Phase Screen Theory Research Articles

On the low-latitude ionospheric irregularities under geomagnetically active and quiet conditions using NavIC observables: A spectral analysis approach

Ionospheric irregularities and associated scintillations under geomagnetically active/quiet conditions have detrimental effects on the reliability and performance of space- and ground-based navigation satellite systems, especially over the low-latitude region. The current work investigates the low-latitude ionospheric irregularities using the phase screen theory and the corresponding temporal Power Spectral Density (PSD) analysis to present an estimate of the outer irregularity scale sizes over these locations. The study uses simultaneous L5 signal C/No observations of NavIC (a set of GEO and GSO navigation satellite systems) near the northern crest of EIA (Indore: 22.52∘N, 75.92∘E, dip: 32.23∘N) and in between the crest and the dip equator (Hyderabad: 17.42∘N, 78.55∘E, dip: 21.69∘N). The study period (2017–2018) covers disturbed and quiet-time conditions in the declining phase of the solar cycle 24. The PSD analysis brings forward the presence of irregularities, of the order of a few hundred meters during weak-to-moderate and quiet-time conditions and up to a few km during the strong event, over both locations. The ROTI values validate the presence of such structures in the Indian region. Furthermore, only for the strong event, a time delay of scintillation occurrence over Indore, with values of 36 min and 50 min for NavIC satellites (PRNs) 5 and 6, respectively, from scintillation occurrence at Hyderabad is observed, suggesting a poleward evolution of irregularity structures. Further observations show a westward propagation of these structures on this day. This study brings forward the advantage of utilizing continuous data from the GEO and GSO satellite systems in understanding the evolution and propagation of the ionospheric irregularities over the low-latitude region.

Modelling and quantitative analysis of tropospheric turbulence impacts on GEO SAR imaging

Geosynchronous orbit synthetic aperture radar (GEO SAR) has a long synthetic aperture time and a large-scale imaging scene. Therefore, various non-ideal factors tend to accumulate, introducing phase errors and decreasing the imaging quality. During the long integration time, troposphere is time varying and space variant, which will result in image shifts and defocusing. According to the characteristics of GEO SAR, this study completes the modelling and the quantitative analysis of tropospheric turbulence. Based on the phase-screen theory, the amplitude and phase random fluctuations caused by the turbulence which will result in the defocus of images are analysed. However, in the natural environment, the imaging of GEO SAR system is affected weakly by the turbulence and this conclusion is proved from the spectral analysis.

A compact multi‐frequency GNSS scintillation model

We present a scintillation model that generates complex scintillation realizations using two-dimensional phase-screen calculations. A compact parameter set simplifies the model. The parameters can be adjusted to reproduce statistically equivalent realizations of target multi-frequency GNSS intensity and phase scintillation time series or defaulted to representative values. Geometric range and TEC inputs can be incorporated to generate realizations of baseband GNSS signals for processor performance evaluation. Selecting model parameters is guided by an efficient encapsulation of the two-dimensional phase-screen theory. Motion of the propagation path through ionospheric structure generates temporal variation. The phase-screen theory incorporates space-to-time conversion via a ratio of the Fresnel scale to an effective scan velocity. A universal strength parameter adjusts the strength of the scintillation. The model is an encapsulation of results that have been used for GPS performance analysis work that is cited in the paper. A MATLAB implementation of the model with examples has been made available.

A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

AbstractWe extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two‐component inverse power law spectrum. The two‐component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two‐dimensional field‐aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self‐similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large‐ and small‐scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.

