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Wireless Communications and Mobile Computing
Volume 2018, Article ID 2379427, 12 pages
https://doi.org/10.1155/2018/2379427
Research Article

Security-Reliability Tradeoff Analysis in Multisource Multirelay Cooperative Networks with Multiple Cochannel Interferers

1State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, Shaanxi 710071, China
2Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an, Shaanxi 710071, China

Correspondence should be addressed to Jiangbo Si; nc.ude.naidix@isbj

Received 3 January 2018; Accepted 14 February 2018; Published 28 June 2018

Academic Editor: Zheng Chu

Copyright © 2018 Weilong Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Cooperative relaying communication is one of the green communication technologies since it shortens the communication distance and saves the transmit power. In this paper, the physical-layer security (PLS) of a multisource multirelay cooperative relaying communication network is investigated by considering the influence of cochannel interference from a security-reliability tradeoff (SRT) perspective. First, the SRT performance is characterized by the outage probability (OP) and the intercept probability (IP). In particular, the IP encountered at the eavesdropper is used to evaluate the security performance, while the reliability performance is analyzed in terms of the OP experienced at the destination. Then, under the impact of multiple cochannel interferers, the intercept probabilities and the outage probabilities of both the conventional direct transmission (DT) strategy and relay selection (RS) strategy are derived in closed-form expressions over Rayleigh fading channels, respectively. Simulation results are provided to validate the theoretical analysis. It is shown that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. Meanwhile, a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, it is also shown that the RS strategy generally outperforms the conventional DT strategy in terms of the product of the IP and the OP.

1. Introduction

With an explosive growth of the number of wireless devices, such as smart phones, tablet computers, and wireless sensors, more and more energy has been consumed by wireless services. According to [1], the amount of the energy consumed by the information and communication technologies accounts for about 2% to 10% of the global energy consumption, which generate nonnegligible amount of the greenhouse gases. What is worst, this percentage will grow rapidly with the development of the information and communication technologies and the increase of number of wireless devices. It will result in more greenhouse gases emission and environment pollution [2]. One promising technique to alleviate such issue is to adopt green communication technology, which can improve both the spectrum efficiency and energy efficiency of wireless communication systems. Cooperative relaying communication is an energy efficient diversity technique, which has been recognized as a green communication technology and attracts unprecedented research interest in both academic and industrial fields. A challenging issue in cooperative relaying communication is wireless security [35]. Because of the inherent broadcast nature of wireless channels, the destination may not successfully obtain source information, while the malicious eavesdropper may overhear and intercept the confidential information, which makes the wireless transmission insecure and vulnerable to eavesdropping attacks [6].

Motivated by the above fact, physical-layer security (PLS) was proposed and has attracted increasing research attention since it is an effective paradigm of achieving information-theoretic security for protecting wireless communications against the eavesdropping attacks by utilizing the physical characteristics of wireless channels [7]. The PLS was first investigated by Shannon [8] and further developed by Wyner, who examined a classical point-to-point discrete memoryless wiretap channel (WTC) scenario consisting of a source node and a destination node as well as an eavesdropper node [9]. It was proven in [9] that perfectly secure and reliable transmission from the source node to the legitimate destination node can be achieved when the main channel from the source node to the destination node is an upgraded version of the wiretap channel from the source node to the eavesdropper node. Later on, in [10, 11], Wyner’s conclusions were, respectively, extended from the discrete memoryless wiretap channel to the nondegraded wiretap channel and the Gaussian degraded wiretap channel, where the notion of secrecy capacity (SC) was introduced. It was derived as the difference between the channel capacity of the legitimate link and that of the wiretap link. Specifically, the SC can make the transmission from the source node to the legitimate destination node secure while achieving zero mutual information between the source node and malicious eavesdropper node. Based on this idea, extensive research efforts have been devoted to improving the SC from an information-theoretic perspective under different scenarios, for example, cooperative relaying [1215] and beamforming techniques [16, 17], cooperative jamming (CJ) methods [1820], and multiple-input multiple-output (MIMO) schemes [21, 22].

