Two‐frequency correlation function of the single‐path HF channel: Theory and comparison with the experiment

S. V. Fridman, O. V. Fridman, K. H. Lin, K. C. Yeh, S. J. Franke

Research output: Contribution to journalArticlepeer-review


The two‐frequency mutual coherence of HF electromagnetic field fluctuations caused by ionospheric irregularities in an oblique radio path is studied. The single scattering approximation is first developed and then extended to stronger field fluctuations by applying Rytov's approximation. Of considerable interest for wideband HF cpmmunication applications is the two‐frequency, two‐time correlation function of the channel 〈u* (ω,t1)u(ω + Ω,t1 + t)〉, where u(ω,t) is the complex amplitude of the radio wave transmitted at a frequency ω, measured by a receiver at time t. Our results show that this particular quantity behaves as though there were no diffraction effects (no Fresnel‐filtering effects). Thus the correlation time τ0 is close to Λ /ν regardless of the ratio between the irregularity size and the Fresnel length. Here Λ is the irregularity size and ν is the component of the drift velocity perpendicular to the ray path. Typical scales for the two‐frequency mutual correlation function are studied, and simple physical interpretations are developed. For example, the correlation bandwidth Ωc is determined by the condition that the rays connecting the transmitter and receiver at ω and ω + Ωc are separated from each other (in the vicinity of the reflection point) by a distance of the order of Λ. A procedure is described which allows the size of irregularities and components of plasma drift to be estimated from one of the mutual correlation functions and from the autocorrelation function. This procedure was applied to measurements from the University of Illinois sounder (transmitter is located in Platteville, Colorado, receiver in Urbana, Illinois). in the examples considered, irregularities with a size of the order of a few hundred meters drifting with a velocity 20–100 m s−1 can explain the fading. The observed magnitude of fading is consistent with an rms irregularity fluctuation of the order of a few tenths of one percent.

Original languageEnglish (US)
Pages (from-to)135-147
Number of pages13
JournalRadio Science
Issue number1
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Earth and Planetary Sciences(all)
  • Electrical and Electronic Engineering


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