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Abstract

We study opportunistic decode-and-forward relaying transmission in cooperative cluster-based wireless sensor networks (WSNs) with secrecy constraints, where a passive eavesdropper may overhear the source message. To deal with this problem, we consider the novel opportunistic relay section cooperative transmission for the cluster configuration of WSNs. The system performance in terms of the secrecy outage probability and the probability of nonzero secrecy capacity are analyzed and the exact closed-form expressions are derived over Rayleigh fading channels. Furthermore, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order. Finally, numerical results are presented to verify the theoretical analysis and depict that node cooperation has a great potential to enhance physical layer security against eavesdropping.

1. Introduction

In recent years, wireless sensor networks (WSNs) have gained worldwide attention for use in different applications, such as military target tracking and surveillance, natural disaster relief, biomedical health monitoring, and industrial automation. Because of the low computational capabilities of wireless motes, their limited battery lifetime, and the broadcast nature of wireless communication, WSNs present significant challenges in designing security schemes [1]. Especially the distribution of the key and the high computational complexity of the traditional cryptographic techniques are at the heart of any security design.

In the last decade, physical layer security (PLS) was drawing a lot of attentions as an alternative technique to achieve secure communication by exploiting the physical characteristics of wireless channels. This work was pioneered by Shannon in [2] and further extended by Wyner in [3]. To improve physical layer security of wireless transmissions, some recent works were proposed by exploiting cooperative diversity [4]. The achievable secrecy rates in cooperative relaying schemes using amplify-and-forward (AF) and decode-and-forward (DF) protocols have been investigated in [5–7], respectively. The secrecy outage performance for DF relay beamforming scheme is considered in [8]. Almost all of the above works are under the assumption that the eavesdropper's channel state information (CSI) is known at the transmitter. Clearly this assumption is sometimes impractical, such as the case of passive eavesdropping, where the instantaneous CSI of the eavesdropper's channel is not available at the transmitter and only an estimation of the average channel gains can be performed. The authors of [9] have proposed a joint cooperative beamforming and jamming scheme to enhance the security of an AF cooperative relay network without the CSI of eavesdropper. The proposed relay selection scheme in [10] selects a trusted relay to assist the secondary transmitter and maximize the achievable secrecy rate for cooperative cognitive networks. Considering no knowledge of the eavesdropper channels is available at the transmitter, the authors in [11] investigate the secrecy outage performance of conventional relay selection scheme. Specially, [11] only focuses on the high SNR regime where all the relay nodes successfully decode the source transmission. Different from [11], the other secrecy performance, that is, the intercept probability and secrecy diversity order, has been derived for several of AF and DF relay selection schemes without any knowledge of the eavesdropper channels in [12]. However, most of previous works focus on general cooperative communication scenario; thus, the security transmission strategy and analysis framework should be modified a lot in cooperative WSNs. On the other hand, cooperative transmission or virtual MIMO has been explored to increase the energy efficiency and improve the reliability of cluster-based WSNs [13, 14]. To the best of our knowledge, there are very few works making use of cooperative transmission to enhance the wireless security against eavesdropping attack in WSNs. In addition, the above observations raise two questions: (1) can cooperative transmission improve the secrecy performance for cluster-based WSNs? (2) How to design the optimal cooperative transmission scheme to enhance the wireless security for cluster-based WSNs?

To address these questions, we study physical layer security transmission in cooperative clustered WSNs in presence of a passive eavesdropper. In order to achieve cooperative diversity to enhance physical layer security, we design a novel opportunistic relay selection cooperative transmission scheme through exploiting the special cluster configuration of WSNs, which includes two time slots: the Intracluster Slot, used for data sharing within the cluster, and the Cooperation Slot, used for transmission from the best node chosen in cluster to the date gathering node faraway. Different from the conventional relay selection scheme, our proposed cooperative transmission scheme chooses the best node among the source and the capable decoding nodes considering the special structure of clustered WSNs. The exact closed-form expressions of the secrecy outage probability and the probability of nonzero secrecy capacity for our opportunistic relay selection cooperative transmission are derived over Rayleigh fading channels. Furthermore, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order performance and shows the secrecy diversity order as $N + 1$ , where N is the number of relay nodes. Finally, numerical results are presented to verify the theoretical analysis and depict that node cooperation not only improves the transmission reliability and coverage performance of WSNs but also has a great potential to enhance physical layer security against eavesdropping.

