A Jamming Game in Wireless Networks with Transmission Cost

We consider jamming in wireless networks with transmission cost for both transmitter and jammer. We use the framework of non-zerosum games. In particular, we prove the existence and uniqueness of Nash equilibrium. It turns out that it is possible to provide analytical expressions for the equilibrium strategies. These expressions is a generalization of the standard water-filling. In fact, since we take into account the cost of transmission, we obtain even a generalization of the water-filling in the case of one player game. The present framework allows us to study both water-filling in time and water-filling in frequency. By means of numerical examples we study an important particular case of jamming of the OFDM system when the jammer is situated close to the base station.

[1]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[2]  R. Varga,et al.  Proof of Theorem 4 , 1983 .

[3]  John M. Cioffi,et al.  Vector coding for partial response channels , 1990, IEEE Trans. Inf. Theory.

[4]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[5]  Pravin Varaiya,et al.  Capacity of fading channels with channel side information , 1997, IEEE Trans. Inf. Theory.

[6]  A. Garnaev.  Search Games and Other Applications of Game Theory , 2000 .

[7]  V. Baston,et al.  A search game with a protector , 2000 .

[8]  Shmuel Gal,et al.  The theory of search games and rendezvous , 2002, International series in operations research and management science.

[9]  Holger Boche,et al.  Performance Analysis of Capacity of MIMO Systems under Multiuser Interference Based on Worst-Case Noise Behavior , 2004, EURASIP J. Wirel. Commun. Netw..

[10]  R. Srikant,et al.  Correlated Jamming on MIMO Gaussian Fading Channels , 2004, IEEE Trans. Inf. Theory.

[11]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[12]  John M. Cioffi,et al.  The Worst-Case Interference in DSL Systems Employing Dynamic Spectrum Management , 2005, 2005 13th European Signal Processing Conference.

[13]  Eitan Altman,et al.  Zero-sum constrained stochastic games with independent state processes , 2005, Math. Methods Oper. Res..

[14]  A. Garnaev.  Technical note: Find a hidden “treasure” , 2007 .

[15]  Hesham El Gamal,et al.  The Water-Filling Game in Fading Multiple-Access Channels , 2005, IEEE Transactions on Information Theory.

[16]  E. Altman,et al.  Robust Waterfilling strategies for the fading channel , 2022 .