Synthetic Aperture Radar (SAR) systems provide images with a resolution related to the transmitted signal and Doppler bandwidths. High resolution systems require large bandwidths, and then high sampling rates. Processing techniques based on Compressive Sensing (CS) can be applied for reducing sampling frequency and/or increasing spatial resolution. They are based on the assumption of a sparse reflectivity map of the imaged scene. The achievable performance depends on the degree of sparsity and on the level of noise affecting processed data. In this paper these issues are investigated by means of numerical experiments on simulated raw data for realistic SAR images.