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A synthetic aperture radar (SAR) raw signal simulator for urban scenes is presented along with models it employs to compute the backscattered field and to account for the imaging radar sensor characteristics. Urban areas are represented as a set of dielectric buildings placed over a random rough nonflat dielectric terrain. The adopted models allow evaluation of the raw signal on a sound physical and mathematical background: the scattering model employs the Kirchhoff approach appropriately extended to include multiple-reflection effects, and the radar model operates in the two-dimensional Fourier transformed domain. Details to assess how and why the simulator is also efficient with respect to the computational time are provided. In addition, relevant examples are discussed to show the simulator potentialities and assess the validity of the main results. It is shown that the simulator is able to quantitatively assess performances of SAR sensors over urban structures. The proposed simulator turns out to be also useful to train numerical schemes devoted to feature extraction, and to test any specific SAR processing technique. Comments for further developments of the simulation tool are presented.