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

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 degrees) and wide-angle (over 20 degrees) regions at mmWave bands (20100 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. This work proposes a mathematical derivation to rigorously prove that, for an absorbing screen, UTD applying the narrow-angle Fresnel approximation is equivalent to KED.image