Enhancement of Physical Layer Security Using Destination Artificial Noise Based on Outage Probability
TThe final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg)
Noname manuscript No. (will be inserted by the editor)
Enhancement of Physical Layer SecurityUsing Destination Artificial NoiseBased on Outage Probability
Ali Rahmanpour · Vahid T. Vakili · S.Mohammad Razavizadeh the date of receipt and acceptance should be inserted later
Abstract
In this paper, we study using Destination Artificial Noise (DAN)besides Source Artificial Noise (SAN) to enhance physical layer secrecy withan outage probability based approach. It is assumed that all nodes in thenetwork (i.e. source, destination and eavesdropper) are equipped with multipleantennas. In addition, the eavesdropper is passive and its channel state andlocation are unknown at the source and destination. In our proposed scheme,by optimized allocation of power to the SAN, DAN and data signal, a minimumvalue for the outage probability is guaranteed at the eavesdropper, and at thesame time a certain level of signal to noise ratio (SNR) at the destination isensured. Our simulation results show that using DAN along with SAN bringsa significant enhancement in power consumption compared to methods thatmerely adopt SAN to achieve the same outage probability at the eavesdropper.
Keywords
Physical Layer Security, Artificial Noise, Destination ArtificialNoise (DAN), Source Artificial Noise (SAN), Full Duplex Communication,Multiple-Input Multiple-Output (MIMO) systems.
Due to weakness of traditional security methods which are based on usingcryptography algorithms in upper layers, physical layer security attracts manyattentions in the recent years. Physical Layer Security was first addressed byWyner’s celebrated paper [11] in which a wiretap channel was studied andthe notion of secrecy capacity was introduced. Since then, several studies haveextended the Wyner’s work, such as [6] for Gaussian wiretap channels, [12] forfading channels and [7] for Multiple-Input Multiple-Output (MIMO) channels.
The authors are with the School of Electrical Engineering, Iran University of Sci-ence and Technology (IUST), Narmak, Tehran 1684613114, Iran. E-mail: [email protected] · [email protected] · [email protected]. a r X i v : . [ c s . I T ] A p r he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) One practical method in this area is using beamforming techniques in com-bination with emission of an Artificial Noise (AN) at the data source side(Alice) to corrupt an eavesdropper’s reception during transmission of datato the destination (Bob) [4]. During past years several works have developedthis idea that most of them aim to maximize secrecy capacity. In a differentway, the authors in [8] proposed a probability based approach for employingAN to guarantee a minimum level of outage probability at an unknown Evewhile satisfying a certain Quality of service (QoS) requirement at the Bob. Itshould be noted that all these works are based on exploiting Source ArtificialNoise (SAN) that means sending a noise-like signal at the data-source side ofa wireless link.Recently, thanks to the development of full-duplex communications, onenode can transmit and receive data signals at the same time and the samefrequency band [9], [13]. By full-duplex communications, it is possible to adoptDestination Artificial Noise (DAN) at the destination along with the SAN atthe source. This idea was first proposed in [10] and then in [2] for Single-Input Multiple-Output (SIMO) communication systems. In [15] the MIMOcommunication systems when only one of the receiver antennas is used fordata reception has been studied, but in [14] destination can allocate moreantennas for receiving the data. Similar to SAN, most works on the DAN arealso based on maximizing secrecy capacity.In this paper unlike to the previous works, we adopt an outage probabilitybased approach for the characterization of the physical layer security thatuses both DAN and SAN. In addition, we propose an optimal power allocationmethod to the DAN, SAN and source information signal to ensure the securityrequirements. We also investigate the effect of considering a power constraintat the destination for the situation in which Bob can only cancel a certainamount of self-interference. It is shown how this power constraint increasesthe total required power for a certain level of security.Our simulation results show that the proposed method brings a significantreduction in the total power consumption compared to the previous workswhere only SAN is used to ensure a certain outage probability at the Eve. Wealso represent the effect of Eve’s location on the performance of the proposedmethod. It is shown that in contrast to previous works, we are able to ensuresecrecy requirements even where Eve is very close to the Bob.This paper is organized as follow. After presenting system model in Sec-tion 2, the power allocation problem is proposed in Section 3. In Section 4,simulation results are presented for both constrained and unconstrained powerscenarios at the destination. Finally in Section 5, the paper has been concluded.