The previous works are mainly focused on enhancing wireless security without paying much attention to communication reliability. Hence, security-reliability tradeoff (SRT) was proposed to make best tradeoff between the outage probability (OP) and the intercept probability (IP). In particular, the IP encountered at the eavesdropper is used to evaluate the security performance, while the reliability performance is measured by the OP experienced at the destination. In [23], the authors studied the employment of various block cipher encryption algorithms from the perspective of both reliability and security and showed that there exists a tradeoff between communication reliability and security. Later on, the authors of [24] investigated the SRT for the downlink cloud radio access networks and the channel estimation errors were considered and the impact of the times of training on the security and reliability performance was also analyzed. The SRT of the cognitive amplify-and-forward (AF) relay network was investigated under imperfect channel estimation in [25]. As a further development, the authors of [26] characterized the SRT and quantified the benefits of opportunistic relay selection (ORS) for the purpose of improving the SRT. In [27], the authors proposed the single-relay and multirelay selection schemes for improving the SRT of general wireless networks. It was proved in [27] that in terms of the SRT the multirelay selection scheme outperformed the single-relay one.

It can been seen from the above works that the PLS of multisource multirelay cooperative networks under the impact of the cochannel interferers is not considered. Motivated by this fact, the main contributions of this paper are summarized as follows: firstly, the PLS of a multisource multirelay cooperative communication network is investigated from an SRT perspective and cochannel interferers are considered. Secondly, a signal-to-interference-plus-noise ratio- (SINR-) based method is proposed and the closed-form expressions of IP and OP are derived for the direct transmission (DT) and the relay selection (RS) schemes over Rayleigh fading, respectively. Finally, simulation results are provided to validate the theoretical analysis. It is shown that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. Meanwhile, a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, it is also shown that the RS strategy generally outperforms the conventional DT strategy in terms of the product of the IP and the OP.

The remainder of this paper is organized as follows. In Section 2, the system models are described. The SRT performance analysis for both the conventional DT and RS schemes over Rayleigh fading channels is presented in Section 3. Section 4 presents simulation results to corroborate the proposed studies. Section 5 concludes the paper.

2. The System Model

2.1. System Model Description

Consider a multisource multirelay cooperative wireless network as shown in Figure 1, which consists of sources , one eavesdropper , one destination , relays , and cochannel interferers . The sources communicate with the corresponding destination via the direct link or with the help of the intermediate relays. At a specific time, only the source having the highest direct-link channel quality is viewed as the best one and is selected to transmit with the aid of relays. Meanwhile, will intercept the information from the selected source and relays. interferers share the same bands with and and cause interferences to them. It can be observed that the system model is practical and can be applied to practical scenarios [2830]. It is assume that all nodes are equipped with single antenna and all channels are Rayleigh fading. Without loss of generality, we consider additive white Gaussian noise (AWGN) with zero mean and variance at each node in networks. We assume that the sources have the global channel state information (CSI) of both the main and wiretap channels and in order to analyze the performance of the worst case, is assumed to know all system parameters of the legitimate transmission from to , except for the signal. Typically, the linear minimum mean-square error (LMMSE) estimation method can be used to obtain the CSI by the destination and the eavesdropper [24, 25]. Note that this assumption has been widely used in [26, 27, 31].

Figure 1: Multisource multirelay cooperative network system model.
2.2. Direct Transmission Strategy

In this subsection, the conventional DT strategy is considered for the purpose of performance comparison. A classical DT communication scenario consisting of sources, one destination, and one eavesdropper with cochannel interferers is considered. Assuming that all sources send messages at a power while the interferers transmit at a power . Let and , respectively, denote the source signal from the selected best source and the interfering signal transmitted by the th interferer . When transmits with the rate at a particular time instant, transmits with the rate . Hence, under the presence of cochannel interferers, the signals received at and nodes can be, respectively, presented aswhere , , , and , respectively, denote the fading gains of the channel from to , that from to , that from to , and that from to . and represent the AWGN encountered at and nodes, respectively. Using Shannon’s capacity formula, the capacity of the channel spanning from to is given bywhere and . Similarly, the channel capacity of - transmission is obtained from (2) asSince fading gains , , , and are modeled as Rayleigh random variables, then , , , and are exponentially distributed. Accordingly, , , , and represent the means of , , , and , respectively.

