A Comparison of Point Target Spectra Derived for Bistatic SAR Processing

Abstract

The existence of a double hyperbola in the bistatic range equation makes it difficult to find an exact analytical solution for the 2D point target spectrum. Several approximate solutions for the spectrum have been derived and used to focus bistatic synthetic aperture radar data. In this paper, we establish the relationship between three independently derived bistatic point target spectra. The first spectrum is Loffeld's bistatic formula, which consists of a quasi-monostatic and a bistatic phase term. The second spectrum makes use of Rocca's smile operator, which transforms bistatic data in a defined configuration to a monostatic equivalent. The third spectrum is derived using a power series - called the method of series reversion (MSR). The MSR spectrum is the most general among the three. This paper shows that this spectrum can be reduced to the same formulation as the former two when certain conditions are met. In addition, a new approximate spectrum is derived using a Taylor series expansion about the two stationary phase points of the transmitter and receiver. We also give an alternative geometrical proof of the relationship between Rocca's smile operator and Loffeld's bistatic deformation term. The accuracies of the point target spectra are demonstrated using simulations of an X-band bistatic airborne radar with a fixed baseline.