Relay-Selection Improves the Security-Reliability Trade...

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 1, JANUARY 2015 215

Relay-Selection Improves the Security-ReliabilityTrade-Off in Cognitive Radio Systems

Yulong Zou, Senior Member, IEEE, Benoit Champagne, Senior Member, IEEE,Wei-Ping Zhu, Senior Member, IEEE, and Lajos Hanzo, Fellow, IEEE

Abstract—We consider a cognitive radio (CR) network consistingof a secondary transmitter (ST), a secondary destination (SD) andmultiple secondary relays (SRs) in the presence of an eavesdropper,where the ST transmits to the SD with the assistance of SRs, whilethe eavesdropper attempts to intercept the secondary transmission.We rely on careful relay selection for protecting the ST-SD trans-mission against the eavesdropper with the aid of both single-relayand multi-relay selection. To be specific, only the “best” SR is cho-sen in the single-relay selection for assisting the secondary trans-mission, whereas the multi-relay selection invokes multiple SRs forsimultaneously forwarding the ST’s transmission to the SD. Weanalyze both the intercept probability and outage probability ofthe proposed single-relay and multi-relay selection schemes for thesecondary transmission relying on realistic spectrum sensing. Wealso evaluate the performance of classic direct transmission andartificial noise based methods for the purpose of comparison withthe proposed relay selection schemes. It is shown that as the inter-cept probability requirement is relaxed, the outage performance ofthe direct transmission, the artificial noise based and the relay se-lection schemes improves, and vice versa. This implies a trade-offbetween the security and reliability of the secondary transmissionin the presence of eavesdropping attacks, which is referred to asthe security-reliability trade-off (SRT). Furthermore, we demon-strate that the SRTs of the single-relay and multi-relay selectionschemes are generally better than that of classic direct trans-mission, explicitly demonstrating the advantage of the proposedrelay selection in terms of protecting the secondary transmissionsagainst eavesdropping attacks. Moreover, as the number of SRsincreases, the SRTs of the proposed single-relay and multi-relay

Manuscript received May 7, 2014; revised August 21, 2014 and October 16,2014; accepted November 27, 2014. Date of publication December 4, 2014;date of current version January 14, 2015. This work was partially supportedby the Priority Academic Program Development of Jiangsu Higher EducationInstitutions, the National Natural Science Foundation of China (Grant Nos.61302104 and 61401223), the Scientific Research Foundation of NanjingUniversity of Posts and Telecommunications (Grant Nos. NY213014 andNY214001), the 1311 Talent Program of Nanjing University of Posts andTelecommunications, the Natural Science Foundation of Jiangsu Province(Grant No. BK20140887), and the Programme de bourses d’excellence pouretudiants etrangers (PBEEE) of the Government of Quebec. The associateeditor coordinating the review of this paper and approving it for publicationwas H. Li.

Y. Zou is with the School of Telecommunications and Information Engineer-ing, Nanjing University of Posts and Telecommunications, Nanjing 210003,China (e-mail: [email protected]).

B. Champagne is with the Department of Electrical & Computer Engi-neering, McGill University, Montreal, QC H3A 1Y1, Canada (e-mail: [email protected]).

W.-P. Zhu is with the Department of Electrical & Computer Engineering,Concordia University, Montreal, QC H3G 1M8, Canada (e-mail: [email protected]).

L. Hanzo is with the Department of Electronics and Computer Science,University of Southampton, Southampton SO17 1BJ, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCOMM.2014.2377239

selection approaches significantly improve. Finally, our numericalresults show that as expected, the multi-relay selection schemeachieves a better SRT performance than the single-relay selection.

Index Terms—Security-reliability trade-off, relay selection,intercept probability, outage probability, eavesdropping attack,cognitive radio.

I. INTRODUCTION

THE security aspects of cognitive radio (CR) systems [1]–[3] have attracted increasing attention from the research

community. Indeed, due to the highly dynamic nature of the CRnetwork architecture, legitimate CR devices become exposedto both internal as well as to external attackers and hence theyare extremely vulnerable to malicious behavior. For example,an illegitimate user may intentionally impose interference (i.e.jamming) for the sake of artificially contaminating the CR envi-ronment [4]. Hence, the CR users fail to accurately characterizetheir surrounding radio environment and may become misledor compromised, which leads to a malfunction. Alternatively,an illegitimate user may attempt to tap the communications ofauthorized CR users by eavesdropping, to intercept confidentialinformation.

Clearly, CR networks face diverse security threats duringboth spectrum sensing [5], [6] as well as spectrum sharing [7],spectrum mobility [8] and spectrum management [9]. Extensivestudies have been carried out for protecting CR networks bothagainst primary user emulation (PUE) [10] and against denial-of-service (DoS) attacks [11]. In addition to PUE and DoS at-tacks, eavesdropping is another main concern in protecting thedata confidentiality [12], although it has received less attentionin the literature on CR network security. Traditionally, crypto-graphic techniques are employed for guaranteeing transmissionconfidentiality against an eavesdropping attack. However, thisintroduces a significant computational overhead [13] as well asimposing additional system complexity in terms of the secretkey management [14]. Furthermore, the existing cryptographicapproaches are not perfectly secure and can still be decryptedby an eavesdropper (E), provided that it has the capacity to carryout exhaustive key search with the aid of brute-force attack [15].

Physical-layer security [16], [17] is emerging as an efficientapproach for defending authorized users against eavesdroppingattacks by exploiting the physical characteristics of wirelesschannels. In [17], Leung-Yan-Cheong and Hellman demon-strated that perfectly secure and reliable transmission can beachieved, when the wiretap channel spanning from the sourceto the eavesdropper is a further degraded version of the main

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216 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 1, JANUARY 2015

channel between the source and destination. They also showedthat the maximal secrecy rate achieved at the legitimate desti-nation, which is termed the secrecy capacity, is the differencebetween the capacity of the main channel and that of thewiretap channel. In [18]–[20], the secrecy capacity limits ofwireless fading channels were further developed and character-ized from an information-theoretic perspective, demonstratingthe detrimental impact of wireless fading on the physical-layer security. To combat the fading effects, both multiple-inputmultiple-output (MIMO) schemes [21], [22] as well as coop-erative relaying [23]–[25] and beamforming techniques [26],[27] were investigated for the sake of enhancing the achievablewireless secrecy capacity. Although extensive research effortswere devoted to improving the security of traditional wirelessnetworks [16]–[27], less attention has been dedicated to CRnetworks. In [28] and [29], the achievable secrecy rate ofthe secondary transmission was investigated under a specificquality-of-service (QoS) constraint imposed on the primarytransmission. Additionally, an overview of the physical-layersecurity aspects of CR networks was provided in [30], whereseveral security attacks as well as the related countermeasuresare discussed. In contrast to conventional non-cognitive wire-less networks, the physical-layer security of CR networks has toconsider diverse additional challenges, including the protectionof the primary user’s QoS and the mitigation of the mutualinterference between the primary and secondary transmissions.

Motivated by the above considerations, we explore thephysical-layer security of a CR network comprised of a sec-ondary transmitter (ST) communicating with a secondary des-tination (SD) with the aid of multiple secondary relays (SRs)in the presence of an unauthorized attacker. Our main focusis on investigating the security-reliability trade-off (SRT) ofthe cognitive relay transmission in the presence of realisticspectrum sensing. The notion of the SRT in wireless physical-layer security was introduced and examined in [31], where thesecurity and reliability was characterized in terms of the inter-cept probability and outage probability, respectively. In contrastto the conventional non-cognitive wireless networks studied in[31], the SRT analysis of CR networks presented in this workadditionally takes into account the mutual interference betweenthe primary user (PU) and secondary user (SU).

The main contributions of this paper are summarized asfollows.

