Opportunistic relaying and jamming with robust design in hybrid full/halfduplex relay system
 Zhi Lin^{1}Email author,
 Yueming Cai^{1},
 Weiwei Yang^{1}Email author and
 Xiaoming Xu^{1}
https://doi.org/10.1186/s1363801606215
© Lin et al. 2016
Received: 1 September 2015
Accepted: 24 April 2016
Published: 10 May 2016
Abstract
Full duplex (FD) protocol has been widely used in wireless communications, which could transmit and receive signals at the meantime. In this paper, considering the worstcase channel uncertainty, opportunistic relaying and jamming strategy in decodeandforward (DF) hybrid full/halfduplex (HD) relay system is proposed to enhance security. Specifically, the relay works in FD protocol to receive the confidential signals and transmit jamming signals at the first time slot. Then, the relay switches to HD protocol to transmit the decoded signals. Meanwhile, jammers emit cooperative jamming (CJ) signals to interfere the eavesdropper at two transmission slots. Suppose that imperfect eavesdropper channel condition is considered, we propose a worstcase robust design to obtain distributed jamming weights, which is solved through semidefinite program (SDP). Furthermore, we analyze secrecy rate and secrecy outage performance of the proposed scheme. As a benchmark, a traditional relay selection strategy with HD protocol in distributed relay system is listed for comparison. Simulation results demonstrate that our hybrid scheme with robust design outperforms the traditional relay selection scheme, because the traditional scheme does not consider hybrid FD/HD protocols and robust design based on imperfect channel conditions.
Keywords
1 Introduction
Due to the broadcast nature of wireless channels which makes communication ubiquitously accessible, security becomes one of the most important issues in wireless communications. Traditionally, communication security is guaranteed through highlayer encryption. With the development of interception technology and computing power, encryption needs to be more complex, leading to higher computation burden. Unlike traditional cryptographic approaches, physical layer security (PLS) takes advantage of the physical characteristics of wireless channels to achieve secure transmission. Wyner pointed out that when the legitimate channel has better propagation conditions than eavesdropping channel, secret transmission is theoretically possible without sharing any key [1].
However, if the channel condition of legitimate user is worse than that of the eavesdropping channels, secrecy rate can be very low or even decline to zero [1]. An efficient solution to enhance the legitimate transmission is through cooperative relaying or confusing the eavesdroppers via cooperative jamming. Recently, relay cooperation diversity has attracted more and more attentions, as it can significantly improve the communication coverage area and secrecy performance [2, 3]. To simplify radio hardware in cooperative diversity setups, relay selection strategy is adopted for multiple relay nodes communication. A distributed opportunistic relay selection approach was proposed in cooperative relay system [4]. This relay selection strategy achieves the same secrecy rate performance with low complexity, compared to the scheme that all nodes participate in aiding the communications.
Alternatively, the cooperative nodes can also act as jammers to transmit artificial jamming signals collaboratively to interfere the eavesdroppers. In [5], the cooperative jamming (CJ) was investigated for Gaussian multiple access and twoway channels. The optimal CJ weights for secrecy rate maximization (SRM) problem in the presence of a single eavesdropper were studied in [6]. Furthermore, hybrid relaying and jamming schemes were proposed to combine the advantages of both strategies in [4, 7].
Fullduplex (FD) operation, which always transmits and receives signals in the entire bandwidth, has attracted extensive attention. And a range of theoretical and practical researches have been investigated to take advantages of characteristic of FD protocol to enhance system performance [8, 9]. An interesting work was proposed in [8], where artificial noise (AN) was sent by a multiantenna FD receiver. In [8], authors aimed to design the optimal jamming vector that maximizes the secrecy rate and mitigates loop interference. To enhance secrecy performance of a multipleinputsingleoutputsingleeavesdropper (MISOSE) relay system, a joint information beamforming and jamming beamforming strategy were proposed to guarantee both transmitting security and receiving security for a FD base station in [9]. Some works also make use of the advantages of both FD and HD protocols to improve system performance. The hybrid scheme that switches between FD and HD protocols can be employed to enhance secrecy performance [10, 11].
However, in the above works [8–11], the perfect instantaneous channel state information (CSI) of all links is needed at the nodes which carry out the optimization procedure. Nevertheless, in practical relay communication networks, the perfect CSI is usually unknown and has to be estimated. The mismatch between the real and estimated CSI is caused by some inevitable factors, such as channel estimation errors, feedback delay, and quantization errors. Obviously, the performance of the designs developed in [8–11] could be heavily degraded by the imperfect CSI. Robust algorithm is an effective way to eliminate the influence of estimation errors. Typically, the existing works usually use deterministic uncertainty model (DUM) to characterize imperfect CSI: it assumes that a nominal value of the instantaneous CSI is available but lies in a bounded uncertainty region defined by some norm. The authors in [12] investigated the worstcase robust transmit covariance design problem of secrecyrate maximization in the presence of multiple eavesdroppers. In [13], cooperative transmission for securing a decodeandforward (DF) twohop network was studied, where only the statistical CSI of the eavesdropping channel is available.