2. System and Channel Model

We consider a clustered WSN with sensors grouped in cooperative clusters (see Figure 1), similar to [12]. Throughout this paper, we consider that there are one source-destination pair (S and D), one eavesdropper E, and N relays, where all nodes are equipped with a single antenna. Such a scenario has applications in wireless sensor networks [13, 14]. Quasistatic fading has been assumed. $h_{D 0}$ and $h_{E 0}$ denote the channel coefficient between the source and the destination and between the source and the eavesdropper, respectively. $h_{R i}$ , $h_{D i}$ , and $h_{E i}$ ( $i = 1, \dots, N$ ) denote the channel coefficients between the source and the ith relay, between the ith relay and the destination, and between the ith relay and the eavesdropper, respectively. We assume that $h_{D 0}$ , $h_{E 0}$ , $h_{R i}$ , $h_{D i}$ , and $h_{E i}$ ( $i = 1, \dots, N$ ) are the independent Raleigh fading coefficients with average power gains $λ_{D 0}$ , $λ_{E 0}$ , $λ_{R i}$ , $λ_{D i}$ , and $λ_{E i}$ , respectively. To simplify the derivation, the received noises at all nodes are assumed as zero-mean additive white Gaussian noise (AWGN) with variance of $N_{0}$ .

Figure 1

Cooperative transmission in clustered wireless sensor networks.

Clustering of sensor nodes is carried out following the opportunistic DF relaying transmission scheme against eavesdropping attacks. When a sensor node has confidential data to transmit, it first broadcasts these data within its cluster, and the other nodes in the cluster decode the received signals. Next, the source and the decodable nodes as relays will act together and perform opportunistic DF relaying scheme, in which the node with the best SNR to the destination among the source and the decodable relays is selected to retransmit/forward the signal encoded by the widely adopted wiretap code [3]. Noticing that, during the first slot, the source talks to the surrounding relays with low power, whereas the destination and eavesdropper are far away from the source and relays and cannot hear such a transmission, and the eavesdropper only can hear the signals in the second slot. We consider a passive eavesdropper, as such the CSI of the eavesdropper's channel is not known at the source and relays. Thus, from eavesdropper's point of view, the optimum node selection for main channel in the second slot is a random node selection for the eavesdropper channel, as the main channel and the eavesdropper channel are uncorrelated.

In the first slot, the source node broadcasts its confidential message with the power $P_{1}$ , and the other nodes in the cluster try to decode the received signal. The instantaneous capacity between the source and the ith relay can be given by

\begin{matrix} C_{S R_{i}} = \frac{1}{2} lo g_{2} (1 + γ_{S R_{i}}), \end{matrix}

(1)

where

γ_{S R_{i}} = P_{1} {|h_{R i}|}^{2} / N_{0}

. The capacity is halved because two time slots are required for completing the whole transmission.

When the capacity is larger than a targeted secrecy data rate $R_{S}$ , that is, $C_{S R_{i}} > R_{S}$ , $R_{i}$ is able to decode the received signals successfully [4, 5]. Given N relays, there are $2^{N}$ possible S-R pair combinations from the full set $R = \{R_{1}, \dots, R_{N}\}$ ; thus, the resultant successful decoding set $D$ is given by

\begin{matrix} D \in \{ϕ, D_{1}, D_{2}, \dots, D_{n}, \dots, D_{2^{N - 1}}\}, \end{matrix}

(2)

where ϕ represents an empty set, while

D_{n}

is the nth nonempty subset.

