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TAS-Based Incremental HybridDecode-Amplify-Forward Relaying for Physical

Layer Security EnhancementYouhong Feng, Student Member, IEEE, Shihao Yan, Member, IEEE, Zhen Yang,

Nan Yang, Member, IEEE, and Wei-Ping Zhu, Senior Member, IEEE

Abstract—In this paper, a transmit antenna selection (TAS)-based incremental hybrid decode-amplify-forward (IHDAF)scheme is proposed to enhance physical layer security in co-operative relay networks. Specifically, TAS is adopted at thesource in order to reduce the feedback overhead. In the proposedTAS-based IHDAF scheme, the network transmits signals to thedestination adaptive select direction transmission mode, AF modeor DF mode depending on the capacity of the source-relay linkand source-relay link. In order to fully examine the benefitsof the proposed TAS-based IHDAF scheme, we first derive itssecrecy outage probability (SOP) in a closed-form expression. Wethen conduct asymptotic analysis on the SOP, which reveals thesecrecy performance floor of the proposed TAS-based IHDAFscheme when no channel state information is available at thesource. Theoretical analysis and simulation results demonstratethat the proposed TAS-based IHDAF scheme outperforms theselective decode-and-forward (SDF), the incremental decode-and-forward (IDF), and the noncooperative direction transmis-sion (DT) schemes in terms of the SOP and effective secrecythroughout, especially when the relay is close to the destination.Furthermore, the proposed TAS-based IHDAF scheme offer agood trade-off between complexity and performance comparewith using all antennas at the source.

Index Terms—Physical layer security, cooperative communi-cations, transmit antenna selection, secrecy outage probability.

I. INTRODUCTION

RECENTLY, physical layer security [1–4] as a comple-mentary and alternative cryptographic method to defend

against eavesdroppers from information-theoretic perspective

Manuscript received October 10, 2016; revised February 19, 2017 and May13, 2017. The editor coordinating the review of this paper and approving itfor publication was Y.-W. P. Hong.

This work was partially supported by the National Natural Science Foun-dation of China (No. 61671252, 61571233, 61501251), the Key NaturalScience Foundation of the Jiangsu Higher Education Institutions of China(No. 14KJA510003), and the Australian Research Council Discovery Project(DP150103905).

Y. Feng and Z. Yang are with the Key Laboratory of Ministry of Educationin Broadband Wireless Communication and Sensor Network Technology,Nanjing University of Posts and Telecommunications, Nanjing 210003, China(e-mail: 2013010213, yangz@njupt.edu.cn). Y. Feng is also with theCollege of Physics and Electronic information Engineering, Anhui NormalUniversity, Wuhu 241000, China.

S. Yan and N. Yang are with the Research School of Engineering, Aus-tralian National University, Canberra, ACT, Australia (emails: shihao.yan,nan.yang@anu.edu.au).

W.-P. Zhu is with the Department of Electrical and Computer Engi-neering, Concordia University, Montreal, QC H3G 1M8, Canada (e-mail:weiping@ece.concordia.ca). He is also an Adjunct Professor with the Schoolof Communication and Information Engineering, Nanjing University of Postsand Telecommunications, Nanjing, China.

has drawn numerous research interests. Physical layer securityoffers two major advantages relative to the traditional crypto-graphic method. First, physical layer security is not condi-tional on the limited computational ability of eavesdroppers,which indicates that the achieved level of secrecy will not becompromised even in the presence of an eavesdropper withunlimited computational capabilities. Second, physical layersecurity techniques can be used to provide direct secure datatransmission, which implies that physical layer security hasa high scalability for the decentralized nature of the network[2]. In addition, we note that physical layer security is com-plementary to the traditional cryptographic techniques (e.g., itcan be used to facilitate the distribution of cryptographic keys).To improve the physical-layer security of wireless communi-cations, multiple-input multiple-out (MIMO) architectures [1,5–9] and cooperative relays [3, 10–15] have been investigatedin the context of physical layer security. For example, whenthe channel state information (CSI) of the eavesdropper isknown to the transmitter, the secrecy capacity achieved bybeamforming was examined for multiple-input single-output(MISO) wiretap channels [1] and MIMO wiretap channels[8] by considering multiple eavesdroppers. When the CSI ofthe eavesdropper is unknown to the transmitter, beamformingwith artificial noise is desirable in MISO or MIMO wiretapchannels due to its robustness [5, 9]. As shown in the literature,such beamforming techniques can effectively improve thesecrecy performance of wiretap channels [5, 9]. However, thesebeamforming methods require precise CSI of the main chan-nel, which incurs high feedback overhead and computationalcost of signal processing. Moreover, the front-end and theradio frequency (RF) modules of a multi-antenna transmitterhave a complex hardware structure, which are expensive toimplement. To avoid the high feedback overhead and complexhardware structure, transmit antenna selection (TAS) has beenapplied at the multi-antenna transmitter to enhance physicallayer security [6]. TAS offers the following benefits relativeto beamforming in the context of physical layer security.First, it requires less feedback overhead and a single RFchain, which leads to the fact that the feedback overheadand the computational complexity of TAS is much lowerthan that of beamforming. Second, the index of the selectedtransmit antenna, which is returned from the destination tothe transmitter over the feedback channel, is meaningless tothe eavesdropper which cannot be exploited to improve hereavesdropping capability [7].

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Apart from the aforementioned studies, which have exam-ined physical layer security of point-to-point MIMO systems,the physical layer security of relay-aided networks has alsodrawn increasing attention [3, 10–15]. This is due to the factthat wireless relaying has been recognized as an effectivemeans to improve the coverage and reliability of mobile net-works. In this context, the secrecy performance of cooperativetransmissions, such as decode-and-forward (DF) [10, 11, 16]and amplify-and-forward (AF) [12, 13, 15, 17], has been exam-ined in the literature. The secrecy performance of DF relayselection scheme was examined by considering different com-bining techniques and different CSI assumptions in [15] and[16] , respectively. Meanwhile, the authors of [17] analyzedthe secrecy performance of dual-hop AF relaying systems bytaking into account the availability of direct link over Rayleighfading channels, in which two linear processing schemes (i.e.,zero-forcing and maximal ratio transmission) at the relay wereproposed to enhance the security of the considered system.In the AF scheme, the relay simultaneously amplifies theinformation and noise, which leads to the propagation of noiseand interference. In the DF scheme, the relay first decodes thereceived signals and then retransmits the recovered signals tothe destination, which often imposes a higher signal processingburden on the relay. Another drawback of DF scheme is thatthe relay may forward signals with decoding errors to thedestination. Motivated by the aforementioned benefits of TAS,the impact of antenna selection at the multi-antenna relay onthe secrecy performance of one-way and two-way cooperativerelaying networks was studied in [13] and [14], respectively.

More recently, in [11], the secrecy outage probabilities(SOPs) of the selective decode-and-forward (SDF) and the in-cremental decode-and-forward (IDF) schemes were analysed,where no CSI is available and TAS is performed at the source.In the SDF scheme, the relay operates in DF mode regardlessof whether the information from the source can be successfullydecoded at the destination. In the IDF scheme, the relay oper-ates in DF mode only when the source’s information cannot bedecoded at the destination in the direction transmission (DT)mode but can be correctly decoded at the relay. As shown in[18], the IDF and SDF schemes achieve the same performancewithout considering physical layer security. Meanwhile, theanalysis in [11] shows that IDF scheme outperforms the SDFscheme in the context of physical layer security while thesecrecy performance of these two schemes is not desirable(i.e., their SOPs are very high) when the relay is close to thedestination.

In order to achieve the benefits offered by both the DF andAF schemes, a new adaptive hybrid relaying scheme (withoutconsidering security), in which the relay switches betweenAF and DF modes based on its decoding capability, wasproposed in [19]. In addition, a similar hybrid relaying schemefor multiple relays was proposed and the performance gainin terms of achieving a lower symbol error probability wasanalyzed in [20]. In order to enhance the information trans-mission security, the authors of [21] proposed an incrementalhybrid decode-amplify (IHDAF) scheme based on the signal-to-noise ratio (SNR) thresholds at the relay and destinationin a single-antenna communication scenario. In this IHDAF

scheme, the relay operates in the AF mode when neither thedestination nor the relay can decode the information from thesource directly. It is shown in [21] that the IHDAF schemesignificantly outperforms both the SDF and IDF schemes as itachieves a lower outage probability or bit error rate. However,the IHDAF scheme has never been utilized to achieve physicallayer security and its secrecy performance relative to theSDF and IDF schemes has never been studied. The lackof the secrecy performance study of the hybrid cooperativetransmissions in the literature and how to further improvethe secrecy performance of SDF and IDF schemes when therelay is close to the destination motivate this work. Our maincontributions are summarized as follows:

• In the present work, for the first time, we propose aTAS-based IHDAF scheme to enhance physical layersecurity in cooperative relay networks. In this scheme thesource transmits signals directly to the destination whensuch signals can be successfully decoded and the relaykeeps silent. Otherwise, the source transmits signals tothe destination with the aid of a relay, which operates ineither DF or AF mode, depending whether or not the relaycan decode the source’s signals. In addition, an efficientTAS scheme is adopted at the source, aiming to avoidhigh feedback overhead, high hardware complexity, andcomplicated cooperations.

• In order to fully examine the secrecy performance ofthe proposed scheme, we first derive a closed-form ex-pression for its SOP. For the sake of comparison, wealso examine the secrecy performance of the tradition-al IDF, SDF, and DT schemes in our considered sys-tem model (multi-antenna communication scenario withTAS scheme). Our examination shows that the proposedscheme significantly outperforms the (TAS-based) IDF,SDF, and DT schemes in terms of achieving a lowerSOP, especially when the relay is close to the destination.We also conduct asymptotic analysis on the SOP of theproposed scheme with the SDF and IDF schemes asbenchmarks. This asymptotic analysis discloses the SOPfloor of the proposed scheme that is lower than or equalto that of the SDF and IDF schemes, which analyticallyconfirms the advantages of our proposed scheme.

• We also examine the effective secrecy throughput (EST)of the proposed scheme by incorporating the differenttime slots incurred in the direct and cooperative transmis-sions. Our examination reveals that the proposed schemeachieves a higher EST relative to other schemes. In orderto study the efficiency of the proposed scheme in terms ofthe feedback overhead, we compare it with a codebook-based beamforming (CB) scheme. Surprisingly, our studyindicates that our proposed scheme can outperform theCB scheme with less feedback overhead and fewer RFchains.

