IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 4, NO. 6, DECEMBER 2015
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Relay Selection for Security-Constrained Cooperative Communication in the Presence of Eavesdropper’s Overhearing and Interference Saeed Vahidian, Sonia Aïssa, Senior Member, IEEE, and Sajad Hatamnia
Abstract—This letter addresses the problem of secure communication in a cooperative network operating in the presence of an eavesdropper as well as co-channel interference. Two opportunistic relay selection techniques are exploited for achieving physicallayer based security. The first one aims at minimizing the amount of information leaked to the eavesdropper by selecting the relay which achieves the lowest capacity to the wiretap node. In the second scheme, the relay, which yields the maximum achievable capacity at the destination node, is chosen. A performance analysis, which generalizes several previous results by accounting for interference affecting the network nodes, is conducted for both schemes and considering both selection combining and maximal ratio combining, in terms of the probability of non-zero achievable secrecy capacity and the secrecy outage probability, and numerical results are provided along with comparisons. Index Terms—Cooperative communication, physical-layer security, relay selection, Shannon capacity.
I. I NTRODUCTION
I
NFORMATION-THEORETIC PHY security has recently attracted considerable attention as a promising way to build secure communication systems [1]. Cooperative techniques, on the other hand, have been shown to be efficient in realizing PHY security [2]. One of the main approaches to establish secure communications in cooperative networks is relay selection. However, while existing works on relay selection for cooperative communications are abundant, studies on cooperative networks under security constraints are still sparse. Recently, [3] explored PHY security in a single-hop cognitive network where the transmit nodes are affected by eavesdroppers and the primary’s interference is Gaussian modeled. [4] studied opportunistic relay selection in networks with secrecy constraints, where a number of eavesdroppers overhear only the relays’ messages. [5] analyzed the performance of several relay selection modes in terms of outage probability for a cognitive system consisting of one source, one destination, and multiple relays affected by an eavesdropper. Tradeoffs between security and reliability of setups with opportunistic relaying and no interference were analyzed in [6] and [7]. In this context, though cooperative secure transmission has been studied in several scenarios, to the best of the authors’ knowledge, no prior work investigated different relay selection schemes with security Manuscript received July 15, 2015; revised August 5, 2015; accepted August 6, 2015. Date of publication August 11, 2015; date of current version December 15, 2015. The associate editor coordinating the review of this paper and approving it for publication was Z. Ding. S. Vahidian and S. Hatamnia are with the Faculty of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran 19697 64499, Iran (e-mail:
[email protected];
[email protected]). S. Aïssa is with the Institut National de la Recherche Scientifique (INRSEMT), University of Quebec, Montreal, QC G1K 9H7, Canada (e-mail: aissa@ emt.inrs.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LWC.2015.2466678
purposes when the source and the relays are both subject to eavesdropping attacks. In this letter, we pursue a detailed and generalized investigation of PHY security via cooperative relaying under co-channel interference (CCI). As such, we do not rely on the idealized noCCI assumption of the above-mentioned works, whereas due to the broadcast nature of wireless communications and the dense frequency reuse, CCI is a dominant factor. The main contributions of this work can be summarized as follows: i) The letter studies the effects of relay selection in the presence of an eavesdropper when the relays and the destination node suffer from CCI, in a network subject to Rayleigh fading and security constraints; ii) The system performance of two relay selection schemes, minimum selection and conventional selection, is investigated and compared in terms of the probability of non-zero achievable secrecy capacity and the secrecy outage probability, for two possible combining schemes at the eavesdropper, selection combining (SC) and maximal ratio combining (MRC). II. S YSTEM M ODEL AND R ELAY S ELECTION A. System and Channel Models We consider a dual-hop network in which a legitimate source, S, and its target destination node, D, wish to exchange confidential information in the presence of an eavesdropper, E, via the assistance of K trusted decode-and-forward (DF) relays, Rk . Each of the destination and the relaying nodes suffer from a finite number of faded CCI signals originating from external sources located in their vicinity. All channels are assumed quasi-static and to undergo flat Rayleigh fading, and global channel state information (CSI) is considered available, a common assumption in the PHY security literature, including the eavesdropper’s channels [3], [4]. Focusing on the relaying link, we assume that no direct link is available between nodes S and D, e.g., due to deep fading [8].1 Each node operates in a halfduplex mode such that in the first phase of transmission the source transmits while the relays listen and, in the cooperative phase, one relay selected among those that successfully decode the source information forwards the re-encoded signal to the destination. Herein, it is assumed that all relays can decode the message correctly [4]. The eavesdropper’s overhearing occurs during both phases. Thus, node E receives signals from two different paths: the relaying link and the S−E link, and then implements either SC [6] or MRC for the signal combining. Assume that S broadcasts its message with power PS in the first phase. Without loss of generality, say Rk is selected to forward its decoded signal to node D with power Pk . Then, the S−Rk −D, Rk −E and S−E channel capacities, in bit/sec/Hz, are given by, 1 1 CSD = min log (1 + γkD ), log2 (1 + γSk ) , (1) 2 2 2 1 Considering the direct link has trivial effect on the relay selection which is the main focus of this letter.