Without loss of generality, because the source and relays locate in the same cluster and are close to each other, we assume that all subchannels from the source to the relays and from the relays to the destination or the eavesdropper are symmetrical; that is, $λ_{R i} = λ_{R}$ , $λ_{E i} = λ_{E}$ , and $λ_{D i} = λ_{D}$ , for all $i = 1, \dots, N$ . Thus, $\Pr \{R_{i} \in D\}$ is exactly the same for all i. Denote the cardinality of the successful decoding set $D$ by $|D|$ ; then, according to the binomial law, we can obtain

\begin{matrix} \Pr (|D| = k) = (\begin{pmatrix} N \\ k \end{pmatrix}) {(1 - \exp (- \frac{θ_{1}}{{\bar{γ}}_{S R}}))}^{N - k} \exp (- \frac{k θ_{1}}{{\bar{γ}}_{S R}}), \end{matrix}

(3)

where

θ_{1} = 2^{2 R_{S}} - 1

and

{\bar{γ}}_{S R} = P_{1} λ_{R} / N_{0}

In order to reduce complexity but still realize the potential benefits of multiple-relay cooperation for cooperative clustered WSNs, relay selection techniques designed for general cooperative communication scenario in [11] may have emerged as a promising solution. However, different from the conventional relay selection scheme in [11], our proposed cooperative transmission scheme has some modification aiming to the special structure of clustered WSNs. If the decoding set is empty, that is, $|D| = 0$ , since no relay node succeeds in perfectly decoding the received signals, all relays will remain silent and the source retransmits the confidential message with the power $P_{2}$ ; if the successful decoding set $D$ is nonempty, the best node among the source and the capable decoding nodes will be chosen to forward or retransmit the confidential message with the power $P_{2}$ . Obviously, our cooperative transmission scheme make use of the clustered architecture of WSNs and can achieve more cooperative diversity gain, which is also verified by the theoretical analysis and simulation results later.

Thus, if the source retransmits the confidential message, the corresponding instantaneous channel capacity of the S-D link and S-E link is given, respectively, by

\begin{matrix} C_{D 0} = \frac{1}{2} lo g_{2} (1 + γ_{S D}), \end{matrix}

(4)

\begin{matrix} C_{E 0} = \frac{1}{2} lo g_{2} (1 + γ_{S E}), \end{matrix}

(5)

where

γ_{S D} = P_{2} {|h_{D 0}|}^{2} / N_{0}

and

γ_{S E} = P_{2} {|h_{E 0}|}^{2} / N_{0}

If the ith relay is selected and forwarded the confidential message, the corresponding instantaneous channel capacity of the $R_{i}$ -D link and $R_{i}$ -E link is given, respectively, by

\begin{matrix} C_{D i} = \frac{1}{2} lo g_{2} (1 + γ_{R_{i} D}), \end{matrix}

(6)

\begin{matrix} C_{E i} = \frac{1}{2} lo g_{2} (1 + γ_{R_{i} E}), \end{matrix}

(7)

where

γ_{R_{i} D} = P_{2} {|h_{D i}|}^{2} / N_{0}

and

γ_{R_{i} E} = P_{2} {|h_{E i}|}^{2} / N_{0}

Hence, combining 4, 5, 6, and 7, the instantaneous secrecy rate is given by [13] as follows:

\begin{matrix} C_{s} = \{\begin{cases} {[C_{D 0} - C_{E 0}]}^{+}, & if S retransmit \\ {[C_{D i} - C_{E i}]}^{+}, & if R_{i} forward, \end{cases} \end{matrix}

(8)

where

{[x]}^{+}

denotes

\max (0, x)

3. Exact Secrecy Performance Analysis

The secrecy outage probability is defined as the probability that the achievable secrecy rate is less than a given secrecy transmission rate $R_{S}$ [15]. Based on the data transmission and our proposed relay selection scheme in previous section, using the law of total probability, the SOP can be formulated as

\begin{array}{l} P_{so} (R_{S}) \\ = \sum_{k = 0}^{N} \Pr (|D| = k) \Pr (C_{s} < R_{S} | |D| = k) \\ = \underset{P_{so}^{1} (R_{S})}{\underset{︸}{\Pr (|D| = 0) \Pr ({[C_{D 0} - C_{E 0}]}^{+} < R_{S})}} \\ + \underset{P_{so}^{2} (R_{S})}{\underset{︸}{\Pr (|D| > 0) \Pr ({[C_{D 0} - C_{E 0}]}^{+} < R_{S} | |D| > 0, S retransmit)}} \\ + \underset{P_{so}^{3} (R_{S})}{\underset{︸}{\Pr (|D| > 0) \Pr ({[C_{D i} - C_{E i}]}^{+} < R_{S} | |D| > 0, R_{i} forward)}}, \end{array}