2.3. Relay Selection Strategy

As shown in Figure 1, this subsection presents a multisource multirelay cooperative wireless network with multiple cochannel interferers existing at relays, and . Specifically, all sources share the relay nodes and the relays employ the decode-and-forward (DF) relaying protocol. Without loss of generality, the total cooperative communication procedure is divided into two time slots. It can also be seen from Figure 1 that the solid and dash lines represent the transmission in the first time slot and that in the second time slot, respectively. In the first time slot, the selected best source node transmits its signals to and all relays, and meanwhile intercepts the transmission of the source. Under the presence of cochannel interferers, the signals received at , , and nodes can be, respectively, presented aswhere and , respectively, denote the fading gains of the channel from to and that from to . represents the AWGN encountered at node. Similar to [7], according to (5), (6), and (7), the capacities of the channel spanning from to , that spanning from to , and that spanning from to can, respectively, be obtained aswhere arises from the fact that two orthogonal slots are needed for completing the overall transmission. Similarly, and are exponentially distributed and accordingly, and and represent the means of and , respectively.

According to the DF protocol, only those relays that succeed in perfectly decoding the source signal form a decoding set denoted by . Thus, in the second time slot, when is a nonempty set, a specific relay is chosen from for forwarding its received signal to node with denoting the transmit power. In particular, is regarded as the selected relay node. Then, the signal received at node can be presented aswhere represents the fading gain of the channel from to . Similarly, according to (11), the capacity of the channel spanning from to is given bywhere is exponentially distributed and represents the mean of . Based on the obtained capacity of the channel spanning from to , the selected relay node with the largest channel capacity is chosen from , that is,where represents the selected best relay node. It can be seen from (12) that the interferers and noise terms are same for the channel capacities of different relays. Then, (13) is simplified as . Thus, the signal received at node with the best relay node can be presented aswhere denotes the fading gain of the channel from to . Thus, according to (14), the capacity of the channel spanning from to is given by where is exponentially distributed and represents the mean of .

Across this paper, for ease of discussion, we assume that and . This assumption can be valid in a statistical sense when all relays are mobile and uniformly distributed around and nodes [7].

3. SRT Performance Analysis over Rayleigh Fading Channels

In this section, the SRT performance analysis of the conventional DT strategy as well as of the RS strategy with the presence of multiple cochannel interferers communicating over Rayleigh fading channels is presented. As discussed in [7], the tradeoff between the security and reliability, characterized by the intercept probability and by the outage probability, is analyzed. In particular, the outage probability represents the probability that the capacity of the main channel is lower than the data rate and the intercept probability represents the probability that the capacity of the wiretap channel is higher than the data rate. Then, the two performance metrics can be expressed aswhere and represent, respectively, the capacity of the main channel achieved at the destination and that of the wiretap channel experienced by the eavesdropper. is the data rate.

3.1. Direct Transmission Strategy

In what follows, the SRT performance of the conventional DT strategy is first analyzed as a benchmark. According to (16), using the law of total probability, the OP of the conventional DT strategy can be formulated aswhere is given by (3). Substituting into (18), the OP is given by where and . Note that, due to the common term , cannot be calculated as the conventional analysis directly. Hence, upon assuming , can be expressed asin which the first term can be obtained asIn (20), it can be found that, for , the second-term . Therefore, there are two cases for the term ; that is,Then substituting (21) and (22) into (20) yieldsProceeding as in Appendix A, one has

Similarly, according to (4) and (17), the IP of the conventional DT strategy is formulated asWith the aid of , the IP can be expressed as where . Similar to the analysis of , can be rewritten aswhere the term can be readily derived asThen substituting (21) and (28) into (27), one hasAfter some appropriate incorporations and necessary mathematical manipulations, can be obtained as