To sum up, the researches above only investigate the secrecy performance in FD or HD networks, and little work has been done for hybrid relay networks with opportunistic relay selection. Moreover, cooperative jamming with robust design is not widely considered in multirelay systems, which can eliminate the influence of estimation errors.

We propose a hybrid FD/HD strategy and opportunistic proactive relay selection approach in our model, where the best relay is selected to switch between FD and HD operation to DF confidential signals. And the other relay nodes send distributed cooperative jamming signals to interfere the receiving signal and interference with noise ratio (SINR) at the eavesdropper.

In order to eliminate the influence of imperfect CSI to enhance the system security performance, we adopt the worstcase robust design to obtain the CJ beamformer under channel uncertainty. The optimization problem based on robust design is solved by SDP and interior method.

We derive the secrecy rate and secrecy outage expressions. Furthermore, we compare our scheme with a traditional relay selection scheme. Simulation results clearly show the advantage of our proposed scheme to improve system secrecy performance.
1.1 Notation
Bold uppercase and lowercase letters denote matrices and vectors, respectively. (•)^{ T } and (•)^{ H } stand for transpose and Hermitian’s transpose of a matrix or vector, respectively. I _{ N } is the N × N identity matrix. CN(τ, σ ^{2}) denotes the circularly symmetric, complex Gaussian distribution of vectors with mean τ and variance σ ^{2}.
2 System model
In particular, we assume the direct path between S and D is blocked by some obstacle so that there is no effective SD link. Otherwise, if SD link exits, system has to separate the useful signals from jamming signals, which will complicate the model. h _{ sr }, h _{ se }, h _{ rd }, h _{ re }, h _{ jr }, h _{ jd }, and h _{ je } denote the channel coefficients of SR, SE, RD, RE, RR, J_{ i }R, J_{ i }D, and J_{ i }E links, respectively, where h _{ jr }, h _{ jd }, and h _{ je } are stacked in M − 1 × 1 vector and other channel coefficients are scalars.
Throughout this paper, the following assumptions are adopted: (1) The channels from transmitting nodes to receiving nodes are symmetric, all the channels involved are considered to remain constant during one operation period and are quasistatic. (2) All the noise distributions are zeromean circular complex Gaussian with unit variance σ ^{2}. (3) All the channel coefficients experience Rayleigh fading, and the corresponding channel gains are obtained as γ _{ i } = P _{ i }h _{ i }^{2}/σ ^{2}, (i ∈ sr, se, rd, re) which are independently exponentially distributed with mean of λ _{ i }, \( {\gamma}_k={P}_k{\left{\mathbf{h}}_k^H\mathbf{f}\right}^2,\left(k\in jr,jd,je\right) \) and γ _{ k } ∼ Erlang(M − 1, λ _{ k }). (4) The selfinterference (SI) γ _{ rr } is well reduced to a tolerable level by efficient SI suppression. (5) The intended user D and legitimate user E employ maximum radio combination (MRC) technology to receive signals.
where x(t) and j(t) denote the transmitted useful signals and jamming signals with Ε{x(t)^{2}, j(t)^{2}} = 1, respectively. The term n _{ r } and n _{ e } represent naturally occurring noise at best relay R and eavesdropper E. At time slot t, the distributed jamming beamforming weight is stacked in vector f _{ r } = [f _{ r1}, f _{ r2}, ⋯, f _{ r(M − 1)}]^{ T }, and since the beamforming weight only determine the transmit direction, we normalize onedimensional vector f _{ r } as \( \left{\mathbf{f}}_r^H{\mathbf{f}}_r\right=1 \). We assume that there exist pernode power constraints of all the nodes. P _{ S } denotes the consumed power of the source, P _{ R } denotes the consumed power of the opportunistic relay, while P _{ Ji }(1 ≤ i ≤ M − 1) denotes the consumed power of cooperative node J_{ i }, respectively. And to relax the complexity, we assume P _{ Ji } = P _{ J }, (1 ≤ i ≤ M − 1). Thus, we can regard the cooperative jamming nodes as a multiantenna jammer to emit weighted jamming signals to interfere eavesdropper.
While at time slot t + 1, the distributed jamming beamforming weight is stacked in vector f _{ d } = [f _{ d1}, f _{ d2}, ⋯, f _{ d(M − 1)}]^{ T }.