• We propose two relay selection schemes, namely bothsingle-relay and multi-relay selection, for protecting thesecondary transmissions against eavesdropping attacks.More specifically, in the single-relay selection (SRS)scheme, only a single relay is chosen from the set of mul-tiple SRs for forwarding the secondary transmissions fromthe ST to the SD. By contrast, the multi-relay selection(MRS) scheme employs multiple SRs for simultaneouslyassisting the ST-SD transmissions.

• We present the mathematical SRT analysis of the proposedSRS and MRS schemes in the presence of realistic spec-trum sensing. Closed-form expressions are derived for theintercept probability (IP) and outage probability (OP) ofboth schemes for transmission over Rayleigh fading chan-nels. The numerical SRT results of conventional direct

Fig. 1. A primary wireless network in coexistence with a secondary CRnetwork.

transmission and artificial noise based schemes are alsoprovided for comparison purposes.

• It is shown that as the spectrum sensing reliability isincreased and/or the false alarm probability is reduced, theSRTs of both the SRS and MRS schemes are improved.Numerical results demonstrate that the proposed SRS andMRS schemes generally outperform the conventional di-rect transmission and artificial noise based approaches interms of their SRTs.

The remainder of this paper is organized as follows.Section II presents the system model of physical-layer securityin CR networks in the context of both the direct transmission aswell as the SRS and MRS schemes. In Section III, we analyzethe SRTs of these schemes in the presence of realistic spectrumsensing over Rayleigh fading channels. Next, numerical SRTresults of the direct transmission, SRS and MRS schemes aregiven in Section IV, where the SRT performance of the artificialnoise based scheme is also numerically evaluated for com-parison purposes. Finally, Section V provides our concludingremarks.

II. RELAY SELECTION AIDED PROTECTION AGAINST

EAVESDROPPING IN CR NETWORKS

We first introduce the overall system model of physical-layersecurity in CR networks. We then present the signal model ofthe conventional direct transmission approach, which will serveas our benchmarker, as well as of the SRS and MRS schemesfor improving the CR system’s security against eavesdroppingattacks.

A. System Model

As shown in Fig. 1, we consider a primary network incoexistence with a secondary network (also referred to as a CRnetwork). The primary network includes a primary base station(PBS) and multiple primary users (PUs), which communicatewith the PBS over the licensed spectrum. By contrast, thesecondary network consisting of one or more STs and SDsexploits the licensed spectrum in an opportunistic way. To

ZOU et al.: RELAY-SELECTION IMPROVES THE SECURITY-RELIABILITY TRADE-OFF IN CR SYSTEMS 217

be specific, a particular ST should first detect with the aidof spectrum sensing whether or not the licensed spectrum isoccupied by the PBS. If so, the ST is not at liberty to transmitto avoid interfering with the PUs. If alternatively, the licensedspectrum is deemed to be unoccupied (i.e. a spectrum holeis detected), then the ST may transmit to the SD over thedetected spectrum hole. Meanwhile, E attempts to intercept thesecondary transmission from the ST to the SD. For notationalconvenience, let H0 and H1 represent the event that the licensedspectrum is unoccupied and occupied by the PBS during aparticular time slot, respectively. Moreover, let H denote thestatus of the licensed spectrum detected by spectrum sensing.Specifically, H = H0 represents the case that the licensedspectrum is deemed to be unoccupied, while H = H1 indicatesthat the licensed spectrum is deemed to be occupied.

The probability Pd of correct detection of the presence ofPBS and the associated false alarm probability Pf are definedas Pd = Pr(H = H1|H1) and Pf = Pr(H = H1|H0), respectively.Due to the background noise and fading effects, it is impossibleto achieve perfectly reliable spectrum sensing without missingthe detection of an active PU and without false alarm, whichsuggests that a spectral band is occupied by a PU, when itis actually unoccupied. Moreover, the missed detection of thepresence of PBS will result in interference between the PUand SU. To guarantee that the interference imposed on thePUs is below a tolerable level, both the successful detectionprobability (SDP) Pd and false alarm probability (FAP) Pf

should be within a meaningful target range. For example, theIEEE 802.22 standard requires Pd > 0.9 and Pf < 0.1 [2]. Forbetter protection of PUs, we consider Pd = 0.99 and Pf = 0.01,unless otherwise stated. Additionally, we consider a Rayleighfading model for characterizing all the channels between anytwo nodes of Fig. 1. Finally, all the received signals are assumedto be corrupted by additive white Gaussian noise (AWGN)having a zero mean and a variance of N0.

B. Direct Transmission

Let us first consider the conventional direct transmissionas a benchmark scheme. Let xp and xs denote the randomsymbols transmitted by the PBS and the ST at a particulartime instance. Without loss of generality, we assume E[|xp|2] =E[|xs|2] = 1, where E[·] represents the expected value operator.The transmit powers of the PBS and ST are denoted by Pp andPs, respectively. Given that the licensed spectrum is deemed tobe unoccupied by the PBS (i.e. H = H0), ST transmits its signalxs at a power of Ps. Then, the signal received at the SD can bewritten as

yd = hsd√

Psxs +hpd√

αPpxp +nd , (1)

where hsd and hpd represent the fading coefficients of thechannel spanning from ST to SD and that from PBS to SD,respectively. Furthermore, nd represents the AWGN received atSD and the random variable (RV) α is defined as

α =

{0, H0

1, H1,(2)

where H0 represents that the licensed spectrum is unoccupiedby PBS and no primary signal is transmitted, leading to α = 0.By contrast, H1 represents that PBS is transmitting its signal xp

over the licensed spectrum, thus α = 1. Meanwhile, due to thebroadcast nature of the wireless medium, the ST’s signal willbe overheard by E and the overheard signal can be expressed as

ye = hse√

Psxs +hpe√

αPpxp +ne, (3)

where hse and hpe represent the fading coefficients of thechannel spanning from ST to E and that from PBS to E,respectively, while ne represents the AWGN received at E.Upon combining Shannon’s capacity formula [31] with (1), weobtain the capacity of the ST-SD channel as

Csd = log2

(1+

|hsd |2γs

α|hpd |2γp +1

), (4)

where γs =Ps/N0 and γp =Pp/N0. Similarly, the capacity of theST-E channel is obtained from (3) as

Cse = log2

(1+

|hse|2γs

α|hpe|2γp +1

). (5)

C. Single-Relay Selection

In this subsection, we consider the cognitive relay networkof Fig. 2, where both SD and E are assumed to be beyondthe coverage area of the ST [24], [25], and N secondaryrelays (SRs) are employed for assisting the cognitive ST-SDtransmission. We assume that a common control channel (CCC)[6] is available for coordinating the actions of the differentnetwork nodes and the decode-and-forward (DF) relaying usingtwo adjacent time slots is employed. More specifically, oncethe licensed spectrum is deemed to be unoccupied, the ST firstbroadcasts its signal xs to the N SRs, which attempt to decodexs from their received signals. For notational convenience, letD represent the set of SRs that succeed in decoding xs. GivenN SRs, there are 2N possible subsets D , thus the sample spaceof D is formulated as

Ω = { /0,D1,D2, · · · ,Dn, · · · ,D2N−1}, (6)

where /0 represents the empty set and Dn represents the n-thnon-empty subset of the N SRs. If the set D is empty, implyingthat no SR decodes xs successfully, then all the SRs remainsilent and thus both SD and E are unable to decode xs in thiscase. If the set D is non-empty, a specific SR is chosen fromD to forward its decoded signal xs to SD. Therefore, givenH = H0 (i.e. the licensed spectrum is deemed unoccupied), STbroadcasts its signal xs to N SRs at a power of Ps and a rate ofR. Hence, the signal received at a specific SRi is given by

yi = hsi√

Psxs +hpi√

αPpxp +ni, (7)

where hsi and hpi represent the fading coefficients of the ST-SRi

channel and that of the PBS-SRi channel, respectively, with


ni representing the AWGN at SRi. From (7), we obtain thecapacity of the ST-SRi channel as