Notation: Scalar variables are denoted by italic symbols;Vectors and matrices are denoted by lower-case and upper-case boldface symbols, respectively; X ∼ CN(µ, σ2) denotesa circularly symmetric complex Gaussian random variable Xwith mean µ and covariance σ2; Pr[·] is the probability; fX(·)

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and FX(·) represent the probability density function (PDF) andcumulative distribution function (CDF) of the random variableX , respectively.

II. SYSTEM MODEL AND TAS-BASED IHDAF SCHEME

A. System Model

In this work, we consider a half-duplex relay networkas illustrated in Fig. 1, in which an NS-antenna source (S)communicates with an ND-antenna destination (D) with theaid of a single-antenna relay (R) in the presence of an NE-antenna eavesdropper (E). We clarify that the communicationbetween S and D can be conducted via both the direct linkand relay link. In this network, we assume that only thereceiver knows the CSI of corresponding channels (i.e., Rknows the CSI of the S-R link, D knows the CSI of the R-D and S-D links, and E knows the CSI of the S-E and R-Elinks). We also assume that the feedback capability of eachlegitimate link (i.e., S-D, R-D, and S-R) is limited and thereceiver cannot feed back the full CSI of each link to thecorresponding transmitter (i.e., the transmitter does not knowthe CSI of each link). Furthermore, we consider a passiveeavesdropping scenario, in which E does not feed back theCSI of the S-E and R-E links and thus such CSI is unknownto other nodes. Meanwhile, in this work we consider a multi-antenna E, who applies maximal radio combining (MRC) tomaximize the probability of the successful eavesdropping.1

We note that multiple antennas may not be available at therelay in this system due to the constraints by the hardwaresize or implementing cost. Therefore, this system is gen-erally applicable to many practical wireless communicationscenarios. For example, in the emerging Internet of Thingsthe far departed nodes may exchange information with the aidof a single-antenna relay [22]. In addition, this system canbe found in device-to-device (D2D) communication scenarioswhere a single-antenna relay assists two multi-antenna devicesto communication with each other [11, 21–25]. Furthermore,we consider the similar scenario adopted in [4, 11, 16, 17, 26],where both the direct links S-D and S-E are assumed to beexistent, and E can intercept the data from both the S and R.

We denote H∈CND×NS as the channel matrix between Sand D, and G∈CNE×NS as the channel matrix between S andE. The entries of H and G are independent and identicallydistributed (i.i.d.) complex Gaussian random variables withzero mean and unit variance. In this network, we adopt theTAS scheme at S, in which the antenna that maximizes theinstantaneous SNR of the S-D link is selected as active [6].As such, the index of the selected antenna, n∗ is determined

1It is noted that, in this work we consider a multi-antenna E, who knowsthe CSI of the S-E and R-E links, and then applies MRC to maximize theprobability of the successful eavesdropping. As such, this multi-antenna Ecan also be interpreted as multiple colluding Es that cooperatively decodethe desired information. Therefore, the operation of the proposed schemedoes not change in order to address physical layer security in the colludingeavesdropping scenario.

relay

hSR

hRD

HgRE

G

destination

source

S

1

NS

D

1

ND

eavesdropper

E

1

NE

Fig. 1. The illustration of a half-duplex cooperative relay network in thepresence of an NE -antenna eavesdropper.

by2

n∗ = arg max1≤n≤NS

∥h(n)∥, (1)

where h(n) denotes the nth column of H. We highlight that thestrongest antenna selected by the TAS scheme is equivalent toa random source antenna for E, since this antenna is solelydetermined by H, which is uncorrelated with G. Thus, Ecannot exploit any diversity benefits from multiple sourceantennas [11]. Furthermore, using TAS method at the multi-antenna transmitter can enhance security and reduce hardwarecomplexity [7]. Also, we assume that MRC is adopted at Dto maximize the quality of the received signal.

B. TAS-based IHDAF Scheme for Physical Layer Security

The operation of the TAS-based IHDAF scheme in theconsidered network is shown in Fig. 2 [21]. With this scheme,the network operates in two phases, namely, the broadcastphase and the cooperative phase. In the broadcast phase, asrepresented by the solid lines in Fig. 1, if the capacity of theS-D link exceeds the codeword rate Rc, the network adoptsDT mode and R keeps silent. Otherwise, the network operatesin the cooperative phase (i.e., as represented by the dash linesin Fig. 1) and R helps the transmission from S to D. Differingfrom the conventional IDF scheme, R operates in either theDF mode or the AF mode, according to the capacity of theS-R link. Specifically, if the capacity of the S-R link, CSR,exceeds the codeword rate Rc, R operates in the DF mode andthus, decodes the received signal and retransmits it towards D.Otherwise, R operates in the AF mode to amplify and forwardthe received signal to D.

In the considered network, the TAS-based IHDAF schemecan be interpreted as follows: S is equipped with NS antennasand employs a TAS scheme, in which D selects the strongestantenna (among the NS available antennas) which maximizesthe instantaneous SNR of S-D link, and then informs the indexof the strongest antenna through an open error-free feedback

2Here, D selects the “strongest” antenna (among the NS available antennasat S) which maximizes the instantaneous SNR of S-D link, and then informsthe index of the strongest antenna through an open error-free feedback channelto S.

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S broadcasts signal

C SD RcYES

DT

NO

C SR RcYES NO

AFDF

Fig. 2. Signal processing diagram of the TAS-based IHDAF scheme incooperative relay networks

channel to S. Then D decides whether it can decode theinformation sent from S according to the instantaneous SNRof the S-D link. If yes, D informs R to keep silent and S toadopt the DT mode. Otherwise, D informs R to be active andR to choose either the DF mode or the AF mode, accordingto the capacity of the S-R link.

We now formulate the broadcast phase and the cooperationphase of the TAS-based IHDAF scheme in the presence ofeavesdropping as follows:

1) Broadcast phase: When the coded confidential informa-tion x is sent by S, the signal received at R, D, and E aregiven by

ySR =√kSRP hSR x+ nR, (2)

ySD =√

kSDP h x+ nD, (3)

andySE =

√kSEP g x+ nE, (4)

respectively, where hSR denotes the channel coefficient fromthe selected transmit antenna of S to R, i.e., hSR , hSR(n

∗), his an ND ×1 vector representing the channel coefficients fromthe selected transmit antenna of S to D, i.e., h , H(:, n∗), andg is an NE × 1 vector representing the channel coefficientsfrom the selected transmit antenna of S to E, i.e., g , G(:, n∗). In (2)–(4), P is the transmit power of S, and we denotekmn = K

(d0

dmn

)v

as the path-loss between nodes m and n,dmn is the distance between the m and n, where m ∈ S, R,n ∈ R, D, E, and m = n [27], d0 is a reference distance, v

is the path loss exponent, and K =(

λ4πd0

)2

is the free-spacepath loss at d0, where λ is the wavelength. We also denotenR, nD and nE as the additive white Gaussian noise (AWGN)at R, D, and E, respectively. We assume that nR ∼ CN(0, σ2

R),nD ∼ CN(0, σ2

DIND), and nE ∼ CN(0, σ2EINE).

We assume that E adopts MRC to combine her receivedsignals from different antennas. Based on (2), (3), and (4), theinstantaneous SNRs of the S-R, S-D, and S-E links are givenby

ρSR = |hSR|2ΩSR = |hSR|2kSRP

σ2R

, (5)

ρSD = ||h||2ΩSD = ||h||2 kSDP

σ2D

, (6)

andρSE = ||g||2ΩSE = ||g||2 kSEP

σ2E

, (7)

respectively, where Ωmn is the average SNR of the m − nlink. Then, the channel capacity between m and n is writtenas

Cmn = log2(1 + ρmn). (8)

Given the target information transmit rate as Rc in bits perchannel use (bpcu), transmission outage occurs when Cmn

falls below Rc [11, 28].2) Cooperation phase: We note that R operates in either the

DF mode or the AF mode in the TAS-based IHDAF Scheme.According to Shannon’s channel theorem, R can successfullydecode x with an ignorable error probability when CSR > Rc

(i.e., when R operates in the DF mode) [3]. As such, when Roperates in the DF mode, the signals received at D and E arewritten as

yRD =√kRDP hRD x+ nRD, (9)

yRE =√kREP gRE x+ nRE, (10)

where hRD ∈ CND×1 and gRE ∈ CNE×1 represent the channelcoefficient vector from R to D and that from R to E, respec-tively. The entries of hRD and gRE are i.i.d. complex Gaussianrandom variables with zero mean and unit variance. When Roperates in the AF mode, the signals received at D and E canbe written as

yRD = β hRD ySR + nRD, (11)

yRE = γ√kREP hRE ySR + nRE, (12)

where the amplification coefficients β and γ are given byβ=

√kRDP√

kRDP |hSR|2+σ2R

and γ=√kREP√

kREP |hSR|2+σ2R

, respectively [29].

Then, the instantaneous SNRs of the R-D and R-E linksare given by ρRD = ||hRD||2 ΩRD and ρRE = ||hRD||2 ΩRE,respectively, where ΩRD = kRDP

σ2D

and ΩRE = kREPσ2

Edenote the

average SNR of the R-D and that of R-E links, respectively. Inthe cooperation phase, D combines the signals from both thedirect link and R link using MRC. This leads to the capacityat D in the DF mode and in the AF mode as [11, 21]

CDFSRD = log2(1 + ρDF

SRD) = log2(1 + ρSD + ρRD), (13)

CAFSRD=log2

(1+ρAF

SRD

)=log2

(1+ρSD+

ρSRρRD

ρSR+ρRD+1

), (14)

where ρDFSRD and ρAF

SRD represent the instantaneous SNRs at Dfor the DF mode and AF mode, respectively. Similarly, thecapacities at E in the DF mode and in the AF mode are givenby

CDFSRE = log2(1 + ρDF

SRE) = log2(1 + ρSE + ρRE), (15)

CAFSRE=log2

(1+ρAF

SRE

)=log2

(1+ρSE+

ρSRρRE

ρSR+ρRE+1

), (16)

where ρDFSRE and ρAF

SRE represent the instantaneous SNRs at Efor the DF and AF modes, respectively.

