was supported in part by the U.K. Royal Academy of Engi-neering Research Fellowship under Grant RF1415\14\22 and by the NewtonInstitutional Link under Grant ID 172719890. The work of H. V. Poor wassupported in part by the U.S. National Science Foundation under GrantCMMI-1435778. This paper has been presented in part at the IEEE GlobalCommunications Conference, San Diego, CA, December 2015.
T. M. Hoang is with Duy Tan University, Da Nang 550000, Vietnam (e-mail: [email protected]).
T. Q. Duong is with the School of Electronics, Electrical Engineering andComputer Science, Queen’s University Belfast, Belfast BT7 1NN, UK (e-mail:[email protected]).
H. A. Suraweera is with the Department of Electrical and ElectronicEngineering, University of Peradeniya, Peradeniya 20400, Sri Lanka (e-mail:[email protected]).
C. Tellambura is with the Department of Electrical and Computer Engi-neering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada (e-mail:[email protected]).
H. V. Poor is with the Department of Electrical Engineering, PrincetonUniversity, Princeton, NJ 08544, USA (e-mail: [email protected]).
Wyner in his seminal work [3] many years ago, only recentlythat it has attracted the wide attention of the academic andindustrial research community in wireless communications.The emergence of PLS has certainly created the need for newsignal processing methods, channel modeling, and commu-nication designs. From the information-theoretic perspective,the secrecy guarantee of wireless networks in the presence ofeavesdroppers mainly relies on a metric called the secrecy rate(SR), which is the capacity difference between the legitimatechannel, i.e., that of intended user, and malicious channel, i.e.,that of eavesdropper [4].
To deal with the vulnerability of malicious attacks fromeavesdroppers, numerous studies have been conducted, e.g.,[5]–[7] and references therein. These studies cover manydifferent system models of wireless networks such as co-operative wiretap channels (e.g., [7]–[24]), wiretap channelswithout cooperative nodes (e.g., [6], [25]), and cognitive radionetworks (e.g., [5]). However, relays allow the benefits ofrange extension and distributed diversity, and thus there is alsoa great deal of interest in the exploitation of cooperative nodesfor PLS. Node cooperation in cooperative wireless networks(CWNs) is thus an effective way to improve PLS [7]–[11]. Itallows single antenna nodes to enjoy the benefits of multiple-antenna systems and is an attractive low cost solution. Sofar, a variety of techniques have been offered to guaranteereliable transmission via CWNs; for instance, relay selectiontechniques [9]–[15] and jamming methods [9], [10], [16]–[18].Meanwhile, the design of beamforming techniques for commu-nication reliability via CWNs has been also considered in [9]–[11] and [15]–[22]. In addition, there are attempts to proposehybrid schemes combining different techniques, for instance,there is the combination between relaying for retransmissionand jamming for eavesdropping attacks in [22] and [23].Furthermore, it is interesting that in [20], the security issue isalso discussed for a large scale multiple-input multiple-output(MIMO) relaying system to get insight into the limitationsof PLS when the number of relays approaches infinity. Inshort, the proposed schemes for improving the security levelin CWNs are relatively diverse. Among the above-mentionedworks on PLS in CWNs, closely related to our work are thecontributions in [19]–[22]. We use cooperative beamformingor user selection techniques for security enhancement, whereas[19]–[21] do not account for multiple users. It is also notedthat there are other system models in [24]–[26] similar to ourwork. However, [24] does not discuss multiple users, while[25] does not use cooperative nodes, and [26] does not takesecurity issue into account. Moreover, [22] and [25] consider
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either cooperative beamforming or user selection only. Tothe best of the authors’ knowledge, previous works have notinvestigated the impact of both cooperative beamforming anduser selection on the security level of multiuser cooperativerelaying networks. We are therefore motivated to examine thesecurity level of such networks when cooperative beamformingis applied in parallel with user selection.
To evaluate the secure performance of a CWN, typicalmetrics such as secrecy rate (SR) [8]–[10] and secrecy outageprobability (SOP) [11], [13]–[15], [20] are usually considered.Besides these two metrics, there is also another metric used toqualify the secure performance in the literature [12], whichis defined in a similar way to traditional diversity gain. Itis well known that traditional space/time/frequency diversitytechniques are not concerned with security issues [27]. Assuch, the concept of traditional diversity gain seems inap-propriate for studying security aspects of wireless networks.To help quantify the secure performance, [12] first introducedthe notion of intercept event (i.e., when SR is negative), andthen presented a new concept of cooperative diversity gain(we shall call it adapted cooperative diversity gain (ACDG)),which relies on the intercept probability of the intercept event.To be more precise, the ACDG defines the rate of decrease ofthe intercept probability with the increase of relative channelpower gain of destination on a log-log scale. This new conceptreveals that the secure performance increases with the ACDG.Due to the similarity of the ACDG to the conventional notionof diversity as well as the relevance of the ACDG to securenetworks, we are motivated to examine it thoroughly.
In this paper, we evaluate the secure performance of a CWNin the presence of an eavesdropper. We divide our systemmodel into two scenarios, namely, i) a system model witha single relay and multiple users, and ii) a system model withmultiple relays and a single user. In both cases, the presenceof an eavesdropper, which is another known user but not adesired destination, is assumed. The first case corresponds toa virtual SIMOSE (i.e., single-input multiple-output channelin the presence of a single eavesdropper), then the secondscenario is seen as virtual MISOSE (i.e., multiple-input single-output in the presence of a single eavesdropper). Finding exactexpressions for the ergodic SRs for the general case of multiplerelays and multiple destinations is difficult. To circumventthis difficulty, we derive upper bounds on the quantities andasymptotic expressions at high transmit power. In addition,we analyze the ergodic SR of the proposed network for thecase of large numbers of relays. We then derive the SOPs forthe SIMOSE and the MISOSE cases. Finally, we borrow theconcept of [12] to introduce the ACDG, and thereby quantifythe secure performance of the proposed system. Furthermore,we show that the ACDG of a virtual SIMOSE (or MISOSE)system is equal to the diversity gain of a SIMO (or MISO)system. In particular, the ACDG reveals it is more compatiblewith secure networks than conventional diversity gain becausesecurity is taken into account.
The remainder of this paper is organized as follows. SectionII describes a CWN with multiple relays, multiple destinations,and a single eavesdropper. In Section III, we present upperbounds on the ergodic SR and its approximation at high
S
E
1
R
M
R
m
R
n
D
1
D
N
D
Fig. 1. System model of a relay network consisting of a source, a set Rof M relays, a set D of N users, and an eavesdropper. Each terminal isequipped with a single-antenna. R performs cooperative beamforming, whileD exploits user selection.
transmit power. Moreover, we analyze the ergodic SR of theproposed system with very large numbers of relays. In SectionsIV and V, the SOPs and the ACDGs are respectively derived.Some numerical examples are presented in Section VI, andconclusions are drawn in VII.
