Two-Step Compensation of Multiorder Dispersion Error for Hypersonic Targets’ SAR Imaging Covered by Plasma Sheath

The objects reentering the Earth’s atmosphere with hypersonic speed will encounter unique challenges due to the plasma sheath, which significantly alters radar signal propagation characteristics. Current methods for mitigating high-order dispersion errors, primarily designed for ionospheric effects, struggle to address the complexities introduced by the plasma sheath. Thus, a novel approach to compensating for the multiorder dispersion errors specific to hypersonic reentry scenarios is urgently needed. This article presents a two-step autofocusing method for compensating these multiorder dispersion errors. An accurate error model for the plasma sheath dispersion effect has been established based on Maxwell’s equations and the Appleton–Hartree formula. Furthermore, the analytical results of the multiorder dispersion phase error derived through Taylor analysis are presented. This model informs the construction of an SAR signal model influenced by these effects, focusing particularly on the impacts of quadratic phase error (QPE) and cubic phase error (CPE) on SAR image generation. Building on these insights, the proposed two-step autofocusing process implements a multiorder dispersion error compensation strategy. Simulation experiments across a range of plasma sheath parameters demonstrate significant improvements in range resolution, improving from 0.1221 to 0.1321 m. Peak sidelobe ratio (PSLR) improves from −3.28 to −13.27 dB, and integrated sidelobe ratio (ISLR) increases from 2.01 to −10.11 dB. Additionally, the structural similarity (SSIM) index for distributed targets dramatically rises from 0.33 to 0.99. Finally, with a signal-to-noise ratio (SNR) of at least 33 dB, the compensated range resolution error remains below 10%. For a signal-to-clutter ratio (SCR) of 35 dB or higher, the resolution compensation error is less than 2.2%, underscoring the efficacy of the proposed compensation method.