Принципи моделювання радіозображень в радарах із синтезованою апертурою, що випромінюють безперервні ЛЧМ-сигнали

This study focuses on the principles of the construction and implementation of a simulation model for image formation in synthetic aperture radars (SAR). Particular attention is given to the reproduction of the physical processes occurring during the processing of reflected signals and the construction of a spatial representation of the radar scene. This study aims to develop a simulation model of image formation in SAR that enables a visual representation and analysis of the main stages of signal processing, the study of various factors affecting image quality, and the verification of image formation algorithms under complex observation conditions. Objectives: The physical and mathematical principles of SAR operation are analyzed. The main components of the model are identified and corresponding mathematical descriptions are constructed. A simulation model including modules for signal generation, scene reflection, platform motion modeling, and signal processing is implemented. Typical radar observation scenarios are simulated considering the spatial configuration of the scene. The results are evaluated and the advantages and limitations of the developed model are determined compared to analytical methods. Methods: The study employs a combination of analytical, numerical, and simulation methods. The construction of the mathematical model is based on the application of electrodynamics equations, the Huygens-Fresnel principle, Ito stochastic integrals, and the system’s point spread function as a means of spatial filtering. Simulation modeling was performed in the MATLAB environment, considering the characteristics of coherent reception, spectral signal processing, platform motion compensation, and spatial convolution with the ambiguity function. Statistical approaches were also used to describe image noise components (speckle noise) for reliable modeling of natural underlying surfaces. Results: The study presents a structural scheme of the SAR image formation simulation model, which implements all key stages – from probing pulse generation to two-dimensional scene image processing and formation. Examples of simulated observation of test objects, including point and extended targets, are provided. The influence of probing signal parameters, imaging geometry, and scene characteristics on positioning accuracy and resolution was analyzed. The model demonstrates fundamental effects typical for SAR, particularly aperture synthesis due to platform motion and sidelobe formation. The obtained results can be used for educational purposes, algorithm verification, and preliminary SAR system performance evaluation under various scenarios.