Performance Limit of Phase Gradient Autofocus Class Method for Synthetic Aperture Radar

Motion errors are a primary obstacle to achieving ideal imaging in airborne Synthetic Aperture Radar (SAR). Due to the precision limitations of motion measurement equipment, autofocus techniques are often necessary. However, there exists an upper limit to the estimable range in practical autofocus, and no suitable model has yet been proposed to explain this phenomenon. Additionally, the complexity of mathematical derivations has hindered comprehensive analysis of defocus effects caused by different types of errors. This paper uses Phase Gradient Autofocus (PGA) as a case study to describe a geometric perspective for understanding the essence of SAR defocus. Based on this model, we can not only intuitively analyze the defocus effects induced by arbitrary errors but also theoretically derive the performance limits of PGA-like algorithms. Finally, the proposed theory is validated through simulations.