Wireless Personal Communications

, Volume 75, Issue 1, pp 665–685 | Cite as

A New Relay and Jammer Selection Schemes for Secure One-Way Cooperative Networks

  • Doaa H. Ibrahim
  • Emad S. Hassan
  • Sami A. El-Dolil
Article

Abstract

This paper presents different relay and jammer selection schemes for one-way cooperative networks to increase the security against malicious eavesdroppers. We consider a single source-destination cooperative network with multiple intermediate nodes and one or more eavesdroppers. The selection in the proposed schemes is made with the presence of direct links and the assumption that the broadcast phase is unsecured. The proposed schemes select three intermediate nodes. The first selected node operates in the conventional relay mode and assists the source to deliver its data to the corresponding destination via a Decode-and-Forward strategy. The second and third selected nodes are used in different communication phases as jammers to create intentional interference at the eavesdroppers’ nodes. Moreover, a hybrid scheme which switches between jamming and non-jamming modes is introduced in this paper. The proposed schemes are analyzed in terms of ergodic secrecy capacity and secrecy outage probability. Extensive analysis and a set of simulation results are presented to demonstrate the effectiveness of the different schemes presented in this work. The obtained results show that the proposed schemes with jamming outperform the conventional non-jamming schemes and the hybrid switching scheme further improves the secrecy capacity. The impact of changing both the eavesdroppers and the relays location on ergodic secrecy capacity and secrecy outage probability is also discussed. Finally, the impact of the presence of multiple eavesdroppers is studied in this paper.

Keywords

Relay and jammer selection Cooperative networks Security 

1 Introduction

Information privacy in wireless networks has been taken a considerable attention for several years due to the broadcast nature of the wireless medium which allows all users in the coverage area of a transmission to overhear the source message. Traditionally, security in wireless networks has been mainly focused on higher layers using cryptographic methods [1]. However, as the implementation of secrecy at higher layers becomes the subject of increasing potential attacks, physical (PHY) layer based security has drawn increasing attention recently [2, 3, 4, 5, 6]. The main objective of PHY-based approaches is to enable source and destination exchanging secure messages at a non-zero rate when the eavesdropper channel is a degraded version of the main channel. In [7] joint optimal power control and optimal scheduling schemes were proposed to enhance the secrecy rate of the intended receiver against cooperative and non-cooperative eavesdropping models. In [8] decode and forward (DF) cooperative protocol was considered to improve the performance of secure wireless communications in the presence of one or more eavesdroppers. The interaction of the cooperative diversity concept with secret communications has also recently been reported as an interesting solution [9, 10, 11]. In [12] the authors proposed a variety of cooperative schemes to achieve secure data transmission with the help of multiple relays in the presence of one or multiple eavesdroppers. In [13] a four-node model was proposed and it was shown that if the relay is closer to the destination than the eavesdropper, a positive secrecy rate can be achieved even if the source-destination rate is zero. In [14] some relay selection metrics have been proposed with different levels of feedback overhead. The authors in [15] extended the work presented in [14] for cooperative networks with jamming protection without taking direct links into account. In [16, 17] different relay selection strategies were introduced for improving the secrecy rate in [14]. In [18, 19, 20] jamming schemes which produce an artificial interference at the eavesdropper node in order to reduce the capacity of the related link seem to be an interesting approach for practical applications. In [21] the interaction between relay and jammer is introduced as a non-cooperative game where both nodes have conflicting objectives and the Nash equilibrium (NE) of the system was derived.

The main contribution of this paper is to investigate relay and jammer selection schemes to increase one-way cooperative networks security in the presence of one or more eavesdroppers. In contrast to [15], the selection in the proposed schemes is made with the presence of direct links, the assumption that broadcast phase is unsecured, and when one or more eavesdroppers are present in the system. We consider a single source-destination cooperative network with one or more eavesdroppers and multiple intermediate nodes to increase security against malicious eavesdroppers. In the proposed schemes an intermediate node is selected to operate in the conventional DF relay mode and assists the source to deliver data to the corresponding destination. Meanwhile, another two intermediate nodes that perform as jamming nodes are selected and transmit artificial interference in order to degrade the eavesdroppers’ links in the first and second phase of data transmission, respectively. The proposed schemes are analyzed for different complexity requirements based on global instantaneous knowledge of all links and average knowledge of the eavesdroppers’ links. The obtained results reveal that the proposed schemes with cooperative jamming can improve the secrecy capacity and the secrecy outage probability of the cooperative network. In addition to the investigation of these jamming-based selection schemes, we show that jamming is not always beneficial for security. According to this observation, a switching scheme between jamming and non-jamming relay selection is proposed. This hybrid scheme overcome jamming limitations and seems to be efficient solutions for practical application with critical secrecy constraints. Moreover, the impact of changing both the eavesdroppers and the relays location on the system performance is also discussed in this paper. Finally, the impact of the presence of multiple eavesdroppers is studied.

The rest of this paper is organized as follows. Section 2 introduces the system model and formulates the problem. Section 3 presents the proposed selection schemes. Numerical results are shown and discussed in Sect. 4, followed by concluding remarks in Sect. 5.

2 System Model and Problem Formulation

In this paper two different scenarios of eavesdropper are considered. The first scenario discusses the effect of presence of one eavesdropper while the second scenario studies the effect of presence more eavesdroppers on cooperative network as follows.

2.1 The Presence of One Eavesdropper

2.1.1 System Model

We consider a single source-destination cooperative network with one eavesdropper \(E\) and an intermediate node set \(\mathrm{{S}}_\mathrm{relay }= \{1, 2, \ldots , N \}\) with \(N\) nodes as shown in Fig. 1. The intermediate nodes operate in half duplex mode therefore, they cannot transmit and receive simultaneously and the communication process performed in two phases. During the broadcasting phase, the source S transmits its data to the destination D and due to the broadcasting nature of the transmission; the intermediate nodes and eavesdropper overhear the transmitted information. In addition, according to security schemes, one node \(J_{1}\) is selected from \(\mathrm{{S}}_\mathrm{relay }\) set to operate as a jammer and transmits intentional interference to degrade the eavesdropper links in this phase. In the cooperative phase, according to security schemes, an intermediate node R is selected to operate as a conventional relay and forwards the source message to the corresponding destination (R must belong to decoding set \(\mathrm{{C}}_{\mathrm{d} }\subseteq \hbox {S}_\mathrm{relay})\). A second jammer \(J_{2}\) is selected from \(\mathrm{{S}}_\mathrm{relay}\), for the same reason as \(J_{1}\). Note that the destination D is not able to mitigate the artificial interference from the jamming nodes (interference is unknown at the destination) and refers to applications with critical secrecy constraints.
Fig. 1

System model with two phases considering one eavesdropper. a Broadcasting phase, b cooperative phase

The main objective of this paper is the investigation of relay and jammer selection criteria for cooperative systems with secrecy constraints. In this work we have the following assumptions:
  • As in most existing cooperative network topology [22], the direct links (\(\mathrm{{S}}\!\!\rightarrow \!\! \mathrm{{D}}\) and \(\mathrm{{S}} \rightarrow \mathrm{{E}})\) are available.

