joint relay and jammer selection for secure two-way relay networks

310 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012

Joint Relay and Jammer Selection for SecureTwo-Way Relay Networks

Jingchao Chen, Rongqing Zhang, Student Member, IEEE, Lingyang Song, Member, IEEE,Zhu Han, Senior Member, IEEE, and Bingli Jiao, Member, IEEE

AbstractIn this paper, we investigate joint relay and jammerselection in two-way cooperative networks, consisting of twosources, a number of intermediate nodes, and one eavesdropper,with the constraints of physical-layer security. Specifically, theproposed algorithms select two or three intermediate nodes toenhance security against the malicious eavesdropper. The firstselected node operates in the conventional relay mode and assiststhe sources to deliver their data to the corresponding destinationsusing an amplify-and-forward protocol. The second and thirdnodes are used in different communication phases as jammersin order to create intentional interference upon the maliciouseavesdropper. First, we find that in a topology where the interme-diate nodes are randomly and sparsely distributed, the proposedschemes with cooperative jamming outperform the conventionalnonjamming schemes within a certain transmitted power regime.We also find that, in the scenario where the intermediate nodesgather as a close cluster, the jamming schemes may be less effectivethan their nonjamming counterparts. Therefore, we introducea hybrid scheme to switch between jamming and nonjammingmodes. Simulation results validate our theoretical analysis andshow that the hybrid switching scheme further improves thesecrecy rate.

Index TermsCooperative jamming, friendly jammer selection,physical-layer security, relay selection, two-way relay.

I. INTRODUCTION

T RADITIONALLY security in wireless networks has beenmainly focused on higher layers using cryptographicmethods [1]. Pioneered by Wyners work [2], which introduced

Manuscript received September 30, 2010; revised July 16, 2011; acceptedAugust 08, 2011. Date of publication August 30, 2011; date of current ver-sion January 13, 2012. This work was supported in part by the US NSF CNS-0953377, CNS-0905556, and CNS-0910461, in part by the National Nature Sci-ence Foundation of China under Grant 60972009 and Grant61061130561, andin part by the National Science and Technology Major Project of China underGrant 2009ZX03003-011, Grant 2010ZX03003-003, and Grant 2011ZX03005-002. The associate editor coordinating the review of this manuscript and ap-proving it for publication was Dr. Wade Trappe.J. Chen, R. Zhang, L. Song, and B. Jiao are with the Wireless Com-

munication and Signal Processing Research Center, School of Elec-tronics Engineering and Computer Science, Peking University, Beijing100871, China (e-mail: [email protected]; [email protected];[email protected]; [email protected]).Z. Han is with the Electrical and Computer Engineering Department, Uni-

versity of Houston, Houston, TX 77204 USA, and also with the Department ofElectronics and Radio Engineering, Kyung Hee Universtiy, Gyeonggi, 446-701,South Korea (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIFS.2011.2166386

the wiretap channel and established fundamental results ofcreating perfectly secure communications without relyingon private keys, physical-layer-based security has drawn in-creasing attention recently. The basic idea of physical-layersecurity is to exploit the physical characteristics of the wirelesschannel to provide secure communications. The security isquantified by the secrecy capacity, which is defined as themaximum rate of reliable information sent from the sourceto the intended destination in the presence of eavesdroppers.Wyner showed that when the wiretap channel is a degradedversion of the main channel, the source and the destination canexchange secure messages at a nonzero rate. The followingresearch work [3] studied the secrecy capacity of the Gaussianwiretap channel, and [4] extended Wyners approach to thetransmission of confidential messages over broadcast channels.Very recently, physical-layer security has been generalizedto investigate wireless fading channels [5][8], and variousmultiple access scenarios [9][12].Note the fact that if the source-wiretapper channel is stronger

than the source-destination channel, the perfect secrecy ratewill be zero [4]. Some work [13][24] has been proposed toovercome this limitation with the help of relay cooperationby cooperative relaying [13], [14], and cooperative jamming[15][17]. For instance, in [13] and [14], the authors proposedeffective decode-and-forward (DF) and amplify-and-forward(AF)-based cooperative relaying protocols for physical-layersecurity, respectively. Cooperative jamming is another ap-proach to improve the secrecy rate by interfering the eaves-dropper with codewords independent of the source messages.In Yener and Tekins work [15], a scheme termed collaborativesecrecy was proposed, in which a nontransmitting user wasselected to help increase the secrecy rate for a transmittinguser by effectively jamming the eavesdropper. Following asimilar idea as [15], they first proposed cooperative jammingin [16] and [17] in order to increase achievable rates in thescenarios where a general Gaussian multiple access wiretapchannel and two-way wiretap channel were assumed, respec-tively. The authors of [18] and [19] investigated the effectsof user cooperation on the secrecy of broadcast channels byconsidering a cooperative relay broadcast channel, and showedthat user cooperation can increase the achievable secrecyregion. The study of communicating through unauthenticatedintermediate relays between a source-destination pair startedfrom Yener and Hes work [20][22]. The relay channel withconfidential messages was also investigated in [23] and [24],where the untrusted relay node acts both as an eavesdropperand a conventional assistant relay.

