物理层安全论文

IEEE COMMUNICATIONS LETTERS, ACCEPTED FOR PUBLICATION 1

Secure Communication via Sending ArtiﬁcialNoise by the Receiver:

Outage Secrecy Capacity/RegionAnalysis

Wei Li, Mounir Ghogho, Senior Member, IEEE, Bin Chen, Chunlin Xiong

Abstract —Anovel approach for ensuring conﬁdentialwireless communication is proposed and analyzed from an information-theoretic standpoint. In this approach, the legitimate receiver generates artiﬁcialnoise (AN)to impair the intruder’schannel. This method is robust because it does not need the feedback of channel state information (CSI)to the transmitter and does not assume that the number of Eve’santennas should be smaller than that of Bob. Furthermore, we propose a new concept of outage secrecy region to evaluate the secrecy performance from a geometrical perspective. This should be useful if we need to know what zone should be protected (ormilitarized). Analysis and simulation results in practical environments show that the proposed method has a good performance.

Index Terms —Artiﬁcialnoise, privacy, outage secrecy region, secrecy capacity, physical layer security.

I. I NTRODUCTION

IRELESS communication is inherently insecure owing to the broadcast nature of the wireless medium. A

passive eavesdropper in an unknown location within “earshot”of a wireless transmission taps information about the trans-mitted signal without risk of detection. A natural framework for information security at the physical layer is the so-called wiretap channel introduced by Wyner [1]and associated notion of secrecy capacity. Secrecy problems involve three nodes:the transmitter (Alice),the legitimate receiver (Bob)and the eavesdropper (Eve).Alice wants to communicate with Bob while leaving Eve unable to decode the secret message. It is shown that perfect secrecy can be achieved without any key, provided that Bob has a better channel than Eve. The secrecy capacity is deﬁnedas the maximum achievable rate from Alice to Bob while keeping Eve completely ignorant of the transmitted message. Later, Wyner’swork was extended to nondegraded discrete memoryless broadcast channels in [2],and then to the Gaussian channel in [3],recently to MIMO channels in [4]and to fading channels in [5].

In order to increase the secrecy capacity, artiﬁcialnoise (AN)based method was suggested in [6].In this method, AN is generated through multiple transmit antennas or the cooperating nodes, and is injected into the null-subspace of Bob’sMIMO channel [7],[8].AN is utilized to impair Eve’s

Manuscript received June 19, 2012. The associate editor coordinating the review of this letter and approving it for publication was M. Tao.

This work was supported in part by the NSFC under Grants 61101096and 61101098, and the NSF of Hunan Province under Grant 11jj4055.

W. Li, B. Chen, and C. Xiong are with the School of Electronic Science and Engineering, National University of Defense Technology, Changsha, 410073P. R. China (e-mail:[email protected];[email protected];[email protected].).

M. Ghogho is with the University of Leeds, Leeds LS29JT, U.K., and also with the International University of Rabat, 11100, Morocco (e-mail:[email protected]).

Digital Object Identiﬁer10.1109/LCOMM.2012.12.121344

channel, while not affecting Bob’schannel. The work in [9],[10]jointly optimizes the beamforming vector and the AN covariance matrix to achieve diverse signal to interference plus noise ratio (SINR)constraints for Bob and Eve. An outage probability-based approach to design the beamformers was proposed in [11].However, these schemes have to face the following challenges:a) The channel state information (CSI)or at least partial CSI of Bob is needed at the transmitter; feeding back the CSI to the transmitter occupies some channel resource; b) If there is an uncertainty on the CSI at the transmitter, the AN may leak to Bob and thus reduces his SNR; this problem is even worse when Eve tries to personate Bob and feeds back her own CSI to Alice; considering the imperfect CSI, a robust Bayesian approach for multiuser MIMO wiretap channels was presented in [12];c) if there are colluding Eves, or Eve has multiple antennas and the number of antennas exceeds the number of Alice’santennas, the AN can be calculated and eliminated if the CSI is perfectly known. In this paper, we propose a novel AN based method to overcome the above problems. Different from the existing works where AN is added at the transmitter, the AN in our method is generated by the intended receiver, Bob, as shown in Fig. 1. The AN impairs the intruder’schannel while it can be counteracted by Bob. This method has the following advantages:a) The CSI is not needed by Alice, so there is no feedback channel and thus the bandwidth resource is saved; uncertainty on the CSI is not an issue which implies robustness of the method; however, in order to use a wire-tap code, the channel capacity of Bob should be known at Alice. b) the AN can be generated by either multiple antennas or a single antenna, which is more practical than the existing AN methods which need multiple antennas at the transmitter; c) this method does not assume that the number of Eve’santennas should be smaller than that of Bob; indeed, even if there is a large number of antennas at Eve or there are colluding Eves, the AN is still hard to be totally eliminated because the CSI between Bob and Eve is not known to Eve; d) the proposed method can be combined with the masked beamforming scheme where an AN is generated at the transmitter to improve secrecy performance; e) it is particularly useful when the receiver has a stronger ability than the transmitter (e.g.the receiver is a base station); f) it is efﬁcientif Eves are located around Bob; this is generally the case in several situations.

