Range-Doppler processing via fourier coefficients: The path to a sub-Nyquist SAR

The increasing demand for wide swath, high-resolution, Synthetic Aperture Radar (SAR) images, requires high sampling rates which are difficult to attain in practice. Consequently, sampling rate reduction is of high practical value in radar imaging. In this paper, we introduce a new algorithm, equivalent to the well-known Range-Doppler method, to process SAR data using the Fourier coefficients of the raw signals. We then demonstrate how to exploit the new algorithm features, particularly, the relationship between the processed signals before and after Range Cells Migration Correction (RCMC), to reduce sampling rate at the acquisition stage and process the signals effectively at sub-Nyquist rates. Beyond sampling rate reduction, the proposed fast recovery algorithm forms a new CS-SAR imaging method that can be applied to high-quality and high-resolution real SAR imaging data acquired at sub-Nyquist rates. The performance of the algorithms is assessed using simulated data sets.

I. Introduction

Various algorithms have been developed in order to process Synthetic Aperture Radar (SAR) data. The Range-Doppler Algorithm (RDA) is the most widely used algorithm for high resolution SAR processing. It is conceptually the simplest, can accommodate range varying parameters and is independent of the transmitted pulse structure [1]. However, the inherent Range Cell Migration Correction (RCMC) operation, which is aimed at decoupling the dependency between the range and azimuth axes, requires fine delay resolution which is obtained by subsequent digital interpolation. Interpolation allows to reduce the sampling rate at the cost of additional computational load required to implement the digital interpolation which effectively increases the rate in the digital domain. In practice, an over sampling factor is added in order to eliminate artifacts caused by digital implementation of the standard RDA processmg.