Optimal Multiband Transmission Under Hostile Jamming

This paper considers optimal multiband transmission under hostile jamming, where both the authorized user and the jammer are power-limited and operate against each other. The strategic decision making of the authorized user and the jammer is modeled as a two-party zero-sum game, where the payoff function is the capacity that can be achieved by the authorized user in the presence of the jammer. First, we investigate the game under AWGN channels. It is found that: either for the authorized user to maximize its capacity, or for the jammer to minimize the capacity of the authorized user, the best strategy for both of them is to distribute the transmission power or jamming power uniformly over all the available spectrum. The minimax capacity can be calculated based on the channel bandwidth and the signal-to-jamming and noise ratio, and it matches with the Shannon channel capacity formula. Second, we consider frequency selective fading channels. We characterize the dynamic relationship between the optimal signal power allocation and the optimal jamming power allocation in the minimax game, and then propose an iterative water pouring algorithm to find the optimal power allocation schemes for both the authorized user and the jammer.