Minimax anti-jammer design for FHSS/QPSK satellite communication systems

In this paper, a minimax anti-jamming strategy in a frequency hopping spread spectrum (FHSS)/quadrature phase-shift keying (QPSK) satellite communication system is developed. The goal of the anti-jammer is to minimize symbol error probability while that of the jammer is to maximize it. The jammer attacks legitimate communication system via two jamming strategies: single-tone jamming and full-band multitone jamming. The jammer maximizes symbol error probability by changing strategies and jamming signal phases. The anti-jammer minimizes symbol error probability by changing decision thresholds when demodulating QPSK signals. The optimal anti-jammer under the worst jamming case is obtained by solving a minimax optimization problem numerically. Numerical results show that when the anti-jammer has no prior knowledge of the phase of the jamming signal, the best decision thresholds are the same as those in the case without attacks. The anti-jammer is able to reduce symbol error probability by increasing signal power or employing more frequency hopping channels. If the jammer knows the anti-jammer's minimax decision thresholds, it is better for the jammer to use single-tone jamming when the jamming power is low or the number of frequency hopping channels is large; when jamming power is high or the number of frequency hopping channels is small, full-band multitone jamming should be used.