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Airborne synthetic aperture radar (SAR) image quality considerably degrades because of motion errors. High-precision motion compensation (MOCO) is necessary in an advanced SAR data processing scheme. In the case of ultra-high resolution, the conventional twostep MOCO algorithm introduces significant range cell migration correction (RCMC) error which causes a loss to resolution. Another method named one-step MOCO can avoid RCMC error, improving image quality obviously. Meanwhile, one-step MOCO can well integrate with the standard Omega-K algorithm succinctly. A comparison of the two MOCO algorithms is demonstrated by analysing the RCMC error. Point targets simulation has validated the proposed research. Introduction: Motion errors are mainly due to atmospheric turbulence, degrading the final image quality considerably in terms of geometric and radiometric resolution losses [1, 2]. Moreover, the effect of motion errors increases for ultra-high resolution imaging. Therefore, motion compensation (MOCO) requires to be studied in depth as the key procedure in airborne synthetic aperture radar (SAR) processing. MOCO approaches based on motion measurement data can correct motion errors effectively [3-7]. The representative algorithm is the two-step MOCO which was proposed based on the chirp scaling algorithm (CSA) in [3]. It consists of first-order MOCO and second-order MOCO. The former is range-independent part and applied before range cell migration correction (RCMC). The latter should be performed at a point where the azimuth signal has not been compressed with RCMC already completed, which is essential to achieve a precise residual range-dependent MOCO. Commonly, the Omega-K algorithm (OKA) is more ideal than the CSA. However, when combined with two-step MOCO, the second-order MOCO is not suitable in the OKA, for the reason that Stolt interpolation completes residual RCMC and residual azimuth compression in company. To overcome this problem, Reigber et al. [2] proposed an extended OKA. Unfortunately, when processing ultra-high resolution SAR data, the result of two-step MOCO is not satisfactory. Even small residual rangedependent errors will result in significant deviations of RCMC. For the reason that range compression can be performed first in the OKA, not as it is in the CSA, another MOCO approach in [6, 7] is more suitable. The two parts of two-step MOCO merge into one, which takes place before RCMC with range compression already completed. By contrast, we call this method one-step MOCO. One-step MOCO compensates integrated range-dependent error directly, to achieve a precise MOCO and accurate RCMC for ultra-high resolution imaging. This Letter first analyses the RCMC error. On this basis, we make a comparison between two-step and one-step MOCOs. Finally, point targets simulation has validated the proposed research.

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