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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 4, NO. 6, DECEMBER 2015
1 CkE = log2 (1 + γkE ), 2 1 CSE = log2 (1 + γSE ), 2
(2) (3)
where k is used to denote relay Rk for short, γkD 2 Pk |hkD |2 , γSk Lk PS |hSk | 2 2 , γkE σPk2 |hkE |2 , γSE L D 2 2
n j=1 IjD |gjD | +σn i=1 Iik |gik | +σn PS 2 , L and L are the number of interferers affecting node |h | D k σn2 SE th D and the k relay, respectively, with IjD the transmit power of the jth interferer affecting D and Iik that of the interferer affecting relay k. Also, gjD, gik are the complex channel gains w.r.t. the interferers affecting D and kth relay, respectively. The
fading coefficient hmn corresponds to the link between nodes m and n. Considering Rayleigh fading, the signal-to-noise ratio (SNR) or interference-to-noise ratio (INR) w.r.t. link m−n is an exponential random variable (RV) with mean parameter mn . For simplicity, we assume kD = D , kE = E , Sk = S and ik = Ik (k = 1, · · · , K, i = 1, · · · , Lk ). Then, the capacity at which information can be transmitted secretly from the source to its destination, termed achievable secrecy capacity, is derived as Csec = [CSD − CE ]+ ,
(4)
where [x]+ = max[x, 0], and the achievable capacity at node E depending on whether it employs SC or MRC is 1 1 CESC = max log2 (1 + γkE ), log2 (1 + γSE ) , (5) 2 2 1 CEMRC = log2 (1 + γkE + γSE ). (6) 2
The secrecy capacity is given by
1 + max {min{γkD , γSk }} 1 sec, k , Ccon = log2 2 1 + γ
where ∈ {SC, MRC}, γSC = max[γk∗ E , γSE ] and γMRC = γk∗ E + γSE . III. P ERFORMANCE A NALYSIS In this section, the secrecy performance of the system, characterized by the probability of non-zero achievable secrecy capacity and by the secrecy outage probability, is analyzed. Closed-form expressions for these metrics are derived for both relay selection strategies and for both combining techniques. A. Minimum Selection Scheme 1) Secrecy Outage Probability: This metric is defined as the probability that the instantaneous secrecy capacity is less than a target rate R [9]: ∞ sec, Psec, = Pr C < R = FX (δ +(δ +1)y) fY (y) dy, (11) out,min min 0
where δ − 1. First, we focus on the SC technique. We use the notations x + 1 and y + 1 to respectively symbolize the numerator and the denominator of the fraction in (8). Making use of the moment generating function (MGF) of RV x, the cumulative distribution function (CDF) of x is LD κ Lk πjD κjD FX (x) = 1 − exp(−ξ x), (12) (x + κjD )(x + κ)Lk j=1 22R
where ξ 1S + 1D , πjD =
B. Relay Selection The choice of relay k is the only controllable factor which could influence the system performance. Therefore, we take advantage of relay selection to achieve PHY security. Our objective is the investigation of two relay selection techniques: minimum selection (“min”) where the main channels are not taken into account and the relay is selected based on the instantaneous capacity of the eavesdropper channel, and conventional selection (“con”) where the relay that provides the best instantaneous capacity toward the destination is chosen. With the minimum selection scheme, during the second hop, the relay that has the lowest instantaneous capacity to the wiretap node forwards the signal to the destination. Thus, the relay selection rule is k∗ = arg min{CE }.
