A zero-sum power allocation game in the parallel Gaussian wiretap channel with an unfriendly jammer

This paper investigates optimal power allocation strategies over a bank of independent parallel Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and an unfriendly jammer. In particular, we formulate a zero-sum power allocation game between the transmitter and the jammer where the payoff function is the secrecy rate. We characterize the optimal power allocation strategies as well as the Nash equilibrium in some asymptotic regimes. We also provide a set of results that cast further insight into the problem. Our scenario, which is applicable to current OFDM communications systems, demonstrates that transmitters that adapt to jammer experience much higher secrecy rates than non-adaptive transmitters.