Notation : Bold symbols in small and capital letter denote vectors and ma-trices. In addition ( . ) H denotes the conjugate transpose and (cid:107) . (cid:107) is the normoperator.he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Title Suppressed Due to Excessive Length 3
In this paper, we consider a network consisting of a data source (Alice), adestination (Bob) and an eavesdropper (Eve). It is assumed that the source andthe destination are equipped with N A ≥ N B ≥ N E ≥ H AB of size N A × N B and it is assumedto be known to all nodes. In the other hand the channel gains between Aliceand Eve is represented by a matrix H AE of size N A × N E and the channelgains between Bob and Eve by a matrix H BE of size N B × N E which areunknown for the legal nodes (Alice and Bob). All channel gains are modelledby independent zero-mean complex Gaussian random variables. The variancesof the above channels are σ H AB , σ H AE and σ H BE for the channel between Aliceand Bob, Alice and Eve and Bob and Eve, respectively. If H be a channel gainsmatrix (small scale fading effects), by considering the path loss effect, we candefine ˆ H as [5],[14] ˆ H = ( λ r − κ ) / H (1)where λ is a constant that is used for showing the power at a reference signaland it determined by empirical measurements. In addition r is the distancebetween two nodes and κ is the path loss exponent and depends on the prop-agation environment. The values of this parameter is typically between 2 and6. We assume that the Eve’s location is unknown to the legal nodes andhas a uniform distribution in a circle with radius r ab , where r ab is the distancebetween Alice and Bob. Also it is assumed that the legitimate users are locatedat the center of the area (Fig. 1).To enhance the security of the system, we assume that only one of thedestination antennas is employed for receiving the data signal and the otherantennas are assigned to the AN propagation (i.e. DAN). On the other hand, allsource antennas could be used to transmit both precoded data signal and AN(i.e. SAN). To decrease the power consumption and enhance the performanceat the Bob, we select its best antenna (i.e. the j th antenna) for receiving datafrom Alice. One approach for selecting this antenna is as follows: j = arg max i (cid:8)(cid:13)(cid:13) H iAB (cid:13)(cid:13)(cid:9) (2)where H iAB is the i th column of H AB which is related to the i th antennaat the destination and i = 1 , , ..., N B . Therefore the channel assigned to thedata transmission between Alice and Bob is denoted by a vector h AB of size N A . In addition, the channel matrix between the remaining Bob’s antennasand Eve is presented by a matrix ˜ H BE of size ( N B − × N E .In addition assuming that Eve uses the selection combining method, thechannel vector between Eve’s k th antenna and Alice is denoted by h AE of size N A , while h BE of size ( N B −
1) denotes the channel between Bob’s remainedantennas and Eve’s k th antenna.he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Fig. 1
System model
Now let x , y B and y E be the precoded data signal transmitted by Alice, thereceived signal at Bob and the received signal at Eve, respectively. Therefore y B = ˆ h HAB x + n B (3) y E = ˆ H HAE x + ˆ ˜ H HBE ν + n E (4)where ν is the DAN emitting by Bob and we assume that its self-interferencecan be completely canceled at the destination. Assuming there is no knowl-edge about the Eve’s Channel State Information (CSI), DAN power must beequally distributed among ( N B −
1) Bob’s antennas that are assigned to DANpropagation. Hence we can write ν = (cid:114) PN B − N B (cid:88) i =1 i (cid:54) = j η ψ i (5)where P ≥ η is a complex scalar with unitmagnitude and uniform random phase, ψ i is a vector of size N B whose i thelement is equal to one and all other elements are equal to zero. n B and n E of size N E are the Gaussian noise terms with zero mean and variances σ B andhe final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Title Suppressed Due to Excessive Length 5 σ E I , respectively. x is the beamformed signal transmitted by Alice and couldbe written as x = (cid:113) ϕ ´ P d t + (cid:113) (1 − ϕ ) ´ P η (6)where 0 ≤ ϕ ≤ P > d is theinformation symbol with E (cid:110) | d | (cid:111) = 1 and t of size ( N A ) is normalized ( (cid:107) t (cid:107) =1) beamforming vector. η is SAN vector of size ( N A ) that is orthogonal to t ( i.e., t H η = 0) and its covariance matrix is denoted by C η as C η = E (cid:8) ηη H (cid:9) (7)Therefore we have T r { C η } = 1. For the beamforming at the source node, asproposed in [3], if t i is the i th eigenvector of h AB h HAB and t is assumed to bethe principal eigenvector, it is assumed that t = t . Based on the orthogonalityof the eigenvectors of h AB h HAB , η is a linear combination of N A − h AB . Since Eve’s CSI is not knownto the legal nodes, the noise power equally is distributed to these eigenvectorsas follows η = (cid:114) N A − N A (cid:88) i =2 η t i . (8)According to the above beamforming model, the signal to noise ratios(SNRs) at the Bob and Eve’s k th antenna can be derived asSNR B = ϕ ´ P (cid:107) ˆ h AB (cid:107) σ B (9)and SNR kE = ϕ ´ P ˆ h HAE t t H ˆ h AE (1 − ϕ ) ´ P ˆ h HAE C η ˆ h AE + PN B − ˆ h HBE ˆ h BE . (10) In this section, we discuss about the problem of power allocation to SAN andDAN. To ensure secrecy, γ b and γ e QoS constraints should be satisfied at Boband Eve and hence the power optimization problem can be written as:min P, ´ P ,ϕ P + ´ P (11a)s . t . SNR B ≥ γ b (11b) P [SNR E ≤ γ e ] ≥ β. (11c)In above optimization problem, (11b) is for satisfying a certain level ofSNR at Bob and (11c) guarantees a minimum value of outage probability atEve.he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) As it can be seen, our object is a joint power optimization for source anddestination. Considering that Eve uses the selection combining method andthe channel matrix coefficients are independent, we have P [SNR E ≤ γ e ] = N E (cid:89) k =1 P [SNR kE ≤ γ e ] = P [SNR kE ≤ γ e ] N E (12)By substituting (9), (10) and (12) into (11) and considering (1), we have:min P, ´ P ,ϕ P + ´ P (13a)s . t .ϕ ´ P ≥ γ b σ B ( λ r − κAB ) − (cid:107) h AB (cid:107) − (13b) P [ ϕ ´ P ( λ r − κAE ) h HAE t t H h AE (1 − ϕ ) ´ P ( λ r − κAE ) h HAE C η h AE + PN B − ( λ r − κBE ) h HBE h BE ≤ γ e ] ≥ β NE (13c)We can rewrite (13c) as P [ h HAE ah AE + b h HBE h BE ≤ σ E ] ≥ β NE (14)where a and b are defined as below a = ´ P λ ¯ r − κae ( ϕγ − e t t H − (1 − ϕ ) C η ) (15a) b = − PN B − λ ¯ r − κbe (15b)where ¯ r ae = E [ r ae ] and ¯ r be = E [ r be ]. The left side in (14) can be interpretedas a Cumulative Distribution Function (CDF). By defining X = h HAE ah AE (16) Y = h HBE h BE (17)and Z = X + bY , we have F Z ( z ) = P [ X + bY ≤ z ]= P [ h HAE ah AE + b h HBE h BE ≤ z ]= (cid:90) + ∞−∞ f Y ( y ) dy (cid:90) z − by −∞ f X ( x ) dx (18)where (cid:82) z − by −∞ f X ( τ ) dτ = F X ( z − by ) is the CDF of X . On the other hand X is an indefinite Hermitian quadratic form for x ≥ F X ( x ) can bederived as [1]: F X ( x ) = u ( x ) + α | λ | e ( − xλ ) u ( xλ ) (19)he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Title Suppressed Due to Excessive Length 7 where α = − λ (1 − λ λ ) ( N A − (20)and λ = ϕ ´ P λ ¯ r − κae γ − e σ H AE ≥ λ = − (1 − ϕ ) ´ P λ ¯ r − κae σ H AE ( N A − − ≤ . (21b)In addition, Y is sum of the squares of 2( N B −
1) independent normalrandom variables and has chi-squared ( χ ) distribution as f Y ( y ; 2( N B − yσ HBE ) ( N B − .e ( − y σ HBE ) σ H BE ( N B − Γ ( N B − u ( y ) . (22)Therefore (18) can be rewritten as F Z ( z ) = (cid:90) + ∞ f Y ( y ) dy (cid:90) z − by −∞ f X ( x ) dx, (23)Considering ( z − by ) ≥
0, substituting (19) and (22) into (23) and considering σ H BE = 1, we have F Z ( z ) = (cid:90) + ∞ ( N B − ( N B − y ( N B − e − . y dy + (cid:90) + ∞ α e ( − zλ ) ( N B − ( N B − | λ | y ( N B − e ( bλ − . y dy (24)After some manipulations, F Z ( z ) in (24) derived as F Z ( z ) = (1 + ( − N B e ( − zλ ) ( N B − (1 − λ λ ) N A − ( bλ − . ( N B − ) . (25)Substituting (21) and (25) into (13), the optimization problem in (13) issimplified asmin P, ´ P ,ϕ P + ´ P (26a)s . t . ϕ ´ P ≥ γ b σ B ( λ r − κAB ) − (cid:107) h AB (cid:107) − (26b)(1 − (1 − N B ) e ( − γeσ Eϕ ´ Pλ r − κae σ HAE ) (1 + (1 − ϕ ) γ e ϕ ( N A − ) ( N A − ( P ¯ r − κbe γ e ( N B − ϕ ´ P ¯ r − κae σ HAE + 0 . ( N B − ) ≥ β NE . (26c)According to (26c), it is obvious that the optimum value for (26b) is ϕ ´ P = γ b σ B ( λ r − κAB ) − (cid:107) h AB (cid:107) − , therefore the optimization method needs to only beapplied to (26c). We use standard numerical methods to solve the problem.he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) In this section, we evaluate the performance of our proposed method by com-puter simulations. In our simulations, it is assumed that σ H AB = σ H AE = σ H BE = 1, r AB = 2 Km , γ E = 0 . σ B = σ N = 