  • The broadcasting phase is unsecured. Therefore, the eavesdropper can overhear the transmitted information.

  • In both two phases, a slow, flat, and block Rayleigh fading environment is assumed, i.e., the channel remains static for one coherence interval and changes independently in different coherence intervals with a variance \(\sigma _{i,j}^2 =d_{i,j}^{-\beta } \), where \(d_{i,j}\) is the Euclidean distance between node \(i\) and node \(j\), and \(\beta \) is the path-loss exponent.

  • Furthermore, additive white Gaussian noise (AWGN) is assumed with zero mean and unit variance.

Let \(P^{(S)}, P^{(R)}\) and \(P^{(J)}\) denote the transmitted power for the source node, the relay node and the jamming nodes, respectively. In order to protect the destination from the artificial interference and maximize the benefits of the proposed schemes, the jamming nodes transmit with a lower power than the relay nodes and thus their transmitted power is defined as \(P^{(J)}=P^{(R)} / L\) (with \(P^{(S)}=P^{(R)})\), where \(L >\) 1 denotes the ratio of the relay power to the jammer power.

2.1.2 Problem Formulation

The instantaneous secrecy capacity for a decoding set C\(_\mathrm{d}\) is given as [7, 13]
$$\begin{aligned}&C_S^{\left| {C_d } \right| } {\begin{array}{l} {(R,J_1 ,J_2 } \\ \nonumber \end{array} })\!=\!\\&\quad \left\{ {{\begin{array}{l} {{\begin{array}{l} {\left[ {\frac{1}{2}\log _2 \left( {1+\frac{\gamma _{S,D} }{1+\gamma _{J_1 ,D} }} \right) -\frac{1}{2}\log _2 \left( {1+\frac{\gamma _{S,E} }{1\!+\!\gamma _{J_1 ,E} }} \right) } \right] ^{\!+\!}}\quad {for\left| {C_d } \right| =0} \\ \end{array} }} \\ {\left[ {\frac{1}{2}\log _2 \left( {1+\frac{\gamma _{S,D} }{1+\gamma _{J_1 ,D}}\!+\!\frac{\gamma _{R,D} }{1\!+\!\gamma _{J_2 ,D} }} \right) -\frac{1}{2}\log _2 \left( {1\!+\!\frac{\gamma _{S,E} }{1\!+\!\gamma _{J_1 ,E} }+\frac{\gamma _{R,E} }{1+\gamma _{J_2 ,E} }} \right) } \right] ^{\!+\!}\quad for\left| {C_d } \right| >0} \\ \end{array}}} \right. \nonumber \\ \end{aligned}$$
(1)
where \(R\in \hbox {C}_\mathrm{d}, J_{1} \in \hbox {S}_\mathrm{relay}\) and \(J_{2}\in \{\hbox {S}_\mathrm{relay} -\hbox {R}^{*}\}, \gamma _{i,j} \stackrel{\Delta }{=}P^{(i)}\mid fi,j \mid ^{2}\) is the instantaneous signal-to-noise ratio (SNR) for the link \(i \rightarrow j\) modeled as a zero-mean, independent, circularly-symmetric complex Gaussian random variable with variance \(\sigma ^{2}_{i,j}, [x]^{+} \stackrel{\Delta }{=} \hbox {max}\{0, x \} \ \hbox {and} \mid \mathcal{F}\mid \) denotes the cardinality of a set \(\mathcal{F}\). Sometimes secrecy performance of the system is characterized by the secrecy outage probability, which is defined as the probability that the instantaneous secrecy capacity is less than a target secrecy rate Rs \(>\) 0 [6]. The secrecy outage probability is written as:
$$\begin{aligned} P_{out} =\sum _{n=1}^{N} {p_{r}} \{C_{S}^{n} (R,J_{1} ,J_{2} )<R_{S}\}p_{r} \{\left| {C_{d}} \right| =n\} \end{aligned}$$
(2)
Our objective is to select appropriate nodes \(R, J_{1}\), and \(J_{2}\) in order to maximize the instantaneous secrecy capacity for different types of channel feedback. The optimization problem can be formulated as:
$$\begin{aligned} \left( {R^{*},J_1^*,J_2^*} \right)&= \arg \max \left\{ {C_s^{\left| {Cd} \right| } \left( {R,J_1 ,J_2 } \right) } \right\} ,\hbox {s.t. }\Psi _i \left( {for\,i=0,1} \right) \nonumber \\&\quad \quad \quad \quad \quad J_1 \in S_{relay} \nonumber \\&\quad \quad \quad \quad \quad R\in \left| {C_d } \right| \nonumber \\&\quad \quad \quad \quad \quad J_2 \in \left\{ {S_{relay} -R^{*}} \right\} \end{aligned}$$
(3)
where \(R^{*}, J_{1}^{*}, J_{2}^{*}\) denote the selected relay and jamming nodes, respectively (note that selected jammers \(J_{1}^{*}, J_{2}^{*}\) in the two phases may be the same node, which is determined by the instantaneous secrecy capacity), \(\Psi _{0} =\) {\(\gamma _\mathrm{n,\,D}, \gamma _{\mathrm{n},\,E}\}, \Psi _{1} =\) {\(\gamma _\mathrm{n,\,D}, \hbox {E}[\gamma _{\mathrm{n},\,E}\)]} with n \(\in \hbox {S}_\mathrm{relay}\) are the feedback knowledge sets; E[.] stands for the expectation operator, \(\Psi _{0}\) denotes a global instantaneous knowledge for all the links and \(\Psi _{1}\) denotes an average channel knowledge for the eavesdropper links.