Notation: [·]T and [·]† denote the transpose operator andHermitian operator, respectively. ∥ · ∥ denotes the Euclideannorm. E · denotes expectation. CN (µµµ,Σ) denotes the com-plex Gaussian distribution with mean µµµ and covariance matrixΣ. Exp (r) denotes the exponential distribution with rate r.Erl (k, r) denotes the Erlang distribution with shape k andrate r. The functions En(z) and 2F1(a, b; c; z) denote theexponential integral function of order n [28, Eq. (5.1.4)] andthe hypergeometric function [29, Eq. (9.14.2)], respectively.
II. SYSTEM MODEL
As shown in Fig. 1, we consider a cooperative relay networkconsisting of a single source, a set of M trusted relays, a set ofN destinations, and one eavesdropper. All the nodes are single-antenna devices operating in the half-duplex mode. For nota-tional simplicity, let S represent the source, Rm represent themth relay (m = 1, . . . ,M), Dn represent the nth destination(n = 1, . . . , N), and E represent the eavesdropper. Also, letR = R1, . . . ,RM represent the set of all relays preselectedfor forwarding the source signal, and D = D1, . . . ,DNrepresent the set of all destinations. We assume that both D andE are far enough from S but close enough to R so that theyare only capable of receiving the signal retransmitted from R.Additionally, the channel state information of the R-Dn link aswell as the R-E link is assumed to be available at R (e.g., [9]–[11]). Next, we assume that each relay Rm ∈ R is successfulin demodulating and decoding the signal received during thefirst time slot (i.e., the DF protocol [30]), and all relays (i.e.,the set R) perform collaborative beamforming (e.g., see [19],[22], [24] and [31]). R then forwards a weighted version ofthe retransmitted signal to D during the second time slot. Theretransmitted signal is also intercepted by the malicious node
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E. Thus, the signals received at a certain Dn and E during thesecond time slot are, respectively, given by
yDn =√PRwhRDnx+ nDn , (1)
yE =√PRwhREx+ nE , (2)
where x is the signal retransmitted by R (assuming thatEx = 0 and E
|x|2
= 1), w = [w1, . . . , wM ] is thebeamforming vector, hRDn = [hR1Dn , . . . , hRMDn ]
T is theR-Dn channel gain vector, and hRE = [hR1E , . . . , hRME ]
T
is the R-E channel gain vector, nDn is additive white Gaussiannoise (AWGN) at Dn, and nE is AWGN at E. Note thathRmDn ∼ CN (0,ΩRD), hRmE ∼ CN (0,ΩRE), nD ∼CN (0, N0), and nE ∼ CN (0, N0).
To proceed, we assume that all relays in R collaborate witheach other to design the beamforming vector w. Meanwhile,all destinations in D also collaborate to select a certainDn as a representative of D in order to receive the signalfrom R. Admittedly, the integration of these two cooperativetechniques will help improve significantly the security levelof the proposed system thanks to the increase in diversity atR and D. Regarding the use of the beamforming scheme, thebeamforming vector w is designed according to the channelbetween R and D∗, in which D∗ is the selected D that has thestrongest link between R and itself. Mathematically, we have
D∗ = arg maxDn∈D
∥hRDn∥2, (3)
∥hRD∗∥2 = maxDn∈D
∥hRDn∥2, (4)
w = h†RD∗/∥hRD∗∥. (5)
Let Θ be the instantaneously received SNR at D∗ for thesignal retransmitted by R in the second time slot. We obtainfrom (1) that
Θ = γR|whRD∗ |2 = γR∥hRD∗∥2 (6)
where γR = PR/N0. Let Xn = γR∥hRDn∥2 =∑Mm=1 γR|hRmDn |2 be a sum of independent and identi-
cally distributed (i.i.d.) exponential variables, then Xn ∼Erl(M, 1
γRΩRD
). By definition of Θ, we have Θ =
maxn=1,...,N Xn. Thus, the cumulative distribution function(CDF) and the probability density function (PDF) of Θ canbe readily deduced from [32] as follows:
FΘ(θ) =
[1−
M−1∑m=0
e− θγRΩRD
m!
(θ
γRΩRD
)m]N
, (7)
and
fΘ(θ) = N
[1−
M−1∑m=0
e− θγRΩRD
m!
(θ
γRΩRD
)m]N−1
×
[M−1∑m=0
(θ
γRΩRD−m
)e− θγRΩRD
m!
θm−1
(γRΩRD)m
].
(8)
Similarly, let Φ be the instantaneously received SNR at theeavesdropper for the signal retransmitted by R in the secondtime slot. We obtain from (2) that
Φ =
(√γRh
†REhRD∗
∥hRD∗∥
)(√γRh
†RD∗hRE
∥hRD∗∥
)︸ ︷︷ ︸
Z
= |Z|2. (9)
It is apparent that SNR appears in (9) as a function of tworandom vectors hRD∗ and hRE . Conditioning on hRD∗ , wehave
Z |hRD∗ ∼ CN
(0,
√γRh
†RD∗
∥hRD∗∥ΩREI
√γRhRD∗
∥hRD∗∥
)⇔ Z |hRD∗ ∼ CN (0, γRΩRE) (10)
leading to Φ |hRD∗ ∼ Exp(
1γRΩRE
)as a result. 1 Note that
Φ |hRD∗ is equivalent to Φ |Θ and Θ is a function of hRD∗
only. Thus, we shall use Φ |Θ in place of Φ |hRD∗ .
III. ERGODIC SECRECY RATE
In this section, we will study the ergodic SR for the systemproposed in Section II. However, analyzing the general casewith M ≥ 2 and N ≥ 2 is difficult. In order to simplifyour analysis, we shall mainly examine the following threescenarios:
• SIMOSE: M = 1 and N ≥ 2.• MISOSE: M ≥ 2 and N = 1.• Large scale MIMOSE: M → ∞ and finite N .
For the first two cases, we derive tight upper bounds as wellas asymptotic expressions for the ergodic SR. Moreover, exactexpression for the ergodic SR is found in the third case.
In order to proceed, we first recall that the channel capacitiesof the links R-D∗ and R-E in nat/s/Hz are, respectively, givenby
CD∗ = ln (1 + Θ) , (11)CE = ln (1 + Φ) . (12)
Thus, the achievable SR in nat/s/Hz can be defined as [4]
C∆ (Θ,Φ) = [CD∗ − CE ]+=
[ln
(1 + Θ
1 + Φ
)]+(13)
where [x]+ = max0, x.The ergodic SR of the proposed system in the general case
(i.e., for a MIMOSE system) is given by
⟨C∆⟩ = EΘ
EΦ|Θ C∆ (Θ,Φ) |Θ = θ
= EΘ
∫ θ
0
ln
(1 + θ
1 + ϕ
)fΦ|Θ (ϕ) dϕ
= A− B, (14)
1Let x ∼ CN (µµµ,Σ). If A is a non-random matrix and b is a non-random vector, then y = Ax + b yields a circularly symmetric complexy ∼ CN
(Aµµµ+ b,AΣA†) [27, Appendix A].
