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256 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011

Wireless Secrecy Regions With Friendly JammingJoo P. Vilela, Matthieu Bloch, Member, IEEE, Joo Barros, and Steven W. McLaughlin, Fellow, IEEE

AbstractInspired by recent results on information-theoretic

security, we consider the transmission of confi

dential messagesover wireless networks, in which the legitimate communicationpartners are aided by friendly jammers. We characterize the secu-rity level of a confined region in a quasi-static fading environmentby computing the probability of secrecy outage in connectionwith two new measures of physical-layer security: the jammingcoverage and the jamming efficiency. Our analysis for various

jamming strategies based on different levels of channel stateinformation provides insight into the design of optimal jammingconfigurations and shows that a single jammer is not sufficient tomaximize both figures of merit simultaneously. Moreover, a single

jammer requires full channel state information to provide securitygains in the vicinity of the legitimate receiver.

Index TermsChannel state information, jamming, secrecy ca-pacity, wireless secrecy.

I. INTRODUCTION

T ODAYS networks are secured essentially by means ofencryption algorithms that are executed at the upper layersof the protocol architecture. These primitives are designed and

implemented assuming data is error-free, an abstraction enabled

by the use of error-correcting codes at the physical layer. In con-

trast, several information-theoretic results, based on Wyners

wiretap channel model [2], support the idea that there is much

to be gained from coding not just for error correction but also

for security at the physical layer. Physical-layer security hasthus known a growing interest in the past few years, motivated

in large part by applications to wireless communications.

A substantial body of work lays its foundation on the

Gaussian wiretap channel [3], in which the channel between the

legitimate partners and the eavesdroppers channel are additive

Manuscript received November 20, 2009; revised December 15, 2010; ac-cepted January 19, 2011. Date of publication February 04, 2011; date of currentversion May 18, 2011. This work was supported in part by the Fundao paraa Cincia e Tecnologia (Portuguese Foundation for Science and Technology)under Grant SFRH/BD/28056/2006 and Grant PTDC/EIA/71362/2006. Partof this work was presented at the IEEE International Conference on Com-munications, Cape Town, South Africa, May 2010. The associate editorcoordinating the review of this manuscript and approving it for publication wasDr. Wade Trappe.

J. P. Vilela is with Instituto de Telecomunicaes, Departamento de Cinciade Computadores, Faculdade de Cincias, Universidade do Porto, 4169-007Porto, Portugal (e-mail: [email protected]).

M. Bloch is withthe Schoolof Electrical andComputerEngineering, GeorgiaInstitute of Technology, Atlanta, GA 30332-0250 USA andalso with GT-CNRSUMI 2958, 57070 Metz, France (e-mail: [email protected]).

J. Barros is with Instituto de Telecomunicaes, Departamentode EngenhariaElectrotcnica e de Computadores, Faculdade de Engenharia, Universidade doPorto, 4200-465 Porto, Portugal (e-mail: [email protected]).

S. W. McLaughlin is with the School of Electrical and Computer En-gineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA(e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TIFS.2011.2111370

white Gaussian noise (AWGN) channels. For this model, the

secrecy capacity, defined as the maximum transmission rate atwhich the eavesdropper is unable to acquire any information,

can be obtained from the signal-to-noise ratios (SNRs) of the

receivers by subtracting the Shannon capacity of the eaves-

droppers channel to the Shannon capacity of the legitimate

receivers channel.

Several fading models have been considered to generalize

the Gaussian wiretap channel model. For quasi-static fading

models, [4] and [5] provide a detailed characterization in terms

of the probability of outage of secrecy capacity and show that

fading alone guarantees that information-theoretic security is

achievable, even when the eavesdropper has a better average

SNR than the legitimate receiver. For ergodic fading models,

[6][9] provide the secrecy capacity under different levels of

channel state information (CSI) and the corresponding optimal

power and rate allocation. The wiretap channel with multiple

antennas is analyzed in [10][12].

Secrecy rate can be increased in two ways: 1) by improving

the SNR of the legitimate receiver (e.g., by shortening the dis-

tance to the transmitter) or 2) by reducing the SNR of the eaves-

dropper (e.g., by adding controlled interference). Interference

then emerges as a valuable resource for wireless security. From

the point of view of the attacker, correlated jamming techniques

are known to cause severe disruption of the communications

flow by exploiting the available information on the transmitted

signals [13]. However, jamming can also be used by the legiti-mate communication partners to increase the noise level of the

eavesdropper and ensure higher secure communication rates.

