Exact analytical two-dimensional spectrum for bistatic synthetic aperture radar in tandem configuration

An exact analytical solution for the two-dimensional (2-D) point target spectrum is usually difficult to obtain because of the existence of a double-square-root (DSR) term in the bistatic range equation. Some approximate solutions for the 2-D spectrum have been derived and used in order to focus bistatic synthetic aperture data. A geometry-based bistatic formula (GBF) method was used for obtaining a quasi-analytical form of a bistatic 2-D spectrum by Zhang (2007). Although the GBF method cannot completely solve the problem of the DSR term, it provides a novel aspect for dealing with this problem. In this study, based on the quasi-analytical spectrum, the authors change the signal expression space and transform the eight-order polynomial equation in terms of the slow time into the four-order polynomial equation in terms of the half quasi-bistatic angle (HQBA) for the tandem configuration. Then the DSR-term problem is successfully solved and a corresponding exact analytical bistatic 2-D spectrum is obtained. It is proved that the spectra acquired by Rocca´s smile operator, Loffeld´s bistatic formula (LBF) and the method of series reversion (MSR) are equivalent to this proposed analytical spectrum when certain conditions are met, and that this exact analytical spectrum is the most accurate among them.