4
where the term A can be expressed as
A , EΘ
ln(1 + θ)FΦ|Θ (θ)
= EΘ
ln(1 + θ)
(1− e−θ/(γRΩRE)
)= EΘ ln(1 + θ) − EΘ
ln(1 + θ)e−θ/(γRΩRE)
, (15)
and the term B can be expressed as
B , EΘ
∫ θ
0
ln (1 + ϕ) fΦ|Θ (ϕ) dϕ
= EΘ
∫ θ
0
ln (1 + ϕ)e−ϕ/(γRΩRE)
γRΩREdϕ
= e1/(γRΩRE)
[E1
(1
γRΩRE
)− EΘ
E1
(1 + θ
γRΩRE
)]− EΘ
ln(1 + θ)e−θ/(γRΩRE)
(16)
where the last equality is obtained with the help of [29, Eq.(4.331.2)].
Substituting (15) and (16) into (14), we obtain
⟨C∆⟩ = EΘ ln(1 + θ) − e1/(γRΩRE)E1 (1/(γRΩRE))
+ e1/(γRΩRE) EΘ E1 ((1 + θ)/(γRΩRE)) . (17)
Unfortunately the expectation EΘ
E1
(1+θ
γRΩRE
)in (17)
cannot be found in a closed-form. We therefore aim at findingan upper bound on the ergodic SR as follows:
⟨C∆⟩ ≤ EΘ ln(1 + θ) − e1/(γRΩRE)E1
(1
γRΩRE
)+ e1/(γRΩRE) EΘ E1 (θ/(γRΩRE))
, ⟨C∆⟩upper (18)
where the inequality follows from the fact that E1 (x) =∫∞x
e−u
u du is a decreasing function.
Lemma 1. At high γR, the asymptotic expression for theergodic SR, defined as ⟨C∆⟩∞, is also that of the upper bound.In other words, we have
⟨C∆⟩∞ , limγR→∞
⟨C∆⟩ = limγR→∞
⟨C∆⟩upper. (19)
Proof. See Appendix A.
A. SIMOSE Wiretap Channel
In this subsection, we present an upper bound on and anasymptotic expression for the ergodic SR for the SIMOSEcase. These results are given in Theorem 1 and Corollary 1.
Theorem 1. In the case of SIMOSE, an upper bound on theergodic SR is given by
⟨C∆⟩upper
=N∑
n=1
(N
n
)(−1)n−1
e
1γRΩRE ln
(1 + n
ΩRE
ΩRD
)
+ en
γRΩRD E1
(n
γRΩRD
)− e
1γRΩRE E1
(1
γRΩRE
).
(20)
Proof. When M = 1, the PDF of Θ in (8) reduces to
fΘ(θ) =
N∑n=1
(N
n
)(−1)n+1 n
γRΩRDe− nθγRΩRD . (21)
Then, the expected values in (18) can be, respectively, calcu-lated as follows:
EΘ ln(1 + θ)
=
N∑n=1
(N
n
)(−1)n+1
∫ ∞
0
ln(1 + θ)ne
− nθγRΩRD
γRΩRDdθ
=N∑
n=1
(N
n
)(−1)n+1e
nγRΩRD E1
(n
γRΩRD
), (22)
and
EΘ E1 (θ/ (γRΩRE))
=N∑
n=1
(N
n
)(−1)n+1
∫ ∞
0
E1
(θ
γRΩRE
)ne
− nθγRΩRD
γRΩRDdθ
=
N∑n=1
(N
n
)(−1)n+1 ln
(1 + n
ΩRE
ΩRD
). (23)
Finally, substituting (22) and (23) into (18) yields (20).
To facilitate the analysis of the asymptotic expression forthe ergodic SR, we now state Proposition 1, which will beapplied to the proof of Corollary 1.
Proposition 1. If a and b are finite numbers, then
L(a, b) , limγ→∞
[E1 (a/γ)− E1 (b/γ)] = ln(b/a). (24)
Proof. Using the Taylor series expansion for the functionE1(x) [29, Eq.(8.214.2)] (note that E1(x) = −Ei(−x)), werewrite E1 (x) = −E − lnx−
∑∞k=1
(−x)k
k!k where E is Euler’sconstant [29, Eq. (8.367.1)]. Then we have the resulting limit
L(a, b) = lim1γ→0
[ln (b/γ)− ln (a/γ) +
∞∑k=1
(−1)k
k!k
(bk − ak
)γk
]= lim
1γ→0
[ln (b/γ)− ln (a/γ)] = ln(b/a). (25)
Corollary 1. In the case of SIMOSE, an asymptotic expressionfor the ergodic SR is given by
⟨C∆⟩∞ =N∑
n=1
(N
n
)(−1)n−1 ln
(1 +
ΩRD
nΩRE
). (26)
Proof. Following Lemma 1, at high γR, the asymptotic ex-pression for the ergodic SR is given by
⟨C∆⟩∞ = limγR→∞
⟨C∆⟩upper
=
N∑n=1
(N
n
)(−1)n−1
ln
(1 + n
ΩRD
ΩRE
)
+ limγR→∞
[E1
(n
γRΩRD
)− E1
(1
γRΩRE
)]︸ ︷︷ ︸
L(
nΩRD
, nΩRE
)
.
(27)
5
Finally, applying Proposition 1 to the limit on the RHS of(27), we arrive at (26) and complete the proof.
B. MISOSE Wiretap Channel
Similar to the previous subsection, we now present an upperbound on and an asymptotic expression for the ergodic SR forthe MISOSE case through Theorem 2 and Corollary 2.
Theorem 2. In the case of MISOSE, an upper bound on theergodic SR is given by
⟨C∆⟩upper
= e1
γRΩRE ln
(1 +
ΩRE
ΩRD
)+ C1(γR) +
M−1∑m=1
1
m!C2(γR)
+ e1
γRΩRE
M−1∑m=1
(ΩRE
ΩRD +ΩRE
)m
×
[1
1 + ΩRDΩRE
1
m+ 12F1
(1,m+ 1;m+ 2;
1
1 + ΩRDΩRE
)
− 1
m2F1
(1,m;m+ 1;
1
1 + ΩRDΩRE
)](28)
where
C1(γR) , e1
γRΩRD E1
(1
γRΩRD
)− e
1γRΩRE E1
(1
γRΩRE
)(29)
and
C2(γR) ,1
(γRΩRD)m
[1
γRΩRDI(
1
γRΩRD,m
)
−mI(
1
γRΩRD,m− 1
)](30)
where the function I(α,m) ,∫∞0θm ln(1+ θ)e−αθdθ, m ∈
N is calculated in Appendix B.