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CHEN et al.: JOINT RELAY AND JAMMER SELECTION FOR SECURE TWO-WAY RELAY NETWORKS 311

Two-way communication is a common scenario in which twonodes transmit information to each other simultaneously. Re-cently, the two-way relay channel [25][29] has attracted muchinterest from both academic and industrial communities, dueto its bandwidth efficiency and potential application to cellularnetworks and peer-to-peer networks. In [25] and [26], both AFand DF protocols for one-way relay channels were extendedto the general full-duplex discrete two-way relay channel andhalf-duplex Gaussian two-way relay channel, respectively. In[27], network and channel coding were used in the two-wayrelay channel to increase the sum-rate of two sources. The workin [28] introduced a two-way memoryless system with relays, inwhich the signal transmitted by the relay is obtained by applyingan instantaneous relay function to the previously received signalin order to optimize the symbol error rate performance. As forsecure communications, in [29], Yener and He investigated therole of feedback in secrecy for two-way networks, and provedthat the loss in secrecy rate when ignoring the feedback is verylimited in a scenario with half-duplex Gaussian two-way relaychannels and an eavesdropper.It is well known that, in a cooperative communication net-

work, proper relay/jammer selection can have a significant im-pact on the performance of the whole system. Several relay se-lection techniques [30][32] have been explored by far. The au-thors in [30] proposed a nonjamming relay selection scheme fortwo-way networks with multiple AF relays in an environmentwithout eavesdroppers, which maximized the worse receivedsignal-to-noise ratio (SNR) of the two end users. In [31], sev-eral relay selection techniques were proposed in one-way coop-erative networks with secrecy constraints. In [32], the authorsinvestigated some relay selection techniques in a two-hop DFcooperative communication system with no central processingunit to optimally select the relay. Although cooperative net-works have received much attention by far, the physical-layersecurity issues with secrecy constraints in two-way schemeshave not yet been well investigated.To this end, in this paper, we propose a scheme that can imple-

ment information exchange in the physical layer against eaves-droppers for two-way cooperative networks, consisting of twosources, a number of intermediate nodes, and one eavesdropper,with the constraints for physical-layer security. Unlike [30], inwhich the relay selection is operated in an environment withno security requirement, our work takes into account the se-crecy constraints. In contrast to [31], where many relay selec-tions based on the DF strategy for one-way cooperative wire-less networks were proposed and a safe broadcasting phase wasassumed, the problem we consider here involves a nonsecuritybroadcasting phase, and the information is transferred bidirec-tionally.Specifically, one node is selected from an intermediate node

set to operate at a conventional relay mode, and then uses an AFstrategy in order to assist the sources to deliver data to the cor-responding destinations. Meanwhile, another two intermediatenodes that perform as jammers are selected to transmit artificialinterference in order to degrade the eavesdropper links in thefirst and second phases of signal transmissions, respectively.Weassume that both destinations cannot mitigate artificial interfer-ence, and thus, the jamming will also degrade the desired infor-

Fig. 1. System model, where the eavesdropper node is able to receive signalsfrom both and .

mation channels. The principal question here is how to select therelay and the jammers in order to increase information security,and meanwhile protect the source messages against the eaves-dropper. Several selection algorithms are proposed, aiming atpromoting the assistance to the sources as well as the interfer-ence to the eavesdropper.The theoretical analysis and simulation results reveal that

the proposed jamming schemes can improve the secrecy rateof the system by a large scale, but only within a certain trans-mitted power range. In some particular scenarios, the proposedschemes become less efficient than the conventional ones. Wethen propose a hybrid scheme with an intelligent switchingmechanism between jamming and nonjamming modes to solvethis problem.The rest of this paper is organized as follows. In Section II,

we describe the system model, and formulate the problemunder consideration. In Section III, we propose several selec-tion techniques, and introduce their hybrid implementations. InSection IV, we provide both quantitative analysis and qualita-tive discussions of different selection schemes in some typicalconfigurations. Numerical results are shown in Section V, andthe main conclusions are drawn in Section VI.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System ModelWe assume a network configuration consisting of two sourcesand , one eavesdropper , and an intermediate node set

with nodes. In Fig. 1 it schematicallyshows the system model. As the intermediate nodes cannottransmit and receive simultaneously (half-duplex assumption),the communication process is performed by two phases. Duringthe first phase, and transmit their data to the intermediatenodes. In addition, according to the security protocol, one nodeis selected from to operate as a jammer and transmit

