# A Repeated Games-Based Secure Multiple-Channels Communications Scheme for Secondary Users with Randomly Attacking Eavesdroppers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

#### Local Spectrum Sensing

## 3. Game Models for Channel Selection

#### 3.1. Game Formulation

#### 3.2. Game Solution

Algorithm 1 Solve the game problem in Equation (18). |

Output of the algorithm: the optimal action of user m, ${a}_{m}^{\ast}$. 1: for ${a}_{m}=1\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}to\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}K$2: Calculate expected payoff $e{\mathcal{U}}_{m}\left({a}_{m}\right)$ of player m3: Initial value $e{\mathcal{U}}_{m}\left({a}_{m}\right)=0$ 4: Define ${\mathbb{z}}_{n}$ as a combination action of $(M-1)$ users, except user m. 5: ${\mathbb{z}}_{n}=\left\{{a}_{1},\dots ,{a}_{\left(m-1\right)},{a}_{\left(m+1\right)},\dots ,{a}_{M}\left|{a}_{j}\in K,j\in \mathcal{M}\setminus m\right.\right\}$ 6: The total number of possible combination actions ${\mathbb{z}}_{n}$: ${\mu}_{\mathbb{z}}={K}^{\left(M-1\right)}$ 7: All combination actions of $(M-1)$ users except m are: $\mathbb{Z}=\{{\mathbb{z}}_{1},{\mathbb{z}}_{2},\dots ,{\mathbb{z}}_{{\mu}_{\mathbb{z}}}\}$ 8: for $n=1\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}to\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}{\mu}_{\mathbb{z}}$9: Calculate 10: $e{\mathcal{U}}_{m}\left({a}_{m}\right)=e{\mathcal{U}}_{m}\left({a}_{m}\right)+{\mathcal{U}}_{m}\left({a}_{m},{\mathbb{z}}_{n}\right)\prod _{j=1}^{M-1}{P}_{j}^{{a}_{j}}$ 11: with ${a}_{j}\in {\mathbb{z}}_{n},j\in \mathcal{M}\setminus m$ 12: ${\mathcal{U}}_{m}\left({a}_{m},{\mathbb{z}}_{n}\right)$ is calculated with Equation (12) 13: end for14: end for15: Find the optimal action of the game, ${a}_{m}^{\ast}$: ${a}_{m}^{\ast}={\displaystyle \underset{{a}_{m}}{arg}}\phantom{\rule{0.166667em}{0ex}}max\left(e{\mathcal{U}}_{m}\left({a}_{m}\right)\right)$ |

## 4. An Anti-Eavesdropper Scheme for the Multiple-Channel Communications of Cognitive Radio Users

Algorithm 2 An anti-eavesdropper scheme based on multiple games for SUs. |

Output of the algorithm: the optimal channel ${a}_{m}^{\ast}$ for user m. Given the state of the system: $\mathcal{S}=\left\{{s}^{k}\right|k=\{1,2,3,\dots ,K\}\}$ as defined in Equation (10), where ${s}_{k}=\{{P}_{0}^{k},{\mathcal{P}}_{i}^{k}|k=\{1,2,3,\dots ,K\}\}$. 1: The first game: We determine pre-selected channel ${a}_{m}^{pre}$ by solving Equation (18) with the state $\mathcal{S}$ where Equation (18) can be solved with Algorithm 1. 2: The user m will perform spectrum sensing on the pre-selected channel ${a}_{m}^{pre}$; according to the sensing result in the channel, we update belief ${P}_{0}^{{a}_{m}^{pre}}$ as Equation (19) or (20). 3: According to the updated belief ${P}_{0}^{{a}_{m}^{pre}}$, we determine the updated state of the system, ${\mathcal{S}}^{u}$, as defined in Equation (10). 4: The second game: The updated state ${\mathcal{S}}^{u}$ will be used to compute the payoff of player m, as shown in Equation (17), which is the object function for the problem in Equation (18). The problem in Equation (18) will be solved to find optimal action ${a}_{m}^{\ast}$ for the user m according to Algorithm 1. 5: The user m will access channel ${a}_{m}^{\ast}$ to achieve its reward. According to the observation of the communications link in the channel, the state of the system will be updated for use in the next time slot as Equations (21)–(24). |