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C. Performance Metric

In [1, 30], the notion of SOP was introduced in the quasi-static Rayleigh fading wiretap channel. If the CSI of thelegitimate link is assumed to be perfectly known by S, theoverall codeword rate Rc can be dynamically chosen asRc = Cb, where Cb is the instantaneous capacity of thelegitimate link. We note that perfect secrecy cannot be alwaysguaranteed in the passive eavesdropping scenario since thereexists a possibility that some messages transmitted by S areleaked to E, and for this reason we define a secrecy rateRs, which is usually fixed. The difference between Rc andRs, i.e., Re = Rc − Rs, is the redundant rate that providessecrecy against eavesdropping. The SOP is thus defined asPrCb − Rs < Ce, where Ce is the instantaneous capacityof E’s channel [11]. Note that the transmission outage doesnot occur when the value of Rc is chosen to be equal to Cb.However, we now study a special case where S does not knowthe CSI about both D and E. In this scenario, since Cb is notknown, to study the secrecy performance, we must choose afixed overall codeword rate Rc and a fixed rate redundancyRe, yielding a fixed secure rate Rs = Rc − Re. Therefore,the SOP is the union of two events, i.e., Cb falls below Rc orRe falls below Ce, which is expressed as [11]

Pso = Pr(Cb < Rc) ∪ (Ce > Re), (17)

where Pr (Cb < Rc) , Pb denotes the probability of thereliability outage event, and Pr (Ce < Re) , Pe refers to thesecrecy outage event [11].

III. EXACT SECRECY OUTAGE PROBABILITY ANALYSISOF TAS-BASED IHDAF SCHEME

In this section, we present a comprehensive analysis on theSOP for cooperative relay networks with perfect and outdatedCSI.

A. Preliminaries

In practical systems, the TAS phase may exceed the co-herent time of the channel. As a result, the main channelmay have already changed since the moment when S receivesthe feedback of the optimal antenna index due to the time-varying nature of the wireless channel. In this case, theoptimal antenna is selected based on the outdated CSI. Leth(t− τ) denote the τ time-delayed version of current CSI(i.e., h(t)). The relationship between h(t−τ) and h(t) canbe modeled as h(t) =

√ρh(t − τ) +

√1− ρe(t) [31, 32],

where e(t) ∼ CN(0, IND) denotes the channel error vector

and ρ = [J0(2πft)]2 is the correction coefficient between

h(t−τ) and h(t), with f as the maximum Doppler frequencyand J0(·) as the zeroth-order Bessel function of the first kind[33, Eq. (8.411)].

We denote X = ρSD = ||h(t)||2ΩSD and X = ρSD =||h(t−τ)||2ΩSD as the current SNR and the time-delayed SNR,respectively. The PDF of the ρSD is given by [34]

fX(x) =

∫ ∞

0

fX|X(x|x)fX(x)dx, (18)

where fX|X(·) denotes the PDF of ρSD conditioned on ρSD,given by [35]

fX|X(x|x) = 1

(1− ρ)ΩSD

(x

ρx

)ND−1

2

e− ρx+x

(1−ρ)ΩSD

× IND−1

(2√ρxx

(1− ρ)ΩSD

), (19)

and In(·) is the n−th modified Bessel function of the firstkind [33, Eq. (8.406.1)]. The PDF of X is given by [31]

fX(x) =NS

(ND − 1)!

NS−1∑i=0

(−1)i(NS − 1

i

)e− (i+1)x

ΩSD

×i(ND−1)∑

j=0

ξjixj+ND−1

Ωj+NDSD

, (20)

where ξji =∑b

x=aξj(i−1)

(j−x)! , with a = max0, j − (ND − 1),b = minj, (i − 1)(ND − 1), ξj0 = ξ0i = 1, ξj1 = 1

j! ,and ξ1i = i. Substituting (20) and (19) into (18), we canrespectively obtain the PDF and CDF of X as

fX(x) =NS

(ND − 1)!

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

Ξ (i, j, k,ΩSD)

× xk+ND−1e− (i+1)x

(i(1−ρ)+1)ΩSD , (21)

and

FX(x) =NS

(ND − 1)!

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

Ξ (i, j, k,ΩSD)

×Γ1

(k +ND, (i+1)x

(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND, (22)

with

Ξ (i, j, k,ΩSD)

=

(NS−1

i

)(j

k

)(j +ND−1)!

(k +ND−1)!

(−1)iξjiρk(1− ρ)j−k

(i(1−ρ)+1)j+k+NDΩk+NDSD

,

(23)

where Γ1(α, x) =∫ x

0e−ttα−1dt is the lower incomplete

Gamma function [33, Eq. (8.350.1)].In the case of ρ = 1, which corresponds to the case with

τ = 0, i.e., perfect feedback without delay, (21) is identical to

(20) and (22) is identical to FX(x)|ρ=1 =[1−

Γ(ND, xΩSD

)

Γ(ND)

]NS .

B. Secrecy Outage Probability Analysis for Outdated CSI

In this section, we analyze the SOP of the proposed TAS-based IHDAF scheme. As shown in Fig. 2, in the cooperativephase of the proposed TAS-based IHDAF scheme, R adaptive-ly selects AF mode or DF mode due to the incremental natureof the proposed scheme (which is different from the SDFand IDF schemes). As such, to derive the overall SOP of theproposed TAS-based IHDAF scheme, we have to consider thefollowing three mutually exclusive events. i) The informationtransmitted from S is successfully decoded by D in the DT

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mode, where R keeps silent. ii) S’s transmission failed at D inthe DT mode, but R decoded it correctly and operates in DFmode to retransmit it to D. iii) Neither D nor R can decode theinformation from S correctly i.e., the capacities of both the S-R link and the S-D link are lower than Rc, and then R operatesin the AF mode to amplify and forward the information to D.As per the rules of the proposed TAS-based IHDAF scheme(as shown in Fig. 2), the probability that S operates in the DTmode is PrCSD≥Rc, the probability that R operates in theDF mode is PrCSR≥RcPrCSD<Rc, and the probabilitythat R operates in the AF mode is PrCSR<RcPrCSD<Rc.Then, the SOPs of the three mutually exclusive events aregiven by

PDTout = Pr(CSD < Rc) ∪ (CSE ≥ Re)|(CSD ≥ Rc)

× PrCSD ≥ Rc, (24)

PDFout = Pr(CDF

SRD<Rc) ∪ (CDFSRE≥Re)|(CSD<Rc, CSR≥Rc)

× PrCSD<Rc, CSR≥Rc, (25)

and

PAFout = Pr(CAF

SRD<Rc) ∪ (CAFSRE≥Re)|(CSD<Rc, CSR<Rc)

× PrCSD<Rc, CSR<Rc, (26)

respectively. Therefore, we can express the SOP of the TAS-based IHDAF scheme as

PIHDAF = PDTout + PDF

out + PAFout. (27)

In the following, we sequentially derive the expressionsfor PDT

out, PDFout, and PAF

out in Theorem 1, Theorem 2, andTheorem 3, respectively.

Theorem 1: The SOP in the first sub-case (i.e., the SOPof DT mode without considering the cooperation transmissionmode of R) is given by

PDTout =

Γ(NE,Te

ΩSE)

Γ(NE)

[1−

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

NSΞ(i, j, k,ΩSD)

(ND − 1)!

×Γ1

(k+ND, (i+1)T

(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND

],

(28)

where T = 2Rc − 1 and Te = 2Re − 1, and Γ(α, x) =∫ +∞x

e−ttα−1dt is the upper incomplete gamma function [33,Eq. (8.350.2)], and Γ(y) =

∫ +∞0

e−tty−1dt is the gammafunction [33, Eq. (8.310.1)].

Proof: Following (24), we have

PDTout

= Pr(CSD<Rc)∪(CSE≥Re)|(CSD≥Rc)PrCSD≥Rc= PrCSE ≥ Re|(CSD ≥ Rc)PrCSD ≥ Rc= PrCSE ≥ Re (1− PrCSD < Rc) , (29)

where we have applied the fact that Pr(CSD < Rc)|(CSD ≥Rc) = 0 and CSE ≥ Re is independent of CSD ≥ Rc.

According to the discussion in Section-II, from E’s point ofview, the optimum TAS scheme for D will be a random TAS

for E, as the main channel and E’ channel are uncorrelated.Then, based on (7), we can obtain the CDFs of ρSE [29]. (i.e.,FρSE(x) =

[1−

Γ(NE , xΩSE

)

Γ(NE)

]). As such, we can achieve

PrCSE≥Re=Prlog2(1+ρSE)≥Re=Γ(NE,

Te

ΩSE)

Γ(NE). (30)

In additional, based on (6) and (22), we can achieve

PrCSD < Rc =Prlog2(1 + ρSD) < Rc

=

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

NSΞ(i, j, k,ΩSD)

(ND − 1)!

×Γ1

(k +ND, (i+1)T

(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND. (31)

Substituting (30) and (31) into (29), we achieve the desiredresult in (28).

Remark 1: In the case of single receive antenna and TASbased on perfect feedback, i.e., ND = 1 and ρ = 1, we canobtain the corresponding SOP from (28) as

PDTout =

Γ(NE,Te

ΩSE)

Γ(NE)

[1−

(1− e

− TΩSD

)NS], (32)

which is a generalization of [11, Eq. (33)]. In other words, [11,Eq. (33)] can be regarded as a special cases of Theorem 1 in(28).

Theorem 2: The SOP for the DF relaying cooperativetransmission mode is given by (33), as shown at the top ofthe next page.

Proof: The proof is presented in Appendix A.Remark 2: In the case of single receive antenna and

TAS based on perfect feedback, i.e., ND = 1 and ρ = 1,we can obtain the corresponding SOP by (25), which is ageneralization of [11, Eq. (35)]. In other words, [11, Eq. (35)]can be regarded as a special cases of Theorem 2.

As neither D nor R received the message from S correctly,instead of remaining silent during the cooperation phase inthe IDF scheme [11], the proposed TAS-based IHDAF schemewill employ AF relaying cooperation to improve the systemsecrecy performance. In this case, the SOP of the third sub-case can be given by

PAFout =Pr(CAF

SRD<Rc) ∪ (CAFSRE>Re)|(CSD<Rc, CSR<Rc)

× PrCSD < Rc, CSR < Rc, (39)

where CAFSRD and CAF

SRD are, respectively, the capacity at D andthat at E when R employs the AF relaying cooperation. Wepresent our new result concerning the SOP in the followingtheorem (See Appendix B for its proof).

Theorem 3: The SOP for the AF relaying cooperativetransmission mode is given by

PAFout = (PAF1

out +PAF2out −PAF1

out PAF2out ) PrCSD < Rc, CSR < Rc,

(40)

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 7

PDFout =

[PrCDF

SRD<Rc+PrCDFSRE≥RePrCSD<Rc − PrCDF

SRE≥RePrCDFSRD<Rc

]PrCSR ≥ Rc, (33)

where

PrCDFSRD < Rc = FρSD(T )−

ND−1∑n=0

Π1

(n,

1

ΩRD

), (34)

and

PrCDFSRE ≥ Re =

Γ(NE,Te

ΩSE)

Γ(NE)+

NE−1∑n=0

Π2

(n,

1

ΩRE

), (35)

with

Π1

(n,

1

ΩRD

)=

∑NS−1i=0

∑i(ND−1)j=0

∑jk=0

∑nn1=0

(nn1

)(−1)n1Ξ (i, j, k,ΩSD)

NSe− T

ΩRD

Γ(ND)ΩnRDn!