intentional interference to degrade the source-eavesdropperlinks in this phase. Since the jamming signal is unknown atthe rest nodes of , the interference will also degrade theperformance of the source-relay links. During the second


phase, according to the security protocol, an intermediatenode, denoted by , is selected to operate as a conventionalrelay and forwards the source messages to the correspondingdestinations. A second jammer is also selected from , forthe same reason as that for . Note that and are not ableto mitigate the artificial interference from the jamming nodes.In both phases, a slow, flat, and block Rayleigh fading en-

vironment is assumed, i.e., the channel gain remains static forone coherence interval and changes independently in differentcoherence intervals with a variance , wheredenotes the Euclidean distance between node and node ,and represents the path-loss exponent. The channel gainbetween node and node is denoted by , which is modeledas a zero-mean, independent, circularly symmetric complexGaussian random variable with variance . Furthermore, ad-ditive white Gaussian noise (AWGN) with zero mean and unitvariance is assumed. Let , , and denote the transmittedpower for the source nodes, the relay node and the jammingnodes, respectively. In order to protect the destinations fromsevere artificial interference, the jamming nodes transmit with alower power than the relay node [31], and thus their transmittedpower can be defined as , where denotesthe power ratio of relay to jammer.In the first phase, the two sources send information symbolsand , respectively, which are mapped to a PSK set. The

intermediate node and eavesdropper thus receive

(1)(2)

where and denote the noise at and , respectively.In the second phase, the intermediate node is selected to

amplify its received signal and forward it to and , i.e.,broadcasts

(3)

where .Since knows (for ), it can cancel the self-inter-

ference. Therefore, , , and get

(4)

(5)

(6)

where , , and represent the noise at , , and ,respectively. Then, , defined as the overall signal to interfer-ence-plus-noise ratio (SINR) of the virtual channel(for , ), can be calculated as

(7)

where represents the instantaneous signal-to-noise ratio(SNR) of link

(8)

(9)

(10)

(11)

Strictly speaking, in order to maximize the overall SINR ofthe eavesdropping links, the eavesdropper can perform what-ever operations as it wishes with the signals received in the pre-vious two phases. Here in this paper, we consider a simple casein which the eavesdropper applies maximal ratio combining(MRC) [34], so as to examine the efficiency of the proposedjamming schemes.1 According to MRC, combines the re-ceived signals by multiplying in (2) and in (6) with properweighting factors and , respectively. Without loss of gen-erality, consider the scenario in which intends to optimize theSINR of link , for , the combined eavesdrop-ping signal can be written as

(12)

where

(13)

(14)

with , , and is the conjugate transpose.and represent the total interference and noise

power terms in and , respectively

(15)

(16)

where

(17)

(18)

(19)(20)(21)

In order to calculate the SINR of link , we assumetwo different channel knowledge sets:1) which denotes a global instantaneous knowledge for allthe links;

2) which denotes an average channel knowledge for theeavesdropping links.

1Please note that the eavesdroppers operation is not limited to MRC. Andthe increasing in secrecy rate of the proposed schemes can still be achieved ifthe eavesdropper takes other operations, since the basic forms of the SINRs andthus of the secrecy rate do not change.


With the assumption of , we can get the instantaneous SNRof any channel in the system. Thus, the SINR of link

can be calculated as

(22)

In an environment where the instantaneous channel knowl-edge set is not available, we can use the expectation of SNRsfor the eavesdropping links , which is provided by theaverage channel knowledge , to get the SINRs

(23)

where stands for the expectation operator.

B. Problem FormulationThe instantaneous secrecy rate with the node set for

source can be expressed as [35]

(24)where , , , and .The overall secrecy performance of the system is character-

ized by the ergodic secrecy rate which is the expectation of thesum of the two sources secrecy rate, , where

(25)

Our objective is to select appropriate nodes , , and ,in order to maximize the instantaneous secrecy rate subject todifferent types of channel feedback. The optimization problemcan be formulated as

(26)

where , , , and denote the selected relay andjamming nodes, respectively. Note that here the selected jam-mers and in the two phases may be the same node, whichis determined by the instantaneous secrecy rate.