(7)
k
In this case, the secrecy capacity is expressed as follows: 1 + min{γk∗ D , γSk∗ } 1 sec, , Cmin = log2 2 1 + γ where ∈ {SC, MRC}, γSC = max min{γkE }, γSE k
γMRC = min{γkE } + γSE .
and
With the conventional scheme, the relay that has the highest equivalent instantaneous capacity to the destination will be targeted to cooperate in the second hop. Thus, the chosen relay is selected according to k∗ = arg max{CSD }. k
(9)
jD D i=1 jD −iD , κjD = jD i=j
S and κ = . Ik
k
and ib γSE . According to [10], FY (y) can be computed and, taking the derivative of FY (y) w.r.t. y, the probability density function (PDF) is obtained as K 1 −y −Ky fY (y) = + −ϑ exp(−ϑy), (13) exp exp SE SE E E where ϑ 1SE + KE . Finally, with the PDF of y and the CDF of x at hand, performing partial fraction on the CDF of x and using concepts of probability [10] and [11, Eq. (3.462.12)], we obtain the secrecy outage probability (OP) of the minimum selection scheme when SC is used: LD Psec,SC = 1 − κ Lk πjD κjD J−1 + JK−1 − Jϑ , (14) out,min SE
E
where Jϑ =
L k −1 β=0
k
LD
We proceed by computing the CDF of y, FY (y) = FIa (y)FIb (y), where FIa (y) and FIb (y) are the CDFs of the RVs ia min{γkE }
j=1
(8)
(10)
A˜ Lk −β ϑ(δ + 1)β−Lk (ξ(δ + 1) + ϑ)Lk −β−1
× exp ξ κ + ϑ(δ + κ)(δ + 1)−1 × β − Lk + 1,(δ + κ) ξ + ϑ(δ + 1)−1 ˜ + Bϑ(δ + 1)−1 exp ξ κjD +ϑ(δ + κjD )(δ + 1)−1 (15) × 0, (δ + κjD ) ξ + ϑ(δ + 1)−1 ,
VAHIDIAN et al.: RELAY SELECTION FOR SECURITY-CONSTRAINED COOPERATIVE COMMUNICATION
and with JK−1 and J−1 obtained by using their subscript E SE in place of ϑ in (15). Also, (., .) is the incomplete Gamma (β) function [11, Eq. (8.350.2)], A˜Lk −β ϕ˜ β!(−κ) , ϕ(t) ˜ (t+κ1 jD ) 1 and ϕ˜ (β) its β th derivative, and B˜ L . (−κjD +κ)
k
Taking the same steps as in finding (14), the secrecy OP of the minimum selection scheme in the MRC case is obtained: LD κ Lk KπjD κjD ,MRC Psec = 1 − exp(−δξ ) out,min KSE − E j=1 ⎤ ⎡ k −1 L A˜Lk −β η−1 −ηK−1 ⎦, (16) × ⎣B˜ χ−1 −χK−1 + SE
E
SE
β=0
E
where η−1 (κ +δ)−Lk +β+1(δ + 1)−1 × 1, −Lk + β + 2; SE −1 and χ (δ + 1)−1 × ξ(κ + δ) + −1 SE (κ + δ)(δ + 1) −1 SE −1 1, 1; ξ(κjD + δ) + −1 , with (., .; .) SE (κjD + δ)(δ + 1) denoting the Tricomi confluent hypergeometric function [11, Eq. (9.210.2)]. 2) Probability of Non-Zero Achievable Secrecy Capacity: Since a non-zero secrecy capacity event occurs when the capacity of the wiretap link, CE , falls below the main link’s capacity, CSD , the probability of non-zero achievable secrecy capacity of the minimum selection scheme is expressed by
∞ sec, Pnz, min = Pr(x > y) = FY (x) fX (x) dx, (17) 0
where ∈ {SC, MRC}. For the SC case, (17) can be obtained by making use of (12) and (13), i.e. the CDF and PDF of the RVs y and x, respectively, and taking the integral w.r.t. x. Alternatively, (17) can be computed by substituting δ with 0 in 1 − Psec,SC out,min . The same approach applies in the MRC case.