×Tn−n1Γ1

(k+ND+n1,(

i+1(i(1−ρ)+1)ΩSD

− 1ΩRD

)T)

(i+1

(i(1−ρ)+1)ΩSD− 1

ΩRD

)k+ND+n1, if i+1

(i(1−ρ)+1)ΩSD= 1

ΩRD∑NS−1i=0

∑i(ND−1)j=0

∑jk=0

∑nn1=0

(nn1

)(−1)n1Ξ (i, j, k,ΩSD)

NSe− T

ΩRD

Γ(ND)ΩnRDn!

Tn+k+ND

n+k+ND, if i+1

(i(1−ρ)+1)ΩSD= 1

ΩRD

(36)

Π2

(n,

1

ΩRE

)=

e− Te

ΩRE

Γ(NE)ΩNESE ΩRE

nn!

∑nk=0

(nk

)(−1)kTn−k

e

Γ1

(NE+k,

(1

ΩSE− 1

ΩRE

)Te

)(

1ΩSE

− 1ΩRE

)NE+k , if 1ΩSE

= 1ΩRE

e− Te

ΩRE

Γ(NE)ΩNESE ΩRE

nn!

∑nk=0

(nk

)(−1)k T

NE+ne

NE+k , if 1ΩSE

= 1ΩRE

(37)

and

FρSD(T ) =

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

NS Ξ(i, j, k,ΩSD)Γ1

(k +ND, (i+1)T

(i(1−ρ)+1)ΩSD

)(ND − 1)!

((i+1)

(i(1−ρ)+1)ΩSD

)k+ND. (38)

where

PAF1out =

η1

1− e− T

ΩSR

+e− T

ΩSR∑ND−1

n=0 Π1

(n, 1

ΩRD

)− η3(

1− e− T

ΩSR

)FρSD(T )

,

(41)

and

PAF2out =

η2

[Γ(NE,

TeΩSE

)

Γ(NE)− 1

]+

[1− e

− TΩSR

Γ(NE,TeΩSE

)

Γ(NE)

]1− e

− TΩSR

+η4 − e

− TΩSR

∑NE−1n=0 Π2

(n, 1

ΩRE

)1− e

− TΩSR

, (42)

with

η1=

ND−1∑m=0

1ΩSR

( 1ΩRD

)m

( 1ΩSR

+ 1ΩRD

)m+1+

( 1ΩRD

)ND

( 1ΩSR

+ 1ΩRD

)ND−e

− TΩSR , (43)

η2 =

NE−1∑m=0

1ΩSR

( 1ΩRE

)m

( 1ΩSR

+ 1ΩRE

)m+1+

( 1ΩRE

)NE

( 1ΩSR

+ 1ΩRE

)NE, (44)

η3 =

[ND−1∑m=0

m∑n=0

1ΩSR

( 1ΩRD

)m

( 1ΩSR

+ 1ΩRD

)m+1+

ND−1∑n=0

( 1ΩRD

)ND

( 1ΩSR

+ 1ΩRD

)ND

]

×Π1

(n,

1

ΩRD+

1

ΩSR

), (45)

and

η4 =

[NE−1∑m=0

m∑n=0

1ΩSR

( 1ΩRE

)m

( 1ΩSR

+ 1ΩRE

)m+1+

NE−1∑n=0

( 1ΩRE

)NE

( 1ΩSR

+ 1ΩRE

)NE

]

×Π2

(n,

1

ΩRE+

1

ΩSR

). (46)

Finally, substituting (28), (33), and (40) into (27), the SOPof the proposed TAS-based IHDAF scheme can be achievedas in (47), as shown at the top of the next page.

Remark 3: Following a similar procedure to derive the SOPof the proposed TAS-based IHDAF scheme, we can obtainthe SOPs of the IDF and SDF schemes as benchmarks todemonstrate the secrecy performance of our proposed TAS-based IHDAF scheme. A thorough comparison among thesethree schemes is provided in Section V.

IV. ASYMPTOTIC SECRECY OUTAGE PROBABILITY ANDEFFECTIVE SECRECY THROUGHPUT OF TAS-BASED

IHDAF SCHEME

In this section, we first analytically determine the asymptoticSOP of the proposed TAS-based IHDAF scheme with theSDF and IDF schemes as benchmarks, aiming to theoreticallyreveal the benefits of the proposed scheme. In addition, weadopt a new performance metric EST (i.e., effective secre-cy throughput) to examine the secrecy performance of thecooperative and DT schemes by taking into account the

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PIHDAF =Γ(NE,

Te

ΩSE)(1− FρSD(T )

)Γ(NE)

+ e− T

ΩSR

(FρSD(T ) +

ND−1∑n=0

Π1

(n,

1

ΩRD

)[Γ(NE,Te

ΩSE)

Γ(NE)+

NE−1∑n=0

Π2

(n,

1

ΩRE

)−1

])

− FρSD(T )

([1−

Γ(NE,Te

ΩSE)

Γ(NE)

]η2 −

[1−

e− T

ΩSR Γ(NE,Te

ΩSE)

Γ(NE)

]+ e

− TΩSR

NE−1∑n=0

Π2

(n,

1

ΩRE

)− η4

)+

1

1− e− T

ΩSR

×(FρSD(T )η1+e

− TΩSR

ND−1∑n=0

Π1

(n,

1

ΩRD

)−η3

)([1−

Γ(NE,Te

ΩSE)

Γ(NE)

][η2−e

TΩSR

]+e

− TΩSR

NE−1∑n=0

Π2

(n,

1

ΩRE

)−η4

). (47)

different time slots required by these schemes. Furthermore,we examine the tradeoff between the secrecy performance andrequired feedback overhead in the considered system model bycomparing our proposed scheme with the CB (i.e., codebook-based beamforming) scheme. Finally, we discuss the impact ofoutdated CSI and the optimal antenna selection on the secrecyperformance of the proposed scheme.

A. Asymptotic Secrecy Outage Probability

In this subsection, we examine the asymptotic SOP of theproposed TAS-based IHDAF scheme with the SDF and IDFschemes as benchmarks to obtain further insights.

Corollary 1: In the case of P/σ2E → 0, we have

limP

σ2E→0

PIHDAF < limP

σ2E→0

PIDF = limP

σ2E→0

PSDF. (48)

Proof: When P/σ2E → 0, following (29), (33), and (39),

we obtain the SOP of the proposed TAS-based IHDAF schemeas

limP

σ2E→0

PIHDAF =PrCDFSRD < RcPrCSR > Rc

+ Pr(CAFSRD < Rc)|(CSD < Rc, CSR < Rc)

× PrCSD < Rc, CSR < Rc. (49)

Likewise, according to [18] and following (29) and (33), weobtain the SOP of the proposed TAS-based SDF and IDFschemes for P/σ2

E → 0 as

limP

σ2E→0

PIDF = limP

σ2E→0

PSDF

=PrCDFSRD < RcPrCSR > Rc

+ Pr(CSD < Rc)|(CSD < Rc, CSR < Rc)× PrCSD < Rc, CSR < Rc. (50)

We note that the only difference between (49) and (50) isthat CAF

SRD in (49) is replaced by CSD in (50). We recall thatCAF

SRD > CSD due to CAFSRD = log2

(1 + ρSD + ρSDρRD

ρSD+ρRD+1

)and

CSD = log2(1+ ρSD

). As such, we achieve the desired result

in (48).Remark 4: Corollary 1 indicates that the proposed TAS-

based IHDAF scheme achieves a lower SOP than the SDF andIDF schemes when P/σ2

E→0, which analytically discloses theadvantages of the proposed scheme. We note that this conclu-sion is still valid for reasonable small but non-zero values ofP/σ2

E (e.g., 0 dB), which will be verified in Section V. Basedon Corollary 1, we also conclude that the performance gain of

proposed scheme over SDF and IDF schemes becomes moreprominent as NS increases when NS is relatively small. This isdue to the fact that CAF

SRD−CSD = log2

(1+ ρSDρRD

(ρSD+ρRD+1)1

(1+ρSD)

)increases with NS when ρ > 0 and the number of antennas atS is relatively small.

Corollary 2: When P/σ2D → ∞, we have

limP

σ2D→∞

PIHDAF = limP

σ2D→∞

PIDF < limP

σ2D→∞

PSDF. (51)

Proof: Following (31), we have

limP

σ2D→∞

PrCSD<Rc = limP

σ2D→∞

NS−1∑i=0

i(ND−1)∑j=0

j∑k=0

NSΞ(i, j, k,ΩSD)

(ND − 1)!

×Γ1

(k +ND, (i+1)T

(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND= 0.

(52)

Based on the above equality, the value of (25) and (26) tendto be zero, and thus we have

limP

σ2D→∞

PIHDAF =Γ(NE,

Te

ΩSE)

Γ(NE). (53)

As per [11, Eq. (42)], we also have

limP

σ2D→∞

PIDF =Γ(NE,

Te

ΩSE)

Γ(NE)< lim

P

σ2D→∞

PSDF. (54)

Comparing (53) with (54), we complete the proof.Remark 5: Corollary 2 indicates that for P/σ2

D →∞ theproposed TAS-based IHDAF scheme achieves a lower SOPthan the SDF scheme, which is the same as that of the IDFscheme. This also demonstrates the advantage of the proposedscheme. In addition, as per (53) we note that the SOP of theproposed scheme for P/σ2

D→∞ does not depend on the SNRof S-D link.

B. Effective Secrecy ThroughputFollowing the definition of EST adopted in [11, 36], which

is the product of the secrecy rate and the secure transmissionprobability, the EST of the proposed scheme is given by

TIHDAF = Rs(1− P outDT ) (55a)

+Rs

2P outDT PrCSR ≥ Rc(1− P out

DF ) (55b)

+Rs

2P outDT PrCSR < Rc(1− P out

AF ), (55c)

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 9

where P outDT = Pr(CSD < Rc) ∪ (CSE ≥ Re), P out

DF =Pr(CDF

SRD < Rc) ∪ (CDFSRE ≥ Re), and P out

AF = Pr(CAFSRD <

Rc) ∪ (CAFSRE ≥ Re). We note that only one time slot is

required for the DT mode while two times slots are usedin the AF and DF mode, which is the reason why we haveRs in (55a) but Rs/2 in (55b) and (55c). Based on (55), wewill numerically examine the EST of the proposed scheme inSection V.