Proof. When N = 1, the PDF of Θ in (8) reduces to
fΘ(θ) =M−1∑m=0
e− θγRΩRD
m! (γRΩRD)m
(θm
γRΩRD−mθm−1
). (31)
Thus, the expected values in (18) can be, respectively, calcu-lated as follows:
EΘ ln(1 + θ)
=1
γRΩRD
∫ ∞
0
ln(1 + θ)e− θγRΩRD dθ
+M−1∑m=1
1
m! (γRΩRD)m
∫ ∞
0
(θm
γRΩRD−mθm−1
)× ln(1 + θ)e
− θγRΩRD dθ
(a)= e
1γRΩRD E1
(1
γRΩRD
)+
M−1∑m=1
1
m! (γRΩRD)m
×
[1
γRΩRDI(
1
γRΩRD,m
)−mI
(1
γRΩRD,m− 1
)],
(32)
and
EΘ E1 (θ/ (γRΩRE))
=
M−1∑m=0
1
m! (γRΩRD)m
∫ ∞
0
E1
(θ
γRΩRE
)×(
θm
γRΩRD−mθm−1
)e− θγRΩRD dθ
(b)= ln
(1 +
ΩRE
ΩRD
)+
M−1∑m=1
(ΩRE
ΩRD +ΩRE
)m
×
[1
1 + ΩRDΩRE
1
m+ 12F1
(1,m+ 1;m+ 2;
1
1 + ΩRDΩRE
)
− 1
m2F1
(1,m;m+ 1;
1
1 + ΩRDΩRE
)](33)
where (a) follows from Proposition 2 (see Appendix B);and (b) is obtained by using [29, Eq. (6.228.2)]. Finally,substituting (32) and (33) into (18) yields (28).
Corollary 2. In the case of MISOSE, an asymptotic expressionfor the ergodic SR is given by
⟨C∆⟩∞
= ln
(1 +
ΩRD
ΩRE
)+
M−1∑m=1
1
m
+M−1∑m=1
(ΩRE
ΩRD +ΩRE
)m
×
[1
1 + ΩRDΩRE
1
m+ 12F1
(1,m+ 1;m+ 2;
1
1 + ΩRDΩRE
)
− 1
m2F1
(1,m;m+ 1;
1
1 + ΩRDΩRE
)](34)
Proof. Again following Lemma 1, at high γR, we have⟨C∆⟩∞ = limγR→∞⟨C∆⟩upper. Upon examining (28), we cansee that taking the limit of ⟨C∆⟩upper relies only on taking thelimits of the expressions C1(γR) and C2(γR). These limits arecalculated as follows:
limγR→∞
C1(γR)
= limγR→∞
[e
1γRΩRD E1
(1
γRΩRD
)− e
1γRΩRE E1
(1
γRΩRE
)]= lim
γR→∞
[E1
(1
γRΩRD
)− E1
(1
γRΩRE
)]= L
(1
ΩRD,
1
ΩRE
)(a)= ln (ΩRD/ΩRE) (35)
6
where (a) follows Proposition 1. And
limγR→∞
C2(γR)
(b)= lim
γR→∞
m∑
k=0
m!
(m− k)!
m−k∑h=1
(h− 1)!
(−γRΩRD)m−k−h
−mm−1∑k=0
(m− 1)!
(m− k − 1)!
m−k−1∑h=1
(h− 1)!
(−γRΩR)m−k−h−1
= m! +m−2∑k=0
m!(m− k − 1)!
(m− k)!+
m−2∑k=0
m!
(m− k − 1)!
× limγR→∞
[(m− k − 2)!
(−1
(m− k)γRΩRD− 1
)
+m−k−2∑h=1
(h− 1)!
(−γRΩRD)m−k−h−1
(−1
(m− k)γRΩRD− 1
)]
= m! +m−2∑k=0
m!(m− k − 1)!
(m− k)!+
m−2∑k=0
m!(m− k − 2)!(−1)
(m− k − 1)!
= m! +m!
(−1 +
m∑k=1
1
k
)−m!
m−1∑k=1
1
k
= (m− 1)! (36)
where (b) is obtained by first substituting (70) from AppendixB into (29) and then simplifying the expression. Finally, takingthe limit of (28) with the aid of (35)–(36), we readily obtainthe desired result (34).
C. Analysis for Large Scale MIMOSE Relaying Systems
Unlike both SIMOSE and MISOSE scenarios discussedabove, in this subsection we consider a limiting scenario witha very large number of relays (i.e., M → ∞) and a moderatenumber of users (i.e., finite N ) to get insight into the ergodicSR of the proposed system [20].
Based on this large-scale MIMO relaying system in thepresence of eavesdropper, we now derive the ergodic SR andstate the following theorem:
Theorem 3. For the proposed system, when the number ofrelays is very large, i.e. M → ∞, the ergodic SR convergesto
⟨C⟩lar = ln(1 +MγRΩRD)− e1
γRΩRE E1
(1
γRΩRE
)+ e
1γRΩRE E1
(1 +MγRΩRD
γRΩRE
). (37)
Proof. Similarly as in [33], we apply the law oflarge numbers [34] to (4) so as to reach the limit1M ∥hRDn∥2
asym→ E|hRmDn |2
= ΩRD where
asym→ denotesthe convergence as M → ∞. As a result, D∗ can be selectedarbitrarily from the set D of finite N users because the factthat D∗ = argmaxDn∈D ∥hRDn∥2
asym→ argmaxDn∈D ΩRD
for all n = 1, . . . , N . Therefore, we obtain the convergenceof Θ as
Θ = γR∥hRD∗∥2 asym→ γRMΩRD. (38)
Applying the Lindeberg-Levy central limit theorem, we have
h†RD∗hRE√
M
dist→ CN (0,ΩRDΩRE) (39)
wheredist→ denotes convergence in distribution as M → ∞.
Employing two convergence properties (38)–(39), we obtainthe convergence of Φ as
Φ = γR|h†
RD∗hRE |2
∥hRD∗∥2dist→ Ψ ∼ Exp
(1
γRΩRE
). (40)
Finally, the ergodic SR of the proposed system with very largeM is derived as
⟨C⟩lar = limM→∞
EΘ,Φ
[ln
(1 + Θ
1 + Φ
)]+
= EΨ
[ln
(1 + γRMΩRD
1 + Ψ
)]+
= ln(1 +MγRΩRD)
(1− e
−MΩRDΩRE
)− 1
γRΩRE
∫ MγRΩRD
0
ln(1 + ψ)e− ψγRΩRE dψ. (41)
Applying integration by parts to the integral in the last equalityand then manipulating the RHS, we easily arrive at (37) andcomplete the proof.
Observation: It is clear that Corollaries 1 and 2 providebetter insight into the influence of the ratio ΩRD/ΩRE onthe ergodic SR. Of course, the asymptotic expressions forthe ergodic SR strictly depend on this ratio when γR is verylarge. Meanwhile, Theorem 3 gives us a relatively compactexpression of the ergodic SR in the MIMOSE case with largeM and moderate N .
