Ray‐tracing analysis of anomalous propagation through horizontally nonuniform surface duct

In a radio communication system using a frequency in the UHF and higher band, the fading due to change of the refractive index profile of the air is a significant problem which must be predicted. In this paper, an analysis using the geometrical optics theory is attempted to determine the propagation characteristics in a nonuniform air in which the refractive index varies in both height and range due to a small-scale nonuniform air mass occurring in the propagation path. After the refractive index of atmosphere is modified by the Earth-flattening approximation, the Euler-Lagrange differential equation is solved directly by numerical means so that the ray path is determined. In regard to low-layer propagation with transmission and reception heights of less than several hundred meters, an air model was conceived in which a surface duct occurred in a part of the propagation path. The relation of the location and size of the duct along the propagation path to the maximum arrival distance (line-of-sight) of the direct ray, divergence and convergence of the direct ray and the reflected ray and the arrival angle at the receiving point was studied in detail. It was found that the maximum arrival distance of the direct ray increases significantly depending on the location of the surface duct if it is small in size, the effect of the ray flux is greater on the convergence of the reflected ray than the divergence of the direct ray, and no significant change in arrival angle is seen at the receiving point for both the direct ray and the reflected ray.