(9)

where

P_{so}^{1} (R_{S})

denotes the secrecy outage probability when the decoding set is empty and the source retransmits the confidential message,

P_{so}^{2} (R_{S})

denotes the secrecy outage probability when the successful decoding set is nonempty but the source is chosen to retransmit the confidential message, and

P_{so}^{3} (R_{S})

denotes the secrecy outage probability when the successful decoding set is nonempty but the best relay is chosen to forward the confidential message.

For $|D| = 0$ , $P_{so}^{1} (R_{S})$ can be rewritten as

\begin{array}{l} P_{so}^{1} (R_{S}) = \Pr (|D| = 0) \Pr (\frac{1 + γ_{S D}}{1 + γ_{S E}} < θ_{2}) \\ = \Pr (|D| = 0) \int_{0}^{\infty} f_{γ_{S E}} (z) F_{γ_{S D}} (θ_{2} (1 + z) - 1) d z \\ = {(1 - \exp (- \frac{θ_{1}}{{\bar{γ}}_{S R}}))}^{N} \\ \times (1 - \frac{{\bar{γ}}_{S D}}{θ_{2} {\bar{γ}}_{S E} + {\bar{γ}}_{S D}} \exp (- \frac{θ_{2} - 1}{{\bar{γ}}_{S D}})), \end{array}

(10)

where

{\bar{γ}}_{S D} = P_{1} λ_{D 0} / N_{0}

{\bar{γ}}_{S E} = P_{1} λ_{E 0} / N_{0}

, and

θ_{2} = 2^{2 R_{S}}

For $|D| = k > 0$ , the source retransmits the confidential message when $γ_{S D} > γ_{R D} = \max \{γ_{R_{1} D}, γ_{R_{2} D}, \dots, γ_{R_{k} D}\}$ . Considering that the CDF of $γ_{R D}$ is $F_{γ_{R D}} (x) = {(1 - \exp (- x / {\bar{γ}}_{R D}))}^{k}$ , $P_{so}^{2} (R_{S})$ can be rewritten as

\begin{array}{l} P_{so}^{2} (R_{S}) \\ = \sum_{k = 1}^{N} \Pr (|D| = k) \Pr (\frac{1 + γ_{S D}}{1 + γ_{S E}} < θ_{2}, γ_{S D} > γ_{R D}) \\ = \sum_{k = 1}^{N} \Pr (|D| = k) \int_{0}^{\infty} \int_{0}^{θ_{2} (1 + γ_{S E}) - 1} f_{γ_{S E}} (γ_{S E}) F_{γ_{R D}} (γ_{S D}) f_{γ_{S D}} \\ \times (γ_{S D}) d γ_{S D} d γ_{S E} \\ = \sum_{k = 1}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) {(1 - \exp (- \frac{θ_{1}}{{\bar{γ}}_{S R}}))}^{N - k} \exp (- \frac{k θ_{1}}{{\bar{γ}}_{S R}}) \\ \times \sum_{m = 0}^{k} {(- 1)}^{m} (\begin{pmatrix} k \\ m \end{pmatrix}) \\ \times \frac{{\bar{γ}}_{R D}}{{\bar{γ}}_{R D} + m {\bar{γ}}_{S D}} [1 - \frac{{\bar{γ}}_{R D} {\bar{γ}}_{S D}}{θ_{2} {\bar{γ}}_{S E} ({\bar{γ}}_{R D} + m {\bar{γ}}_{S D}) + {\bar{γ}}_{R D} {\bar{γ}}_{S D}} \\ \times e^{- (({\bar{γ}}_{R D} + m {\bar{γ}}_{S D}) / {\bar{γ}}_{R D} {\bar{γ}}_{S D}) θ_{2}}] . \end{array}

