1、 Rep. ITU-R P.2097 1 REPORT ITU-R P.2097 Transionospheric radio propagation The Global Ionospheric Scintillation Model (GISM) (2007) TABLE OF CONTENTS Page 1 Introduction 2 2 Inhomogeneities characteristics 2 3 Dependency of inhomogeneities on the latitude. 3 4 GISM propagation model . 5 4.1 Medium
2、modelling 5 4.2 Algorithm 5 5 Scintillations at receiver level 7 5.1 GPS receiver architecture . 7 5.2 Phase noise at receiver level . 8 6 Loss of lock probability 11 7 Positioning errors 13 8 Simultaneous loss of lock. 15 9 Comparisons models results and measurements 16 10 References 18 2 Rep. ITU-
3、R P.2097 1 Introduction Ionospheric scintillations are rapid variations of phase and amplitude of a signal, which passes through the ionosphere. They are very pronounced in equatorial regions where they appear every day after sunset and may last for a few hours. They are related in particular to sol
4、ar activity and the season. The main factors whose dependency has been established are indicated hereafter. At mid-latitudes, the scintillations are rather weak, except during conditions of ionospheric storms. Very strong effects relating to storms can be observed in the auroral regions. Scintillati
5、ons are created by random fluctuations of the mediums refractive index, which are caused by inhomogeneities inside the medium. These inhomogeneities in the ionosphere are the result of several mechanisms (E x B gradient drift, streaming instabilities (Kelvin Helmholtz), Rayleigh Taylor, etc.). Chara
6、cteristic dimensions and different growth rates correspond to each one of the existing processes. The overall problem is very complex and difficult to reproduce theoretically on a large scale. The inhomogeneities create a number of modifications of transmitted signals, among them phase and intensity
7、 fluctuations, fluctuations of the angle of arrival, dispersivity, Doppler, etc. This problem has been studied extensively in the past. Methods presented include the Rytov approximation in the case of weak fluctuations, the phase screen theory and the parabolic equation (PE) method. The Global Ionos
8、pheric Scintillation Model (GISM) uses the multiple phase screen (MPS) technique. It consists in a resolution of the PE for a medium divided into successive layers, each of them acting as a phase screen. The GISM model provides the statistical characteristics of the transmitted signals, in particula
9、r the scintillation index, fade durations and the cumulative probability of the signal allowing the determination of the margins to be included in a budget link. Maps of the scintillation index S4 and of the phase standard deviation may also be obtained. 2 Inhomogeneities characteristics Ionosphere
10、inhomogeneities are of two kinds: random inhomogeneities and travelling ionospheric disturbances (TID). These last have large dimensions and are equivalent to gravity waves. They are beyond the scope of GISM. Only the random inhomogeneities are taken into account by the model. The following paramete
11、rs have to be specified: the spectral density of their electron density fluctuations; their correlation distance; the altitude to which they develop; their velocity and direction of displacement. a) Spectral density The scintillations spectrum usually exhibits a linear variation with the logarithm o
12、f frequency. The most important parameter is the inclination index of this spectrum: p. The cut-off frequency is related to the correlation distance of inhomogeneities. The value of p depends on the specific conditions of development of the turbulences, in particular the instability process involved
13、, the latitude, the altitude, etc. As observed by measurements, in particular with satellite ETS-2 Afraimovitch et al., 1994, the slope value is usually between 2 and 4. Rep. ITU-R P.2097 3 b) Correlation length The correlation length is of primary importance in the characterization of the inhomogen
14、eities. With respect to these inhomogeneities, the medium may be simulated by a number of scatterers randomly distributed in space. One important parameter to consider is the size of the first Fresnel zone at the altitude under examination. As an example, for a transmitted signal at frequency 137 MH
15、z and at height 300 km, the size of the first Fresnel zone is r = h 1 km. Inhomogeneities whose size is lower or comparable to this dimension will create scintillation phenomena. As for the power spectrum index value, the coherence length of inhomogeneities varies with local specific conditions. To
16、perform a propagation calculation, the medium is considered as statistically homogeneous. To do this, we assign to each particular region of the ionosphere (altitude, latitude) typical characteristics of the inhomogeneities at the region under examination. The mean value of the correlation length de
17、duced from measurements is about 800 m at the F layer altitude Afraimovitch et al., 1994. Drift of the irregularities causes a Doppler shift of the diffraction pattern. Both the direction and the modulus of velocity are important and are taken into account in the characterization of the statistical