2.2 The Presence of Multiple Eavesdroppers

2.2.1 System Model

In this scenario we consider M eavesdroppers, S\(_\mathrm{eves}=\) {1, 2,..., M} as shown in Fig. 2.
Fig. 2

System model with two phases considering multiple eavesdroppers. a Broadcasting phase, b cooperative phase

2.2.2 Problem Formulation

The instantaneous secrecy capacity for a decoding set C\(_{\mathrm{d}}\) is given by Liang et al. [7], Lai and El Gamal [13]
$$\begin{aligned}&C_{S}^{\left| {C_{d}} \right| } {\begin{array}{l} {(R,J_{1} ,J_{2})} \\ \nonumber \end{array} }=\\&\left\{ {{\begin{array}{l} {{\begin{array}{l} {\left[ {\frac{1}{2}\log _{2} \left( {1+\frac{\gamma _{S,D}}{1\!+\!\gamma _{J_1 ,D}}} \right) -\frac{1}{2}\log _2 \left( {1\!+\!\mathop \sum \limits _{m=1}^{M} {\left( {\frac{\gamma _{S,E_{m}}}{1\!+\!\gamma _{J_{1} ,E_{m}}}} \right) }} \right) } \right] ^{+}}\quad {for\left| {C_{d}} \right| =0} \\ \end{array} }} \\ {\left[ {\frac{1}{2}\log _{2} \left( {1\!+\!\frac{\gamma _{S,D} }{1\!+\!\gamma _{J_{1} ,D} }\!+\!\frac{\gamma _{R,D} }{1+\gamma _{J_{2} ,D} }} \right) \!-\!\frac{1}{2}\log _{2} \left( {1+\mathop \sum \limits _{m\!=\!1}^{M} {\left( {\frac{\gamma _{S,E_{m}}}{1+\gamma _{J_{1} ,E_{m}}}\!+\!\frac{\gamma _{R,E_{m}}}{1+\gamma _{J_{2}, E_{m}}}}\right) }} \right) } \right] ^{\!+\!} \quad for\left| {C_{d}} \right| >0} \\ \end{array} }} \right. \nonumber \\ \end{aligned}$$
(4)
Note that in Eq. (4), the malicious eavesdroppers cooperate together in order to overhear the source message, and this is complicate the process of exchanging secure information between the source and the destination.

3 Relay and Jammers Selection Schemes

In order to investigate the effect of jamming we will distinguish between the following three cases; no jammer selection, conventional jamming (where the jamming signal is unknown at the destination) and controlled jamming (where the jamming signal is known at the destination) as will be explained in the next subsections.

3.1 The Presence of One Eavesdropper

3.1.1 Selection Schemes Without Jamming

This category of solutions does not involve a jamming process and therefore only a conventional relay accesses the channel during the second phase of the protocol. The existing selections are summarized as follows:
  • Conventional Selection (CS): This solution does not take the eavesdropper channels into account and the relay node is selected according to the instantaneous quality of the S \(\rightarrow \) D link [14]. Although it is an effective solution for non-eavesdropper environments, it cannot support systems with secrecy constraints. The conventional selection is written as
    $$\begin{aligned} R^{*}=\arg {\mathop {\max }\limits _{R\in C_d}} \left\{ {1+\gamma _{S,D} +\gamma _{R,D}} \right\} \end{aligned}$$
    (5)
  • Optimal selection (OS): This solution takes into account the relay-eavesdropper links and decides the relay node according to the knowledge set \(\Psi _{0}\).The optimal selection is given as [14]
    $$\begin{aligned} R^{*}=\arg {\mathop {\max }\limits _{R\in C_d}} \left\{ {\frac{1+\gamma _{S,D} +\gamma _{R,D}}{1+\gamma _{S,E} +\gamma _{R,E} }} \right\} \end{aligned}$$
    (6)
  • Suboptimal Selection (SS): It avoids the instantaneous estimate of the relay eavesdropper links by deciding the appropriate relay based on the knowledge set \(\Psi _{1}\). It is a solution which efficiently fills the gap between optimal and conventional selection with a low implementation/complexity overhead. The suboptimal selection is expressed as [14]
    $$\begin{aligned} R^{*}=\arg {\mathop {\max }\limits _{R\in C_d}} \left\{ {\frac{1+\gamma _{S,D} +\gamma _{R,D} }{1+\mathrm{E}\left[ {\gamma _{S,E} } \right] +\mathrm{E}\left[ {\gamma _{R,E} } \right] }} \right\} \end{aligned}$$
    (7)

3.1.2 Selection Schemes with Conventional Jamming

In this subsection, we present an extension to the above eavesdropper-based relay selection schemes for systems with jamming via several relay and jammers selection schemes based on the optimization problem given by Eq. (3).
  • Optimal Selection with Jamming (OSJ)

The optimal selection with jamming assumes the knowledge of the set \(\Psi _{0}\) and ensures a maximization of the instantaneous secrecy capacity given in Eq. (1). The selection policy which maximizes Eq. (1) assuming that \(\mid \hbox {C}_{\mathrm{d}}\mid >\) 0 is given as
$$\begin{aligned} (R^{*},J_1^{*} ,J_{2}^{*})=\arg {\mathop {\mathop {\mathop {\max }\limits _{J_{1} \in S_{relay}}}\limits _{R\in C_d}}\limits _{J_{2} \in \left\{ S_{relay}-R^{*}\right\} }} \left\{ {\frac{1+\frac{\gamma _{S,D} }{1+\gamma _{J_{1} ,D} }+\frac{\gamma _{R,D} }{1+\gamma _{J_{2} ,D}}}{1+\frac{\gamma _{S,E} }{1+\gamma _{J_{1} ,E} }+\frac{\gamma _{R,E} }{1+\gamma _{J_2,E}}}} \right\} \end{aligned}$$
(8)
The selection process in (8) requires a large number of comparisons and algebraic computations. Therefore, a simpler selection policy can be proposed considering a high SNR, where all the relay nodes can decode the source message (P\(_{\mathrm{r}}\) {\(\mid \)C\(_{\mathrm{d}}\!\mid =\mid \!\) S\(_{\mathrm{relay}}\!\mid \)=N} \(=\) 1) and the assumption that the jammer power is much less than the source and relay powers [15], it can be shown that
$$\begin{aligned} (R^{*}\, ,J_{1}^{*}\, ,J_{2}^{*}\,)=\arg \mathop {\mathop {\mathop {\max }\limits _{J_1 \in S_{relay} } }\limits _{R\in C_{d}} }\limits _{J_{2} \in \left\{ {S_{relay}-R^{*}} \right\} } \left\{ {\frac{\frac{\gamma _{S,D} }{\gamma _{J_{1}, D} }+\frac{\gamma _{R,D} }{\gamma _{J_{2} ,D} }}{\frac{\gamma _{S,E} }{\gamma _{J_{1}, E} }+\frac{\gamma _{R,E} }{\gamma _{J_{2} ,E} }}} \right\} \end{aligned}$$
(9)
According to Eq. (9) we can obtain,
$$\begin{aligned} J_{1}^{*}&= \arg {\begin{array}{c}\\ {\mathop {\max }\limits _{J_1 \in S_{relay} }} \\ \end{array} }\left\{ {\frac{\gamma _{J_{1} ,E} }{\gamma _{J_{1} ,D} }} \right\} \hbox { and }R^{*}=\arg {\begin{array}{c}\\ {\mathop {\max }\limits _{R\in C_{d} } }\\ \end{array} }\left\{ {\frac{\gamma _{R,D} }{\gamma _{R,E} }} \right\} \nonumber \\ J_{2}^{*}&= \arg {\begin{array}{c}\\ {\mathop {\max }\limits _{J_{2} \in \left\{ {S_{relay} -R^{*}} \right\} }} \\ \end{array} }\left\{ {\frac{\gamma _{J_{2} ,E} }{\gamma _{J_2 ,D} }} \right\} \end{aligned}$$
(10)
With regard to the relay and the jamming nodes, the relay selection tries to maximize the ratio \(\gamma _\mathrm{n,D}, \gamma _{\mathrm{n},E}\), while the jamming nodes try to minimize the same function, consequently the selection policy is independent of the selection order and will always select different relay terminals.
  • Optimal Switching (OW)