C. Tradeoff between Secrecy Performance and FeedbackOverhead

In this work, we adopt TAS in the proposed scheme due thefollowing three aspects.

• In some communication scenario, such as Internet ofThings and Device-to-Device communications, the sys-tem may only support a few bits feedback overhead due tolimited resources, which leads to that the techniques (e.g.,beamforming) that require high feedback overhead are notapplicable. Considering such limited feedback overhead,we adopt TAS in this work since it only requires ⌈logNS⌉bits feedback overhead.

• In the context of physical layer security, TAS can enablelegitimate nodes to achieve a high diversity gain whiledoes not offer benefits to E (i.e., the eavesdropper). This isdue to the fact that the strongest antenna selected in TASis equivalent to a random source antenna for E based onthe valid assumption that legitimate links are independentof the eavesdropping links.

• A multi-antenna transmitter suffers from a complex hard-ware structure (e.g., multiple RF chains), which areexpensive to implement. We adopt TAS at the multi-antenna S in order avoid this complex hardware structuresince TAS only requires one active RF chain.

In practice, if only the feedback overhead is the bottle-neck of the system, another transmission scheme, namely,CB(i.e.,codebook-based beamforming) scheme, was proposedin [31, 37]. In this CB scheme, all transmit antennas atthe source are active and the required feedback overhead isdetermined by the number of codebook vectors available toselect. Specifically, in this scheme a pre-designed codebookof N unit-norm vectors is known to both the transmitterand receiver. Then, the receiver selects the best codebookvector (using it as a beamforming vector) that maximizes theSNR of the channel based on the known CSI and feeds backthe index of the selected vector through an open error-freefeedback channel to the transmitter. As such, the amount offeedback overhead required by the CB scheme is ⌈logN⌉.Here, we adopt this CB scheme as a benchmark to study theefficiency of the proposed scheme in terms of the tradeoffbetween its achieved secrecy performance and the requiredfeedback overhead. In order to guarantee a fair comparisonbetween the proposed scheme and the CB scheme, we alsoassume that D selects the best codebook vector based on theS-D link and feeds back the its index to S. We refer to theIHDAF scheme with CB (instead of TAS) as the CB-IHDAFscheme while refer to the TAS-based IHDAF as TAS-IHDAFwhen comparing with CB-IHDAF. Particularly, we adopt two

different codebooks in the CB scheme for comparison (i.e.,N = 4 and N = 16). For N = 4, we adopt the codebookgenerated based on the Generalized Lloyd Algorithm (GLA)(also known as LBG algorithm) presented in [38]. For N = 16,we use a Grassmannian codebook proposed in [39]. We furtherrefer to the CB-IHDAF scheme with N = 4 and N = 16 asCB(N = 4)-IHDAF and CB(N = 16)-IHDAF, respectively.We will compare the secrecy performance of the proposedscheme with that of the CB-IHDAF scheme in Section V tofurther demonstrate the advantages of our proposed scheme.

D. Discussion on Optimal Antenna Selection

As mentioned in Section II-A, the antenna selection givenin (1) is not optimal. The optimal antenna selection shoulddepend on the working mode of the proposed scheme. Specif-ically, the current selection is optimal when DT mode is active,the optimal selection should maximize ρDF

SRD (i.e., the SNR atD for DF mode) when DF mode is active at R, and the optimalselection should maximize ρAF

SRD (i.e., the SNR at D for AFmode) when AF mode is active at R. As such, the optimalselection not only depends on the S-D and S-R links, butalso relates to the R-D link. Therefore, the optimal selectionrequires the cooperation between R and D (e.g., R has tofeedback the CSI of the S-R link to D in order to enablethis optimal selection), which costs extra resources (e.g., timeslots, feedback overhead). In order to avoid such cost and toachieve an efficient scheme of low complexity, we adopt asub-optimal selection scheme in the current work. However,we will examine the performance gap between the adoptedsub-optimal selection and the optimal selection numerically inSection V.

V. NUMERICAL RESULTS

In this section, we provide numerical results to examine thesecrecy performance of the proposed scheme. The SDF, IDF,and DT 3 schemes are also shown for comparison. We showthat the proposed TAS-based IHDAF scheme outperformsother schemes by achieving a lower SOP and a higher EST,especially in the scenario where R is close to D. Moreover,Monte Carlo simulations are also performed to verify theanalytical results given in this paper. In the simulation, welocate R on a straight line between S and D, which is a typicaltopology applied in relay networks. We set the path-loss factoras ν = 4, and that the reference distance for the antenna far-field as d0 = 1m. All nodes transmit at a carrier frequency offc = 2.4GHz, corresponding to a wavelength of λ = 125mm,B = 10MHz, and N0 = −174dBn/Hz [11].

Fig. 3 plots the SOP versus the normalized distance betweenS and R (e.g., the value of δ) with different values of ND. In

3It is noted that the SOP of the non-cooperative DT scheme isgiven by P out

DT = Pr(CSD < Rc) ∪ (CSE > Re) =

NS∑NS−1

i=0

∑i(ND−1)j=0

∑jk=0

Ξ(i,j,k,ΩSD)(ND−1)!

Γ1

(k+ND,

(i+1)T(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND

[1 −

Γ(NE,TeΩSE

)

Γ(NE)

]+

Γ(NE,TeΩSE

)

Γ(NE). Moreover, due to the multiplexing loss of the

cooperative schemes, we also assume that the three cooperative schemes (i.e.,the IDF, SDF and IHDAF shcemes) transmit with twice of the rate of theNon-cooperative scheme [11].

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

−4

10−3

10−2

10−1

100

relative distance δ

Sec

recy

Ou

tag

e P

rob

abili

ty

DT (ND

= 1)

DT (ND

= 2)

DT (ND

= 3)

SDF (ND

= 1)

SDF (ND

= 2)

SDF (ND

= 3)

IDF (ND

= 1)

IDF (ND

= 2)

IDF (ND

= 3)

IHDAF (ND

= 1)

IHDAF (ND

= 2)

IHDAF (ND

= 3)

Simulations (DT)Simulations (SDF)Simulations (IDF)Simulations (IHDAF)

Fig. 3. Secrecy outage probability versus the normalized distance betweenS and R (i.e., δ) with ΩSE = ΩRE = 0dB, ΩSD = 20 dB, Re = 2 bpcu,Rc = 3.6 bpcu, ρ = 1, NS = 2, and NE = 4.

this figure, we first observe that the simulation and analyticalresults match well for different values of δ and ND, whichconfirms the correctness of the derived analytical expressionof the SOP. We also observe that all the SDF, IDF, and IHDAFschemes outperform the DT scheme in terms of achievinglower SOPs, illustrating the security benefits of exploitingcooperative relays to prevent eavesdropping attacks. Fig. 3shows that the SOPs of all cooperative relaying schemesdecrease as the normalized distance between S and R increasesfor δ > 0.5, and the proposed IHDAF scheme achievesthe best secrecy performance. Particularly, the IDF and theproposed IHDAF schemes outperform the SDF scheme interms of achieving similar secrecy performance gain whenδ < 0.2, while the proposed scheme gains more prominentadvantages when δ > 0.2. This is due to the fact that whenR is close to S, the average SNR of the S-R link is highand thus the probability of adopting AF mode in the proposedIHDAF scheme is low, which leads to marginal benefits in theproposed scheme relative to the IDF scheme. However, whenR is far from S, the average SNR of the S-R link is low and theprobability that the proposed scheme adopts AF mode (whilethe IDF scheme fails) is high, which results in the dramaticadvantages of the proposed IHDAF scheme.

Fig. 4 plots the SOP versus SNR at E for different number oftransmit antennas at S. One can see from Fig. 4 that the SOPsof all the schemes decrease with the SNR at E, while ourproposed IHDAF scheme achieves the best performance forΩSE > −6 dB. Fig. 4 also illustrates the secrecy performanceof the proposed scheme relative to SDF and IDF schemesbecomes more prominent as the number of antennas at Sincreases (i.e., from NS = 2 to NS = 4). This can be explainedby Remark 4 in Section IV.

As mentioned in Section IV-D, in Fig. 5 we numericallyexamine the performance gap between the adopted sub-optimalantenna selection and the optimal antenna selection in theproposed scheme. Surprisingly, in this figure we observe that

−8 −6 −4 −2 0 2 4 6 8 10 1210

−6

10−5

10−4

10−3

10−2

10−1

100

ΩSE

Sec

recy

Ou

tag

e P

rob

abili

ty

DT(NS = 2)

DT(NS = 4)

SDF(NS = 2)

SDF(NS = 4)

IDF(NS = 2)

IDF(NS = 4)

IHDAF(NS = 2)

IHDAF(NS = 4)

Simulations (DT)Simulations (SDF)Simulations (IDF)Simulations (IHDAF)

Asymptotic (DT)Asymptotic (SDF)Asymptotic (IDF)Asymptotic (IHDAF)

Fig. 4. Secrecy outage probability versus the SNR at E with ΩSD = 20 dB,Re = 2 bpcu, Rc = 3.6 bpcu, δ = 0.5, ρ = 1, ND = 2, NE = 4, andNS = 2, 4.

0 10 20 30 40

10−4

10−3

10−2

10−1

100

ΩSD

Sec

recy

Out

age

Pro

babi

lity

IHDAF(δ=0.2)−−Suboptimal TASIHDAF(δ=0.2)−−Optimal TASIHDAF(δ=0.5)−−Suboptimal TASIHDAF(δ=0.5)−−Optimal TASIHDAF(δ=0.8)−−Suboptimal TASIHDAF(δ=0.8)−−Optimal TAS

δ=0.8

δ=0.2

δ=0.5

Fig. 5. Secrecy outage probability of the proposed TAS-based IHDAF schemewith sub-optimal and optimal antenna selections, with ΩSE = ΩRE = 0 dB,Re = 2 bpcu, Rc = 3.6 bpcu, δ = 0.2, 0.5, 0.8, ρ = 1, NE = 4, ND = 2,and NS = 2.

this gap in terms of the difference in the achieved SOP is notsignificant. Specifically, this gap is negligible when ΩSD isrelatively large, which is due to the fact that optimal selectionwill depend more on the S-D link when the S-D link becomesstrong (e.g., the probability that the proposed scheme operatesin the DT mode is high, for which our sub-optimal selectionis optimal). Also, this gap is extremely small when δ is closeto 0 or 1 (i.e., R is close to S or D). This is due to thefact that the cooperative link (i.e., S-R-D) is weak whenone of the S-R and R-D links is weak (i.e., δ is close to0 or 1) since the quality of the cooperative link is mainlydetermined by the link of the lower quality in relay networks,and thus the optimal selection will be mainly determined bythe S-D link. These observations confirm the validness ofthe adopted sub-optimal antenna selection, which costs lower

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 11

0

2

4

6

1

2

310

−4

10−3

10−2

10−1

100

Rs

NS

Sec

recy

Out

age

Pro

babi

lity

DT

IDF

IHDAF

Fig. 6. Secrecy outage probability versus Rs for ΩSE = ΩRE = 0dB,ΩSD = 20 dB, δ = 0.5, ρ = 1, NE = 4, ND = 2, and Re = 2 bpcu.

feedback overhead and cooperation complexity. The analysisof the above examples show that the IDF scheme alwaysoutperforms the SDF scheme. In the following simulations,only the simulation results for the proposed TAS-based IHDAFscheme, IDF and DT schemes are shown for better exposition.

