Physical Layer Security of Wireless Networks under Hardware Impairments Kyusung Shim∗ , Nhu Tri Do† , Beongku An‡ ∗ Information
System Graduate School of Smart City Science Management Hongik University, Republic of Korea of Electronic and Computer Engineering in Graduate School, Hongik University, Republic of Korea ‡ Dept. of Computer and Information Communications Engineering, Hongik University, Republic of Korea Emails: ∗
[email protected], †
[email protected], ‡
[email protected]
† Dept.
II. S YSTEM M ODEL
Abstract—In this paper, we study physical layer security of wireless networks in presence of one eavesdropper. Assume that the channel state information of the eavesdropper cannot be obtained at the transmitter, it is estimated through the channel state information of a torch node. In addition, considering the impact of hardware impairments at the transmitter, we analyze system performance in terms of secrecy outage probability over Rayleigh fading channels. The closed-form expression of the system secrecy outage probability is derived. Analytical results are validated by Monte-Carlo simulation results. The numerical results reveal the effects of the hardware impairment and the use of the torch node on physical layer security of the wireless system. Index Terms—physical layer security, hardware impairment, torch node, channel state information, secrecy outage probability
Let us consider a direct communication from a source S to a destination D as depicted in Fig. 1. In addition, the transmission is observed by one eavesdropper E. There is a torch node T is that deployed to help evaluating the CSI of the eavesdropper. Considering hardware impairment at the E T hSR
I. I NTRODUCTION
hST
hSD
D
S
According to information-theoretic perspective, physical layer security (PLS) secures the wireless communications by evaluating the physical characteristics of the wireless channels. In related works [1], authors assumed that the eavesdropper also sends its channel state information(CSI) to transmitter. However, in this paper, we consider the scenario in which eavesdropper does not send its CSI to transmitters. In order to obtain the CSI of the eavesdropper, we deploy one torch node which is located near the eavesdropper and the torch node reports its CSI to the source [2]. Through the torch node’s CSI, we estimated the eavesdropper channel by using the model of imperfect CSI channel. On the other hand, Hardware impairment refers to the distortions caused by both transmitters and receivers. In [3], and the referenced therein, the impact of hardware impairments on relay communications was investigated in detail. The main contributions in this paper are as follows. First, we try to resolve practical issues of wireless communications that we did not receive the CSI of the eavesdropper and the hardware impairment at the transmitter. Second, we obtain the closed-form expression of the secrecy outage probability(SOP) of the considered system. The rest of this paper is organized as follows. Section II describes the system model. Section III presents outage performance analysis with closed-formexpression. The performance evaluation with numerical results is presented in Section IV. Finally, the paper is concluded in Section V.
DF
Transmitter
Receiver
Fig. 1. The source-destination transmission is overheard by one eavesdropper. In addition, the hardware impairment effect is taken into account at the source and the destination.
transmitter, the received signal from S to D is given by [3] √ ySD = PhSD (xS + ηS ) + ωD , (1) where ηS ∼ CN (0, Pκ2 ) represents distortion noise. The role of the T is to provide its CSI to the S. We can represent the channel coefficient hSE by using hST that is given by p hSE = ρhST + 1 − ρ2 , (0 < ρ ≤ 1), (2) where ρ denotes the correlation coefficient that indicates the accuracy of channel estimate over channel state of hST . the received signal at the eavesdropper ySE is given by p √ ySE = P(ρhST + 1 − ρ2 )(xS + ηS ) + ωE . (3) The signal-to-noise-plus-distortion ratio(SNDR) of main and eavesdropper channel are given by [3] γSD =
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PgSD , PgSD κ2 + N0
(4)
γSE =
Pρ2 gST + P(1 − ρ2 )N0 , Pρ2 gST κ2 + P(1 − ρ2 )N0 κ2 + N0
observe that the Psop decrease as the transmit power increased at transmit power from -10dB to 10dB. However, the Psop increases as the transmit power increased at transmit power from 10dB to 30dB. As κ increased, the Psop is increased. The patterns of simulation result curve and analysis result curve are similar.
