Skip to main content
SpringerLink
Log in

An optimal transmission strategy in zero-sum matrix games under intelligent jamming attacks

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

Cognitive radio networks are more susceptible to jamming attacks due to the nature of unlicensed users accessing the spectrum by performing dynamic spectrum access. In such a context, a natural concern for operators is the resilience of the system. We model such a scenario as one of adversity in the system consisting of a single legitimate (LU) pair and malicious user (MU). The aim of the LU is to maximize throughput of transmissions, while the MU is to minimize the throughput of the LU completely. We present the achievable transmission rate of the LU pair under jamming attacks taking into account mainly on the transmission power per channel. Furthermore, we embed our utility function in a zero-sum matrix game and extend this by employing a fictitious play when both players learn each other’s strategy over time, e.g., such an equilibrium becomes the system’s global operating point. We further extend this to a reinforcement learning (RL) approach, where the LU is given the advantage of incorporating RL methods to maximize its throughput for fixed jamming strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Kandeepan, S., Gomez, K., Gorratti, L., Rasheed, T., & Baldini, G. (2016). Power controlling for device to device transmissions in aerial access networks. In IEEE ATC, pp. 48–53.

  2. Al-Hourani, A., Kandeepan, S., & Hossain, E. (2016). Relay-assisted device-to-device communication: a stochastic analysis of energy saving. In: IEEE TMC.

  3. Khare, A., Saxena, M., Thakur, R. S., & Chourasia, K. (2013). Attacks and preventions of cognitive networks: A survey. IJARCET, 2(3), 1002–1006.

    Google Scholar 

  4. Haykin, S. (2005). Cognitive radio: Brain-empowered wireless communications. IEEE Journal on Selected Areas of Communications, 23(2), 201–220.

    Article  Google Scholar 

  5. Mitola, J., & Maguire, G. (1999). Cognitive radio: Making software radios more personal. IEEE Personal Communications, 6(4), 13–18.

    Article  Google Scholar 

  6. Al-Hourani, A., & Kandeepan, S. (Dec. 2013). Cognitive relay nodes for airborne LTE emergency networks. In IEEE ICSPCS, pp. 1–9.

  7. Doumi, T., Dolan, M. F., Tatesh, S., Casati, A., Tsirtsis, G., Anchan, K., et al. (2013). LTE for public safety networks. IEEE Wireless Communications, 51(2), 106–112.

    Google Scholar 

  8. Sesia, S., Toufik, I., & Baker, M. (2009). The UMTS long term evolution from theory to practice (2nd ed.). Hoboken: Wiley.

    Google Scholar 

  9. Fodor, G., Dalman, E., Mildh, G., Parkvall, S., Reider, N., Miklós, G., et al. (2012). Design aspect of network assisted device-to-device communications. IEEE Wireless Communication, 50(3), 170–177.

    Google Scholar 

  10. Doppler, K., Rinne, M., Wijting, C., Ribeiro, C. B., & Hugl, K. (2012). Device-to-device communication as an uderlay to LTE-advanced networks. IEEE Wireless Communications Magazine, 47(12), 42–49.

    Article  Google Scholar 

  11. Aerial Base Stations with Opportunistic Links for Unexpected and Temporary Events (ABSOLUTE). EU FP7 Integrated Project. http://www.absolute-project.eu/.

  12. Wang, B., Wu, Y., & Ray Liu, K. J. (2009). Optimal power allocation strategy against jamming attacks using the Colonel Blotto game. In Proceedings of IEEE GLOBECOM, pp. 1–5.

  13. Wu, Y., Wang, B., Ray Liu, K. J., & Clancy, T. C. (2012). Anti-jamming games in multi-channel cognitive radio networks. IEEE Communications, 30(1), 1–12.

    Google Scholar 

  14. Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning: An introduction. Cambridge: MIT Press.

