Range Doppler SAR Processing Using the Fractional Fourier Transform Carmine Clemente, John J. Soraghan Centre of Excellence for Image and Signal Processing, University of Strathclyde, Glasgow, U.K. e-mail: carmine.clemente@eee.strath.ac.uk Abstract—The Fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications including radar involving the use and detection of chirp signals, pattern recognition and Synthetic Aperture Radar (SAR) image processing. In this paper the Fractional Fourier transform is applied to the Range Doppler Algorithm in order to obtain a better result in terms of resolution. The proposed technique takes advantage from the property of the FrFT to resolve with high precision chirp signals. Preliminary results are encouraging and confirms that the FrFT can be useful to perform high resolution SAR processing. I. I NTRODUCTION Synthetic Aperture Radar (SAR) is an imaging radar for earth observation from satellite and airborne manned/unmanned platforms; it is currently operational in recently launched polar-orbiting platforms such as TerraSAR-X, RadarSAT-2 and Cosmo SkyMed as well as in previous missions. Applicatons are tailored to disaster observation and management, mapping of renewable resources, geological mapping, snow/ice map- ping and strategic surveillance of military sites. Moreover, the scientific community is more and more oriented to a wide range of applications where the first step is the focalization of SAR data [1]. The use of new signal processing techniques is a good way to achieve better resolution especially using high resolution sensors where the feature of the smaller scatterer increases its importance. In [2], [3] the Fractional Fourier Transform has been applied to the Chirp Scaling Algorithm [4] to obtain good results in terms of resolution. The remainder of this paper is organized as follows. Section 2 provides some background on the SAR acquisition geometry , in section 3 an overview of the Range Doppler Algorithm in given. Section 4 introduces the Fractional Fourier Transform and in section 5 the Fractional RDA is introcuced. Sections 5 and 6 include some preliminary results and conclusions. II. SAR GEOMETRY The basic geometry of a SAR system is shown in Figure 1. The antenna system, looking across the flight direction, transmits a short chirped waveform, with a pulse repetition time 1/PRF much longer than the waveform duration; the echoes reflected by the earth surface are received through the antenna pattern and digitized line by line at each platform position as a two- dimensional array of samples. The Azimuth direction refers to the along-track direction, i.e. parallel to the flight direction Figure 1. Syntetic Aperture Radar system geometry while Range refers to the across-track direction. The equirange surfaces are concentric spheres whose intersection with the flat terrain generates concentric circles. Surfaces with identical Doppler shift are coaxial cones with the flight line as the axis and the radar platform as the apex. The intersection of these cones with the flat terrain generates hyperbolae. Objects lying along the same hyperbola will provide equi-Doppler returns. Since the received signal can be viewed as a superposition of returns from elementary scatters, the processing problem comprises a deconvolution of the received signal that is spread out in both range and azimuth directions. III. RANGE DOPPLER ALGORITHM OVERVIEW SAR data processing consists of a set of procedures for obtaining the final spatial and radiometric resolutions from the instrument. It should satisfy requirements of accuracy, computational complexity and technical feasibility. In the relatively small set of available techiques for SAR data pro- cessing (also referred to as SAR focusing), the range-Doppler algorithm and its variants is one of the most widely used. It was first developed by MacDonald Dettwiler and Associates (MDA) and the Jet Propulsion Lab (JPL) in 1979 for the processing of SEASAT data [5], [6]. The algorithm is designed to achieve block processing efficiency, using frequency domain