Features of Functioning and Synthesis of Mathematical Models with Time-Shift Multi-Fragment Nonlinear-Frequency-Modulated Signals
DOI:
https://doi.org/10.64915/RADAP.2025.102.%25pKeywords:
nonlinear frequency modulation, mathematical model, instantaneous phase jump, autocorrelation function, maximum level of side lobesAbstract
A known method of reducing the maximum level of side lobes of the autocorrelation function of signals with intra-pulse frequency modulation, for example, linearly-frequency-modulated signals, is using their weight processing in a radio receiving device. An alternative to weight processing is rounding the amplitude-frequency spectrum, for which nonlinear-frequency-modulated signals are used. Many varieties of mathematical models of such signals are known, but the task of synthesizing new mathematical models of signals with nonlinear frequency modulation does not lose its relevance today.
The authors of the article previously synthesized mathematical models of two- and three-fragment nonlinear-frequency-modulated signals, which provide a decrease in the level of side lobes of the correlation function due to compensation for frequency-phase distortions at the joints of fragments. The reasons for the occurrence of these distortions are determined, substantiated analytically, and verified by modeling the mechanisms of their compensation.
To further reduce the maximum level of side lobes, it is proposed to increase the number of linearly-frequency-modulated fragments from three to five, for which the components of the mathematical model are calculated, which provide compensation for the instantaneous phase jumps of the resulting signal at the joints of all its fragments.
The structure of the work is due to the logic of the study. In the first section of the work, an analysis of known publications was carried out, which indicates the absence of mathematical models of shifted time of five-fragment nonlinear-frequency-modulated signals. From this, the task of the study is formulated in the second section of the article. The third section of the work is theoretical; it is devoted to the analytical definition of compensation components to avoid distortions of the instantaneous phase at the moments of transition from one fragment of the signal to the next. It is determined that the frequency-time parameters of all previous fragments contribute to forming phase jumps at the joints. The validity of the obtained theoretical results was checked by modeling.
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