MATHEMATICAL MODEL OF THE CURRENT TIME FOR THREE-FRAGMENT RADAR SIGNAL WITH NON-LINEAR FREQUENCY MODULATION

Context. The authors of the article have developed a new mathematical model that allows taking into account frequency and phase distortions that occur in a three-fragment signal during the transition from one fragment to another, when the rate of frequency modulation of the signal changes. The object of research is the process of formation and processing of radar non-linear frequency modulation signals. Objective. The purpose of the work is to develop and research a mathematical model of current time for a signal with non-linear frequency modulation, which consists of three linear frequency modulated fragments. Method. The article provides a theoretical justification of the need to develop a mathematical model in the current time for a three-fragment signal with non-linear frequency modulation, capacity for work of the created model is demonstrated on the example of several radio signals that differ in frequency parameters. With the same signal parameters, the obtained results were compared with the results of the known model, for which known methods of spectral and correlation analysis were used. A distinctive feature of the proposed model is the consideration of jumps in the instantaneous frequency and phase of the signal that occur during the transition from one linear-frequency modulated fragment to the next. Such jump-like changes in frequency and phase in known models of signals with non-linear frequency modulation are not compensated for, which causes distortion of their spectra and an increase the side lobes level of auto-correlation (mutual-correlation) functions. Results. A comparative check of the developed and known signal models indicates a decrease the side lobes level of the autocorrelation function by 3 dB or more, depending on the given frequency-time parameters. Conclusions. The application of the proposed mathematical model makes it possible to form and process radar signals, which include three linear-frequency modulated fragments. Compensation of jump-like changes in frequency and phase leads to a decrease in the degree of distortion of the spectrum and, as a result, an increase in its effective width, which ensures a narrowing of the main lobe and a decrease the side lobes level of the auto-correlation function.