Page 127 - ITUJournal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

9.12 Proof of Proposition 10 [11] A. Garnaev, A. Petropulu, W. Trappe, and H.V Poor.
“A Power Control Game with Uncertainty On the
First note that procedure Ω( ) re lects the bisection Type of the Jammer”. In: Proc. IEEE Global Confer‑
method to solve equation ( , ) = for a ixed . ence on Signal and Information Processing (Global‑
By Proposition 2, this procedure converges. Procedure SIP). 2019.
Strategies() re lects the bisection method to solve equa‑
tion ̃ (Ω( ), )− = 0. By Proposition 3, this procedure [12] N. Namvar, W. Saad, N. Bahadori, and B. Kel‑
also converges. Thus, Algorithm 1 converges as a super‑ leys. “Jamming in the Internet of Things: A Game‑
position of two converging procedures. Theoretic Perspective”. In: Proc. IEEE Global Com‑
munications Conference (GLOBECOM). 2016.
[13] Y. Wu, B. Wang, and K.J.R Liu. “Optimal power allo‑
REFERENCES cation strategy against jamming attacks using the

[1] S. Vadlamania, B. Eksioglub, H. Medala, and A. Nan‑ Colonel Blotto game”. In: Proc. IEEE Global Telecom‑
dia. “Jamming attacks on wireless networks: A tax‑ munications Conference (GLOBECOM). 2009, pp. 1–
onomic survey”. In: International Journal of Produc‑ 5.
tion Economics 172 (2016), pp. 76–94. [14] G.D Nguyen, S. Kompella, C. Kam, J.E Wieselth‑
ier, and A. Ephremides. “Wireless link connectiv‑
[2] Z. Han, D. Niyato, W. Saad, T. Basar, and A.
Hjrungnes. Game Theory in Wireless and Communi‑ ity under hostile interference: Nash and Stackel‑
cation Networks: Theory, Models, and Applications. berg equilibria”. In: Proc. 14th International Sym‑
Cambridge University Press, 2012. posium on Modeling and Optimization in Mobile, Ad
Hoc, and Wireless Networks (WiOpt). 2016.
[3] D. Yang, G. Xue, J. Zhang, A. Richa, and X. Fang. “Cop‑
ing with a Smart Jammer in Wireless Networks: A [15] G.D Nguyen, S. Kompella, C. Kam, J.E Wieselthier,
Stackelberg Game Approach”. In: IEEE Transactions and A. Ephremides. “Impact of Hostile Interference
on Wireless Communications 12 (2013), pp. 4038– on Wireless Link Connectivity”. In: IEEE Trans‑
4047. actions on Control of Network Systems 5 (2018),
pp. 1445–1456.
[4] A. Garnaev, A. Petropulu, W. Trappe, and H.V Poor. [16] R. El‑Bardan, S. Brahma, and P.K Varshney. “Power
“A Jamming Game with Rival‑Type Uncertainty”. In: control with jammer location uncertainty: A game
IEEE Transactions on Wireless Communication 19 theoretic perspective”. In: Proc. 48th Annual Con‑
(2020), pp. 5359–5372.
ference on Information Sciences and Systems (CISS).
[5] F.M Aziz, J.S Shamma, and G.L Stuber. “Jammer‑type 2014, pp. 1–6.
estimation in LTE with a smart jammer repeated [17] A. Garnaev and W. Trappe. “Stability of commu‑
game”. In: IEEE Transactions on Vehicular Technol‑ nication link connectivity against hostile interfer‑
ogy 66 (2017), pp. 7422–7431.
ence”. In: Proc. IEEE Global Conference on Signal
[6] T. Song, W.E Stark, T. Li, and J.K Tugnait. “Opti‑ and Information Processing (GlobalSIP). 2017.
mal Multiband Transmission Under Hostile Jam‑ [18] M. Hajimirsaadeghi and N.B Mandayam. “A dy‑
ming”. In: IEEE Transactions on Communications 64 namic Colonel Blotto game model for spectrum
(2016), pp. 4013–4027.
sharing in wireless networks”. In: Proc. 55th An‑
[7] L. Xiao, D. Jiang, D. Xu, H. Zhu, Y. Zhang, and nual Allerton Conference on Communication, Con‑
H.V Poor. “Two‑Dimensional Antijamming Mobile trol, and Computing (Allerton). 2017, pp. 287–294.
Communication Based on Reinforcement Learn‑ [19] M. Labib, S. Ha, W. Saad, and J.H Reed. “A Colonel
ing”. In: IEEE Transactions on Vehicular Technology Blotto Game for Anti‑Jamming in the Internet of
67 (2018), pp. 9499–9512.
Things”. In: Proc. IEEE Global Communications Con‑
[8] N. Abuzainab and W. Saad. “Dynamic Connectiv‑ ference (GLOBECOM). 2015, pp. 1–6.
ity Game for Adversarial Internet of Battle ield [20] C. Guo, Y. Zhang, M. Sheng, Wang X, and Y. Li. “ ‑Fair
Things Systems”. In: IEEE Internet of Things Journal Power Allocation in Spectrum‑Sharing Networks”.
5 (2018), pp. 378–390. In: IEEE Transactions on Vehicular Technology 65
[9] Y. Gao, Y. Xiao, M. Wu, M. Xiao, and J. Shao. (2016), pp. 3771–3777.
“Game Theory‑Based Anti‑Jamming Strategies for [21] E. Altman, K. Avrachenkov, and A. Garnaev. “Fair
Frequency Hopping Wireless Communications”. In: Resource Allocation in Wireless Networks in the
IEEE Transactions on Wireless Communications 17 Presence of a Jammer”. In: Performance Evaluation
(2018), pp. 5314–5326. 67 (2010), pp. 338–349.
[10] A. Garnaev, A. Petropulu, W. Trappe, and H.V Poor. [22] E. Altman, K. Avrachenkov, and A. Garnaev. “Closed
“A Muli‑Jammer Game with Latency as the User’s Form Solutions for Water‑Filling Problem in Opti‑
Communication Utility”. In: IEEE Communications mization and Game Frameworks”. In: Telecommu‑
Letters 24 (2020), pp. 1899–1903. nication Systems Journal 47 (2011), pp. 153–164.

© International Telecommunication Union, 2021 111