IV. SECRECY OUTAGE PROBABILITY
In this section, we present the SOP, which is defined asthe probability that the instantaneous SR is below a thresholdvalue ϵ. The SOP will be derived for two cases: SIMOSEsystems and MISOSE systems.
The SOP of the proposed system in the general case (i.e.,for a MIMOSE system) is given by
Pout = P C∆(Θ,Φ) < ϵ = P
1 + Θ
1 + Φ< eϵ
= 1− P
Φ ≤ e−ϵ(1 + Θ)− 1
= 1−
∫ ∞
eϵ−1
FΦ|Θ(e−ϵ(1 + θ)− 1
)fΘ(θ)dθ (42)
where the last equality follows from the fact thatFΦ|Θ (e−ϵ(1 + θ)− 1) = 0 where θ ≤ eϵ − 1. On recalling
7
that Φ|hRD∗ ↔ Φ|Θ leads to Φ|Θ ∼ Exp(
1γRΩRE
), we can
proceed to formulate (42) as
Pout = 1−∫ ∞
eϵ−1
[1− e−(e
−ϵ(1+θ)−1)/(γRΩRE)]fΘ(θ)dθ
= 1−∫ ∞
eϵ−1
fΘ(θ)dθ
+
∫ ∞
eϵ−1
e−(e−ϵ(1+θ)−1)/(γRΩRE)fΘ(θ)dθ
= FΘ (eϵ − 1) + e(1−e−ϵ)/(γRΩRE)G(ϵ) (43)
where the integral G(ϵ) is defined as
G(ϵ) ,∫ ∞
eϵ−1
e−θe−ϵ/(γRΩRE)fΘ(θ)dθ. (44)
A. SIMOSE Wiretap Channel
Theorem 4. In the case of SIMOSE, the SOP can be writtenas
Pout =(1− e
1−eϵγRΩRD
)N+
N∑n=1
(N
n
)(−1)n+1 n
γRΩRD
×(
e−ϵ
γRΩRE+
n
γRΩRD
)−1
e(1−eϵ)nγRΩRD .
(45)
Proof. When M = 1, the CDF of Θ in (7) reduces to
FΘ(θ) =[1− e
− θγRΩRD
]N. (46)
Moreover, by substituting (21) into (44), G(ϵ) can becalculated as follows:
G(ϵ) =N∑
n=1
(N
n
)(−1)n+1 n
γRΩRD
×∫ ∞
eϵ−1
e−θ
(e−ϵ
γRΩRE+ nγRΩRD
)dθ
=N∑
n=1
(N
n
)(−1)n+1 n
γRΩRD
×(
e−ϵ
γRΩRE+
n
γRΩRD
)−1
e−(eϵ−1)
(e−ϵ
γRΩRE+ nγRΩRD
).
(47)
Finally, using (46) and substituting (47) into (43), we arriveat the SOP shown in (45).
Corollary 3. In the case of SIMOSE, an asymptotic expressionfor Pout at high γR (γR → ∞) is obtained by taking the limitof (45), i.e.,
Pasymout = lim
γR→∞Pout
=N∑
n=1
(N
n
)(−1)n+1
(ΩRD
ΩRE
e−ϵ
n+ 1
)−1
. (48)
B. MISOSE Wiretap Channel
Theorem 5. In the case of MISOSE, the SOP can be writtenas
Pout = 1− e(1−eϵ)γRΩRD
M−1∑m=0
1
m!
(eϵ − 1
γRΩRD
)m
+ e(1−e−ϵ)γRΩRE
M−1∑m=0
(1 + e−ϵΩRD
ΩRE
)−m
e−(eϵ−1)β
×
m−1∑i=0
[(1 + e−ϵΩRD
ΩRE
)−1
− 1
][(eϵ − 1)β]i
i!
+
(1 + e−ϵΩRD
ΩRE
)−1[(eϵ − 1)β]m
m!
. (49)
Proof. When N = 1, the CDF of Θ in (7) reduces to
FΘ(θ) = 1−M−1∑m=0
e− θγRΩRD
m!
(θ
γRΩRD
)m
. (50)
Moreover, by substituting (31) into (44), G(ϵ) can becalculated as follows:
G(ϵ)
=
M−1∑m=0
1
m! (γRΩRD)m
∫ ∞
eϵ−1
(θm
γRΩRD−mθm−1
)e−θβdθ
=M−1∑m=0
(1 + e−ϵΩRD
ΩRE
)−m
e−(eϵ−1)β
×
m−1∑i=0
[(1 + e−ϵΩRD
ΩRE
)−1
− 1
][(eϵ − 1)β]i
i!
+
(1 + e−ϵΩRD
ΩRE
)−1[(eϵ − 1)β]m
m!
(51)
where β ,(
e−ϵ
γRΩRE+ 1
γRΩRD
). The second equality is
obtained by applying [29, Eq. (2.33.10)] to the integral andthen using the definition of the incomplete gamma function[29, Eq. (8.352.4)]. Finally, using (50) and substituting (51)into (43), we arrive at the SOP shown in (49).
Corollary 4. In the case of MISOSE, an asymptotic expressionfor Pout at high γR (γR → ∞) is obtained by taking the limitof (49), i.e.,
Pasymout = lim
γR→∞Pout
= 1−M−1∑m=0
1
ΩmRD
(e−ϵ
ΩRE+
1
ΩRD
)−m
×
[1− 1
ΩRD
(e−ϵ
ΩRE+
1
ΩRD
)−1]. (52)
Observation: To evaluate the SOP at high γR, we can usethe simple expressions shown in Corollaries 3 and 4 ratherthan the exact expressions shown in Theorems 4 and 5.
8
V. ADAPTED COOPERATIVE DIVERSITY GAIN
Inspired by the work in [12], in this section, we presentthe ACDG for two scenarios: SIMOSE systems and MISOSEsystems. According to [12], the conventional concept of coop-erative diversity gain is inappropriate to study security issuesin CWNs. Instead, a new concept of cooperative diversitygain, namely, the ACDG, is defined in a manner similar tothe conventional one.
Before defining the ACDG, we first state that an interceptevent occurs when the channel capacity of the link R-D∗
becomes less than of the link R-E, i.e., CD∗ < CE . Theintercept probability is then given by
Pint , P CD∗ < CE = P Θ < Φ
= 1−∫ ∞
0
FΦ|Θ(θ)fΘ(θ)dθ
=
∫ ∞
0
e− θγRΩRE fΘ(θ)dθ. (53)
We next define λ as the ratio of the average channel gain ofthe link R-D∗ to that of the link R-E, i.e.,
λ ,E∥hRD∗∥2
E ∥hRE∥2
=
∑Mm=1 E
|hRmD∗ |2
∑Mm=1 E |hRmE |2
=ΩRD
ΩRE.