    MATH  Google Scholar 

  15. Chen, C., Song, M., Xin, C., & Backens, J. (2013). A game-theoretical anti-jamming scheme for cognitive radio networks. IEEE Networks, 27(3), 22–27.

    Article  Google Scholar 

  16. Li, Y., Yang, R., & Ye, F. (2010). Non-cooperative spectrum allocation based on game theory in cognitive radio networks. In IEEE BIC-TA, pp. 1134–1137.

  17. Singh, S., & Trivedi, A. (Sept. 2012). Anti-jamming in cognitive radio networks using reinforcement learning algorithms. In IEEE WOCN, pp. 1–5.

  18. Sodagari, S., & Charles Clancy, T. (2011). An anti-jamming strategy for channel access in cognitive radio networks. Berlin: Springer.

    Book  Google Scholar 

  19. Gwon, Y., Dastangooand Carl Fossa, S., & Kung, H. T. (Feb. 2013). Competing mobile network game: Embracing antijamming and jamming strategies with reinforcement learning. In IEEE conference on communications and network security (CNS).

  20. Goratti, L., Gomez, K. M., Fedrizzi, R., & Rasheed, T. (Dec. 2013). A novel device-to-device communication protocol for public safety applications. In IEEE Globecom 2013 D2D Workshop, Atlanta.

  21. Firouzbakht, K., Noubir, G., & Salehi, M. (2012). On the capacity of rate-adaptive packetized wireless communication links under jamming. In Proceedings of the ACM WISEC conference.

  22. Hanawal, M. K., Abdel-Rahman, M. J., & Krunz, M. (2014). Game theoretic anti-jamming dynamic frequency hopping and rate adaptation in wireless systems. In Proceedings of the WiOpt conference.

  23. Hanawal, M. K., Abdel-Rahman, M. J., & Krunz, M. (2015). Joint adaptation of frequency hopping and transmission rate for anti-jamming wireless systems. IEEE Transactions on Mobile Computing.

  24. Xiao, L., Li, Y., & Zhao, Y. (2015). Power control with reinforcement learning in cooperative cognitive radio networks against jamming. Springer Journal of Supercomputing, 71(9), 3237–3257.

    Article  Google Scholar 

  25. Xiao, L., Liu, J., Li, Q., Mandayam, N., & Poor, V. H. (2015). User-centric view of jamming games in cognitive radio networks. IEEE Transactions on Information Forensics & Security, 10(12), 2578–2590.

    Article  Google Scholar 

  26. Zhou, B., Hu, H., Huang, S. Q., & Chen, H. H. (2013). Intracluster device-to-device relay algorithm with optimal resource utilization. IEEE Transactions on Vehicular Technology, 62(5), 2315–2326.

    Article  Google Scholar 

  27. Raghothaman, B., Deng, E., Pragada, R., Sternberg, G., Deng, T., & Vanganuru, K. (2013). Computing, networking and communications (ICNC). In 2013 international conference on architecture and protocols for LTE-based device to device communication, pp. 895–899.

  28. Arunthavanathan, S., Goratti, L., Maggi, L., de Pellegrini, F., & Kandeepan, S. (Jun. 2014). On the achievable rate in a D2D cognitive secondary network under jamming attacks. In IEEE CrownComm, pp. 39–44.

  29. Tague, P., Li, M., & Poovendran, R. (2009). Mitigation of control channel jamming under node capture attacks. IEEE Transactions on Mobile Computing, 8(9), 1221–1234.

    Article  Google Scholar 

  30. Garnaev, A., & Trappe, W. (2015). One-time spectrum coexistence in dynamic spectrum access when the secondary user may be malicious. IEEE Transactions on Information Forensics and Security, 10(5), 1064–1075.

    Article  Google Scholar 

  31. Arunthavanathan, S., Kandeepan, S., & Evans, R. (Sept. 2013). Spectrum sensing and detection of incumbent-UEs in secondary-LTE based aerial-terrestrial networks for disaster recovery. In IEEE CAMAD, pp. 201–206.