The original idea of using jamming nodes is to introduce interference on the eavesdropper links. Based on the assumption that the destination cannot mitigate artificial interference from the jamming nodes, continuous jamming in both phases is not always beneficial for the system. More specifically, for some operational scenarios (i.e. jammers are close to the destination), the continuous use of jamming decreases secrecy and acts as a bottleneck for the system. In order to overcome this limitation, we propose intelligent switching between optimal selection with jamming and optimal selection without jamming. This hybrid selection scheme overcomes problems of “negative jamming” which leads to excessive interference at destination and is introduced as the optimal general solution for the problem under consideration. The required condition for the participation of the jamming nodes is
$$\begin{aligned} \frac{1}{2}\log _2 \left[ {\frac{1+\frac{\gamma _{S,D} }{1+\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{1+\gamma _{J_2 ,D} }}{1+\frac{\gamma _{S,E} }{1+\gamma _{J_1 ,E} }+\frac{\gamma _{R,E} }{1+\gamma _{J_2 ,E} }}} \right] ^{+}>\frac{1}{2}\log _2 \left[ {\frac{1+\gamma _{S,D} +\gamma _{R,D} }{1+\gamma _{S,E} +\gamma _{R,E} }} \right] ^{+} \end{aligned}$$
(11)
For high SNRs and based on an appropriate power allocation [15], the secrecy capacity for the OSJ and OS schemes can be simplified and therefore Eq. (11) can be rewritten as
$$\begin{aligned} \frac{1}{2}\log _2 \left[ {\frac{\frac{\gamma _{S,D} }{\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{\gamma _{J_2 ,D} }}{\frac{\gamma _{S,E} }{\gamma _{J_1 ,E} }+\frac{\gamma _{R,E} }{\gamma _{J_2 ,E} }}} \right] ^{+}>\frac{1}{2}\log _2 \left[ {\frac{\gamma _{S,D} +\gamma _{R,D} }{\gamma _{S,E} +\gamma _{R,E} }} \right] ^{+} \end{aligned}$$
(12)
If the above condition achieved, the OSJ scheme provides higher instantaneous secrecy capacity than OS does and is preferred. Otherwise the OS scheme is more efficient in promoting the system’s secrecy performance and should be employed. Because of the uncertainty of the channel coefficient \(h_{i,\, j}\) for each channel \(i \rightarrow j\), OW should outperform either the continuous jamming scheme or the non-jamming one.
  • Suboptimal Selection with Jamming (SSJ)

Although the assumption \(\Psi _{0}\) provides some optimal selection metrics, its practical interest is limited to some special applications (e.g. military applications), where the instantaneous quality of the eavesdropper links can be measured by some specific protocols. In practice, only an average knowledge of eavesdropper links would be available from long-term supervision of the eavesdropper transmission. The selection metric is modified as
$$\begin{aligned} J_{1}^{*}&= \arg \mathop {\max }\limits _{J_1 \in S_{relay} } \left\{ {\frac{\mathrm{E}[\gamma _{J_1 ,E} ]}{\gamma _{J_1 ,D} }} \right\} \hbox { and }R^{*}=\arg \mathop {\max }\limits _{R\in C_d } \left\{ {\frac{\gamma _{R,D} }{\mathrm{E}[\gamma _{R,E} ]}} \right\} \nonumber \\ J_{2}^{*}&= \arg {\begin{array}{c}\\ {\mathop {\max }\limits _{J_2 \in \left\{ {S_{relay} -R^{*}} \right\} }} \\ \end{array} }\left\{ {\frac{\mathrm{E}[\gamma _{J_2 ,E} ]}{\gamma _{J_2 ,D} }} \right\} \end{aligned}$$
(13)
  • Suboptimal Switching (SW)

Given the fact that jamming is not always a positive process for the performance of the system, the suboptimal switching refers to the practical application of the intelligent switching between SSJ and SS schemes. The basic idea is the same as OW, but the switching criterion uses the available knowledge set \(\Psi _{1}\). More specifically, the required condition for switching from SS to SSJ is
$$\begin{aligned} \frac{1}{2}\log _2 \left[ {\frac{1+\frac{\gamma _{S,D} }{1+\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{1+\gamma _{J_2 ,D} }}{1+\frac{\mathrm{E}[\gamma _{S,E} ]}{1+\mathrm{E}[\gamma _{J_1 ,E} ]}+\frac{\mathrm{E}[\gamma _{R,E} ]}{1+\mathrm{E}[\gamma _{J_2 ,E} ]}}} \right] ^{+}>\frac{1}{2}\log _2 \left[ {\frac{1+\gamma _{S,D} +\gamma _{R,D} }{1+\mathrm{E}[\gamma _{S,E} ]+\mathrm{E}[\gamma _{R,E} ]}} \right] ^{+} \end{aligned}$$
(14)
Following the same assumptions in obtaining Eq. (12)
$$\begin{aligned} \frac{1}{2}\log _2 \left[ {\frac{\frac{\gamma _{S,D} }{\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{\gamma _{J_2 ,D} }}{\frac{\mathrm{E}[\gamma _{S,E} ]}{\mathrm{E}[\gamma _{J_1 ,E} ]}+\frac{\mathrm{E}[\gamma _{R,E} ]}{\mathrm{E}[\gamma _{J_2 ,E} ]}}} \right] ^{+}>\frac{1}{2}\log _2 \left[ {\frac{\gamma _{S,D} +\gamma _{R,D} }{\mathrm{E}[\gamma _{S,E} ]+\mathrm{E}[\gamma _{R,E} ]}} \right] ^{+} \end{aligned}$$
(15)