(54)
Based on the intercept probability Pint and the ratio λ, wefinally define the ACDG as
d = − limλ→∞
logPint
log λ. (55)
Herein, the similarity between the concept of the ACDGand the conventional definition of diversity can be easilyrecognized. From the intercept probability point of view, thecorrelation between the secure metric Pint and the ratio λcan be examined. In this way, the ACDG d is viewed as thekey factor that affects the slope of the Pint curve to enhancecommunication reliability. In the following, we will examinethe ACDG for two cases: i) SIMOSE and ii) MISOSE wiretapchannels.
A. SIMOSE Wiretap Channel
Theorem 6. When M = 1 and N ≥ 1, the ACDG of theproposed system is equal to d = N .
Proof. Substituting (21) into (53) and then introducing t ,θ/ (γRΩRD), we can rewrite (53) as
Pint =
∫ ∞
0
e−λt
[N∑
n=1
(N
n
)(−1)n−1ne−nt
]dt
=
∫ ∞
0
e−λtd[(1− e−t)N
]=
∫ ∞
0
e−λtNe−t(1− e−t
)N−1︸ ︷︷ ︸,Υ1(t)
dt. (56)
Moreover, Υ1(t) can be expanded as
Υ1(t) = N
[1 +
∞∑k=1
(−t)k
k!
][−
∞∑k=1
(−t)k
k!
]N−1
= NtN−1 + o(tN ), (57)
in some neighbourhood of t = 0+. Note that the symbol o(·)in (57) is the little-o notation.
Now, in order to investigate the asymptotic behavior of theintegral in (56) we apply Watson’s lemma [35, Lemma 1.2]and write
Pint = NΓ((N − 1) + 1)
λ(N−1)+1+ o
(1
λN+1
)=N !
λN+ o
(1
λN+1
)as λ→ ∞. (58)
Finally, the ACDG of the proposed system with M = 1 andN ≥ 1 can be derived as
d = − limλ→∞
[log (N !)− log
(λN)]
log λ= N. (59)
This result reveals that Pint decreases inversely with N , andtherefore the security performance is improved by increasingN . This completes the proof.
B. MISOSE Wiretap ChannelTheorem 7. When N = 1 and M ≥ 1, the ACDG of theproposed system is equal to d =M .
Proof. Substituting (31) into (53) and then introducing t ,θ/ (γRΩRD), we can rewrite (53) as
Pint =
∫ ∞
0
e−λt
[e−t
M−1∑m=0
1
m!
(tm −mtm−1
)]dt
=
∫ ∞
0
e−λt
[e−t tM−1
(M − 1)!
]︸ ︷︷ ︸
,Υ2(t)
dt. (60)
Moreover, Υ2(t) can be expanded as
Υ2(t) =
[1 +
∞∑k=1
(−t)k
k!
]tM−1
(M − 1)!=
tM−1
(M − 1)!+ o
(tM),
(61)
in some neighbourhood of t = 0+.Therefore, Watson’s lemma is applicable to (60) and we can
express
Pint =1
(M − 1)!
Γ((M − 1) + 1)
λ(M−1)+1+ o
(1
λM+1
)=
M
λM+ o
(1
λM+1
)as λ→ ∞. (62)
Finally, the ACDG of the proposed system with N = 1 andM ≥ 1 can be written as
d = − limλ→∞
[logM − log λM
]log λ
=M. (63)
This result reveals that Pint decreases inversely with M ,therefore the security performance is improved by increasingM . This completes the proof.
9
0 5 10 15 20 25 300.3
0.6
0.9
1.2
N = 2, 3, 4, 5
(dB)R
Upper bound Asymtotic Simulation
Erg
odic
Sec
recy
Rat
e (n
at/s
/Hz)
Fig. 2. Ergodic secrecy rate and its upper bound versus γR. Systemparameters: M = 1, N = 2, . . . , 6, ΩRD = 2.5, and ΩRE = 4.
VI. NUMERICAL RESULTS AND DISCUSSION
This section gives some numerical examples to verify theanalysis presented in Sections III–V, and illustrate the keybehaviors of the system when different network parametersare varied. Without loss of generality, N0 is set to 0 dB, andso γR is referred to as PR.
In Figs. 2 and 3, the mean channel powers of the linksRm-Dn and Rm-E are set to ΩRD = 2.5 and ΩRE = 4respectively. Fig. 2 considers the proposed system with M = 1and N = 2, 3, 4, 5, 6, whereas Fig. 3 considers the proposedsystem with M = 2, 3, 4, 5, 6 and N = 1. For each figure,we observe that the upper bound gets closer to the ergodic SRas γR (or PR) increases from 0 dB to 30 dB. This can be easilyexplained by assessing that E1
(1+θ
γRΩRE
)≈ E1
(θ
γRΩRE
)with large enough θ due to the fact that θ = γR∥hRD∗∥2.On this observation, the upper bound can be referred to asan approximation to the ergodic SR at high γR. Moreover, theasymptotic line agrees exactly with both the simulation and theupper bound at high γR, which confirms again the correctnessof our analyses.
In Fig. 4, we show the ergodic SR for the case of a verylarge MIMO relaying system. Although M is assumed toapproach to infinity, we illustrate a more practical scenariowith M = 50, 100, 150. For each given M , we considerN = 1, 2, 3 for comparison. Likewise, we choose ΩRD =2.5 and ΩRE = 4. The figure shows the convergence of theergodic SR (as stated in Theorem 3) in the case that M ismuch greater than N . When the ratio M
N becomes larger, theagreement between the simulation and the analysis becomescloser. As expected, when N = 1 and M = 50, the simulatedpoints lie slightly lower than the analytical curve becausethe analysis is intended for M → ∞. However, they nearlycoincide with each other when N = 1 and M = 150. Thissuggests that exact agreement is achievable when N = 1 andM takes very large number.
Figs. 5 and 6 show the secrecy outage probabilities in twoscenarios of interest, the proposed system with M = 1 (i.e.,
0 5 10 15 20 25 300.5
1.0
1.5
2.0 Upper bound Asymptotic Simulation
(dB)R
M = 2, 3, 4, 5
Erg
odic
Sec
recy
Rat
e (n
at/s
/Hz)
Fig. 3. Ergodic secrecy rate and its upper bound versus γR. Systemparameters: M = 2, . . . , 6, N = 1, ΩRD = 2.5, and ΩRE = 4.
