Perets K. Methods for the Formation and Reconstruction of Ensembles of Complex Signals under Interference Conditions in Telecommunication Systems

In the dissertation, an urgent scientific and practical problem of developing methods for the formation and reconstruction of complex signal ensembles aimed at improving their interference immunity and ensuring correlation-structural consistency under conditions of a complex interference environment has been solved. The object of the study is the process of formation and reconstruction of complex signal ensembles in telecommunication systems, while the subject of the study comprises the methods, models, and algorithms for their formation and reconstruction in the time-frequency domain. The purpose of the research is to improve the interference immunity of complex signal ensembles by developing methods for their formation and recovery with due regard to nonlinear interactions, spectral reconstruction, and multicriteria optimization. The introduction substantiates the relevance of the topic and presents the scientific novelty, practical significance, the applicant’s personal contribution, and information on the approbation of the obtained results. The first chapter analyzes current methods for the formation and reconstruction of complex signal ensembles and establishes that existing approaches do not ensure sufficient recovery efficiency under conditions of nonlinear interactions, intensive interference, and high parameter dimensionality. This has substantiated the expediency of developing an integrated approach combining nonlinear modeling, controlled regularization of spectral components, and multicriteria optimization. The second chapter proposes, for the first time, an integrated method for the formation and reconstruction of complex signal ensembles in the time-frequency domain, which includes the stages of spectral representation, reconstruction under interference conditions, and accounting for nonlinear interactions among spectral components. The method combines spectral reconstruction based on the Volterra series, controlled parameter regularization, and multicriteria optimization while satisfying ensemble orthogonality constraints. The third chapter develops a method for regularization and multicriteria optimization of reconstruction parameters for complex signal ensembles in the time-frequency domain. To quantitatively assess the effect of sparsity and regularization, the Geman–McClure function extended by the parameter γ is employed, while the optimization problem is formulated using Lagrange multipliers. The effectiveness of the method is experimentally verified on 4G LTE and 5G NR signals over a wide SNR range in comparison with existing approaches. The fourth chapter develops a method for consistent signal reconstruction in the time and frequency domains. A mechanism of controlled switching between global frequency-domain reconstruction and local time-domain reconstruction depending on the signal state is proposed. Local time-domain reconstruction is improved through the introduction of a time mask and a smoothing window kernel. Experimental results confirm the preservation of consistency of global spectral characteristics while providing a more accurate reproduction of the local signal structure. The main results of the dissertation are as follows: for the first time, an integrated method for the formation and reconstruction of complex signal ensembles in the time-frequency domain has been developed; the method of signal reconstruction in the frequency domain based on the Volterra series has been improved by introducing spectral regularization using the Geman–McClure function; and the method of multicriteria optimization for the formation and reconstruction of complex signal ensembles based on Lagrange multipliers has been improved. The practical significance of the obtained results lies in the development of algorithms and software implementation of the integrated method for the formation and reconstruction of complex signal ensembles, spectral reconstruction under interference conditions, mechanisms of controlled regularization and parameter optimization, as well as coordinated local time-domain and global frequency-domain reconstruction. The obtained results provide a reduction in reconstruction error, improvement in interference immunity and reconstruction robustness, and preservation of the structural and correlation properties of signal ensembles, thereby increasing the reliability of telecommunication systems operating under complex interference conditions.