Simulating the effects of scintillation on transionospheric signals with a two‐way phase screen constructed from ALTAIR phase‐derived TEC

Severe scintillation on transionospheric radio signals caused by small‐scale plasma irregularities can greatly disrupt wideband communication, surveillance, and navigation systems. Development of techniques to mitigate the effects of scintillation requires accurate characterization of the ionospheric propagation channel. To achieve this goal, multiple campaigns were conducted as part of the joint U.S. ‐UK Wideband Ionospheric Distortion Experiment to obtain ionospheric signatures from various instruments located on Kwajalein Atoll. We use tracking data from the VHF/UHF Advanced Research Project Agency Long‐Range Tracking and Instrumentation Radar for overflights of passive calibration spheres in low‐Earth orbit to demonstrate the validity of a one‐dimensional (1‐D) phase screen model to represent the propagation channel through a disturbed ionosphere. The 1‐D phase screen is constructed from radar phase‐derived estimates of the total electron content. We present a detailed comparison of simulated radar cross section after propagation through the phase screen with observed radar returns under both disturbed and quiet ionospheric conditions. Successful reproduction of radar amplitude enhancements and fades adds to our understanding of small‐scale plasma irregularities and moves us toward our goal of providing precise predictions of radar system performance. Doing so will allow for the development of better mitigation/compensation algorithms for detrimental ionospheric effects. Result from this study also provide an assessment of the tools required for incorporating in situ density measurements along with phase screen theory into situational awareness products to offer an accurate nowcast/forecast of system impacts to users in the communication, navigation, and surveillance communities.

Deterministic retrieval of ionospheric phase screen from amplitude scintillations

In the phase screen theory of ionospheric scintillations the ionospheric irregularities are considered as pure phase objects, and the diffraction pattern produced on the ground, by radio waves propagating through this phase screen, is obtained from conventional Fresnel diffraction theory. In the present paper the inverse problem of retrieving phase variations in the screen from the diffraction pattern on the ground is treated by using the transport‐of‐intensity equation (TIE), which is derived from the Fresnel diffraction theory result. An approximate version of the TIE is solved to obtain the phase variation in the screen from the intensity distribution on the ground. It is seen that when the phase variations involve spatial scale lengths ∼400 m, phase fluctuations of ∼5 rad can be recovered from intensity variations on the ground, for a 300‐MHz signal. For larger spatial scale lengths and higher frequencies this method can be used to retrieve larger phase variations in the screen.

VHF scintillations as a diagnostic tool for the study of ionospheric irregularities

In this paper we present the results of observations of the scintillations of radio beacon on 250.351 MHz from geostationary satellite FLEETSAT (73° E) recorded at Bombay on April 9–10, 1992 during night hours. The scintillation index,S4, is used to describe the strength of the scintillations. The variation of scintillation index with local time shows a maxima of 0.589 at 02:55 IST. This scintillation activity is linked with the spreadF-irregularities. A brief description of the scintillation theories like phase screen theory and theory for weak scintillations - Rytov solution is given. These theories provide an integral measure of the fluctuations in terms of phase and amplitude fluctuations imposed on VHF signals while traversing through the ionosphere. Power spectrum analysis for the log-amplitude and phase departure and cross spectrum between them have also been carried out. Using spectral indexp = 1, we have shown that the scale sizes for the ionospheric irregularities are greater than 1 km.

Numerical investigations of two‐frequency mutual coherence functions of an ionospheric reflection channel

The ionospheric communication channel is characterized by its transfer function. Each frequency component of the transfer function is given by the ratio of the wave field received to that transmitted. Many works exist which deal with the computation of the ionospheric transfer function when electron density varies smoothly. As frequently happens, the ionosphere is permeated by random irregularities; this paper is concerned with the computation of transfer functions in such a complex ionosphere. Each frequency component of the transfer function can be computed by using the phase‐screen‐diffraction‐layer method, also called the split‐step algorithm, in underwater acoustics. Stepping along the ray path, the random phase fluctuations in each slab are lumped into a phase screen. Diffractions between the phase screens are taken into account by assuming the waves are propagating in the background medium. Since different frequencies follow different paths between the transmitter and the receiver, care must be exercised by taking proper correlations between the different ray paths. The simulation scheme presented briefly in this paper introduces the concept of correlated phase screens to achieve proper correlations between ray paths at different frequencies. Although this concept is not limited by the channel bandwidth, the computations presented here are restricted to a bandwidth of the order of the coherence bandwidth of the channel. The result of the simulation is used to compute the two‐frequency mutual coherence function, which is widely used to characterize a random communication channel. One very important parameter of the two‐frequency mutual coherence function is the coherence bandwidth. This parameter can also be derived from a much simpler treatment of the phase screen theory. Comparisons are made and show the need for further investigations.