Regarding the available CSI in a wireless communication system, the receiver usually estimates the channel using a training sequence (pilot symbols). At the transmitter, the CSI can be obtained through a feedback channel or from previous received signals, exploiting the channel reciprocity in time division duplexing (TDD) (see [14] for an overview of different channel estimation strategies). In this paper, we assume that the CSI h _{ je } is partially known at jammers, and this situation is reasonable while E is a legitimate user but also a potential active eavesdropper in wireless network [15–17]. Since the wireless system tries to enhance secrecy performance through signal processing at distributed jammers, thus, the system requires the receiving nodes feedback corresponding CSI to jammers. The potential eavesdropper additionally exchanges messages with the relay, appearing as a legitimate user. The goal of E is not only to intercept private message but also to feedback false training signals to interfere the estimation on SE and J_{ i }E links.
where \( {\tilde{\mathbf{h}}}_{je} \) denotes estimation of the channel h _{ je } and e _{ je }denotes channel uncertainty. Since we assume the ECSI at jamming nodes are imperfect, we consider DUM, where the error is deterministically bounded, i.e., e _{ je } ∈ ℜ{e : ‖e‖ ≤ ε}, where ε is assumed to be the upper bound on the channel uncertainty.
3 Opportunistic relaying and jamming
3.1 Opportunistic relaying
where ζ denotes power allocation at the source. In this case, the communication through the best relay would fail to outage while either S ‐ R ^{*} or R ^{*} ‐ D links occur outage.
In proactive selection strategy, selecting a single relay before the source transmission could potentially results in degraded performance. On the other hand, selecting a single relay for information forwarding before source transmission simplifies the receiver design and the overall network operation, since proactive selection is equivalent to routing. Although active selection is more precise because it depends on instantaneous CSI during the communication, it would cost additional spectrum during transmission to select best relay. Conversely, proactive selection can facilitate the receiver operation and system design while all the cooperative nodes stay idle except the opportunistic relay during the transmission. Thus, our opportunistic proactive relay strategy can be viewed as energy efficient.
3.2 Cooperative jamming with robust design
Unlike traditional opportunistic relay selection, except the chosen relay, the remaining nodes would stay idle. In our proposed scheme, the other cooperative nodes operate as jammers to suppress the eavesdropping process.
If the ECSI is known (for instance, the eavesdropper is an active user in the wireless network, it has to feed back its CSI), the source transmits designed CJ beamformer to enhance the security of system, which suppresses or eliminates the information leakage to eavesdropper. During the two time slots, cooperative jamming beamformer depends on JR and JD links, respectively; thus, jamming signals would have no influence on the chosen relay and legitimate D.
where \( \mathbf{H}={\mathbf{h}}_{jr}{\left({\mathbf{h}}_{jr}^H{\mathbf{h}}_{jr}\right)}^{1}{\mathbf{h}}_{jr}^H \) is the orthogonal matrix onto the subspace spanned by h _{ jr }. On the other hand, the optimal CJ beamformer f _{ d } at time slot t + 1 can be obtained with the same way.
Proof See Appendix.
Problem (16) can be efficiently solved by wellstudied interiorpoint algorithmbased package SeDuMi [18]. After \( {\mathbf{Q}}_z^{\ast } \) and e _{ je } are obtained, then, we can get the optimal f _{ d }. Meanwhile, the optimal f _{ r } can be obtained with the same approach.
4 Performance analysis
4.1 Secrecy rate
where \( {\gamma}_{jer}={P}_J{\left{\tilde{\mathbf{h}}}_{je}^H{\mathbf{f}}_r\right}^2/{\sigma}^2,{\gamma}_{jed}={P}_J{\left{\tilde{\mathbf{h}}}_{je}^H{\mathbf{f}}_d\right}^2/{\sigma}^2 \).
where [G]^{+} = max(G, 0).
4.2 Secrecy outage probability
4.3 Comparison with existing work
As shown above, an opportunistic relaying strategy with CJ is proposed in distributed relay networks. In comparison, cooperative transmission for securing a DF dualhop network where massive cooperative nodes coexist with a potential single eavesdropper is investigated. In [19], it adopts opportunistic relay strategy and works in HD model. Besides, it assumes instantaneous perfect CSI of the eavesdropper’s channel is available.
