Jamming defense against a resource-replenishing adversary in multi-channel wireless systems

We revisit the jamming defense problem in a multi-channel wireless system, using a general formulation of online learning against an adversary via repeated game-playing. We provide the explicit form of the worst-case optimal channel-hopping strategy of a legitimate user in a multi-stage interaction with a resource-replenishing jamming attacker. Interestingly, we show that the worst imaginary enemy can be given as an adversary who behaves in an i.i.d. manner in this multi-stage interaction, and the optimal strategy of the user is determined by the induced random walk of the adversarial behavior. In addition to the jamming defense, our framework is also applicable to other competitive game problems with finite action spaces.