3.2. Relay Selection Strategy

This subsection focuses on the SRT performance analysis of the RS strategy. According to (16) and using the theory of total probability, the OP of the RS strategy is formulated aswhere represents the number of elements in successful decoding set and denotes the relay set. As can be observed, when is an empty set (i.e., ), it shows that no relay can be chosen for forwarding the received signal. In this case, only the direct link is available, that is, , where is a nonempty set and selection combining is considered to combine the received signal copies at from the selected best source and the selected best relay during the two time slots. In this case, the capacity achieved by is the higher one between and , that is, . Substituting these results into (31), one haswhere the terms and are, respectively, given byIn (32), the term denotes the probability that there exist relays decoding the source signal successfully. Thus, considering and , one haswhere and is the complementary set of the successful decoding set . By utilizing a similar way, the term is calculated asAs discussed before, by utilizing a similar way as , can be obtained asSimilar to (20), the term is expressed asProceeding as in Appendix B, can be obtained as

On the other hand, similarly, according to (17) and using the theory of total probability, the IP of the RS strategy is formulated asDuring the two slots, note that will intercept the message transmitted by both the selected best source and the selected best relay and perform detection using both received signal copies. Thus, (40) can be rewritten asin which the terms and are, respectively, given byAs discussed before, similar to , can be obtained asSimilar to (38), the term can be rewritten asAfter some appropriate substitutions and via utilizing a similar derivation for , can be obtained as

Therefore, after some incorporations and iterations, the closed-form outage probability and intercept probability expressions of both the DT and RS schemes with multiple cochannel interferers can be achieved.

4. Simulation Evaluations

In this section, the SRT performances of the DT and RS schemes are evaluated by simulations. The simulation parameters are set as follows: , , , and .

Figures 24 show the curves of the theoretical SRT analysis. As can be seen from the figures the intercept probability is presented as a function of the outage probability. Obviously, it can be seen that the simulation results match well with the theoretical analysis. Figure 2 shows the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different (). Figure 2 also shows that as the outage probabilities increase, the intercept probabilities of the conventional DT and the RS schemes decrease. This confirms that there exists a tradeoff between the intercept probability and the outage probability. Another phenomenon can be observed in Figure 2; that is, the SRT of the RS strategy always outperforms that of the conventional DT strategy. Moreover, the SRT of the RS strategy is also improved with increasing (from to ). This is due to the reason that the diversity gain can be obtained with the increase of the number of relays.

Figure 2: SRTs of the conventional DT strategy and RS strategy for different numbers of relays with , , and .
Figure 3: SRTs of the conventional DT strategy and RS strategy for different numbers of cochannel interferers with , , and .
Figure 4: SRTs of the conventional DT strategy and RS strategy for different numbers of sources with , , and .

Figure 3 depicts the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different (). Figure 3 also shows that when the outage probabilities change from to , the intercept probabilities of the conventional DT and the RS schemes decrease correspondingly. Moreover, for a given , the SRT of the RS strategy performs better than that of the conventional DT strategy. It is also seen that the SRTs of the conventional DT and the RS schemes are also improved with increasing (from to ).

Figure 4 shows the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different (). Similar to Figure 3, the intercept probabilities of the conventional DT and the RS schemes decrease correspondingly, as the outage probabilities increase from to . Moreover, for a given , the SRT of the RS strategy always outperforms that of the conventional DT strategy. The SRTs of the conventional DT and the RS schemes are also improved with increasing (from to ). By jointly considering Figures 24, it is found that as the outage probabilities increase, the intercept probabilities of the conventional DT and the RS schemes decrease, implying that the SRT indeed exists between the intercept probability and the outage probability. Meanwhile, the improvement of the SRT is obtained with increasing the number of sources, relays, and cochannel interferers. Moreover, it is also shown that the SRT of the RS strategy consistently outperforms that of the conventional DT strategy.