Daytime scintillations induced by high‐power HF waves at Tromsø, Norway

During March 1984 the high‐power HF heating facility located at Ramfjordmoen (69.6°N, 19.2°E geographic) near Tromsø, Norway, was used to modify the ionospheric F region in the daytime. The intensity and phase scintillations of 250‐MHz transmissions from the quasi‐stationary polar beacon satellite were measured when the ray path from the observing site to the satellite intercepted the modified ionospheric volume. Narrow band spectral enhancements corresponding to an irregularity scale length of 750 m were detected in the intensity spectra when the radiated HF power developed an estimated power density of about 0.3 mW/m² at the height of reflection. Spectral enhancements at larger scales were not detected in the phase spectra. From the growth and decay of the intensity spectral enhancements during the successive 10‐min “on” and 10‐min “off” periods of the heater the e‐folding growth and decay times of ∼750 m irregularities were estimated to be on the order of 30 s and 2 min, respectively. The threshold power densities required for the generation of the observed irregularity scale sizes were calculated from the self‐focusing instability theory of Cragin et al. (1977) by the use of ionospheric background parameters measured by the EISCAT radar. The theoretical estimates were found to be within a factor of 2 of the HF power densities employed in the experiment. The presence of Fresnel oscillations in the intensity and phase spectra were attributed to a limited irregularity layer thickness less than 50 km. By using the formulations of the thin phase screen theory, it was found that the observed intensity scintillations at 250 MHz correspond to irregularity amplitudes (ΔN/N) of 3% with an outer scale of 1 km.

HF produced ionospheric electron density irregularities diagnosed by UHF radio star scintillations

High frequency waves incident on an overdense ionosphere (i.e. HF < penetration frequency) are known to produce large-scale irregularities with scale sizes of several hundred meters in the F-region of the ionosphere. Three observations of radio star intensity fluctuations at UHF are reported for HF ionospheric modification experiments performed at the Arecibo Observatory. Two observations at 430 MHz and one observation at 1400 MHz indicate that the thin phase screen theory is a good approximation to the observed power spectra. However, the theory has to be extended to include antenna filtering. Such filtering is important for UHF radio star scintillations since the antenna usually has a narrow beam width. HF power densities of less than 37 μW m −2 incident on the ionosphere produce electron density irregularities larger than 13% of the ambient density (at 260 km) having scale sizes of ~510 m perpendicular to the geomagnetic field. The irregularities form within 20–25 s after the HF power is turned on. From the observed power spectra driftvelocities of the irregularities can be estimated.

On the application of phase screen models to the interpretation of ionospheric scintillation data

Phase screen models have been used for nearly three decades to facilitate the application of the scintillation theory to data interpretation. Only recently, however, as large amounts of multifrequency phase‐coherent beacon data have been analyzed, has the full potential of the model been realized. This paper presents a review of the application of the phase screen model to the interpretation of data from the Defense Nuclear Agency's Wideband satellite (international designation P76‐5), which was operational from May 1976 until August 1979. The signal structure and experiment configuration allowed measurements of temporal, spatial, and frequency coherence for a wide variety of scintillation conditions. The derived scintillation parameters are in excellent agreement with the phase screen theory. Moreover, the inferred irregularity structure has been confirmed by recent in situ measurements. The principal results can be summarized with simple algebraic formulas for the scintillation level, spatial/temporal coherence, and frequency coherence or coherence bandwidth. With appropriate manipulations, the formulas fully accommodate the propagation angle dependence in highly anisotropic media.