This idea has already appeared in the literature under the name

of artificial noise [14] or cooperative jamming [15], and has

been used in other contexts, such as secure relaying [16].

To develop our understanding of the benefits of jamming for

secure communications in wireless networks, we make the fol-

lowing contributions:

1) Security measures for jamming: we introduce the jamming

coverage and the jamming efficiency as security measures;

2) Jamming strategies: we characterize the secrecy outage

probability for three jamming strategies that rely on var-ious levels of channel state information (CSI);

3) Effect of CSI on secrecy: we analyze how the variation of

jammer location and power affects the coverage and effi-

ciency for jamming strategies with different CSI require-

ment;

4) Multiple jammers: we evaluate the effect of additional jam-

mers on the security of the wireless system.

Our work differs from previous studies of jamming for secure

communications [15], [16] because it puts forward two new as-

pects that were not previously accounted for:

1) CSI: we study the effect of access to CSI and show that it

has a profound impact on secrecy. In particular, CSI about

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The helpful interference region is defined as the set of eaves-

droppers positions for which .

Similarly, the harmful interference region is the set of eaves-

droppers positions that satisfy .

Our measures of interest are 1) the jamming coverage, defined

as the total area of the helpful interference region, and 2) the

jamming efficiency, defined as the average over

all belonging to a confined region . For a given system

setup (i.e., location and power of source and jammers, and lo-

cation of receiver and eavesdroppers), is an exact value

obtained analytically with the formulas of Section III. In gen-

eral, jamming coverage and jamming efficiency cannot be ob-

tained in closed form; we evaluate them numerically by spatial

sampling. For each location of the eavesdropper is cal-

culated and the corresponding samples containing for all

eavesdropper locations are then used to derive the jamming cov-

erage and efficiency.

Ideally, we would like to maximize jamming coverage, while

ensuring high jamming efficiency. We will see that, in general,

this goal cannot be achieved with a single jammer.

B. Jamming Strategies

Several jamming strategies have already been investigated

in the literature, such as strategies based on Gaussian noise

[14], [16], Gaussian codebooks [15], [17], or more structured

codebooks based on lattices [18]. The latter strategies have been

shown to outperform jamming with Gaussian noise for situations

inwhichthejammerhasaccesstoperfectCSIforallchannels,and

a comprehensive survey of these techniques canbe found in [19].

To analyze how the availability of CSI affects the secrecy

benefits of jamming, we restrict ourselves to the simplest jam-

ming strategy, in which the jammer emits white Gaussian noise.Whilewe do notclaim that this choice is necessarily optimal, we

note that jamming noise is still relevant from a practical stand-

point because it does not require interfering signals to be per-

fectly synchronized when they reach the eavesdroppers device.

III. WIRELESS SECRECY WITH ONE JAMMER

A. Secrecy Outage Probability for Blunt Jamming

In this section, we consider the situation in which the jammer

emitswhite Gaussian noise with variance at all times. We call

this jammer a blunt jammer because it disregards any possible

CSI and transmits at a constant power .

Proposition 1: The secrecy outage probability for the blunt

jammer is given by

(3)

Fig. 1. Example of the impact of blunt jamming on the secrecy outage proba-bility. For each position of the eavesdropper on the map, we compute the factorof change of the secrecy outage probability with blunt jamming, . Thelocations of the transmitter (Tx), receiver (Rx), and jammer (J) are (0, 0), (0,

5), and (7, 0), respectively. Secrecy outage probabilities are obtained for atarget secrecy rate and path-loss . The target secrecy rate isnormalized with respect to the capacity of the AWGN channel with the sameaverage SNR.

with , and .1

Proof: See Appendix A.

The effect of blunt jamming on the secrecy outage proba-

bility is illustrated in Fig. 1, in which each point represents

a potential location of the eavesdropper and shows the cor-

responding value of . The helpful interference region,

delimited by the thick white line around the jammer, is the area

where the jammers interference reduces the secrecy outage

probability. The harmful interference region corresponds to

the area where the jammers interference is more harmful to

the legitimate receiver than the jammer. The lighter the region

around the jammer, the smaller the secrecy outage probability.

For example, if the eavesdropper is located close to the jammerat the position (6, 0), jamming reduces the secrecy outage

probability from 0.39 to 0.12 (i.e., ).

Understanding the trade-off between these two types of in-

terference and the impact of CSI is crucial. Factors such as re-

ceived power and distance, as well as channel quality from the

jammer to other nodes play an important role in securing the

wireless system. This observation calls for jamming strategies

that dynamically adjust to the environment and whose goal is

to maximize the helpful interference region while keeping the

harmful interference region constrained.

