Joint Adaptation of Frequency Hopping and Transmission Rate for Anti-Jamming Wireless Systems

Wireless transmissions are inherently vulnerable to jamming attacks. Frequency hopping (FH) and transmission rate adaptation (RA) have been separately used to mitigate jamming. When RA is used alone, it has been shown that a jammer who randomizes its power levels can force the transmitter to always operate at the lowest rate, by maintaining the average jamming power above a certain threshold. On the other hand, when only FH is used, a high throughput overhead is incurred due to frequent channel switching. In this paper, we propose to mitigate jamming by jointly optimizing the FH and RA techniques. This way, the transmitter can escape the jammer by changing its channel, adjusting its rate, or both. We consider a power-constrained "reactive-sweep" jammer who aims at degrading the throughput of the wireless link. The jammer sweeps through the set of channels, jamming a subset of them at a time, using the optimal jamming power. We model the interactions between the legitimate transmitter and jammer as a constrained zero-sum Markov game. The transmitter's optimal defense strategy is derived by obtaining the equilibria of the constrained Markov game. This policy informs the transmitter when to hop to another channel and when to stay on the current channel. Furthermore, it gives the best transmission rate to use in both cases (hop or stay). The structure of the transmitter's optimal policy is shown to be threshold type, whereby the transmitter stays on the same channel up to a certain number of time slots after which it hops. We analyze the "constrained Nash equilibrium" of the Markov game and show that the equilibrium defense strategy of the transmitter is deterministic. Numerical investigations show that the new scheme improves the average throughput and provides better jamming resiliency.