18、properties of the medium. c) Height of irregularities The height at which the instabilities develop may be obtained from the diffraction pattern of the transmitted signals. This last is related to the location of the first Fresnel zone. The corresponding frequency is obtained from the spectral densi
19、ty spectrum of the irregularities. Once this frequency is measured, the altitude where the irregularities develop can be easily obtained. Histograms of measurements show a peak value at altitudes between 300 and 500 km, consequently at the F layer altitude Afraimovitch et al., 1994 and Mc Dougall, 1
20、981. 3 Dependency of inhomogeneities on the latitude Scintillations are most severe and prevalent in and north of the auroral zone and near the geomagnetic equator Aarons, 1982. The equatorial region extends approximately from 20 to 20 and auroral regions from 55 to 90. These boundaries change with
21、the time of the day, the season of the year, the sunspot number and the magnetic activity. a) Equatorial scintillations Scintillation is predominantly a night time phenomenon in the equatorial region occurring for more than 40% of the year during the 20:00-02:00 local time period. It also shows a st
22、rong seasonal dependence with a pronounced minimum at the southern solstice and relatively high scintillation activity at the northern solstice. Equatorial scintillations also show a tendency to occur more often during years in which the sunspot number is high. The r.m.s. amplitude of electron densi
23、ty irregularities is equal to 20% in the most severe cases. Two regimes may be identified. For values of the amplitude scintillation index (S4) below approximately 0.5, the RMS value of phase and intensity fluctuations seems to be linearly correlated and approximately equal. For greater values of S4
24、, there is no obvious correlation and measured values are greater for intensity than for phase Doherty et al., 2000. If we considered the case of GPS L2 scintillations, the typical value of S4 at equatorial regions is 0.3. Its occurrence is related to the season and the solar activity. It may reach
25、a value of 0.5 with an occurrence 10% below and a value of 0.8 or even 1 in a few cases. 4 Rep. ITU-R P.2097 FIGURE 1 Dependency of scintillations on the solar spot number b) High latitude scintillations Contrary to equatorial fluctuations, the polar fluctuations exhibit more phase than intensity fl
26、uctuations. The intensity scintillation index is usually quite low. It rarely exceeds 0.2 and the probability of occurrence is very low in summer and always below the values obtained at equatorial regions. The situation is reverse for phase fluctuations. They may exist all the year. The values are q
27、uite high and seem to be related to magnetic activity. FIGURE 2 High latitude scintillations (intensity) Rep. ITU-R P.2097 5 FIGURE 3 High latitude scintillations (phase) 4 GISM propagation model 4.1 Medium modelling The electronic density inside the medium is calculated by the NeQuick model develop
28、ed by the University of Graz and ICTP Trieste. Inputs of this model are the solar flux number, the year, the day of the year and the local time. It provides the electronic density average value for any point in the ionosphere (latitude, longitude, altitude). The NeQuick model is used as a subroutine
29、 in the GISM model. Fluctuations of the electronic density mostly develop at night-time, at the F layer altitude and at equatorial and polar latitudes. To account for these fluctuations in the model, a database has been constituted from results published in the literature. The magnetic parameters ar
30、e computed from a Schmidt quasi-normalized spherical harmonic model of the magnetic field. These are the declination, the inclination, the vertical intensity and the components of the field. Accuracies for the angular components (declination and inclination) are less than 30 min. Accuracies for the
31、force components (horizontal, north, east, vertical and total force) are generally less than 25 nanoTeslas. The code used has been developed by the National Geophysical Data Center, NOAA, Boulder, Colorado. It is used as a subroutine in the GISM code. Given the location of a point on a ray, it provi
32、des the magnetic parameters. This allows the calculation of the Faraday rotation. 4.2 Algorithm There are two kinds of propagation errors: mean errors; scintillations and more generally higher order moments of the signal. 6 Rep. ITU-R P.2097 Mean errors are obtained solving the ray equation. The ray
33、 differential equation is solved by the Runge Kutta algorithm. The line of sight (LoS) is defined taking the electron density gradient at each point along the ray into account. This is done with respect to the three axes in a geodesic referential system. This is an iterative algorithm. It is stopped