## 5. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Liang, Y.C.; Chen, K.C.; Li, G.Y.; Mahonen, P. Cognitive Radio Networking and Communications: An Overview. IEEE Trans. Veh. Technol.
**2011**, 60, 3386–3407. [Google Scholar] [CrossRef] - Mitola, J.; Maguire, G.Q. Cognitive Radio: Making Software Radios More Personal. IEEE Pers. Commun.
**1999**, 6, 13–18. [Google Scholar] [CrossRef] - Haykin, S. Cognitive Radio: Brain-Empowered Wireless Communications. IEEE J. Sel. Areas Commun.
**2005**, 23, 201–220. [Google Scholar] [CrossRef] - Ghasemi, A.; Sousa, E.S. Collaborative Spectrum Sensing for Opportunistic Access in Fading Environments. In Proceedings of the First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), Baltimore, MD, USA, 8–11 November 2005; pp. 131–136. [Google Scholar]
- Letaief, K.B.; Zhang, W. Cooperative Spectrum Sensing. In Cognitive Wireless Communication Networks; Springer: Boston, MA, USA, 2007; pp. 115–138. [Google Scholar]
- Sun, C.; Zhang, W.; Letaief, K.B. Cluster-Based Cooperative Spectrum Sensing in Cognitive Radio Systems. In Proceedings of the IEEE International Conference on Communications, Glasgow, UK, 24–28 June 2007; pp. 2511–2515. [Google Scholar]
- Lee, C.H.; Wolf, W. Energy Efficient Techniques for Cooperative Spectrum Sensing in Cognitive Radios. In Proceedings of the IEEE Consumer Communications and Networking Conference, Las Vegas, NV, USA, 10–12 January 2008; pp. 968–972. [Google Scholar]
- Ghurumuruhan, G.; Li, Y.G. Cooperative Spectrum Sensing in Cognitive Radio: Part I: Two User Networks. IEEE Trans. Wirel. Commun.
**2007**, 6, 2204–2213. [Google Scholar] - Ghurumuruhan, G.; Li, Y.G. Cooperative Spectrum Sensing in Cognitive Radio: Part II: Multiuser Networks. IEEE Trans. Wirel. Commun.
**2007**, 6, 2214–2222. [Google Scholar] - Networks, A. Worldwide Infrastructure Security Report. 2015. Available online: https://pages.arbornetworks.com/rs/082-kna-087/images/12th_worldwide_infrastructure_security_report.pdf (accessed on 20 November 2019).
- Gao, Q.; Huo, Y.; Ma, L.; Xing, X.; Cheng, X.; Jing, T.; Liu, H. Optimal Stopping Theory Based Jammer Selection for Securing Cooperative Cognitive Radio Networks. In Proceedings of the 2016 IEEE Global Communications Conference (GLOBECOM), Washington, DC, USA, 4–8 December 2016; pp. 265–270. [Google Scholar]
- Lou, L.; Fan, J.H. An Anti-Jamming Routing Selection Criteria Based on The Cross-Layer Constraints of Channel State Information for Manets. In Proceedings of the 2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing, China, 19–20 December 2015; pp. 1000–1004. [Google Scholar]
- Wang, B.; Wu, Y.; Liu, K.J.R.; Clancy, T.C. An Anti-Jamming Stochastic Game for Cognitive Radio Networks. IEEE J. Sel. Areas Commun.
**2011**, 29, 877–889. [Google Scholar] [CrossRef] - Slimeni, F.; Scheers, B.; Nir, V.L.; Chtourou, Z.; Attia, R. Learning Multi-Channel Power Allocation Against Smart Jammer in Cognitive Radio Networks. In Proceedings of the 2016 International Conference on Military Communications and Information Systems (ICMCIS), Brussels, Belgium, 23–24 May 2016; pp. 1–7. [Google Scholar]
- Xu, X.; He, B.; Yang, W.; Zhou, X.; Cai, Y. Secure transmission design for cognitive radio networks with poisson distributed eavesdroppers. IEEE Trans. Inf. Forensics Secur.
**2016**, 11, 373–387. [Google Scholar] [CrossRef] - Zhang, H.; Wang, T.; Song, L.; Han, Z. Interference improves PHY security for cognitive radio networks. IEEE Trans. Inf. Forensics Secur.
**2016**, 11, 609–620. [Google Scholar] [CrossRef] - Al-Talabani, A.; Deng, Y.; Nallanathan, A.; Nguyen, H.X. Enhancing secrecy rate in cognitive radio networks via multilevel stackelberg game. IEEE Commun. Lett.
**2016**, 20, 1112–1115. [Google Scholar] [CrossRef] - Zhu, F.; Yao, M. Improving physical-layer security for CRNs using SINR-based cooperative beamforming. IEEE Trans. Veh. Technol.
**2016**, 65, 1835–1841. [Google Scholar] [CrossRef] - Clancy, T.; Goergen, N. Security in Cognitive Radio Networks: Threats and Mitigation. In Proceedings of the 3rd International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CrownCom), Singapore, 15–17 May 2008; pp. 1–8. [Google Scholar]
- Aggarwal, V.; Sankar, L.; Calderbank, A.; Poor, H. Information Secrecy from Multiple Eavesdroppers in Orthogonal Relay Channels. In Proceedings of the IEEE International Symposium on Information Theory, Seoul, Korea, 28 June–3 July 2009; pp. 2607–2611. [Google Scholar]
