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Secure Switch-and-Stay Combining (SSSC) for Cognitive RelayNetworks

Fan, L., Zhang, S., Duong, T. Q., & Karagiannidis, G. K. (2016). Secure Switch-and-Stay Combining (SSSC) forCognitive Relay Networks. IEEE Transactions on Communications, 64(1), 70-82. DOI:10.1109/TCOMM.2015.2497308

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ACCEPTED FOR PUBLICATION ON IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. X, NO. XX, XXXXX 2015 1

Secure Switch-and-Stay Combining (SSSC) forCognitive Relay Networks

Lisheng Fan, Shengli Zhang, Trung Q. Duong,Senior Member, IEEE, and George K. Karagiannidis,Fellow, IEEE

Abstract—In this paper, we study a two-phase underlay cog-nitive relay network, where there exists an eavesdropper whocan overhear the message. The secure data transmission fromthe secondary source to secondary destination is assisted bytwo decode-and-forward (DF) relays. Although the traditionalopportunistic relaying technique can choose one relay to providethe best secure performance, it needs to continuously have thechannel state information (CSI) of both relays, and may resultin a high relay switching rate. To overcome these limitations, asecure switch-and-stay combining (SSSC) protocol is proposedwhere only one out of the two relays is activated to assist thesecure data transmission, and the secure relay switching occurswhen the relay cannot support the secure communication anylonger. This security switching is assisted by either instantaneousor statistical eavesdropping CSI. For these two cases, we studythe system secure performance of SSSC protocol, by derivingthe analytical secrecy outage probability as well as an asymptoticexpression for the high main-to-eavesdropper ratio (MER) region.We show that SSSC can substantially reduce the system com-plexity while achieving or approaching the full diversity orderof opportunistic relaying in the presence of the instantaneous orstatistical eavesdropping CSI.

Index Terms—Secure switch-and-stay combining (SSSC), cog-nitive relay networks, secure communication, diversity order.

I. I NTRODUCTION

Due to the broadcast nature, the wireless link from thesource to destination may be overheard by some non-intendedeavesdroppers, which causes the severe issue of wirelesssecurity. To prevent the wiretap, physical-layer security(PLS)

The review of this paper was coordinated by Prof. H.-C. Yang.Thiswork was presented in part at the IEEE Global CommunicationsConference(GLOBECOM), San Diego, CA, Dec. 2015. S. Zhang is the correspondingauthor.

L. Fan is with the School of Computer Science and EducationalSoft-ware, Guangzhou University, National Mobile Communications ResearchLaboratory, Southeast University, and Shantou University, China (email:[email protected]).

S. Zhang is with college of information engineering, Shenzhen University,China. (email:[email protected]).

T. Q. Duong is with Queen’s University Belfast, UK (email:[email protected]).

G. K. Karagiannidis is with the Department of Electrical andComputer En-gineering, Aristotle University of Thessaloniki, 54 124, Thessaloniki, Greeceand with the Department of Electrical and Computer Engineering, KhalifaUniversity, PO Box 127788, Abu Dhabi, UAE (e-mail: [email protected]).

This work was supported by the U.K. Royal Academy of Engineer-ing Research Fellowship under Grant RF1415\14\22, NSF of China(No. 61372129/61372078/61471229), NSF of Guangdong Province, China(No. 2014A030306027), the National 973 project (No. 2013CB336700),the open research fund of National Mobile Communications ResearchLaboratory, Southeast University (No. 2013D04), trainingprogram ofexcellent young teachers in Higher Education Institutionsof Guang-dong Province (No. Yq2013070), the Foundation of Shenzhen City (No.KQCX20140509172609163), and the Natural Science Foundation of Shen-zhen University (No. 00002501).

as well as high-layer security has been proposed and exten-sively studied in the literature [1]–[5]. In this field, Wynerfirstly introduced the wiretap model to analyze the securetransmission [1], and pointed out that perfect secrecy canbe achieved with properly designed encoder and decoder.Pioneered by this work, many researchers have extensivelyanalyzed the PLS performance in fading channels. In [2],the authors studied the secure transmission by analyzing thesecrecy capacity with full or partial channel state information(CSI), and demonstrated that the channel fading has a positiveimpact on the secrecy capacity. Furthermore, the authors in[3] studied the secure performance over correlated fadingchannels, by analyzing the secrecy capacity and secrecy outageprobability (SOP), and showed that the channel correlationseverely degrades the secure transmission. To enhance thesystem security, antenna selection can be applied for multiple-input multiple-output (MIMO) wiretap channels, where thechannel fluctuation among antennas can be exploited to obtainthe full system diversity gain.

As relaying techniques [6]–[9] can increase the transmissionreliability, system capacity, and coverage area without addi-tional transmit power at the transmitter, the secure transmissionin relay networks has attracted much attention in recent works.There are two fundamental relaying protocols, i.e., amplify-and-forward (AF) and decode-and-forward (DF) relaying. Theintercept probability of multiple AF relay networks has beenstudied in [10], and the opportunistic relaying technique isused to exploit the full diversity gain for enhancing thesecurity. As an extension of intercept probability, the SOPis studied for multiuser multiple AF relay networks in [11],where several users and relay selection schemes are proposedto enhance the system security. In addition, the asymptoticsecure performance is investigated with the high main-to-eavesdropper ratio (MER), defined as the ratio of averagechannel gain from the relay to intended receiver to that fromrelay to eavesdropper. The secure characteristics of the DFrelay network has been studied in [12], and it is found thatthe placement of the DF relay can also affect the system securemetrics, such as secrecy capacity and SOP. For multiuser DFrelay networks [13], opportunistic relaying can be used toexploit the channel fluctuation among relays, and hence thefull diversity of wireless system can be achieved. To furtherenhance the network security, the other techniques such asjamming, beamforming and resource allocation have beeninvestigated for relay networks [14]–[24].

Due to the scarce radio frequency spectrum, the cognitivetechnique [25] is encouraged to be incorporated into relaynetworks to form a promising system for the next generation


of wireless communications networks. Hence, the PLS of cog-nitive relay networks should be studied to guarantee the securetransmission. Various resource allocation strategies have beenproposed to enhance the system security of cognitive relaynetworks. Specifically, power allocation can be applied tooptimize the total transmit power among network nodes toimprove the transmission security [26], [27]. For cognitiverelay networks with multiple relays, opportunistic relaying canbe used to choose the best relay to assist the secure trans-mission [28]–[30]. Although the opportunistic relaying canefficiently exploit the full system diversity, it has two majorlimitations [31]–[38]. The first limitation is the heavy loaddue to the system’s needs to estimate the channel parametersof each relay continuously. The second limitation is the highrelay switching rate, which is harmful to the network stability.Therefore, it is of vital importance to overcome these twolimitations to ensure the security of the network.