Csi =12

log2

(1+

|hsi|2γs

α|hpi|2γp +1

), (8)

where the factor 12 arises from the fact that two orthogonal time

slots are required for completing the message transmission fromST to SD via SRi. According to Shannon’s coding theorem,if the data rate is higher than the channel capacity, the re-ceiver becomes unable to successfully decode the source signal,regardless of the decoding algorithm adopted. Otherwise, thereceiver can succeed in decoding the source signal. Thus, using(8), we can describe the event of D = /0 as

Csi < R, i ∈ {1,2, · · · ,N}. (9)

Meanwhile, the event of D = Dn is described as

Csi > R, i ∈ Dn

Cs j < R, j ∈ Dn, (10)

where Dn represents the complementary set of Dn. Withoutloss of generality, we assume that SRi is chosen within Dn totransmit its decoded result xs at a power of Ps, thus the signalreceived at SD can be written as

yd = hid√

Psxs +hpd√

αPpxp +nd , (11)

where hid represents the fading coefficient of the SRi − SDchannel. From (11), the capacity of the SRi − SD channel isgiven by

Cid =12

log2

(1+

|hid |2γs

α|hpd |2γp +1

), (12)

where i ∈ Dn. In general, the specific SRi having the highestinstantaneous capacity to SD is chosen as the “best” SR for as-sisting the ST’s transmission. Therefore, the best relay selectioncriterion is expressed from (12) as

Best SR = argmaxi∈Dn

Cid = argmaxi∈Dn

|hid |2, (13)

which shows that only the channel state information (CSI) |hid |2is required for performing the relay selection without the needfor the eavesdropper’s CSI knowledge. Upon combining (12)and (13), we obtain the capacity of the channel spanning fromthe “best” SR to SD as

Cbd =12

log2

(1+

γs

α|hpd |2γp +1maxi∈Dn

|hid |2), (14)

where the subscript ‘b’ in Cbd denotes the best SR. It is observedfrom (14) that the legitimate transmission capacity of the SRSscheme is determined by the maximum of independent randomvariables (RVs) |hid |2 for different SRs. By contrast, one cansee from (4) that the capacity of classic direct transmission isaffected by the single RV |hsd |2. If all RVs |hid |2 and |hsd |2 areindependent and identically distributed (i.i.d), it would be mostlikely that max

i∈Dn

|hid |2 is much higher than |hsd |2 for a sufficiently

Fig. 2. A cognitive relay network consists of one ST, one SD and N SRs inthe presence of an E.

large number of SRs, resulting in a performance improvementfor the SRS scheme over the classic direct transmission. How-ever, if the RVs |hid |2 and |hsd |2 are non-identically distributedand the mean value of |hsd |2 is much higher than that of |hid |2,then it may be more likely that max

i∈Dn

|hid |2 is smaller than |hsd |2

for a given number of SRs. In this extreme case, the classicdirect transmission may perform better than the SRS scheme.It is worth mentioning that in practice, the average fading gainof the SRi − SD channel, |hid |2, should not be less than thatof the ST-SD channel |hsd |2, since SRs are typically placedin the middle between the ST and SD. Hence, a performanceimprovement for the SRS scheme over classic direct transmis-sion would be achieved in practical wireless systems. Notethat although a factor 1/2 in (14) is imposed on the capacityof the main channel, it would not affect the performance ofthe SRS scheme from a SRT perspective, since the capacityof the wiretap channel is also multiplied by 1/2 as will beshown in (16).

Additionally, given that the selected SR transmits itsdecoded result xs at a power of Ps, the signal received at E isexpressed as

ye = hbe√

Psxs +hpe√

αPpxp +ne, (15)

where hbe and hpe represent the fading coefficients of the chan-nel from “best” SR to E and that from PBS to E, respectively.From (15), the capacity of the channel spanning from the “best”SR to E is given by

Cbe =12

log2

(1+

|hbe|2γs

α|hpe|2γp +1

), (16)

where b ∈ Dn is determined by the relay selection criteriongiven in (13). As shown in (16), the eavesdropper’s channelcapacity is affected by the channel state information (CSI)|hbe|2 of the wiretap channel spanning from the “best” relay tothe eavesdropper. However, one can see from (13) that the bestrelay is selected from the decoding set Dn solely based on themain channel’s CSI |hid |2 i.e. without taking into account theeavesdropper’s CSI knowledge of |hie|2. This means that theselection of the best relay aiming for maximizing the legitimatetransmission capacity of (14) would not lead to significantly


beneficial or adverse impact on the eavesdropper’s channelcapacity, since the main channel and the wiretap channel areindependent of each other.

For example, if the random variables (RVs) |hie|2 related tothe different relays are i.i.d, we can readily infer by the lawof total probability that |hbe|2 has the same probability den-sity function (PDF) as |hie|2, implying that the eavesdropper’schannel capacity of (16) is not affected by the selection of thebest relay given by (13). Therefore, the SRS scheme has noobvious advantage over the classic direct transmission in termsof minimizing the capacity of the wiretap channel. To elaboratea little further, according to the SRT trade-off, a reduction ofthe outage probability (OP) due to the capacity enhancementof the main channel achieved by using the selection of thebest relay would be converted into an intercept probability(IP) improvement, which will be numerically illustrated inSection IV.

D. Multi-Relay Selection

This subsection presents a MRS scheme, where multiple SRsare employed for simultaneously forwarding the source signalxs to SD. To be specific, ST first transmits xs to N SRs over adetected spectrum hole. As mentioned in Subsection II-C, wedenote by D the set of SRs that successfully decode xs. If Dis empty, all SRs fail to decode xs and will not forward thesource signal, thus both SD and E are unable to decode xs. IfD is non-empty (i.e. D = Dn), all SRs within Dn are utilizedfor simultaneously transmitting xs to SD. This differs from theSRS scheme, where only a single SR is chosen from Dn forforwarding xs to SD. To make effective use of multiple SRs, aweight vector denoted by w = [w1,w2, · · · ,w|Dn|]

T is employedat the SRs for transmitting xs, where |Dn| is the cardinality ofthe set Dn. For the sake of a fair comparison with the SRSscheme in terms of power consumption, the total transmit poweracross all SRs within Dn shall be constrained to Ps and thus theweight vector w should be normalized according to ‖w‖ = 1.Thus, given D = Dn and considering that all SRs within Dn areselected for simultaneously transmitting xs with a weight vectorw, the signal received at SD is expressed as

ymultid =

√Psw

T Hdxs +√

αPphpdxp +nd , (17)

where Hd = [h1d ,h2d , · · · ,h|Dn|d ]T . Similarly, the signal received

at E can be written as

ymultie =

√Psw

T Hexs +√

αPphpexp +ne, (18)

where He = [h1e,h2e, · · · ,h|Dn|e]T . From (17) and (18), the

signal-to-interference-plus-noise ratios (SINRs) at SD and Eare, respectively, given by

SINRmultid =

γs

α|hpd |2γp +1|wT Hd |

2, (19)

and

SINRmultie =

γs

α|hpe|2γp +1|wT He|

2. (20)

In this work, the weight vector w is optimized by maximizingthe SINR at SD, yielding

maxw

SINRmultid , s.t. ‖w‖= 1, (21)

where the constraint is used for normalization purposes. Usingthe Cauchy-Schwarz inequality [32], we can readily obtain theoptimal weight vector wopt from (21) as

wopt =H∗

d

|Hd |, (22)

which indicates that the optimal vector design only requires theSR-SD CSI Hd , whilst dispensing with the eavesdropper’s CSIHe. Substituting the optimal vector wopt from (22) into (19) and(20) and using Shannon’s capacity formula, we can obtain thechannel capacities achieved at both SD and E as