3.1.3 Selection Schemes with Controlled Jamming

The previous selection schemes are proposed based on the assumption that jamming signal is unknown at the destination. This assumption avoids the initialization period in which the jamming sequence is defined, and thus, it reduces the risk of giving out the artificial interference to the eavesdropper. For comparison reasons, we propose a control scheme, in which the jamming signal can be decoded at the destination D, but not at the eavesdropper \(E\). This scheme is called optimal selection with controlled jamming (OSCJ). In this scheme, the secrecy capacity expression given in Eq. (1) is modified as follows
$$\begin{aligned} C_S^{\left| {C_d } \right| } {\begin{array}{l} {(R,J_1 ,J_2 } \\ \end{array} })=\left[ {\frac{1}{2}\log _2 \frac{1+\gamma _{S,D+} \gamma _{R,D} }{1+\frac{\gamma _{S,E} }{1+\gamma _{J_1 ,E} }+\frac{\gamma _{R,E} }{1+\gamma _{J_2 ,E} }}} \right] ^{+}\quad \quad for\left| {C_d } \right| >0 \end{aligned}$$
(16)
Following the same assumptions in obtaining (12), the selection policy that maximizes the secrecy capacity given in (16) is given by
$$\begin{aligned} J_{1}^{*}&= \arg \mathop {\max }\limits _{J_1 \in S_{relay} } \{\gamma _{J_1 ,E} \}\hbox { and }R^{*}=\arg \mathop {\max }\limits _{R\in C_d } \left\{ {\frac{\gamma _{R,D} }{\gamma _{R,E} }} \right\} \nonumber \\ J_{2}^{*}&= \arg \mathop {\max }\limits _{J_2 \in \left\{ {S_{relay} -R^{*}} \right\} } \{\gamma _{J_2 ,E} \} \end{aligned}$$
(17)

3.2 The Presence of Multiple Eavesdroppers

3.2.1 Selection Schemes Without Jamming

As in [23] the optimal relay selection is given by
$$\begin{aligned} R^{*}=\arg \mathop {\max }\limits _{R\in C_d } \left\{ {\frac{1+\gamma _{S,D} +\gamma _{R,D} }{1+\mathop {\sum }\nolimits _{m=1}^{M} {\left( {\gamma _{S,E_{m}} +\gamma _{R,E_{m}}} \right) } }} \right\} \end{aligned}$$
(18)

3.2.2 Selection Schemes with Conventional Jamming

As in [23] the selection policy which maximizes the instantaneous secrecy capacity given in Eq. (4) assuming that \(\mid \hbox {C}_{\mathrm{d}} \mid >\) 0 is given as
$$\begin{aligned} (R^{*},J_{1}^{*} ,J_{2}^{*})=\arg {\mathop {\mathop {\mathop {\max }\limits _{J_1 \in S_{relay}}}\limits _{R\in C_{d}}}\limits _{J_{2} \in \left\{ S_{relay}-R^{*}\right\} }} \left\{ {\frac{1+\frac{\gamma _{S,D} }{1+\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{1+\gamma _{J_2, D} }}{1+\mathop \sum \nolimits _{m=1}^{M} {\left( {\frac{\gamma _{S,E_{m}}}{1+\gamma _{J_1 ,E_m } }+\frac{\gamma _{R,E_{m}}}{1+\gamma _{J_{2}, E_{m}}}} \right) }}} \right\} \end{aligned}$$
(19)
Following the same assumptions in obtaining Eq. (12) it can be shown that a simpler selection policy can be proposed as following
$$\begin{aligned} (R^{*},J_1^*,J_2^*)=\arg \mathop {\mathop {\mathop {\max }\limits _{J_1 \in S_{relay} } }\limits _{R\in C_d } }\limits _{J_2 \in \left\{ {S_{relay} -R^{*}} \right\} } \left\{ {\frac{\frac{\gamma _{S,D} }{\gamma _{J_1 ,D} }+\frac{\gamma _{R,D} }{\gamma _{J_2 ,D} }}{\mathop \sum \nolimits _{m=1}^{M} {\left( {\frac{\gamma _{S,E_m } }{\gamma _{J_1 ,E_m } }+\frac{\gamma _{R,E_m } }{\gamma _{J_2 ,E_m } }} \right) } }} \right\} \end{aligned}$$
(20)
According to Eq. (20) we can obtain,
$$\begin{aligned}&\displaystyle J_{1}^{*} = \arg \mathop {\min }\limits _{J_1 \in S_{relay} } \left\{ {\frac{\gamma _{J_1 ,D} }{\mathop \sum \limits _{\forall m\in S_{eves} } {\gamma _{J_1 ,E_m } } }} \right\} \hbox { and }R^{*}=\arg \mathop {\max }\limits _{R\in C_d } \left\{ {\frac{\gamma _{R,D} }{\mathop \sum \limits _{\forall m\in S_{eves} } {\gamma _{R,E_m } } }} \right\} \nonumber \\&\displaystyle J_{2}^{*} = \arg \mathop {\min }\limits _{J_2 \in \left\{ {S_{relay} -R^{*}} \right\} } \left\{ {\frac{\gamma _{J_2 ,D} }{\mathop \sum \limits _{\forall m\in S_{eves} } {\gamma _{J_2 ,E_m } } }} \right\} \end{aligned}$$
(21)

