Optimal Jamming Against Digital Modulation

Jamming attacks can significantly impact the performance of wireless communication systems, and can lead to significant overhead in terms of re-transmissions and increased power consumption. This paper considers the problem of optimal jamming over an additive white Gaussian noise channel. We derive the optimal jamming signal for various digital amplitude-phase-modulated constellations and show that it is not always optimal to match the jammer's signal to the victim signal in order to maximize the error probability at the victim receiver. Connections between the optimum jammer obtained in this analysis and the well-known pulsed jammer, popularly analyzed in the context of spread spectrum communication systems, are illustrated. The gains obtained by the jammer when it knows the victim's modulation scheme and uses the optimal jamming signals obtained in this paper as opposed to conventional additive white Gaussian noise jamming are evaluated in terms of the additional signal power needed by the victim receiver to achieve the same error rates under these two jamming strategies. We then extend these findings to obtain the optimal jamming signal distribution: 1) when the victim uses an orthogonal frequency-division multiplexing (OFDM)-modulated signal and 2) when there is multiple jammer attacking a single victim transmitter-receiver pair. Numerical results are presented in all the above cases to validate the theoretical inferences presented.