An analysis of time-frequency methods in SAR imaging of moving targets

Imaging of moving targets using synthetic aperture radar (SAR) is a challenging task. Target motion in the range direction causes a cross-range shift of the target in the reconstructed image. Target motion in the cross-range direction causes blurring in the reconstructed image. In prevoius years, a number of researchers have applied time-frequency (T-F) techniques, based on the Wigner-Ville distribution, to SAR imaging of moving targets. Specifically, a series of Wigner-Ville or other T-F transforms is substituted for the series of cross-range FFTs in the customary SAR image formation algorithm. The result is a series of SAR images (instead of just one image), indexed as a function of cross-range, in which the blurring of the target due to cross-range motion is largely eliminated. The cross-range shift due to range motion remains, but can be estimated. We analyze the T-F approach by deriving an approximate closed-form expression for the point-target response of the SAR imaging system, assuming a point target moving with constant velocity and T-F processing using the Wigner-Ville distribution. We then use the point-target response to assess the blur reduction and resolving capabilities of the T-F approach. Simulation results for point targets are presented to validate the derived expression