3.2.3 Selection Schemes with Controlled Jamming

In this scheme, the secrecy capacity expression given in Eq. (4) is modified as [23]
$$\begin{aligned} C_S^{\left| {C_d } \right| } {\begin{array}{l} {(R,J_1 ,J_2 } \\ \end{array} })=\left[ {\frac{1}{2}\log _2 \frac{1+\gamma _{S,D+} \gamma _{R,D} }{1+\mathop \sum \nolimits _{m=1}^M {\left( {\frac{\gamma _{S,E_m } }{1+\gamma _{J_1 ,E_m } }+\frac{\gamma _{R,E_m } }{1+\gamma _{J_2 ,E_m } }} \right) } }} \right] ^{+}\quad \quad for \left| {C_d } \right| >0\nonumber \\ \end{aligned}$$
(22)
Following the same assumptions in obtaining Eq. (12), the selection policy that maximizes the secrecy capacity given in (22) is given by
$$\begin{aligned}&\displaystyle J_{1}^{*} = \arg \mathop {\max }\limits _{J_1 \in S_{relay} } \left( {\mathop \sum \limits _{m=1}^M {\gamma _{J_1 ,E_m } } } \right) \hbox { and }R^{*}=\arg \mathop {\max }\limits _{R\in C_d } \left( {\frac{\gamma _{R,D} }{\sum _{m=1}^M {\gamma _{R,E_m } } }} \right) \nonumber \\&\displaystyle J_{2}^{*} = \arg \mathop {\max }\limits _{J_2 \in \left\{ {S_{relay} -R^{*}} \right\} } \left( {\mathop \sum \limits _{m=1}^M {\gamma _{J_2 ,E_{m}}}} \right) \end{aligned}$$
(23)

4 Numerical Results and Discussion

In this section, we investigate the effectiveness of the proposed selection schemes via computer simulations. The simulation environment follows the model explained in Fig. 1 and consists of a 2-D square topology where the nodes S, D and E are located as {X\(_{\mathrm{S}}\), Y\(_{\mathrm{S}}\)} \(=\) {0, 0}, {X\(_{\mathrm{D}}\), Y\(_{\mathrm{D}}\)} \(=\) {1, 0}, {X\(_{E}\), Y\(_{E}\)} \(=\) {0, 1}, respectively and the direct paths S \(\rightarrow \) D, S \(\rightarrow E\) are available. For simplicity, the source and relay nodes transmit with the same power, i.e. P\(^{(\mathrm{S})} =\) P\(^{(\mathrm{R})}\). The relay and jammer nodes transmit with a relay-jammer power ratio \(L\)\(=\) 100. The number of the relays N \(=\) 4 and the relays are located randomly in the 2-D space considered; their exact location is given for each example considered. The path-loss exponent is set to \(\beta \)=\( 3\), the area of the network is a 1 \(\times \) 1 unit square, the transmission spectral efficiency is equal to R\(_{0}\)\(=\) 2 bits per channel use (BPCU) and the target secrecy rate is equal to R\(_{\mathrm{s}}\)\(=\) 0.1 BPCU. In this paper, the adopted performance metrics are the ergodic secrecy capacity and secrecy outage probability.

4.1 The Impact of Changing the N-Relays Set Location with Respect to the Destination and the Eavesdropper

To study the effect of relays location in system performance we have three different scenarios as follows;

1st scenario: When the N-Relays are located in the middle of the space between D and E

Figure 3 shows the topology of this scenario where the 4 relays have comparable links with D and E.
Fig. 3

The 1\(\times \)1 simulation environment with \(N = 4, \beta =3\)

Figure 4 shows the ergodic secrecy capacity of the different selection schemes versus the transmitted power P. From this figure it is clear that selection with jamming outperforms the corresponding non jamming schemes. The integration of jamming in the optimal selection increases the ergodic secrecy capacity to 2.6087 BPCU rather 1.3702 BPCU for the non-jamming case. This significant gain introduces jamming selection as an efficient technique to support secrecy constraints. The integration of jamming also improves the suboptimal selection protocols based on average channel knowledge; the ergodic secrecy capacity for the SSJ scheme converges to 2.2717 BPCU rather 1.2551 BPCU for the SS scheme with a gain higher for the higher SNRs.
Fig. 4

Ergodic secrecy capacity versus transmitted power (P) for different selection schemes

Regarding to the hybrid schemes, it can be seen that OW outperforms all the selection schemes and provides the best performance where its secrecy capacity converges to 2.6413 BPCU. This result validates that an appropriate mechanism for switching between OS and OSJ overcomes the cases where the interference decreases the secrecy. For the suboptimal case, SW outperforms SS and SSJ selection schemes (its secrecy capacity converges to 2.3876 BPCU). An observation of OSCJ scheme performance shows that it outperforms all the other selection schemes, providing the highest ergodic secrecy capacity when the transmitted power increases due to the ability of the destination to decode the artificial interference in this scheme.

Figure 5 presents the secrecy outage probability metric for the considered selection schemes using the above configuration. The presented results are in line with the above secrecy ergodic capacity results and show that jamming provides lower secrecy outage probability for both OS and SS schemes. Regarding the hybrid schemes, the OW outperforms all schemes and SW has a higher gain than SSJ in terms of outage probability. We also note that the OSCJ scheme gives the best performance because the effect of jamming signals is removed at the main destination node.
Fig. 5

Secrecy outage probability versus P for the different selection schemes with \(\mathrm{{R}}_{\mathrm{s}} = 0.1\) BPCU and \(\mathrm{{R}}_{0} = 2\) BPCU

2nd scenario: When the N-Relays are close to the eavesdropper

Figure 6 shows the considered topology, as well as the secrecy ergodic capacity of the different selection schemes. It is clear that the non-jamming approaches are inefficient as the relays have a strong link with the eavesdropper. On the other hand, jamming schemes confuse the eavesdropper and increase significantly the secrecy ergodic capacity. For this configuration, the proposed hybrid schemes (OW, SW) have a similar performance to the jamming schemes (OSJ, SSJ), as jamming is always beneficial in this case.
Fig. 6

Ergodic secrecy capacity versus P for a scenario where relays are located close to the eavesdropper

Figure 7 shows the secrecy outage probability metric for the considered selection schemes using the above configuration. The obtained results show that jamming provides lower secrecy outage probability for both OS and SS schemes. Regarding the hybrid schemes, the OW outperforms all schemes. We also note that the OSCJ scheme gives the best performance because the effect of jamming signals is removed at the main destination node.
Fig. 7

Secrecy outage probability versus P for the different selection schemes with \(\mathrm{{R}}_{\mathrm{s}} = 0.1\) BPCU and \(\mathrm{{R}}_{0} = 2\) BPCU

Figure 8 presents a comparison between the proposed schemes and the schemes presented in [15] in terms of secrecy outage probability. The obtained results show that the proposed schemes outperform the schemes presented in [15] when the relays are located close to the eavesdropper E.
Fig. 8

Secrecy outage probability versus P for the proposed selection schemes and the schemes presented in [15]

