a location prediction-based helper selection scheme for...

Research ArticleA Location Prediction-Based Helper SelectionScheme for Suspicious Eavesdroppers

Yan Huo1 Yuqi Tian1 Chunqiang Hu23 Qinghe Gao13 and Tao Jing1

1School of Electronics and Information Engineering Beijing Jiaotong University Beijing China2School of Computer Science Chongqing University Chongqing China3Department of Computer Science The George Washington University Washington DC USA

Correspondence should be addressed to Yan Huo yhuobjtueducn

Received 20 July 2017 Revised 14 October 2017 Accepted 31 October 2017 Published 4 December 2017

Academic Editor Chaokun Wang

Copyright copy 2017 Yan Huo et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper aims to improve security performance of data transmission with a mobile eavesdropper in a wireless networkThe instantaneous channel state information (CSI) of the mobile eavesdropper is unknown to legitimate users during thecommunication process Different from existing work we intend to reduce power consumption of friendly jamming signalsMotivated by the goal this work presents a location-based prediction scheme to predict where the eavesdropper will be later andto decide whether a friendly jamming measure should be selected against the eavesdropper The legitimate users only take themeasure when the prediction result shows that there will be a risk during data transmission According to the proposed methodsystem power can be saved to a large degree Particularly we first derive the expression of the secrecy outage probability and set asecrecy performance target After providing a Markov mobile model of an eavesdropper we design a prediction scheme to predictits location so as to decide whether to employ cooperative jamming or not and then design a power allocation scheme and a fastsuboptimal helper selection method to achieve targeted and efficient cooperative jamming Finally numerical simulation resultsdemonstrate the effectiveness of the proposed schemes

1 Introduction

As a promising technology an Internet of Things (IoT)network offers opportunities to directly transform physicalthings into information world without human interventions[1ndash3] It may be composed of billions of low-end devices thatconnect everyday objects and surrounding environmentsThese devices equipped with various sensors and actuatorscan be connected to the Internet via heterogeneous wirelessnetworks We can exploit the devices to collect meaningfuland suitable data conveniently to achieve information shar-ing computing and controlling remotely Obviously thesedata contain sensitive and private information such as socialrelationships and financial transactions [4] As a result thesecurity of IoT networks is of critical importance for the widedeployment and acceptance of big data services in the future

Due to properties of broadcast communication and signalsuperposition in wireless networking scenarios it is difficult

to shield transmitted signals from unauthorized receiversas well as protect legitimate receivers from unintendedoverlapping of multiple signals These facts make securitybecome a vital issue especially in the openness of the wirelessmedium As a result many works have been done to meetsecurity requirements These works mainly exploit crypto-graphic techniques at the upper layers of wireless networks[5ndash7] As a complement to the measures at the upper layersthe idea of physical layer security (PLS) is proposed andhas been widely discussed in recent years To be specificPLS is to exploit channel characteristics to enhance secureperformance of data transmission which means the inherentrandomness of the noise and communication channels areused to limit the amount of information to be extractedby unauthorized receivers [8] A number of studies in thisfield propose to address the problem of either active orpassive attacks inwireless networks [9] As for passive attackseavesdropping is a well-known security risk in the whole

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 1832051 11 pageshttpsdoiorg10115520171832051

2 Wireless Communications and Mobile Computing

communication processThe strategies of antieavesdroppingasWyner described in his classic wiretap channel model [10]have recently regained substantial research attention [11ndash15]

To the best of our knowledge many studies aiming ateavesdropping usually design different schemes to ensuresecure transmission according to whether the channel stateinformation (CSI) of the eavesdropper is known to legitimateusers For one thing it is possible to design a targeted andefficient security scheme when the CSI of the eavesdropper isknown to legitimate users which means the exact locationof the eavesdropper is known Because of knowing theeavesdropperrsquos CSI the equation of the secrecy performancemetric can be deduced into a convex optimization problemthat can be solved For another however the design of asecure scheme becomes challenging if the CSI of the eaves-dropper is partially or even totally unknown to legitimateusers The general solution is to guarantee the robust secrecyperformance in the worst case and to design a suboptimalalgorithm Also there exist other tactical methods such asthe artificial noise alignment schemes [16] that do not usethe knowledge of the eavesdroppers channel gains Amongthese schemes few of them consider a network model witha mobile eavesdropper whose CSI is unknown to legitimateusers because of the unexpected movement

A mobile eavesdropper is like an unexpected risk tothe communication process of legitimate users Due to thecontinuous randommovement in the network all the time itis difficult to decide when the eavesdropper will move closeto the legitimate transmitter and start to wiretap informationThis kind of wiretapping exists widely in our real lifeespecially mobile social networks Data transmission amonglegitimate users should be kept from information stealingby an unauthorized passerby Regarding this issue manyPLS-based security schemes are designed by transmittingjamming signals during the whole communication processWith enough and accurate CSI of an eavesdropper theseschemes are achievable and effective at the expense of alarge amount of power consumption Different from theseschemes we want to deal with this secure issue in a morepractical situationThe legitimate users do not have to act in adefensive way during the whole communication periodTheyonly have to take a security measure against the eavesdropperwhen they find out the risk of privacy disclosure Suchbehavior can save system power to a great degree

To address these challenges we have proposed a novelrisk prediction scheme in our conference paper [17] Thisscheme is aimed at the network model with a mobileeavesdropper whose CSI is unknown to the legitimate usersAfter studying the mobile eavesdropping model we analyzethe network model and derive an expression of the secrecyoutage probability as the security metric and set a targetsecrecy outage probability for the risk decision in this paperConsidering the mobile path prediction of the eavesdroppernext a Markov chain is exploited to set up a Markovmobile model of the eavesdropper According to the mobilemodel we perform the prediction by exploiting the historymovement information of the eavesdropper After predictingthe location where the eavesdropper will be we exploit theprediction results to decide whether the eavesdropper might

be harmful to data transmission later or not If it will be thecorresponding security measures will be taken against it andthe power allocation scheme is designed to achievemaximumsecrecy capacity At last this paper also demonstrates theeffectiveness of our scheme via a series of simulations Themain contributions of this paper can be summarized asfollows

(i) We propose a Markov chain-based location predic-tion scheme for a mobile eavesdropper by its historymovement information

(ii) Based on prediction results we formulate an opti-mization problem to allocate power for transmitterand helper so as to obtain the maximum achievablesecrecy rate after selecting a suitable helper

(iii) In order to enhance the friendly jamming efficiency ofa helper we design a fast suboptimal helper selectionalgorithm that takes into account both algorithmcomplexity and secrecy performance

The rest of the paper is organized as follows The relatedworks are described in Section 2 We present the systemmodel and derive the expression of the secrecy outageprobability in Section 3 followed by the detailed illustrationof our location prediction-based helper selection scheme inSection 4 Moreover the numerical simulation is shown andanalyzed in Section 5 Finally we conclude this article inSection 6

2 Related Work

Jamming is generally treated as an unfavorable factor inwireless communications [18] It may overlap with informa-tion signals which finally impacts decoding performanceIn spite of the negative side some studies suggested thatfriendly jamming can be used as an effective tool to protectinformation signals from malicious adversaries From theperspective of the wiretap channel model perfect secrecycan be achieved when channel condition of legitimate usersis better than that of eavesdroppers Accordingly the basicidea of friendly jamming strategies is to degrade the wiretapchannel quality of eavesdroppers