In order to further evaluate the SRT, the products of the intercept probabilities and the outage probabilities of the conventional DT strategy as well as the RS strategy are plotted in Figures 57. Figure 5 shows the products of the conventional DT strategy as well as the RS strategy against the transmit SNR at different numbers of available relays (). Figure 5 also shows that there exists an peak with the increase of the transmit SNR . This is due to the reason that the IP in the low SNR regime comes close to 0, and the OP in the high SNR regime comes close to 0. Particularly, the presence of the peak is another perspective that the SRT indeed exists between the intercept probability and the outage probability. Clearly, it is also seen from Figure 5 that the maximum product of the RS strategy is smaller than that of the conventional DT strategy, which means the RS strategy is always better than the conventional DT strategy in terms of the product. Moreover, the maximum product decreases significantly with increasing (from to ). It implies the SRT of the RS strategy is improved accordingly.

Figure 5: versus the transmit SNR of the conventional DT strategy and RS strategy for different numbers of relays with , , and .
Figure 6: versus the transmit SNR of the conventional DT strategy and RS strategy for different numbers of cochannel interferers with , , and .
Figure 7: versus the transmit SNR of the conventional DT strategy and RS strategy for different numbers of sources with , , and .

Figure 6 shows the products of the conventional DT strategy as well as the RS strategy against the transmit SNR at different (). Similar to Figure 5, there also exists an peak with the increase of the transmit SNR . Figure 6 also shows that, for a given , the RS strategy outperforms the DT strategy in terms of the product. Moreover, the SRTs of the conventional DT and the RS schemes are also improved with increasing (from to ).

Figure 7 shows the products of the conventional DT strategy as well as the RS strategy versus the transmit SNR at different (). Similar to Figure 5, there also exists an peak with the increase of the transmit SNR . Meanwhile, for a given , the RS strategy outperforms the conventional DT strategy in terms of the product, and when the number of sources increases from to , the maximum product can be minimized so that the SRTs of the conventional DT and the RS schemes are improved. By jointly considering Figures 57, the improvement of the SRT performance in terms of the product can be achieved by increasing the number of relays, sources, and cochannel interferers. Moreover, it is also shown that the SRT performance of the RS strategy is better than that of the conventional DT strategy in terms of the product of the IP and the OP.

5. Conclusions

In this paper, we presented the PLS of a multisource multirelay cooperative communication network by considering the influence of cochannel interference from an SRT perspective. Under impact of cochannel interferers, we adopted an SINR-based method to analyze the SRT performance characterized by the OP and the IP. We derived the closed-form IP and OP expressions of both the conventional DT strategy and RS strategy over Rayleigh fading channels, respectively. We showed that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. We also showed that a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, the RS strategy generally outperforms the conventional DT strategy in terms of the product of the OP and the IP.

Appendix

A. Derivation of (24)

According to (23), is rewritten as

After some incorporations and necessary mathematical manipulations, can be calculated as

For notational convenience, considering and and using the equation [32], can be achieved as shown in (24).

This completes the derivation of (24).

B. Derivation of (39)

According to (38), the second term can be expressed as where the term can be calculated asSubstituting (B.2) into (B.1), one hasUsing the equation [32], can be calculated as By utilizing a similar way, can be obtained as Substituting (21) and (B.1) into (38), can be expressed as

Then, incorporating (B.4) into (B.6) and employing some mathematical manipulations, can be calculated as By utilizing a similar way, can be obtained as

Incorporating (B.7) and (B.8) into (B.6), and for simplicity, considering and , can be obtained as shown in (39).

This completes the derivation of (39).

Data Availability

The underlying data comes from simulation results.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The research reported in this article was supported by the National Natural Science Foundation of China (61501356 and 61501354), by the Key Project of National Natural Science Foundation of China (61631015), by the National Key Scientific and Technological Innovation Team Plan (2016KCT-01), and by the Fundamental Research Funds for the Central Universities (7215433803).