Using [10], FZ (z|u) and the PDF of u are given by K κ Lk exp − 1S z − δ(u+1) D , FZ (z |u ) = 1 − z + κ Lk LD πjD u exp − . fU (u) = jD jD
1) Secrecy Outage Probability: Based on (10), the secrecy OP is defined as ∞ sec, sec,SC Pout,con= Pr Ccon < R = FZ (δ +(δ+1)w) fW (w)dw. (18) 0
First, we focus on SC case. Let z + 1 and w + 1 denote the numerator and the denominator of the fraction in (10), respectively. In the analysis, we consider the existence of a common RV, given by the channel fading coefficients from the interferers to the destination. From (10), we note that the common RV LD IjD 2 j=1 σn2 |gjD | u, for k = 1, · · · , K, leads to a statistical dependence related to RV z, which raises complexity in deriving the CDF of z. Here, we first apply the conditional statistics on u. Due to the independence among the remaining RVs, the CDF of z conditioned on u is FZ (z |u ) =
K k=1
Iε =
kL k −1
FXk (xk ).
(19)
(20) (21)
j=1
Then, using (19)–(21), and the binomial theorem, we get LD K πjD K μ exp(−kξ z) , (22) FZ (z) = 1− (−1)k−1 jD k (z+κ)kLk(z+ ) j=1 k=1 D where k and μ κ kLk kD . Next, we obtain the PDF of w as jD 1 1 w w fW (w) = + − ε exp(−εw), exp − exp − E E SE SE (23) 1 1 where ε SE + E . Finally, the secrecy OP of the scheme with conventional selection in the SC case is obtained as LD K πjD μ K sec,SC Pout,con = 1− (−1)k−1 I−1 + I−1 − Iε , (24) E SE jD k j=1 k=1
where Iε is given by (25), shown at the bottom of the page. (α) 1 (α) its α th derivative, AkLk −α = ϕ α!(−κ) , ϕ(t) = (t+ ) and ϕ 1 . Using the same approach as in deriving and B = (− +κ)kLk (24), the secrecy OP of the scheme with conventional selection and MRC is obtained as LD K πjD μ K ,MRC Psec = 1− (−1)k−1 exp(−δkξ ) out,con ¯ ¯ k ( − ) SE E j=1 k=1 jD ⎡ ⎤ k −1 kL × ⎣B Q−1 + Q−1 + AkLk −α −1 −−1 ⎦ , (26) SE
B. Conventional Selection Scheme
579
E
SE
α=0
E
−1 × ( + δ)(δ + 1) where Q−1 = 1,1; k( + δ)ξ + −1 SE SE (δ + 1)−1 and −1 = (δ + 1)−1 (κ + δ)−kLk +α+1 × 1, SE −1 . −kLk + α + 2; k(κ + δ)ξ + −1 SE (κ + δ)(δ + 1) 2) Probability of Non-Zero Achievable Secrecy Capacity: For the conventional selection scheme, this metric is given by
∞ sec, Pnz,con = Pr(z > w) = FW (z) fZ (z) dz. (27) 0
In the case of SC, (27) can be computed by use of the CDF in (22) and the PDF in (23), and taking the integral w.r.t. z. Again (27) can be evaluated by setting δ = 0 in 1 − Psec,SC out,con . For the sec ,MRC MRC case, Pnz,con is obtained in a similar way. C. Special Case of Interest Next, we particularize the above results of the secrecy OP to the interference-free scenario as generally assumed in related
AkLk −α ε(δ + 1)−kLk +α (kξ(δ + 1) + ε)kLk −α−1 exp ξ kκ + (δ + κ)ε(δ + 1)−1
α=0 × α−kLk +1, (δ +κ) kξ +ε(δ +1)−1 +B(δ+1)−1ε exp ξ k +(δ + )ε(δ +1)−1 0, (δ + ) kξ +ε(δ+1)−1 . (25)
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Fig. 1. Secrecy outage probability for different numbers of relays (K) and interferers (LD , Lk ); R = 0.5 bit/sec/Hz.