0 5 10 15 20 25 303.5
4.0
4.5
5.0
5.5
M = 50, 100, 150
Large M analysis Sim. (N=1) Sim. (N=2) Sim. (N=3)
(dB)R
Erg
odic
Sec
recy
Rat
e (n
at/s
/Hz)
Fig. 4. Ergodic secrecy rate versus γR. System parameters: M =50, 100, 150, N = 1, 2, 3, ΩRD = 2.5, and ΩRE = 4.
the SIMOSE scenario), and the proposed system with N = 1(i.e., the MISOSE scenario). We also choose ΩRD = 2.5, andΩRE = 4. The outage threshold is chosen to be ϵ = 0.5 ln 2 (innat/s/Hz). As we can see from these figures, when γR increasesfrom 0 dB to 40 dB, the secrecy outage probabilities decreaseslightly, while increasing N (the SIMOSE scenario) or M (theMISOSE scenario) improves the system performance moresignificantly. These observations suggest that increasing thenumber of relaying/destination nodes is a much more effectivestrategy than increasing the transmit power at the relays.
Figs. 7 and 8 show the intercept probabilities versus theratio λ = ΩRD
ΩREin two scenarios of interest, namely, SIMOSE
and MISOSE. For each of these figures, we can see that theworst case occurs when M = 1 and N = 1, while the interceptprobability decreases strongly with the number of nodes and λ.As proved in Theorems 6 and 7, the number of nodes is equalto the ACDG, which serves to shift the intercept probability
10
1 2 3 4 5 6 7 8 9 100.01
0.1
1
0, 40 dBR
The number of users (N)
Analysis Simulation
Sec
recy
Out
age
Pro
babi
lity
Fig. 5. Secrecy outage probability versus N . System parameters: M = 1,ΩRD = 5, ΩRE = 2, ϵ = 0.5 ln 2 nat/s/Hz, and γR = 0, 40 dB.
curves to the left and therefore improves the reliability of theproposed system from the security point of view. Furthermore,these figures reveal striking similarities of the ACDG to theconventional cooperative diversity gain. As such, the conceptof the ACDG seems to be more compatible with security issueof wireless networks than the concept of traditional diversitygain.
VII. CONCLUSIONS
We have considered the use of cooperative beamformingand user selection for relay network security. First, we haveanalyzed the ergodic SRs for three cases: SIMOSE systems(M = 1, N ≥ 2), MISOSE systems (M ≥ 2, N = 1),and very large scale MIMOSE systems (M → ∞, finite N ).Bounds on and asymptotic expressions for the ergodic SR forthe first two cases, and an exact expression for the ergodicSR at very large M for the third case have been derived.Secondly, we have evaluated the security performance forSIMOSE and MISOSE systems in terms of outage probability.We have quantified the ACDG, similar to conventional co-operative diversity gain, for SIMOSE and MISOSE systems.The validity of our expressions have been verified throughsimulation results. For future work, we plan to investigate themore generic case of the proposed network and the effects ofother factors, e.g. imperfect channel state information.
APPENDIX
A. Proof of Lemma 1
Proof. It is clear from (18) that proving Lemma 1 is equivalentto proving
limγR→∞
EΘ
E1
(1 + θ
γRΩRE
)= lim
γR→∞EΘ
E1
(θ
γRΩRE
).
(64)
1 2 3 4 5 6 7 8 9 101E-4
1E-3
0.01
0.1
1
0, 40 dBR
The number of relays (M)
Analysis Simulation
Sec
recy
Out
age
Pro
babi
lity
Fig. 6. Secrecy outage probability versus M . System parameters: N = 1,ΩRD = 5, ΩRE = 2, ϵ = 0.5 ln 2 nat/s/Hz, and γR = 0, 40 dB.
First, we rewrite the left hand side (LHS) of (64) as
LHS(64) = limγR→∞
∫ ∞
0
E1
(1 + θ
γRΩRE
)fΘ(θ)dθ
= limγR→∞
∫ ∞
0
E1
(1 + γRz
γRΩRE
)f∥hRD∗∥2(z)︸ ︷︷ ︸
~γR (z)
dz (65)
where fΘ(θ) is given in (8) and f∥hRD∗∥2(z) = γRfΘ(γRz)due to the relation in (6). Additionally, it is easy to con-firm that f∥hRD∗∥2(z) is no longer dependent on γR, whileE1
(1+γRzγRΩRE
)is an increasing function of γR.
We therefore come to the conclusion that ~γR(z) is increas-ing in γR ≥ 0, is bounded above and has the limit
limγR→∞
~γR(z) = E1
(z
ΩRE
)f∥hRD∗∥2(z). (66)
Following these observations, we have
LHS(64) = limγR→∞
∫ ∞
0
~γR(z)dz
=
∫ ∞
0
E1
(z
ΩRE
)f∥hRD∗∥2(z)dz. (67)
Because the right hand side (RHS) of (67) is independent ofγR, we can also rewrite it as the limit of a constant, i.e., (67)becomes
LHS(64) = limγR→∞
∫ ∞
0
E1
(z
ΩRE
)f∥hRD∗∥2(z)dz
= limγR→∞
EΘ
E1
(θ
γRΩRE
)≡ RHS(64) (68)
and the proof is complete.
B. Integral
Proposition 2. Let us define
I(α,m) ,∫ ∞
0
θm ln(1 + θ)e−αθdθ, m ∈ N. (69)
11
Then I(α,m) can be expressed in two ways:• Either [29, Eq.(4.222.8)]
I(α,m) = α−(m+1)m∑
k=0
m!
(m− k)!
[(−1)m−keαE1(α)
αm−k
+
m−k∑h=1
(h− 1)!
(−1/α)m−k−h
](70)
• or
I(α,m) = α−(m+1)G1,33,2
(α−1
∣∣∣∣ −m, 1, 11, 0
)(71)
where Gm,np,q
(z
∣∣∣∣ (ap)(bq)
)is Meijer G-function [36,
Eq.(1.122)].If m = 0, then both (70) and (71) reduce to
I(α, 0) = α−1eαE1(α). (72)
Proof. Rewriting ln(1+θ) in terms of Meijer G-function [37,Eq.(8.4.6.5)], we have
ln(1 + θ) = G1,22,2
(θ
∣∣∣∣ 1, 11, 0
).
Then I(α,m) can be evaluated as follows:
I(α,m) =
∫ ∞
0
θmG1,22,2
(θ
∣∣∣∣ 1, 11, 0
)e−αθdθ
= L
θmG1,2
2,2
(θ
∣∣∣∣ 1, 11, 0
);α
= α−(m+1)H1,3
3,2
[α−1
∣∣∣∣ (−m, 1), (1, 1), (1, 1)(1, 1), (0, 1)
](73)
where Lf(θ);α denotes the Laplace transform [36, Eq.
(2.11)] and Hm,np,q
[z
∣∣∣∣ (ap, Ap)(bq, Bq)
]is the H-function [36, Eq.
(1.2)]. The last equality is obtained by using the Laplacetransform of the Meijer G-function [36, Eq. (2.29)]. Evaluatingthe RHS of (73) again with the help of [37, Eq. (8.3.2.21)],
i.e. Hm,np,q
[z
∣∣∣∣ (ap, 1)(bq, 1)
]= Gm,n
p,q
(z
∣∣∣∣ (ap)(bq)
), we arrive at
(71). In addition, if m = 0, we can apply directly [29, Eq.(4.337.2)] to (69) in order to obtain (72). We thus completethe proof.