Motivated by the aforementioned discussion, in this paper,we propose a secure switching-and-stay combining (SSSC)protocol for the cognitive relay networks with two DF relays,in the presence of an eavesdropper. In SSSC, one relay outof two is chosen to be activated to assist the secure datatransmission for the secondary source to secondary destination.The relay switching occurs if the relay cannot support thesecure transmission any longer; otherwise, the same relaycontinues to be used. The secure relay switching is assistedby the instantaneous eavesdropping CSI (I-ECSI) or statis-tical eavesdropping CSI (S-ECSI). In comparison with theconventional opportunistic relaying for secure cognitiverelaynetworks [28]–[30], SSSC can reduce the channel estimationcomplexity, decrease the relay switching rate, and simultane-ously maintain the secure performance. The key contributionsof this paper are summarized as follow:

• We propose the SSSC protocol for the cognitive relaynetworks, in order to reduce the channel estimation com-plexity, keep the network stability, and simultaneouslymaintain the secure performance.

• For the SSSC with either I-ECSI or S-ECSI, we presentan analytical expression for the system secrecy outageprobability, in order to investigate the secure performanceachieved by SSSC.

• We present new results for the asymptotic secrecy out-age probability of SSSC. These asymptotic expressionsenable us to determine the major factors that regulate thesecure performance in the high transmit power and MERregions.

• Based on the asymptotic results, it is shown that SSSCwith instantaneous eavesdropping CSI can achieve thesystem full diversity, and SSSC with statistical eavesdrop-ping CSI can also approach this diversity.

The organization of this paper is as follows. After theintroduction, Section II describes the model of a securecognitive relay network with two DF relays, and Section IIIpresents the SSSC protocol. For SSSC with either I-ECSI orS-ECSI, Section IV gives the secrecy outage probabilities,including the derivations for both the exact and asymptoticresults. Numerical results are provided in Section V to offer

E

R2

S

D

Eavesdropper linkMain link

Interference link

PU

First phaseSecond phase

R1

Fig. 1. Secure communication of two-phase underlay cognitive relaynetworks with two DF relays.

valuable insights into the secure performance. Conclusions aredrawn in Section VI.

Notation: The notationCN (0, σ2) denotes a circularlysymmetric complex Gaussian random variable with zero meanand varianceσ2. We usefX(·) to represent the probabilitydensity function of random variableX . NotationPr[·] returnsthe probability.

II. SYSTEM MODEL

Fig. 1 depicts the considered two-phase underlay cognitiverelay network with two DF relays{Ri|i = 1, 2} which canassist the communication from the secondary sourceS to thesecondary destinationD. In the underlay spectrum-sharingmode, the transmit power of both the secondary user and relaysis constrained to limit the interference to the primary userPU , in order to guarantee the Quality-of-Service (QoS) ofprimary communications. The eavesdropperE in the networkcan overhear the message from the relays, which yields theissue of information wiretap. We consider severe shadowingenvironments, so that the direct links from the source S to Dand E do not exist. While it is interesting to consider moderateshadowing environments and study the impact of direct linkson the secure performance [14], [39], this is beyond the scopeof this work. The considered system model in Fig. 1 canbe applied to the communication of cognitive relay networksin unsecure environments, where the secondary informationtransmission may be wiretapped.

To provide the best secure performance, opportunistic re-laying technique can be used to choose one relay out of two.However, opportunistic relaying needs continuous channelestimation, which leads to an increase in system complexityand may result in a high relay switching rate. To resolve theseissues, the proposed SSSC protocol will be used, where one


relay is activated while the other is silent1. Before presentingthe SSSC protocol, we first detail the two-phase data trans-mission process, as follows.

Assume that the relayRi (i = 1, or 2) is activated, whilethe other relayRj (j 6= i) is silent. All nodes in the networkare equipped with a single antenna due to the size limitation,and operate in a time-division half-duplex mode. Moreover,all the links in the network experience independent Rayleighfading. In the first phase, the secondary userS transmits itssignalxS of unit-variance, andRi receivesyRi

as

yRi=

√

PShS,RixS + nRi

, (1)

wherehS,Ri∼ CN (0, αi) is the instantaneous channel param-

eter of theS–Ri link and nRi∼ CN (0, σ2) is the additive

white Gaussian noise (AWGN) at the relayRi. We denotePS

as the transmit power ofS, and to guarantee the quality ofprimary communication, it is limited by

PS =IP

|hS,PU |2, (2)

where IP is the maximum interference level andhS,PU ∼CN (0, η0) is the instantaneous channel parameter of theS-PU link. From (1)-(2), the received SNR atRi is given by

SNRRi= IP

ui

t0, (3)

whereui = |hS,Ri|2 and t0 = |hS,PU |2 are the associated

channel gains of theS–Ri andS–PU links, respectively, andIP = IP /σ

2 is the maximum interference level-to-noise ratio.Suppose thatRi can correctly decode the message from thesource with data rateRd being constrained by

1

2log2(1 + SNRRi

) ≥ Rd, (4)

which is equivalent toSNRRi≥ γ0, with γ0 = 22Rd − 1

being a given SNR threshold. In this case,Ri forwards thecorrectly decoded signal, and the received signals atD andEare respectively given by

yD =√

PRihRi,DxS + nD, (5)

yE =√

PRihRi,ExS + nE , (6)

where hRi,D ∼ CN (0, βi), hRi,E ∼ CN (0, εi) are theinstantaneous channel parameters ofRi–D andRi–E links,respectively, whilenD ∼ CN (0, σ2) andnE ∼ CN (0, σ2) arethe AWGNs atD andE, respectively. In addition,PRi

is thetransmit power of relayRi, which is limited by

PRi=

IP|hRi,PU |2

, (7)

to guarantee the QoS of primary communications, wherehRi,PU ∼ CN (0, ηi) is the instantaneous channel parameter

1Note that the main purpose of this work is to reduce the implementationcomplexity of the secure relay networks and simultaneouslymaintain thesecure performance. Although the other relay can use the cooperative jammingto enhance the system security, it will cause an increase in the implementationcomplexity, such as synchronization and message exchange between thenetwork nodes [14]–[16]. Hence jamming technique is not considered in thiswork.

of theRi–PU link. From (5)-(7), the received SNRs atD andE are written respectively as

SNRD = IPviti, (8)

SNRE = IPwi

ti, (9)

wherevi = |hRi,D|2, wi = |hRi,E |2 and ti = |hRi,PU |2 are

the associated channel gains.Given a predetermined secure data rateRs, the system

secure transmission will be in outage if

1

2log2(1 + SNRD)−

1

2log2(1 + SNRE) < Rs. (10)

From (10), we can find that the received SNR at eavesdropperE should not exceed the SNR atD to obtain a non-zerosecrecy rate. This constraint is different from that at theprimary user, and hence the eavesdropper cannot be assumedas another primary user. After some manipulations, (10) canbe further written as

1 + IPviti

1 + IPwi

ti

< γs, (11)

whereγs = 22Rs is the secrecy threshold.

III. D ESCRIPTION OF THESSSC PROTOCOL

Before the data transmission, the system needs to deter-mine which relay to be activated for assisting the securetransmission. Suppose that the relayRi (i = 1, or 2) wasused in the previous data transmission. Then at the beginningof the current data transmission, the system first estimatesthe channel parameters of the links withRi from the helpof pilot signals. ThenRi gathers all the channel parametersthrough some dedicated feedback channels. Specifically, thesecondaryRi can gather the channel parameters of interferencelinks from the primary user by using several techniques,e.g., direct feedback from PU, indirect feedback from bandmanager. More details about acquiring the channel informationof interference links can be found in [40]–[43]. As to thechannel parameters of eavesdropper links, the secondaryRi

can obtain these parameters through some feedback when theeavesdropper is active, e.g., the eavesdropper is another activeuser in the network. On the other hand, when the eavesdropperis passive,Ri can still obtain the statistical information ofeavesdropper links, by some ways, such as estimating theeavesdropper’s location in the network. More details aboutacquiring the channel information of eavesdropper links canbe found in [11], [44].

