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Ship motions during long coherent processing interval (CPI) have six degrees of freedom, and the oscillatory motions are roughly periodical. The traditional ship imaging methods usually use a short time interval to form an image, while the image quality may suffer from low resolution, poor signal-to-noise ratio (SNR), and scatter scintillation. Using a longer CPI to generate an image may improve the quality but, however, largely increase the focusing difficulty. In this article, we investigate the focusing challenges of oscillatory ships with long CPI. Through analyzing the relative motion between the radar and the ship, the properties of wavenumber domain support (WDS) and point spreading function (PSF) of oscillatory ship imaging are studied. It is illustrated that the WDS is a 3-D sparse curved surface generated by the complex relative motion, with a time-variant energy density, nonparallel spectrum boundaries, and a …