This idea was first introduced in [19] Negi and Goelattempted to exploit artificially generated noise to degradethe eavesdroppers channel but not to affect the informationsignals They discussed the secrecy capacity over the mul-tiple transmit antennas scenario and the multiple helpersscenario Following this work a number of studies havebeen performed Wang et al proposed a targeted jammingscheme against the eavesdropper in [20] In the work theydesigned an asymptotic power allocation method to solvean achievable secrecy rate maximization problem Besidesthey provided a jammer selection method to make a decisionfor reducing the abuse rate of jammers Similarly Zhang etal also investigated secure communications for cooperativecognitive radio networks in [21] They studied a joint timeand power allocation scheme to achieve the maximumsecrecy rate for relay-jammer scenario and then presented aweight and time allocation strategy for cluster-beamforming

Wireless Communications and Mobile Computing 3

scenario All these proposed schemes are designed underthe assumption that the eavesdropper channel condition isknown In that case the jammer among legitimate users canmake target jamming and optimizing power allocation ispossible to achieve

Yet a more practical assumption is the unknown CSIof eavesdroppers Obviously it is more difficult to achievetarget jamming and performance Some researchers exploitedthe secrecy outage probability and 120598-outage secrecy capacityto describe the system secrecy performance According tothe above two indicators a series of suboptimal algorithmswere studied In [22] Li and Ma considered a worst-caserobust secrecy rate maximization problem with incompleteEversquos CSI They presented a suboptimal but safe solutionto an outage-constrained robust secrecy rate maximizationproblem In [23] Jiang et al derived closed-form expressionsof secrecy indicators for unknown CSI of eavesdroppersAlso they developed a joint zero-forcing and successiveinterference cancellation method to analyze the individualsecrecy performance for a multiple access wiretap channel Afriendly cooperative jamming strategy for IoT networks withimperfect eavesdropperrsquos CSI was also investigated in [24]The authors in [24] transformed this challenge into the worst-case eavesdropperrsquos CSI and formulated a two-stage robustoptimization problem to find the optimal solution

Although there still exist numerous studies on theunknown or imperfect CSI of eavesdroppers [25ndash27] all ofthese only focused on the wiretap by static eavesdroppersThe more general case is that eavesdroppers may have otherbehaviors For instance they can still wiretap informationsignals when they are in mobile state In that case the CSI ofmobile eavesdroppers may be changeable with the changinglocation In this paper we intend to analyze and predictthe mobility of eavesdroppers With the mobility predictionwe can decide whether it may steal the information viathe legitimate channel In terms of the prediction of themobile path the Markov chain is a good way to realizeit In [28] Fazio and Marano employed a distributed setof hidden Markov chains to predict the probable cells thata mobile node may visit in the future Besides [29] alsoformulated a Markov-history model for realistic mobility ofnodes in a network All these studies inspire us to predict thelocation (ie CSI) of a mobile eavesdropper According tothis a power allocation and jammer selection scheme is putforward To the best of our knowledge this work is the firstone to investigate the PHY layer security issue in the mobileeavesdroppers scenario

3 System Model

Considering a typical wireless wiretapping network thereexists a legitimate transceiver pair (called Alice and Bob) aneavesdropper (Eve) and several helpers shown in Figure 1Each of them in the network is equipped with a singleomnidirectional antenna Alice sends its message to Bob viaa legitimate channel ℎ119886119887 At that time Eve a random mobilepassive adversary is likely to come within the area aroundAlice to wiretap Alicersquos message through a wiretappingchannel ℎ119886119890 To prevent this wiretapping attack a helper

Alice

BobEve

ldquoSecrecy outage regionrdquoldquoMobile pathrdquo

Helper 1 Helper 2

Helper 3

Alice

BobEve

ldquoSecrecy outage regioMobile pathrdquo

Helplper 3

ℎae ℎab

Figure 1 Description of the network layout

may be selected to broadcast jamming signals (eg artificialnoises) to degrade the reception quality of Eve which is alsocalled a friendly jamming strategy

In this scenario we define 119889119886119887 as the distance betweenAlice and Bob and 119889119886119890 as the distance between Alice and EveThe legitimate channel (from Alice to Bob) is denoted by ℎ119886119887and the wiretap channel (between Alice and Eve) is denotedby ℎ119886119890 We assume both channels are modeled as Rayleighfading channels Signal to interference plus noise ratio (SINR)of both legitimate and unauthorized users is decided by path-loss and fading effects [30] Then we can first characterizechannel vectors as follows

ℎ = 119871 sdot 119891 (119866) (1)

where 119871 is the path-loss coefficient and 119891(119866) is the channelpower fading coefficient Here 119871 can be characterized bythe path-loss exponent 120572 and the distance 119889 between twocommunicating parties that is

119871 = 119888119889120572 (2)

where 119888 is the path-loss constant In addition 119891(119866) followsexponential distribution that is

119891 (119866) = 120582119890minus120582119866 (3)

Without loss of generality the coefficient 119866 is modeled as arandom variable with unit mean and hence 120582 = 1

When Alice selects a helper to be the friendly helper topreserve its privacy transmission to Bob the received signalsof Bob and Eve are

119910119886119887 = radic119875119904ℎ119886119887119904 + radic119875119869120596119867119869 ℎ119895119887119904 + 119899119886119887119910119886119890 = radic119875119904ℎ119886119890119904 + radic119875119869120596119867119869 ℎ119895119890119904 + 119899119886119890 (4)

respectively where 119875119904 and 119875119869 are information signal powerand jamming signal power respectively120596119867119869 is the beamform-ing vector at Alice to transmit the jamming signal whichis used to eliminate the interference of the jamming signalat Bob 119899119886119887 and 119899119886119890 are the additive white Gaussian noise(AWGN) with zero mean and variance 1205902119899 at Bob and Eve


respectively The SINR at Bob and at Eve can be respectivelypresented as

SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119895119887ℎ119867119895119887120596119869 SINR119886119890 = 119875119904 1003817100381710038171003817ℎ119886119890100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869

(5)

Accordingly the secrecy capacity at Bob can be deducedas follows which is defined as the difference between themutual information of the legitimate channel and that of thewiretap channel

119862119904 = [119868 (119904 119910119886119887) minus 119868 (119904 119910119886119890)]+= [log2 (1 + SINR119886119887) minus log2 (1 + SINR119886119890)]+ (6)

where 119911+ = max[119911 0] 119868(119904 119910119886119887) and 119868(119904 119910119886119890) denote themutual information of the channels between Alice and Boband between Alice and Eve respectively Secrecy capacityis the maximum achievable rate between the legitimatetransmitter and receiver that can guarantee perfect secrecyIt gives the upper bound of the transmission rate subject toconstraints of unauthorized users Obviously the communi-cation link is secure when 119862119904 gt 0 On the contrary it has therisk of information leakage because Eve experiences a betterchannel condition than Bob

However it is hard for Alice to be aware of the channelinformation of Eve ℎ119886119890 in a passive eavesdropping mode Asa result we can characterize the secrecy outage probabilityIt is the probability that the instantaneous secrecy capacity isless than a target secrecy rate 119877119904119875out (119877119904) = 119875 (119862119904 lt 119877119904) (7)

