Approximative Threshold Optimization From Single Antenna to Massive SIMO Authentication

In a wireless sensor network, data from various sensors are gathered to estimate the system-state of a process system. However, adversaries aim at distorting the estimation, for which they may infiltrate sensors or position additional devices in the environment. For authentication, the receiver can evaluate the integrity of measurements from different sensors jointly with the temporal integrity of channel measurements from each sensor. Therefore, we design a security protocol, in which Kalman filters predict the system-state and the channel-state values. Then, the received data is authenticated by a hypothesis test. We theoretically analyze the adversarial success probability and the reliability in two ways, based on chi-square and Gaussian approximations. The two approximations are exact for small and large data vectors, respectively. Hence, the Gaussian approximation is suitable for analyzing massive single-input multiple-output (SIMO) setups. This approximation is adapted to channel hardening, which occurs in massive SIMO fading channels. As adversaries always look for the weakest point, a time-independent security level is required. Hence, the approximations are used to propose time-varying thresholds for the hypothesis test, which approximately attain a constant security level. Numerical results show that either the security level or the threshold value can be time-independent, but not both.