Distributed Binary Event Detection Under Data-Falsification and Energy-Bandwidth Limitation

Abstract

We address the problem of centralized detection of a binary event in the presence of falsifiable sensor nodes (SNs) (i.e., controlled by an attacker) for a bandwidth constrained under–attack spatially uncorrelated distributed wireless sensor network. The SNs send their quantized test statistics over orthogonal channels to the fusion center (FC), which linearly combines them to reach a final decision. First (considering that the FC and the attacker do not act strategically), we derive: 1) the FC optimal weight combining; 2) the optimal SN to FC transmit power; and 3) the test statistic quantization bits that maximize the probability of detection ( $P_{d}$ ). We also derive an expression for the attacker strategy that causes the maximum possible FC degradation. But in these expressions, both the optimum FC strategy and the attacker strategy require a-priori knowledge that cannot be obtained in practice. The performance analysis of sub-optimum FC strategies is then characterized, and based on the (compromised) SNs willingness to collaborate, we also derive analytically the sub-optimum attacker strategies. Then, considering that the FC and the attacker now act strategically, we recast the problem as a minimax game between the FC and the attacker and prove that the Nash equilibrium (NE) exists. Finally, we find this NE numerically in the simulation results and this gives insight into the detection performance of the proposed strategies.