Cmultid =

12

log2

(1+

γs

αγp|hpd |2 +1 ∑i∈Dn

|hid |2), (23)

and

Cmultie =

12

log2

(1+

γs

αγp|hpe|2 +1

∣∣HHd He

∣∣2|Hd |2

), (24)

for D = Dn, where H represents the Hermitian transpose. Onecan observe from (14) and (23) that the difference between thecapacity expressions Cbd and Cmulti

d only lies in the fact thatthe maximum of RVs |hid |2 for different SRs (i.e., max

i∈Dn

|hid |2)

is used for the SRS scheme, while the sum of RVs |hid |2(i.e., ∑

i∈Dn

|hid |2) is employed for the MRS scheme. Clearly,

we have ∑i∈Dn

|hid |2 > maxi∈Dn

|hid |2, resulting in a performance

gain for MRS over SRS in terms of maximizing the legitimatetransmission capacity. Moreover, since the main channel Hd

and the wiretap channel He are independent of each other, theoptimal weights assigned for the multiple relays based on Hd

will only slightly affect the eavesdropper’s channel capacity.This means that the MRS and SRS schemes achieve more orless the same performance in terms of the capacity of the wire-tap channel. Nevertheless, given a fixed outage requirement,the MRS scheme can achieve a better intercept performancethan the SRS scheme, because according to the SRT, an outagereduction achieved by the capacity enhancement of the legiti-mate transmission relying on the MRS would be converted intoan intercept improvement. To be specific, given an enhancedcapacity of the legitimate transmission, we may increase thedata rate R based on the OP definition of (25) for maintaininga fixed OP, which, in turn leads to a reduction of the IP, since ahigher data rate would result in a lower IP, according to the IPdefinition of (26).

It needs to be pointed out that in the MRS scheme, ahigh-complexity symbol-level synchronization is required formultiple distributed SRs, when simultaneously transmitting toSD, whereas the SRS does not require such a complex synchro-nization process. Thus, the performance improvement of MRSover SRS is achieved at the cost of a higher implementation


complexity. Additionally, the synchronization imperfections ofthe MRS scheme will impose a performance degradation, whichmay even lead to a performance for the MRS scheme becomingworse than that of the SRS scheme.

Throughout this paper, the Rayleigh model is used for char-acterizing the fading amplitudes (e.g., |hsd |, |hsi|, |hid |, etc.) ofwireless channels, which, in turn, implies that the fading squaremagnitudes |hsd |2, |hsi|2 and |hid |2 are exponentially distributedrandom variables (RVs). So far, we have completed the presen-tation of the signal model of the direct transmission, of the SRS,and of the MRS schemes for CR networks applications in thepresence of eavesdropping attacks.

III. SRT ANALYSIS OVER RAYLEIGH FADING CHANNELS

This section presents the SRT analysis of the direct transmis-sion, SRS and MRS schemes over Rayleigh fading channels.As discussed in [31], the security and reliability are quantifiedin terms of the IP and OP experienced by the eavesdropper anddestination, respectively. It is pointed out that in CR networks,ST starts to transmit its signal only when an available spectrumhole is detected. Similarly to [34], the OP and IP are thuscalculated under the condition that the licensed spectrum isdetected to be unoccupied by the PBS. The following gives thedefinition of OP and IP.

Definition 1: Let Cd and Ce represent the channel capacitiesachieved at the destination and eavesdropper, respectively. TheOP and IP are, respectively, defined as

Pout = Pr(Cd < R|H = H0), (25)

and

Pint = Pr(Ce > R|H = H0), (26)

where R is the data rate.

A. Direct Transmission

Let us first analyze the SRT performance of the conventionaldirect transmission. Given that a spectrum hole has been de-tected, the OP of direct transmission is obtained from (25) as

Pdirectout = Pr(Csd < R|H = H0), (27)

where Csd is given by (4). Using the law of total probability, wecan rewrite (27) as

Pdirectout =Pr(Csd <R,H0|H=H0)+Pr(Csd <R,H1|H=H0), (28)

which can be further expressed as

Pdirectout = Pr(Csd < R|H0, H = H0)Pr(H0|H = H0)

+Pr(Csd < R|H1, H = H0)Pr(H1|H = H0). (29)

It is shown from (2) that given H0 and H1, the parameter α isobtained as α = 0 and α = 1, respectively. Thus, combining (2)

and (4), we have Csd = log2(1+ |hsd |2γs) given H0 and Csd =

log2

(1+ |hsd |2γs

|hpd |2γp+1

)given H1. Substituting this result into (29)

yields

Pdirectout = Pr(|hsd |2γs < 2R −1)Pr(H0|H = H0)

+Pr

(|hsd |2γs

|hpd |2γp +1< 2R −1

)Pr(H1|H = H0). (30)

Moreover, the terms Pr(H0|H = H0) and Pr(H1|H = H0) can beobtained by using Bayes’ theorem as

Pr(H0|H = H0) =Pr(H = H0|H0)Pr(H0)

∑i∈{0,1}

Pr(H = H0|Hi)Pr(Hi)

=P0(1−Pf )

P0(1−Pf )+(1−P0)(1−Pd)

Δ= π0, (31)

and

Pr(H1|H = H0) =(1−P0)(1−Pd)

P0(1−Pf )+(1−P0)(1−Pd)

Δ= π1, (32)

where P0 = Pr(H0) is the probability that the licensed spec-trum band is unoccupied by PBS, while Pd = Pr(H = H1|H1)and Pf = Pr(H = H1|H0) are the SDP and FAP, respectively.For notational convenience, we introduce the shorthand π0 =

Pr(H0|H = H0), π1 = Pr(H1|H = H0) and Δ = 2R−1γs

. Then,using (31) and (32), we rewrite (30) as

Pdirectout =π0 Pr

(|hsd |2<Δ

)+π1 Pr

(|hsd |2−|hpd |2γpΔ<Δ

). (33)

Noting that |hsd |2 and |hpd |2 are independently and exponen-tially distributed RVs with respective means of σ2

sd and σ2pd ,

we obtain

Pr(|hsd |2 < Δ

)= 1− exp

(− Δ

σ2sd

), (34)

and

Pr(|hsd |2−|hpd |2γpΔ<Δ

)=1− σ2

sd

σ2pdγpΔ+σ2

sd

exp

(− Δ

σ2sd

). (35)

Additionally, we observe from (26) that an intercept eventoccurs, when the capacity of the ST-E channel becomes higherthan the data rate. Thus, given that a spectrum hole has been de-tected (i.e. H = H0), ST starts transmitting its signal to SD andE may overhear the ST-SD transmission. The corresponding IPis given by

Pdirectint = Pr(Cse > R|H = H0), (36)

which can be further expressed as

Pdirectint = Pr(Cse > R|H = H0,H0)Pr(H0|H = H0)

+Pr(Cse > R|H = H0,H1)Pr(H1|H = H0)

=π0Pr(|hse|2>Δ

)+π1 Pr

(|hse|2−|hpe|2γpΔ>Δ

), (37)


where the second equality is obtained by using Cse from (5).Noting that RVs |hse|2 and |hpe|2 are exponentially distributedand independent of each other, we can express the termsPr(|hse|2 > Δ) and Pr(|hse|2 −|hpe|2γpΔ > Δ) as

Pr(|hse|2 > Δ

)= exp

(− Δ

σ2se

), (38)

and

Pr(|hse|2−|hpe|2γpΔ > Δ

)=

σ2se

σ2peγpΔ+σ2

seexp

(− Δ

σ2se

), (39)

where σ2se and σ2

pe are the expected values of RVs |hse|2 and|hpe|2, respectively.

