Radar Signals Composed of Fragments With Square-Root and Linear Laws of Frequency Modulation
DOI:
https://doi.org/10.64915/RADAP.2026.104.33-41Keywords:
nonlinear frequency modulation, mathematical model, instantaneous frequency and phase discontinuity, autocorrelation function, maximum level of the side lobesAbstract
Application of digital waveform generation and signal processing technologies provides extensive opportunities for implementing radar probing pulses with various laws of frequency (phase) modulation (coding). With the introduction of linear frequency-modulated signals into radio engineering systems, research was initiated into reducing the peak level of side lobes in their autocorrelation functions, and this topic remains relevant today. One of the approaches to reducing this level is based on the use of signals with nonlinear frequency modulation composed of multiple segments. It has been established that, in order to avoid distortions in the resulting signal, it is necessary to introduce compensating terms that account for frequency-phase distortions at the first and subsequent junctions, as well as additional phase increments within the segments themselves, starting from the second segment.
This study is devoted to the development of a new mathematical model of a three-segment signal consisting of a first segment with a square-root frequency modulation law and two subsequent segments with linear frequency modulation. Such a signal provides a reduction in the peak side lobe level compared to a classical linear frequency-modulated signal by 11.43 dB. A distinctive feature of the proposed mathematical model is the definition and incorporation of new compensating components into the expressions describing the second and third signal segments.
The logic of the study determines the structure of the work. The first section is devoted to an analysis of existing publications, which indicates a lack of research in this direction, thereby confirming the relevance and necessity of the study, formulated in the second section. The third section provides a theoretical substantiation of the main principles – identifying the mechanisms of occurrence and deriving analytical expressions for compensating frequency-phase distortions arising at the first and second junctions, as well as within the second and third signal segments, for the case where the first segment has a nonlinear frequency modulation law and the subsequent two are linear.
Further research is planned to focus on assessing the feasibility and features of combined application of spectral and time-domain window functions in radar signal processing.
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