Parameter identification for FIR systems with simultaneously quantized inputs and outputs against replay attacks: a stochastic defense scheme

Replay attacks disrupt the temporal correspondence between system inputs and outputs, significantly complicating system identification. While existing methods predominantly employ fixed time-point strategies for attack estimation, such deterministic approaches exhibit vulnerability to attacker reconnaissance, resulting in degraded detection performance or potential failures. This paper proposes a stochastic defense scheme to enhance detection effectiveness and identification accuracy. Furthermore, diverging from conventional studies focused solely on single-threshold output quantization, we investigate system identification problem for Finite Impulse Response (FIR) with simultaneously quantized inputs and outputs against replay attacks. Regarding attack behavior analysis, random replay attacks' degradation effect on the Non Attack Quasi-Convex Combination Estimator (NA-QCCE) is evaluated. An energy-constrained optimization problem establishes optimal attack configurations that maximize NA-QCCE impairment while minimizing energy expenditure. For defense research, an indirect identification framework is developed using the stochastic data processing scheme. Corresponding defense algorithms via compensation-enhanced identification achieve consistent convergence in both attack strategy and system parameter. Feasibility of this algorithm preserves its asymptotic normality in parameter estimation. Minimum-variance identification is obtained via defense parameter optimization, with an actual implementation process provided for optimal deployment. All theorems and conclusions are experimentally validated via numerical simulations.