We propose a method for direct diagnostics of a stochastic ionospheric radio channel. This method can recalculate probe signal characteristics into transmitted signal characteristics. We derive analytical equations of second-order statistical moments for trajectory characteristics of the main and probe signals propagating in a three-dimensional randomly inhomogeneous ionosphere. We take into account boundary conditions at signal transmission and reception points. As a model of random irregularities of permittivity of the ionosphere, we utilize the concept of a changing space-time correlation ellipsoid, which is self-consistent with spatial changes in the average ionosphere. Time fluctuations of random irregularities are taken into account by the hypothesis of frozen transfer. We use analytical relationships to calculate the expected statistical characteristics of decameter signals along oblique probing paths of the ionosphere. An operational numerical algorithmization of the formulas derived is proposed. We report results of numerical experiments to determine the expected phase variances, group delay, and Doppler frequency shift of the main signal on a given single-hop path, based on measurements of these characteristics of a probe signal on a secondary path. We demonstrate the efficiency of the proposed method for diagnosing statistical trajectory characteristics of a decameter signal along single-hop paths under conditions when ground points of transmission and reception of the main and probe signals are outside the vicinity of focusing points of the wave field.

No abstract

An operational method for calculating fluctuations of the Doppler frequency shift of a radio signal reflected from a randomly inhomogeneous ionosphere is proposed. The method is based on a numerical and analytical solutions of stochastic ray equations. The integral expressions are obtained for the average and root-mean-square deviations of the frequency of the radio signal along the oblique sounding path in the approximation of the perturbation method. The motion of chaotic ionospheric irregularities is taken into account in the framework of the hypothesis of the frozen turbulence transfer. The integral expressions for statistical moments are reduced to a system of ordinary differential equations of the first order and are solved numerically together with the ray equations in the regular ionosphere. This can significantly reduce the computer time spent calculating the Doppler frequency shift of the radio signal in a randomly inhomogeneous ionosphere. The results of mathematical modeling of frequency fluctuations of a decameter radio signal on a single-hop track in various geophysical conditions are presented.

A method for determining the parameters of the thin turbulent structure of a large-scale ionospheric irregularity from the trajectory characteristics of decametre radio signals emitted from the spacecraft is proposed. The spatial parameters of large-scale heterogeneity are determined by the results of numerical synthesis of the distance-frequency characteristics of radio signals. The statistical moments of signals’ trajectory characteristics at various operating frequencies, obtained by analytically solving stochastic ray equations, are used to diagnose the thin structure of the irregularity.