IEEE Access (Jan 2023)
Design of Parameters of Fast Fourier Transform for Three-Dimensional Split Step Parabolic Equations and Mirror Kirchhoff Approximation
Abstract
This paper proposes the simulation parameters of the fast Fourier transform (FFT) for the 3-dimensional (3D) split step parabolic equation (SSPE) and the mirror Kirchhoff approximation (MKA). The SSPE/MKA calculates the forward scattering by repeatedly applying the FFT between the space and angular spectral domains. The lacking designs for the parameters in the 3D SSPE/MKA, such as the sampling interval in the angular spectral domain, the truncation size in the space domain, and the windowing functions in the space and angular spectral domains, have motivated the establishment of the simulation parameters. The authors design the sampling interval in the angular spectral domain and the truncation size in the space domain for the 3D SSPE/MKA. In the space domain, a novel 3D windowing function combining a raised-cosine filter and the Fresnel zone number is proposed. In the angular spectral domain, the rectangular windowing function is extended to the 3D problem. The details of the proposed parameters are introduced and explained. The authors validate the proposals for a circular absorber screen and a dielectric sphere by using a reference Kirchhoff approximation (KA) and the exact solution of a dielectric sphere, respectively. Simulations are conducted by varying the object’s locations, proposed parameters, and frequencies at millimeter waves and terahertz bands. The results show that the KA and 3D SSPE/MKA with the proposed parameters can present a good accuracy, which has a low root-mean-square error of less than 1 dB by comparing them with a reference KA and the exact solution, respectively. Furthermore, the parameter, which can achieve a good balance between accuracy and computational time, is designed.
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