Jamming in wireless networks under uncertainty

The problem of jamming plays an important role in ensuring the quality and security of wireless communications, especially at this moment when wireless networks are quickly becoming ubiquitous. Since jamming can be considered as a game in which jammer is playing against the user (transmitter) who would like to transmit signal with good quality and at the same time with a reasonable amount of energy, game theory is an appropriate tool for dealing with jamming. Here we investigate the effect of partially available information and correlation among sub-carriers on the user behavior. Specifically, to do so we deal with the scenario when the user does not know how jamming efforts are distributed among sub-carriers and the user does not know the fading channels' gains with certainty. As an object function for the user we consider SINR. We consider zero-sum games, so all of them can also be viewed as a minimax problem for the user playing against the nature. We study independent fading channel gains scenario as well as dependent fading channel gains scenario, both in discrete and continuous versions. We show that in all the scenarii the jammers equalize the quality of the best sub-carriers for the transmitter on as low level as their power constraints allow. Meanwhile the transmitter distributes his power among these jamming sub-carriers. We find the equilibrium strategies in closed form and specify the range of sub-carriers where the transmitter can expect the jamming attack. Also, we show for independent plot these strategies depend only on the expected value of the transmitters channel gains meanwhile for the dependent plot they depend on the whole spectra of these gains. Thus, for independent plot the behaviour of the jammer is less fine tuned under environment since it works with the expected gains. The user for both scenarios has to take the whole spectra of the jamming gains but, of course, for the independent scenario he is less specific because of the jammer.