Another contribution of this paper is the introduction of the concepts of outage secrecy region (OSR)using a geometrical perspective. In practical communication systems, when the eavesdroppers are passive, it is impossible to calculate the secrecy capacity or Eve’sbit error rate. In [8]a probabilistic framework using stochastic geometry is presented to quantify

1089-7798/12$31.002012IEEE

AN added by Bob

(a)add AN at transmitter (b)add AN at receiver

Fig. 1:Secret communication using artiﬁcialnoise. the probability of secrecy versus the spatial density of the eavesdroppers, the power of the AN, the range of commu-nication and antenna conﬁgurations.In this paper, by taking into account both path loss and small scale fading, we adopt the outage capacity approach to determine the OSR which is deﬁnedas follows. For a given rate R and maximum outage probability ε, the OSR consists of the coordinates of Eve for which the probability that the secrecy capacity is lower than R region, is lower the than probability or equal that to she ε, i.e. can if decode Eve is the the (transmitted R, ε)-OSR signal (ofrate R ) can reach ε. The minimum noise power from Bob required to achieve a given outage security region can also be derived. The analysis allows us to identify the zone that needs to be protected (ormilitarized) to guarantee some physical layer security speciﬁcations.This is particularly useful for military applications.

The rest of this paper is organized as follows. In Section II, we describe the system model and present the secure com-munication mechanism. Section III deﬁnesthe outage security region and analyzes the secrecy performance of our scheme. Numerical results are shown in Section V , and conclusions are drawn in Section VI.

II. S YSTEM M ODEL

We assume that Alice has a single antenna, Bob has one receiving antenna and one transmitting antenna, and Eve has a single receiving antenna. In the security technique, Eve’slocation and channel are not known to Alice. However, in the security region analysis, we assume that Eve’snoise variance is known, although we also consider the worst case scenario where this noise power is zero. As shown in Fig. 1(b),Bob sends the AN while receiving the desired signal from Alice. The discrete-time system model is constructed as follows,

z (k ) =h ab x (k ) +h bb w (k ) +n (k ) , (1)y (k ) =h ae x (k ) +h be w (k ) +e (k ) ,

(2)

for k =1, 2,... , where x (k ) is the transmitted signal variance σ2

with

x =P z A , w (k ) is the AN sent by Bob whose power is equal to P B , (k ) and y (k ) are the received signals at Bob and Eve respectively, h ab , h ae and h be are respectively the channels between Alice and Bob, Alice and Eve, and Bob and Eve, h of bb is the channel between the transmit and receive antennas Bob, n (k ) and e (k noises with powers equal to σ2) are complex white Gaussian

and σ2The crucial problem is how b

to design e respectively. the AN signal w (k ) and counteract the effect of the AN on Bob. Because the

IEEE COMMUNICATIONS LETTERS, ACCEPTED FOR PUBLICATION

CSI of Eve is unknown to Bob, the best w (k ) is a complex white Gaussian noise with the same bandwidth as that of x the (k ) technology . To cancel of the full effect duplex of the wireless AN on [13],Bob, [14].we Through can use antenna cancellation, RF interference cancellation and digital cancellation, the AN can be counteracted to an acceptable degree. Authors in [13]proposed a two-antenna full duplex radio design that uses a balun. The transmit antenna transmits the positive signal, and to cancel self-interference, the radio combines the negative signal with its received signal after adjusting the delay and attenuation of the negative signal to match the self-interference.

Therefore, because the AN and channel h Bob, the residual noise can be rebuilt and eliminated bb are known to by digital interference cancellation as follows:

z (k ) =z (k ) −h bb w (k ) =h ab x (k ) +n (k ) .