B. Single-Relay Selection

In this subsection, we present the SRT analysis of the pro-posed SRS scheme. Given H = H0, the OP of the cognitivetransmission relying on SRS is given by

Psingleout = Pr(Cbd < R,D = /0|H = H0)

+2N−1

∑n=1

Pr(Cbd < R,D = Dn|H = H0), (40)

where Cbd represents the capacity of the channel from the“best” SR to SD. In the case of D = /0, no SR is chosen toforward the source signal, which leads to Cbd = 0 for D = /0.Substituting this result into (40) gives

Psingleout = Pr(D = /0|H = H0)

+2N−1

∑n=1

Pr(Cbd < R,D = Dn|H = H0). (41)

Using (2), (9), (10), and (14), we can rewrite (41) as (42),shown at the bottom of the page, where Λ = 22R−1

γs. Noting

that |hsi|2 and |hpi|2 are independent exponentially distributed

random variables with respective means of σ2si and σ2

pi, we have

Pr(|hsi|2 < Λ

)= 1− exp

(− Λ

σ2si

), (43)

and

Pr(|hsi|2<Λ|hpi|2γp+Λ

)=1− σ2

si

σ2piγpΛ+σ2

si

exp

(− Λ

σ2si

), (44)

where the terms Pr(|hsi|2 > Λ), Pr(|hs j|2 < Λ), and Pr(|hsi|2 >Λ|hpi|2γp + Λ) can be similarly determined in closed-form.Moreover, based on Appendix A, we obtain Pr(max

i∈Dn

|hid |2 < Λ)

and Pr(maxi∈Dn

|hid |2 < Λ|hpd |2γp +Λ) as

Pr

(maxi∈Dn

|hid |2 < Λ)= ∏

i∈Dn

[1− exp

(− Λ

σ2id

)], (45)

and

Pr

(maxi∈Dn

|hid |2 < Λ|hpd |2γp +Λ)

= 1+2|Dn|−1

∑m=1

(−1)|Dn(m)| exp

⎛⎝− ∑

i∈Dn(m)

Λσ2

id

⎞⎠

×

⎛⎝1+ ∑

i∈Dn(m)

Λγpσ2pd

σ2id

⎞⎠

−1

, (46)

where Dn(m) represents the m-th non-empty subset of Dn.Additionally, the IP of the SRS scheme can be expressed as

Psingleint = Pr(Cbe > R,D = /0|H = H0)

+2N−1

∑n=1

Pr(Cbe > R,D = Dn|H = H0), (47)

where Cbe represents the capacity of the channel spanning fromthe “best” SR to E. Given D = /0, we have Cbe = 0, sinceno relay is chosen for forwarding the source signal. Thus,

Psingleout =π0

N

∏i=1

Pr(|hsi|2 < Λ

)+π1

N

∏i=1

Pr(|hsi|2 < Λ|hpi|2γp +Λ

)

+π0

2N−1

∑n=1

∏i∈Dn

Pr(|hsi|2 > Λ

)∏j∈Dn

Pr(|hs j|2 < Λ

)Pr

(maxi∈Dn

|hid |2 < Λ)

+π1

2N−1

∑n=1

∏i∈Dn

Pr(|hsi|2 > Λ|hpi|2γp +Λ

)∏j∈Dn

Pr(|hs j|2 < Λ|hp j|2γp +Λ

)

×Pr

(maxi∈Dn

|hid |2 < Λ|hpd |2γp +Λ)

(42)


substituting this result into (47) and using (2), (9), (10), and(16), we arrive at

Psingleint =π0

2N−1

∑n=1

∏i∈Dn

Pr(|hsi|2 > Λ

)∏j∈Dn

Pr(|hs j|2 < Λ

)

×Pr(|hbe|2 > Λ

)+π1

2N−1

∑n=1

∏i∈Dn


)× ∏

j∈Dn


)

×Pr(|hbe|2 > Λ|hpe|2γp +Λ

), (48)

where the closed-form expressions of Pr(|hsi|2 > Λ) andPr(|hsi|2 > Λ|hpi|2γp + Λ) can be readily obtained by using(43) and (44). Using the results in Appendix B, we can expressPr(|hbe|2 > Λ) and Pr(|hbe|2 > Λ|hpe|2γp +Λ) as

Pr(|hbe|2 > Λ

)= ∑

i∈Dn

exp

(− Λ

σ2ie

)

×

⎡⎣1+

2|Dn|−1−1

∑m=1

(−1)|Cn(m)|(

1+ ∑j∈Cn(m)

σ2id

σ2jd

)−1⎤⎦, (49)

and

Pr(|hbe|2>Λ|hpe|2γp+Λ

)= ∑

i∈Dn

σ2ie

σ2peγpΛ+σ2

ie

exp

(− Λ

σ2ie

)

×

⎡⎣1+

2|Dn|−1−1

∑m=1

(−1)|Cn(m)|(

1+ ∑j∈Cn(m)

σ2id

σ2jd

)−1⎤⎦, (50)

where Cn(m) represents the m-th non-empty subset of Dn −{i}and ‘−’ represents the set difference.

C. Multi-Relay Selection

This subsection analyzes the SRT of our MRS scheme fortransmission over Rayleigh fading channels. Similarly to (41),

the OP in this case is given by

Pmultiout = Pr(D = /0|H = H0)

+2N−1

∑n=1

Pr(

Cmultid < R,D = Dn|H = H0

). (51)

Using (2), (9), (10) and (23), we can rewrite (51) as (52), shownat the bottom of the page, where the closed-form expressionsof Pr(|hsi|2 < Λ), Pr(|hsi|2 < Λ|hpi|2γp + Λ), Pr(|hsi|2 > Λ),Pr(|hs j|2 < Λ) and Pr(|hsi|2 > Λ|hpi|2γp + Λ) can be readilyderived, as shown in (43) and (44). However, it is challengingto obtain the closed-form expressions of Pr( ∑

i∈Dn

|hid |2 < Λ) and

Pr( ∑i∈Dn

|hid |2 < γpΛ|hpd |2 +Λ). For simplicity, we assume that

the fading coefficients of all SRs-SD channels, i.e. |hid |2 fori ∈ {1,2, · · · ,N}, are i.i.d. RVs having the same mean (averagechannel gain) denoted by σ2

d = E(|hid |2). This assumption iswidely used in the cooperative relaying literature and it isvalid in a statistical sense, provided that all SRs are uniformlydistributed over a certain geographical area. Assuming thatRVs of |hid |2 for i ∈ Dn are i.i.d., based on Appendix C,we arrive at

Pr

(∑

i∈Dn

|hid |2 < Λ

)= Γ

(Λσ2

d

, |Dn|), (53)

and

Pr

(∑

i∈Dn

|hid |2 < γpΛ|hpd |2 +Λ

)= Γ

(Λσ2

d

, |Dn|)

+

[1−Γ

(Λσ−2

d +σ−2pd γ−1

p , |Dn|)]

(1+σ2

dσ−2pd γ−1

p Λ−1)|Dn|

e1/

(σ2

pdγp

), (54)

where Γ(x,k) =∫ x

0tk−1

Γ(k)e−tdt is known as the incompleteGamma function [32]. Substituting (53) and (54) into (52)yields a closed-form OP expression for the proposed MRSscheme.

Pmultiout =π0

N

∏i=1

Pr(|hsi|2 < Λ

)+π1

N

∏i=1

Pr(|hsi|2 < Λ|hpi|2γp +Λ

)

+π0

2N−1

∑n=1

∏i∈Dn

Pr(|hsi|2 > Λ

)∏j∈Dn

Pr(|hs j|2 < Λ

)Pr

(∑

i∈Dn

|hid |2 < Λ

)

+π1

2N−1

∑n=1

∏i∈Dn


)∏j∈Dn


)

×Pr

(∑

i∈Dn

|hid |2 < γpΛ|hpd |2 +Λ

)(52)


Next, we present the IP analysis of the MRS scheme. Simi-larly to (48), the IP of the MRS can be obtained from (24) as

Pmultiint =π0

2N−1

∑n=1

∏i∈Dn

Pr(|hsi|2 > Λ

)∏j∈Dn

Pr(|hs j|2 < Λ

)

×Pr

(∣∣HHd He

∣∣2|Hd |2

> Λ

)

+π1

2N−1

∑n=1

∏i∈Dn


)× ∏

j∈Dn


)

×Pr

(∣∣HHd He

∣∣2|Hd |2

> γpΛ|hpe|2 +Λ

), (55)

where the closed-form expressions of Pr(|hsi|2 > Λ),Pr(|hs j|2 < Λ), Pr(|hsi|2 > Λ|hpi|2γp + Λ) and Pr(|hs j|2 <Λ|hp j|2γp +Λ) may be readily derived by using (43) and (44).However, it is challenging to obtain the closed-form solutions

for Pr

(|HH

d He|2|Hd |2

> Λ)

and Pr

(|HH

d He|2|Hd |2

> γpΛ|hpe|2 +Λ)

.