According to [31] we get the following expression

119875out (119877119904) = 1 minus SINR119886119887SINR119886119887 + 2119877119904SINR119886119890 119890minus(2119877119904minus1)SINR119886119887 (8)

Here 119875out is a function of SINR119886119887 and SINR119886119890 SinceSINR is a function of 119889 as shown in (1) to (3) we candeduce that 119875out(119877119904) is a function of 119889119886119887 and 119889119886119890 Taking thelocations of Alice Bob and Eve into account the secrecyoutage regions corresponding to different secrecy outageprobabilities should be calculated

Since Alice and Bob are communicating with their loca-tions settled secrecy outage probabilities of other locations inthe network can be calculated If we can predict the locationwhere the randomly moving eavesdropper will be later wecan calculate the secrecy outage probability of the predictedlocation and decide whether it may steal the informationfromAlice or notWith the decision we can takemeasures toguarantee security beforehand The criterion of the decisionis based on specific secure requirements Here we set a targetsecrecy outage probability 120574th to define whether Eve will beharmful to the communication later The value of 120574th is setbased on actual requirements of users or administrators in

the network For various network scenarios this value canbe set variously When 119875out(119877119904) lt 120574th we consider that thecommunication is secure Conversely when 119875out(119877119904) gt 120574thwe consider that the communication is suffering from therisk of being eavesdropped andwe need to take some securitymeasures

4 A Location Prediction-Based HelperSelection Scheme

In this section we propose a prediction scheme to predictwhere Eve will be in its later movement so as to decidewhether security measures should be taken against Eve toguarantee security As we discussed in Section 2 the Markovchain shows effectiveness for mobility prediction in suchnetwork scenarios Hence we decide to exploit it to achieveour prediction We first present a detailed illustration of ourscheme Then we introduce the metrics of our scheme

41 The Prediction Scheme To give a clear illustration of ourscheme we first introduce some definitions As we assumethat Eve keeps moving in an area all the time its mobilepath is continuous We predict Eversquos location at intervals ofone moment where one moment is set to be one length oftime That is to say the mobile path that we predict is adiscrete one We consider that the area is composed of aninfinite number of points (locations) and Eve moves fromone location to another from the current moment to the nextmoment This is called one-step movement For example wecan define 119905minus1 as the current moment 119905 as the next momentand so on Because Eve may keep moving randomly in thearea all the time the history information of its movementcan be of great usefulness to the prediction We assume thatthe historymovement information of Eve is known Note thatwhen there is a newly coming eavesdropper that provides nopattern for mobile path the prediction scheme is unsuitableWe just treat it as a threat and make the jammer selection asthe method shown in Sections 42 and 43

In the prediction scheme we first use the Markov chainto set up a mobile model of Eve and then try to extract somecharacteristics from the statistics of history movement infor-mation This is called the transition matrix in the Markovmodel Finally we calculate and compare the probabilities oflocations at the next moment to decide which location Evewill move to

As for setting up aMarkovmobilemodel it is obvious thatevery location in the area can be seen as a state However itis invalid to carry out the prediction scheme in the case ofinfinite number of locations as the state space It inevitablyresults in high computation complexity whichmay cost hugeresources Thus to improve the efficiency of our predictionscheme we divide the whole area into an119872 times 119872 griddingas shown in Figure 2 We define each grid as a state WhenEve is moving in the same grid we consider that it stays atthe same state The length of every grid is set to be 1 and thedistance between each pair of adjacent grids is set to be 1 Andwe assume that the grid is the minimum unit of the area

To better elaborate the process of modeling we use a3 times 3 gridding as an exampleThe example gridding is shown


Bob

Alice

Eve

Figure 2 The grid division of the network

c1 c2 c3

c6c5c4

c7 c8 c9

Figure 3 A 3 times 3 example gridding model

in Figure 3 Here we number the grids as 1198881 1198882 1198889 Thestate space of this Markov model is SPeg = 1198881 1198882 1198889And the corresponding transition matrix is a 9 times 9 matrix119875eg written as

119875eg =

[[[[[[[[[[[[[[[[[[[[

11990111 11990112 0 11990114 11990115 0 0 0 011990121 11990122 11990123 11990124 11990125 11990126 0 0 00 11990132 11990133 0 11990135 11990136 0 0 011990141 11990142 0 11990144 11990145 0 11990147 11990148 011990151 11990152 11990153 11990154 11990155 11990156 11990157 11990158 119901590 11990162 11990163 0 11990165 11990166 0 11990168 119901690 0 0 11990174 11990175 0 11990177 11990178 00 0 0 11990184 11990185 11990186 11990187 11990188 119901890 0 0 0 11990195 11990196 0 11990198 11990199

]]]]]]]]]]]]]]]]]]]]

(9)

where 119901119906V (1 le 119906 le 9 1 le V le 9) denotes the transitionprobability in the 119894th row and the 119895th column of the transitionmatrix 119875eg which is the probability that Eve is in grid 119888119894 theformer moment and chooses to move to grid 119888119895 the lattermoment For the one-step movement Eve can only movefrom its current grid to the adjacent grids or stay still (whichmeans it is moving in the same grid) Thus some of the

probabilities in the transition matrix are meant to be 0 Forexample if Eve stays in 1198881 at the current moment it can onlybe in 1198881 1198882 1198884 or 1198885 at the next moment and cannot be in1198883 1198886 1198887 1198888 or 1198889 So the probabilities 11990113 11990116 11990117 11990118 and11990119 in the transition matrix 119875eg are 0

Now back to the119872times119872 gridding Markov mobile modelwe are going to discuss how to get the transition matrix ofit We use 119873total to denote the total number of grids where119873total = 119872 times 119872 Like the example above the state space ofthis119872times119872 gridding model is SP = 1198881 1198882 119888119873total And thecorresponding transition matrix is an 119873total times 119873total matrixWe use 119901119894119895 (1 le 119894 le 119873total 1 le 119895 le 119873total) to denote thetransition probability in the 119894th row and the 119895th column of thetransition matrix 119875 Every 119901119894119895 can be calculated based on thestatistics of history movement information We use 119873119894119895 (1 le119894 le 119873total 1 le 119895 le 119873total) to denote the total number of timesthat Evemoves from grid 119888119894 to grid 119888119895 in its movement historythus 119901119894119895 can be expressed as

119901119894119895 = 119873119894119895sum119873total119895=1 119873119894119895 (1 le 119894 119895 le 119873total) (10)

After we get the transition matrix 119875 which is also calledthe one-step transition matrix we can further derive the 119899-step transition matrix 119875(119899) By exploiting 119862minus119870 equation wecan see that 119875 (119899) = 119875 sdot 119875 (119899 minus 1) = 119875 (119899 minus 1) sdot 119875 (11)

