Asymptotic Calculation of the Received Intensity of Multi-Path Millimeter Waves Transmitted over an Undulating Surface

Abstract

This paper presents the initial results of a study of an asymptotic method for calculating the received intensity of multi-path millimeter waves transmitted over an undulating surface. First, an integral expression of the received intensity is derived using a physical optics approximation. Then its zero-th order asymptotic expression is derived, using the Pearcey integral, for the case where the phase function appearing in the integrand can be approximated by a quartic polynomial. A numerical examination made at 59.5GHz showed that the asymptotic method is in good agreement with the physical optics method, even in cases where the geometrical optics method deviates significantly from the physical optics method, and that the range of applicability of the asymptotic method has its upper bound somewhere around a transmission distance to surface undulation wavelength ratio of 2.