Although finding a general closed-form IP expression for theMRS scheme is challenging, we can obtain the numerical IPresults with the aid of computer simulations.

IV. NUMERICAL RESULTS AND DISCUSSIONS

In this section, we present our performance comparisonsamong the direct transmission, the SRS and MRS schemesin terms of their SRT. To be specific, the analytic IP versusOP of the three schemes are obtained by plotting (33), (37),(42), (48), (52), and (55). The simulated IP and OP results ofthe three schemes are also given to verify the correctness ofthe theoretical SRT analysis. In our computer simulations, thefading amplitudes (e.g., |hsd |, |hsi|, |hid |, etc.) are first generatedbased on the Rayleigh distribution having different variancesfor different channels. Then, the randomly generated fadingamplitudes are substituted into the definition of an outage (orintercept) event, which would determine whether an outage (orintercept) event occurs or not. By repeatedly achieving this pro-cess, we can calculate the relative frequency of occurrence foran outage (intercept) event, which is the simulated OP (or IP).Additionally, the SDP Pd and FAP Pf are set to Pd = 0.99and Pf = 0.01, unless otherwise stated. The primary signal-to-noise ratio (SNR) of γp = 10 dB and the data rate ofR = 1 bit/s/Hz are used in our numerical evaluations.

The artificial noise based method [35], [36] is also consid-ered for the purpose of numerical comparison with the relayselection schemes. To be specific, in the artificial noise basedscheme, ST directly transmits its signal xs to SD, while N SRsattempt to confuse the eavesdropper by sending an interferingsignal (referred to as artificial noise) that is approximatelydesigned to lie in the null-space of the legitimate main channel.In this way, the artificial noise will impose interference on theeavesdropper without affecting the SD. For a fair comparison,the total transmit power of the desired signal xs and the artificialnoise are constrained to Ps. Moreover, the equal power alloca-tion method [35] is used in the numerical evaluation.

Fig. 3. IP versus OP of the direct transmission, the SRS and the MRS schemesfor different P0 with P0 = 0.8, γs ∈ [0,35 dB], N = 6, σ2

sd = σ2si = σ2

id = 1,σ2

se = σ2ie = 0.1, and σ2

pd = σ2pe = σ2

pi = 0.2.

Fig. 3 shows the IP versus OP of the direct transmission,as well as the SRS and MRS schemes for P0 = 0.8, wherethe solid lines and discrete marker symbols represent the an-alytic and simulated results, respectively. It can be seen fromFig. 3 that the IP of the direct transmission, the artificial noisebased as well as of the proposed SRS and MRS schemes allimprove upon tolerating a higher OP, implying that a trade-offexists between the IP (security) and the OP (reliability) of CRtransmissions. Fig. 3 also shows that both the proposed SRSand MRS schemes outperform the direct transmission and theartificial noise based approaches in terms of their SRT, showingthe advantage of exploiting relay selection against the eaves-dropping attack. Moreover, the SRT performance of the MRS isbetter than that of the SRS. Although the MRS achieves a betterSRT performance than its SRS-aided counterpart, this resultis obtained at the cost of a higher implementation complexity,since multiple SRs require high-complexity symbol-level syn-chronization for simultaneously transmitting to the SD, whereasthe SRS does not require such elaborate synchronization.

Fig. 4 illustrates our numerical SRT comparison between theSRS and MRS schemes for P0 = 0.2 and P0 = 0.8. Observefrom Fig. 4 that the MRS scheme performs better than the SRSin terms of its SRT performance for both P0 = 0.2 and P0 = 0.8.It is also seen from Fig. 4 that as P0 increases from 0.2 to0.8, the SRT of both the SRS and MRS schemes improves.This is because upon increasing P0, the licensed band becomesunoccupied by the PUs with a higher probability and hence thesecondary users (SUs) have more opportunities for accessingthe licensed band for their data transmissions, which leadsto a reduction of the OP for CR transmissions. Meanwhile,increasing P0 may simultaneously result in an increase of the IP,since the eavesdropper also has more opportunities for tappingthe cognitive transmissions. However, in both the SRS andMRS schemes, the relay selection is performed for the sakeof maximizing the legitimate transmission capacity withoutaffecting the eavesdropper’s channel capacity. Hence, uponincreasing P0, it becomes more likely that the reduction of OPis more significant than the increase of IP, hence leading to anoverall SRT improvement for the SRS and MRS schemes.


Fig. 4. IP versus OP of the SRS and MRS schemes for different P0 withγs ∈ [0,30 dB], N = 6, σ2

sd = σ2si = σ2

id = 1, σ2se = σ2

ie = 0.1, and σ2pd = σ2

pe =

σ2pi = 0.2.

Fig. 5. IP versus OP of the SRS and the MRS schemes for different (Pd ,Pf )

with P0 = 0.8, γs ∈ [0,30 dB], N = 6, σ2sd = σ2

si = σ2id = 1, σ2

se = σ2ie = 0.1, and

σ2pd = σ2

pe = σ2pi = 0.2.

In Fig. 5, we depict the IP versus OP of the SRS and MRSschemes for different spectrum sensing reliabilities, where(Pd ,Pf ) = (0.9,0.1) and (Pd ,Pf ) = (0.99,0.01) are considered.It is observed that as the spectrum sensing reliability is im-proved from (Pd ,Pf ) = (0.9,0.1) to (Pd ,Pf ) = (0.99,0.01), theSRTs of the SRS and MRS schemes improve accordingly. Thisis due to the fact that for an improved sensing reliability, anunoccupied licensed band would be detected more accuratelyand hence less mutual interference occurs between the PUsand SUs, which results in a better SRT for the secondarytransmissions. Fig. 5 also shows that for (Pd ,Pf ) = (0.9,0.1)and (Pd ,Pf ) = (0.99,0.01), the MRS approach outperforms theSRS scheme in terms of the SRT, which further confirms the ad-vantage of the MRS for protecting the secondary transmissionsagainst eavesdropping attacks.

Fig. 6 shows the IP versus OP of the conventional directtransmission as well as of the proposed SRS and MRS schemesfor N = 2, N = 4, and N = 8. It is seen from Fig. 6 that the SRTs

Fig. 6. IP versus OP of the direct transmission, the SRS and the MRS schemesfor different N with P0 = 0.8, γs ∈ [0,30 dB], σ2

sd = σ2si = σ2

id = 1, σ2se = σ2

ie =

0.1, and σ2pd = σ2

pe = σ2pi = 0.2.

of the proposed SRS and MRS schemes are generally betterthan that of the conventional direct transmission for N = 2,N = 4 and N = 8. Moreover, as the number of SRs increasesfrom N = 2 to 8, the SRT of the SRS and MRS schemessignificantly improves, explicitly demonstrating the securityand reliability benefits of exploiting multiple SRs for assistingthe secondary transmissions. In other words, the security andreliability of the secondary transmissions can be concurrentlyimproved by increasing the number of SRs. Additionally, asshown in Fig. 6, upon increasing the number of SRs fromN = 2 to 8, the SRT improvement of MRS over SRS becomesmore notable. Again, the SRT advantage of the MRS over theSRS comes at the expense of requiring elaborate symbol-levelsynchronization among the multiple SRs for simultaneouslytransmitting to the SD.