Thus 119875 (119899) = 119875119899 (12)We consider that the location of Eve at the nextmoment is

related to the historymovement information that is the tran-sition matrix and its states of former 119896 steps of movements Itis obvious that if the moment of the state is nearer to the nextmoment this state may have more influence on Eversquos nextmoment movement And the states of the far past momentscan be negligible There exists an optimal value of 119896 whichcan lead to the best prediction performance We can obtainthe value by simulation experiences Based on the foregoinganalysis we decide to use a weighted way to calculate theprobabilities of every location at the next moment that is119883 (119905) = 1198861119878 (119905 minus 1) 119875 + 1198862119878 (119905 minus 2) 1198752 + sdot sdot sdot+ 119886119896119878 (119905 minus 119896) 119875119896 (13)

where119883(119905) is a 1 times 119873total matrix containing the probabilitiesof all states 119878(119898) (119905 minus 119896 le 119898 le 119905minus1) is a set containing statesrsquoinformation It represents the state Eve was at the former119898thmoment before the next moment It is also a 1times119873total matrixIts value at the first row with the 119898th column is 1 whileother values are 0 1198861 1198862 119886119896 are weighted coefficientsrepresenting different influence degrees that movements atthe former 1st 2nd 119896th moment before the next momenthave on the next momentrsquos movement respectively Note thatwe consider that the influence degree is a relative valueThusthe summation of 1198861 1198862 119886119896 is not 1


Initialization119878119875 = 1198881 1198882 119888119873total 119878 = 1199041 1199042 119904119905119873119894119895 (1 le 119894 le 119873total 1 le 119895 le 119873total)(1) Calculate transition probabilities 119875119894119895 by119873119894119895(2) Calculate 119899 step transition matrix (1 le 119899 le 119896) 119875 1198752 119875119896(3) Calculate the predicted probabilities119883(119905)(4) Set119883V larr 0(V are sequence numbers of unreachable states)(5) Find (119883119898119886119909 = max(119883(119905)))(6) Calculate 119875out(119877119904) with max(7) if 119875out(119877119904) gt 120574th then(8) Take security measures against Eve(9) else(10) Break(11) end if(12)Modify119873119894119895 for the next time prediction

Algorithm 1 The risk prediction rule

When obtaining119883(119905) we can compare these probabilitiesto decide which state Eve will be at the next moment As theprevious assumption of Eversquos movement state (move to theadjacent grids or stay still) we can set the probabilities ofthose unreachable states to be 0 and only have to comparethe probabilities of potential states The state which themaximumprobability is corresponding to is where Evewill beat the next moment Noting that the result is the location wepredict it may not be the location which Eve actually movesto at the nextmoment Every time Eve performs amovementwe need to count 119873119894119895 again to get the new statistics of thehistory movement information and to modify the transitionmatrix so as to get a more accurate prediction result nexttime

Since the location of Eve at the next moment is predictedwe can use this result to decide whether we should takemeasures against Eve The way is basically mentioned inSection 3 In particular we first substitute the predictedlocation of Eve to the calculation process of the secrecyoutage probability119875out(119877119904) and then checkwhether119875out(119877119904) issmaller than the threshold probability 120574th If the answer is yeswe consider that the communication is secure else we takesecuritymeasuresThewhole decision process is summarizedas Algorithm 1

42 Power Allocation for Cooperative Friendly JammingAccording to the above discussion Alice may be aware ofthe predicted CSI of Eve Assuming that the helper has beenselected we would like to design a prediction-based powerallocation algorithm to optimize the proportion of 119875119904 and 119875119869in the total power 119875119879 The goal of the allocation algorithm isto achieve maximum secrecy rate at Bob that is

max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)

In general jamming signals are deliberately designedin nullspace of the legitimate channel In this manner theselected helper may adjust its transmit covariance matrix tojam Eve and simultaneously null out interference at Bob As aresult the reception SINR at Bob can be described as follows

SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)

Accordingly if we assume that 119875119904 and 119875119869 are much greaterthan the noise power 1205902119899 we would like to deduce the aboveoptimization as

max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)

Obviously (16) is a convex analysis optimization Herewe employ the method of Lagrange multipliers and theKarush-Kuhn-Tucker (KKT) conditions to provide a closed-form solution of this mathematical optimization We firstintroduce an auxiliary function of the optimization objectivein (16)

119871 (119875119904 119875119869 120582) = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172+ 120582 (119875119879 minus 119875119904 minus 119875119869)

(17)

where 120582 is a Lagrange multiplier and then solve the corre-sponding gradient expressions

nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)


InitializationThe predicted Eversquos CSI119878helper = 1198691 1198692 119869119873 119862119904119894 (1 le 119894 le 119873)(1) Determine whether there exist a risk of secure communication between Alice and Bob based on Algorithm 1(2) Calculate secrecy rates 119862119904119894 for all helpers based on the predicted Eversquos CSI(3) Find a helper 119869lowast as a jammer by comparing every 119862119904119894 (4) Calculate information signal power 119875119904 and jamming signal power 119875119869 by (19) and (20) for the 119869lowast helper(5)The 119869lowast helper broadcasts artificial noises to jam Eve

Algorithm 2 The fast helper selection scheme

Note that (18) amounts to solving three equations in threeunknowns As a result we can find the following optimalsolutions

119875119904 = 119875119879radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (19)

119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)

120582 = radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 1003817100381710038171003817ℎ119886119890100381710038171003817100381721205902119899 (radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817) (21)

Finally we can calculate themaximum achievable secrecyrate 119862119904 by the following equation

119862119904 = [[[log2(1198751198791205902119899

radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 1003817100381710038171003817ℎ11988611989010038171003817100381710038172(radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817))]]]+

(22)

43 A Fast Suboptimal Helper Selection Scheme In order toensure secure communication from Alice to Bob a suitablehelper may be selected to broadcast jamming signals Weassume there are several helpers in the network and oneof them can satisfy the security requirements if it broad-casts jamming signals Obviously this helper should not beselected randomly due to the requirement of secrecy rateOn the contrary the selected helper should have enoughjamming power to prevent Eve from getting informationillegally Here we would like to design a fast suboptimalhelper selection scheme for the mobile Eve

In the above subsection themaximumachievable secrecyrate has been calculated via (22) For every helper we are ableto obtain different 119862119904 according to different Eve locationsIntuitively Alice may select the helper as a jammer that canhelp Alice obtain the maximum achievable secrecy rate whenEve is in a certain locationThus the helper selection schemecan be described as a mathematical expression that is119869lowast = arg

119869lowastisin119878helper

max119862119904 (23)

where 119869lowast represents the selected helper and 119878helper is the set ofall candidate helpers in the network Accordingly the secrecyrate at Bob can be computed as follows

119862lowast119904 = log2(1205902119899 + 119875lowast119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899times 1205902119899 + 119875lowast119869 120596119867119869lowastℎ119895lowast119890ℎ119867119895lowast119890120596119869lowast1205902119899 + 119875lowast119869 120596119867119869lowastℎ119895lowast119890ℎ119867119895lowast119890120596119869lowast + 119875lowast119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172)

(24)

where ℎ119895lowast119890 and 120596119869lowast denote the channel state vector and thebeamforming vector between the selected helper 119869lowast and Everespectively 119875lowast119904 and 119875lowast119869 are the information signal power andthe jamming signal power that are calculated by the optimalpower allocation algorithm

Obviously we can exploit the exhaustive search methodto find the optimal helper 119869lowast This method is suitable forthe scenario of static eavesdropping Nevertheless Eve isa mobile passive eavesdropper in our system model Theprocess of searching for and selecting the optimal jammerneeds to be repeated which may undoubtedly result in highcomputational complexity To deal with the challenge weintend to design a suboptimal helper selection scheme

