A Theoretical Study of Velocity SAR Imaging of a Moving, Nonstationary Scene

The concept of the “velocity synthetic aperture radar” (VSAR)-a multiaperture sensor capable of measuring radial velocities in the scene and utilizing this information to correct motion-induced imaging distortions inherent to SAR-was proposed two decades ago. Lately, with the emergence of truly multichannel systems featuring antenna arrays with dozens of elements, the approach has been enjoying a renewed interest. The viability and effectiveness of the algorithm were successfully demonstrated in a series of airborne field campaigns that involved imaging both man-made targets and natural maritime features. These experiments and the wealth of resulting data also underscored the need for comprehensive mathematical descriptions of expected target signatures in the collected “image stacks” and for further refinements of the VSAR imaging theory. This paper addresses both tasks by building upon the available mathematical results developed for the along-track interferometric SAR imagery of distributed evolving targets. The approach allows simultaneous accounting for all essential effects known to impact SAR imagery of a target or an extended feature: its azimuth velocity, radial velocity and acceleration, as well as finite coherence time. The emphasis is on obtaining closed-form expressions that could readily illustrate the structure and behavior of the VSAR stack spectrum of such a target and help gauge anticipated focusing improvement stemming from the VSAR image correction. In particular, it is rigorously shown that the VSAR algorithm is successful in situations when SAR defocusing arises predominantly from radial motion and short coherence times-the resulting resolution is generally no worse than that of the corresponding real-aperture radar. On the other hand, strong defocusing due to azimuth translation may be problematic to compensate within the VSAR approach framework.