(5)
where gSD , gST are channel gains of main and eavesdropper, respectively. The secrecy capacity is determined by the difference between the capacity of the main channel and that of the eavesdropper channel [1]. Thus the secrecy capacity is given by ! PgSD 1 + PgSD κ2 +N0 CS = max log2 ,0 . (6) PgSE 1 + PgSE κ2 +N0
1
III. O UTAGE P ERFORMANCE A NALYSIS
0.8
The Psop is the probability of the event that the secrecy capacity drops below a predefined target secrecy rate [4]. For predefined target secrecy rate R, the Psop in our system is given by
PSOP
0.7 0.6 0.5
Psop = Pr(CS < R) PgSD = Pr (7) PgSD κ2 + N0 R 2 R 2 2 Pρ gST + 2 P(1 − ρ )N0 < (2R − 1) + . Pρ2 gST κ2 + P(1 − ρ2 )N0 κ2 + N0
0.4 0.3 −10
−5
0
5
10 P (dB)
15
20
25
30
Fig. 2. System secrecy outage probability Psop as a function of transmit power P with N0 = 1, λX = 3.7, λY = 1.3, κ = 0.03 and R = 0.5 bit/s/Hz.
Let a1 = P, a2 = Pκ2 , a3 = N0 ; and b0 = 2R − 1, b1 = 2R Pρ, b2 = 2R P(1 − ρ2 )N0 , b3 = Pρκ2 , b4 = 1x P(1 − ρ2 )κ2 N0 + N0 ); Ω = a2ax+a ; (7) is re-written as 3 follows: a1 x b1 y + b2 Psop = Pr < b0 + a x + a3 b3 y + b4 2 (8) b1 y + b2 = Pr Ω < b0 + , b3 y + b4
V. C ONCLUSIONS In this paper, we study the physical layer security of wireless networks under the effects of hardware impairments. More specifically, we assume that the eavesdropper did not send its channel state information at the transmitter. Thus, a torch node is deployed to the eavesdropper in order to estimate the channel state information of the eavesdropper channel. In addition, hardware impairment is considered at the transmitter. The closed-form expression of secrecy outage probability is obtained and derived. The numerical results show that distortion noise effects on the secrecy outage probability.
where z1 = b0 + bb24 , z2 = b0 + bb13 , c1 = a1 b0 b3 + a1 b0 , c2 = a1 b0 b4 + a1 b2 , c3 = a2 b3 − a3 b0 b3 + a3 b1 and c4 = a2 b4 − a3 b0 b4 + a3 b2 . After some algebraic manipulations, the closed-form expression of Psop is given by 1 Psop = exp(− z1 ) λY 1 d24 z22 + 2d2 d5 z2 + d25 + λY d1 d4 z22 + 2d2 d5 z2 + (d2 d5 − d3 d4 ) d1 z22 + d2 z2 + d3 × exp − d4 z2 + d5 2 2 d4 z1 + 2d2 d5 z1 + d25 1 − 2 λY d1 d4 z1 + 2d2 d5 z1 + (d2 d5 − d3 d4 ) d1 z12 + d2 z1 + d3 , × exp − d4 z1 + d5
Exact (κ = 0.03) Simulation (κ = 0.03) Exact (κ = 0.05) Simulation (κ = 0.05)
0.9
ACKNOWLEDGMENT This research was supported by the MSIP(Ministry of Science, ICT and Future Planning), Korea, under the ICT/SW Creative Research program (IITP-2015-R2212150026) supervised by the IITP(Institute for Information & communication Technology Promotion). R EFERENCES [1] Y. Zou, X. Li, and Y. chang Liang, “Secrecy outage and diversity analysis of cognitive radio systems,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 11, pp. 2222–2236, November 2014. [2] Y. Choi and D. Kim, “Performance analysis with and without torch node in secure communications,” 2015 International Conference on Advanced Technologies for Communications (ATC), October 2015. [3] E. Bjornson, M. Matthaiou, and M. Debbah, “A new look at dual-hop relaying: Performance limits with hardware impairments,” IEEE Transactions on Communications, vol. 61, no. 11, pp. 4512–4525, November 2013. [4] V. N. Q. Bao, N. Linh-Trung, and M. Debbah, “Relay selection schemes for dual-hop networks under security constraints with multiple eavesdroppers,” IEEE Transactions on Wireless Communications, vol. 12, no. 12, pp. 6076–6085, December 2013.
(9)
where d1 = λX c3 , d2 = λX c4 + λY c1 , d3 = λY c2 , d4 = λX λY c1 and d5 = λX λY c4 . IV. N UMERICAL R ESULTS In this section, we present simulation results obtained by carrying out the Monte-Carlo simulations. Fig. 2 shows the Psop of the our system model as a function of transmit power P where κ is a different value. From Fig. 2, we can
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