According to (24) we are aware that 119862119904 is mainlyaffected by ℎ119895119890 Also the channel state vector ℎ119895119890 is inverselyproportional to the distance from the jammer to Eve As aresult we can select the nearest helper fromEve as the jammerwithout hesitation that is119869lowast = arg


max 119889119895119890 (25)

The whole process of helper selection can be summarizedas Algorithm 2

Remark 1 There is still an extreme case where there area huge number of helpers in the network To reduce thecomputational complexity Alice may stop searching once itfinds a helper that satisfies the security requirement In otherwords 119875out(119877119904) that a helper provides is lower than 120574th Thefeasible solution is as follows119869lowast = arg


119862119904 (119875out (119877119904) le 120574th) (26)


5 Numerical Simulation

51 Production Evaluation Metrics As for a predictionscheme obviously an important issue is the accuracy Whenit comes to our systemmodel what we care about most is theaccuracy of the risk prediction not simply the accuracy of theposition predictionWewant to know how possible it is whenthe prediction tells us there are or there are not any risks inthe communication process Actually we can employ a sumof two different errors to describe the accuracy of predictionThe first error is caused by misdetection In that case Eve isactually in the secrecy outage region although the predictionresult says the communication is secure which will lead toinformation leakage Second a false alarm also introducesprediction errors This may let the system take unnecessarysecurity measures and waste system power According to theabove description we define an index119875119890 to represent the errorlevel of our prediction scheme that is

119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)

where 1 means true (there exist risks in the communicationprocess) and 0means false1198631 denotes that the decision resultis true and 1198630 denotes that the decision result is false 1198671denotes that the actual result is true and1198670 denotes that theactual result is false 119878(119886 | 119887) denotes the amount of the stateswith the actual state 119886 and the predicted state 119887119873count denotesthe total time of the prediction And the simulation results inSection 5 show the error level of our scheme

52 Prediction Performance Analysis In this subsectionsimulation results are shown to verify the effectiveness ofour prediction scheme (here we first employ the transitionprobability of Eversquos location to simulate its movement ina predefined secrecy outage region this probability can becomputed by the historical data collected by Alice whichwill be presented in our future work also in the futurework we will provide real-life datasets based on typical socialapplications eg WeChat or Facebook to conduct furtherexperiments and analyses) We observe the error probability119875119890 in scenarios with different settings of parameter valueswhich are the number of grids of the area119873total the numberof the considered former steps of movements before the nextmoment 119896 and the number of history movements 119873 Thoseparameters may cause varying degrees of influences on theerror probability of the prediction scheme Therefore weintend to divide the area into a 10 times 10 20 times 20 and 30 times 30gridding respectively In other words the area respectivelyconsists of 100 400 900 grids Besides we set 119896 to be 3 5 10and119873 to be 2000 4000 8000 and set the target secrecy outageprobability 120574th to be 08 whose value can be adjusted based onactual requirements

Figure 4 provides a description of 119875119890 with different valuesof 119873total and different values of 119896 As for the relationshipbetween 119875119890 and 119873total it is shown that 119875119890 is monotonouslydecreasing with 119873total indicating that as the division unit ofthe area goes smaller the accuracy degree of the predictionscheme goes higher There exist two reasons to illustratethe result One is that when the division unit of the area is

0

50

100

150

200

250

300

k = 10

k = 5

k = 3

10 lowast 10 20 lowast 20 30 lowast 30

The number of grids

Pe

(lowast10minus4)

Figure 4 119875119890 versus 119873total and 119896 Parameters setting 119873 = 2000119873total = 10 times 10 20 times 20 30 times 30 and 119896 = 3 5 10large this grid division will lead to a take-security-measuredecision if Eve moves around the edge of the target secrecyoutage region Both the neighboring area in the target secrecyoutage region and the neighboring area out of the targetsecrecy outage region can be in the same grid which impactsthe decision Another reason is that when the division unit ofthe area is smaller the number of paths in the same grid goessmaller As a result the history movements can provide moreinformation for setting up the correspondingMarkov mobilemodel so as to perform a more accurate prediction

Besides as for the relationship between 119875119890 and 119896 theresult in Figure 4 also demonstrates that as the value of 119896increases the value of 119875119890 goes down at first and then goes upObviously the value of 119875119890 is at the minimum if 119896 = 5 Theresult indicates that in the prediction process it may give riseto a better accuracy performance without employing moreprevious steps of movements When too much former stepsof movements are considered which are not that related tothe movement of Eve at the next moment this considerationwill impact the prediction result reversely

In Figure 5 we present a description of 119875119890 with differentvalues of 119873total and different values of 119873 It is shown that119875119890 is monotonously decreasing with 119873 indicating that theerror probability of the prediction scheme decreases alongwith the increase in the number of historymovementsThis isreasonable because the history movements are crucial to thegeneration of the transitionmatrix of theMarkov chainMorehistory movements can provide more information about themobile characteristics of Eve Thus more historical move-ment information data should make the transition matrixmore specific to represent those mobile characteristics Inone word the prediction result with more history movementinformation can be more accurate


The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)

Figure 5 119875119890 versus119873total and119873 Parameters setting 119896 = 3119873total =10 times 10 20 times 20 30 times 30 and119873 = 2000 4000 8000

From these simulation results we can see that the valueof the error probability in our proposed risk predictionscheme is in a relatively acceptable range that is to saythe secrecy performance of this risk prediction schemecan be guaranteed If we want to achieve a better secrecyperformance we need to divide the area into more grids andto gather and utilize more history movement informationthus to lower the value of the error probability

53 Secrecy Performance Analyses In this section we con-duct several simulations to verify the secrecy performanceof the proposed power allocation scheme as well as thecorresponding helper selection method Without loss ofgenerality we assume that channels among all nodes in thenetwork aremodeled as Rayleigh fading channels Also thereexists the additive white Gaussian noise (AWGN) with mean0 and variance 1205902119899 The CSI of legitimate nodes is knownto each other while that of Eve has been estimated by thelocation prediction scheme

We first study the secrecy performance of the optimalhelper selection scheme and the suboptimal scheme Sup-posing Eve is at a position in the secrecy outage region weconduct 30 simulations to compare the difference betweentwo schemes in the case of various distributions of helpers

It can be seen from Figure 6 that the difference of secrecyrate between two selection schemes is not significant Andthey even have the same secrecy rate sometimes (ie the twoschemes choose the same helper as a jammer) Yet comparedwith the optimal helper selection scheme the suboptimal onecan drastically reduce the computational complexity of theselection procedure in the case of similar security rate

Next we investigate the effect of total system power onthe secrecy rate when the number of helpers is 10 Here we

0 5 10 15 20 25 304

45

5

55

6

65

The number of simulations

Secr

ecy

rate

(bps

Hz)

The optimal helper selection schemeThe suboptimal helper selection scheme

Figure 6 The instantaneous secrecy rate between two selectionschemes with119873helper = 10 and 119875119879 = 30 dB

0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)