C. Selection Without JammingIn a conventional cooperative network, the relay scheme does

not have the help from jamming nodes. We derive the followingsolutions under this scenario.1) Conventional Selection (CS): The conventional selection

does not take the eavesdropper channels into account, and the

relay node is selected according to the instantaneous SNR ofthe channel between node and node only. Therefore, theSINR given in (7) becomes

(27)

where represents the SINR of the virtual channel(for , ) without considering the eavesdropper.Hence, the conventional selection scheme can be expressed

as

(28)

with and for ( , ) given by (8) and(11), respectively. Since (28) shows that this selection does notconsider the eavesdropping links, the CS scheme may not beable to support systems with secrecy constraints even though itmay be effective in noneavesdropper environments.2) Optimal Selection (OS): This solution takes the eaves-

dropper into account and selects the relay node based on ,which provides the instantaneous channel knowledge for all thelinks. Then, the SINR of link in (22) can be rewrittenas

(29)

The optimal selection scheme is given as

(30)

where

(31)

3) Suboptimal Selection (SS): The suboptimal selection im-plements the relay selection based on the knowledge set ,which gives the average estimate of the eavesdropping links.Therefore, it avoids the difficulty of getting instantaneous esti-mate of channel feedback. Similar to the OS scheme in (30), thesuboptimal selection scheme can be written as

(32)


where

(33)

(34)

Note that in comparison of the OS scheme in (30), the onlydifference of the SS scheme in (32) is that it requires the averagechannel state information which would be more useful inpractice.

III. SELECTIONS WITH JAMMING IN TWO-WAY RELAYSYSTEMS

In this section, we present several node selection techniquesbased on the optimization problem given by (26) in the two-waysystem. Unlike [31], where the selection techniques only con-cern the secrecy performance in the second phase of transmis-sion, here, our work takes into account both the two phases inorder to select a set of relay and jammers that can maximize theoverall expectation of secrecy rate.

A. Optimal Selection With Maximum Sum InstantaneousSecrecy Rate (OS-MSISR)The optimal selection with maximum sum instantaneous se-

crecy rate assumes a knowledge set and ensures a maximiza-tion of the sum of instantaneous secrecy rate of node andnode given in (25), which gives credit to

(35)

where and are given by (7) and (22), respectively.The approach in (35) reflects the basic idea of using both co-

operative relaying and cooperative jamming in order to promotethe systems secrecy performance. Specifically, the OS-MSISRscheme here tends to select a set of relay and jammers that maxi-mizes , which means promoting the assistance to the sources.Meanwhile, this relay and jammer set tends to minimize ,which is equivalent to enhance the interference to the eaves-dropper.Although the OS-MSISR scheme seems to be a straightfor-

ward application for cooperative relaying and cooperative jam-ming, the actual selection procedure usually involves trade-offs.For instance, according to (7) and (9), we should select the relayand jammer set that minimizes in order to make ashigh as possible. Considering (19), (20), and (22), however, thelower is, the higher is, which is undesirable. Thus,we have to make a trade-off between raising and inhibiting

in order to optimize the right part of (35).

B. Optimal Selection With MaxMin Instantaneous SecrecyRate (OS-MMISR)It is obvious that the OS-MSISR scheme in (35) is compli-

cated; thus, in this subsection, we propose a reduced-complexityalgorithm. It is common that the sum secrecy rate of the twosources, i.e., , may be driven

down to a low level by the source with the lower secrecy rate.As a result, for low complexity, the intermediate nodes, whichmaximize the minimum secrecy rate of the two sources, can beselected to achieve the near-optimal performance. In addition,in some scenarios, the considered secrecy performance takesinto account not only the total secrecy rate of both the sources,but also the individual secrecy rate of each one. If one sourcehas a low secrecy rate, the whole system is regarded as se-crecy inefficient. Furthermore, assuring each individual source ahigh secrecy rate is another perspective of increasing the wholesystems secrecy performance.The OS-MMISR scheme maximizes the worse instantaneous

secrecy rate of the two sources with the assumption of knowl-edge set , and we can get

(36)

where and are given by (7) and (22), respectively.

C. Optimal Switching (OSW)The original idea of using jamming nodes is to introduce in-

terference on the eavesdropping links. However, there are twoside-effects of using jamming. Such as the jamming node in thesecond phase , it also poses undesired interference directlyonto the destinations. Given the assumption that the destinationscannot mitigate this artificial interference, continuous jammingin both phases is not always beneficial for the whole system. Insome specific situations (e.g., is close to one destination), thecontinuous jamming may decrease the secrecy rate of both thesources seriously, and act as a bottleneck for the system. In orderto overcome this problem, we introduce the idea of intelligentswitching between the OS-MSISR and OS schemes in order toreduce the impact of negative interference. The threshold forthe involvement of the jamming nodes is

(37)

where

(38)

Thus, (37) can be further written as

(39)

where , , , and are given by (7), (22), (31), and(29), respectively.For each time slot, if (39) is met, the OS-MSISR scheme pro-

vides higher instantaneous secrecy rate than the OS scheme doesand is preferred. Otherwise, the OS scheme is more efficientin promoting the systems secrecy performance, which shouldbe employed. Because of the uncertainty of the channel coef-ficient for each channel , the OSW scheme shouldoutperform either the continuous jamming schemes or the non-jamming ones.


