The propagation of fading waves

Abstract

A scalar wave with random variations of amplitude and phase across the wave-front is assumed as a simple model of a radio wave after it has left the ionosphere. The second-order moments of the in-phase and quadrature components of the fluctuating part of the field are found using the Fresnel diffraction formula. It is assumed that these two components have a joint Gaussian distribution, and a parameter ρN, oalled the intrinsic correlation of the fading, is introduced; this serves as a measure of the ecoentricity of the ellipse of constant probability. It is shown that ρN is the amplitude of the diffraction pattern produced by a distribution of intensity proportional to the spatial correlation function of the fluctuations over the wave-front. As the wave propagates the correlation tends to zero. It is shown that for a given irregularity size and wavelength, the irregularities may be supposed to be situated at any height, up to a certain maximum height, at which ρN = 1. An analysis of day time fading on 16 kc/s has been made. It appears that the intrinsio correlation of the wave at the ionosphere is very near one, and that the ionosphere imposes phase modulation on the wave.