: Remote sensing is the science related to gathering information without direct contact with a phenomenon. Synthetic aperture radar (SAR), due to their wide applications and high performances have an important role in this field. The function of SAR, which is categorized as airborne and spaceborne radars, is the same as pulsed radars. In the SAR, the transmitted signal is generally Chirp and the received signal is expansioned in both range and azimuth in two-dimensional directions, where it named as raw data SAR. There is a relative motion between the radar platform and target point, and so the distance from the radar platform to target point during synthetic aperture varies. This makes the target data to move towards the range direction and it is called the Range Cell Migration (RCM). So for extractingimage, the image forming algorithms must be performed. There are various algorithms for image formation and one of the most commonly used is the Range Doppler Algorithms (RDA). One of the important parameter in SAR is image resolution in both directions of range and azimuth and using the chirp signal improves these resolutions. There are some methods for compressing of the chirp signal in the receiver, wherein the SAR, generally matched filter is utilized. But recently, the Fractional Fourier Transform (FrFT) is proposed in chirp signal compression, and ISLR criterion shows that it has better performance than the matched filter. Since FrFT has the ability to eliminate the second order factors on the signal phase,and RCM has the second order polynomial equation, in this thesis, an algorithm is presented based on RDA, wherein the RCM is corrected too by the use of FrFT in addition to pulse compression. Coherent processing of the raw data, which is considered as one of the most important issue in image formation algorithms, requires the maintenance phase sequence of the received signal at the receiver. Since the range equation affects in the received signal phase, the radar platform must moves in a predetermined direction to have coherent processing. But due to the lack of ideal navigation systems and the presence of atmospheric disturbances, deviation from predetermined path is inevitable. This phenomenon is termed as the error motion. In practice, the amount of displacement of the actual trajectory should be measured from the ideal trajectory and the additional amount of signal phase for coherent processing is added, thisprocedure is called motion compensation. Range equation not only effects on the received signal phase, but also it affects the delay of the received signal called the Non symmetric range cell migration (NsRCM). Conventional methods for motion compensation technique only compensate the error on the phase of the azimuth signal. In this thesis, a new method is proposed for motion compensation where the NsRCM is considered and its effect is compensated. Simulation results show that the proposed compensation algorithms has better performance based on IRW, PSLR, and ISLR criteria. Keywords: Synthetic Aperture Radar, Chirp Signal, Range Cell Migration, Image Formation,Fractional Fourier Transform, Motion Compensation