3rd scenario: When the N-Relays are close to the destination

Figure 9 shows the considered topology, as well as secrecy ergodic capacity of the different selection schemes. As can be seen, for this scenario, continuous jamming schemes introduce high interference at the destination and become less efficient. The main reason for this result is that for strong relay destination links, jamming becomes stronger at high SNRs and can decrease the secrecy performance achieved. On the other hand, non-jamming schemes increase significantly the secrecy ergodic capacity. As far as the hybrid schemes is concerned, appropriate switching improves significantly the performance compared with the continuous jamming schemes. Both OW and SW schemes yield a higher gain than previous configurations. From Figs. 6 and 9 we can conclude that jamming is an interesting solution for scenarios with strong relay-eavesdropper links. The hybrid schemes avoid strong interference at the destination and are thus promising solutions to maximize secrecy capacity.
Fig. 9

Ergodic secrecy capacity versus P for a scenario where relays are located close to the destination

4.2 The Impact of Changing the Eavesdropper Location with Respect to the Source and the Destination

Assuming the locations of the source, relays and the destination are fixed as in Fig. 3 and the eavesdropper location has two different scenarios.

1st scenario:\(\{X_{E}, Y_{E}\} = \{0.2, 0.2\}\)i.e. the eavesdropper is close to the source

Figure 10 shows the ergodic secrecy capacity versus transmitted power (P) for the different selection schemes when the eavesdropper is close to the source. It is clear that the non-jamming approaches are inefficient due to the strong link between the source and the eavesdropper. On the other hand, jamming schemes confuse the eavesdropper and increase significantly the secrecy ergodic capacity. The ergodic secrecy capacity for the OSJ scheme converges to 1.1433 BPCU rather 0.0765 BPCU for the OS scheme and converges to 1.0417 BPCU for SSJ rather 0.0679 BPCU for the SS scheme. For hybrid schemes (OW, SW) they have a similar performance to the jamming schemes (OSJ, SSJ), as jamming is always beneficial in this case. For OSCJ scheme it provides the highest ergodic secrecy capacity than all the other selection schemes.
Fig. 10

Ergodic secrecy capacity versus P for the different selection schemes when the eavesdropper is close to the source

2nd scenario:\(\{X_{E}, Y_{E}\} = \{0.8, 0.2\}\)i.e. the eavesdropper is close to the destination

Figure 11 shows the ergodic secrecy capacity versus transmitted power (P) for the different selection schemes when the eavesdropper is close to the destination. From this figure it is clear that the non-jamming approaches are inefficient and almost no improvement in the secrecy ergodic capacity is achieved. On the other hand, jamming schemes increase significantly the secrecy ergodic capacity; ergodic secrecy capacity for the OSJ scheme converges to 2.3998 BPCU rather 0.2375 BPCU for the OS scheme and converges to 1.1275 BPCU for SSJ rather 0.0867 BPCU for the SS scheme. For hybrid schemes (OW, SW) they have a similar performance to the jamming schemes (OSJ, SSJ), as jamming is always beneficial in this case. For OSCJ scheme it provides the highest ergodic secrecy capacity than all the other selection schemes.
Fig. 11

Ergodic secrecy capacity versus P for the different selection schemes when the eavesdropper is close to the destination

From Figs. 10 and 11 we can conclude the following:
  • The worst results of the secrecy ergodic capacity for all selection schemes are obtained when the eavesdropper is close to the source.

  • When eavesdropper is close to the source or close to the destination the non-jamming schemes are inefficient.

  • There is no need to apply the hybrid switching schemes as they follow the jamming schemes behavior.

  • OSCJ scheme provides the highest secrecy ergodic capacity than the other selection schemes for both cases.

Comparing Figs. 410 and 11 we note that as long as the eavesdropper is far from the source and the destination, an improvement in the secrecy ergodic capacity is achieved for both jamming and non-jamming schemes.
Figure 12 shows the secrecy outage probability comparison for both eavesdropper scenarios; when the eavesdropper is close to the source and close to the destination. It is clear that the best results of the secrecy outage probability for OSCJ, OSJ, and OW selection schemes are obtained when the eavesdropper is close to the destination while SSJ and SW selection schemes show a slight degradation for \(P > 25\, d\!B\).
Fig. 12

Secrecy outage probability versus P for both eavesdropper scenarios (close to the source and close to the destination)

4.3 The Impact of the Presence of Multiple Eavesdroppers

The simulation environment follows the model presented in Fig. 2. In the following, we consider two scenarios with different number of the eavesdroppers.
  • 1st scenario: Number of eavesdroppers M \(=\) 2 and their locations are fixed at \(\{x_{E_i } ,y_{E_i } \}_{i=1}^2 =\{(0,1),(1,1)\}\)

  • 2nd scenario: Number of eavesdroppers M \(=\) 3 and their locations are fixed at \(\{x_{E_i } ,y_{E_i } \}_{i=1}^3 =\{(0,1),(0.5,0.5),(1,1)\}\)

From Figs. 13 and 14 it is clear that by increasing the number of eavesdroppers in the system;
Fig. 13

Ergodic secrecy capacity versus P for N \(=\) 4 and M \(=\) 2

Fig. 14

Ergodic secrecy capacity versus P for N \(=\) 4 and M \(=\) 3

  • The performance of different selection schemes is degraded.

  • Optimal selection scheme without jamming (OS) becomes inefficient and should not be used in these systems.

  • Optimal selection scheme with jamming (OSJ) is preferred in these systems due to the ability of jamming nodes to confuse eavesdroppers and increase significantly the secrecy ergodic capacity.

  • Optimal selection scheme with controlled jamming (OSCJ) achieves the best performance due to the ability of the destination node to decode the jamming signals.

Comparing Figs. 413 and 14 we can conclude that: Ergodic secrecy capacity is decreased when the number of eavesdroppers increased for different relay selection schemes.
  • For M \(=\) 1: C_os \(=\) 1.3702, C_osj \(=\) 2.6087, and C_oscj \(=\) 5.7494.

  • For M \(=\) 2: C_os \(=\) 0.6695, C_osj \(=\) 1.6950, and C_oscj \(=\) 4.6367.

  • For M \(=\) 3: C_os \(=\) 0.0292, C_osj \(=\) 1.0233, and C_oscj \(=\) 3.7812.

