[1] A new model for scintillation on transionospheric links, based on a hybrid method and valid for strong scintillations, has been developed and used to construct a software transionospheric channel simulator. The method is a combination of the complex phase method and the random screen technique. The parameters of the random screen are determined as the result of a rigorous solution to the problem of propagation inside the ionosphere using the extended Rytov approximation (the complex phase method). The random two-dimensional spatial spectrum at the screen is then transferred down to the Earth's surface employing the rigorous relationships of the random screen theory. Thus the complex phase method can adequately introduce a random screen below the ionosphere for L-band frequencies. The technique is capable of producing statistical characteristics and simulating time realizations of the field for a wide range of input parameters. Preliminary results are presented for both weak and strong scintillations.

[1] This paper addresses the effects of scintillation on high-latitude paths of propagation. To specify the high-latitude ionosphere environment as a time-dependent threedimensional distribution of the electron density, the first-principles ionospheric model UAF EPPIM (University of Alaska Fairbanks Eulerian Parallel Polar Ionosphere Model) is utilized. For the specification of time-varying small-scale irregularities, superimposed onto the background EPPIM, the full three-dimensional inverse power law spectrum is chosen. It is augmented with the introduction of the irregularities' aspect ratio for two mutually perpendicular directions: transverse (to the geomagnetic field) direction and for the longitudinal direction to the transverse one. This full description of the propagation environment, comprised of the ''background'' and ''irregularities'' components, is further merged with the propagation scintillation model to set up the computational suite, capable of modeling the scintillation effects. The parameters of the spectrum of the electron density fluctuations, as well as the models of meso-scale local polar structures (e.g., patches) are chosen empirically. The integrated simulator enables realistic predictions of the scintillation effects for high-latitude transionospheric propagation for a number of different propagation scenarios for GPS L-band and other UHF transionospheric signals. The specific scintillation effects, caused by ionospheric patches, are simulated.Citation: Maurits, S. A., V. E. Gherm, N. N. Zernov, and H. J. Strangeways (2008), Modeling of scintillation effects on highlatitude transionospheric paths using ionospheric model (UAF EPPIM) for background electron density specifications, Radio Sci., 43, RS4001,

[1] A wideband HF simulator has been constructed on the basis of a detailed physical model of propagation which can generate a time realization of the HF wideband channel for any HF carrier frequency, bandwidth, transmitter receiver path and background, and stochastic (irregularity) ionosphere models. To accomplish this, a comprehensive solution has been obtained on the basis of the complex phase method (Rytov's method) to the problem of HF wave propagation for the most general case of a three-dimensional (3-D) inhomogeneous ionosphere with time-varying electron density fluctuations. A simulation is presented for a 1000 km path for which E and low-and high-angle F mode paths exist. The time-varying field owing to each of these paths is summed at the receiving location, enabling the calculation of the scattering function and also the time realization of the received signal shown as a function of both fast and slow time.Citation: Gherm, V. E., N. N. Zernov, and H. J. Strangeways (2005), HF propagation in a wideband ionospheric fluctuating reflection channel: Physically based software simulator of the channel, Radio Sci., 40, RS1001,

[1] A previously developed scintillation propagation model for L band signals on transionospheric paths has been further extended to describe the effects caused by the localized structure of plasma bubbles in the low-latitude ionosphere. This takes into account quasi-deterministic and random structures typical of bubbles. The model can produce signal statistical moments (power spectra, correlation functions, scintillation index, etc.) and generate random time series including the case of through bubble propagation. The simulated random time series of the field demonstrate the characteristic nonstationary behavior caused by the presence and motion of the bubble structures through the path of propagation, showing that strong enhancements of the scintillation index (S 4 ) can occur depending on the parameters of the bubble and the path. Modeling results are compared with scintillation records due to bubbles passing through GPS signal paths to a receiver at Douala, Cameroon. This shows good agreement providing validation for the bubble and propagation model.

