We consider a synthetic aperture radar (SAR) system that usesultra-narrowband continuous waveforms (CW) as an illumination source. Such asystem has many practical advantages, such as the use of relatively simple,low-cost and low-power transmitters, and in some cases, using the transmittersof opportunity, such as TV, radio stations. Additionally, ultra-narrowband CWsignals are suitable for motion estimation due to their ability to acquire highresolution Doppler information. In this paper, we present a novel syntheticaperture imaging method for moving targets using a bi-static SAR systemtransmitting ultra-narrowband continuous waveforms. Our method exploits thehigh Doppler resolution provided by ultra-narrowband CW signals to image boththe scene reflectivity and to determine the velocity of multiple movingtargets. Starting from the first principle, we develop a novel forward modelbased on the temporal Doppler induced by the movement of antennas and movingtargets. We form the reflectivity image of the scene and estimate the motionparameters using a filtered-backprojection technique combined with a contrastoptimization method. Analysis of the point spread function of our imageformation method shows that reflectivity images are focused when the motionparameters are estimated correctly. We present analysis of the velocityresolution and the resolution of reconstructed reflectivity images. We analyzethe error between the correct and reconstructed position of targets due toerrors in velocity estimation. Extensive numerical simulations demonstrate theperformance of our method and validate the theoretical results.
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