This article is devoted a mathematical model of stochastic signal transmission under conditions of radio-electronic interference based on the combined application of the Karhunen–Loev transform and adaptive Volterra series. The relevance of the study is due to modern requirements for combat control information systems, which in the conditions of large-scale armed aggression against Ukraine have become the main means of operational, tactical and strategic control of troops. Traditional linear signal processing methods do not provide the necessary compromise between spectral compactness, noise immunity and adaptability under conditions of non-stationary interference, multi-path fading and active radio-electronic interference, and also do not fully take into account the stochastic nature of signals, channel memory effects and nonlinear distortions arising under the influence of interference. To solve the problem, a combined application of the Karhunen–Loev transform for preliminary decorrelation and energy densification of stochastic signals with subsequent adaptive nonlinear processing using second-order Volterra series is proposed. The adaptability of the system is ensured by a multi-criteria optimization functional with dynamic adjustment of weight coefficients depending on the combat application scenario (stealth mode or active electronic warfare). The model describes the process of signal transmission through the channel, taking into account the impulse response of the environment and the generalized interference effect. The results of the study were obtained by simulation modeling in the Python 3.11 environment. A comparative analysis of the proposed approach with traditional signal processing methods (Fourier filtering, wavelet transform, Z-transform, classical Volterra model and separate application of the Karhunen–Loev transform) for different types of stochastic signals is carried out. The proposed approach provides increased spectral efficiency, noise immunity and adaptability of combat control information systems, which creates the prerequisites for its practical implementation in wireless combat control systems, secure communication facilities and sensor networks, where they are of particular importance.
Гарячий et al. (Thu,) studied this question.