Phase fluctuations of a radio wave in the case of total internal reflection from a randomly inhomogeneous ionosphere

Abstract

Based on the geometrical-optics approximation, we propose a method for calculation of statistical moments of the radio-wave phase in the case of total internal reflection from a randomly inhomogeneous ionosphere with a monotonic height profile of regular dielectric permittivity. To take into account the radio-wave scattering at the reflection point in a correct way, we perform analytical transformation of the eikonal equation solution derived in a first approximation of the perturbation method.Allowance for the features of the phase fluctuations of a radio wave in the case of total internal reflection from the ionosphere is significant for solutiion of the problems of prediction of radio-path characteristics and diagnostics of ionospheric irregularities [1]. Profound analysis of the reflection region on phase fluctuations was performed in [2][3][4][5], where the problems of scattering of radio waves vertically and obliquely incident on the linear layer of the ionosphere with random dielectric-permittivity irregularities given by the Gaussian correlation function were studied on the basis of the geometrical-optics approximation and the perturbation method. The result was an important conclusion that the ionospheric irregularities located in the vicinity of the reflection point of a radio wave have the dominant effect on its phase fluctuations.Solving the problems of remote sounding of the ionosphere under the actual geophysical conditions [6] requires a method for calculation of statistical moments of the radio-wave phase in a multiscale randomly inhomogeneous medium where the profile of the regular dielectric permittivity ε 0 (z) is different from the linear one. In the present paper, we consider the possibility of calculation of the phase moments of the reflected radio wave in the case of its normal incidence on the turbulent ionospheric layer with the monotonic dependence ε 0 (z).Let the wave from the source located at the point z = −z p be incident vertically upward on the ionospheric layer with random irregularities of the dielectric permittivity. Represent the dielectric permittivityε(x, y, z) of the medium as the sumwhere the functionε 1 (x, y, z) characterizes the ionosphere turbulence.Assuming that the fluctuation component of the medium satisfies the condition |ε 1 (x, y, z)| ε 0 (z),for calculation of the phase fluctuationΦ 1 of the wave we will use the solution of the eikonal equation in a *

Diagnostics of the integral parameters of the upper atmosphere’s thin structure from radio-beacons’ data

“…The information on the parameters of the upper atmosphere's thin structure is required to calculate the expected statistical characteristics of decameter signals on working radio paths 1,2,3,4 . In general, the ionized part of the atmosphere is a plasma with irregularities, the parameters of which are known only with a certain degree of probability 5,6 .…”

Diagnostics of the Stochastic Ionospheric Channel in the Decameter Band of Radio Waves

“…Meanwhile, the problem of estimating statistical characteristics of the decameter signal in the ionospheric radio channel can be solved using a model of randomly inhomogeneous ionosphere with generalized (integral) features. In this regard, significant results have been obtained due to the introduction of concepts about the effective correlation ellipsoid that approximately describes random irregularities of the medium [Gusev, Ovchinnikova, 1980;Vologdin et al, 2007Vologdin et al, , 2012Afanasiev et al, 2009] and significantly simplifies analytical calculations of statistical moments of a signal. Although the ionosphere is a multiscale randomly inhomogeneous medium and features a power spectrum of ir-regularities, in some cases, when calculating the lowest moments of trajectory characteristics of a signal, we can use a Gaussian correlation ellipsoid of irregularities with effective parameters.…”

“…Although the ionosphere is a multiscale randomly inhomogeneous medium and features a power spectrum of ir-regularities, in some cases, when calculating the lowest moments of trajectory characteristics of a signal, we can use a Gaussian correlation ellipsoid of irregularities with effective parameters. In particular, the studies [Alimov et al, 1997;Afanasiev et al, 2009;Afanasiev et al, 2010] have shown that when calculating the phase variance of a decameter radio signal in a multiscale randomly inhomogeneous medium we can adopt a Gaussian correlation ellipsoid model provided that as the spatial scale of irregularities we take the external scale of the ionospheric turbulence given by the power spectrum. This is due to the fact that the high-frequency part of the spectrum of irregularities affects to a greater extent the signal amplitude and to a lesser extent its phase [Ishimaru, 1999].…”

Diagnostics of the stochastic ionospheric channel in the decameter band of radio waves

“…Несмотря на то, что ионосфера является многомасштабной случайно-неоднородной средой и характеризуется степенным спектром неоднородностей, в ряде случаев при расчетах низших моментов траекторных характеристик сигнала можно использовать гауссов корреляционный эллипсоид неоднородностей с эффективными параметрами. В частности, исследования [Алимов и др., 1997;Афанасьев и др., 2009;Afanasiev et al, 2010] показали, что при расчетах дисперсии фазы декаметрового радиосигнала в многомасштабной случайно-неоднородной среде можно использовать гауссову модель корреляционного эллипсоида, если в качестве пространственного масштаба неоднородностей считать внешний масштаб ионосферной турбулентности, заданной степенным спектром. Связано это с тем, что высокочастотная часть спектра неоднородностей в большей степени оказывает влияние на амплитуду сигнала и в меньшей степени на его фазу [Ishimaru, 1999].…”