After obtaining the required channel information, SSSC willuse the same relayRi for the current data transmission whenRi can correctly decode the message from the source and moreimportantly, it can guarantee a secure transmission as

1 + IPviti

1 + IPwi

ti

≥ T, (12)

whereT is a given secure switching threshold. Otherwise, ifRi cannot correctly decode the message or fails to guaranteethe secure transmission as described by (12), a relay switching


Pout = p1 Pr[

IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPw1

≥ T,t1 + IP v1

t1 + IPw1

< γs

]

︸︷︷︸

J1

+p1Pr[

IPu1

t0< γ0||

t1 + IP v1

t1 + IPw1

< T, IPu2

t0≥ γ0,

t2 + IP v2

t2 + IPw2

< γs

]

︸︷︷︸

J2

+ p2 Pr[

IPu2

t0≥ γ0,

t2 + IP v2

t2 + IPw2

≥ T,t2 + IP v2

t2 + IPw2

< γs

]

︸︷︷︸

J3

+p2 Pr[

IPu2

t0< γ0||

t2 + IP v2

t2 + IPw2

< T, IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPw1

< γs

]

︸︷︷︸

J4

,

(14)

occurs, which is notified to the other nodes in the networkthrough a dedicated feedback channel. Then, the other relayRj

will be activated, and the system needs to estimate the channelparameters of main and interference links withRj , with thehelp of pilot signals. After that, the current data transmissionstarts through the help ofRj .

Note that in (12), the relayRi needs to know the instan-taneous CSI of the eavesdropper link, in order to determinewhether the secure relay switching occurs or not. In somecommunication scenarios, the instantaneous CSI of eavesdrop-per link is however hard to obtain, and only its statisticalinformation may be known. In this case, the secure relayswitching metric in (12) becomes

1 + IPviti

1 + IPE{wi}

ti

≥ T, (13)

whereE{·} denotes the statistical expectation. If the aboveequation holds andRi can correctly decode the message, thesame relayRi will continue to be used for the current datatransmission. Otherwise, the secure relay switching occurs andthe other relayRj will be activated to assist the current datatransmission.

From (12) and (13), we can conclude that the relay switch-ing of SSSC depends not only on the transmission quality ofmain links, but also on whether the relay can support a securetransmission or not. In contrast, the relay switching of SSCinnon-secure networks [31]–[38] depends only on the transmis-sion quality of main links. As such, the switching mechanismof SSSC is much more complicated than that of SSC in non-secure networks. More importantly, the mathematical analysisof the system performance becomes much more complex. Inthe following section, we study the secure performance of theSSSC protocol by analyzing SOP in the two cases of I-ECSIand S-ECSI.

IV. SECURE PERFORMANCEANALYSIS

A. Analytical SOP with I-ECSI

For a secure transmission system, the system SOP is definedas the probability that the difference in data rate between themain link and eavesdropper link drops below a predetermineddata rate. From this definition and (10)-(11), we can writethe SOP of SSSC with I-ECSI in (14) at the top of this page,where the notation|| denotes the logical OR operation.p1 andp2 are the probabilities that the relayR1 andR2 are activated,respectively. Note thatJ1 andJ3 represent the SOP whenR1

andR2 continue to be used for the current data transmission,

respectively, whileJ2 and J4 correspond to the SOP whenthe relay switching occurs fromR1 to R2, and vice versa,respectively. Alsop1 andp2 are given by

p1 =c1

c1 + c2, (15)

p2 =c2

c1 + c2, (16)

where

c1 = Pr[

IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPw1

≥ T]

, (17)

c2 = Pr[

IPu2

t0≥ γ0,

t2 + IP v2

t2 + IPw2

≥ T]

, (18)

correspond to the probabilities thatR1 andR2 continue to beused for the current data transmission, respectively. Notethatthe two relay branches share the common random variable oft0 related to the transmit powerPS at the secondary source,when the secure relay switching occurs inJ2 and J4. Thiscauses the data transmission of both branches to be correlatedand makes the mathematical analysis more complicated.

To solve this mathematical troublesome, we present theanalytical expressions ofc1, J1 and J2 in the followingproposition,

Proposition 1: An analytical expression ofc1 is given by

c1 = L(γ0η0

IPα1

)L( (T − 1)η1

IPβ1

)

L(Tε1β1

), (19)

whereL(x) = (1+x)−1 and (19) is obtained by applying theprobability density functions offu1

(x) = 1α1

e− x

α1 , ft0(x) =1η0

e−xη0 , ft1(x) =

1η1

e−xη1 , fv1(x) =

1β1

e−xβ1 andfw1

(x) =1ε1e− x

ε1 [45]. The analytical expressions ofJ1 andJ2 are givenby

J1 =

L(γ0η0

IPα1

)[

L((T − 1)η1

IPβ1

)

L(Tε1β1

)

−L(

(γs−1)η1

IP β1

)

L(γsε1β1

)]

, If T < γs

0, If T ≥ γs

.

(20)

J2 =[

1− L((γs − 1)η2

IPβ2

)

L(γsε2β2

)][

L(γ0η0

IPα2

)

− L(

(1

α1+

1

α2)γ0η0

IP

)

L((T − 1η1)

IPβ1

)

L(Tε1β1

)]

. (21)

Proof: See Appendix A.


Pout = p1 Pr[

IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPE{w1}≥ T,

t1 + IP v1

t1 + IPw1

< γs

]

︸︷︷︸

J1

+p1Pr[

IPu1

t0< γ0||

t1 + IP v1

t1 + IPE{w1}< T, IP

u2

t0≥ γ0,

t2 + IP v2

t2 + IPw2

< γs

︸︷︷

J2

+ p2 Pr[

IPu2

t0≥ γ0,

t2 + IP v2

t2 + IPE{w2}≥ T,

t2 + IP v2

t2 + IPw2

< γs

]

︸︷︷︸

J3

+p2 Pr[

IPu2

t0< γ0||

t2 + IP v2

t2 + IPE{w2}< T, IP

u1

t0≥ γ0,

t1 + IP v1

t1 + IPw1

< γs

︸︷︷

J4

(22)

θ =

[

L((T − 1)η1

IPβ1

)

− L(γsε1β1

)L( (γs − 1)η1

IPβ1

)]

e−q0 + L((T − 1)η1

IPβ1

)

L(−q1γsε1)

×(

e−Tε1β1

−q1Tε1 − e−q0

)

− L(

(γs−1)η1

IP β1

)

L(

( γs

β1

− q2γs)ε1

)(

e−q2Tε1 − e−q0

)

If T < γs

L((T − γs)η1

IP ε1γs+

(T − 1)η1

IPβ1

)(

1− L(γsε1β1

))

e−q0 , If T ≥ γs

. (30)

By replacingα1, β1, η1 andε1 by α2, β2, η2 andε2 respec-tively, we can obtain the analytical expression ofc2 from theexpression ofc1 in Proposition 1. This leads to the analyticalexpressions ofp1 and p2. Similarly, by swappingα1 withα2, β1 with β2, andη1 with η2, we can obtain the analyticalexpressions ofJ3 andJ4 from the expressions ofJ1 andJ2 inProposition 1. In this way, we arrive at the analytical expres-sion of SOP with I-ECSI asPout = p1(J1+J2)+p2(J3+J4).

