A New Perspective on the Fast Time-Domain Algorithm in the General Bistatic SAR Imaging

The polar coordinate system fast time-domain algorithm is more efficient than the original back-projection (BP) algorithm. However, it still has complex coordinate transformation and 2-D interpolation. The Cartesian coordinate system fast time-domain algorithm (CCS-FTDA) can avoid these operations. In CCS-FTDA, the accurate wavenumber-domain analytical expression is the basic for designing wavenumber spectrum correction filters, which is used to compress the wavenumber spectrum width, but it is hard to be obtained in the general bistatic synthetic aperture radar (GBiSAR) systems. This article proposes an improved CCS-FTDA that does not require exact analytical expression. First, according to the Fourier transform (FT) relationship between spatial domain and wavenumber domain, the mapping relationships between azimuth time, modulation frequency, and wavenumber variables are derived. Then, a new imaging Cartesian coordinate system (CCS) is constructed to eliminate the tilt of the wavenumber spectrum along one coordinate axis. Furthermore, a wavenumber spectrum center correction method and a wavenumber spectrum tilt correction method are proposed to eliminate the ambiguity and the tilt along another coordinate axis of the wavenumber spectrum. After the above operation, we can minimize the Nyquist sampling requirement (NSR) in spatial domain and reduce the computational burden. Finally, the boundary conditions of the improved CCS-FTDA are analyzed. The proposed algorithm is a simpler and more general algorithm because it realizes the wavenumber spectrum correction without depending on the exact wavenumber-domain analytical expression. The results of simulation and raw data verify the effectiveness of the improved CCS-FTDA.