Distributed Quantized Detection of Sparse Signals Under Byzantine Attacks

This paper investigates distributed detection of sparse stochastic signals with quantized measurements under Byzantine attacks. Under this type of attack, sensors in the networks might send falsified data to degrade system performance. The Bernoulli-Gaussian (BG) distribution in terms of the sparsity degree of the stochastic signal is utilized for modeling the sparsity of signals. Several detectors with improved detection performance are proposed by incorporating the estimated attack parameters into the detection process. First, we propose the generalized likelihood ratio test with reference sensors (GLRTRS) and the locally most powerful test with reference sensors (LMPTRS) detectors with adaptive thresholds, given that the sparsity degree and the attack parameters are unknown. Our simulation results show that the LMPTRS and GLRTRS detectors outperform the LMPT and GLRT detectors proposed for an attack-free environment and are more robust against attacks. The proposed detectors can achieve the detection performance close to the benchmark likelihood ratio test (LRT) detector, which has perfect knowledge of the attack parameters and sparsity degree. When the fraction of Byzantine nodes are assumed to be known, we can further improve the system's detection performance. We propose the enhanced LMPTRS (E-LMPTRS) and enhanced GLRTRS (E-GLRTRS) detectors by filtering out potential malicious sensors with the knowledge of the fraction of Byzantine nodes in the network. Simulation results show the superiority of proposed enhanced detectors over LMPTRS and GLRTRS detectors.