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\begin{document}

\title{Equivalence of knife-edge diffraction model and uniform geometrical
theory of diffraction applying Fresnel approximation for an absorbing
screen}



\author[1]{Xin Du}%
\author[1]{Jun-ichi Takada}%
\affil[1]{Tokyo Institute of Technology}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
The knife-edge diffraction model (KED) and the uniform geometrical
theory of diffraction (UTD) have been widely used to predict the
shadowing effect at millimetre-wave (mmWave) bands. This letter proposes
a mathematical derivation to rigorously prove that, for an absorbing
screen, UTD applying the narrow-angle Fresnel approximation is
equivalent to KED. The simulation scenarios are designed to validate the
proposal by comparing KED with UTD in the narrow-angle (less than
20\textsuperscript{*}) and wide-angle (over 20\textsuperscript{*})
regions at mmWave bands (20 GHz - 100 GHz). Simulated results agree with
the proposal that KED is identical to UTD with a low error of less than
0.1 dB in the narrow-angle region, while they have a difference with an
error of over 1 dB in the wide-angle region. In addition, the average
computational time is measured and results in both UTD and KED taking
approximately 8.0 ms for one test. From the proposal, it can be
theoretically explained the differences and similarities between KED and
UTD for an absorbing screen.%
\end{abstract}%



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