Fig. 6 demonstrates the impact of the secrecy rate on theSOPs performance of the two cooperative relaying schemesand the DT scheme. In this figure, we observe that all thecooperative relaying schemes achieve higher secrecy rates fora fixed SOP. We also observe that the cooperative schemesoutperform DT scheme when Rs < 2.5bpcu in terms ofachieving lower SOPs. For a given equivocation rate (e.g.,Re=2bpcu), the DT scheme may obtain a larger secrecy rateat the cost of a higher SOP. We noted that if there exists amaximum allowable SOP, the DT scheme may fail to providesecrecy transmission while the cooperative schemes can [9].Finally, we observe that when NS = 1, the proposed schemestill outperforms the IDF and DT schemes, which demonstratesthat the advantage of the proposed scheme does not come fromTAS.

Fig. 7 plots the EST of different schemes versus Re. Inthis figure, we first observe that the cooperative schemessignificantly outperform the DT scheme in terms of achievinga higher EST. This is due to the fact that the relay can aidthe transmission between S and D when the DT fails, whichdemonstrates the benefits of relaying protocols. In addition, weobserve that the proposed scheme can achieve a higher ESTthan other schemes. Specifically, the maximum EST of theproposed scheme is much higher than that of any other scheme,which is due to the fact that the proposed scheme takes intothe advantages of both the AF and DF modes. Finally, weobserve that the EST gain of the proposed scheme relative tothe IDF scheme increases as the distance between S and Rincreases. This observation again confirms that the proposedscheme outperforms the IDF scheme, especially when R isclose to D.

In Fig. 8 , we compare the SOP of the proposed scheme

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

Re

Eff

ecti

ve S

ecre

cy T

hro

ug

ho

ut

DT(δ=0.5)DT(δ=0.8)IDF(δ=0.5)IDF(δ=0.8)IHDAF(δ=0.5)IHDAF(δ=0.8)

δ=0.5

δ=0.8

Fig. 7. Effective secrecy throughput of the IHDAF, IDF and DT schemeswith ΩSE = ΩRE = 0 dB, ΩSD = 20 dB, δ = 0.5, 0.8, ρ = 1, NE = 4,ND = 2, NS = 2, and Rc = 4 bpcu.

−5 0 5 1010

−4

10−3

10−2

10−1

100

ΩSE

Sec

recy

Out

age

Pro

babi

lity

TAS−IHDAFCB(N=4)−IHDAFCB(N=16)−IHDAF

Fig. 8. Secrecy outage probability of the TAS-IHDAF, CB(N =4)-IHDAF,and CB(N = 16)-IHDAF schemes with Re = 2bpcu, Rc = 3 bpcu, ΩSD =20 dB, δ = 0.5, ρ = 1, NS = 4, ND = 1, and NE = 2.

(TAS-IHDAF) with that of the CB-IHDAF scheme. In thisfigure, we first observe that the proposed TAS-IHDAF achievesa lower SOP than the CB(N = 4)-IHDAF scheme. We notethat these two schemes require the same amount of feedbackoverhead, which is ⌈log2 4⌉ = 2 bits due to NS = N = 4.As such, this observation demonstrates the advantage of theproposed TAS-IHDAF scheme in terms of achieving a highersecrecy performance with the same feedback overhead. Be-sides this advantage, we note that the proposed TAS-IHDAFonly require one active RF chain while CB-IHDAF schemerequests NS (which is 4 in this figure). As expected, weobserve that in the low regime of ΩSE (e.g., < 0 dB) theCB(N=16)-IHDAF scheme outperforms the proposed schemeat the cost of a higher feedback overhead (i.e., CB(N = 16)-IHDAF costs 4 bits feedback overhead while TAS-IHDAFonly requires 2 bits). However, we also observe that the

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

−4

10−3

10−2

10−1

100

relative distance δ

Sec

recy

Ou

tag

e P

rob

ab

ilit

y

DT (ρ = 0.6)DT (ρ = 0.8)DT (ρ = 1)

IDF (ρ = 0.6)IDF (ρ = 0.8)IDF (ρ = 1)

IHDAF (ρ = 0.6)IHDAF (ρ = 0.8)IHDAF (ρ = 1)

Simulations (DT)Simulations (IDF)Simulations (IHDAF)

NS=1

NS=3

Fig. 9. Secrecy outage probability versus the normalized distance betweenS and R (i.e., δ) with ΩSE = ΩRE = 0 dB, ΩSD = 20 dB, Re = 2 bpcu,Rc = 3.6 bpcu , ND = 2, NE = 2, and ρ = 0.6, 0.8, 1.

proposed TAS-IHDAF scheme achieves a lower SOP than theCB(N = 16)-IHDAF scheme in the medium and high regimesof ΩSE (e.g., ≥ 0 dB). This is due to the fact that in theCB-IHDAF scheme all antennas at S are active and E canobtain some diversity gain on average, while in the proposedTAS-IHDAF scheme only one antenna is active (which is thestrongest one for D but random for E) and no such gain canbe achieved at E. This gain increases as the S-E link becomesstronger (i.e., as ΩSE increases), and thus once ΩSE becomeslarger than some specific value the CB-IHDAF scheme losesits benefits offered by the extra feedback overhead. This canbe confirmed by the observation in this figure that the SOPsof the CB(N = 4)-IHDAF and CB(N = 16)-IHDAF schemesconverge together in the high regime of ΩSE.

Fig. 9 plots the SOP versus the normalized distance betweenS and R (i.e., the value of δ) with different values of NSand ρ. As expected, we first observe that delayed feedback(i.e., outdated CSI) has detrimental effect on the secrecyperformance of different schemes, and the SOPs of all theschemes decrease as ρ increases. Fig. 9 shows that, whenNS = 1, the SOPs of all schemes (i.e., DT, IDF, and IHDAFschemes) keep constant regardless of the value of ρ. This is dueto the fact that the link of S-D is unique when NS = 1 and noantenna selection is conducted. Fig. 9 also shows that the IDFand IHDAF schemes achieve better secrecy performance asNS increases, and the advantage of the IHDAF scheme relativeto the IDF scheme becomes more prominent as ρ increases.

In Fig. 10 , we further examine the impact of imperfect (i.e.,outdated) CSI on the secrecy performance of the proposedscheme. As expected, in this figure we observe that the SOPsof all schemes increase as ρ decreases, since a smaller ρindicates a severer imperfect impact (e.g., ρ = 0 representsa fully outdated CSI, while ρ = 1 represents perfect CSI). Wealso observe that with the imperfect CSI our proposed schemestill outperforms the other schemes, which demonstrates therobustness of the proposed scheme. This is mainly due to the

0 5 10 15 20 25 30 3510

−4

10−3

10−2

10−1

100

ΩSD

Sec

recy

Out

age

Pro

babi

lity

DT (ρ= 0)DT (ρ= 0.5)DT (ρ= 1)IDF (ρ = 0)IDF (ρ = 0.5)IDF (ρ = 1)IHDAF (ρ = 0)IHDAF (ρ = 0.5)IHDAF (ρ = 1)

ρ=0;0.5;1

Fig. 10. Secrecy outage probability versus SNR at D with different values ofρ when NE = 4, NS = ND = 2, Re = 2 bpcu, Rc = 3.6 bpcu, δ = 0.5,and ΩSE = ΩRE = 0 dB.

fact that the benefits of the proposed scheme are not due toTAS but the IHDAF strategy.

VI. CONCLUSION

In this paper, for the first time, we propose the TAS-based IHDAF scheme to enhance physical layer security whilemaintaining low feedback overhead and hardware complexityin a cooperative relay network. In order to fully examine thesecrecy performance of the proposed scheme, its SOP was firstderived in a closed-form expression by considering no CSIat S. Then, asymptotic analysis on the SOP was conductedwith the SDF and IDF schemes as benchmarks, disclosing asecrecy performance floor of the proposed TAS-based IHDAFscheme. Furthermore, we examine the impact of the number ofantennas, relay locations, average SNRs, and secrecy rates onthe SOP of the proposed scheme. It has been shown that theproposed TAS-based IHDAF scheme significantly outperformsthe IDF, SDF, and DT schemes in view of the a lowerSOP and a higher EST achieved, especially when R is closeto D. Furthermore, the proposed TAS-based IHDAF schemecan outperform the CB scheme with less feedback overheadand fewer RF chains. For future work, we will examine thesecrecy performance of IHDAF in multiple-antenna relayingnetworks, where antenna selection or artificial-noise-aidedsecure transmissions will be considered at the multiple-antennarelay.

APPENDIX APROOF OF THEOREM 2

When the S-D transmission fails in the DT mode, but R candecode it correctly, R operates in the DF mode. According to

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 13

the Bayes’ rule, the SOP given in (25) can be expressed as

PDFout =

[Pr

CDF

SRD<Rc

+Pr

CDF

SRE≥Re

Pr CSD<Rc

− PrCDF

SRE ≥ Re

Pr

CDF

SRD < Rc

]Pr CSR ≥ Rc ,

(56)

with

PrCSR ≥ Rc = 1− PrCSR < Rc = e− T

ΩSR . (57)

This is due to the fact that the TAS scheme at S is based on theS-D link, and thus the CDF of ρSR as FρSR(x) = (1−e

− xΩSR ).