4 × − . For thepath loss, it is assumed that λ = 10 − and κ = 3. Also the channel be-tween Alice and Bob, H AB is generated randomly with a distribution of H AB ∼ CN (0 , σ H AB I ).To represent how changes in the main parameters of our problem influencethe security and power consumption, we first consider a scenario in which thedestination has no power constraint for DAN. Then we also investigate theeffect of a power constraint on DAN at the destination.Case a) Destination has no power constraint for DANAs mentioned before, we assume that the Eve’s location is distributed uni-formly on the area and ¯ r ae = ¯ r be = 1000. In addition we first assume that N E = N A = N B = 4. As it is seen in Fig. 2, in the case that both DAN andSAN are used, the required power for AN to achieve a given outage probabilityat the Eve is much less than the case that only SAN is used. In addition, inboth cases, with increasing γ B , more power is needed to guarantee the givenoutage probability at the Eve.In Fig. 3, we investigate the effect of different number of antennas at theEve on the required power for the case N A = N B = 4. It could be seenthat when Eve has more capabilities, more power is needed to achieve a givenoutage probability. In Fig. 4, the required power for AN is shown for differentvalues of N A and N B , when N E = 4.In another scenario, we assume Alice and Bob are located at locations( − ,
0) and (1000 , N E = N A = N B = 4, γ B = 0 . β = 0 .
6. Thetotal power should be allocated to AN to achieve a target outage probabilityat Eve ( β ) while Eve moves from ( − ,
0) to (15000 ,
0) is shown in Fig. 5.From this figure, it is seen that by using DAN we need less power to guaranteea similar β . Especially in the case that Eve is close to Bob, it is still possibleto guarantee a given security.Case b) Destination has a power constraintAlthough Full Duplex technique is advancing so fast and today it is possibleto cancel even high levels of
Self-Interference at the destination ([9] and [13]),but it is still useful to investigate how power consumption will be changedby limiting the maximum power allocated to the DAN. This is the case thatis considered in Fig. 6. As we see in this figure, at the outage probability β = 0 . N E = N A = N B = 4, when DAN power limitation decreasesfrom 2 mW to 0 . mW , total required Power for AN increases from 15 mW to20 mW .he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Title Suppressed Due to Excessive Length 9
Intended Outage Probability at Eve Th e P o w e r A ll o ca t e d t o t h e A r t i f i c i a l N o i se ( m W ) SAN + DAN ( γ E =0.4)Only SAN ( γ E =0.4)SAN + DAN ( γ E =0.6)Only SAN ( γ E =0.6) Fig. 2
The required power for AN (total SAN and DAN) versus the target outage proba-bility ( β ) at the Eve, for N E = 4, for γ E = 0 . . In this paper, using destination artificial noise along with source artificialnoise is introduced to guarantee an intended outage probability at Eve, whileensuring a certain SNR at Bob. For both constrained and unconstrained powerallocation scenarios it has been shown how using the DAN, decreases thetotal power which is required to guarantee an intended outage probability atEve. Using outage probability approach instead of secrecy capacity, makes oursolution appropriate for the quasi-static channels.
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Number of Antennas at Eve Th e P o w e r A ll o ca t e d t h e A r t i f i c i a l N o i se ( m W ) β =0.6 β =0.8 Fig. 3
The required power for AN versus the number of antennas at Eve, for β = 0 . .
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Eve Location at the X-axis (m) -1500 -1000 -500 0 500 1000 1500 To t a l P o w e r A ll o ca t e d t o t h e A r t i f i c i a l N o i se ( m W ) SAN + DANOnly SAN
SecurityOutage
Fig. 5
The optimal power is needed for AN (total SAN and DAN) versus Eve’s locationchanges from ( − ,
0) to (1500 , β = 0 . mization. Mathematical Problems in Engineering 2013:Article ID: 686,403he final publication is available at Springer http://dx.doi.org/10.1007/s11277-016-3865-9 (Read Online at http://rdcu.be/qmtg) Title Suppressed Due to Excessive Length 13
Intended Outage Probability at Eve To t a l P o w e r A ll o ca t e d t o t h e A r t i f i c i a l N o i se ( m W ) DAN power constraint = 2 mWDAN power constraint = 1 mWDAN power constraint = 0.5 mW
Fig. 6
The optimal power is needed for AN (total SAN and DAN) versus target outageprobability ( ββ