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-15 -10 -5 0 5 10 151E-4
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Tiep M. Hoang was born in Daklak, Vietnam,in 1989. He received the B.S. degree in ElectricalEngineering from Ho Chi Minh City University ofTechnology, Vietnam, in 2012, and the M.S. degreein Electrical Engineering from Kyung Hee Univer-sity, Yongin, Korea, in 2014. He is now with DuyTan University, Vietnam, as a Research Assistant.His current research interests include cooperativenetworks and wireless security.
Trung Q. Duong (S’05, M’12, SM’13) received hisPh.D. degree in Telecommunications Systems fromBlekinge Institute of Technology (BTH), Sweden in2012. Since 2013, he has joined Queen’s UniversityBelfast, UK as a Lecturer (Assistant Professor).His current research interests include cooperativecommunications, cognitive radio networks, physicallayer security, massive MIMO, cross-layer design,mm-waves communications, and localization for ra-dios and networks. He is the author or co-author of170 technical papers published in scientific journals
and presented at international conferences.Dr. Duong currently serves as an Editor for the IEEE TRANSACTIONS
ON COMMUNICATIONS, IEEE COMMUNICATIONS LETTERS, IET COM-MUNICATIONS, WILEY TRANSACTIONS ON EMERGING TELECOMMUNICA-TIONS TECHNOLOGIES, and ELECTRONICS LETTERS. He has also servedas the Guest Editor of the special issue on some major journals includingIEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IET COM-MUNICATIONS, IEEE WIRELESS COMMUNICATIONS MAGAZINE, IEEECOMMUNICATIONS MAGAZINE, EURASIP JOURNAL ON WIRELESS COM-MUNICATIONS AND NETWORKING, EURASIP JOURNAL ON ADVANCESSIGNAL PROCESSING. He was awarded the Best Paper Award at the IEEEVehicular Technology Conference (VTC-Spring) in 2013, IEEE InternationalConference on Communications (ICC) 2014.
Himal A. Suraweera (S’04, M’07, SM’15) receivedthe B.Sc. degree (first class honors) in Electrical andElectronic Engineering, Peradeniya University, SriLanka, in 2001 and the Ph.D. degree from MonashUniversity, Melbourne, Australia, in 2007. He wasalso awarded the 2007 Mollie Holman Doctoral and2007 Kenneth Hunt Medals for his doctoral thesisupon graduating from Monash University.
From October 2006 to January 2007 he was atMonash University as a Research Associate. FromFebruary 2007 to June 2009, he was at the center for
Telecommunications and Microelectronics, Victoria University, Melbourne,Australia as a Research Fellow. From July 2009 to January 2011, he was withthe Department of Electrical and Computer Engineering, National Universityof Singapore, Singapore as a Research Fellow. From January 2011 to May2013, he was a Post-Doctoral Research Associate at the Singapore Universityof Technology and Design, Singapore. Currently he is a Senior Lecturerat the Department of Electrical and Electronic Engineering, University ofPeradeniya. His main research interests include cooperative communications,energy harvesting and Green communications, full-duplex communications,massive MIMO, cognitive radio and wireless security.
Dr. Suraweera serves as an editor for the IEEE TRANSACTIONS ONWIRELESS COMMUNICATIONS, the IEEE COMMUNICATIONS LETTERS andthe Green Communications and Networking Series of the IEEE JOURNAL ONSELECTED AREAS IN COMMUNICATIONS. He received an IEEE Communi-cations Letters exemplary reviewer certificate in 2009, two IEEE WirelessCommunications Letters exemplary certificates in 2012 and 2013 and anIEEE Transactions on Vehicular Technology Top Reviewer Award in 2013. Hereceived an IEEE Communications Society Asia-Pacific Outstanding YoungResearcher Award in 2011 and the Best Paper Award at the WCSP 2013Conference.
13
Chintha Tellambura (F’11) received the B.Sc. de-gree (with first-class honor) from the University ofMoratuwa, Sri Lanka, in 1986, the M.Sc. degree inElectronics from the University of London, UnitedKingdom, in 1988, and the Ph.D. degree in ElectricalEngineering from the University of Victoria, Canada,in 1993. He was a Postdoctoral Research Fellowwith the University of Victoria (1993-1994) and theUniversity of Bradford (1995-1996). He was withMonash University, Australia, from 1997 to 2002.Presently, he is a Professor with the Department
of Electrical and Computer Engineering, University of Alberta. His currentresearch interests include the design, modelling and analysis of cognitiveradio networks, heterogeneous cellular networks and multiple-antenna wirelessnetworks.
Prof. Tellambura served as an editor for both IEEE Transactions onCommunications (1999-2011) and IEEE Transactions on Wireless Communi-cations (2001-2007) and was the Area Editor for Wireless CommunicationsSystems and Theory in the IEEE Transactions on Wireless Communicationsduring 2007-2012. Prof. Tellambura and co-authors received the Communi-cation Theory Symposium best paper award in the 2012 IEEE InternationalConference on Communications, Ottawa, Canada. He is the winner of theprestigious McCalla Professorship and the Killam Annual Professorship fromthe University of Alberta. Prof. Tellambura has authored or coauthored over480 journal and conference publications with total citations more than 10,000and an h-index of 52 (Google Scholar).
H. Vincent Poor (S’72, M’77, SM’82, F’87) re-ceived the Ph.D. degree in EECS from PrincetonUniversity in 1977. From 1977 until 1990, he wason the faculty of the University of Illinois at Urbana-Champaign. Since 1990 he has been on the facultyat Princeton, where he is the Michael Henry StraterUniversity Professor of Electrical Engineering andDean of the School of Engineering and AppliedScience. His research interests are in the areas ofinformation theory, statistical signal processing andstochastic analysis, and their applications in wireless
networks and related fields. Among his publications in these areas are the re-cent books Principles of Cognitive Radio (Cambridge University Press, 2013)and Mechanisms and Games for Dynamic Spectrum Allocation (CambridgeUniversity Press, 2014).
Dr. Poor is a member of the National Academy of Engineering, the NationalAcademy of Sciences, and is a foreign member of Academia Europaea andthe Royal Society. He is also a fellow of the American Academy of Arts andSciences, the Royal Academy of Engineering (U. K), and the Royal Societyof Edinburgh. He received the Marconi and Armstrong Awards of the IEEECommunications Society in 2007 and 2009, respectively. Recent recognitionof his work includes the 2014 URSI Booker Gold Medal, the 2015 EURASIPAthanasios Papoulis Award, and honorary doctorates from Aalborg University,Aalto University, the Hong Kong University of Science and Technology, andthe University of Edinburgh.