- Bian, K.; Park, J.M. Security Vulnerabilities in IEEE 802.22. In Proceedings of the Fourth International Wireless Internet Conference (WICON2008), Maui, HI, USA, 17–19 November 2008. [Google Scholar]
- Chen, R.; Park, J.M.; Bian, K. Robust Distributed Spectrum Sensing in Cognitive Radio Networks. In Proceedings of the IEEE Infocom 2008 Conference on Computer Communications, Phoenix, AZ, USA, 13–18 April 2008; pp. 1876–1884. [Google Scholar]
- Wang, W.; Li, H.; Sun, Y.; Han, Z. Attack-Proof Collaborative Spectrum Sensing in Cognitive Radio Systems. In Proceedings of the Conference on Information Sciences and Systems (CISS), Baltimore, MD, USA, 18–20 March 2009; pp. 130–134. [Google Scholar]
- Chen, R.; Park, J.-M.; Reed, J.H. Defense Against Primary User Emulation Attacks in Cognitive Radio Networks. IEEE J. Sel. Areas Commun.
**2007**, 26, 1. [Google Scholar] [CrossRef] - Goel, S.; Negi, R. Guaranteeing Secrecy Using Artificial Noise. IEEE Trans. Wirel. Commun.
**2008**, 7, 2180–2189. [Google Scholar] [CrossRef] - Zhou, X.; McKay, M.R. Physical Layer Security with Artificial Noise: Secrecy Capacity and Optimal Power Allocation. In Proceedings of the 3rd International Conference on Signal Processing and Communication Systems, Omaha, NE, USA, 28–30 September 2009; pp. 1–5. [Google Scholar]
- Zou, Y.; Wang, X.; Shen, W. Physical Layer Security with Multiuser Scheduling in Cognitive Radio Networks. IEEE Trans. Commun.
**2013**, 61, 5103–5113. [Google Scholar] [CrossRef] - Zhai, Y.B.; Wu, X.; Huang, X.L.; Wu, J. Channel Quality Ranking in Cognitive Radio Networks. In Proceedings of the Wireless Communications, Networking and Mobile Computing Conference, Beijing, China, 26–28 September 2014; pp. 191–194. [Google Scholar]
- Ali, A.; Sakhare, M.; Hwang, K.; Suh, D.Y. A novel channel indexing-based channel selection algorithm for cognitive radio networks. In Proceedings of the ICT Convergence (ICTC), Jeju, Korea, 14–16 October 2013; pp. 682–687. [Google Scholar]
- Torabi, N.; Rostamzadeh, K.; Leung, V.C. Rank-optimal channel selection strategy in cognitive networks. In Proceedings of the 2012 IEEE Global Communications Conference (GLOBECOM), Anaheim, CA, USA, 3–7 December 2012; pp. 410–415. [Google Scholar]
- Xing, X.; Jing, T.; Huo, Y.; Li, H.; Cheng, X. Channel quality prediction based on Bayesian inference in cognitive radio networks. In Proceedings of the INFOCOM 2013, Turin, Italy, 14–19 April 2013; pp. 1465–1473. [Google Scholar]
- Sengottuvelan, S.; Ansari, J.; Mähönen, P.; Venkatesh, T.G.; Petrova, M. Channel selection algorithm for cognitive radio networks with heavy-tailed idle times. IEEE Trans. Mob. Comput.
**2017**, 16, 1258–1271. [Google Scholar] [CrossRef] - Aslam, S.; Lee, K.G. CSPA: Channel selection and parameter adaptation scheme based on genetic algorithm for cognitive radio ad hoc networks. EURASIP J. Wirel. Commun. Netw.
**2012**, 2012, 349. [Google Scholar] [CrossRef] - Arjoune, Y.; Mrabet, Z.E.; Kaabouch, N. Multi-Attributes, Utility-Based, Channel Quality Ranking Mechanism for Cognitive Radio Networks. Appl. Sci.
**2018**, 8, 628. [Google Scholar] [CrossRef] - Zhang, W.; Mallik, R.K.; Letaief, K.B. Optimization of cooperative spectrum sensing with energy detection in cognitive radio networks. IEEE Trans. Wirel. Commun.
**2009**, 8, 5761–5766. [Google Scholar] [CrossRef] - Atapattu, S.; Tellambura, C.; Jiang, H. Energy Detection for Spectrum Sensing in Cognitive Radio; Springer: New York, NY, USA, 2014; pp. 11–27. [Google Scholar]
- Quan, Z.; Cui, S.; Sayed, A.H. Optimal linear cooperation for spectrum sensing in cognitive radio networks. IEEE J. Sel. Top. Signal Process.
**2008**, 2, 28–40. [Google Scholar] [CrossRef]

