Doppler Crosswind Relations in Radio Tropo-Scatter Beam Swinging for a Thin Scatter Layer

Abstract

This paper examines the form of the Doppler spectrum of the signals scattered by a thin, horizontally homogeneous, refractively turbulent layer via a bistatic radio link. Relations are developed between the mode f, of the Doppler spectrum, and the beam offset angle or distance Y, from the great circle at mid-path, as a function of the height of the scatter layer, the crosswind speed at that height, and the form of the refractivity spectrum. In the case of a theoretical “zero beamwidth” scatter link, f is linear with Y, with slope directly proportional to the crosswind, corresponding exactly to the Doppler shift of the scatterers on the beam axis. With real beams, the spectrum is weighted by the high reflectivity scatterers on the great circle side of the beam axis, |f| is always less than that of the scatterers at |Y|, and the relation is nonlinear. At sufficiently large beam offsets, however, the |f| − |Y| curve again becomes linear with slope slightly greater than expected for “zero” beamwidth; moreover, the slope becomes insensitive to either the height of the layer or the form of the refractivity spectrum. Accordingly, the crosswind speed can be estimated within a few per cent. The |f| − |Y| data may then be processed to provide an estimate of the layer height, the form of the refractivity spectrum, and the dependence of the layer reflectivity on distance from the great circle. Mention is also made of the relations of mean signal power and the variance of the Doppler spectrum to the parameters of the scatter layer and those of the scatter link. These measurables aid in resolving ambiguities when the atmospheric structure deviates from that of the simple model.