References

  1. X. Huang, T. Han, and N. Ansari, “On green-energy-powered cognitive radio networks,” IEEE Communications Surveys & Tutorials, vol. 17, no. 2, pp. 827–842, 2015. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Zhang, K. Cumanan, and A. Burr, “Secure energy efficiency optimization for MISO cognitive radio network with energy harvesting,” in Proceedings of the 2017 9th International Conference on Wireless Communications and Signal Processing (WCSP), pp. 1–6, Nanjing, October 2017. View at Publisher · View at Google Scholar
  3. A. G. Fragkiadakis, E. Z. Tragos, and I. G. Askoxylakis, “A survey on security threats and detection techniques in cognitive radio networks,” IEEE Communications Surveys & Tutorials, vol. 15, no. 1, pp. 428–445, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. F. Zhou, Z. Li, J. Cheng, Q. Li, and J. Si, “Robust AN-Aided Beamforming and Power Splitting Design for Secure MISO Cognitive Radio with SWIPT,” IEEE Transactions on Wireless Communications, vol. 16, no. 4, pp. 2450–2464, 2017. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Wu, R. Schober, D. W. Ng, C. Xiao, and G. Caire, “Secure massive {MIMO} transmission with an active eavesdropper,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 62, no. 7, pp. 3880–3900, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Bloch, J. Barros, M. R. Rodrigues, and S. W. McLaughlin, “Wireless information-theoretic security,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 54, no. 6, pp. 2515–2534, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. Zou, J. Zhu, X. Wang, and L. Hanzo, “A survey on wireless security: technical challenges, recent advances, and future trends,” Proceedings of the IEEE, vol. 104, no. 9, pp. 1727–1765, 2016. View at Publisher · View at Google Scholar · View at Scopus
  8. C. E. Shannon, “Communication theory of secrecy systems,” Bell Labs Technical Journal, vol. 28, pp. 656–715, 1949. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. A. D. Wyner, “The wire-tap channel,” Bell Labs Technical Journal, vol. 54, no. 8, pp. 1355–1387, 1975. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. I. Csisz and J. Köner, “Broadcast channels with confidential messages,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 24, no. 3, pp. 339–348, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. l. Y. Cheong and M. E. Hellman, “The Gaussian wire-tap channel,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 24, no. 4, pp. 451–456, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. Zou, Y. D. Yao, and B. Zheng, “Cooperative relay techniques for cognitive radio systems: spectrum sensing and secondary user transmissions,” IEEE Communications Magazine, vol. 50, no. 4, pp. 98–103, 2012. View at Publisher · View at Google Scholar
  13. H. Sakran, M. Shokair, O. Nasr, S. El-Rabaie, and A. A. El-Azm, “Proposed relay selection scheme for physical layer security in cognitive radio networks,” IET Communications, vol. 6, no. 16, pp. 2676–2687, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. B. V. Nguyen and K. Kim, “Secrecy outage probability of optimal relay selection for secure AnF cooperative networks,” IEEE Communications Letters, vol. 19, no. 12, pp. 2086–2089, 2015. View at Publisher · View at Google Scholar
  15. L. J. Rodriguez, N. H. Tran, T. Q. Duong, T. Le-Ngoc, M. Elkashlan, and S. Shetty, “Physical layer security in wireless cooperative relay networks: State of the art and beyond,” IEEE Communications Magazine, vol. 53, no. 12, pp. 32–39, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. H. M. Wang, Q. Yin, and X. G. Xia, “Distributed beamforming for physical-layer security of two-way relay networks,” IEEE Transactions on Signal Processing, vol. 60, no. 7, pp. 3532–3545, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. M. Wang, F. Liu, and M. Yang, “Joint Cooperative Beamforming, Jamming, and Power Allocation to Secure AF Relay Systems,” IEEE Transactions on Vehicular Technology, vol. 64, no. 10, pp. 4893–4898, 2015. View at Publisher · View at Google Scholar · View at Scopus
