**Xing Chen, Tianzhu Yi, Feng He, Zhihua He and Zhen Dong \***

College of Electronic Science, National University of Defense Technology, No. 109 De Ya Road, Changsha 410073, China

**\*** Correspondence: dongzhen@nudt.edu.cn; Tel.: +86-156-1622-6428

Received: 2 June 2019; Accepted: 7 August 2019; Published: 10 August 2019

**Abstract:** The high-resolution low frequency synthetic aperture radar (SAR) has serious range-azimuth phase coupling due to the large bandwidth and long integration time. High-resolution SAR processing methods are necessary for focusing the raw data of such radar. The generalized chirp scaling algorithm (GCSA) is generally accepted as an attractive solution to focus SAR systems with low frequency, large bandwidth and wide beam bandwidth. However, as the bandwidth and/or beamwidth increase, the serious phase coupling limits the performance of the current GCSA and degrades the imaging quality. The degradation is mainly caused by two reasons: the residual high-order coupling phase and the non-negligible error introduced by the linear approximation of stationary phase point using the principle of stationary phase (POSP). According to the characteristics of a high-resolution low frequency SAR signal, this paper firstly presents a principle to determine the required order of range frequency. After compensating for the range-independent coupling phase above 3rd order, an improved GCSA based on Lagrange inversion theorem is analytically derived. The Lagrange inversion enables the high-order range-dependent coupling phase to be accurately compensated. Imaging results of Pand L-band SAR data demonstrate the excellent performance of the proposed algorithm compared to the existing GCSA. The image quality and focusing depth in range dimension are greatly improved. The improved method provides the possibility to efficiently process high-resolution low frequency SAR data with wide swath.

**Keywords:** synthetic aperture radar (SAR); low frequency; high-resolution; large bandwidth; improved generalized chirp scaling (GCS); Lagrange inversion theorem; range-dependent coupling
