TWO-FRAGMENT NON-LINEAR-FREQUENCY MODULATED SIGNALS WITH ROOTS OF QUADRATIC AND LINEAR LAWS FREQUENCY CHANGES
Authors: Kostyria O. O. , Нryzo A. A. , Khudov H. V. , Dodukh O. M. , Lisohorskyi B. А. 
Published: April 2024

Context. The rapid development of the technology of digital synthesis and processing of radar signals, which has been observed in recent decades, has practically removed restrictions on the possibility of implementing arbitrary laws of frequency modulation of radio oscillations. Along with the traditional use of linearly-frequency-modulated signals, modern radar means use probing signals with non-linear frequency modulation, which provide a lower level of maximum side lobes and a higher rate of their descent. These factors, in turn, contribute to improving the detection characteristics of targets under conditions of passive interference, as well as increasing the probability of detecting small targets against the background of targets with larger effective scattering surfaces. In this regard, a large number of studies are conducted in the direction of further improvement of existing and synthesis of radar signals with new laws of frequency modulation. The use of multifragment nonlinear-frequency-modulated signals, which include fragments with both linear and nonlinear modulation, provides an increase in the number of possible versions of the laws of frequency modulation and synthesis of signals with predicted characteristics. Synthesis of new multifragment signals with a reduced level of side lobes of autocorrelation functions and a higher rate of their descent is an important scientific and technical task, the solution of which is devoted to this article.
Objective. The purpose of the work is to develop mathematical models of the current and shifted time of two-fragment nonlinear-frequency modulated signals for the case when the first fragment has a root-quadratic, and the second linear frequency modulation and determine the feasibility of using such a signal in radar applications.
Method. The article theoretically confirms that for the mathematical model of the current time, when moving from the first fragment to the second at the junction of fragments, jumps of instantaneous frequency and phase (or only phases for the mathematical model of shifted time) occur, which can significantly distort the resulting signal. Determination of value of frequency-phase jumps for their further elimination is performed by finding difference between value of initial phase of second fragment and final value of phase of first fragment. A distinctive feature of the developed mathematical models is the use of the first fragment of the signal with root-quadratic, and the second – linear frequency modulation.
Results. Comparison of the signal, the first fragment of which has root-square frequency modulation, and the signal with two linearly-frequency-modulated fragments, provided that the total duration and frequency deviation are equal, shows that for the new synthesized signal the maximum level of side lobes decreased by 1.5 dB, and their rate of decay increased by 6.5 dB/dec.
Conclusions. A new two-fragment signal was synthesized, the first fragment of which has root-quadratic, and the second – linear frequency modulation. Mathematical models of the current time and with a time shift for calculating the values of the instantaneous phase of such a signal have been developed. A distinctive feature of these models is the presence of components to compensate for frequency-phase distortions, taking into account the modulation law of the frequency of the first fragment. The resulting oscillograms, spectra and autocorrelation functions of the synthesized two-fragment signals do not contradict the known theoretical position, which indicates the reliability and adequacy of the proposed mathematical models.