B. Jamming Strategies

In this section, we characterize alternative jamming strategies

that rely on different levels of CSI.

1) Cautious Jamming: A cautious jammer takes advan-

tage of the knowledge of the CSI between itself and both the

legitimate receiver and the eavesdropper and decides oppor-

tunistically when to jam. It jams whenever it has a higher gain

to the eavesdropper than to the legitimate receiver, and switches

off otherwise. The power transmitted by a cautious jammer

is then given by

if

otherwise.

1 represents the exponential integrala nonelementary function givenby the integral . This integral is easily computable numerically.

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VILELA et al.: WIRELESS SECRECY REGIONS WITH FRIENDLY JAMMING 259

Proposition 2: The secrecy outage probability for the cau-

tious jammer is given by

where ,if

and

if.

The variables and are defined as in Proposition 1, and

and

Proof: See Appendix B.2) Adaptive Jamming: An adaptive jammer has CSI about

the channel to the legitimate receiver only. This strategy corre-

sponds to a situation in which the eavesdropper intercepts the

communications without providing any sign of its presence. In

this case, the jammer defines a threshold for the channel quality

, above which it will stop jamming since it is likely that his

induced noise will hurt the legitimate receiver more than a po-

tential eavesdropper. The transmission power of the jammer

is then given by

if

otherwise.

Proposition 3: The secrecy outage probability for the adap-

tive jammer is given by the equation at bottom of page, where

and are defined as in Proposition 1, and , , , and are

defined as in Proposition 2.

Proof: See Appendix B.

IV. IMPACT OF CHANNEL STATE INFORMATION ON SECRECY

Although the jammer can have an adverse effect on the le-

gitimate receiver, a careful selection of the location and trans-

mission power can enhance security by causing controlled in-

terference to the eavesdropper. Fig. 2 shows an example of the

potential benefits of increased transmit power for a specific lo-

cation of the jammer. Notice that up to a certain jamming power,

the efficiency increases without a significant loss of coverage.

However, the exact trade-off between coverage and efficiency

depends on the jamming strategy used. In the remainder of this

section, we analyze how the variation of jammer location and

transmission power affects coverage and efficiency for the var-

ious jamming strategies, in connection with their requirements

in terms of CSI.

A. System Setup and Measure Computation

We consider a scenario in which the transmitter and the re-

ceiver are located in a confined area (say a building or a con-

ference room) and wish to communicate securely with the aid

of a friendly jammer. In particular, any eavesdropper located

within the confined region should not be able to extract much

information from the intercepted signals. To model the wire-

less nature of the medium, we set the path loss exponent to 4

and the normalization constant to the free-space path gain for

2.4-GHz transmission at the reference distance of 1 m, which

is common for micro-cellular systems [20]. The transmitter andreceiver are fixed at locations of (0, 0) and (0, 5), respectively.

The target secure transmission rate is set to 10% of the capacity

of the AWGN channel with the same average SNR. All nodes

can transmit with power up to 10 dB, and the transmitter em-

ploys a fixed power dB.

We consider the confined region m

m, and a sampling interval for the locations of

the eavesdropper of 0.18 m. This results in 9025 samples of

eavesdropper locations being considered for each system setup.

The jamming coverage and efficiency thus provide a measure to

assess the security benefits of a particular jammer configuration

(location and transmit power), irrespective of the location of

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Fig. 2. Example of the effect of varying the transmit power of the jammer onthejamming coverage andefficiencyfor a specific locationof the jammer (

, ). (a) Ef ficiency; (b) coverage.

the eavesdropper. To analyze the effect of different jamming

configurations, for each strategy we select a sample of locations

on a grid and, for each location, we consider 30 different levels

of transmit power, from 10 dBm to 10 dB. From this set, we

consider the optimal configurations of each strategy, i.e., the

location and power of the jammer that, for a given strategy,

leads to the largest coverage and efficiency. Using the optimal

configurations, we compare the different jamming strategies

under identical system conditions.

B. Jamming Coverage

First, we analyze the effect of different jamming configura-

tions on coverage. The configurations maximizing coverage de-

pend on the jamming strategy, but for all strategies, the largest

coverage is achieved with low transmit power by the jammer.

Moreover, since proximity to the legitimate receiver is harmful,

all strategies lead to regions where placing the jammer provides

maximum coverage in the upper part of the confined region.