B. Analytical SOP with S-ECSI

According to the definition of SOP, we can write the SOP ofSSSC with S-ECSI in (22) at the top of the next page, whereJ1 and J3 represent the SOP whenR1 and R2 continue tobe used for the current data transmission, respectively, whileJ2 and J4 correspond to the SOP when the relay switchingoccurs fromR1 to R2, and that fromR2 to R1, respectively.Also, p1 and p2 are given by

p1 =c1

c1 + c2, (23)

p2 =c2

c1 + c2, (24)

where

c1 = Pr[

IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPE{w1}≥ T

]

, (25)

c2 = Pr[

IPu2

t0≥ γ0,

t2 + IP v2

t2 + IPE{w2}≥ T

]

, (26)

correspond to the probabilities thatR1 andR2 continue to beused for the current data transmission, respectively. Similar tothe analysis ofJ2 and J4, the two relay branches share thecommon random variable oft0, when the secure relay switch-ing occurs inJ2 and J4. This makes the data transmissionof both branches correlated, and the mathematical analysisbecomes more complicated. Moreover, the secure switchingmetric t1+IP v1

t1+IPE{w1}is highly correlated with the outage metric

t1+IP v1t1+IP w1

, but not the same. This correlation will also causemuch difficulty to the mathematical analysis.

To resolve the complicated mathematical analysis, we givethe analytical expressions ofc1, J1 and J2 in the followingproposition,

Proposition 2: The analytical expression ofc1 is given by

c1 = L(γ0η0

IPα1

)L( (T − 1)η1

IPβ1

)

e−ε1T

β1 . (27)

The analytical expressions ofJ1 and J2 are given by

J1 = L(γ0η0

IPα1

)θ, (28)

J2 =[

1− L((γs − 1)η2

IPβ2

)

L(γsε2β2

)][

L(γ0η0

IPα2

)

− L(

(1

α1+

1

α2)γ0η0

IP

)

L((T − 1)η1

IPβ1

)

e−Tε1β1

]

, (29)

whereθ is given by (30) at the top of this page, and

q0 =T

γs+

Tε1β1

q1 = (1

η1+

T − 1

IPβ1

)IP

γs − T

q2 = (1

η1+

γs − 1

IPβ1

)IP

γs − T

. (31)

Proof: See Appendix B.Similarly, by replacingα1 by α2, β1 with β2, and η1 withη2, we can obtain the analytical expression ofc2 from theexpression ofc1 in Proposition 2. This leads to the analyticalexpressions ofp1 and p2. By swappingα1 with α2, β1 withβ2, andη1 with η2, we can obtain the analytical expressionsof J3 andJ4 from the expressions ofJ1 andJ2 in Proposition2. In this way, we arrive at the analytical expression of SOPwith S-ECSI asPout = p1(J1 + J2) + p2(J3 + J4).


C. Asymptotic SOP with I-ECSI

To obtain additional insights on the system performance,we now extend to analyze the asymptotic SOP performanceof SSSC with I-ECSI, in high transmit power and high MERregions, where MER is defined as the ratio of average channelgain from the relay to intended receiver to that from relay toeavesdropper [11]. The asymptotic SOP with I-ECSI is givenby the following proposition,

Proposition 3: The asymptoticc1 andc2 with high transmitpower and high MER can be approximated from [36, eq.(1.112)] as

c1 ≃ 1, c2 ≃ 1. (32)

We further write the asymptotic SOP of SSSC with I-ECSI inhigh transmit power and high MER region as

Pout ≃

ε1 + ε22λ1λ2

+γs − T

2

(1 + ζ1λ1

+1 + ζ2λ2

)

, If T < γs

ε1 + ε22λ1λ2

, If T ≥ γs

,

(33)

where

ζ1 =ρ1η1β1

, ζ2 =ρ2η2β2

ρ1 =λ1

IP, ρ2 =

λ2

IP

ε1 = [γs + (γs − 1)ζ2] · [T + (T − 1)ζ1 + γ0η0ρ1/α1]

ε2 = [γs + (γs − 1)ζ1] · [T + (T − 1)ζ2 + γ0η0ρ2/α2]

.

(34)

Proof: See Appendix C.In particular, when the transmit power is much larger thanMER with IP ≫ λi (i = 1, 2), ρi approaches to zero, causingthat ζi ≃ 0 and εi ≃ 0. In this case, we can simplify theasymptotic SOP in (33) as

Pout ≃

Tγsλ1λ2

+γs − T

2

( 1

λ1+

1

λ2

), If T < γs

Tγsλ1λ2

, If T ≥ γs

. (35)

From the above asymptotic expressions, we can get the fol-lowing insights on the system:Remark 1: In high IP and MER region, bothc1 and c2approach to one, indicating that the same relay will continueto be used for a long time. Hence, the system only needsto estimate the channel parameters with a single relay. Thiscan substantially reduce the implementation complexity inpractice.Remark 2: When T ≥ γs, the system can achieve the fulldiversity order of two, as a large value ofT can guaranteean effective secure relay switching. On the other hand, whenT < γs, the system diversity order falls into[1, 2), indicatingthat too small a value ofT cannot effectively exploit the tworelays to guarantee the secure transmission.Remark 3: The optimal value of the secure switching thresholdT ∗ is equal to the system secrecy thresholdγs.

D. Asymptotic SOP with S-ECSI

To obtain some insights on the system of SSSC protocolwith S-ECSI, we now derive the asymptotic SOP with largeIP and MER, in the following proposition,

Proposition 4: The asymptoticc1 andc2 with largeIP andMER can be written from [36, eq. (1.112)] as

c1 ≃ 1, c2 ≃ 1. (36)

Then we approximate the SOP of SSSC with S-ECSI in highIP and high MER regions as

Pout ≃

ε1 + ε22λ1λ2

+γs2e−

Tγs

[1− ε23e− T

γs

1−ε3ε3

(1− ε3)λ1

+1− ε24e

− Tγs

1−ε4ε4

(1− ε4)λ2

]

, If T < γs

ε1 + ε22λ1λ2

+γs2e−

Tγs

( 1

(1− ε3)λ1

+1

(1− ε4)λ2

)

, If T ≥ γs

,

(37)

with{

ε3 = (γs − T )ζ1/γs

ε4 = (γs − T )ζ2/γs. (38)

Proof: See Appendix D.In particular, when the transmit power is much larger thanthe value of MER withIP ≫ λi (i = 1, 2), both ε3 andε4 approach to zero due toζi ≃ 0. In this condition, theasymptotic SOP of SSSC with S-ECSI is simplified as

Pout ≃γsT

λ1λ2+

γs2

( 1

λ1+

1

λ2

)

e−Tγs . (39)

By setting the derivative of abovePout with respect toT intozero, we can readily obtain the minimumPout as

Pout,min =γ2s

λ1λ2

(

1 + lnλ1 + λ2

2γs

)

. (40)

From these asymptotic results, we can achieve the followinginsights on the system performance with S-ECSI:Remark 1: As both c1 and c2 approach to 1 in highIPand MER region, the same relay will continue to be usedfor data transmission in a long time. Hence, even with S-ECSI, the SSSC protocol can substantially reduce the systemimplementation complexity compared with the opportunisticrelaying protocol.Remark 2: From the above asymptotic results ofPout, we canfind that the system diversity order falls between one and two.In particular, the system diversity order can approach to twofor a large value ofT , which can effectively exploit the tworelays to guarantee the secure transmission.Remark 3: By comparing the minimum asymptoticPout ofS-ECSI with that of I-ECSI, we can find that the systemperformance is degraded, since the eavesdropping CSI is notfully known in the secure switching process.