The optimal power allocationThe average power allocation

Figure 7 Secrecy rate versus 119875119879 with119873helper = 10assume the total power 119875119879 = 10 20 30 40 50 dB In Figure 7we are aware that the secrecy rate increases as the total powergrows for two schemesThis is because the stronger jammingpower may further deteriorate the receiving signal quality ofEve Besides it is obvious that the proposed optimal powerallocation scheme has better secrecy performance than theaverage method

As a benchmark we also derive the effect of the numberof helpers on the secrecy rate by running the experiment with119873helper = 5 10 20 30 40 50 to compare the performanceof our power allocation scheme and the average scheme InFigure 8 along with the increase in the number of nodes in


10 20 30 40 50The number of helpers

45

5

55

6Se

crec

y ra

te (b

psH

z)


Figure 8 Secrecy rate versus119873helper with 119875119879 = 30 dB

the network we can see that the secrecy rates of both schemesare growing fast at first and then flatten The reason is thatthere may be some adjacent helpers as the number of helpersin the network increases These adjacent helpers may have asimilar impact on Eve

According to these simulation results we can find thatthe proposed schemes are effective in achieving the require-ment of secrecy rate at the legitimate receiver Also theproposed suboptimal helper selection scheme can save thesystem resources while ensuring the secure communicationof legitimate channel

6 Conclusion

This paper proposes a location prediction-based helperselection scheme to address physical layer security in thecommunication scenewith a suspiciousmobile eavesdropperthe case where the eavesdropperrsquos CSI is unknown to thelegitimate users In this scheme we exploit the secrecy outageprobability as the security metric set a target secrecy outageprobability for the risk decision and perform the predictionby using the Markov chain With a Markov mobile model ofthe eavesdropper set up the history movement informationof the eavesdropper is employed to form the transitionmatrix Besides the position of the eavesdropper at the nextmoment we want to predict is related to both the historymovement information and its own former states Basedon this a weighted method is used to do the predictionNext a power allocation scheme and a fast suboptimal helperselection method are developed to interfere with a mobileeavesdropper In order to demonstrate the effectiveness andthe secrecy performance of our scheme a set of simulationsare conducted These simulation results illustrate that theprediction scheme is with low error probability Also secrecyperformance analyses demonstrate that the optimal power

allocation with suboptimal helper selection scheme canachieve the requirement of secrecy rate

Note that in this paper we only discuss the mobileeavesdropper in a basic single-antenna networkmodel As forfuture work we are going to reinvestigate such problem ina MIMO (multiple-input-multiple-output) system and comeup with a specific physical layer security strategy

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (Grants nos 2017JBM004and 2016JBZ003) the National Natural Science Founda-tion of China (Grants nos 61471028 61572070 61371069and 61702062) and the Open Project of Science andTechnology on Communication Networks Laboratory (noKX162600033)

References

[1] C Perera A Zaslavsky P Christen and D GeorgakopoulosldquoContext aware computing for the internet of things a surveyrdquoIEEE Communications Surveys amp Tutorials vol 16 no 1 pp414ndash454 2014

[2] L Atzori A Iera and G Morabito ldquoThe internet of things asurveyrdquoComputer Networks vol 54 no 15 pp 2787ndash2805 2010

[3] Z Cai Z He X Guan and Y Li ldquoCollective data-sanitizationfor preventing sensitive information inference attacks in socialnetworksrdquo IEEE Transactions on Dependable and Secure Com-puting 2016

[4] Z He Z Cai J Yu X Wang Y Sun and Y Li ldquoCost-efficientstrategies for restraining rumor spreading in mobile socialnetworksrdquo IEEE Transactions on Vehicular Technology vol 66no 3 pp 2789ndash2800 2017

[5] L Zhang Z Cai and X Wang ldquoFakeMask A Novel PrivacyPreserving Approach for Smartphonesrdquo IEEE Transactions onNetwork and Service Management vol 13 no 2 pp 335ndash3482016

[6] X Zheng Z Cai J Li and H Gao ldquoLocation-privacy-awarereview publication mechanism for local business service sys-temsrdquo in Proceedings of the IEEE INFOCOM 2017 - IEEEConference on Computer Communications pp 1ndash9 Atlanta GAUSA May 2017

[7] C Hu H Li Y Huo T Xiang and X Liao ldquoSecure andEfficient Data Communication Protocol for Wireless BodyArea Networksrdquo IEEE Transactions on Multi-Scale ComputingSystems vol 2 no 2 pp 94ndash107 2016

[8] S A AMukherjee J Fakoorian and A L Huang ldquoPrinciples ofphysical layer security inmultiuser wireless networks a surveyrdquoIEEE Communications Surveys amp Tutorials vol 16 no 3 pp1550ndash1573 2014

[9] Y-S Shiu S Y Chang H-C Wu S C-H Huang and H-HChen ldquoPhysical layer security in wireless networks a tutorialrdquoIEEEWireless Communications Magazine vol 18 no 2 pp 66ndash74 2011

[10] A D Wyner ldquoThe wire-tap channelrdquo Bell Labs TechnicalJournal vol 54 no 8 pp 1355ndash1387 1975


[11] Z Li T Jing X Cheng Y Huo W Zhou and D ChenldquoCooperative jamming for secure communications in MIMOCooperative Cognitive Radio Networksrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 7609ndash7614 UK June 2015

[12] P-H Lin S-H Lai S-C Lin and H-J Su ldquoOn secrecy rate ofthe generalized artificial-noise assisted secure beamforming forwiretap channelsrdquo IEEE Journal on Selected Areas in Communi-cations vol 31 no 9 pp 1728ndash1740 2013

[13] R Zhang L Song Z Han and B Jiao ldquoPhysical layer securityfor two-way untrusted relaying with friendly jammersrdquo IEEETransactions on Vehicular Technology vol 61 no 8 pp 3693ndash3704 2012

[14] H-M Wang and F Liu ldquoSecrecy signal and artificial noisedesigns in cellular networkrdquo in Proceedings of the IEEE ChinaSummit and International Conference on Signal and InformationProcessing ChinaSIP 2015 pp 273ndash277 China July 2015

[15] J Wang J Lee F Wang and T Q S Quek ldquoJamming-AidedSecure Communication in Massive MIMO Rician ChannelsrdquoIEEE Transactions on Wireless Communications vol 14 no 12pp 6854ndash6868 2015

[16] A Khisti and D Zhang ldquoArtificial-noise alignment for securemulticast using multiple antennasrdquo IEEE Communications Let-ters vol 17 no 8 pp 1568ndash1571 2013

[17] Y Tian Y Huo C Hu Q Gao and T Jing ldquoA LocationPrediction-basedPhysical Layer Security Scheme for SuspiciousEavesdroppersrdquo in Wireless Algorithms Systems and Applica-tions vol 10251 of Lecture Notes in Computer Science pp 854ndash859 Springer International Publishing Cham 2017

[18] S Kim ldquoCognitive radio anti-jamming scheme for security pro-visioning IoT communicationsrdquo KSII Transactions on Internetand Information Systems vol 9 no 10 Article ID A4177 pp4177ndash4190 2015

[19] R Negi and S Goel ldquoSecret communication using artificialnoiserdquo in Proceedings of the 62nd Vehicular Technology Confer-ence VTC 2005 pp 1906ndash1910 USA September 2005

