UWB RCS calculations of smooth targets via the multi-band beam summation method

We present an ultra-wide-band beam-summation (UWB-BS) algorithm for calculating the radar cross-section (RCS) of large smooth targets whose asymptotic numerical complexity is of $ O(1) $ O(1). In this approach, the incident field is expanded into a sparse set of iso-diffracting Gaussian beams (ID-GB), tiling the phase space (PS) of beam origins and directions. The field of each ID-GB is then tracked through reflections from the scatterer until the beam emerges from the target zone and propagates to the far zone using a closed-form near-to-far (N2F) zone transformation, and finally, the beam contributions are aggregated to obtain the scattered field. The algorithm can accommodate a multi-octave frequency band by dividing it into octave-wide sub-bands and introducing a UWB-BS scheme such that the PS beam lattices in the higher sub-bands are obtained by spatial-spectral upsampling those of the lower bands. The PS summation of ID-GBs is a priori localized and involves a roughly constant relatively small number of contributing beams in all the sub-bands, leading to an $ O(1) $ O(1) (frequency-independent) asymptotic computational complexity. Furthermore, with the ID parametrization, the beam axes and their propagation and scattering parameters are frequency-independent and, therefore, need to be calculated only once and then reused for all frequencies, thus greatly reducing the numerical cost of computing the RCS at multiple frequencies. The paper describes all aspects of the algorithm, including the choice of the beam parameters for asymptotic error convergence and the utilization of localization for algorithmic efficacy.