E. Complexity Analysis

In this subsection, we briefly discuss the channel estimationcomplexity of the proposed SSSC protocol. When the securerelay switching does not occur, the system only needs toestimate the channel parameters of a single relay, and hencethe channel estimation complexity of SSSC is just half of thatof the opportunistic relaying. On the other hand, when thesecure relay switching happens, the system needs to estimatethe channel parameters of both relays, and SSSC requires thesame channel estimation complexity as opportunistic relaying.In summary, the channel estimation complexity of SSSC withI-ECSI, normalized by that of opportunistic relaying, is givenby

µI = p1

[c12

+ (1− c1)]

+ p2

[c22

+ (1− c2)]

= 1−1

2

c21 + c22c1 + c2

. (41)

Similarly, for SSSC with S-ECSI, its normalized channelestimation complexity is given by

µS = 1−1

2

c21 + c22c1 + c2

. (42)

As the stay probabilitiesci andci are both in the interval[0, 1]for i = 1, 2, one can find that the normalized complexity ofSSSC falls into[0.5, 1]. Moreover, as bothci andci approach 1with high transmit power and MER, SSSC protocol can reducethe channel estimation complexity of opportunistic relaying toalmost half.

V. SIMULATION AND NUMERICAL RESULTS

In this section, numerical and simulation results are pre-sented to verify the proposed system. All the links in thesystem experience flat Rayleigh fading. The distance betweenthe secondary source and destination is set to unity, and thetwo relays are between in them. LetD1 and D2 denotethe distance from the secondary source to relayR1 andR2,respectively. Accordingly, the average channel gains of thetwo-hop main links are set toα1 = D−4

1 , α2 = D−42 ,

β1 = (1 − D1)−4, and β2 = (1 − D2)

−4, where the path-loss model with loss factor of four is used. Without loss ofgenerality, we set the average channel gains of interferencelinks to unity, so thatη0 = η1 = η2 = 1.The source data rateRd is set to 1 bps/Hz, so that the associatedγ0 is equal to3. The secrecy data rateRs is set to0.5 bps/Hz, so that thesecrecy SNR thresholdγs is equal to 2.

Fig. 2 depicts the analytical, asymptotic and simulated SOPsof SSSC versus MER withλ1 = λ2 = λ and IP = 20dB2,where the asymptotic results are computed from eqs. (33) and(37), respectively. The secure switching thresholdT varies in{0.5, 1, 2}T ∗ 3, where the optimal switching thresholdT ∗ isset toγs for I-ECSI, while for S-ECSI,T ∗ can be obtained

2We consider communication scenarios withIP = 20dB, indicating thatthe primary user can tolerate a high interference level, which is widely usedin cognitive relay networks [40]–[43].

3Besides the optimal secure switching threshold, two other typical values,0.5T ∗ and2T ∗, are set forT to show the impact ofT on the system secureperformance.

0 5 10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

MER λ (dB)

Se

cre

cy o

uta

ge

pro

ba

bili

ty

P ou

t

19.95 20 20.05

10−3.3

10−3.1

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB~

T=0.5T*

T=T*

T=2T*

Simulation

SimulationRelay system

with one relay

AsymptoticAnalysis

SimulationOpportunistc relaying:

SSSC:

(a) I-ECSI

0 5 10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

MER λ (dB)

Se

cre

cy o

uta

ge

pro

ba

bili

ty

Po

ut

19.95 20 20.0510

−3

10−2

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB~

T=0.5T*T=2T*T=T*

Simulation


with one relay

AsymptoticAnalysis


SSSC:

(b) S-ECSI

Fig. 2. Secrecy outage probability versus MER.

by some numerical methods from (37) [31]–[37]. Fig. 2 (a)and (b) correspond to the SSSC with I-ECSI and S-ECSI,respectively. For comparison, we plot the simulated secrecyoutage probabilities of opportunistic relaying and the relaysystem with only one relay as the lower and upper bounds,respectively. As observed from Fig. 2 (a) and (b), we canfind that for both cases of I-ECSI and S-ECSI, the analyticalresult of SSSC matches well with the simulation one, andthe asymptotic result converges to the exact value with highMER more than 20dB. This verifies the validity of the derivedanalytical secrecy outage probability of SSSC and asymptoticexpression. Moreover, SSSC with I-ECSI can have the samesecure performance as opportunistic relaying whenT = T ∗,and hence achieve the full diversity order. ForT = 2T ∗,SSSC of I-ECSI can also achieve the system full diversityorder of two. ForT = 0.5T ∗, the curve line of SSSC withI-ECSI is parallel with the relay system with only one relay,indicating that the system diversity degenerates into one.Onthe other hand, although SSSC with S-ECSI cannot achievethe same performance as opportunistic relaying, the lines withT ∈ {1, 2}T ∗ are approximately parallel with opportunisticrelaying, indicating that SSSC with S-ECSI can also approach


T=T*

0 5 10 15 20 25 30 35 4010

−6

10−5

10−4

10−3

10−2

10−1

100

Peak interference to noise power ratio (dB)

Secrecy outage probability P out

19.95 20 20.05

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=30dB

Simulation


with one relay

AsymptoticAnalysis


SSSC:

T=0.5T*

T=2T*

10−5

10−4.7

(a) I-ECSI

0 5 10 15 20 25 30 35 4010

−6

10−5

10−4

10−3

10−2

10−1

100

Peak interference to noise power ratio (dB)

Se

cre

cy o

uta

ge

pro

ba

bili

ty

P ou

t

19.95 20 20.0510

−4.3

10−4.1

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=30dB

T=0.5T*T=2T*T=T*

Simulation


with one relay

AsymptoticAnalysis


SSSC:

(b) S-ECSI

Fig. 3. Secrecy outage probability versusIP .

the system full diversity order of two in high MER region. Thiscan be explained from the asymptotic analysis in (37), whichcontains two terms on the right hand side. Hence the diversityof SSSC falls between one and two, causing the curve of SSSCapproximately parallel with opportunistic relaying. Whenthesecure switching threshold becomes very large, SSSC with S-ECSI approaches to the system full diversity order of two,since the exponential decreasing term of (37) converges tozero.