**Figure 4.**Secrecy rate of the CR system versus the number SUs when the number of EVs is six and the number of channels is 10.

**Figure 5.**Secrecy rate of the CR system versus the number EVs when the number of SUs is five and number of channels is 10.

**Figure 6.**Secrecy rate of the CR system versus the number channels when the number of EVs is six and the number of SUs is five.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vu, V.-H.; Thien, H.T.; Koo, I. A Repeated Games-Based Secure Multiple-Channels Communications Scheme for Secondary Users with Randomly Attacking Eavesdroppers. *Appl. Sci.* **2019**, *9*, 868.
https://doi.org/10.3390/app9050868

**AMA Style**

Vu V-H, Thien HT, Koo I. A Repeated Games-Based Secure Multiple-Channels Communications Scheme for Secondary Users with Randomly Attacking Eavesdroppers. *Applied Sciences*. 2019; 9(5):868.
https://doi.org/10.3390/app9050868

**Chicago/Turabian Style**

Vu, Van-Hiep, Huynh Thanh Thien, and Insoo Koo. 2019. "A Repeated Games-Based Secure Multiple-Channels Communications Scheme for Secondary Users with Randomly Attacking Eavesdroppers" *Applied Sciences* 9, no. 5: 868.
https://doi.org/10.3390/app9050868