Higher-Order Statistics in Signal Detection Tasks in Correlated Non-Gaussian Noise

Signal detection in noise is critical in telecommunications, navigation and radar systems, image processing and biomedical research, where noise often deviates from a normal distribution, and sample values exhibit statistical dependence. Traditional methods for analyzing and designing such systems face significant limitations, including algorithmic and computational complexity, severely restricting their practical application. An effective approach to developing signal detection systems involves using moment and cumulant descriptions of random variables, simplifying the design of detection systems for signals with various probability density functions. The authors propose a novel approach based on one-dimensional (1D) and two-dimensional (2D) moment-cumulant models to describe correlated non-Gaussian processes. This approach enables the modification of the moment-based criterion for statistical hypothesis testing and synthesising polynomial stochastic decision rules for detecting signals in correlated non-Gaussian noise. The study demonstrates that the nonlinear processing of sample values and the application of higher-order statistics to describe the investigated processes account for the structure of non-Gaussian noise and its statistical dependencies. This reduces the error probabilities of the synthesized decision rules compared to traditional Gaussian models. The study aims to enhance the efficiency of signal detection systems under additive interaction with correlated non-Gaussian noise by developing new moment-cumulant models of the investigated processes, modifying the moment-based criterion for hypothesis testing, and designing polynomial decision rules. The study's practical significance lies in creating simple-to-implement algorithms with high accuracy that achieve lower error probabilities in decision rules compared to existing methods.