Fig. 3 shows the effect ofIP on the system secrecy outageprobability of SSSC, where the secure switching thresholdT varies in {0.5, 1, 2}T ∗, λ1 = λ2 = 30dB. Specifically,Fig. 3 (a) and (b) correspond to the SSSC with I-ECSI andS-ECSI, respectively. We can see from this figure that fordifferent values ofT and IP , the analytical result of SSSCis very close to the simulation one, and the asymptotic resultconverges to the exact value in highIP region. This alsovalidates the derived analytical and asymptotic expressionsof SOP for SSSC with I-ECSI and S-ECSI. Moreover, SSSCwith I-ECSI and optimal secure switching threshold presentsthe same performance as opportunistic relaying. In contrast,there is a performance gap between SSSC and opportunistic

T=T*

0 5 10 15 20 25 300.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MER λ (dB)

Value

of c 1

T=0.5T*

T=2T*

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB~

Analysis

Simulation

(a) I-ECSI

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MER λ (dB)

Value

of c 1

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB

T=0.5T*

~

Analysis

Simulation

~

T=T*

T=2T*

(b) S-ECSI

Fig. 4. Effect ofT on c1 and c1 versus MER.

relaying when S-ECSI is known, indicating that the securerelaying switching is more effective with I-ECSI.

Fig. 4 illustrates the effect ofT on the simulation andanalytical results ofc1 and c1

4 of SSSC versus MER withλ1 = λ2 = λ and IP = 20dB, where the secure switchingthresholdT varies in {0.5, 1, 2}T ∗. Specifically, Fig. 4 (a)and (b) correspond to the SSSC with I-ECSI and S-ECSI,respectively. From this figure, we can find that for both I-ECSIand S-ECSI,c1 and c1 increase with largerIP and smallerT .In particular,c1 and c1 converge to unity with large value ofIP , indicating that the secure relay switching seldom occursand the system needs to estimate the channel parameters ofonly one relay. In other words, the SSSC technique can reducethe channel estimation complexity of opportunistic relayingto almost half and meanwhile substantially reduce the relayswitching rate.

Fig. 5 demonstrates the normalized channel estimationcomplexity of SSSC versus MER withλ1 = λ2 = λ andIP = 20dB, where the secure switching thresholdT varies in{0.5, 1, 2}T ∗. In particular, Fig. 5 (a) and (b) correspond to

4As c2 and c2 show the similar behavior asc1 and c1, the results ofc2and c2 are not plotted in this figure for clarity.


T=0.5T*

T=T*

0 5 10 15 20 25 300.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

MER λ (dB)

Normalized

channel estimation

complexity

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB~

T=2T*

µΙ

(a) I-ECSI

0 5 10 15 20 25 300.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

MER λ (dB)

Normalized

channel estimation

complexity

η0=η1=η2=1D1=0.5, D2=0.3λ1=λ2=λ

IP =20 dB~

T=0.5T*

T=T*

T=2T*

µS

(b) S-ECSI

Fig. 5. Normalized channel estimation complexity of SSSC versus MER.

SSSC with I-ECSI and S-ECSI, respectively. We can observefrom Fig. 5 that for both I-ECSI and S-ECSI, the channelestimation complexity of SSSC decreases with larger MERor smaller switching threshold, as the secure relay switchinghappens less. Moreover, SSSC can reduce the channel estima-tion complexity of opportunistic relaying to almost half inthehigh MER region, which validates the advantages of SSSCover opportunistic relaying.

VI. CONCLUSIONS

This paper proposed SSSC technique for the secure cog-nitive relay networks with two DF relays. In SSSC, onerelay out of two was chosen to be activated to assist thedata transmission from the secondary source to secondarydestination. The same relay continued to be used for datatransmission when the relay could support the secure datatransmission; otherwise the secure relay switching occurredand the other relay would be activated. It has been shownby the simulation and numerical results that SSSC with I-ECSI can exploit the system full diversity, and SSSC withS-ECSI can approach to the full diversity with large securerelaying switching threshold. Moreover, SSSC can reduce the

channel estimation complexity of opportunistic relaying toalmost half in high MER region, and provide a stable networkconfiguration.

APPENDIX APROOF OFPROPOSITION1

As the variableu1

t0is independent oft1+IP v1

t1+IPw1

, we can writec1 from (17) as

c1 = Pr(u1

t0≥

γ0

IP) · Pr

( t1 + IP v1

t1 + IPw1

≥ T)

. (A.1)

By applying the probability density functions offu1(u1) =

1α1

e−u1

α1 , ft0(t0) = 1η0

e−t0η0 , ft1(t1) = 1

η1

e−t1η1 , fv1(v1) =

1β1e−

v1β1 and fw1

(w1) =1ε1e−

w1

ε1 , we can computePr(u1

t0≥

γ0

IP) andPr

(t1+IP v1t1+IPw1

≥ T)

as

Pr(u1

t0≥

γ0

IP) =

∫ ∞

0

ft0(t0)

∫ ∞

γ0IP

t0

fu1(u1)du1dt0 (A.2)

= L(γ0η0

IPα1

), (A.3)

(A.4)

Pr( t1 + IP v1

t1 + IPw1

≥ T)

= Pr(

v1 ≥T − 1

IPt1 + Tw1

)

(A.5)

=

∫ ∞

0

ft1(t1)

∫ ∞

0

fw1(w1)

∫ ∞

T−1

IPt1+Tw1

fv1(v1)dv1dw1dt1

(A.6)

= L(Tε1β1

)L((T − 1)η1

IPβ1

)

, (A.7)

whereL(x) = (1+x)−1. By combining eqs. (A.3) and (A.7),we can obtain the analytical expression ofc1, as shown in (19)of Proposition 1.

We now turn to derive the analytical expression ofJ1. Asthe variableu1

t0is independent oft1+IP v1

t1+IP w1

, we can writeJ1as

J1 = Pr(u1

t0>

γ0

IP) · Pr

( t1 + IP v1

t1 + IPw1

≥ T,t1 + IP v1

t1 + IPw1

< γs

)

(A.8)

= L(γ0η0

IPα1

) Pr( t1 + IP v1

t1 + IPw1

≥ T,t1 + IP v1

t1 + IPw1

< γs

)

,

(A.9)

where we apply the result of (A.3) in the last equality. WhenT ≥ γs, t1+IP v1

t1+IPw1

≥ T contradicts witht1+IP v1t1+IPw1

< γs, causingthatJ1 = 0. On the other hand, whenT < γs, we can furtherwrite J1 as

J1 = L(γ0η0

IPα1

)[

Pr( t1 + IP v1

t1 + IPw1

≥ T)

− Pr( t1 + IP v1

t1 + IPw1

≥ γs

)]

(A.10)

= L(γ0η0

IPα1

)[

L((T − 1)η1

IPβ1

)

L(Tε1β1

)

− L((γs − 1)η1

IPβ1

)

L(γsε1β1

)]

, (A.11)


where we apply the result of (A.7) in the last equality.We now turn to derive the analytical expression ofJ2 as

J2 = Pr( t2 + IP v2

t2 + IPw2

< γs

)

× Pr(

IPu1

t0< γ0||

t1 + IP v1

t1 + IPw1

< T, IPu2

t0≥ γ0

)

