METHOD FOR RECOVERING CONTROL PARAMETERS OF A CHAOTIC GENERATOR UNDER ADDITIVE NOISE IN THE COMMUNICATION CHANNEL

Abstract

This paper addresses the problem of reliable recovery of control parameters of a chaotic generator operating under additive noise in a communication channel. Accurate estimation of such parameters is a key requirement for chaos-based communication systems, where information can be encoded in the values of system parameters rather than in the waveform itself. In noisy channels, however, the chaotic signal and its attractor are significantly distorted, which makes direct parameter estimation from observed time series a challenging task.

The study focuses on the Rucklidge chaotic generator, chosen due to its well-known properties and suitability for analytical and numerical analysis. The influence of additive noise intensity, expressed through the signal-to-noise ratio (SNR), and the duration of moving average smoothing applied to the received signal on the accuracy of parameter recovery is systematically investigated. An analytical approach is combined with numerical simulation to derive instantaneous estimates of the generator control parameters, which are then statistically processed using median averaging over finite observation intervals.

The results demonstrate that parameter estimation errors exhibit a nonlinear dependence on both SNR and the smoothing window duration. For each control parameter, there exists an optimal combination of noise level and averaging window that minimizes the recovery error. Based on extensive numerical experiments, regions of reliable parameter recovery are identified using a ±2% relative error criterion. These regions define practical operating limits for chaos-based communication systems in the presence of additive noise.

Furthermore, the obtained boundary data are approximated using single-exponential models that describe the relationship between the required averaging window duration and SNR. The resulting analytical expressions provide a compact and practical tool for adaptive receiver design, allowing the smoothing parameters to be dynamically adjusted according to the current noise conditions in the channel. This enables a favorable trade-off between noise robustness and information transmission speed.

The proposed method enhances the feasibility of parameter-based chaotic modulation schemes and can be extended to other classes of chaotic generators and more complex channel models, making it relevant for the development of secure and noise-robust communication systems.