Derivation of the far-field limit of PFA for SAR moving target imaging

In this paper, a new derivation of the polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) imaging is presented, which is useful when investigating its response to the moving target. Our derivation starts with examining the mostly adopted implementation of the PFA, i.e., the separable 1-D range and azimuth resampling procedures for their roles in range cell migration (RCM) correction, respectively. It is shown that the former performs RCM pre-deformation, while the latter is substantially the combination of RCM linearization and the keystone transform (KT), i.e., a well-known technique for SAR imaging of moving targets. The new formulation approach is applied to analyze the moving target. The far-field limit of the PFA for moving target focusing is derived, which can be used to predict the target´s impulse response function (IRF). The presented work might be helpful when considering a SAR system with the capability of ground moving target indication and imaging (GMTI&Im).