Secure Cooperative Untrusted-Relay Network With Outdated CSI Asma Mabrouk
Kamel Tourki
Noureddine Hamdi
HANA Research Lab, ENSI, Mathematical and Algorithmic Sciences Lab, HANA Research Lab, ENSI, Manouba University France Research Center, Manouba University Email:
[email protected] Huawei Technologies Co. Ltd. Email:
[email protected] Email:
[email protected]
purposes. Assuming global channel state information (CSI) knowledge of both the main link and of the eavesdropper link, amplify-and-Forward (AF) and DF-based optimal relay selection schemes in dual-hop relay system are studied in [5]. A two-stage relay and destination selection scheme was proposed in [6] for a single carrier multi-relay network with multiple destinations and eavesdroppers. Additionally, cooperative jamming (CJ) approaches which involve the transmission of artificial interference with information bearing signal have been widely adopted for enhancing PLS. In these techniques, a helper or the destination itself cooperates with the source by sending a jamming signal to degrade the performance of the eavesdropper channel [7]. Furthermore, hybrid relaying and jamming schemes are proposed to benefit from secrecy gains of the two methods [8]. In [9], authors investigated the problem of whether the helper should act as a relay or a jammer to improve the secrecy. Constrained by the maximum transmit power, the best relay-destination link selection criterion was proposed in [10] for an optimized cooperative jamming scheme. Relay-based communication may be threatened by external eavesdroppers, however, the relay nodes could be untrusted trying to intercept the information while assisting a wireless communication. Secure communications with single untrusted relay were investigated in [11]–[14]. Using a destination based jamming technique, authors in [12] and [13] showed that positive secrecy rate is achieved even if the relay is untrusted. The lower bound of the ergodic secrecy capacity (ESC) was derived in [12]. In [13] the impact of large scale antenna arrays at either the source or the destination was studied. Authors in [14] proposed an opportunistic cooperative transmission scheme where the untrusted relay can support the transmission only for poor conditions of the direct link. In [15] authors present a study of the secrecy performance of opportunistic relay selection systems employing an alternate jamming method to secure the transmissions from the relays during both the first and the second phases. A distributed beamforming technique and opportunistic relaying through K untrustworthy relays was proposed in [16] to enhance the secrecy performance in an AF wireless relay network. Nevertheless, a key assupmtion of these aforementioned works is the availability of perfect CSI. However, this premise
Abstract—This paper studies the secrecy performance of an untrusted amplify-and-forward relaying network where both the relaying and the direct links are used to convey the source’s information. Since relays act as eavesdroppers, a source-based jamming technique is proposed to keep the source’s message secret from these helper nodes. We analyze the secrecy capacity of partial relay selection based on outdated channel state information. The study is conducted analytically by deriving the lower-bound expression for the ergodic secrecy capacity (ESC). We demonstrate through the simulation results the tightness of the derived bound. The use of the direct link is shown to improve the secrecy performance of the proposed scheme. In this case, we found that ESC performance with maximum ratio combining at the destination is better than that with selection combining. The system performance worsens as the correlation coefficient decreases. Furthermore, the maximum of ESC is achieved when relays are in the middle between the source and the destination with equal power allocation between the information and the jamming signals at the source. Keywords—Source-based jamming; partial relay selection; untrusted relaying; outdated channel state information; ergodic secrecy capacity (ESC).
I. I NTRODUCTION Cooperative communication is used as an effective means for saving power consumption and increasing the capacity in wireless networks [1]. Under this way, nodes cooperation methods have a great potential not only to improve the reliability of wireless transmissions, but also to enhance the wireless security against eavesdropping attacks. Motivated by these issues, extensive works examined relaying schemes for increasing the information security at the physical layer of wireless networks [2], [3]. Introduced as a new security paradigm, physical-layer security (PLS), is not meant to replace existing traditional security techniques but intend to enhance the security level by taking advantage of the inherent varying characteristics of wireless channels without exchange of private keys as for cryptography protocols. A. Related works In the context of secure relay channels, authors in [4] have analyzed an energy-efficient secure communication over a decode-and-forward (DF) relay network in the presence of a potential eavesdropper. Besides, relay selection (RS) has been widely used in cooperative relay networks for secrecy
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gij denotes the Rayleigh channel from i, (i ∈ {S, Rk }), to j (j ∈ {D, Rk }, j = i). The noise over all channels is zero-mean additive white Gaussian (AWGN) with the same variance N0 . In the nth phase of transmission, n ∈ {1, 2}, (n) the AWGN at the receiver j is denoted by nj ∼ CN(0, N0 ).
