基于分数阶Fourier变换的高性能SAR成像算法

传统距离多普勒算法（RD）较低精度的SAR成像质量越来越不能满足当前实际应用的需要。为解决传统距离多普勒算法成像性能低的问题,本文提出基于分数阶Fourier变换的高性能SAR成像算法（FrFT-RD）。本文详细推导SAR距离向信号运用分数阶Fourier变换时最佳阶数的计算表达式,同时给出方位向相应的计算式。理论分析表明距离（方位）向最佳阶数均取决于SAR成像参数并具有唯一性,无须迭代运算,可极大提高FrFT-RD算法的工程实用性。根据计算得到的距离向和方位向上最优阶数,在分数阶Fourier变换域完成FrFT-RD算法的构建。机载SAR模拟数据和星载SAR实测数据测试表明,FrFT-RD算法在分辨率、峰值旁瓣比（PSLR）成像性能方面比传统RD算法均得到显著提高,其中距离向和方位向分辨率提高比值分别为45.92%和48.06%;距离向PSLR和ISLR降低幅度为1.45 dB和2.59 dB,而FrFT-RD算法在方位向PSLR和ISLR成像性能方面与传统RD算法相当。

Research on a High-performance Imaging Algorithm of Synthetic Aperture Radar via Fractional Fourier Transform

The Traditional Range Doppler (RD) algorithm has become the most classic method in Synthetic Aperture Radar (SAR) image processing because of its advantages of easy implementation and high efficiency. However, its low imaging quality is unable to meet the needs of practical applications nowadays. To resolve this problem, we propose a high-performance imaging procesing algorithm (FrFT-RD) in this paper. The expression of optimal order of SAR range signals using fractional Fourier transform is deduced, and the corresponding formula of the azimuth direction is also given. The theoretical analysis shows that the optimal orders of the range and azimuth direction both depend on the SAR imaging parameters and are unique. Thus, the engineering practicability of FrFT-RD algorithm are large without iteration approaches. The construction of the FrFT-RD algorithm includes: Firstly, the FrFT-RD algorithm based on the traditional range Doppler algorithm is established in the fractional Fourier transform domain using the calculated optimal orders of the range and azimuth direction; Secondly, the fractional Fourier transform of corresponding order is used to process the range signals and the reference function of the range direction to complete the range pulse compression and the range cell migration correction (RCMC). The range signals are reconstructed by the inverse fractional Fourier transform (IFrFT) with the order of 1; Thirdly, the fractional Fourier transform of the corresponding order is used to process the azimuth signals and the reference function of the azimuth direction to complete the azimuth pulse compression. The azimuth signals are finally reconstructed by the inverse fractional Fourier transform (IFrFT) with the order of 1. By comparing results of airborne SAR simulation with spaceborne SAR measurement data, we find that the FrFT-RD algorithm significantly improves the imaging performance on resolution, and peak side lobe ratio (PSLR) compared to traditional RD algorithm. The resolutions of the range and azimuth directions are increased by 45.92% and 48.06%, respectively, and the PSLR and ISLR of the range and direction are decreased by 1.45 dB and 2.59 dB, respectively. While the Frft-RD algorithm almost has the same imaging performance as the traditional RD algorithm in PSLR and ISLR on the azimuth direction.