D. Suboptimal Selection With Maximum Sum InstantaneousSecrecy Rate (SS-MSISR)

With the assumption of , we can get some optimal selectionmetrics. However, its practical interest and potential implementsare only limited to some special (e.g., military) applications,where the instantaneous quality of the eavesdropping links canbe measured by some specific protocols. In practice, only anaverage knowledge of these links would be available fromlong-term eavesdropper supervision. The selection metrics ismodified as

(40)

where and are given by (7) and (23), respectively.From (40), we can predict that for a scenario in which

the intermediate nodes are sparsely distributed across theconsidered area, the SS-MSISR scheme can provide similarrelay and jammer selection performance with the OS-MSISRscheme. This is because a slight difference betweenprovided by and provided by would not be enoughfor the scheme to select another faraway intermediate node.Thus, under this condition, the average eavesdropper channelknowledge set may contain sufficient channel informationas well for a quasi-optimal selection.

E. Suboptimal Selection With MaxMin Instantaneous SecrecyRate (SS-MMISR)

This scheme refers to the practical application of the aboveselection with maximizing worse instantaneous secrecy rate in(36). The basic idea of considering as the average behavior ofthe eavesdropping links is the same as the SS-MSISR scheme,but aimed at looking for the maximum worse instantaneous se-crecy rate, which is written as

(41)

where and are given by (7) and (23), respectively.

F. Suboptimal Switching (SSW)

Given the fact that jamming is not always a positive processfor the performance of the system, the suboptimal switchingscheme refers to the practical application of the intelligentswitching between the SS-MSISR and SS schemes. The basicidea is the same as the OSW scheme, but the switching criterionuses the available knowledge set . More specifically, therequired condition for switching from SS-MSISR to SS mode is

(42)

where , , , and are given by (7), (23), (33), and(34), respectively.

G. Optimal Selection With Known Jamming (OSKJ)

The previous selection techniques are proposed based on theassumption that the jamming signal is unknown at both destina-tions. This assumption avoids the initialization period in whichthe jamming sequence is defined, and thus, it reduces the riskof giving out the artificial interference to the eavesdropper. Forcomparison reasons, here we propose a control scheme, inwhich the jamming signal can be decoded at destinations and, but not at eavesdropper . In this case, the SINR of the link

from (for ) to remains the same as given by(22). The SINR of the link from to (for , )is modified as follows:

(43)

The OSKJ scheme is taken into consideration in the numer-ical results section as a reference. This, however, is not theideal jamming scheme since the artificial interference fromthe jammers only degrades the eavesdropping links. As we havediscovered and will discuss in Section V, in some particularscenarios, the OSKJ scheme is outperformed by the OSW andSSW schemes presented above, for the jamming has changedthe value of given in (3).

IV. PERFORMANCE ANALYSIS

In this section, we first do some quantitative analysis on theasymptotic performance of both the proposed jamming and non-jamming schemes in high transmitted power range. Then, weprovide a qualitative discussion of the secrecy performance ofdifferent selection schemes in some typical scenarios based onthe system model in Section II.

A. Asymptotic Performance for Selections Without Jamming

Without loss of generality, we take the OS scheme for ex-ample. With high transmitted power , we can get

(44)

(45)

We can see that grows rapidly as increases, whileconverges to a value that depends only on the relative dis-

tances between the sources and the eavesdropper as well as thesources and the relay. Therefore, the ergodic secrecy ratealso increases rapidly with the transmitted power . Based on(44) and (45), the slope of the versus curve (measuredby decibels) can be approximately calculated as


(46)

For the other nonjamming schemes (i.e., CS and SS), wenote that they share the same asymptotic performance as theOS scheme with a linear increment of slope about 0.3322 as thetransmitted power increases.

B. Asymptotic Analysis for Selections With ContinuousJammingWe use the same method as in the previous analysis for the

nonjamming schemes to analyze the asymptotic performanceof the proposed jamming schemes. As the transmitted powerincreases to a relatively high value, it yields (47) and (48),

shown at the bottom of the page.It is clear that both and are independent of , which

means that for high , the ergodic secrecy rate stopsincreasing and converges to a fixed value. Consider the asymp-totic performance of the OS scheme that grows linearly with theincrement of as described in (46); it is safe to predict thatthere will be a crossover point between the ergodic secrecyrate v.s. transmitted power curve with jamming and the one withnonjamming. In the power range below , the jamming schemeoutperforms the nonjamming one, while above this point, thejamming scheme loses its advantage in providing higher ergodicsecrecy rate.We note that the analysis above can apply to any scheme

with continuous jamming (i.e., OS-MSISR, OS-MMISR,SS-MSISR, and SS-MMISR), which indicates that they sharethe same asymptotic behavior as increases. In other words,the proposed selection techniques (except for OSW and SSW)behave better than the nonjamming schemes only within acertain transmitted power range. Fortunately, in a practicalcase, is always limited in a relatively low range and willnot increase infinitely.

