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Inverse synthetic aperture radar (ISAR) is a radar imaging method by which the rotation of a target is utilized to produce a two dimensional image. To achieve high resolution in both range and cross range, a series of stepped frequency waveforms are transmitted. These sample the target's radar response in frequency and time. Frequency transforms to time, which is proportional to range, and time transforms to doppler frequency, which is proportional to cross range. Therefore a two dimensional Fourier transform can be applied to the two dimensional data set to produce a radar image. However this is an approximation as the data is in a polar format, which only approximates a rectangular grid. Therefore resampling (interpolation) is required to change the grid from a polar to a rectangular format. The resampling in this case is straightforward. In an attempt to obtain higher resolution images, the Fourier transform has been replaced by the multiple signal classification (MUSIC) algorithm. The justification for this is that the targets of interest are manmade and so have sharp edges and corners. Therefore they consist of a number of corner reflectors with a background of continuous reflectors. The corner reflectors by their nature will generally give much stronger reflections, so one can with a certain degree of accuracy, approximate the ship as a collection of corner reflectors. Over the small change in aspect angle for which ISAR imaging is performed, corner reflectors can be approximated as point scatterers. This leads to the data being modeled as a collection of complex exponentials with added white Gaussian noise. The noise being due to thermal noise in the radar system. This type of data set is ideal for the two dimensional MUSIC algorithm. There are two major difficulties in applying the MUSIC algorithm to ISAR imaging. First, the MUSIC estimator is more sensitive to the sampling grid being polar than the Fourier transform is. Second, the resampling is less effective for the MUSIC algorithm than for the Fourier transform. Therefore it is more important to perform resampling when using the MUSIC algorithm, but harder to do it effectively. The reasons for this problem and possible ways of solving it, are the topic of this paper.
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