is not realistic since practical channel estimation causes CSI imperfections. In particular, due to the time varying nature of the channel, an outdated CSI may be used for relay selection. As a result, the system performance is adversely affected. The security performance for transmit beamforming in a multiple-antennas, mutiple relaying network concidering a relay selection process under feedback delay constraint is investigated in [17]. A study of the impact of outdated CSI on the secrecy outage performance of multiple-input singleoutput Nakagami-m wiretap channels with transmit antenna selection is investigated in [18]. The effect of feedback delay on the joint DF-based relay and jammer selection scheme has been investigated in [19].
R R111
1
Ri
B. Our contribution Authors in [10] provided a lower bound for the ESC of partial RS in cooperative relay network considering a passive eavesdropper. The problem of secure transmission in cooperative network with multiple untrusted relays is addressed in [15], [16]. Here, as in [20], we consider the availability of the direct source-destination path. Assuming an AF relay-based system, the main contributions of this paper are as follows • Unlike the aforementioned works, we do not rely on perfect CSI knowledge assumption whereas due to the time variance of the channel and the feedback delay the RS scheme is designed assuming outdated CSI. • Unlike [10] and [15], instead of cooperating with the source by sending jamming signal, the destination profit from the direct link to receive the information. Therefore, to prevent the two-phase information leakage a sourcebased jamming (SBJ) technique is proposed. To create interference only at the untrusted relay side, the jamming signal sent by the source is a priori known at the destination [21]. • We derive a closed-form expression for the lower bound of the ergodic secrecy capacity in such an untrusted AF relay system while considering the presence of the direct source-destination path. The combining schemes at the destination and the non-selected relays are the maxumim ratio combining (MRC) and the selection combining (SC) schemes, respectively. The remainder of this paper is organized as follows. In Section II, the system and the transmission models are described. The lower bound of the average secrecy capacity is analyzed in Section III. In Section IV, the numerical results are summarized, and then, we conclude this paper in Section V.
R
K
D
S
Broadcast phase. Relaying phase.
Fig. 1. Secure dual-hop partial relay selection amplify-and-forward relaying network.
In addition, an average transmit power constraint P is imposed for data transmission where α is defined as the power allocation factor that indicates the power scale for the jamming signal in the first phase. The total transmit power of the system is evenly divided amongst the two transmission phases, i.e. Ps = Pr = P2 where Ps and Pr represent the transmit power at the source and the selected relay, respectively. The average signal-to-noise ratio (SNR) on each transmission phase is P . Thus, the instantaneous SNR over the given by λ = 2N 0 channel between nodes i and j is given by γij = λ|gij |2 . To exploit the multi-relay diversity, AF relay selection is adopted at the beginning of each transmission phase. In practical communication scenarios, it is difficult for the system to obtain the CSI of eavesdropper links. Therefore, the relay selection decision is based on the instantaneous SNR of the second hop. We consider a realistic scenario, where there is a delay between the RS phase and data transmission. Denoting the outdated channel gain of the Rk − D links at the time of selection by hRk d , the correlation relationship between gRk D and hRk D can be modeled as (1) gRk D = ρhRk D + 1 − ρ2 wkd ,
II. S YSTEM MODEL We consider a single source (S)-destination (D) cooperative relay system with K untrusted relays, denoted by Rk where k ∈ {1, ..., K}. The direct link between S and D is not ignored. All nodes are equipped with a single antenna. The relays operate in a half-duplex mode so that cooperative transmission is carried out in two phases, namely, the broadcast phase and the relaying phase. We assume that
where wkd is a random variable having the same variance as hRk D ; ρ is the correlation coefficient between gRk D and hRk D , which, using the Jakes autocorrelation model is given by ρ = J0 (2πfD T ) where T denotes the time delay between the RS phase and the data transmission, fD is the maximum
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however, the SINR at Rk is given by
Doppler frequency shift of the channel between the relays and D, and J0 (.) denotes the zero-order Bessel function of the first kind [22, Eq.(8.411)]. Therefore, the relay selection decision is formulated as i = arg max (hRk D ) . k
(2)
γ Rk =
(1)
Γe = max{γRi ,
However, the destination have the knowledge of the jamming signal. This can be implemented in practice with a small amount of overhead. For example, the jamming signal can be a Gaussian noise generated by a pseudo-random generator with finite states, and only the state of the pseudo-random generator needs to be sent to the destination via a separate and secure control channel [23]. Thus, after cancelling the jamming signal, the received signal at D is given by (1) (1) (4) yD = (1 − α)Ps gSD s + nD .
