On Ordered Transmission Based Distributed Gaussian Shift-in-Mean Detection Under Byzantine Attacks

The ordered transmission based (OT-based) schemes reduce the number of transmissions needed in a distributed detection network without any loss in the probability of error performance. In this paper, we investigate the performance of a conventional OT-based system in the presence of additive Byzantine attacks in Gaussian shift in mean problems. In this work, by launching additive Byzantine attacks, attackers are able to alter the order as well as the data for the binary hypothesis testing problem. We also determine the optimal attack strategy for the Byzantine sensors. Furthermore, we analyze a communication efficient OT-based (CEOT-based) scheme in the presence of additive Byzantine attacks. We obtain the probabilities of error for both the OT-based system and the CEOT-based system under attack and evaluate the number of transmissions they save. We also derive analytical bounds for the number of transmissions saved in both systems under attack. Simulation results show that the additive Byzantine attacks have significant impact on the number of transmissions saved even when the signal strength is sufficiently large. A comparison of detection performance between the conventional OT-based system and the CEOT-based system reveals that the CEOT-based system is more robust to additive Byzantine attacks.