Abstract. The complex phase method has been further extended to the problem of electromagnetic (EM) field scintillations on Earth-satellite GPS paths of propagation. The numerical and analytic technique based on the method has been developed to characterize the transionospheric channel of propagation. The effects of additional range errors due to the ionospheric electron density fluctuations in space and time have been studied taking into account the ray bending due to the inhomogeneous background ionosphere and the diffraction on local random ionospheric inhomogeneities. In the method developed, the impact of the Earth's magnetic field is accounted for by the anisotropic spatial spectrum of the ionospheric turbulence with different outer scales along and across the magnetic field lines. The variances of the EM field phase (yielding range errors) and level (log amplitude) fluctuations have been calculated for different models of the background ionospheres characterized by different height electron density profiles and total electron content. The conditions of the saturated regime of propagation, which will likely result in the degradation of a GPS navigation system, have been discussed. In addition, the scattering function of the GPS transionospheric channel of propagation has been constructed and simulated for a wideband signal.

[1] It can be important to determine the correlation of different frequency signals in L band that have followed transionospheric paths. In the future, both GPS and the new Galileo satellite system will broadcast three frequencies enabling more advanced three frequency correction schemes so that knowledge of correlations of different frequency pairs for scintillation conditions is desirable. Even at present, it would be helpful to know how dual-frequency Global Navigation Satellite Systems positioning can be affected by lack of correlation between the L1 and L2 signals. To treat this problem of signal correlation for the case of strong scintillation, a previously constructed simulator program, based on the hybrid method, has been further modified to simulate the fields for both frequencies on the ground, taking account of their cross correlation. Then, the errors in the two-frequency range finding method caused by scintillation have been estimated for particular ionospheric conditions and for a realistic fully three-dimensional model of the ionospheric turbulence. The results which are presented for five different frequency pairs (L1/L2, L1/L3, L1/L5, L2/L3, and L2/L5) show the dependence of diffractional errors on the scintillation index S4 and that the errors diverge from a linear relationship, the stronger are scintillation effects, and may reach up to ten centimeters, or more. The correlation of the phases at spaced frequencies has also been studied and found that the correlation coefficients for different pairs of frequencies depend on the procedure of phase retrieval, and reduce slowly as both the variance of the electron density fluctuations and cycle slips increase.Citation: Gherm, V. E., N. N. Zernov, and H. J. Strangeways (2011), Effects of diffraction by ionospheric electron density irregularities on the range error in GNSS dual-frequency positioning and phase decorrelation, Radio Sci., 46, RS3002,

Abstract. This paper is devoted to the investigation of the two-frequency, twoposition, time coherence function and the ionospheric scattering function describing the HF ionospheric fluctuating radio channel. The complex phase method is applied to obtain the analytical expressions for the coherence and correlation functions, which are then calculated numerically for the realistic models of the fluctuating ionosphere. The numerical Fourier transformation of the correlation function gives the ionospheric scattering function. The numerical results obtained lead to the conclusion that in the general case the large variability of shapes of the scattering function of the fluctuating ionosphere exists depending on the concrete conditions of propagation. In particular, the well-known delay-Doppler coupling can be more or less pronounced in different propagation conditions. We have shown that the presence of the coupling is exclusively due to the nonzero imaginary part of the correlation function of the scattered field, which means that this effect has a purely diffractional nature and cannot be obtained in the geometrical optics approximation.

The analytical theory of the Global Navigation Satellite Systems (GNSS) signal propagation through the inhomogeneous ionosphere with time-varying embedded localized random inhomogeneities of electron density is constructed in order to describe the regime of strong scintillation of the wave field propagating in the inhomogeneous ionospheric layer. The theory is based on the solutions of the appropriate Markov's parabolic moment equations, extended to the case of the inhomogeneous background medium. The solutions are validated by the comparison with some rigorous (numerical) solutions known for some limiting cases. The developed theory forms the theoretical background for constructing the physically based software simulator of the random transionospheric GNSS signals.