A Modified Frequency Domain Algorithm Based on Optimal Azimuth Quadratic Factor Compensation for Geosynchronous SAR Imaging

The Doppler rate of geosynchronous synthetic aperture radar (GEO SAR) may be positive, negative, or even zero at different orbital positions. When the Doppler rate is zero or near zero at some special positions, the range cell migration cannot be corrected in the range Doppler (RD) domain by traditional frequency domain algorithms. To solve this problem, a modified frequency domain algorithm based on optimal quadratic factor compensation, including phase and envelope compensation, is proposed in this paper. First, the quadratic factor compensation in the two-dimensional (2-D) time domain is introduced to expand the folded azimuth spectrum and transform the nonlinear frequency versus time relationship into a linear relationship. Moreover, an analytical method for obtaining the optimal compensation factor is proposed to reduce the variance of the azimuth phase and increase the azimuth size of a well-focused image. Using the proposed algorithm, a 400 km × 200 km (groundrange × azimuth) image is obtained at the orbit position with a zero Doppler rate. The proposed algorithm is also suitable for positions where the Doppler rate is nonzero, and the maximum azimuth size of well-focused images is greater than that of conventional imaging algorithms. Finally, the validity of the proposed algorithm is verified by computer simulations.