On the Use of Start-Stop Approximation for Spaceborne SAR Imaging

The start-stop approximation is a standard tool for processing radar data in synthetic aperture imaging. It assumes that the antenna is motionless when a pulse is emitted and the scattered signal received, after which the antenna moves to its next sending/receiving position along the flight track. However, when the antenna is mounted on a satellite, as opposed to an airplane, its relatively high speed raises at least two questions. The first one is whether the image may be affected by the actual displacement of the antenna during the pulse round-trip time between the orbit and the Earth’s surface. This displacement, in fact, can be rather large. Nonetheless, by analyzing the corresponding generalized ambiguity function of a synthetic aperture radar (SAR) sensor we show that in practice this issue can be disregarded. The second question is related to the Doppler frequency shift, which, again, is larger for spaceborne radars than for airborne radars. In the early SAR studies, this frequency shift provided a venue for understanding the azimuthal resolution of a radar. However, in a more rigorous analysis based on the generalized ambiguity function, the Doppler effect is typically left out of consideration. We show that for the image to stay largely unaffected by Doppler, the frequency shift must be included in the definition of a matched filter. Otherwise, there will be a geometric shift (translation) of the entire imaged scene from its true position, and there may also be a slight deterioration of the image sharpness (contrast).