V. CONCLUSION

In this paper, we proposed relay selection schemes fora CR network consisting of a ST, a SD and multiple SRscommunicating in the presence of an eavesdropper. We ex-amined the SRT performance of the SRS and MRS assistedsecondary transmissions in the presence of realistic spectrumsensing, where both the security and reliability of secondarytransmissions are characterized in terms of their IP and OP,respectively. We also analyzed the SRT of the conventionaldirect transmission as a benchmark. It was illustrated that as thespectrum sensing reliability increases, the SRTs of both the SRSand MRS schemes improve. We also showed that the proposedSRS and MRS schemes generally outperform the conventionaldirect transmission and artificial noise based approaches interms of their SRT. Moreover, the SRT performance of MRSis better than that of SRS. Additionally, as the number of SRsincreases, the SRTs of both the SRS and of the MRS schemesimprove significantly, demonstrating their benefits in termsof enhancing both the security and reliability of secondarytransmissions.


APPENDIX ADERIVATION OF (45) AND (46)

Letting |hid |2 = xi and |hpd |2 = y, the left hand side of (45)and (46) can be rewritten as Pr(max

i∈Dn

xi < Λ) and Pr(maxi∈Dn

xi <

Λγpy+Λ), respectively. Noting that random variables |hid |2 and|hpd |2 are exponentially distributed with respective means σ2

idand σ2

pd , and independent of each other, we obtain

Pr

(maxi∈Dn

xi < Λ)= ∏

i∈Dn

Pr(|hid |2 < Λ

)

= ∏i∈Dn

[1− exp

(− Λ

σ2id

)], (A.1)

which is (45). Similarly, the term Pr(maxi∈Dn

xi < Λγpy+Λ) can be

computed as

Pr

(maxi∈Dn

xi < Λγpy+Λ)

=∫ ∞

0

1

σ2pd

exp

(− y

σ2pd

)∏

i∈Dn

(1− exp

(−Λγpy+Λ

σ2id

))dy,

(A.2)

wherein ∏i∈Dn

(1− exp

(−Λγpy+Λ

σ2id

))can be further expanded

as

∏i∈Dn

(1− exp

(−Λγpy+Λ

σ2id

))= 1

+2|Dn|−1

∑m=1

(−1)|Dn(m)| exp

⎛⎝− ∑

i∈Dn(m)

Λγpy+Λσ2

id

⎞⎠ ,

(A.3)

where |Dn| is the cardinality of set Dn, Dn(m) represents them-th non-empty subset of Dn, and |Dn(m)| is the cardinality

of set Dn(m). Substituting ∏i∈Dn

(1− exp

(−Λγpy+Λ

σ2id

))from

(A.3) into (A.2) yields

Pr

(maxi∈Dn

xi < Λγpy+Λ)=

∫ ∞

0

1

σ2pd

exp

(− y

σ2pd

)dy

+2|Dn|−1

∑m=1

(−1)|Dn(m)| 1

σ2pd

×∫ ∞

0exp

⎛⎝− y

σ2pd

− ∑i∈Dn(m)

Λγpy+Λσ2

id

⎞⎠dy. (A.4)

Finally, performing the integration of (A.4) yields

Pr

(maxi∈Dn

xi < Λγpy+Λ)= 1

+2|Dn|−1

∑m=1

(−1)|Dn(m)| exp

⎛⎝− ∑

i∈Dn(m)

Λσ2

id

⎞⎠

×

⎛⎝1+ ∑

i∈Dn(m)

Λγpσ2pd

σ2id

⎞⎠

−1

. (A.5)

This completes the proof of (45) and (46).

APPENDIX BPROOF OF (49) AND (50)

Given D = Dn, any SR within Dn can be selected as the“best” relay for forwarding the source signal. Thus, using thelaw of total probability, we have

Pr(|hbe|2 > Λ

)= ∑

i∈Dn

Pr(|hie|2 > Λ,b = i

)= ∑

i∈Dn

Pr

(|hie|2 > Λ, |hid |2 > max

j∈Dn−{i}|h jd |2

)

= ∑i∈Dn

Pr(|hie|2 > Λ

)Pr

(max

j∈Dn−{i}|h jd |2 < |hid |2

), (B.1)

where in the first line, variable ‘b’ stands for the best SR andthe second equality is obtained from (13) and ‘−’ represents theset difference. Noting that |hie|2 is an exponentially distributedrandom variable with a mean of σ2

ie, we obtain

Pr(|hie|2 > Λ

)= exp

(− Λ

σ2ie

). (B.2)

Letting |h jd |2 = x j and |hid |2 = y, we have

Pr

(max

j∈Dn−{i}|h jd |2 < |hid |2

)

=∫ ∞

0

1

σ2id

exp

(− y

σ2id

)∏

j∈Dn−{i}

(1−exp

(− y

σ2jd

))dy, (B.3)

wherein ∏j∈Dn−{i}

(1− exp

(− y

σ2jd

))is expanded by

∏j∈Dn−{i}

(1− exp

(− y

σ2jd

))= 1

+2|Dn|−1−1

∑m=1

(−1)|Cn(m)| exp

(− ∑

j∈Cn(m)

y

σ2jd

), (B.4)

where |Dn| denotes the cardinality of the set Dn and Cn(m)represents the m-th non-empty subset of “Dn−{i}”. Combining(B.3) and (B.4), we obtain

Pr

(max

j∈Dn−{i}|h jd |2 < |hid |2

)= 1

+2|Dn|−1−1

∑m=1

(−1)|Cn(m)|(

1+ ∑j∈Cn(m)

σ2id

σ2jd

)−1

. (B.5)


Substituting (B.2) and (B.5) into (B.1) gives (B.6), shown atthe bottom of the page, which is (49). Similarly to (B.1), wecan rewrite Pr(|hbe|2 > Λ|hpe|2γp +Λ) as

Pr(|hbe|2 > Λ|hpe|2γp +Λ

)= ∑

i∈Dn

Pr(|hie|2 > Λ|hpe|2γp +Λ

)

×Pr

(max

j∈{Dn−i}|h jd |2 < |hid |2

). (B.7)

Since the random variables |hie|2 and |hpe|2 are independentlyand exponentially distributed with respective means of σ2

ie andσ2

pe, we readily arrive at

Pr(|hie|2>Λ|hpe|2γp+Λ

)=

σ2ie

σ2peγpΛ+σ2

ie

exp

(− Λ

σ2ie

). (B.8)

Substituting (B.5) and (B.8) into (B.7) gives (B.9), shown at thebottom of the page, which is (50).

APPENDIX CPROOF OF (53) AND (54)

Upon introducing the notation of X = ∑i∈Dn

|hid |2 and Y =

|hpd |2, we can rewrite the terms Pr( ∑i∈Dn

|hid |2 < Λ) and

Pr( ∑i∈Dn

|hid |2 < γpΛ|hpd |2 + Λ) as Pr(X < Λ) and Pr(X <

γpΛY +Λ), respectively. Noting that the fading coefficients ofall SR-SD channels, i.e. |hid |2 for i ∈ {1,2, · · · ,N}, are assumedto be i.i.d., we obtain the probability density function (PDF) ofX = ∑

i∈Dn

|hid |2 as

fX (x) =1

Γ(|Dn|)σ2|Dn|d

x|Dn|−1 exp

(− x

σ2d

), (C.1)

where σ2d = E(|hid |2). Meanwhile, the random variable Y =

|hpd |2 is exponentially distributed and its PDF is given by

fY (y) =1

σ2pd

exp

(− y

σ2pd

), (C.2)

where σ2pd = E(|hpd |2). Using (C.1), we arrive at

Pr(X < Λ) =∫ Λ

0

1

Γ(|Dn|)σ2|Dn|d

x|Dn|−1 exp

(− x

σ2d

)dx

=∫ Λ

σ2d

0

t |Dn|−1

Γ(|Dn|)exp(−t)dt

=Γ(

Λσ2

d

, |Dn|), (C.3)

where the second equality is obtained by substituting xσ2

d= t and

Γ(a,k) =∫ a

0tk−1

Γ(k) exp(−t)dt is known as the incomplete Gammafunction. Additionally, considering that the random variables Xand Y are independent of each other, we obtain Pr(X < γpΛY +Λ) as

Pr(X < γpΛY +Λ) =∫ Λ

0fX (x)dx

+∫ ∞

Λ

∫ ∞

x−γpΛ− 1

γp

fX (x) fY (y)dxdy. (C.4)

Substituting fX (x) and fY (y) from (C.1) and (C.2) into (C.4)yields

Pr(X < γpΛY +Λ)

= Γ(

Λσ2

d

, |Dn|)

+∫ ∞

Λ

e1/

(σ2

pdγp

)x|Dn|−1

Γ(|Dn|)σ2|Dn|d

exp

(− x

σ2d

− x

σ2pdγpΛ

)dx

= Γ(

Λσ2

d

, |Dn|)+

[1−Γ

(Λσ−2

d +σ−2pd γ−1

p , |Dn|)]

(1+σ2

dσ−2pd γ−1

p Λ−1)|Dn|

e1/

(σ2

pdγp

),

(C.5)

where the second equality is obtained by using xσ2

d+ x

σ2pdγpΛ = t.

