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The traditional radar system needs large bandwidth, and the increasing number of channels brings huge amount of data. These data can easily overflow the memory of the sensor or the bandwidth of the signal which transferred to the ground station. In order to solve this problem, a new method of acquiring Synthetic Aperture Radar (SAR) raw data and compressing pulse which based on the theory of Compressive Sensing (CS) theory are presented. In this method, CS SAR imaging is affected by noise, sampling rate and the sparsity of signal. Furthermore, Donoho-Tanner phase transition diagram is applied to show the performance of CS pulse compression. Engineers can intuitively find the scene and the sampling rate which is suitable for using compressed sensing synthetic aperture radar pulse compression.