Inverse Source Solutions With Simultaneous Localization in the Spatial and Spectral Domains—Sparse Sampling for Directive Antennas

Inverse source solvers determine spatially distributed radiation sources in a way that their fields reproduce known observations, commonly obtained by measurements. The spatial extent of the sources in relation to the wavelength determines, in general, the necessary spatial sample density of the observations. If the plane-wave spectrum of the sources is restricted in its extent, as in the case of directive antennas, the spatial sample density and the corresponding acquisition time can, however, be reduced considerably. In order to take advantage of this, an inverse source solver is presented and analyzed, which imposes filtering of the plane-wave spectrum of the localized source distribution during the solution process. The solver is based on propagating plane-wave representations as known from the multilevel fast multipole method (MLFMM), where, however, also Weyl translation operators (TLOPs) are utilized, which have here advantages as compared with the common FMM TLOPs. The functionality of the inverse source solver with spectral filtering is demonstrated for directive antennas utilizing planar and quasi-planar observation data. It is found that the observation sample step size can be increased up to several wavelengths, while spatial diagnostics of antenna faults is still possible. Moreover, considerable computational speedup and reduced memory requirements are observed.