Hence, we have completed the proof of (53) and (54) as (C.3)and (C.5), respectively.

Pr(|hbe|2 > Λ

)= ∑

i∈Dn

exp

(− Λ

σ2ie

)⎡⎣1+

2|Dn|−1−1

∑m=1

(−1)|Cn(m)|(

1+ ∑j∈Cn(m)

σ2id

σ2jd

)−1⎤⎦ (B.6)

Pr(|hbe|2 > Λ|hpe|2γp +Λ

)= ∑

i∈Dn

σ2ie

σ2peγpΛ+σ2

ie

exp

(− Λ

σ2ie

)⎡⎣1+

2|Dn|−1−1

∑m=1

(−1)|Cn(m)|(

1+ ∑j∈Cn(m)

σ2id

σ2jd

)−1⎤⎦ (B.9)


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Yulong Zou (S’07–M’12–SM’13) received theB.Eng. degree in information engineering fromNUPT, Nanjing, China, in July 2006, the first Ph.D.degree in electrical engineering from the Stevens In-stitute of Technology, New Jersey, the United States,in May 2012, and the second Ph.D. degree in signaland information processing from NUPT, Nanjing,China, in July 2012. He is a Full Professor at theNanjing University of Posts and Telecommunica-tions (NUPT), Nanjing, China. His research interestsspan a wide range of topics in wireless commu-

nications and signal processing, including the cooperative communications,cognitive radio, wireless security, and energy-efficient communications.

He is currently serving as an editor for the IEEE Communications Surveys& Tutorials, IEEE COMMUNICATIONS LETTERS, EURASIP Journal on Ad-vances in Signal Processing, and KSII Transactions on Internet and InformationSystems. He served as the lead guest editor for a special issue on “SecurityChallenges and Issues in Cognitive Radio Networks” in the EURASIP Journalon Advances in Signal Processing. He is also serving as the lead guesteditor for a special issue on “Security and Reliability Challenges in IndustrialWireless Sensor Networks” in the IEEE TRANSACTIONS ON INDUSTRIAL

INFORMATICS. In addition, he has acted as symposium chairs, session chairs,and TPC members for a number of IEEE sponsored conferences, including theIEEE WIRELESS COMMUNICATIONS and Networking Conference (WCNC),IEEE Global Communications Conference (GLOBECOM), IEEE InternationalConference on Communications (ICC), IEEE Vehicular Technology Confer-ence (VTC), International Conference on Communications in China (ICCC),and so on.


Benoit Champagne (S’87–M’89–SM’03) was bornin Joliette (PQ), Canada, in 1961. He received theB.Ing. degree in engineering physics and the M.Sc.degree in physics from the University of Montreal in1983 and 1985, respectively, and the Ph.D. degree inelectrical engineering from the University of Torontoin 1990. From 1990 to 1999, he was with INRS,University of Quebec, where he held the positionsof Assistant and then Associate Professor. In 1999,he joined McGill University, Montreal, as an Asso-ciate Professor with the Department of Electrical and

Computer Engineering. He served as Associate Chairman of Graduate Studiesin the Department from 2004 to 2007 and is now a Full Professor.

His research interests focus on the investigation of new computationalalgorithms for the digital processing of information bearing signals and over-lap many sub-areas of statistical signal processing, including: detection andestimation, sensor array processing, adaptive filtering, multirate systems, andapplications thereof to broadband voice and data communications. Over theyears, he has supervised many graduate students in these areas and co-authoredseveral papers, including key works on subspace tracking, speech enhancement,time delay estimation and spread sources localization.

Wei-Ping Zhu (SM’97) received the B.E. andM.E. degrees from Nanjing University of Posts andTelecommunications, and the Ph.D. degree fromSoutheast University, Nanjing, China, in 1982, 1985,and 1991, respectively, all in electrical engineering.He was a Postdoctoral Fellow from 1991 to 1992and a Research Associate from 1996 to 1998 withthe Department of Electrical and Computer Engi-neering, Concordia University, Montreal, Canada.During 1993–1996, he was an Associate Professorwith the Department of Information Engineering,

Nanjing University of Posts and Telecommunications. From 1998 to 2001, heworked with hi-tech companies in Ottawa, Canada, including Nortel Networksand SR Telecom Inc. Since July 2001, he has been with Concordia’s Electricaland Computer Engineering Department as a full-time faculty member, wherehe is presently a Full Professor. His research interests include digital signalprocessing fundamentals, speech and audio processing, and signal processingfor wireless communication with a particular focus on MIMO systems andcooperative relay networks.

Dr. Zhu was an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS

AND SYSTEMS PART I: Fundamental Theory and Applications from 2001to 2003, and an Associate Editor of Circuits, Systems and Signal Processingfrom 2006 to 2009. He was also a Guest Editor for the IEEE JOURNAL ON

SELECTED AREAS IN COMMUNICATIONS for the special issues of: BroadbandWireless Communications for High Speed Vehicles, and Virtual MIMO during2011–2013. Since 2011, he has served as an Associate Editor for the IEEETRANSACTIONS ON CIRCUITS AND SYSTEMS PART II: Express Briefs. Dr.Zhu was the Secretary of Digital Signal Processing Technical Committee(DSPTC) of the IEEE Circuits and System Society during 2012–2014, wherehe is presently the Chair of the DSPTC.

Lajos Hanzo received the degree in electronics in1976 and the doctorate in 1983. In 2009 he wasawarded “Doctor Honoris Causa” by the TechnicalUniversity of Budapest. During his 37-year career intelecommunications he has held various research andacademic posts in Hungary, Germany, and the UK.Since 1986 he has been with the School of Electron-ics and Computer Science, University of Southamp-ton, UK, where he holds the chair in telecommunica-tions. He has successfully supervised 80+ Ph.D. stu-dents, co-authored 20 John Wiley/IEEE Press books

on mobile radio communications totalling in excess of 10 000 pages, published1400+ research entries at IEEE Xplore, acted both as TPC and General Chair ofIEEE conferences, presented keynote lectures and has been awarded a numberof distinctions. Currently he is directing a 100-strong academic research team,working on a range of research projects in the field of wireless multimediacommunications sponsored by industry, the Engineering and Physical SciencesResearch Council (EPSRC) UK, the European Research Council’s AdvancedFellow Grant and the Royal Society’s Wolfson Research Merit Award. He is anenthusiastic supporter of industrial and academic liaison and he offers a range ofindustrial courses. He is also a Governor of the IEEE VTS. During 2008–2012he was the Editor-in-Chief of the IEEE Press and a Chaired Professor alsoat Tsinghua University, Beijing. His research is funded by the EuropeanResearch Council’s Senior Research Fellow Grant. For further information onresearch in progress and associated publications please refer to http://www-mobile.ecs.soton.ac.uk Lajos has 20 000+ citations.

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