(A.12)

=[

1− L((γs − 1)η2

IPβ2

)

L(γsε2β2

)]

× Pr(

IPu1

t0< γ0||

t1 + IP v1

t1 + IPw1

< T, IPu2

t0≥ γ0

)

︸︷︷︸

J21

,

(A.13)

where the last equality is obtained by applying the result of(A.7). We further writeJ21 as

J21 = Pr(u2

t0≥

γ0

IP

)

− Pr(

IPu1

t0≥ γ0,

t1 + IP v1

t1 + IPw1

≥ T,u2

t0≥

γ0

IP

)

(A.14)

= L(γ0η0

IPα2

)− Pr(

IPu1

t0≥ γ0, IP

u2

t0≥ γ0

)

× Pr( t1 + IP v1

t1 + IPw1

≥ T)

(A.15)

= L(γ0η0

IPα2

)− Pr(

IPu1

t0≥ γ0, IP

u2

t0≥ γ0

)

× L((T − 1)η1

IPβ1

)

L(Tε1β1

), (A.16)

where we apply the results of eqs. (A.3) and (A.7) into eqs.(A.15) and (A.16), respectively. In further, the probability ofPr

(

IPu1

t0≥ γ0, IP

u2

t0≥ γ0

)

can be computed as

Pr(u1

t0≥

γ0

IP,u2

t0≥

γ0

IP

)

=

∫ ∞

0

ft0(t0)

∫ ∞

γ0

IPt0

fu1(u1)du1

∫ ∞

γ0

IPt0

fu2(u2)du2dt0

(A.17)

= L(

(1

α1+

1

α2)γ0η0

IP

)

. (A.18)

By combining the above eqs. (A.13), (A.16) and (A.18), wecan arrive at the analytical expression ofJ2, as shown in (21)of Proposition 1. In this way, we have completed the proof ofProposition 1.

APPENDIX BPROOF OFPROPOSITION2

From (25), we can writec1 with S-ECSI as

c1 = Pr(u1

t0≥

γ0

IP

)

· Pr( t1 + IP v1

t1 + IPE{w1}≥ T

)

(B.1)

= L( γ0η0

IPα1

)

Pr( t1 + IP v1

t1 + IP ε1≥ T

)

, (B.2)

where we apply the result of (A.3) in the last equality.Pr

(t1+IP v1t1+IP ε1

≥ T)

can be computed as

Pr( t1 + IP v1

t1 + IP ε1≥ T

)

= Pr(

v1 ≥T − 1

IPt1 + Tε1

)

(B.3)

=

∫ ∞

0

ft1(t1)

∫ ∞

T−1

IPt1+Tε1

fv1(v1)dv1dt1 (B.4)

= L((T − 1)η1

IPβ1

)

e−

ε1T

β1 , (B.5)

By combining the results of eqs. (B.2) and (B.5), we can obtainthe analytical expression ofc1, as shown in (27) of Proposition2.

We now turn to derive the analytical expression ofJ1 in(22) as

J1 = Pr(u1

t0≥

γ0

IP

)

× Pr( t1 + IP v1

t1 + IPE{w1}≥ T,

t1 + IP v1

t1 + IPw1

< γs

)

(B.6)

= L( γ0η0

IPα1

)

× Pr(

v1 ≥T − 1

IPt1 + Tε1, v1 <

γs − 1

IPt1 + Tw1

)

︸︷︷︸

J11

,

(B.7)

where we apply the result of (A.3) in the last equality. InJ11,γs−1

IPt1 + Tw1 needs to be larger thanT−1

IPt1 + Tε1, causing

that

γsw1 ≥T − γs

IPt1 + Tε1. (B.8)

Hence we now consider the two cases ofT ≥ γs andT < γs.If T ≥ γs, the condition of (B.8) becomes

w1 ≥T − 1

IPγst1 +

Tε1γs

, (B.9)

and J11 is computed as

J11 =

∫ ∞

0

ft1(t1)

∫ ∞

T−1

IP γst1+

Tε1γs

fw1(w1)

∫ γs−1

IPt1+Tw1

T−1

IPt1+Tε1

fv1(v1)dv1dw1dt1 (B.10)

= L((T − γs)η1

IP ε1γs+

(T − 1)η1

IPβ1

)(

1− L(γsε1β1

))

e−q0 ,

(B.11)

whereq0 is defined in (31).On the other hand, whenT < γs holds, the condition of

(B.8) becomes

w1 +γs − T

IP γst1 ≥

Tε1γs

. (B.12)

This condition can be specified into two integral regionsof w1 ≥ Tε1

γsand w1 < Tε1

γswith t1 ≥ IPTε1−IP γsw1

γs−T.


Accordingly, we can computeJ11 as

J11 =

∫ ∞

0

ft1(t1)

∫ ∞

Tε1γs

fw1(w1)

∫ γs−1

IPt1+Tw1

T−1

IPt1+Tε1

fv1(v1)dv1dw1dt1

+

∫ Tε1γs

0

fw1(w1)

∫ ∞

IP Tε1−IP γsw1

γs−T

ft1(t1)

∫ γs−1

IPt1+Tw1

T−1

IPt1+Tε1

fv1(v1)dv1dt1dw1 (B.13)

=[

L((T − 1)η1

IPβ1

)

− L(γsε1β1

)L((γs − 1)η1

IPβ1

)]

e−q0

+ L((T − 1)η1

IPβ1

)

L(−q1γsε1)(

e−

Tε1β1

−q1Tε1 − e−q0)

− L((γs − 1)η1

IPβ1

)

L(

(γsβ1

− q2γs)ε1

)(

e−q2Tε1 − e−q0)

,

(B.14)

whereq1 andq2 are defined in (31). By combining eqs. (B.7),(B.11) and (B.14), we can arrive at the analytical expressionof J1, as shown in (28) of Proposition 2.

We now turn to derive the analytical expression ofJ2. From(22), we can writeJ2 as

J2 = Pr( t2 + IP v2

t2 + IPw2

< γs

)

× Pr(u1

t0<

γ0

IP||t1 + IP v1

t1 + IP ε1< T,

u2

t0≥

γ0

IP

)

(B.15)

=[

1− L((γs − 1)η2

IPβ2

)

L(γsε2β2

)]

× Pr(u1

t0<

γ0

IP||t1 + IP v1

t1 + IP ε1< T,

u2

t0≥

γ0

IP

)

︸︷︷︸

J21

, (B.16)

where we apply the result of (A.7) in the last equality. Infurther, J21 can be computed as

J21 = Pr(u2

t0≥

γ0

IP

)

− Pr(u1

t0≥

γ0

IP,t1 + IP v1

t1 + IP ε1≥ T,

u2

t0≥

γ0

IP

)

(B.17)

= Pr(u2

t0≥

γ0

IP

)

− Pr(u1

t0≥

γ0

IP,u2

t0≥

γ0

IP

)

× Pr( t1 + IP v1

t1 + IP ε1≥ T

)

(B.18)

= L(γ0η0

IPα2

)− L(

(1

α1+

1

α2)γ0η0

IP

)

L((T − 1)η1

IPβ1

)

e−Tε1β1 ,

(B.19)

where we apply the results of eqs. (A.3), (A.7) and (B.5) inthe last equality. By combining the results in eqs. (B.16) and(B.19), we can obtain the analytical expression ofJ2 with S-ECSI, as shown in (29) of Proposition 2. In this way, we havecompleted the proof of Proposition 2.

