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There has been a considerable interest in the use of lower frequency (VHF/UHF) space-based synthetic aperture radar (SAR) for realizing the foliage and ground penetration. The phase perturbation, signal distortion and imaging resolution degradation by the ionosphere will be particularly severe, however the model is not yet well established and still needs to be further studied. In this paper, on the basis of possible improvements for the model proposed by Ishimaru and others, potential ionospheric effects on SAR imaging are evaluated. First, for analyzing azimuthal resolution, we apply the fourth moment recently obtained in general case of strong fluctuation regimes, which is expected to give results for wider conditions. The Gaussian approximation was used in the previous model: however it is only valid in the fully saturated regimes. Second, for analyzing image shift and distortion, besides group delay, the higher-order dispersion is considered. Third, for discussing range resolution degraded due to pulse broadening, besides the dispersion, the multiple scattering of ionospheric turbulence is studied. Fourth, the Faraday rotation effect is analyzed. Numerical simulations are shown using ionospheric turbulence spectrum and TEC inferred from the International Reference Ionosphere (IRI) and satellite beacon observations. Index Terms--Electromagnetic propagation in random media, ionospheric electromagnetic propagation, synthetic aperture radar (SAR).

The fourth moment plays an important role in wave propagation and scattering in random media. However, in the strong scattering regimes, it remains to be solved although a rich variety of methods have been proposed. The fourth moment equation is solved using the modified Gaussian solution method proposed in this paper. The fourth moment can be considered as a sum of the Gaussian solution and non-Gaussian correction term. The Gaussian solution is the fourth moment in the saturated regime, and can be obtained as a sum of products of the second-order moments. The derived equation of the non-Gaussian correction term is solved using the Rytov approximation and the Green's function. The fourth moment solution obtained is general for without restrictions on incident wave forms. Specifically, the solution for a plane wave is derived and applied to study the amplitude scintillation and intensity correlation function of transionospheric radio signals. The theoretical calculation on the scintillation index agrees well with the experimental results, which confirms the fourth moment solution to some extent. Index Terms--Electromagnetic propagation in random media, electromagnetic scattering by random media, ionospheric electromagnetic propagation, ionospheric scintillation.

Higher order symmetrical moments play an important role in wave propagation and scattering in random media, however it remains to be solved under strong fluctuations. In this paper, a modified Gaussian solution method is proposed for analytically solving the n-nth moment. After propagating through a random medium in the fully saturated regime, the higher order symmetrical moment of the received wave is the sum of products of the second moments, i.e., the Gaussian solution. In strong scattering regimes, the higher order symmetrical moment can be considered as a sum of the Gaussian solution and a non-Gaussian correction term, where the key issue is how to solve the derived equation of the correction term. Two methods are proposed, i.e., Green's function method and the Rytov approximation approach. Green's function method leads to a rigorous solution form, but it is complicated due to an integral equation. The approach using the Rytov approximation is found to be reasonable, as the correction is relatively small. Index Terms--Electromagnetic propagation in random media, electromagnetic scattering by random media, ionospheric electromagnetic propagation.

An efficient numerical procedure for computing the scattering coefficients of a multilayered sphere is discussed. The stability of the numerical scheme allows us to extend the feasible range of computations, both in size parameter and in number of layers for a given size, by several orders of magnitude with respect to previously published algorithms. Exemplifying results, such as scattering diagrams and cross-sectional curves, including the case of Gaussian beam illumination, are provided. Particular attention is paid to scattering at the rainbow angle for which approaches based on geometrical optics might fail to provide accurate enough results.