Physical layer security of multiband communications under hostile jamming

This paper considers a game between a power-limited authorized user and a power-limited jammer, who operate independently over the same AWGN channel consisting of multiple bands. We explore the possibility for the authorized user or the jammer to randomly utilize part (or all) of the available spectrum and/or apply nonuniform power allocation. 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. Numerical results are provided to illustrate the theoretical analysis.