Back-projection algorithm based on elliptical polar coordinate for low frequency ultra wide band one-stationary bistatic SAR imaging

Low frequency ultra-wide band (UWB) one-stationary bistatic synthetic aperture radar (OS-BiSAR) has serious azimuth-variance and longer synthetic aperture, which greatly complicate the range-azimuth coupling and motion errors and limits the application of frequency domain algorithms. The back-projection (BP) algorithm has the well ability to handle the range-azimuth coupling and motion compensation, so it is a reliable method to process the low frequency UWB OS-BiSAR data. In this paper, a new derivation of BP algorithm based on elliptical polar coordinate for low frequency UWB OS-BiSAR is presented, which unites BP algorithm and fast BP algorithm in elliptical polar coordinate. Based on the deduction, the comparative analysis of the performances of the two algorithms is easily carried out, which will provide a sound basis for the following study of the fast BP algorithm for OS-BiSAR in theory. First of all, the imaging geometric model of the OS-BiSAR with motion errors is provided, and the characteristics of the echo signal are analyzed. Then, the elliptical polar coordinate system for OS-BiSAR is derived, and the analytic expression of BP algorithm in elliptical polar coordinate is deduced in detail. Finally, simulation experiment results are presented to prove the validity of the proposed algorithms.