Models and Methods for Signal Processing in Correlated Excess Processes
DOI:
https://doi.org/10.20535/RADAP.2025.101.%25pKeywords:
moment-cumulant models, signal detection, higher-order statistics, polynomial decision rules, modified moment criterion, correlated non-Gaussian processesAbstract
The paper presents new mathematical models and signal processing methods developed in correlated excess non-Gaussian noise, which is commonly encountered in telecommunication systems, radar devices, technical control systems, and other applied domains. The foundation of the proposed approach is the moment-cumulant representation of random processes, which makes it possible to describe not only the basic statistical characteristics of the observed signals but also to account for the influence of non-Gaussian parameters, particularly the excess coefficient and the correlation between sample values. This approach becomes especially relevant when conventional and widely used Gaussian models fail to provide adequate accuracy in describing the processes under study, and when constructing a complete multidimensional probability density function (PDF) is computationally infeasible or practically impossible.
The paper proposes methods for the synthesis of polynomial stochastic decision rules (DRs), based on a modified moment-based quality criterion used to estimate the upper bounds of error probabilities in statistical signal detection problems. Both linear and nonlinear DRs have been developed for different polynomial orders, enabling the adaptation of the model to a variety of interference conditions. The study investigates the impact of excess coefficients and correlation parameters on detection efficiency. It is demonstrated that the use of higher-order statistics and nonlinear processing of sample values leads to a reduction in the probabilities of type I and type II errors for the decision rules. The proposed models and signal detection methods can be integrated into intelligent information processing systems and applied to the development of adaptive real-time detection algorithms.
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Copyright (c) 2025 В. В. Палагін , О. А. Палагіна , Т. В. Воробкало , С. С. Мартиненко , О. С. Зорін
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