+
Cs = [Cd − Ce ] ,
(12)
A. Preliminaries To analyze the secrecy capacity performance of the proposed scheme, the statistics of γRi D and Γe are required. Assuming that fading channels are independent, from (11) the cumulative density function of the received SNR at the eavesdropper is given by
(6)
FΓe (x) = P
max
k,k=1,...,K
K (1) {γRk } < x = FγSRk
K x (a) − = 1 − e (1−α(1+x))γ SR .
k=0
x 1 − α(1 + x)
(13)
where (a) is obtained from the cluster-based relay network assumption .i.e. relays communicate in a short range network. Thus, the distances between the relays is short compared to the distances between the cluster the source and the destination, respectively. In this case, we assume γ SRk = γ SR and γ Rk D = γ RD , ∀k ∈ {1, .., K}. Using outdated CSI and considering the correlation model in (1), the probability density function (PDF) of γRi D is given by [25, Eq.(27)]
(2)
(7)
therefore, the end-to-end SNR from S to D through the relay can be expressed as (1 − α)γSRi γRi D , = γSRi + γRi D + 1
(11)
where [x]+ = max(0, x), Cd = 12 log2 (1 + Γd ) is the instantaneous capacity between S and D, and Ce = 12 log2 (1 + Γe ) denotes the capacity of the eavesdropper’s channel.
At the end of the second phase the received signal at the destination, with removing the jamming signal, is given by (2) (1) (2) yD = (1 − α)Ps GgSRi gRi D s + GgRi D nRi + nD , (8)
(2) γD
1≤k≤K
As defined in [24], the secrecy capacity is the maximal rate of secret information transmission from S to D. This metric reflects the amount of information that can be reliably transmitted without any information leakage, and is given by
In the relaying phase, the selected relay amplifies its received Pr signal by a variable-gain, G = Ps |gSRi |2 +N0 , and retransmits the resultant signal to the destination. Once selected, Ri receives the source signal in the broadcast phase only, however the remaining (K − 1) (Rk (k = i)) relays are referred to as eavesdroppers who can intercept the transmission during the 2nd phase. Then, the received signal at Rk in the relaying phase is given by (2) yRk = (1 − α)Ps GgSRi gRi Rk s + αPs GgSRi gRi Rk z (1)
γRk } = max {γRk }.
III. S ECRECY CAPACITY PERFORMANCE
On the other hand, the received signal-to-interference-plusnoise ratio (SINR) at Rk , k ∈ {1, ..., K}, is given by
+ GgRi Rk nRi + nRk .
(1)
max
1≤k≤K,k=i
Notably, the information leakage from the selected relay is considered.