Then, the key to obtaining the PDFout is to compute PrCDF

SRD <Rc and PrCDF

SRE ≥ Re. According to [11], PrCDFSRD < Rc

can be expressed as

PrCDFSRD < Rc = Pr log2(1 + ρSD + ρRD) < Rc

= Pr ρSD + ρRD < T . (58)

Defining Y = ρRD, we note that Y is a sum of the squaresof ND independent Gaussian random variables, therefore, thePDF of Y is obtained as [9]

fY (y) =e− y

ΩRD yND−1

(ΩRD)ND Γ(ND). (59)

Using (21) and (59), we can further express (58) as

PrCDFSRD < Rc = Pr

ρSD + ρRD < T

=

∫ T

0

fX(x)[ ∫ T−x

0

fY (y)dy]dx. (60)

By applying the PDFs of X and Y into (60), we obtain(34). Following similar steps as in obtaining PrCDF

SRD < Rc,PrCDF

SRE ≥ Re can be further written as

PrCDFSRE ≥ Re = 1− PrCDF

SRE < Re= 1− PrρSE + ρRE < Te. (61)

It is important to note that the selection of the strongesttransmit antenna for D corresponds to selecting a randomtransmit antenna for E. As such for E with MRC, we caneasily find that ρSE, ρRE, and ρRD have the same PDF and CDF.According to these characteristics and some mathematicalmanipulations, we can obtain (35), where we have calculatedthe resultant integral using [33, Eq. (3.381.1))] and [33,Eq. (3.382.1))]. Therefore, the SOP of PDF

out is obtained bysubstituting (31), (34), (35), and (57) into (33). This completesthe Proof.

APPENDIX BPROOF OF THEOREM 3

If neither D nor R has received the message from Scorrectly, R operates in AF mode. Using equation (39), theSOP can be further expressed as (62), which is shown at thetop of the next page.

Using (13), Pr(CAFSRD < Rc)|(CSD < Rc, CSR < Rc) can

be expressed as

Pr(CAFSRD < Rc)|(CSD < Rc, CSR < Rc)

=Prlog2(1+ρSD+ρSRρRD

ρSR+ρRD+1)<Rc|(Φ1,Φ2). (63)

For notational convenience, here we introduce the shorthandΦ1 = (CSR < Rc) and Φ2 = (CSD < Rc). We have

Pr log2(1 + ρSD +ρSRρRD

ρSR + ρRD + 1) < Rc|Φ1,Φ2 (64)

' Prlog2(1 + ρSD +min(ρSR, ρRD)) < Rc |Φ1,Φ2 (65)

= PrρSD + ρdmin < T |Φ1,Φ2, (66)

with ρdmin = min(ρSR, ρRD), where (65) is obtained using theapproximation of S1 S2

S1+S2+1 < S1 S2

S1+S2< min[S1, S2] [29], and

the effect of the approximation error can be neglected in highSNR regions. In addition, this effect can also be ignored whenconsidering a secrecy transmission as in this paper. As shownin Section V, our simulation results corroborate the theoreticalanalysis, and the approximation is actually very accurate forthe whole SNR region.

To proceed, according to [21], the expressions of Prρdmin <x |Φ1, and Pr(ρSD ≤ y |Φ2 and their corresponding PDFscan be obtained as in (67) and (68), which are shown at thetop of the next page. Then, we compute

PrρSD + ρdmin < T |Φ1, Φ2

=

∫ T

0

∫ T−x

0

fρdmin

(x|Φ1 )fρSD(y|Φ2 )dydx. (69)

By substituting (67) and (68) into (69), and performingsome mathematical manipulations, we can obtain (41), wherewe have introduced the shorthand PAF1

out = Pr (CAFSRD <

Rc)|(CSD < Rc, CSR < Rc) for notational convenience.Similarly, we can obtain Pr(CAF

SRE > Re)|(CSR < Rc as

Pr (CAFSRE ≥ Re)|CSR < Rc)

= Prlog2(1+ρSE +

ρSRρRE

ρSE+ρRE+1

)≥Re| log2(1+ρSR)<Rc

' Prlog2(1 + ρSE +min(ρSE, ρRE)) ≥ Re |Φ1= 1− PrρSE + ρemin < Te |Φ1, (70)

with ρemin = min(ρSR, ρRE). Furthermore, we have

fρemin

(x|Φ1)

=∂

∂x

[Pr(ρemin≤x,Φ1)

Pr(Φ1)

]=

ΩREe−xΩSR Γ(NE,

xΩRE

) + ΩSRe−xΩRE ( x

ΩRE)NE−1[e

− xΩSR − e

− TΩSR ]

ΩSRΩREΓ(NE)(1−e− T

ΩSR ).

(71)

According to fρSE(y) in Theorem 2 and fρemin

(x |Φ1 ) in (71),PrρSE + ρemin < 2Re − 1 |Φ1 in (70) can be rewritten as

PrρSE + ρemin < Te |Φ1

=

∫ Te

0

∫ Te−y

0

fρemin

(x|Φ1)fρSE(y)dxdy. (72)

With some mathematical manipulations, and the shorthandPAF2out = Pr(CAF

SRE ≥ Re)|(CSR < Rc), we can finally obtain(42). Hence, we complete the proof of Theorem 3 .

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 14

PAFout =

[Pr(CAF

SRD < Rc)|(CSD < Rc, CSR < Rc)+ Pr(CAFSRE ≥ Re)|(CSR < Rc)

− Pr(CAFSRD < Rc)|(CSD < Rc, CSR < Rc)Pr(CAF

SRE ≥ Re)|(CSR < Rc)]PrCSD < Rc, CSR < Rc. (62)

fρdmin

(x|Φ1) =∂

∂x

[Pr(ρdmin ≤ x,Φ1)

Pr(Φ1)

]=

ΩRDe−xΩSR Γ(ND,

xΩRD

) + ΩSRe−xΩRD ( x

ΩRD)ND−1[e

− xΩSR − e

− TΩSR ]

ΩSRΩRDΓ(ND)(1− e− T

ΩSR ), (67)

fρSD(y|Φ2) =∂

∂y

[Pr(ρSD ≤ y,Φ2)

Pr(Φ2)

]=

∑NS−1i=0

∑i(ND−1)j=0

∑jk=0 Ξ (i, j, k,ΩSD) e

− (i+1)y(i(1−ρ)+1)ΩSD yk+ND−1

∑NS−1i=0

∑i(ND−1)j=0

∑jk=0 Ξ (i, j, k,ΩSD)

Γ1

(k+ND,

(i+1)T(i(1−ρ)+1)ΩSD

)(

(i+1)(i(1−ρ)+1)ΩSD

)k+ND

. (68)

REFERENCES

[1] A. Khisti and G. W. Wornell, “Secure transmission with multipleantennas-Part I: The MISOME wire-tap channel,” IEEE Trans. Inf.Theory, vol. 56, no. 7, pp. 3088–3104, Jul. 2010.

[2] N. Yang, L. Wang, G. Geraci, M. Elkashlan, J. Yuan, and M. Di Renzo,“Safeguarding 5G wireless communication networks using physical layersecurity,” IEEE Commun. Mag., vol. 53, no. 4, pp. 20–27, Apr. 2015.

[3] Y. Zou, X. Wang, and W. Shen, “Optimal relay selection for physical-layersecurity in cooperative wireless networks,” IEEE J. Sel. Areas Commun.,vol. 31, no. 10, pp. 2099–2111, Oct. 2013.

[4] Y. W. P. Hong, P. C. Lan, and C. C. J. Kuo, “Enhancing physical-layer secrecy in multi-antenna wireless systems: An overview of signalprocessing approaches,” IEEE Signal Process. Mag., vol. 30, no. 5, pp.29–40, Sep. 2013.

[5] A. Mukherjee and A. L. Swindlehurst, “Robust beamforming for securityin MIMO wiretap channels with imperfect CSI,” IEEE Trans. SignalProcess., vol. 59, no. 1, pp. 351–361, Jan. 2011.

[6] N. Yang, P. Yeoh, M. Elkashlan, R. Schober, and I. Collings, “Transmitantenna selection for security enhancement in MIMO wiretap channels,”IEEE Trans. Commun., vol. 61, no. 1, pp. 144–154, Jan. 2013.

[7] H. Alves, R. D. Souza, M. Debbah, and M. Bennis, “Performance oftransmit antenna selection physical layer security schemes,” IEEE SignalProcess. Lett., vol. 19, no. 6, pp. 372–375, Jun. 2012.

[8] F. Oggier and B. Hassibi,“The secrecy capacity of the MIMO wiretapchannel,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961–4972, Aug.2011.

[9] N. Yang, M. Elkashlan, T. Q. Duong, J. Yuan, and R. Malaney, “Optimaltransmission with artificial noise in MISOME wiretap channels,” IEEETrans. Veh. Technol., vol. 65, no. 4, pp. 2170–2181, Apr. 2016.

[10] Y. Zou, B. Champagne, W.-P. Zhu, and L. Hanzo, “Relay-selectionimproves the security-reliability trade-off in cognitive radio systems,”IEEE Trans. Commun., vol. 63, no.1, pp. 215–218, Jan. 2015.

[11] G. Brante, H. Alves, R. Souza, and M. Latva-aho, “Secrecy analysisof transmit antenna selection cooperative schemes with no channel stateinformation at the transmitter,” IEEE Trans. Commun., vol. 63, no. 4,pp. 1330–1342, Apr. 2015.

[12] Y. Feng, Z. Yang, W.-P. Zhu, Q. Li, and B. Lv, “Robust cooperativesecure beamforming for simultaneous wireless information and powertransfer in amplify-and-forward relay networks,” IEEE Trans. Veh. Tech-nol., vol. 66, no. 3, pp. 2354–2366 Mar. 2017

[13] J. Huang, A. Mukherjee, and A. L. Swindlehurst, “Secrecy analysis ofunauthenticated amplify-and-forward relaying with antenna selection,” inProc. IEEE ICASSP, Mar. 2012.

[14] Z. Ding, Z. Ma, and P. Fan, “Asymptotic studies for the impact ofantenna selection on secure two-way relaying communications withartificial noise,” IEEE Trans. Wireless Commun., vol. 13, no. 4, pp. 2189–2203, Mar. 2014.

[15] C. Kundu, S. Ghose, and R. Bose, “Secrecy outage of dual-hop regen-erative multi-relay system with relay selection,” IEEE Trans. Commun.,vol. 14, no. 8, pp. 4614–4625, Aug. 2015.

[16] F. S. Al-Qahtani, C. Zhong, and H. M. Alnuweiri, “Opportunistic relayselection for secrecy enhancement in cooperative networks,” IEEE Trans.Commun., vol. 63, no. 5, pp. 1756–1770, May 2015.

[17] Y. Huang, C. Zhong, J. Wang, T. Duong, Q. Wu, and G. Karagiannidis,“Improving the security of cooperative relaying networks with multipleantennas,” in Proc. IEEE VTC Spring, May 2016, pp. 1–6.