(11)

On the other hand, for $|D| = k > 0$ , if the ith relay is selected and forwards the confidential message when $γ_{S D} < γ_{R D} = γ_{R_{i} D} = \max \{γ_{R_{1} D}, γ_{R_{2} D}, \dots, γ_{R_{k} D}\}$ , then $P_{so}^{3} (R_{S})$ can be rewritten as

\begin{array}{l} P_{so}^{3} (R_{S}) \\ = \sum_{k = 1}^{N} \Pr (|D| = k) \Pr (\frac{1 + γ_{R_{i} D}}{1 + γ_{R_{i} E}} < θ_{2}, γ_{S D} < γ_{R D}) \\ = \sum_{k = 1}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) {(1 - \exp (- \frac{θ_{1}}{{\bar{γ}}_{S R}}))}^{N - k} \exp (- \frac{k θ_{1}}{{\bar{γ}}_{S R}}) \\ \times \{\sum_{n = 0}^{k} (\begin{pmatrix} k \\ n \end{pmatrix}) {(- 1)}^{n} \\ \times (\frac{{\bar{γ}}_{R D} \exp (- (n (2^{R_{S}} - 1) / {\bar{γ}}_{R D}))}{θ_{2} n {\bar{γ}}_{R E} + {\bar{γ}}_{R D}} \\ - \frac{{\bar{γ}}_{R D} {\bar{γ}}_{S D} \exp (- (({\bar{γ}}_{R D} + n {\bar{γ}}_{S D}) / {\bar{γ}}_{R D} {\bar{γ}}_{S D}) θ_{2})}{θ_{2} {\bar{γ}}_{R E} ({\bar{γ}}_{R D} + n {\bar{γ}}_{S D}) + {\bar{γ}}_{R D} {\bar{γ}}_{S D}}) \\ - \sum_{m = 0}^{k} (\begin{pmatrix} k \\ m \end{pmatrix}) {(- 1)}^{m} \frac{{\bar{γ}}_{R D}}{{\bar{γ}}_{R D} + m {\bar{γ}}_{S D}} \\ \times  ( 1  -  \frac{{\bar{γ}}_{R D} {\bar{γ}}_{S D} \exp ( - (({\bar{γ}}_{R D}  +  m {\bar{γ}}_{S D})  / {\bar{γ}}_{R D} {\bar{γ}}_{S D}) θ_{2})}{θ_{2} {\bar{γ}}_{R E} ({\bar{γ}}_{R D} +  m {\bar{γ}}_{S D}) + {\bar{γ}}_{R D} {\bar{γ}}_{S D}} ) \} . \end{array}

(12)

By combining 10, 11, and 12, the exact closed-form expressions of the secrecy outage probability are shown as

\begin{array}{l} P_{out} (R_{S}) \\ = \sum_{k = 0}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) {(1 - \exp (- \frac{θ_{1}}{{\bar{γ}}_{S R}}))}^{N - k} \\ \times \exp (- \frac{k θ_{1}}{{\bar{γ}}_{S R}}) \sum_{n = 0}^{k} (\begin{pmatrix} k \\ n \end{pmatrix}) {(- 1)}^{n} \\ \times (\frac{{\bar{γ}}_{R D} \exp (- (n θ_{2} / {\bar{γ}}_{R D}))}{θ_{2} n {\bar{γ}}_{R E} + {\bar{γ}}_{R D}} \\ - \frac{{\bar{γ}}_{R D} {\bar{γ}}_{S D} \exp (- (({\bar{γ}}_{R D} + n {\bar{γ}}_{S D}) / {\bar{γ}}_{R D} {\bar{γ}}_{S D}) θ_{2})}{θ_{2} {\bar{γ}}_{R E} ({\bar{γ}}_{R D} + n {\bar{γ}}_{S D}) + {\bar{γ}}_{R D} {\bar{γ}}_{S D}}) . \end{array}

(13)

The secrecy outage probability expression in 13 is derived in closed-form and is useful to evaluate the impacts of the transmit power and the number of relays on the secrecy performance of cooperative clustered WSNs.