(3)

III. O UTAGE S ECRECY R EGION

We start by recalling the results of [3]for the Gaussian wiretap channel, where it is assumed that Alice and Bob communicate over a standard additive (AWGN)channel with noise power σ2

white Gaussian noise

is also corrupted by Gaussian noise with b

, and Eve’sobservation power σ2

2capacity in this case is

e +P B |h be |. The secrecy C =(log2(1+γB ) −log 2(1+γE ))

(4)

where γB =|h ab |2

2P A and γE =|h ae |2

P A max σb σ2e +P B |h be |

2; x +

=Since (x, 0) we .

do not know Eve’sCSI, we cannot calculate the secrecy capacity. In this situation, we could adopt a probabilistic approach which quantiﬁesthe probability that the secrecy capacity is larger than a certain rate. Here, we introduce the concept of OSR, which is related to the outage secrecy capacity. Assuming that Bob’slocation is known to Alice, we deﬁnethe OSR as follows.

Deﬁnition(OutageSecrecy Region):For a given transmis-sion rate R , and an outage probability ε, the (R, ε) -OSR is deﬁnedas a region over which the probability that the secrecy capacity is lower than R is lower than or equal to ε, and is mathematically formulated as

R s ={θe |p out (R ) ≤ε}.

(5)

where p out (R ) :=Pr(C s with

p 1−Pr log 1+α

out (R ) =2ab t ab

1+1+αae αt ae

≥R (6)be t be

where αλPab =λPA d −ab κ/σ2b , αae =λPt A d −ae κ/σ2

e and αbe =B d −be κ/σ2e . Since t ab , t ae and be are independent, their joint probability density function is exp(−t ae −t be −t ab ) .

LI et al. :SECURE COMMUNICATION VIA SENDING ARTIFICIAL NOISE BY THE RECEIVER:OUTAGE SECRECY CAPACITY/REGIONANALYSIS 3

Thus we have p

out (R ) =1−

exp(−t ae −t be −t ab ) dt ae dt be dt ab (7)

where D ={(t ae , t be , t T = ab ) |t ae ≥0, t be ≥0, t ab ≥T }, Further, α2R

where

1+1+αae αt ae 1

be t be −αab ≥0. we have p out (R ) ==1−exp

1− that

∞

∞ ∞0e −t ae − 0 e −t be ∞

T e −t ab dt ab dt be dt ae α2R ab

+α1e −t be

ab 0α2R αae dt be ab

(1+αbe t be )

(8)

Now using the result (obtainedafter some algebra)

∞e −t a +1

0b 1+a

bt +1

dt =1+e Ei −a +1 b a b where Ei (x ) is the exponential integral x

2R α−∞(e t /t) dt , for a =

αae

ab and b =αbe , we obtain the ﬁnalexpression

p out (R ) =1 −exp −α2R

ab +αab

×1+exp 2R ααae R αab +1be Ei −2ααae αab

αae (9)be αab αbe Using the above expression, the (R, ε) -OSR is obtained by ﬁndingthe coordinates of Eve for which (5)is satisﬁed.Since Eve’spower may not be known, we now consider the worst case scenario where Eve is noise-free, i.e. σthis also addresses the case where Eve’santenna gain, e 2=0; which may be unknown, is (much)higher than that of Bob; in fact, setting σe 2=0is equivalent to setting Eve’santenna gain to inﬁnity.In this case, we have that

σlim 2p ) =1−exp −(2R +1) σ2

out (R b

e →0λPA d −κ(10)×(1+exp (Ψ)E ab

i (−Ψ)Ψ)where Ψ=

2R σ2b d −κλPB d −Again, eq. (5)can be used to determine the (R, ε) be κae

-OSR d −ab

κ. in this case.

IV. D ISCUSSIONS AND E XTENSIONS

Combining with the masked Beamforming scheme

If Alice has more than one antenna, we can combine our method with the masked beamforming scheme, which consists of Alice transmitting the sum of the information bearing signal and an AN signal [8]:

x (k ) =p s (k ) +w A (k )

(11)

where p is the normalized beamforming vector which is set

to p =h H ab / h ab , s (k ) is the scalar complex information signal with power equal to P covariance K A , w A (k ) is a complex Gaussian vector with combination of the vectors w that A , and chosen to be a linear span the null space of h ab , i.e. h H ab w A (k ) =0. The secrecy capacity in this case is

C =(log2(1+γB ) −log 2(1+γE ))

(12)

where γB = h ab 2

2P A and γE = h ae 2

P A From (12)we σb can see that the σ2combined e

+P B h be 2strategy +h ae K w A has h H ae . the advantage that the eavesdroppers around Alice as well as those around Bob suffer strong interference. Therefore, the secrecy

performance is improved. Due to space limitation, the OSR in

this scenario is not investigated here. Further, power allocation is also an interesting issue to investigate. The case of multi-antenna Eve

In our system model, the CSI from Alice to Eve, h known to Eve, but not the CSI between Bob ae , is assumed and Eve, h be . Indeed, since Bob only transmits white noise, Eve cannot estimate h the AN be . So it is almost impossible for Eve to counteract totally. Thus, it is reasonable to assume that Eve treats the AN as white noise. So our method is still useful even if Eve has multiple antennas.

