Justification of the Efficiency of Time Segment Permutation in a Multilevel Optimization Method for Signal Ensembles

Abstract

The article proposes a multilevel method for optimizing the duration of time segments in signal ensembles. The method is based on a combination of gradient descent and the Levenberg–Marquardt algorithm, providing adaptive tuning of signal processing parameters considering mutual correlation structure and energy characteristics. Within the framework of the proposed approach, two permutation strategies for time segments were experimentally analyzed: a random permutation method (which disregards correlation structure) and the “nearest neighbor” method (which aims to minimize mutual correlation between adjacent segments). Experimental modeling was performed on five types of quasi-orthogonal sequences (M-sequences, Kasami, Gold, Fibonacci, and exponential sequences). The results demonstrate that the «nearest neighbor» method yields superior performance in terms of mutual correlation and ensemble properties of signals compared to the random permutation approach. In particular, the method achieved a reduction in the variance of the mutual correlation function by up to 22% and an improvement in ensemble characteristics within the range of 8–12%. Signal visualization after permutation confirms a more ordered structure and reduced local amplitude fluctuations. These findings support the rationale for using an adaptive permutation mechanism as one of the essential stages in the formation of signal ensembles with improved correlation properties. Future research directions include extending the optimization model to account for nonlinear channel distortions and integrating the algorithm into cognitive radio systems with dynamic spectrum management