In addition, we note that 13 is useful to calculate other secrecy metrics, such as the probability of nonzero secrecy capacity discussed in [15]. As is known, positive secrecy is achievable when the mail link between legitimate users has better propagation conditions than the wiretap link from the legitimate users to eavesdropper. Thus, the probability of nonzero secrecy capacity for our opportunistic relaying transmission scheme is obtained as

\begin{array}{l} P_{r} (C_{S} > 0) \\ = 1 - P_{out} (0) \\ = \sum_{k = 0}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) {(1 - e^{- (θ_{1} / {\bar{γ}}_{S R})})}^{N - k} e^{- (k θ_{1} / {\bar{γ}}_{S R})} \sum_{n = 0}^{k} (\begin{pmatrix} k \\ n \end{pmatrix}) {(- 1)}^{n} \\ \times (\frac{{\bar{γ}}_{R D}}{n {\bar{γ}}_{R E} + {\bar{γ}}_{R D}} - \frac{{\bar{γ}}_{R D} {\bar{γ}}_{S D}}{{\bar{γ}}_{R E} ({\bar{γ}}_{R D} + n {\bar{γ}}_{S D}) + {\bar{γ}}_{R D} {\bar{γ}}_{S D}}) . \end{array}

(14)

4. Asymptotic Behavior and Secrecy Diversity Gain

In this section, we turn our attention to the asymptotic analysis to characterize the behavior of secrecy outage probability when the average SNR of the main channel is sufficiently high. The asymptotic result will enable us to explicitly examine the impact of opportunistic relaying transmission on the secrecy performance in terms of the secrecy outage diversity order, which is the slope of the secrecy outage probability curve, describes how fast the secrecy outage probability decreases with the increase of the average SNR.

Without loss of generality, let $P_{1} = ε P_{2} = P$ , $λ_{E 0} = λ_{E i} = λ_{E}$ , and $λ_{D 0} = λ_{D i} = λ_{D}$ , for all $i = 1, \dots, N$ . Then, we will investigate the asymptotic behavior of the SOP by two special cases.

( 1) Case of $P \to \infty$ . This case corresponds to the scenario where the nodes in the cooperative WSNs can increase their transmit power significantly. Due to $P \to \infty$ , $γ_{S R_{i}} = P_{1} {|h_{R i}|}^{2} / N_{0} \to \infty$ , which means all the relays can successfully decode the message; that is, $|D| = N$ . Thus, the secrecy outage probability for $P \to \infty$ can be rewritten as

\begin{array}{l} P_{out}^{P \to \infty} (R_{S}) \\ = \lim_{P \to \infty} P_{out} (R_{S}) \\ = \Pr (γ_{R D} < γ_{S D} < θ_{2} γ_{S E} | |D| = N) \\ + \Pr (γ_{S D} < γ_{R D} < θ_{2} γ_{R E} | |D| = N) \\ = \Pr (\max \{{|h_{D 1}|}^{2}, {|h_{D 2}|}^{2}, \dots, {|h_{D N}|}^{2}\} \\ < {|h_{D 0}|}^{2} < θ_{2} {|h_{E 0}|}^{2} | |D| = N) \\ + \Pr ({|h_{D 0}|}^{2} < \max \{{|h_{D 1}|}^{2}, {|h_{D 2}|}^{2}, \dots, {|h_{D N}|}^{2}\} \\ < θ_{2} {|h_{E i}|}^{2} | |D| = N) . \end{array}

(15)

Considering that ${|h_{D i}|}^{2}$ and ${|h_{E i}|}^{2}$ , $i = 0, \dots, N$ , are the independent exponentially distributed variables with parameters $λ_{D}$ and $λ_{E}$ , respectively, 15 can be computed as

\begin{array}{l} P_{out}^{P \to \infty} (R_{S}) \\ = \sum_{k = 0}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) \frac{{(- 1)}^{k}}{(k + 1)} [1 - \frac{λ_{D}}{θ_{2} (k + 1) λ_{E} + λ_{D}}] \\ + \sum_{k = 0}^{N} (\begin{pmatrix} N \\ k \end{pmatrix}) \frac{{(- 1)}^{k} λ_{D}}{θ_{2} k λ_{E} + λ_{D}} \\ - N \sum_{l = 0}^{N - 1} (\begin{pmatrix} N - 1 \\ l \end{pmatrix}) \frac{{(- 1)}^{l}}{l + 2} [1 - \frac{λ_{D}}{θ_{2} (l + 2) λ_{E} + λ_{D}}] . \end{array}