  18. G. Zheng, L. C. Choo, and K. K. Wong, “Optimal cooperative jamming to enhance physical layer security using relays,” IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 1317–1322, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. F. Zhu, F. Gao, M. Yao, and H. Zou, “Joint information- and jamming-beamforming for physical layer security with full duplex base station,” IEEE Transactions on Signal Processing, vol. 62, no. 24, pp. 6391–6401, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. B. Han, J. Li, J. Su, M. Guo, and B. Zhao, “Secrecy capacity optimization via cooperative relaying and jamming for WANETs,” IEEE Transactions on Parallel and Distributed Systems, vol. 26, no. 4, pp. 1117–1128, 2015. View at Publisher · View at Google Scholar · View at Scopus
  21. S. A. Fakoorian and A. L. Swindlehurst, “Solutions for the {MIMO} Gaussian wiretap channel with a cooperative jammer,” IEEE Transactions on Signal Processing, vol. 59, no. 10, pp. 5013–5022, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. Jeong, I. M. Kim, and D. I. Kim, “Joint secure beamforming design at the source and the relay for an amplify-and-forward {MIMO} untrusted relay system,” IEEE Transactions on Signal Processing, vol. 60, no. 1, pp. 310–325, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. Yin, S. Wei, J. Yuan, X. Shan, and X. Wang, “Tradeoff between reliability and security in block ciphering systems with physical channel errors,” in Proceedings of the IEEE Military Communications Conference (MILCOM '10), pp. 2156–2161, San Jose, Claif, USA, November 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. J. You, Z. Zhong, G. Wang, and B. Ai, “Security and Reliability Performance Analysis for Cloud Radio Access Networks with Channel Estimation Errors,” IEEE Access, vol. 2, pp. 1348–1358, 2014. View at Publisher · View at Google Scholar · View at Scopus
  25. Q. Gu, G. Wang, L. Gao, and M. Peng, “Security-reliability performance of cognitive AF relay-based wireless communication system with channel estimation error Security Challenges and Issues in Cognitive Radio Networks,” EURASIP Journal on Advances in Signal Processing, vol. 2014, no. 1, article no. 28, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Zou, X. Wang, W. Shen, and L. Hanzo, “Security versus reliability analysis of opportunistic relaying,” IEEE Transactions on Vehicular Technology, vol. 63, no. 6, pp. 2653–2661, 2014. View at Publisher · View at Google Scholar · View at Scopus
  27. J. Zhu, Y. Zou, B. Champagne, W.-P. Zhu, and L. Hanzo, “Security-reliability trade-off analysis of multi-relay aided decode-and-forward cooperation systems,” IEEE Transactions on Vehicular Technology, vol. 65, no. 7, pp. 5825–5831, 2016. View at Publisher · View at Google Scholar
  28. L. Fan, X. Lei, N. Yang, T. Q. Duong, and G. K. Karagiannidis, “Secure Multiple Amplify-and-Forward Relaying with Cochannel Interference,” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 8, pp. 1494–1505, 2016. View at Publisher · View at Google Scholar · View at Scopus
  29. M. Ahmadian-Attari, S. Vahidian, M. Mohammadi, and S. Hataminia, “Performance analysis of two-way decode-and-forward relaying in the presence of co-channel interferences,” IET Communications, vol. 8, no. 18, pp. 3349–3356, 2014. View at Publisher · View at Google Scholar
  30. S. Vahidian, S. Aïssa, and S. Hatamnia, “Relay selection for Security-Constrained cooperative communication in the presence of eavesdropper's overhearing and interference,” IEEE Wireless Communications Letters, vol. 4, no. 6, pp. 577–580, 2015. View at Publisher · View at Google Scholar · View at Scopus
  31. W. Hu, Z. Li, H. Li, J. Si, and H. Huang, “SRT analysis of relay selection in the presence of multiple co-channel interferers,” IET Communications, vol. 11, no. 6, pp. 809–816, 2017. View at Publisher · View at Google Scholar · View at Scopus
  32. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, Inc., San Diego, CA, USA, 7th edition, 1996. View at MathSciNet