  32. Altman, E., Avrachenkov, K., & Garnaev, A. (2010). Fair resource allocation in wireless networks in the presence of a jammer. Performance Evaluation, 67(4), 338–349.

    Article  Google Scholar 

  33. Von Neumann, J. (1928). Zur theorie der gesellschaftsspiele. Mathematische Annalen, 100, 295–320.

    Article  MathSciNet  MATH  Google Scholar 

  34. Myerson, R. B. (1997). Game theory: Analysis of conflict. Cambridge: Harvard University Press.

    MATH  Google Scholar 

  35. Brown, G. W. (1951). Iterative solutions of games by fictitious play in activity analysis of production and allocation. In T. C. Koopmans (Ed.), Activity analysis of production and allocation (pp. 374–376). Hoboken: Wiley.

    Google Scholar 

  36. Brown, G. W., & von Neumann, J. (1950). Solutions of games by differential equations: Contributions to the theory of games I: Annals of mathemathical studies (Vol. 24, pp. 73–79). Princeton: Princeton University Press.

    Google Scholar 

  37. Robinson, J. (1951). An iterative method of solving a game. Annals of Mathematical Statistics, 54, 296–301.

    Article  MathSciNet  MATH  Google Scholar 

  38. Arunthavanathan, S., Kandeepan, S., & Evans, R. J. (2016). A Markov decision process-based opportunistic spectral access. IEEE Wireless Communication Letters, 5(5), 544–547.

    Article  Google Scholar 

  39. Eltom, H., Kandeepan, S., Liang, Y. C., Moran, B., & Evans, R. J. (2016). HMM based cooperative spectrum occupancy prediction using hard fusion. In IEEE ICC, pp. 669–675.

  40. Arunthavanathan, S., Kandeepan, S., & Evans, R. (Dec. 2013). Reinforcement learning based secondary user transmissions in cognitive radio networks. Globecom Workshops (IEEE GC Wkshps), pp. 374–379.

  41. Bkassiny, M., Li, Y., & Jayaweera, S. (2012). A survey on machine-learning techniques in cognitive radios. IEEE Communications Surveys and Tutorials, 99, 1–24.

    Google Scholar 

  42. Kaelbling, L., Littman, M., & Moore, A. (1996). Reinforcement learning: A survey. Journal of Artificial Intelligence Research, 4, 237–285.

    Article  Google Scholar 

Download references

Acknowledgements

The research of S. Arunthavanathan, L. Goratti, and S. Kandeepan, leading to these results, has received partial funding from the EC 7 Framework Programme (FP7-2011-8) under the Grant Agreement FP7-ICT-318632. The work of F. De Pellegrini and L. Maggi has been partially supported by the European Commission within the framework of the CONGAS project FP7-ICT-2011-8-317672, see www.congas-project.eu.

Author information

Authors and Affiliations

  1. Electrical and Computer Engineering, RMIT University, Melbourne, VIC, 3001, Australia

    Senthuran Arunthavanathan & Sithamparanathan Kandeepan

  2. CREATE-Net, 31628, Trento, Italy

    Leonardo Goratti & Francesco de Pellegrini

  3. Huawei Technologies, Lannion, France

    Lorenzo Maggi

  4. Department of Engineering, Macquarie University, Sydney, NSW, 2109, Australia

    Sam Reisenfield

Authors
  1. Senthuran Arunthavanathan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonardo Goratti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lorenzo Maggi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Francesco de Pellegrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sithamparanathan Kandeepan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sam Reisenfield
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Senthuran Arunthavanathan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arunthavanathan, S., Goratti, L., Maggi, L. et al. An optimal transmission strategy in zero-sum matrix games under intelligent jamming attacks. Wireless Netw 25, 1777–1789 (2019). https://doi.org/10.1007/s11276-017-1629-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-017-1629-4

Keywords

Search

Navigation