A Beam Summation Scheme for Ultra-wideband RCS Calculations in the High-frequency Regime

An ultra-wideband (UWB) Gaussian beam (GB) summation scheme for calculating the radar cross section (RCS) of arbitrary shaped scatterers is introduced. To allow high frequency approximations, the scatterers are assumed to be piecewise-smooth comprising surfaces with radii of curvature much larger than the wavelength. The formulation is based on the windowed Fourier transform (WFT) frame theory applied to the incident wave on the expansion plane. The incident plane wave is expanded into a frequency independent iso-diffracting Gaussian beam (ID-GB) lattice, emerging from the phase-space (PS) lattice. The choice of iso-diffracting Gaussian window provides the optimal frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, these beams are fully characterized by frequency independent parameters hence need to be traced and calculated once for all the frequencies in the band. The field of each GB is then tracked through multiple reflections by multiple surfaces within the scatterer domain until the beam emerges out and propagates to the scattering zone, where the beam contributions are summed up to obtain the scattered field, hence eventually radar cross section.