Abstract
This paper proposes an asymptotic method for calculating the received intensity of multi-path millimeter waves transmitted over an undulating surface. This method is a generalization of the asymptotic method that the authors previously derived, based on a quartic phase function approximation, from the physical optics integral expression of the received intensity. The applicability of the previous method is limited to ratios of transmission distance (D) to surface undulation wavelength (λs) of roughly less than 2. This is because the method is based on a quartic phase function approximation. In this paper, this limitation is resolved through this method's generalization, which is achieved by incorporating a technique for calculating the diffraction integral with a higher-degree phase function by using the steepest descent technique with a procedure for systematically identifying the active saddles of the phase function. Numerical examples demonstrate that the proposed asymptotic method can attain calculation accuracy comparable with the physical optics method, even in the case of large D/λs values.