Fig. 2. Probability of non-zero achievable secrecy capacity for different numbers of relays (K) and interferers (LD , Lk ).
works. Setting IjD = 0 (LD = 0) and Iik = 0 (Lk = 0), (14), (16), (24) and (26) simplify to −1 Psec,SC out,min = 1 − exp(−ξ δ) (ξ(δ + 1)SE + 1) +K(ξ(δ + 1)E + K)−1 + ϑ(ξ(δ + 1) + ϑ)−1 , K K sec,SC Pout,con = 1− (−1)k−1 exp(−kδξ ) (E ξ k(δ+1)+1)−1 k k=1 +(SE ξ k(δ + 1) + 1)−1 − ε(ξ k(δ + 1) + ε)−1 ,
dominant factor because the eavesdropper E overhears during both hops to extract information. The plots also illustrate how the performance improves with the number of the relays. The probability of non-zero achievable secrecy capacity is plotted in Fig. 2 for different numbers of relays and interferers. In the low-to-medium SNR range, the probability of non-zero secrecy capacity is almost unity. At high SNRs, the minimum selection scheme yields lower probability of non-zero secrecy capacity. As both figures attest, the conventional selection scheme always outperforms the minimum selection approach.
Psec,MRC K exp(−δξ )(KSE − E )−1 out,min = 1 − −1 −1 −1 −1 × (1+δ)ξ +SE − (1+δ)ξ +KE ,
V. C ONCLUSION This letter investigated the secrecy performance of two relay selection schemes, minimum selection and conventional selection, under security constraints in the presence of external interferences and an eavesdropper implementing SC or MRC combining techniques. Closed-form expressions for two key performance metrics, the probability of non-zero achievable secrecy capacity and the secrecy outage probability, were derived. Numerical results and comparisons were provided, and it was shown that conventional selection outperforms the minimum selection technique.
K exp(−kδξ ) k k=1 −1 −1 −1 . × (1+δ)kξ +−1 − (1+δ)kξ + E SE
Psec,MRC out,con = 1 −
K
(−1)k−1 (SE − E )−1
These results help understand how noise at the relays and the destination affect performance (see discussions in Section IV). IV. N UMERICAL R ESULTS AND C OMPARISONS The performance of the relay selection schemes, minimum (min) and conventional (con), for the two combining techniques, SC and MRC, is compared based on the previous analysis and simulations (shown with markers in the figures). Fig. 1 depicts the secrecy OP versus SNR, for different numbers of relays (K) and interferers (LD , Lk ). The agreement between the analytical results (using (14), (16), (24) and (26)) and simulations is attested. For the minimum selection scheme, the MRC and SC curves overlap, which means that it makes no difference for node E to employ SC or MRC since both yield almost the same secrecy OP. For the minimum selection scheme, SC is a better choice for its lower implementation complexity. For the conventional selection scheme, when E employs MRC the secrecy OP aggravates compared to the SC case. As observed from the figure, the two combining methods give the same results at low SNRs, and no more than 7 × 103 difference at high SNRs, which implies that due to the trade-off between complexity and performance, employing MRC may not be justified. In Fig. 1, the performance of the interference-free network is also included. In the ideal no-CCI case, for low values of PS and Pk , the effect of the noise power on performance is highlighted. For high values of PS , the effect of noise is negligible. The CCI induces performance degradation especially at high SNRs. Although higher SNR provides better performance (lower OP), it also increases the amount of information leakage, which is the
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