Fig. 3(a) shows such a region and the corresponding maximum

coverage location for blunt jamming. Cautious jamming leads

to a larger coverage than blunt jamming by using CSI to en-

compass locations in which the eavesdropper is further away. In

the case of adaptive jamming, which is based solely on CSI for

the channel to the legitimate receiver, the location and transmit

power of the jammer can be adjusted to provide large coverage,

albeit with a cost in terms of efficiency.

Fig. 4 compares the different strategies with optimal coverage

configurations. Namely, it depicts the area (y-axis) over which agiven strategy is able to achieve a above a certain value

(x-axis). The figure shows that although all strategies provide

large coverage (the lowest being blunt jamming with a coverage

of 197 m ), only low values of are achieved and over

small regions. For example, none of the strategies is able to re-

duce the secrecy outage by half . This happens be-

cause the jammer employs low transmit power on these optimal

configurations, thus resulting in little interference to eavesdrop-

pers. As we will see with the optimal efficiency configurations,

a controlled increase of the transmit power of the jammer can

lead to higher values.

C. Jamming Ef ficiency

Locations where placing a jammer provides the largest effi-

ciencies appear close to the source, yet tending towards the op-

posite direction of the main receiver, as illustrated in Fig. 3(b)

for the case of blunt jamming. This is natural, since it is close

to the source that the secrecy outage probability is higher and,

therefore, the jammer is able to provide highest security bene-

fits. The harmful effect of the jammer when close to the receiver

makes the region asymmetric with respect to the source. For

the three strategies, the optimal configurations also result from

the jammer employing higher transmit powers dB ,

whenever active, thus leading to increased interference to pos-

sible eavesdroppers.Fig. 5 compares the optimal efficiency configurations for the

three strategies. As expected, blunt jamming provides the lowest

coverage, but the highest efficiency. Cautious jamming leads

to a smaller efficiency over large regions, and the operation of

adaptive jamming can be adjusted with the typical coverage-

efficiency trade-off. Notice that, apart from the advantage in

efficiency, blunt jamming also leads to a much higher maximum

value. In particular, this strategy is able to reduce the

secrecy outage probability by at least one half in

a region of 15 m . This shows that this strategy excels in terms

of jamming efficiency.

D. Relevance of CSI

Irrespective of the jamming strategy considered, the optimal

configurations of the jammer favor a large distance to the re-

ceiver. In such cases, we have seen that CSI proves useful to pro-

vide large coverage, although it fails to provide desirable

values, therefore resulting in low jamming efficiency. Although

a precise analytical comparison of the jamming strategies seems

beyond reach, it is possible to establish generic ordering results

that confirms the effect of CSI and the inherent trade-off be-

tween coverage and efficiency.

Proposition 4: Let denote the coverage of a jamming

strategy. The strategies satisfy the following coverage ordering:

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Fig. 6. Variation of (a) the coverage and (b) the efficiency measures accordingto the distance to the receiver for optimal power allocations of the jammer.

Note that the only way to avoid harming the receiver more

than the eavesdropper at all timeswould be to exploitthe knowl-

edge of CSI for all channels. Consequently, cautious and adap-

tive jamming, which do not exploit CSI for the channels from

the transmitter to the receiver and the eavesdropper, are un-

able to detect all favorable jamming opportunities. This explains

the lower values of and the resulting lower effi

cienciesachieved by these strategies.

Even with partial information, the benefit of CSI becomes

apparent when the jammer is closer to the legitimate receiver.

Fig. 6(a) illustrates the effect of increased distance between the

jammer and the legitimate receiver on coverage. For all strate-

gies, the coverage grows with increased distance. However, cau-

tious jamming is able to sustain a large coverage even at small

distances to the receiver. Thishappens because this strategy uses

CSI to reduce the impact on the legitimate receiver. In terms

of efficiency, Fig. 6(b) shows that the conservative approach of

cautious jamming again leads to better results at smaller dis-

tances. As distance increases, the impact of the jammer on the

legitimate receiver is lower and the strategy of cautious jam-

ming becomes less useful, eventually getting surpassed by a

simpler approach such as blunt jamming. This result highlights

once more the importance of CSI to improve secrecy, most no-

tably in the vicinity of the legitimate receiver.

V. MULTIPLE JAMMERS

None of the aforementioned strategies is capable of achieving

high efficiency over large regions. Furthermore, the strategiesthat are capable to detect beneficial jamming opportunities

require CSI that may not always be available. To overcome

these difficulties, we now extend our analysis to more than

one jammer. Specifically, we provide a characterization of

the secrecy outage probability for the case of multiple blunt

jammers and discuss the effect of having more jammers on the

defined secrecy measures.

