An Efficient and Accurate GB-SAR Imaging Algorithm Based on the Fractional Fourier Transform

In this paper, an efficient and accurate imaging algorithm is presented for Ground-Based Synthetic Aperture Radar (GB-SAR) or other radar systems that could be formed by a physical or synthetic linear aperture. The imaging algorithm is based on the fractional Fourier transform (FrFT) for the azimuth compression. A mathematical framework is derived according to the projection of a sample reflectivity image onto the pseudopolar coordinate, and its implementation was presented. With the data acquisition geometry and the pseudopolar imaging coordinate, the phase of a point target can be expressed as a quadratic phase exponential. It makes that only 1-D FrFT is needed for the azimuth compression of the time-domain backscatter data for the GB-SAR imaging problem. By further research, the optimal transformation order that represents the spatial frequency changes by the FrFT was given subsequently. Taking advantage of this optimal representation, the proposed approach avoids the large calculation that occurs in the time-domain back projection (TDBP). Comparing to the far-field pseudopolar format algorithm (FPFA), the accuracy of the proposed algorithm is much improved. Meanwhile, the proposed approach holds almost the same computational cost and complexity as the FPFA. The proposed approach keeps the advantages of the imaging quality of the TDBP and the computational cost of the FPFA that are two important aspects of the GB-SAR applications. Both the numerical simulation and the field GB-SAR experiment show that the algorithm is more suitable for the high-precision GB-SAR imaging, especially for the near field.