The Use of Angular Distance in Estimating Transmission Loss and Fading Range for Propagation through a Turbulent Atmosphere over Irregular Terrain

A discussion is given of the transmission loss expected in free space with various types of antennas, followed by a description of theoretical prediction curves for the transmission loss expected in tropospheric propagation on over-land paths. The Bremmer-van der Pol theory of diffraction and the Booker-Gordon and Weisskopf-Villars theories of tropospheric forward scattering are then developed in terms of angular distance as a parameter. Angular distance is the angle in the great circle plane between the radio horizon rays from the transmitting and receiving antennas. It is shown that this parameter replaces, to a first order of approximation, both the transmission path length and the antenna heights. Angular distance is shown to be useful for predicting the short term within-the-hour fading range as well as the median transmission loss. Illustrations are presented of the theoretical dependence of transmission loss on the angular distance, transmission path length, antenna height, radio frequency, and a parameter ΔN which is a measure of the vertical gradient of atmospheric refractive index. Most of the long-term variations of the scattered field intensities with time, as well as the climatological variations, are attributed to changes in ΔN. A new theory of obstacle gain is developed, and it is shown that this is particularly useful for explaining some of the unusually strong fields which have been observed just beyond the horizon in overland propagation.