Multi-Antenna Jamming in Covert Communication

Covert communication conceals transmission of messages from Alice to Bob out of a watchful adversary, Willie, which tries to determine if a transmission took place or not. While covert communication in a basic, vanilla settings where all variables are known to Willie results in the well known square-root law, when a jammer is present and assists Alice by creating uncertainty in Willie's decoder, this transmission may have a positive rate.In this work, we analyze the case where the jammer is equipped with multiple antennas and obtain the optimal transmission strategy of the jammer in order to maximize his assistance to Alice, in terms of maximizing a ratio between Willie's and Bob's noise variance. We show that the optimal strategy of the jammer is to perform beamforming towards a single direction with all his available power. This direction though, is not trivial, since it reflects an optimal tradeoff point between minimizing the interference at Bob and maximizing the interference at Willie.