(16)

Base on 16, it is worthy that increase of transmit power will not always lead to the improvement of secrecy performance, which is significantly different from the traditional wireless communication systems. Obviously, the SOP is independent of the transmit power in the high transmit power, and the secure outage probability is converge to constant values as the performance floors. Thus, the traditional diversity order [16], which characterizes the slope of bit error rate (BER) curve as SNR tends to infinity, is not applicable to measure the secrecy performance.

( 2) Case of $λ_{R} = β λ_{D} = λ \to \infty$ . This case corresponds to the scenario where the relays are close to the source, which corresponds to the scenario where the source and relays locate in the same cluster, and the destination is located much closer to the relays than the eavesdropper, which is a practical scenario of interest [15]. Due to $λ_{R} = β λ_{D} = λ \to \infty$ , ${\bar{γ}}_{S R} = P_{1} λ_{R} / N_{0} \to \infty$ which means all the relays can successfully decode the message; that is, $|D| = N$ . For a given $λ_{E}$ , the secrecy outage probability in high λ regime can be rewritten as

\begin{array}{l} P_{out}^{λ \to \infty} (R_{S}) \\ = \lim_{λ \to \infty} P_{out} (R_{S}) \\ = \lim_{λ \to \infty} \Pr (γ_{R D} < γ_{S D} < θ_{2} γ_{S E} | |D| = N) \\ + \Pr (γ_{S D} < γ_{R D} < θ_{2} γ_{R E} | |D| = N) \\ = \lim_{λ \to \infty} \int_{0}^{\infty} \int_{0}^{θ_{2} y} {[1 - \exp (- \frac{x}{λ_{D}})]}^{N} \frac{1}{λ_{D}} \\ \times \exp (- \frac{x}{λ_{D}}) \frac{1}{λ_{E}} \exp (- \frac{y}{λ_{E}}) d x d y \\ + \int_{0}^{\infty} \int_{0}^{θ_{2} y} [1 - \exp (- \frac{x}{λ_{D}})] N {[1 - \exp (- \frac{x}{λ_{D}})]}^{N - 1} \\ \times \frac{1}{λ_{D}} \exp (- \frac{x}{λ_{D}}) \frac{1}{λ_{E}} \exp (- \frac{y}{λ_{E}}) d x d y . \end{array}

(17)

Using $\lim_{z \to 0} [1 - \exp (- z)] = z$ and $\lim_{z \to 0} \exp (- z) = 1$ , we can obtain

\begin{matrix} P_{out}^{λ \to \infty} (R_{S}) = (N + 1)! θ_{2}^{N + 1} {(\frac{λ}{λ_{E}})}^{- N + 1} . \end{matrix}

(18)

From 18, we can observe that the SOP $P_{out}^{\infty} (R_{S})$ behaves as $(1 / λ)^{N + 1}$ as $λ \to \infty$ . To provide an insight into the impact of the number of the relays on secrecy performance, we investigate the generalized secrecy diversity order introduced in [12]. Similar to [12], a generalized secrecy diversity order of our proposed opportunistic relaying transmission scheme can be defined as

\begin{matrix} d_{secure} = - \lim_{λ \to \infty} \frac{\log (P_{out}^{λ \to \infty} (R_{S}))}{\log (λ)} = N + 1, \end{matrix}

(19)

which shows that the secrecy diversity order is the same as the number of nodes in the cooperative cluster including relays and source node, revealing the fact that full secrecy diversity is achieved by the proposed opportunistic relaying transmission scheme. In contrast, by increasing the number of nodes in the cooperative cluster, the SOP will decrease at a faster speed. Therefore, exploiting cooperative transmission can effectively improve the secrecy performance for cluster-based WSNs.

