Mutual Information Jammer-Relay Games

We consider a two-person zero-sum mutual information game between one jammer (J) and one relay (R), in a non-fading scenario. Supposing that the source (S) and the destination (D) are unaware of the game, we derive optimal pure or mixed strategies for J and R depending on the link qualities and whether the players are active during the S rarr D channel training. When both J and R have full knowledge of the source signal, the optimal strategies amount to linear jamming (LJ) and linear relaying (LR), respectively. When the S rarr J and S rarr R links are noisy, LJ strategies (pure or mixed) are still optimal under LR. In this case, instead of always transmitting with full power as when the S rarr R link is perfect, R should adjust transmit-power according to its power constraint and the reliability of the source signal it receives.