SAR is not compensating for the doppler of moving targets. It only compensates for the doppler shift of stationary targets as it assumes that all targets are stationary on Earth. SAR has side lobes because of which when those capture doppler, they might not suffice Nyquist criterion.
Two filters,which differ only in the signs of the phase responses, are used to defocus the complex image respectively. In the two defocused images,each stationary target is blurred to the same extent,but each moving target is blurred to different extents. Therefore, moving targets can be indicated by patch-by-patch sharpness comparison of the two defocused images.