Focusing Challenges of Ships with Oscillatory Motions and Long Coherent Processing Interval

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 complex structure. The PSF of an oscillatory ship may have a 3-D resolution but also multiple high-level sidelobes. The relationship between the WDS and the nonideal PSF is illustrated with the projection slice theorem (PST). Moreover, it is discussed that the scatterers distributed on a 3-D ship cannot be focused uniformly on a 2-D imaging plane (IP) due to the variation of the slant-range plane (SRP). The projection relationships of the resolutions and focusing positions between the SRP and the IP are also derived. Simulation results are presented to validate the analyses throughout this article.