Signal subspace comparison between Physical & synthesized array data in echo imaging

In Synthetic Aperture Radar(SAR) imaging, the echoed data are collected by moving radar's position with respect to the target area, and this operation actually gives effect of synthesizing aperture size, which in turn gives better cross range resolution of reconstructed target scene. Among several inversion scheme for SAR Imaging, we uses an inversion scheme which uses no approximation in wave propagation analysis, and try to verify whether the collected data with synthesized aperture actually gives the same support as that with physical aperture in the same size. To do this, we make a signal subspace comparison of two imaging models with physical and synthesized arrays, respectively. Theoretical comparison and numerical analysis using Gram-Schmidt procedures had been performed. The results showed that the synthesized array data fully span the physical array data with the same system geometry and strongly support the proposed inversion scheme valuable in high resolution radar imaging.