Sequence-type replay attacks detection of FIR systems with binary-valued observations under communication uncertainty

This paper addresses the detection of sequential replay attacks in finite impulse response systems subject to communication uncertainty and quantized observations. Owing to stochastic communication disturbances, replay attacks become highly covert and difficult to identify using conventional methods. A statistically based detection scheme is proposed. A sliding-window detection statistic is constructed within a quantized system framework that explicitly incorporates random communication effects. The detector is defined as the mean difference between the detection window and a reference window, and attack presence is determined through threshold-based hypothesis testing. The asymptotic normality of the proposed statistic is established under both the no-attack and replay-attack hypotheses. Closed-form expressions for the false alarm rate and miss detection rate are derived, enabling analytical performance characterization. An equivalent sample size is introduced to quantify the joint contribution of the two windows. The analysis shows that the false alarm rate depends only on the detection threshold, while the miss detection rate decreases monotonically with increasing reference window length, exhibiting diminishing returns. Numerical simulations confirm the theoretical distribution results and demonstrate strong agreement between empirical and analytical detection performance, validating the effectiveness and robustness of the proposed method under communication uncertainty.