 (1)Conventional selection (CS): This solutions does not take the eavesdropper channels into account, and the relay node is selected based on the instantaneous CSI of the SD links. Although it is an effective solution for noneavesdropper environments, it cannot support systems with secrecy constraints. The conventional selection is written as$$ {R}^{\ast }= \arg \underset{R_i,i=1,\dots, M}{ \max}\left\{{\gamma}_{R_iD}\right\}. $$(29)
 (2)Optimal selection (OS): The optimal selection scheme takes the relayeavesdropper links into account and decides the relay node based on the knowledge of both RD and RE links. The optimal selection maximizes the secrecy capacity and is given as$$ {R}^{\ast }= \arg \underset{R_i,i=1,\dots, M}{ \max}\left\{\frac{\gamma_{R_iD}}{\gamma_{R_iE}}\right\}. $$(30)
 (3)
Suboptimal selection (SS): The suboptimal selection consists of a practical implementation of the optimal selection as it avoids the instantaneous estimate of the RE links by deciding the appropriate relay based on the knowledge of expectation of RE CSI. 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
In this comparison, we assume opportunistic relay selection strategy in [19] adopts reactive relay selection and OS, which is optimal in the above three strategy. However, due the effect of estimation errors, we assume the instantaneous knowledge of the eavesdropping channel is imperfect.

The authors in [19] deal with relay selection in cooperative networks with secrecy constraints. The proposed scheme in [19] enables an opportunistic selection of relay nodes to increase secrecy performance. The selected relay assists the source to deliver confidential information to destination via DF strategy. The proposed selection technique protects the primary destination against interference and eavesdropping. However, the approach is analyzed based on instantaneous perfect knowledge of the eavesdropper channels, which is assumed imperfect.

Unlike the traditional relay selection strategy in [19], after the best relay is selected, it would not select the optimal jammer to transmit artificial jamming signals. Our proposed scheme selects the best relay to switch between FD and HD operation to deteriorate the receiving SINR at the eavesdropper. At the first time slot, the best relay works in FD protocol to receive useful signals from source and emit artificial jamming signals to interfere eavesdropper. At the second time slot, source transmits artificial jamming signals and relay switch to HD protocol to DF the confidential signals. It can simultaneously avoid the interference at destination from the source and degrade the receiving at eavesdropper.

Besides, the instantaneous knowledge of all links and average knowledge of the eavesdropper links are considered in [19]. However, in practical, the perfect CSI is usually unknown and has to be estimated. The performance of the designs based on imperfect CSI will be heavily degraded. In our proposed scheme, we propose a worstcase robust design to obtain the CJ beamformer under channel uncertainty to improve secrecy performance, while traditional relay selection scheme [19] is based on estimated ECSI. Our robust algorithm can be viewed as an effective way to eliminate the influence of estimation errors.
5 Numerical analysis
In this section, we present simulation results to illustrate the performance analysis mentioned in Section 4 and compare our proposed scheme with [19]. For convenience, we assume the noise power σ ^{2} = 1 and number of cooperative nodes is M = 5. To simplify the deducing, we consider Gaussian’s noise in the channel estimation and define spherical uncertainty regions with a radius equal to \( \varepsilon =g\left\Vert {\tilde{\mathbf{h}}}_{je}\right\Vert, 0\le g\le 1 \). Note that for these uncertainty regions, \( {\mathbf{h}}_{je}={\tilde{\mathbf{h}}}_{je}+{\mathbf{e}}_{je}\ne \mathbf{0},\forall {\mathbf{e}}_{je}\in \mathrm{\Re} \).
Finally, we compare the computational complexity of our proposed scheme and TRS scheme. For the sake of notational simplicity, we evaluate how the computational complexity of both schemes scale with the number of nodes M. In our proposed scheme, the complexity of the opportunistic relay selection is O(M). The complexity order of obtain f _{ r } and f _{ d } through solving the SDP problem (11)–(16) is O(M ^{5}) [20]. Thus, the computational complexity of our proposed scheme is O(M ^{5}). For the TRS scheme, the major computation task is how to obtain best relay R ^{*} based on imperfect CSI (30), which has complexity order of O(M). Thus, the computational complexity of traditional CJ scheme is O(M). Based on the analysis above, we find that our proposed scheme has a higher complexity than traditional one. However, the proposed scheme outperforms TRS scheme both on secrecy rate and secrecy outage probability.
6 Conclusions
In this paper, we addressed a hybrid opportunistic relaying and jamming strategy in multirelay system under imperfect channel estimation. A proactive opportunistic relay selection is proposed, in which the criteria are based on the channel conditions. To enhance secrecy performance of cooperative jamming under channel uncertainty, we transform the optimization problem into a SDP with some LMI constraints, which is solved by the interior point approach. Furthermore, we derive the secrecy rate and deduce the outage probability. Since our proposed scheme takes advantages of cooperative jamming with robust design and increases interference on eavesdropper through hybrid FD/HD protocols, simulation results demonstrated that the proposed scheme leads to significant improvement than TRS strategy in distributed relay system.
Declarations
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No.61371122 and No. 61471393) and the China Postdoctoral Science Foundation under a Special Financial Grant No. 2013T60912.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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