TIME-DOMAIN FORMATION OF SIGNAL ENSEMBLES USING LPT-SEQUENCES

Abstract

The article proposes a method for forming signal ensembles in the time domain based on LPT-sequences, aimed at improving scalability, reducing mutual signal correlation, and ensuring uniform energy distribution within the ensemble. The proposed approach relies on deterministic permutations of time intervals generated using LPT-sequences, which provide uniform coverage of the time-permutation space while preserving the structural diversity of signals. A key feature of the method is the combination of properties of low-discrepancy uniformly distributed sequences with the principles of time-domain signal decomposition, which allows the formation of ensembles with improved correlation metrics without reducing their volume or energy stability. Unlike known energy-based or stochastic methods, the LPT-sequence-based approach ensures a controlled structure of time-segment permutations, enabling the minimization of mutual interference and the stabilization of the ensemble’s internal organization as its size increases. Analytical dependencies have been derived to assess the scalability and cross-correlation characteristics of ensembles formed using LPT-permutations, and a comparative simulation with the energy-based S_h-energy method has been conducted. The results show that the average ensemble volume generated using LPT-permutations exceeds that of the Sh-energy method by an average of 6.8%, with the gain ranging from ≈3.8% at P = 100 to ≈9.7% at P = 2089. This confirms the high scalability of the method and its ability to generate a larger number of unique admissible signals without deterioration of correlation properties. Thus, the LPT-permutation method achieves an optimal balance between deterministic signal structure and a low level of mutual correlation. Its deterministic nature ensures uniform coverage of the time-permutation space, allowing the formation of signal ensembles 6–10% larger than those produced by existing methods while simultaneously reducing mutual correlation by approximately 20–25%. The obtained results confirm the effectiveness of using LPT-permutations for generating ensembles of complex signals in cognitive telecommunication systems.