A. Secrecy Outage Probability for Multiple Blunt Jammers

Propostion 5: Letting , and

, the secrecy outage probability for multiple

blunt jammers is given by

with given by

Case 1:

Case 2:

Proof: See Appendix C.

B. Analysis

Let be a set of active jammers. When , the capacity

of the receiver and eavesdropper channels are likely to decrease

as a result of added interference. In the limit, we have

, i.e., across the entire region. However,

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VILELA et al.: WIRELESS SECRECY REGIONS WITH FRIENDLY JAMMING 265

Likewise, for

Let the pdf of be . Since the pdf of is

given by , we have

This finally leads to the results presented in Propostion 5.

ACKNOWLEDGMENT

The authors gratefully acknowledge useful discussions with

Tiago T. V. Vinhoza and Rui A. Costa from Universidade do

Porto, Portugal.

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[6] Z. Li, R. Yates, and W. Trappe, Secrecy capacity of independent par-allel channels, in Proc. 44th Annu. Allerton Conf. Communication,Control, and Computing, Monticello, IL, Sep. 2006.

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[8] P. K. Gopala, L. Lai, and H. E. Gamal, On the secrecy capacityof fading channels, IEEE Trans. Inf. Theory, vol. 54, no. 10, pp.46874698, Oct. 2008.

[9] A. Khisti, A. Tchamkerten, and G. W. Wornell, Secure broadcastingover fading channels, IEEE Trans. Inf. Theory, vol. 54, no. 6, pp.24532469, Jun. 2008.

[10] A. Khisti and G. W. Wornell, The MIMOME channel, in Proc. 45thAnnu. Allerton Conf. Communication, Control, a nd C omputing, Mon-ticello, IL, Sep. 2007.

[11] F. Oggier and B. Hassibi, The secrecy capacity of the MIMO wiretapchannel, in Proc. IEEE Int. Symp. Information Theory, Toronto, ON,Canada, Jul. 2008, pp. 524528.

[12] S. Shafiee, N. Liu, and S. Ulukus, Towards the secrecy capacity of thegaussian MIMO wiretap channel: The 2-2-1 channel, IEEE Trans. Inf.Theory, vol. 55, no. 9, pp. 40334039, Sep. 2009.

[13] M. Mdard, Capacity of correlated jamming channels, in Proc. 35thAllerton Conf. Communication Control and Computing, Monticello,IL, Sep. 29Oct. 1 1997, pp. 10431052.

[14] S. Goel and R. Negi, Guaranteeing secrecy using artificial noise,IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 21802189, Jun.2008.

[15] E. Tekin and A. Yener, The general gaussian multiple-access andtwo-way wire-tap channels: Achievable rates and cooperative jam-ming, IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 27352751, Jun.2008.

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Joo P. Vilela received the Computer Science andNetwork Engineering degree in 2005 and the M.S.degree in information systems in 2007, both fromUniversity of Porto, Porto, Portugal. He is currentlypursuing the Ph.D. degree in computer science in thesame University.

He is a researcher with the Instituto de Telecomu-nicaes in Porto, Portugal. His research interests in-clude security and cooperation in wireless networks,wireless network models, protocol design, and dis-tributed systems.

Mr. Vilela was awarded a doctoral scholarship from the Portuguese Founda-tion for Science and Technology.

Matthieu Bloch (S07M08) received the En-

gineering degree from Suplec, Gif-sur-Yvettes,France, the M.S. degree in electrical engineeringfrom the Georgia Institute of Technology, Atlanta, in2003, the Ph.D. degree in engineering science fromthe Universit de Franche-Comt, Besanon, France,in 2006, and the Ph.D. degree in electrical engi-neering from the Georgia Institute of Technology in2008.

From 2008 to 2009, he was a postdoctoral researchassociate at the University of Notre Dame, South

Bend, IN. Since July 2009, Dr. Bloch has been on the faculty of the School ofElectrical and Computer Engineering at the Georgia Institute of Technology,where he is currently an Assistant Professor. His research interests are in theareas of information theory, error-control coding, wireless communications,and quantum cryptography. He currently serves as the Chair of the OnlineCommittee of the IEEE Information Theory Society. He is the Cochair of

the ICC 2011 Workshop on Physical-Layer Security and the coauthor ofPhysical-Layer Security: From Information Theory to Security Engineering,which will be published by Cambridge University Press in July 2011.

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