Optimal privacy-preserving transmission scheduling of cyber-physical systems against eavesdropping attacks

Cyber-physical systems (CPS), as a fundamental enabling technology for the Internet of Things (IoT), face privacy threats under eavesdropping attacks over wireless networks. This paper investigates privacy-preserving remote state estimation for stable systems where the state tends to be steady and noise naturally decays over time. An optimal transmission scheduling is proposed to mitigate privacy leakage while keeping estimation performance desirable, leveraging pre-arranged indicators to replace vulnerable acknowledgment (Ack) signals. The sensor selectively transmits between the state estimate and multi-level energy noise with the same characteristics as state estimate to disrupt the eavesdropper and reduce energy consumption. A linear combination of noise transmission energy consumption and the expected error covariance for legitimate estimator and eavesdropper is designed to minimize legitimate estimator error and transmission cost while maximizing eavesdropper error. Furthermore, the optimal scheduling is extended to scenarios where eavesdropper information is unknown by introducing belief vector to model its distribution. The optimal transmission scheduling exhibits a threshold structure, which holds for known and unknown eavesdropper information cases. Numerical simulations demonstrate that the proposed method outperforms existing approaches, balancing privacy preservation with energy constraint, and significantly degrading eavesdropper performance.