METHOD OF TIME PERMUTATIONS BASED ON MARKOV MODELS

Abstract

The paper proposes a Markov-based permutation method designed to optimize ensembles of complex signals in the time domain under conditions of interference and stochastic uncertainty. The distinctive feature of the method is a forecast-oriented selection of time-segment permutations, implemented through Markov modeling of state transitions within the signal ensemble. Unlike conventional approaches that rely only on the current correlation level, the proposed method incorporates the predicted ensemble dynamics, allowing minimization of the risk of transition to highly correlated states and maintaining the temporal stability of signal structures. Within the developed framework, a set of candidate permutations in the time domain is generated, for each of which the expected value of the predicted correlation and the entropy-based uncertainty measure are calculated. The integral optimality criterion provides a comprehensive assessment of the energy balance and structural-temporal coherence of the ensemble. Introducing the uncertainty coefficient β enables adaptive control of the trade-off between decorrelation speed and ensemble stability: at β ≈ 0,15, the number of state transitions decreases by about 60 % with minimal loss in forecast accuracy. Experimental studies performed for broadband communication signals with a sampling frequency of 10 MHz demonstrated a reduction of the average mutual correlation coefficient from 0,496 to 0,272 (≈ 45 %) and an improvement of the integrated side-lobe level (ISL) by ≈ 3 dB. The spectral flatness measure (SFM) increased from 0,67 to 0,83, confirming improved structural organization and temporal alignment of the ensemble. It was shown that algorithmic convergence is achieved within 10–12 iterations. Thus, the developed method ensures adaptive minimization of mutual correlation, stabilization of energy parameters, and enhancement of interference immunity of complex signal ensembles. The obtained results confirm the effectiveness of the proposed approach for application in cognitive telecommunication environments with multiple access and dynamically varying transmission conditions.