Narrowband Bistatic Synthetic Aperture Radar Ambiguity Function Analysis and Design using Angular Harmonics

Bistatic synthetic aperture radar (BSAR) is an emerging remote sensing technology, which utilizes additional geometric complexity to improve the imaging capability. BSAR capabilities are dependent on a combination of waveform spectral properties and collection geometry. In order to develop new BSAR applications, new tools are needed to describe imaging performance for any bistatic collection geometry. The point spread function (PSF) and the associated ambiguity function (AF) fully describe coherent imaging performance but are nonlinear and spatially variant making them difficult to use as a design tool. In this study, a convolutional back projection kernel (CBPK) is used to approximate the PSF in order to overcomes the nonlinear and spatially variant limitations of the PSF, but the waveform spectrum is coupled with the collection geometry. Waveform spectrum is decoupled from collection geometry by transforming the CBPK in to a Fourier series. The PSF and the CBPK are periodic in angle and are represented as a multidimensional Fourier series. The Fourier coefficients can be decomposed into the product of a term dependent on frequency and scene radius and a second term solely dependent on collection geometry. Certain geometries have been identified that can be represented as a Fourier series with fewer dimensions and have more desirable characteristics than higher dimension series. A waveform that varies frequency with time can be used to compensate for a complex BSAR geometry such that the resulting CBPK is represented with a lower dimension Fourier series.