# RCM

RCM is a phase error induced by the long synthetic aperture time. RCM reflects the changes of the instantaneous slant range, and exists in both the stationary and moving targets. The existence of RCM will lead to the energy of the target smear among multiple range gates, and will severely deteriorate the imaging quality.

According to the last exponential term of Eq. 2.2.5, in a broadside airborne SAR system, only the range curve migration exists. Thus, for the stationary target that locates at the center of the scene, its range curve migration reaches its largest value at the edge of the synthetic aperture. The largest range curvature can be expressed as

Equations 2.3.6c and 2.3.6d are the RCM of a moving target. It can be noted that an additional RWM is induced by the cross-track velocity of the moving target, and the range curvature of a moving target is different from that of a stationary target. The range walk and curve migration of a moving target are expressed respectively as

The changes of RCM can be expressed as

According to the system parameters in Table 2.2, the values of Eq. 2.3.14 to Eqs. 2.3.15a, 2.3.15b can be calculated. Suppose the cross-track velocity of the moving target is 10 m/s, the cross-track acceleration is 0.1 m/s^{2}, and the along-track velocity is 10 m/s, in an airborne SAR situation, the range walk and curve migration of the moving target is 17 and 2.6299 m, and the range curve change is 0.3805 m. Compared with the range resolution 1.25 m, the RCM is far larger than the range resolution, which has to be corrected during imaging.

However, in the spaceborne SAR situation, the RCM of a stationary target is 3.0365 m, and the range walk and curve migration of the moving target is 3.2 and 3.0228 m. Compared with the range resolution 6.25 m, the RCM of the moving target is small, and the image resolution will not be significantly affected by the RCM of the moving target.

In conclusion, the RCM is much more severer in an airborne SAR system than in a spaceborne SAR system. Since the RCM is related to the motion parameters of a moving target, it is a very important parameter in GMTI and GMTIm algorithms.