Extending Loffeld's bistatic formula for the general bistatic SAR configuration

Abstract

This study derives an accurate bistatic point target reference spectrum based on a zeroth-order polynomial model. The spectrum contains only two hyperbolic square root terms that are very analogous in form to the analytical monostatic spectrum. The new formulation can be considered as an improvement of the Loffeld's bistatic formula (LBF) and allows it to handle a wider range of bistatic configurations. The original LBF works well only in the case where the contributions of transmitter and receiver to the total Doppler modulation are approximately equal. An earlier paper on the extended LBF (EBLF) uses time bandwidth product (TBP) to weight the azimuth phase modulation from each platform. However, this extension is valid only in the low squint bistatic geometry. Both LBF and ELBF are expanded up to the quadratic term to derive an approximate bistatic spectrum; however, they do not show a good focusing performance in the more complex bistatic geometry, for example, the high squint case. This is due to the inaccurate individual time-Doppler correspondences. In this study, a norm in Euclidean space is defined to derive the optimal individual time-Doppler correspondences. Using the accurate individual time-Doppler correspondences, a zeroth-order polynomial model can be used to readily derive a more accurate bistatic spectrum. Two simulation experiments in the high squint geometry are used to verify the accuracy of this new formulation. The first experiment uses a parallel-track spaceborne/spaceborne configuration, and the second experiment involves an orthogonal-track airborne/airborne case.