Frequency agility increases the difficulty of jammers to predict and estimate the carrier frequency and, thus, improves the radar electronic counter-countermeasures (ECCM) performance. In this article, frequency agility is introduced into synthetic aperture radar (SAR). The characteristic of the Doppler history of frequency-agile SAR (FASAR) is analyzed, which shows that the azimuth compression could not be achieved by the classic imaging algorithms. In order to reconstruct the images of interested targets, a three-channel sparse imaging method is proposed based on approximated observation model by using the echo data of different carrier frequencies. By deriving the equivalent observation model, it is concluded that the reconstruction performance can be enhanced by improving the coherence of match filter imaging results in different channels. The image characteristic of different channels in FASAR is analyzed based on the chirp scaling imaging operator. A phase compensation method is then proposed to improve the coherence of images of interested targets in different channels. Specifically, the SAR mode of random frequency agility is proposed to improve the reconstruction performance. Finally, simulations are carried out to demonstrate the effectiveness of imaging methods and ECCM performance. Theoretical analysis and simulation results demonstrate that images generated in random FASAR have better performance than those in stepped FASAR. By performing the phase compensation, the reconstruction performance of small targets can be significantly improved.
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