5. Numerical Results

This section presents the numerical results to examine the impacts of the average SNRs and the number of relays on the secrecy performance. We see from the figures that the exact curves precisely agree with the simulations, which validate the accuracy of our analytical results. In all cases, $R_{S} = 0.5 bits / s / Hz$ , and $ε = 0.1$ . Most importantly, we compare the secrecy performance of our opportunistic relaying transmission scheme (ORT) with the conventional relay selection scheme (CRS) in [11], which only focuses on the high SNR regime and assumes that all the relay nodes can successfully decode the source transmission.

Figure 2 depicts the impact of the average SNR $\bar{γ} = P / N_{0}$ on the exact secrecy outage probability and the asymptotic secrecy outage probability according to 13 and 16 with different number of relays $N = 2,3, 4$ . We see there is a pronounced decrease in the SOP with increasing N. This can be explained by the fact that N exerts an increasing effect on the secrecy diversity order via its proportional contribution. For a given $R_{S}$ , increasing the average SNR $\bar{γ}$ leads to a different increase in the shape of the secrecy outage probabilities for different N in low and medium SNR regimes. Specially, as $\bar{γ} \to \infty$ , the curves for different N have the same slope. This is due to the fact that the secrecy performance is limited by the second hop and then converges to constant values as the performance floors. In addition, due to the SOP being independent of the transmit power in the high transmit power, the traditional diversity order [16], as SNR tends to infinity, is not applicable to measure the secrecy performance.

Figure 2

Secrecy outage probability versus $\bar{γ}$ .

In Figure 3, the impact of $λ_{R} = β λ_{D} = λ$ on the SOP with different number of relays $N = 2,4$ is illustrated. We assume that the average SNR $\bar{γ} = P / N_{0} = 1 dB$ , $β = 10$ , and $λ_{E} = 1$ , and the relays are close to the source; that is, $λ_{R} \to \infty$ , which results in all the relay nodes successfully decoding the source transmission similar to [11]. We further plot asymptotic curves to predict the secrecy diversity order. As can be seen from the corresponding curves, the asymptotic analysis efficiently approximates the convergence of the exact secrecy outage probability and this observation validates our analysis for the high λ regime. For a given $R_{S}$ , increasing λ leads to a different increase in the shape of the secrecy outage probabilities for different transmission schemes and different N. In addition, we can see that the secrecy outage probability of our ORT scheme is strictly lower than that of the CRS scheme corresponding to $N = 2,4$ , respectively, which can be explained that the achievable secrecy diversity order of our ORT scheme is $N + 1$ rather than N achieved by the CRS scheme without exploiting the source-destination link in the second slot in [11].

Figure 3

Secrecy outage probability versus λ.

6. Conclusions

In this paper, we investigate the physical layer security in cooperative clustered WSNs in presence of a passive eavesdropper. In order to exploit the cluster configuration of WSNs, we propose the novel opportunistic relay section cooperative transmission to enhance physical layer security. The exact closed-form expression of the secrecy outage probability for the opportunistic decode-and-forward relaying transmission scheme is derived over Rayleigh fading channels. In addition, the asymptotic behavior of the secrecy outage probability and the secrecy diversity order are discussed via two special cases. Both theoretical analysis and numerical results depict that node cooperation not only improves the transmission reliability and coverage performance of WSNs but also has great potential to enhance physical layer security against eavesdropping, and the achievable secrecy diversity order of our opportunistic relaying transmission scheme is $N + 1$ rather than N achieved by the conventional relay selection scheme without exploiting the cluster structure in the second slot in [11].

Footnotes

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (no. 61371122 and no. 61471393) and the China Postdoctoral Science Foundation under a Special Finance Foundation (no. 2013T60912).

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Cooperative Transmission for Security Enhancement in Clustered Wireless Sensor Networks

Abstract

1. Introduction

2. System and Channel Model

3. Exact Secrecy Performance Analysis

4. Asymptotic Behavior and Secrecy Diversity Gain

5. Numerical Results

6. Conclusions

Footnotes

Conflict of Interests

Acknowledgments

References