Geometrical control of the ratio of intensity and phase scintillation indices

Early observations of complex-signal scintillation revealed a sizeable difference in the ratio of the intensity scintillation index, S 4, to the phase scintillation index, σ φ , when measured at mid-latitude, auroral-zone, and equatorial stations. The differences observed between auroral and equatorial stations receiving a beacon signal from a polar-orbiting satellite have now been found to persist, for non-saturated values of S 4. The phase-screen theory for production of scintillation is employed in this paper to identify four factors that control the S 4 σ φ ratio, and the behavior of two of them is explored for models describing both sheetlike and rodlike plasma-density irregularities. The analysis permits rejection of the effects of static diffraction by field-aligned irregularities (whether rodlike or sheetlike) as the factor controlling the different behaviours observed. It is shown, on the other hand, that geometrical control of the effective outer scale imposed by detrend filtering in the presence of highly anisotropic irregularities can readily explain the observed behavior. Such effects arise in virtually all experiments and radio systems operating in the presence of a power-law spectrum with a very large outer scale, and they are important in controlling the relationship between phase and intensity scintillation.

Use of physical concepts in dealing with problems of multiple scatter

A physical picture is presented of the processes which produce intensity fluctuations in a wave propagating in a random medium in the case of multiple scatter. Two different mechanisms which can lead to intensity fluctuations are identified, and it is shown why a scintillation index greater than unity can arise when a parameter γ which characterises different media, is very large. The position of this focal region is shown to behave like γ − 1 3 , in agreement with other theories. It is shown that when γ is large the field in the medium is similar to that produced by a deeply modulated phase-screen and that the results of deep phase-screen theory can be usefully applied to the extended medium. Many of the results of the paper have been obtained before, but the present approach based on simple physical concepts illustrates why the effects occur and provides some very direct derivations enabling more complicated theories to be checked. The framework of physical concepts is also useful in deciding which general effects are to be expected in specific multiple scattering situations, and it allows us to discuss the probability distributions of amplitude and phase of the field in a multiply scattering random medium.

Coherence properties of wideband satellite signals caused by ionospheric scintillation

Radio scintillation on satellite signals caused by small‐scale irregularities in F‐region ionospheric electron density can be an important limitation on earth‐satellite communication and navigation systems. Scintillation imposes distortion in both amplitude and phase on wideband signals. In the present work, the shallow‐modulated phase screen theory is developed in terms of coherence bandwidth including a model based on a turbulent‐like power‐law description of the irregularities. The model results usually show a greater coherence bandwidth in the signal phase than in the signal amplitude. Therefore, systems that require phase coherence over a large bandwidth should be less affected than those requiring amplitude coherence.

Non-Gaussian fluctuations in electromagnetic radiation scattered by a random phase screen. II. Application to dynamic scattering in liquid crystal

For pt.I see ibid., vol.8, 369 (1975). The authors have studied experimentally the statistical, spatial coherence and temporal coherence properties of non-Gaussian fluctuations in light scattered by a thin layer of liquid crystal (MBBA) in its dynamic scattering state. The results are consistent with the deep phase-screen theory developed in the previous paper. With 20 V applied to the sample, experimental values of the parameters of the model are: mean square phase deviation phi 2=45.6+or-8.0 rad2, phase correlation length xi =2.63+or-0.24 mu m and phase coherence time 2.2+or-0.2s. Indications are found that, while phase fluctuations in the emergent wave-front are probably dominant, amplitude fluctuations are not entirely negligible. It is argued, however, that the effects of amplitude fluctuations on the values of the above parameters are probably quite small. Taking a broader view, the results confirm that, in many scattering experiments, detailed information concerning the scattering process can be obtained from measurements in the non-Gaussian regime.