[18] J. N. Laneman, D. N. C. Tse, and G.W.Wornell, “Cooperative diversity inwireless networks: Efficient protocols and outage behavior,” IEEE Trans.Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[19] T. Q. Duong and H. J. Zepernick, “On the performance gain ofhybrid decode-amplify-forward cooperative communications,” EURASIPJ. Wireless Commun. Netw., pp. 1-10, May 2009.

[20] T. Duong and H.-J. Zepernick, “Hybrid decode-amplify-forward coop-erative communications with multiple relays,” in Proc. IEEE WirelessCommunications and Networking Conference, Apr. 2009, pp.1-6.

[21] Z. Bai, J. Jia, C.-X. Wang, and D. Yuan, “Performance analysis of SNR-based incremental hybrid decode-amplify-forward cooperative relayingprotocol,” IEEE Trans. Commun., vol. 63, no. 6, pp. 2094–2106, Jun.2015.

[22] M. Yang, D. Guo, Y. Huang, T. Q. Duong, and B. Zhang, “ Securemultiuser scheduling in downlink dual-hop regenerative relay networksover Nakagami-m fading channels,” IEEE Trans. Wireless Commun., vol.15, no. 12, pp. 8009–8024, Nov. 2016.

[23] Y. Huang, F. Al-Qahtani, C. Zhong, Q. Wu, J. Wang, and H. Alnuweiri,“Performance analysis of multiuser multiple antenna relaying networkswith co-channel interference and feedback delay,” IEEE Trans. Commun.,vol. 62, no. 1, pp. 59–73, Jan. 2014.

[24] S. Yadav, P. K. Upadhyay, and S. Prakriya, “Performance evaluationand optimization for two-way relaying with multi-antenna sources,” IEEETrans. Veh. Technol., vol. 63, no. 6, pp. 2982–2989, Jul. 2014.

[25] Y. Wu, B. Zhang, X. Yi, and Y. Tang, “Communication-motion planningfor wireless telay-assisted multi-robot system,” IEEE Wireless Commun.Lett., vol. 5, no. 6, pp. 568–571, Dec. 2016.

[26] H. Guo, Z. Yang, L. Zhang, J. Zhu, and Y. Zou, “Power-constrainedsecrecy rate maximization for joint relay and jammer selection assistedwireless networks,” IEEE Trans. Commun., vol. PP, no. 99, pp. 1–1, 2017.

[27] A. Goldsmith, Wireless Communications, 1st ed. Cambridge, U.K:Cambridge Univ. Press, 2005.

[28] M. N. Khormuji and E. G. Larsson, “Cooperative transmission based ondecode-and-forward relaying with partial repetition coding,” IEEE Trans.Wireless Commun., vol. 8, no. 4, pp. 1716–1725, Apr. 2009.

[29] L. Fan, X. Lei, T. Q. Duong, M. Elkashlan, and G. Karagiannidis,“Secure multiuser communications in multiple amplify-and-forward relaynetworks,” IEEE Trans. Commun., vol. 62, no. 9, pp. 3299-3310, Sep.2014.

[30] S. Yan, N. Yang, G. Geraci, R. Malaney, and J. Yuan, “Optimization ofcode rates in SISOME wiretap channels,” IEEE Trans. Wireless Commun.,vol. 14, no. 11, pp. 6377–6388, May 2015.

[31] J. Xiong, Y. Tang, D. Ma, P. Xiao, and K. K. Wong, “Secrecy perfor-mance analysis for TAS-MRC system with imperfect feedback,” IEEETrans. Inf. Theory, vol. 10, no. 8, pp. 1617-1629, Aug. 2015.

[32] Y. Huang, F. S. Al-Qahtani, T. Q. Duong, and J. Wang, “Securetransmission in MIMO wiretap channels using general-order transmitantenna selection with outdated CSI,” IEEE Trans. Commun., vol. 63,no. 8, pp. 2959–2971, Aug. 2015.

[33] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series andProducts, 7th edition. Academic, 2007.

IEEE TRANSACTIONS ON COMMUNICATIONS, ACCEPTED FOR PUBLICATION 15

[34] J. Tang and X. Zhang, “Transmit selection diversity with maximalratiocombining for multicarrier DS-CDMA wireless networks over Nakagami-m fading channels,” IEEE J. Sel. Areas Commun., vol. 24, no. 1, pp.104–112, Jan. 2006.

[35] M. K. Simon and M.-S. Alouini, Digital Communications Over FadingChannels: A Unified Approach to Performance Analysis, 1st ed. NewYork, NY, USA: Wiley, 2000.

[36] H. Gamal, G. Caire, and M. Damen, “The MIMO ARQ channel:diversity-multiplexing-delay tradeoff,” IEEE Trans. Inf. Theory, vol. 52,no. 8, pp. 3601–3621, Aug. 2006.

[37] S. Bashar, Z. Ding, and G. Y. Li, “On secrecy of codebook-basedtransmission beamforming under receiver limited feedback,” IEEE Trans.Wireless Commun., vol. 10, no. 4, pp. 1212–1223, Apr. 2011.

[38] S. Zhou and B. Li, “BER criterion and codebook construction forfiniterate precoded spatial multiplexing with linear receivers,” IEEETrans. Signal Process., vol. 54, no. 5, pp. 1653–1665, May 2006.

[39] Available: http://engineering.purdue.edu/ djlove/grass.html

Youhong Feng (S’16) received the B.S. degree andthe M.S. degree in information engineering fromChang’an University, Xi’an, China, in 2003 and2006, respectively. He is currently working towardthe Ph.D. degree with Nanjing University of Postsand Telecommunications. He is currently an As-sociate Professor with the College of Physics andElectronic information Engineering, Anhui NormalUniversity. His research interests include coopera-tive communications, energy-efficient communica-tions and physical layer security.

Shihao Yan (S’11-M’15) received the Ph.D degreein Electrical Engineering from The University ofNew South Wales, Sydney, Australia, in 2015. Hereceived the B.S. in Communication Engineeringand the M.S. in Communication and InformationSystems from Shandong University, Jinan, China, in2009 and 2012, respectively. He is currently a Post-doctoral Research Fellow in the Research Schoolof Engineering, The Australian National University,Canberra, Australia. His current research interestsare in the areas of wireless communications and

statistical signal processing, including physical layer security, covert wirelesscommunications, and location verification.

Zhen Yang received his B.Eng. and M.Eng. degreesfrom Nanjing University of Posts and Telecommu-nications, China in 1983 and 1988, respectively, andhis Ph.D. degree from Shanghai Jiao Tong Univer-sity,China in 1999, all in electrical engineering. Hewas initially employed as a Lecturer in 1983 by Nan-jing University of Posts and Telecommunications,where he was promoted to Associate Professor in1995 and then a Full Professor in 2000. He was avisiting scholar at Bremen University, Germany dur-ing 1992-1993, and an exchange scholar at Maryland

University, USA in 2003. His research interests include various aspects ofsignal processing and communication, such as communication systems andnetworks, cognitive radio, spectrum sensing, speech and audio processing,compressive sensing and wireless communication. He has published morethan 200 papers in academic journals and conferences.

Prof. Yang serves as Vice Chairman and Fellow of Chinese Institute ofCommunications, Chairman of Jiangsu Institute of Internets, Vice Director ofEditorial Board of The Journal on Communications. He is also a Member ofEditorial Board for several other journals such as Chinese Journal of Electron-ics, China Communications, Data Collection and Processing et al, the Chair ofAPCC(Asian Pacific Communication Conference) Steering Committee during2013-2014.

Nan Yang (S’09–M’11) received the B.S. degreein electronics from China Agricultural University in2005, and the M.S. and Ph.D. degrees in electronicengineering from the Beijing Institute of Technologyin 2007 and 2011, respectively. He has been withthe Research School of Engineering at the Aus-tralian National University since July 2014, wherehe currently works as a Future Engineering ResearchLeadership Fellow and a Senior Lecturer. Prior tothis, he was a Postdoctoral Research Fellow at theUniversity of New South Wales from 2012 to 2014

and a Postdoctoral Research Fellow at the Commonwealth Scientific and In-dustrial Research Organization from 2010 to 2012. He received the ExemplaryReviewer Award of the IEEE TRANSACTIONS ON COMMUNICATIONS in2015 and 2016, the Top Reviewer Award from the IEEE TRANSACTIONSON VEHICULAR TECHNOLOGY in 2015, the IEEE ComSoc Asia-Pacific Out-standing Young Researcher Award and the Exemplary Reviewer Award of theIEEE WIRELESS COMMUNICATIONS LETTERS in 2014, and the ExemplaryReviewer Award of the IEEE COMMUNICATIONS LETTERS in 2013 and2012. He is also a co-recipient of the Best Paper Awards from the IEEEGlobeCOM 2016 and the IEEE VTC 2013-Spring. He is currently servingin the Editorial Board of the IEEE TRANSACTIONS ON WIRELESS COM-MUNICATIONS, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, andTRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES.His general research interests lie in the areas of communications theory andsignal processing, with specific interests in massive multi-antenna systems,millimeter wave communications, ultra-reliable low latency communications,cyber-physical security, and molecular communications.

Wei-Ping Zhu (SM97) received the B.E. and M.E.degrees from Nanjing University of Posts and T-elecommunications, 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 Concordias Electricaland Computer Engineering Department as a full-time faculty member, wherehe is presently a Full Professor. Since 2008, he has been an Adjunct Professorat Nanjing University of Posts and Telecommunications, Nanjing, China. Hisresearch interests include digital signal processing fundamentals, speech andstatistical signal processing, and signal processing for wireless communicationwith a particular focus on MIMO systems and cooperative communication.

Dr. Zhu served as an Associate Editor for the IEEE Transactions on Circuitsand Systems Part I: Fundamental Theory and Applications during 2001-2003, an Associate Editor for Circuits, Systems and Signal Processing during2006-2009, and an Associate Editor for the IEEE Transactions on Circuitsand Systems Part II: Transactions Briefs during 2011-2015. He was also aGuest Editor for the IEEE Journal on Selected Areas in Communications forthe special issues of: Broadband Wireless Communications for High SpeedVehicles, and Virtual MIMO during 2011-2013. Currently, he is an AssociateEditor of Journal of The Franklin Institute. Dr. Zhu was the Chair-Elect ofDigital Signal Processing Technical Committee (DSPTC) of the IEEE Circuitsand System Society during June 2012-May 2014, and the Chair of the DSPTCduring June 2014-May 2016.