C. Secrecy Performance With Sparsely DistributedIntermediate NodesThis is a common configuration in which eavesdropper has

similar distances with two sources and and the interme-diate nodes spread randomly within the considered area. With

a relatively far distance in between, the interference link be-tween and becomes weak. As predicted in the previoussubsection, within a certain transmitted power range (less thanthe crossover point ), the selection schemes with continuousjamming are able to provide a higher ergodic secrecy rate thanthe nonjamming ones. This gain proves the introduction of jam-ming in selection schemes as an effective technique. Outsidethis range, the secrecy rate of the conventional nonjammingschemes continue to grow with a slope of 0.3322 as verifiedin (46), whereas those of the continuous jamming schemes con-verge to a fixed value. Inside this scope, the continuous jammingschemes lose their efficiency in providing a better secrecy per-formance for the system.We note that in some particular scenarios, the systems in-

tegrated secrecy performance is not measured by the sum ofthe sources secrecy rate, but by the minimum secrecy rate ofthe sources in the system. In this situation, the OS-MMISR andSS-MMISR schemes can optimize the overall secrecy perfor-mance of the whole system. For the hybrid schemes, the OSWand SSW schemes are able to provide better secrecy perfor-mance in the whole transmitted power scope, since it overcomesthe bottleneck caused by negative interference on the relay-des-tination links.

D. Secrecy Performance With a Close Cluster of theIntermediate Nodes

Under the condition that all the intermediate nodes are locatedvery close to each other, we note that the continuous jammingselections will lose their efficiency in meeting the secrecy con-straints. Specifically, we will discuss two extreme situations inwhich the intermediate nodes cluster is near to one of the desti-nations, and to the eavesdropper, respectively.1) Intermediate Nodes Cluster Locates Near to One of the

Destinations: There are two reasons that make the proposedcontinuous jamming schemes inefficient. First, the nodes of therelay/jammer cluster gather too close to each other, such that theselected jammer in the first phase has too much negative im-pact on the selected relay , which further decreases the SINRsin the second phase. Second, the jamming signal from in thesecond phase also has an overly strong interference on the des-tination it stays close to.2) Intermediate Nodes Cluster Locates Near to the Eaves-

dropper: Aside from the first reason presented above, in thisconfiguration, the direct link between relay and eavesdroppergets too strong, which will seriously sabotage the secrecy per-

formance of the continuous jamming schemes.

(47)

(48)


Fig. 2. The 1 1 simulation environment with intermediate nodes.

On the other hand, the hybrid schemes (i.e., OSW and SSW)will still be the most effective ones in this configuration, sincethe systems secrecy performance considered here is measuredby the ergodic secrecy rate.

E. Secrecy Performance With the Eavesdropper Near to Oneof the Source NodesThis is the situation in which eavesdropper can get the

communicating informationmost easily, since the direct link be-tween and any one of the sources is strong, which makes theintroduction of jamming very necessary. The jamming schemesshould be efficient within quite a large power range, and thehybrid schemes should still perform as the best selection tech-niques within the whole power scope.

V. NUMERICAL RESULTSIn this section, we provide computer simulations in order to

validate the analysis in the previous section. The simulation en-vironment consists of two sources and , one eavesdropper, and an intermediate node cluster with nodes. All the

nodes are located in a 2-D square topology within a 1 1 unitsquare. For simplicity, we assume that the sources and the relaytransmit with the same power, i.e., , while the jammerstransmit with a power subject to the relay-jammer power ratio

, i.e., . As assumed in Section II, the powerof the AWGN is . The path-loss exponent is set to .In this paper, the adopted performance metric is the ergodic se-crecy rate. Meanwhile, some results are also provided in termsof the secrecy outage probability ,where denotes probability, and is the target secrecy rate.First, we consider a scenario where , , and are located

at , , and, respectively. The intermediate nodes spread randomly

within the square space, as shown in Fig. 2.Fig. 3 shows the ergodic secrecy rate versus the transmitted

power of different selection schemes. We can observe that theselection schemes with jamming outperform their nonjammingcounterparts within a certain transmitted power range (

Fig. 3. Ergodic secrecy rate versus transmitted power with different selec-tion techniques.

