A study of the relationship between multipath distortion and wavenumber spectrum of refractive index in radio links

The study reported here is concerned with relating the multipath and frequency selective fading characteristics of radio links caused by scatter phenomena to the statistical spatial characteristics of the refractive index. Two specific antenna configurations are studied in detail: the LOS (line-of-sight) case where the two antennas are pointed concentrically and the OTH (over-the-horizon) case where the antennas point along a great circle path. For each of these antenna configurations two scatter situations are considered: isotropic scatter with the propagation medium controlling the focusing of energy and locally isotropic scatter with narrow-beam antennas. In all cases single scattering theory is used and narrow-band signal transmission is assumed. It is found that when multipath is of any importance in causing signal distortion for a LOS link, the scatter portion of the channel may be modeled as a continuum of uncorrelated scatterers. Also OTH links are found to be characterizable in the same way. Single integrals and specific analytic and numerical examples are given relating frequency correlation functions and delay power spectra to the wavenumber spectra of assumed refractive index fluctuations. It is shown that a measurement of the frequency correlation function or delay power spectrum can yield an estimate of the wavenumber spectrum of the refractive index fluctuations.