APPENDIX CPROOF OFPROPOSITION3

We first derive the asymptotic expressions ofc1 andc2. Tothis end, we use the approximation of(1 + x)−1 ≃ 1− x for

small value of|x| [36, eq. (1.112)] and obtain the asymptoticc1 andc2 as

c1 ≃ 1, c2 ≃ 1, (C.1)

which leads top1 ≃ 0.5 and p2 ≃ 0.5. We now derive theasymptotic expressions ofJ1, J2, J3 andJ4. WhenT < γs,we apply the approximation of(1 + x)−1 ≃ 1− x and obtainthe asymptotic expression ofJ1 with high IP and MER as

J1 ≃γs − T

λ1

(

1 +η1ρ1β1

)

, (C.2)

whereρ1 is defined in (34). We further apply the approxima-tion of (1+x)−1 ≃ 1−x into the expression ofJ2, and obtainthe asymptoticJ2 with high IP and MER as

J2 ≃ε1

λ1λ2, (C.3)

where ε1 is defined in (34). Similarly, we can obtain theasymptotic expressions ofJ3 and J3. By combining theasymptotic results ofJ1, J2, J3 andJ4, we can arrive at theasymptotic SOP with highIP and MER, as shown in (33). Inthis way, we have finished the proof of Proposition 3.

APPENDIX DPROOF OFPROPOSITION4

By applying the approximation of(1 + x)−1 ≃ 1 − x forsmall value of|x| [36, eq. (1.112)], we can approximate theexpressions ofc1 and c2 with large IP and MER as

c1 ≃ 1, c2 ≃ 1. (D.1)

Accordingly, the asymptoticp1 and p2 are given by

p1 ≃1

2, p2 ≃

1

2. (D.2)

We then extend to derive the asymptotic expressions ofJ1,J2, J3 and J4 with high IP and high MER. By applying theapproximation of(1 + x)−1 ≃ 1 − x for small value of|x|[36, eq. (1.112)], we can obtain the asymptotic expression ofJ1 and J2 as

J1 ≃

γsλ1

e−Tγs

1

1− ε3

(

1− ε23e− T

γs

1−ε3ε3

)

, If T < γs

γsλ1

e−Tγs

1

1− ε3, If T ≥ γs

,

(D.3)

J2 ≃ε1

λ1λ2, (D.4)

whereε3 is defined in (38). In a similar way, we can obtainthe asymptotic expressions ofJ3 and J4 with high IP andhigh MER. By summarizing these asymptotic expressions, wecan arrive at the asymptotic SOP of SSSC with S-ECSI. Inthis way, we have completed the proof of Proposition 4.


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Lisheng Fan received the bachelor and master de-grees from Fudan University and Tsinghua Univer-sity, China, in 2002 and 2005, respectively, bothfrom Department of Electronic Engineering. He re-ceived the Ph.D degree from Deparment of Com-munications and Integrated Systems of Tokyo In-stitute of Technology, Japan, in 2008. From 2014,he has been an Professor. His research interestsspan in the areas of wireless cooperative commu-nications, physical-layer secure communications, in-terference modeling, and system performance eval-

ulation. Lisheng Fan has published many papers in international journalssuch as IEEE Transaction on Wireless Communications, IEEE Transactionon Vehicular Technology, IEEE Communications Letters and IEEE WirelessCommunications Letters, as well as papers in conferences such as IEEE ICC,IEEE Globecom, and IEEE WCNC. He is a guest editor of EURASIP Journalon Wireless Communications and Networking , and served as the chair ofWireless Communications and Networking Symposium for Chinacom 2014.He has also served as a member of Technical Program Committees for IEEEconferences such as Globecom, ICC, WCNC, and VTC.

Shengli Zhang received his B. Eng. degree inelectronic engineering and the M. Eng. degree incommunication and information engineering fromthe University of Science and Technology of China(USTC), Hefei, China, in 2002 and 2005, respec-tively. He received his Ph.D in the Departmentof Information Engineering, the Chinese UniversityUniversity of Hong Kong (CUHK), in 2008. Afterthat, he worked as a research associate in CUHK. InMay. 2009, he joined the Communication Engineer-ing Department, Shenzhen University. Now, he holds

an associate professor there. From 2014 to 2015, he was a visiting associateprofessor at Stanford University. His research interests include physical layernetwork coding, known interference cancellation, and cooperative wirelessnetworks.

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 ONEMERGING TELECOMMUNICA-TIONS TECHNOLOGIES, and ELECTRONICSLETTERS. He has also servedas the Guest Editor of the special issue on some major journals includingIEEE JOURNAL IN SELECTED AREAS ON COMMUNICATIONS, IET COM-MUNICATIONS, IEEE WIRELESS COMMUNICATIONS MAGAZINE, IEEECOMMUNICATIONS MAGAZINE, EURASIP JOURNAL ON WIRELESSCOM-MUNICATIONS AND NETWORKING, EURASIP JOURNAL ON ADVANCES

SIGNAL PROCESSING. He was awarded the Best Paper Award at the IEEEVehicular Technology Conference (VTC-Spring) in 2013, IEEE InternationalConference on Communications (ICC) 2014.

George K. Karagiannidis (M’96-SM’03-F’14) wasborn in Pithagorion, Samos Island, Greece. He re-ceived the University Diploma (5 years) and PhDdegree, both in electrical and computer engineeringfrom the University of Patras, in 1987 and 1999, re-spectively. From 2000 to 2004, he was a Senior Re-searcher at the Institute for Space Applications andRemote Sensing, National Observatory of Athens,Greece. In June 2004, he joined the faculty ofAristotle University of Thessaloniki, Greece wherehe is currently Professor in the Electrical Computer

Engineering Dept. and Director of Digital Telecommunications Systems andNetworks Laboratory. His research interests are in the broad area of digitalcommunications systems with emphasis on communications theory, energyefficient MIMO and cooperative communications, satellite communications,cognitive radio, localization, smart grid and optical wireless communications.He is the author or co-author of more than 300 technical papers publishedin scientific journals and presented at international conferences. He is alsoauthor of the Greek edition of a book on ”TelecommunicationsSystems” andco-author of the book ”Advanced Optical Wireless Communications Systems”,Cambridge Publications, 2012. Dr. Karagiannidis has been amember ofTechnical Program Committees for several IEEE conferencessuch as ICC,GLOBECOM, VTC, etc. In the past he was Editor in IEEE Transactions onCommunications, Senior Editor of IEEE Communications Letters and Editorof the EURASIP Journal of Wireless Communications Networks. He was LeadGuest Editor of the special issue on ”Optical Wireless Communications” ofthe IEEE Journal on Selected Areas in Communications and Guest Editorof the special issue on ”Large-scale multiple antenna wireless systems”.Dr. Karagiannidis has been selected as a 2015 Thomson Reuters HighlyCited Researcher and since January 2012 he is the Editor-in Chief of IEEECommunications Letters.

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