, dB), where the ergodic secrecy rate of OS-MSISRis approximately higher than that of OS by 1 bit per channel use(BPCU). Outside this range , the ergodic secrecy rateof OS-MSISR converges to a power-independent value whichis approximately 4.1 BPCU, whereas the ergodic secrecy rate ofOS continues to grow with a slope of 0.3322, as proved in (46).This validates the secrecy performance analysis in Section IV.In addition, we can see that in this topology, the suboptimalschemes (e.g., SS-MSISR and SS-MMISR) which are based onaverage channel knowledge perform almost the same as the cor-responding optimal ones (e.g., OS-MSISR and OS-MMISR),which implies that in this configuration where the intermediatenodes are sparsely distributed, an average channel knowledgemay also provide enough information in order to get optimalrelay and jammer selection.In Fig. 3, a comparison between OS-MSISR and OS-MMISR

shows that OS-MSISR has slightly higher ergodic secrecy rateby about 0.25 BPCU than OS-MMISR does corresponding tothe transmitted power . The same comparison result can beobserved from SS-MSISR and SS-MMISR, which matches ourprevious analysis. Furthermore, it can be seen that OSW per-forms better than any other selection techniques with or withoutcontinuous jamming. At a low power range where ,OSW performs slightly better than OS-MSISR, but much betterthan OS (by about 1.2 BPCU), for the reason that in this rangecontinuous jamming is almost always needed. After growsmuch higher than , OSW outperforms both the other twoschemes by a large scale. For the suboptimal case, we can seethat SSW provides almost the same performance as OSW inthis topology, which validates the practical value of this hybridscheme. An observation of the performance of OSKJ shows thatit outperforms all the other selection techniques, providing thehighest ergodic secrecy rate when the transmitted power in-creases due to its ability of the destinations to decode the artifi-cial interference in this OSKJ scheme.Within this configuration, we also compare the performance

of different selection techniques measured by the secrecy outage


Fig. 4. Secrecy outage probability versus transmitted power with differentselection techniques when BPCU.

Fig. 5. Ergodic secrecy rate for a scenario where the intermediate nodes areclose to .

probability, as shown in Fig. 4. The target secrecy rate is setas 0.2 BPCU. It can be seen that the selection schemes with jam-ming provides lower secrecy outage probability within a cer-tain transmitted power range ( , dB). Out-side this range, the conventional selection scheme without jam-ming achieves better secrecy outage probability. Regarding thehybrid schemes, OSW outperforms the nonswitching selectiontechniques.In Fig. 5, it deals with a configuration where the intermediate

nodes cluster, which also includes nodes, is located closeto one of the two destinations (e.g., node , without loss of gen-erality). We can see that the ergodic secrecy rate of the proposedselection schemes in this topology differs greatly from those inthe previous configuration. We observe that the continuous jam-ming schemes (i.e., OS-MSISR, OS-MMISR, SS-MSISR, andSS-MMISR) are inefficient here, which converge to less than0.5 BPCU, validating our discussions in Section IV.

Fig. 6. Ergodic secrecy rate for a scenario where the intermediate nodes areclose to eavesdropper .

On the other hand, OSW and SSW still outperform all theother selection techniques by quite a large scale (more than4 BPCU) when is very high, as shown in Fig. 5. We alsonote that in this topology, OSW and SSW perform even betterthan OSKJ, which seems to be an interesting result. Further in-vestigation reveals that the involvement of jammer in OSKJcauses a different value of compared with that of OSW andSSW,which results in a lower secrecy rate in OSKJ than in OSWand SSW. This indicates that the proposed OSW/SSW schemesmay perform even better than the ideal case where the destina-tions can mitigate the artificial interference. All of these validatethe value of the selection techniques with intelligent switchingin potential practical use.In Fig. 6, we set the intermediate nodes cluster close to eaves-

dropper . Here the continuous jamming schemes also performworse than the nonjamming ones in most of the transmittedpower range. It also shows that the range that the continuousjamming schemes perform better than the nonjamming ones inthis topology is slightly larger than that of the previous one. Re-garding to the hybrid schemes, OSW and SSW still perform asthe best selection techniques in providing the highest secrecyrate.Finally, we place eavesdropper near to one of the two

sources (e.g., ) to examine the results. The location ofeavesdropper is set to (0,0.5), and the intermediate nodesspread randomly across the considered rectangle area, as shownin the inset of Fig. 7. We get a similar simulation result withthat of the first configuration, in which eavesdropper hasthe same distance to and . The nonjamming schemes(i.e., CS, OS, and SS) here are less effective in promoting thesecrecy performance. On the contrary, the selection techniqueswith continuous jamming (i.e., OS-MSISR, OS-MMISR,SS-MSISR, and SS-MMISR) provide a much higher secrecyrate in a large transmitted power range dB . Withinthis power range, the hybrid schemes (i.e., OSW and SSW)perform slightly better than the continuous jamming schemesbecause jamming is almost always needed in this configuration.