[20] C-L Wang T-N Cho and F Liu ldquoPower allocation and jam-mer selection of a cooperative jamming strategy for physical-layer securityrdquo in Proceedings of the 2014 79th IEEE VehicularTechnology Conference VTC 2014-Spring Republic of KoreaMay 2014

[21] N Zhang N Lu N Cheng J W Mark and X Shen ldquoCoop-erative networking towards secure communications for CRNsrdquoin Proceedings of the 2013 IEEE Wireless Communications andNetworking Conference WCNC 2013 pp 1691ndash1696 ChinaApril 2013

[22] Q Li and W-K Ma ldquoSpatially selective artificial-noise aidedtransmit optimization for MISO multi-eves secrecy rate max-imizationrdquo IEEE Transactions on Signal Processing vol 61 no10 pp 2704ndash2717 2013

[23] K Jiang T Jing F Zhang Y Huo and Z Li ldquoZF-SIC BasedIndividual Secrecy in SIMOMultiple AccessWiretap ChannelrdquoIEEE Access vol 5 pp 7244ndash7253 2017

[24] Z Li T Jing L Ma Y Huo and J Qian ldquoWorst-case cooper-ative jamming for secure communications in CIoT networksrdquoSensors vol 16 no 3 article no 339 2016

[25] J Yang Q Li Y Cai Y Zou L Hanzo and B ChampagneldquoJoint Secure AF Relaying and Artificial Noise OptimizationA Penalized Difference-of-Convex Programming FrameworkrdquoIEEE Access vol 4 pp 10076ndash10095 2016

[26] J Xiong Y Tang DMa P Xiao and K-KWong ldquoSecrecy per-formance analysis for tas-mrc system with imperfect feedbackrdquo

IEEE Transactions on Information Forensics and Security vol 10no 8 pp 1617ndash1629 2015

[27] Z Zhu Z Chu Z Wang and I Lee ldquoOutage ConstrainedRobust Beamforming for Secure Broadcasting Systems withEnergy Harvestingrdquo IEEE Transactions on Wireless Communi-cations vol PP no 99 2016

[28] P Fazio and SMarano ldquoMobility prediction and resource reser-vation in cellular networks with distributed Markov chainsrdquo inProceedings of the 8th IEEE International Wireless Communica-tions andMobile Computing Conference IWCMC 2012 pp 878ndash882 Cyprus August 2012

[29] S Bitam and A Mellouk ldquoMarkov-history based modeling forrealistic mobility of vehicles in VANETsrdquo in Proceedings of the2013 IEEE 77th Vehicular Technology Conference VTC Spring2013 Germany June 2013

[30] J P Vilela M Bloch J Barros and SWMcLaughlin ldquoWirelesssecrecy regions with friendly jammingrdquo IEEE Transactions onInformation Forensics and Security vol 6 no 2 pp 256ndash2662011

[31] H Li X Wang and W Hou ldquoSecurity enhancement incooperative Jamming using compromised secrecy region min-imizationrdquo in Proceedings of the 2013 13th Canadian Workshopon Information Theory CWIT 2013 pp 214ndash218 Canada June2013

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



communication processThe strategies of antieavesdroppingasWyner described in his classic wiretap channel model [10]have recently regained substantial research attention [11ndash15]

To the best of our knowledge many studies aiming ateavesdropping usually design different schemes to ensuresecure transmission according to whether the channel stateinformation (CSI) of the eavesdropper is known to legitimateusers For one thing it is possible to design a targeted andefficient security scheme when the CSI of the eavesdropper isknown to legitimate users which means the exact locationof the eavesdropper is known Because of knowing theeavesdropperrsquos CSI the equation of the secrecy performancemetric can be deduced into a convex optimization problemthat can be solved For another however the design of asecure scheme becomes challenging if the CSI of the eaves-dropper is partially or even totally unknown to legitimateusers The general solution is to guarantee the robust secrecyperformance in the worst case and to design a suboptimalalgorithm Also there exist other tactical methods such asthe artificial noise alignment schemes [16] that do not usethe knowledge of the eavesdroppers channel gains Amongthese schemes few of them consider a network model witha mobile eavesdropper whose CSI is unknown to legitimateusers because of the unexpected movement

A mobile eavesdropper is like an unexpected risk tothe communication process of legitimate users Due to thecontinuous randommovement in the network all the time itis difficult to decide when the eavesdropper will move closeto the legitimate transmitter and start to wiretap informationThis kind of wiretapping exists widely in our real lifeespecially mobile social networks Data transmission amonglegitimate users should be kept from information stealingby an unauthorized passerby Regarding this issue manyPLS-based security schemes are designed by transmittingjamming signals during the whole communication processWith enough and accurate CSI of an eavesdropper theseschemes are achievable and effective at the expense of alarge amount of power consumption Different from theseschemes we want to deal with this secure issue in a morepractical situationThe legitimate users do not have to act in adefensive way during the whole communication periodTheyonly have to take a security measure against the eavesdropperwhen they find out the risk of privacy disclosure Suchbehavior can save system power to a great degree

To address these challenges we have proposed a novelrisk prediction scheme in our conference paper [17] Thisscheme is aimed at the network model with a mobileeavesdropper whose CSI is unknown to the legitimate usersAfter studying the mobile eavesdropping model we analyzethe network model and derive an expression of the secrecyoutage probability as the security metric and set a targetsecrecy outage probability for the risk decision in this paperConsidering the mobile path prediction of the eavesdroppernext a Markov chain is exploited to set up a Markovmobile model of the eavesdropper According to the mobilemodel we perform the prediction by exploiting the historymovement information of the eavesdropper After predictingthe location where the eavesdropper will be we exploit theprediction results to decide whether the eavesdropper might

be harmful to data transmission later or not If it will be thecorresponding security measures will be taken against it andthe power allocation scheme is designed to achievemaximumsecrecy capacity At last this paper also demonstrates theeffectiveness of our scheme via a series of simulations Themain contributions of this paper can be summarized asfollows

(i) We propose a Markov chain-based location predic-tion scheme for a mobile eavesdropper by its historymovement information

(ii) Based on prediction results we formulate an opti-mization problem to allocate power for transmitterand helper so as to obtain the maximum achievablesecrecy rate after selecting a suitable helper

(iii) In order to enhance the friendly jamming efficiency ofa helper we design a fast suboptimal helper selectionalgorithm that takes into account both algorithmcomplexity and secrecy performance

The rest of the paper is organized as follows The relatedworks are described in Section 2 We present the systemmodel and derive the expression of the secrecy outageprobability in Section 3 followed by the detailed illustrationof our location prediction-based helper selection scheme inSection 4 Moreover the numerical simulation is shown andanalyzed in Section 5 Finally we conclude this article inSection 6

2 Related Work

Jamming is generally treated as an unfavorable factor inwireless communications [18] It may overlap with informa-tion signals which finally impacts decoding performanceIn spite of the negative side some studies suggested thatfriendly jamming can be used as an effective tool to protectinformation signals from malicious adversaries From theperspective of the wiretap channel model perfect secrecycan be achieved when channel condition of legitimate usersis better than that of eavesdroppers Accordingly the basicidea of friendly jamming strategies is to degrade the wiretapchannel quality of eavesdroppers

