SAR Sensor Trajectory Deviations: Fourier Domain Formulation and Extended Scene Simulation of Raw Signal

Synthetic aperture radar (SAR) raw signal simulation is a useful tool for SAR system design, mission planning, processing algorithm testing, and inversion algorithm design. A two-dimensional (2-D) Fourier domain SAR raw signal simulator, exploiting the efficiency of fast Fourier transform algorithms, has been presented some years ago and is able to generate the raw signal corresponding to extended scenes. However, it cannot account for the effects of sensor trajectory deviations with respect to the nominal straight-line path. This paper explores the possibility of extending the efficient Fourier domain simulation approach to the case of sensor trajectory deviations, which is more realistic for airborne SAR systems. We first of all obtain a general and compact Fourier domain formulation of the SAR raw signal in the presence of arbitrary trajectory deviations, and show that in this general case no efficient simulation scheme can be devised. However, we demonstrate that, if a narrow beam and slow trajectory deviation assumption is made, a full 2-D Fourier domain simulation can be used. This approach can be applied only to some SAR systems and/or trajectory deviations, but it has the advantage that processing time is practically not increased with respect to the nominal trajectory case. The validity limits of the approach are analytically evaluated. Some simulation results are finally presented in order to verify the effectiveness of the proposed simulation scheme. In another paper, which is the second part of this work, it will be shown that the narrow beam-slow deviation assumption can be relaxed, at the expense of computation efficiency, if a one-dimensional azimuth Fourier domain processing followed by a range time-domain integration is used