An operational method for calculating the frequency fluctuations of a radio signal in a randomly inhomogeneous ionosphere

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. (paper)