This idea was first introduced in [19] Negi and Goelattempted to exploit artificially generated noise to degradethe eavesdroppers channel but not to affect the informationsignals They discussed the secrecy capacity over the mul-tiple transmit antennas scenario and the multiple helpersscenario Following this work a number of studies havebeen performed Wang et al proposed a targeted jammingscheme against the eavesdropper in [20] In the work theydesigned an asymptotic power allocation method to solvean achievable secrecy rate maximization problem Besidesthey provided a jammer selection method to make a decisionfor reducing the abuse rate of jammers Similarly Zhang etal also investigated secure communications for cooperativecognitive radio networks in [21] They studied a joint timeand power allocation scheme to achieve the maximumsecrecy rate for relay-jammer scenario and then presented aweight and time allocation strategy for cluster-beamforming





3 System Model


Alice

BobEve


Helper 1 Helper 2

Helper 3

Alice

BobEve


Helplper 3

ℎae ℎab




ℎ = 119871 sdot 119891 (119866) (1)


119871 = 119888119889120572 (2)


119891 (119866) = 120582119890minus120582119866 (3)







SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119895119887ℎ119867119895119887120596119869 SINR119886119890 = 119875119904 1003817100381710038171003817ℎ119886119890100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869

(5)

















Bob

Alice

Eve


c1 c2 c3

c6c5c4

c7 c8 c9



119875eg =

[[[[[[[[[[[[[[[[[[[[

11990111 11990112 0 11990114 11990115 0 0 0 011990121 11990122 11990123 11990124 11990125 11990126 0 0 00 11990132 11990133 0 11990135 11990136 0 0 011990141 11990142 0 11990144 11990145 0 11990147 11990148 011990151 11990152 11990153 11990154 11990155 11990156 11990157 11990158 119901590 11990162 11990163 0 11990165 11990166 0 11990168 119901690 0 0 11990174 11990175 0 11990177 11990178 00 0 0 11990184 11990185 11990186 11990187 11990188 119901890 0 0 0 11990195 11990196 0 11990198 11990199

]]]]]]]]]]]]]]]]]]]]

(9)















max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)


SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)


max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)



(17)


nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)






119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













3 System Model


Alice

BobEve


Helper 1 Helper 2

Helper 3

Alice

BobEve


Helplper 3

ℎae ℎab




ℎ = 119871 sdot 119891 (119866) (1)


119871 = 119888119889120572 (2)


119891 (119866) = 120582119890minus120582119866 (3)







SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119895119887ℎ119867119895119887120596119869 SINR119886119890 = 119875119904 1003817100381710038171003817ℎ119886119890100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869

(5)

















Bob

Alice

Eve


c1 c2 c3

c6c5c4

c7 c8 c9



119875eg =

[[[[[[[[[[[[[[[[[[[[

11990111 11990112 0 11990114 11990115 0 0 0 011990121 11990122 11990123 11990124 11990125 11990126 0 0 00 11990132 11990133 0 11990135 11990136 0 0 011990141 11990142 0 11990144 11990145 0 11990147 11990148 011990151 11990152 11990153 11990154 11990155 11990156 11990157 11990158 119901590 11990162 11990163 0 11990165 11990166 0 11990168 119901690 0 0 11990174 11990175 0 11990177 11990178 00 0 0 11990184 11990185 11990186 11990187 11990188 119901890 0 0 0 11990195 11990196 0 11990198 11990199

]]]]]]]]]]]]]]]]]]]]

(9)















max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)


SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)


max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)



(17)


nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)






119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119895119887ℎ119867119895119887120596119869 SINR119886119890 = 119875119904 1003817100381710038171003817ℎ119886119890100381710038171003817100381721205902119899 + 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869

(5)

















Bob

Alice

Eve


c1 c2 c3

c6c5c4

c7 c8 c9



119875eg =

[[[[[[[[[[[[[[[[[[[[

11990111 11990112 0 11990114 11990115 0 0 0 011990121 11990122 11990123 11990124 11990125 11990126 0 0 00 11990132 11990133 0 11990135 11990136 0 0 011990141 11990142 0 11990144 11990145 0 11990147 11990148 011990151 11990152 11990153 11990154 11990155 11990156 11990157 11990158 119901590 11990162 11990163 0 11990165 11990166 0 11990168 119901690 0 0 11990174 11990175 0 11990177 11990178 00 0 0 11990184 11990185 11990186 11990187 11990188 119901890 0 0 0 11990195 11990196 0 11990198 11990199

]]]]]]]]]]]]]]]]]]]]

(9)















max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)


SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)


max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)



(17)


nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)






119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Bob

Alice

Eve


c1 c2 c3

c6c5c4

c7 c8 c9



119875eg =

[[[[[[[[[[[[[[[[[[[[

11990111 11990112 0 11990114 11990115 0 0 0 011990121 11990122 11990123 11990124 11990125 11990126 0 0 00 11990132 11990133 0 11990135 11990136 0 0 011990141 11990142 0 11990144 11990145 0 11990147 11990148 011990151 11990152 11990153 11990154 11990155 11990156 11990157 11990158 119901590 11990162 11990163 0 11990165 11990166 0 11990168 119901690 0 0 11990174 11990175 0 11990177 11990178 00 0 0 11990184 11990185 11990186 11990187 11990188 119901890 0 0 0 11990195 11990196 0 11990198 11990199

]]]]]]]]]]]]]]]]]]]]

(9)















max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)


SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)


max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)



(17)


nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)






119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















max119875119904119875119869

119862119904st 119875119904 + 119875119869 ⩽ 119875119879119875119904 + 119875119869 gt 119875119879

(14)


SINR119886119887 = 119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 (15)


max119875119904 119875119869

119875119904 1003817100381710038171003817ℎ119886119887100381710038171003817100381721205902119899 times 119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869119875119869120596119867119869 ℎ119890119887ℎ119867119890119887120596119869 + 119875119904 1003817100381710038171003817ℎ11988611989010038171003817100381710038172st 119875119904 + 119875119869 ⩽ 119875119879

119875119904 + 119875119869 gt 119875119879(16)



(17)


nabla119875119904 119875119869120582119871 (119875119904 119875119869 120582) = 0 (18)






119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119875119869 = 119875119879 1003817100381710038171003817ℎ1198861198901003817100381710038171003817radic120596119867119869 ℎ119895119890ℎ119867119895119890120596119869 + 1003817100381710038171003817ℎ1198861198901003817100381710038171003817 (20)



119862119904 = [[[log2(1198751198791205902119899


(22)




max119862119904 (23)



(24)





max 119889119895119890 (25)




119862119904 (119875out (119877119904) le 120574th) (26)




119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119875119890 = sum119878 (1198630 | 1198671) + sum 119878 (1198631 | 1198670)119873count (27)




0

50

100

150

200

250

300

k = 10

k = 5

k = 3


The number of grids

Pe

(lowast10minus4)





The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










The number of grids

0

50

100

150

200

250


N = 2000

N = 4000

N = 8000

Pe

(lowast10minus4)







0 5 10 15 20 25 304

45

5

55

6

65


Secr

ecy

rate

(bps

Hz)



0 10 20 30 40 50Total power (dB)

0

2

4

6

8

10

12

Secr

ecy

rate

(bps

Hz)






45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











45

5

55

6Se

crec

y ra

te (b

psH

z)





6 Conclusion






Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









a location prediction-based helper selection scheme for...

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