Exploring the Validity of Plane and Spherical Millimeter-Wave Incidences for Multiple-Diffraction Calculations in Wireless Communication Systems

The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried out-for various millimeter-wave frequencies, inter-obstacle spacings, and angles of incidence-by employing a pair of two-dimensional (2D) hybrid formulations based on both the uniform theory of diffraction and physical optics (UTD-PO). This way, we seek to demonstrate under which circumstances each wave incidence assumption can be valid in environments that entail millimeter-wave bands. Based on this, we may ensure the minimum necessary distance from the transmitter to the first diffracting obstacle for the convergence of the spherical wave incidence solution onto that of the plane wave with a relative error below 0.1%. Our results demonstrate that for less than four diffracting elements, the minimum necessary distance engages in quasi-linear behavior under variations in both the angle of incidence and obstacle spacing. Notably, the considered frequencies (60-100 GHz) have almost no bearing on the results. Our findings will facilitate the simplified, more accurate and realistic planning of millimeter-wave radio communication systems, with multiple diffractions across various obstacles.