Jamming Strategies in Covert Communication.

Consider the communication problem where Alice tries to send a message towards Bob while trying to conceal the presence of communication from a watchful adversary, Willie, which tries to determine if a transmission took place or not. Under the basic settings, where all variables are known to Willie, the total amount of information bits that can be transmitted covertly and reliably in n independent channel uses is O(root n) (a.k.a the square-root law). Thus, the resulting rate is O(root n/n) which goes to zero as n -> infinity. However, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, this transmission may have a strictly positive rate. In this work, we consider the case where the jammer is equipped with multiple antennas. We analyze this case and present transmission strategies for the jammer in order to maximize his assistance to Alice, in terms of maximizing a ratio between Willie's and Bob's noise variances. Specifically, the analysis is performed for the cases were Bob is equipped with multiple antennas and employs a linear receiver. Our results indicate that the jammer's transmission strategy is to perform beamforming towards a single direction which depends on the channel coefficients of both the legitimate receiver and the adversary. However, in case Bob is able to cancel the jammer's interference completely, then the jammer's strategy becomes independent and may be set according to the channel coefficients of the adversary alone.