Therefore, the first phase SNR at the destination can be expressed as (1) γD = (1 − α)γSD . (5)
(1 − α)γSRk . = αγSRk + 1
(10)
To combine the received signals from S and the selected relay, D adopts the MRC technique. In [15], it is worth noting that employing SC combining method at the non-selected relays yields almost the same ESC as when using MRC. Therefore, the received SNR at D and the k th untrusted relay are given (1) (2) (1) (2) by Γd = γD + γD and γRk = max{γRk , γRk }, respectively. The focus is on the untrusted relay with the highest received (1) SNR Γe = max{γRi , max1≤k≤K,k=i γRk } which will be referred to as eavesdropper. Therefore, following the same steps given in [15], Γe can be simplified as
(2)
To shield information from being leaked to untrusted relays, a source based jamming (SBJ) method is proposed, the details of which are summarized as follows: In the broadcast phase, S transmits the information signal s with power (1 − α)Ps , in addition to the jamming signal z with power αPs . The source message is eavesdropped during the first phase by all the untrusted relays. Thus, the received signal at the Rk relay is given by (1) (1) yRk = (1 − α)Ps gSRk s + αPs gSRk z + nRk , (3)
(1) γ Rk
(1 − α)γSRi γRi Rk . αγSRi γRi Rk + γSRi + γRi Rk + 1
fγRi D (x) = K
(9)
92
K−1 k=0
(−1)k−1 γ RD
− k+1 x K − 1 e (k(1−ρ2 )+1)γ RD . (14) k(1 − ρ2 ) + 1 k
Let X = γSRi + γRi D , then, the PDF of X is given by fX (x) = ⎧ −γx K−1 K−1 K(−1)k ⎪ SR ⎪ k=0 k γ SR γ RD xe ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ k ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
, θγ SR = 1 (15)
K−1 K(−1) k=0 γ RD (k(1−ρ2 )+1)(θ γ SR −1)
where θ =
× 1−e
−
θγ SR −1 x γ SR
Now, using (13), we can calculate the ergodic capacity at the eavesdropper, E{Ce }, as 1−α α 1 1 E{Ce } = (1 − FΓe (x)) dx, 2 ln 2 0 1+x K k 1 K (21) (−1)k−1 e αγ SR = k 2 ln 2 k=0 (1−α)k k k − . × Ei − − e αγ SR Ei − αγ SR γ SR
, θ γ SR = 1
Substitute (18), (19), (20) and (21) into (16), we obtain the lower bound expression of the ergodic secrecy capacity for the proposed scheme.
k+1 (k(1−ρ2 )+1)γ RD .
B. Ergodic secrecy capacity
IV. N UMERICAL RESULTS
ESC is the main performance metric investigated in this paper. Using (12), ESC of the system is bounded as
+ + C s = E [Cd − Ce ] (16) ≥ [E{Cd } − E{Ce }]
Here, we evaluate the performance of the proposed scheme based on numerical simulations to validate the derived analytical results in Section. III. We consider a linear topology network comprising a cluster of K = 5 relay nodes where the distance between S and D is normalized (dSD = 1) so that dSRi + dRi D = 1, dij is the distance between nodes i and j. We set the channels path loss exponent to 4. In Fig. 2 we present the ergodic secrecy capacity results as function of the average SNR λ. The tightness of the derived lower bound of the ESC is quite evident. For comparison, we also show results where the direct S − D path is ignored as well as when SC technique is applied at D. By doing so, it can be noted from Fig. 2 that the ESC increases when the direct link is taken into account regardless the combining techniques applied at D. Obviously, we reconfirm that MRCbased scheme outperforms its SC counterpart. In Fig. 3, we evaluate the ESC as a function of dSRi for different correlation coefficient ρ and jamming power factor α when λ = 30dB. It can be observed that, for the cases α = 0.2, 0.5, 0.9, ESC increases with ρ. However, the secrecy capacity decreases when the relay cluster moves away from the midpoint position between the S and D. It is worth noting that a better secrecy performance is achieved with perfect CSI knowledge (ρ = 1). In Fig. 4, the ergodic capacity is depicted as function of the jamming power factor α with different number of relays K when λ = 30dB and ρ = 0.7. It comes that an equal power allocation α = 0.5 provides the maximum ESC for different relay cluster position. It is shown that the secrecy performance improves when the relay cluster is closer to the source and the number of involved relays increases as well. Finally, Fig. 5 depicts the effect of varying the relay cluster location and the power allocation when ρ = 0.5 on the ESC. Results show that the area around the midway position between source and the destination is more secure especially for equal power allocation between the source’s information and the jamming signal.