V. S IMULATION R ESULTS

In order to evaluate the secrecy performance of the proposed method, the following scenario is considered in the simula-tions. We locate Alice at (0,0), and Bob at (1,0). The channel bandwidth is set to 5MHz. The transmit power at Alice is 1W. The maximum transmit power at Bob is 10W. The noise power density is -180dBm/Hz,and the path-loss propagation model (indB) is 128. 1+37. 6log 10(d ) (whered is the distance in km) [15].In the simulations, Eve has a single antenna, and Bob has two antennas (onefor receiving and one for transmitting). All channels experience Rayleigh fading.

Fig.2illustrates the OSR for the transmission rate R =1. 5×103bit/sand different values of outage probability ε. The result shows that the OSR corresponding to high probability of outage is around Alice, and thus the area around Alice is not likely to be secure; the ﬁgureshows that the area around Bob is however very likely to be secure, i.e. it is associated with a very low probability of outage ε. This means that Eve has to be very close to Alice for successful eavesdropping. Fig.3illustrates the outage probability for different AN power P B versus the x -coordinate of Eve when she moves on the line y =0. 5. We see that the outage probability decreases as P B increases. It also increases when Eve gets closer to Alice, and decreases when Eve gets closer to Bob.

Fig.4depicts the simulated averaged (ergodic)secrecy capacity for different strategies. Eve moves along the line y of =ﬁve0. 5strategies:from (-3,0.5)a) to AN (3,0.5).sent by We Bob compare with the P performance and B =1W and P A =1W ; Alice has a single antenna Bob has one receive antenna and one transmit antenna; b) AN sent by Alice with equal powers for the information signal and the AN; P A =0. 5W , tr (K w A ) =0. 5W ; Alice has 2antennas and Bob has single antenna; c) combined strategy:AN sent by both Alice and Bob with P B =1W and P A =0. 5W , tr (K w A ) =0. 5W ; Alice has 2antennas, Bob has one transmit antenna and one receive antenna; d) Alice has single antenna, Bob has 2receive antennas, P antennas, Bob has 2receive antennas; A =1W ; e) Alice has 2AN is added by Alice with P A =0. 5W , tr (K w A ) =0. 5W .

It is shown that strategy (a)achieves better performance when Eve is located close to Bob whereas strategy (b)achieves better performance when Eve is located close to Alice. Strat-egy (c)captures the advantages of strategies (a)and (b);it is useful when both the transmitter and receiver have extra power and antenna to send AN. Strategy (d)achieves the worst performance when Eve is close to Alice. Strategy (e)achieves

4Fig. 2:Outage secrecy region for different values of ε, P W, P =10W, R=1.5e3

bit/s.

A =1B Fig. 3:Outage probability versus Eve’sx -coordinate when she moves on line y=0.5.

the largest secrecy capacity, because the 2X2MIMO system increases the capacity of Bob signiﬁcantly.From the result, we conclude that in the presence of Eve, if the number of Bob’santennas is less than Alice’santennas, it is better to use all of Bob’santennas to receive Alice’ssignal; otherwise it is better to use some of Bob’santenna to transmit AN to disturb Eve.

VI. C ONCLUSION

In this paper, we have introduced a novel method to provide secure communication via sending an artiﬁcialnoise by the transmit antenna of the legitimate receiver. We also consider the far-ﬁeldpath loss component and introduce the concept of outage secrecy region which may be helpful in guiding the design of physical layer security solutions. Simulation results show that the proposed method can achieve high security in practical settings, especially when the intruder’slocation is near the intended receiver. Finally, the proposed method can be combined with the existing mask beamforming method to further improve secrecy

performance.

IEEE COMMUNICATIONS LETTERS, ACCEPTED FOR

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Fig. 4:Average secrecy capacity of 5methods versus Eve’sx -coordinate when Eve moves on line y=0.5.

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