Fig. 7. Ergodic secrecy rate for a scenario where eavesdropper is close to .

Outside this regime, where the nonjamming schemes performbetter, the difference between the intelligent switching andcontinuous jamming schemes increases and the hybrid schemesstill perform as the most efficient ones.

VI. CONCLUSIONThis paper has studied joint relay and jammer selection in

two-way cooperative networks with physical-layer securityconsideration. The proposed schemes achieve an opportunisticselection of one conventional relay node and one (or two) jam-ming nodes to enhance security against eavesdroppers based onboth instantaneous and average knowledge of the eavesdropperchannels. The selected relay node helps the information trans-mission between the two sources in an AF strategy, while thejamming nodes are used to produce intentional interference atthe eavesdropper in different transmission phases.We found thatthe proposed jamming schemes (i.e., OS-MSISR, OS-MMISR,SS-MSISR, and SS-MMISR) are effectivewithin a certain trans-mitted power range for scenarios with the intermediate nodessparsely distributed. Meanwhile, the nonjamming schemes(i.e., CS, OS, and SS) are preferred in configurations wherethe intermediate nodes are confined close to each other. TheOSW scheme which switches intelligently between jammingand nonjammingmodes is very efficient in providing the highestsecrecy rate in almost the whole transmitted power regimein two-way cooperative networks, but it requires an instanta-neous eavesdropper channel knowledge. On the other hand, theSSW scheme, which is based on the average knowledge of theeavesdropper channel and thus much more practical, provides acomparable secrecy performance with the OSW scheme.

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JingchaoChen received the B.S. degree in electronicengineering from Peking University, China, in 2011.He is working toward the M.S. degree in wirelesscommunication at UCLA.His current research interest mainly focuses on

physical-layer security.

Rongqing Zhang (S11) received the B.S. degreein electronic engineering from Peking University,Beijing, China, in 2009. He is currently workingtoward the Ph.D. degree in wireless communicationand signal processing at Peking University.His research interests mainly include phys-

ical-layer security, game theory, and wirelessresource allocation.

Lingyang Song (S03M06) received the B.S. de-gree in communication engineering from Jilin Uni-versity, China, in 2002, and the Ph.D. degree in dif-ferential space time codes and MIMO from the Uni-versity of York, U.K., in 2007.He worked as a postdoctoral research fellow at the

University of Oslo, Norway, until rejoining PhilipsResearch U.K. in March 2008. Now, he is a full pro-fessor with School of Electronics Engineering andComputer Science, Peking University, China. He wasa visiting research fellow at Harvard University and

the University of York. His main research interests include adaptive signal pro-cessing, estimation and optimization theory, cognitive and collaborative com-munications, channel coding, wireless mesh/sensor networks, broadband wire-less access, and future communication systems. He is coinventor of a numberof patents and author or coauthor of over 100 journal and conference papers.Dr. Song received the K. M. Stott Prize for excellent research from the Uni-

versity of York. He is currently on the Editorial Board of the InternationalJournal of Communications, Network and System Sciences, Journal of Networkand Computer Applications, and International Journal of Smart Homes, anda guest editor of Elsevier Computer Communications and EURASIP Journalon Wireless Communications and Networking. He serves as a member of Tech-nical Program Committee and Cochair for several international conferences andworkshops. He is a member of IEEE ComSoc.

Zhu Han (S01M04SM09) received the B.S. de-gree in electronic engineering from Tsinghua Univer-sity, in 1997, and the M.S. and Ph.D. degrees in elec-trical engineering from the University of Maryland,College Park, in 1999 and 2003, respectively.From 2000 to 2002, he was an R&D Engineer of

JDSU,Germantown,MD. From 2003 to 2006, he wasa Research Associate at the University of Maryland.From 2006 to 2008, he was an assistant professor inBoise State University, Idaho. Currently, he is an As-sistant Professor in the Electrical and Computer Engi-

neering Department, University of Houston, TX. His research interests includewireless resource allocation and management, wireless communications andnetworking, game theory, wireless multimedia, security, and smart grid com-munication.Dr. Han is an Associate Editor of IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS since 2010. He is the winner of the Fred W. Ellersick Prize2011. He is an NSF CAREER award recipient in 2010. He is the coauthor forthe papers that won the best paper awards in IEEE International Conferenceon Communications, 2009, and the 7th International Symposium on Modelingand Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt09).

Bingli Jiao (M05) received the B.S. and M.S.degrees from Peking University, China, in 1983 and1988, respectively, and the Ph.D. degree from theUniversity of Sarrbruecken, Germany, in 1995.He became an associate professor and professor

with Peking University in 1995 and 2000, respec-tively. His current interests include communicationtheory and techniques and sensor design.

joint relay and jammer selection for secure two-way relay networks

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