Figure 15 presents the secrecy outage probability comparison for two different numbers of eavesdroppers; when M \(=\) 2 and M \(=\) 3. It is clear that the secrecy outage probability increased by increasing the eavesdroppers’ number for different relay selection schemes.
Fig. 15

Secrecy outage probability versus P for M \(=\) 2 and M \(=\) 3

5 Conclusion

This paper has studied different relay and jammer selection schemes for one-way cooperative networks with physical layer secrecy consideration. The proposed schemes achieve an opportunistic selection of one conventional relay node and two jamming nodes to increase security against eavesdroppers based on both instantaneous and average knowledge of the eavesdroppers’ channels. Selection in the proposed schemes was made with the presence of direct links and the assumption that the broadcast phase was unsecured. The obtained results showed that the jamming schemes such as OSJ and SSJ are effective for scenarios with strong eavesdropper links. In order to overcome jamming limitations for scenarios with weak eavesdropper links, a hybrid scheme for switching between jamming and non-jamming schemes was introduced which further improves the system performance in terms of ergodic secrecy capacity and secrecy outage probability. The obtained results showed also that as long as the eavesdropper has comparable links with the source and the destination, the ergodic secrecy capacity and the secrecy outage probability are improved. Finally, increasing the eavesdropper nodes in the system degrade the system performance.

References

  1. 1.
    Silva, E. D., Santos, A. L. D., Albini, L. C. P., & Lima, M. (2008). Identity-based key management in mobile ad hoc networks: Schemes and applications. IEEE Wireless Communications, 15, 46–52.CrossRefGoogle Scholar
  2. 2.
    Wyner, A. D. (1975). The wire-tap channel. Bell System Technical Journal, 54, 1355–1387.CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Csiszar, I., & Korner, J. (1978). Broadcast channels with confidential messages. IEEE Transactions on Information Theory, 24, 451–456.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Liu, R., Maric, I., Spasojevic, P., & Yates, R. D. (2008). Discrete memoryless interference and broadcast channels with confidential messages: Secrecy rate regions. IEEE Transactions on Information Theory, 54, 2493–2507.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bloch, M., Barros, J., Rodrigues, M. R. D., & McLaughlin, S. W. (2008). Wireless information-theoretic security. IEEE Transactions on Information Theory, 54, 2515–2534.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Barros, J., & Rodrigues, M. R. D. (2006, July) Secrecy capacity of wireless channels. In Proceedings of IEEE international symposium on information theory (pp. 356–360). Seattle, USA.Google Scholar
  7. 7.
    Liang, Y., Poor, H. V., & Ying, L. (2008, February) Wireless broadcast networks: Reliability, security, and stability. In Proceedings of the 3rd workshop on information theory and applications (pp. 249–255). San Diego, CA, USA.Google Scholar
  8. 8.
    Dong, L., Han, Z., Petropulu, A. P., & Poor, H. V. (2008, September). Secure wireless communications via cooperation. In Proceedings of Allerton conference on communication, control and computing, Urbana-Champaign, IL, USA.Google Scholar
  9. 9.
    Laneman, J. N., Tse, D. N. C., & Wornell, G. W. (2004). Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory, 50, 3062–3080.CrossRefMathSciNetGoogle Scholar
  10. 10.
    Bletsas, A., Shin, H., & Win, M. Z. (2007). Cooperative communications with outage-optimal opportunistic relaying. IEEE Transactions on Wireless Communications, 6, 3450–3460.CrossRefGoogle Scholar
  11. 11.
    Yang, S., & Belfiore, J.-C. (2007). Towards the optimal amplify-and-forward cooperative diversity scheme. IEEE Transactions on Information Theory, 53, 3114–3126.CrossRefMathSciNetGoogle Scholar
  12. 12.
    Dong, L., Han, Z., Petropulu, A., & Poor, H. V. (2010). Improving wireless physical layer security via cooperating relays. IEEE Transaction on Signal Processing, 58, 1875–1888.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Lai, L., & El Gamal, H. (2008). The relay-eavesdropper channel: Cooperation for secrecy. IEEE Transactions on Information Theory, 54, 4005–4019.CrossRefMathSciNetGoogle Scholar
  14. 14.
    Krikidis, I. (2010). Opportunistic relay selection for cooperative networks with secrecy constraints. IET Communications, 4, 1787–1791.CrossRefGoogle Scholar
  15. 15.
    Krikidis, I. (2009). Relay selection for secure cooperative networks with jamming. IEEE Transactions on Wireless Communications, 8, 5003–5011.CrossRefGoogle Scholar
  16. 16.
    Beres, E., & Adve, R. (2008). Selection cooperation in multi-source cooperative networks. IEEE Transactions on Wireless Communications, 7, 118–127.CrossRefGoogle Scholar
  17. 17.
    Ibrahim, A. S., Sadek, A. K., Su, W., & Liu, K. J. (2008). Cooperative communications with relay selection: When to cooperate and whom to cooperate with. IEEE Transactions on Wireless Communication, 7, 2814–2827.CrossRefGoogle Scholar
  18. 18.
    Simeone, O., & Popovski, P. (2008). Secure communications via cooperating base stations. IEEE Communications Letters, 12, 188–190.CrossRefGoogle Scholar
  19. 19.
    Popovski, P., & Simeone, O. (2009). Wireless secrecy in cellular systems with infrastructure-aided cooperation. IEEE Transactions on Information Forensics and Security, 4, 242–256.CrossRefGoogle Scholar
  20. 20.
    Tekin, E., & Yener, A. (2008). The general Gaussian multiple access and two-way wire-tap channels: Achievable rates and cooperative jamming. IEEE Transactions on Information Theory, 54, 2735–2751.CrossRefMathSciNetGoogle Scholar
  21. 21.
    Wang, T., & Giannakis, G. B. (2008). Mutual information jammer-relay games. IEEE Transactions on Information Forensics and Security, 3, 290–303.CrossRefGoogle Scholar
  22. 22.
    Hassan, E. S. (2012). Energy-efficient hybrid opportunistic cooperative protocol for single-carrier frequency division multiple access-based networks. IET Communications, 6(16), 2602–2612.CrossRefGoogle Scholar
  23. 23.
    Al-nahari, A. Y., Krikidis, I., Ibrahim, A. S., Dessouky, M. I., Abd El-Samie, F. E. (2012, November) Relaying techniques for enhancing the physical layer secrecy in cooperative networks with multiple eavesdroppers. Transactions on Emerging Telecommunications Technologies. doi:10.1002/ett.2581.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Doaa H. Ibrahim
    • 1
  • Emad S. Hassan
    • 1
  • Sami A. El-Dolil
    • 1
  1. 1.Department of Electronics and Electrical Communications, Faculty of Electronic EngineeringMenoufia UniversityMenouf Egypt

Personalised recommendations