Spatial and frequency coherence of oblique, one-hop, high-frequency paths

We consider the effect of random index of refraction fluctuations upon long-distance, ionospherically-reflected, hf paths. Along with deterministic effects such as multipath and dispersion, such fluctuations have a deleterious impact on hf communication including nonabsorptive fading, time-of-arrival spread, angle-of-arrival spread, and Doppler spread. We develop a formalism to calculate the mutual coherence functions for spatial and frequency separations based upon a path integral solution of the parabolic wave equation for a single refracted path through an ionosphere which contains random electron density fluctuations. The statistics of the hf path depend directly on the strength and statistics of the electron density fluctuations; we model the spatial power spectrum of the density fluctuation as a power law behavior versus frequency and with outer and inner scales