34、 when the ray crosses the plane perpendicular to the line of sight and containing the source point. The mean errors: range, angular and Faraday rotation are subsequently determined. The calculation of fluctuations is a 2D calculation. The first dimension is the LoS previously determined. The second
35、dimension is perpendicular to that one. Symmetry of revolution is consequently assumed. To obtain the signal scintillations, the propagation equation is solved considering that the dielectric constant, , and subsequently the wave number k, are random numbers. 022=+ UkU (1) Assuming that the field va
36、riation is mainly in the direction perpendicular to the main propagation axis (parabolic approximation), equation (1) can be written as: 0 222=+UkUzUj kt(2) where z is the variable related to the main propagation axis. To solve equation (2), the medium is divided into successive layers, each one bei
37、ng characterized by stationary statistical properties. Iterating successively scattering and propagation calculations gives the solution as detailed below. In the Fourier transform domain, equation (2) can be written: 0 222=+UkUpzUj k (3) Variables p and x are the corresponding variables in the Four
38、ier transform: = xjpxzxUpzU d)exp(),(),( (4) The x variable is the variable related to the direction perpendicular to the propagation main axis (the z axis). The solution is consequently obtained in the (x, z) plane. The equation (3) solution is: +=+ pkzjpjpzpzzUzzxU )d/(2)exp(,(),(2(5) This equatio
39、n is the Kirchhoff integral equation. It can be used to calculate the field radiated by an arbitrary field distribution on a screen. It applies in particular to the free-space far-field calculation from the ionized medium output to the observation point. The calculation proceeds by alternating integ
40、ral calculations of equations (4) and (5). All these calculations are performed using fast Fourier transform (FFT) techniques. This technique is referred in the literature as multiple phase screen (MPS) technique. Rep. ITU-R P.2097 7 Random medium synthesis The spectral density of the phase at the o
41、utput of the medium is written as the product of the Fourier transform of a centred Gaussian random variable and the square root of the spectral density of the signal to be synthesized. The resulting random variable meets the required conditions. The corresponding signal is obtained taking the inver
42、se Fourier transform of this product. For a given layer the transmitted phase spectral density of the signal is: ()/2220)(PpqqCq+=(6) with: q0= 0/ 2 L L0: average size of the inhomogeneities (m). Input data are the slope of the electron density spectrum, the dimension of inhomogeneities and their dr
43、ift velocity. FFT limitations The extent of the medium in the direction perpendicular to the main propagation axis must be large compared to the autocorrelation distance of the inhomogeneities. Moreover, the space step must be a fraction of a wavelength. These two requirements influence the number o
44、f points used in the FFT algorithm. It has been set to 16 384 for signal propagation up to 2 GHz. It should be increased for propagation at higher frequencies. 5 Scintillations at receiver level 5.1 GPS receiver architecture A GPS receiver is a spread spectrum receiver, requiring several essential p
45、arts for acquisition, tracking and extracting useful information from the incoming satellite signal. It can be broadly divided into three sections: the RF front-end (RFF), digital signal processing (DSP) and the navigation data processing (NDP). The RFF and DSP sections generally consist of various
46、hardware modules, whereas the NDP section is implemented using software. Figure 4 shows a simple block diagram of a typical single frequency GPS receiver with major interfaces and input/output signals of the essential blocks. The DSP performs the acquisition and tracking of the GPS signal. Tradition
47、al signal demodulation such as those used for FM or AM cannot be used for spread spectrum signals such as GPS because the signal level is below the noise level. Instead, the signal must be coherently integrated over time so that the noise is averaged out, thereby raising the signal above the noise f
48、loor. Any GPS receiver locking up on a GPS satellite has to do a two-dimensional search for the signal. The first dimension is time. The GPS signal structure for each satellite consists of a 1 023 bit long pseudo-random number (PRN) sequence sent at a rate of 1 023 Mbit/s, i.e. the code repeats ever
49、y millisecond. To acquire in this dimension, the receiver needs to set an internal clock to the correct one of the 1 023 possible time slots by trying all possible values. Once the correct delay is found, it is tracked with a delay lock loop (DLL). 8 Rep. ITU-R P.2097 FIGURE 4 Block diagram of a generic GPS receiver The second dimension is frequency. The receiver must correct for inaccuracies in the apparent Doppler frequency. Once the carrier frequency is evaluated, it is tracked with a phase lock loop (PLL). Figure 5 shows an extre
