A Method for Calculating and Compensating Frequency-Phase Distortions at the Junction and in Signal Fragments With Nonlinear Frequency Modulation
DOI:
https://doi.org/10.20535/RADAP.2025.100.%25pKeywords:
nonlinear frequency modulation, mathematical model, instantaneous frequency and phase jump, autocorrelation functions, maximum level of side lobesAbstract
The use of nonlinear frequency modulated signals in radar technology is due to the possibility of reducing the maximum level of the side lobes of their autocorrelation functions compared to linear frequency modulated signals. One of the promising areas of development of the theory of synthesis of signals with nonlinear frequency modulation is the study of a thin signal structure that is distorted when switching to a new signal fragment.
In particular, it was found that jumps in instantaneous frequency and phase at the boundary between fragments cause additional distortions in the frequency-phase structure in subsequent fragments. These phenomena had previously been ignored by researchers.
Previous work on the development and study of mathematical models of nonlinear frequency-modulated signals has revealed regularities that describe the change in the frequency-phase structure of the next fragment when the value or order of the oldest derivative of the instantaneous phase function changes. It is found that the number of components in the distortion spectrum is determined by the order of this derivative: for phase distortions — according to its value, for frequency distortions — by one less. Constant components have a physical interpretation and correspond to jumps in instantaneous frequency or phase at the boundary of fragments.
The structure of the paper is determined by the research logic. The first section of the paper analyzes the available publications and shows that there is no research in this area. This substantiates the expediency and relevance of the research task set forth in the second section. The third section is devoted to the theoretical substantiation of the main provisions: the calculation expressions for determining the components of frequency-phase distortion in cases where the order of the instantaneous phase function does not change with the transition to a new fragment, increases by one or two.
In further research, it is planned to consider the case when the order of the instantaneous phase function decreases with the transition to the next fragment of a nonlinear frequency-modulated signal.
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