Based on (5) and (9) and by applying Jensen’s inequality for the convex function ln (1 + aex + bey ), the ergodic capacity at D can be bounded as 1 ln 1 + (1 − α)eE{ln(γSD )} E{Cd } ≥ 2 ln 2 (17) +(1 − α)eE{ln(γSRi γRi D )}−E{ln(γSRi +γRi D +1)} . Using [22, Eq.(4.331.1)] and fY (x) where Y = {γD , γSRi , γRi D }, E{ln(γD )} and E{ln(γSRi γRi D )} are given by ∞ E{ln(γSD )} = ln(x)fγSD (x) dx = ln (γ SD )−ε, (18) 0
and
E{ln(γSRi γRi D )} =
∞
∞
ln(xy)fγSRi (x)fγRi D (y) dxdy
K−1 K − 1 K(−1)k−1 = (ln (γ SR ) − ε) + k k+1 k=0 k+1 × ε + ln , (k(1 − ρ2 ) + 1)γ RD (19) 0
0
respectively, where ε is the Euler constant [22, Eq.(8.367.1)]. Using (15) and [22, Eq.(4.337.5)], E{ln(X + 1)} is given by E{ln(X + 1)} = ⎧ K−1 K−1
K(−1)k−1 ⎪ ⎪ k=0 ⎪ k γ RD (k(1−ρ2 )+1) ⎪ 1 ⎪ ⎪ 1 γ SR ⎪ , θγ SR = 1 × (γ − 1)e Ei γ − − ⎪ SR SR γ ⎨ SR
⎪ K−1 K−1
⎪ K(−1)k ⎪ ⎪ ⎪ k=0 γ RD (k(1−ρ2 )+1)(θγ SR k ⎪ −1) ⎪ 1 ⎪ 1 θ γs ⎩ , × θ e Ei(−θ) − γ SR e Ei − γ 1 SR
θγ SR = 1 (20)
V. C ONCLUSION
where Ei(.) is the exponential integral function defined in [22, Eq.(8.211.1)].
The ergodic secrecy capacity performance of AF system with partial relay selection under outdated CSI over Rayleigh
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fading channels has been studied. A lower bound expression for the ESC of this system has been derived. Numerical results have shown the tightness of the derived analytical lower bound. Furthermore, it can be observed that the ESC improves when the correlation coefficient and the number of relays increase. Moreover, we find that the performance can be further improved by placing the relay cluster at the middle between S and D and using an equal power allocation between the information and the jamming signals at the source.
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7 2.8 2.8 2.6 2.6 2.4 2.4 5 2.2 2.2 2 2 4 10 10
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d=0.5, K=5 d=0.5, K=15 d=0.7, K=15 d=0.7, K=5 d=0.3, K=5 d=0.3, K=15
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Fig. 2. ESC as function of the system average SNR with and without direct link, when K = 5, α = 0.5 and ρ = 0.8. Results for MRC and SC combining techniques at D are presented.
3.5 0.1
α=0.2, ρ=0.4 α=0.2, ρ=0.8 α=0.2, ρ=1 α=0.5, ρ=0.4 α=0.5, ρ=0.8 α=0.5, ρ=1 α=0.9, ρ=0.4 α=0.9, ρ=0.8 α=0.9, ρ=1
α=0.5 5
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0.5 α
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Fig. 4. ESC performance as function of the jamming power level for different values of K and dSR when ρ = 0.7 and λ = 30dB.
5.5
5 0.9 4.5
0.8 0.7
4 0.6 α
Ergodic secrecy capacity
4.5
4
0.5
3.5
α=0.2 0.4 α=0.9
3
0.3 3.5 0.1
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0.3
0.4
0.5 dsr
0.6
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2.5
0.1
Fig. 3. Ergodic secrecy capacity as function of dSR , when K = 5 and λ = 30dB with different values of ρ and α.
0.1
0.2
0.3
0.4
0.5 d
0.6
0.7
0.8
0.9
sr
Fig. 5. ESC performance in term of the jamming power level with different relay position, when K = 5 and ρ = 10.
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