A general bistatic SAR focusing algorithm for azimuth variant and invariant configurations Qurat Ul-Ann, Otmar Loffeld, Holger Nies, Robert Wang* University of Siegen, Siegen, Germany, ul-ann@ipp.zess.uni-siegen.de *Chinese Academy of Sciences, Beijing, China Keywords: Bistatic Synthetic Aperture Radar (SAR), bistatic point target reference spectrum, method of stationary phase, scaled inverse Fourier transformation Abstract This paper presents a general bistatic SAR focusing algorithm for azimuth variant and invariant configurations. The approach used in this paper is based on Loffeld’s Bistatic Formula (LBF). We considered different azimuth contributions of the transmitter and the receiver phase terms in the derivation of the Bistatic Point Target Reference Spectrum (BPTRS). An efficient focusing algorithm is implemented using Scaled Inverse Fourier Transformation (SIFT) and is verified with focusing results of azimuth variant and invariant configurations. 1 Introduction Bistatic SAR has gained much attention over the past years [1-18]. A general bistatic SAR configuration offers a complex geometry, with transmitter and receiver located at different platforms, moving in different directions and with different velocities. It not only allows different data acquisition geometries but also provides more information about the imaging scene. Several techniques have been used for the derivation of BPTRS [1-18]. [2] elucidates a two stage approach, first preprocessing the raw data and subsequently using a monostatic processor. A technique called “dip move out (DMO)” is used in [1] and further considered in [9]. In [17], an Omega-k algorithm is used for bistatic focusing. In [18], a range Doppler algorithm is proposed for the analytical spectrum and is derived using the Method of Series Reversion (MSR) for azimuth invariant configurations. The bistatic focusing for tandem and Translationally Invariant (TI) configurations is considered in [7] and is extended to general configurations in [8], where a 2-D SIFT is used to focus bistatic SAR data. In [8], different azimuth contributions of the transmitter and receiver phase terms have not been taken into account, therefore it does not work well for spaceborne/airborne configurations. The BPTRS based on LBF is considered in this paper, which consists of a quasi monostatic and a bistatic deformation phase term [10]. In [15], the linearization of BPTRS accommodates both the bistatic deformation and the quasi monostatic phase terms. It involves many phase terms and computationally complex range and azimuth variant modulation and scaling terms, in spite of the fact that the contribution of linearized bistatic deformation term is negligible towards them. This paper is structured as follows: In the next section, we describe the geometry and signal model of a general bistatic SAR configuration. The point target reference spectrum based on different azimuth contributions of the transmitter and the receiver phase terms is considered. The spectrum of the complete scene is derived and a focusing algorithm is provided in section 3. We analyze azimuth invariant and variant configurations in sections 4 and 5 respectively and focusing results are provided for both cases. Finally, some conclusions are drawn in the last section. 2 Geometrical model and the bistatic point target reference spectrum A geometrical model of a general bistatic SAR configuration is shown in figure 1. The azimuth time is denoted by W . are the velocities of transmitter and receiver. , T R v v 0 0 , T R W W are the azimuth times, and are the slant ranges, when transmitter and receiver are at their closest distances from the point target 0 0 , T R R R   0 0 , R R PT R W . In our approach [10], all the terms are defined with respect to the receiver’s coordinates   0 0 , R R R W . T v G R v G  R R W G 0T R G   0 0 , R R PT R W  T R W G 0 R R G Figure 1: General Bistatic SAR Geometry The complete bistatic slant range history is the sum of transmitter and receiver slant range histories and is given as:             0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 , , , , , , ; B R R R R R T R R R R R R T T T R R R R R R R R v R R v W W W W W W W W W W W         0T W (1) 1