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1 2 2 k dF 2
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IONOSPHERIC RADIO PROPAGATION
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Finally, for p0 4 we get   1 2 2 k dF I k 32h F i sin 2 1 k2 L2 2 0
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Therefore, substituting in (7.98) for different I k from (7.100) leads to the following equations for sI : for p0 2 s2 I for p0 3 p 2 2 p dF h F 2 i pL0 p 2 d h F 2 i 2L2 F 0 7:101a
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Computation of intensity spectrum have been performed in accordance with Equations (7.97) (7.98) for strong uctuations and formulas (7.100) (7.101) for weak uctuations for an outer scale L0 10dF and inner scale Li 10 2 dF and for the spectral index p0 3, 4, 5. Figures 7.10 7.12 represent the scintillation index calculated numerically according to (7.100) (7.101) for weak signals and according to (7.97) (7.98) for strong signal phase uctuations, respectively, versus square mean deviations of signal phase for various parameters of 1D-spectrum p0 p 2 and different scales of ionospheric irregularities, respectively. It is seen from Fig. 7.11 that for p0 2 the scintillation index with an increase of phase uctuations limits to the unit. For higher spectral index (p0 > 2) sI exceeds the unit, which explain the focusing properties of the ionospheric layer consisting of various irregularities for strong variations of signal phase after passing the ionosphere. Signal Phase Fluctuations. We once again model the ionospheric F-region as a slab of ionization of mean ionization density N with a uniform mean square fractional uctuation of ionization density N=N 2 (see Fig. 7.8) with the thickness D and the outer scale L0 . We suppose that on the Earth s plane we receive radiation of wavelength l from a distant point source at zenith angle w. In our computations, to illustrate results obtained in References [34,41], we shall take the outer scale equal to the scale height H of the F-region, and we shall also take the thickness of the F-region to be H. In such notations, the mean square uctuation of signal phase experienced on passage through the F-region may
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Scintillation index/Outer scale
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p=3 p=4 5 10 15 20 25 30 35 40 45 50 55 60 L0 dF
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mean square fluc. of phase=0.1
p=3 p=4 2 4 6 8 10 12 14 16 18 20
L0 (b)
FIGURE 7.10. (a) Illustration for various values of the spectral index; the scintillation index sI , as a function of the normalized outer scale L0 ; 1:5dF L0 50dF ; h F 2 i 0:1. (b) Illustration for various values of the spectral index; the scintillation index sI , as a function of the normalized outer scale L0 ; 1:5dF L0 20dF ; h F 2 i 0:1. 279
IONOSPHERIC RADIO PROPAGATION
1.2
Scintillation index/Outer scale
mean square fluc. of phase=1
0.4 p=2 0.2 p=3 p=4 0 5 10 15 20 25 30 35 40 45 50 L0 dF
1.2
Scintillation index/Outer scale
mean square fluc. of phase=1
0.6 p=2 0.4 p=3 0.2 p=4
12 L0 dF
FIGURE 7.11. (a) Illustration for various values of the spectral index; the scintillation index sI , as a function of the normalized outer scale L0 ; 1:2dF L0 50dF ; h F 2 i 1: (b) Illustration for various values of the spectral index; the scintillation index sI , as a function of the normalized outer scale L0 ; 1:2dF L0 20dF ; h F 2 i 1.
EFFECTS OF THE INHOMOGENEOUS IONOSPHERE ON RADIO PROPAGATION
2 104 Zenith angles: 10 deg, 45 deg
Wave frequency [MHZ]=32 10
100 320
Solid line : 10 deg Dashed line: 45 deg
1000 3200 10000 32000 60000
N1 N 2
(a) Zenith angle: 60 deg, 80 deg
2 10
Wave frequency [MHZ]=32 10
100 320
Solid line : 60 deg Dashed line: 80 deg
1000 3200 10000
32000 60000
10 N1 2 N2
FIGURE 7.12. (a) The RMS uctuations of phase versus the fractional uctuations of ionization density for different frequencies at zenith angles of 10 ; 45 . The outer scale is equal to a layer thickness of L 10 km. Mean ionization density is 1012 m 3 . (b) The RMS uctuations of phase versus the fractional uctuations of ionization density for different frequencies at zenith angles of 60 ; 80 . The outer scale is equal to a layer thickness of L 10 km. Mean ionization density is 1012 m 3 .
IONOSPHERIC RADIO PROPAGATION
then be taken as h F i 
hF2 i 1
2 4re N 2
*  + N1 2 2 2 l H sec w N0
7:102
Here all parameters are de ned above; re is the radius of the electron. For numerical computations we take H 100 km and N0 1012 m 3 . The curves in Figures 7.12a,b present the RMS uctuation of a phase as a function of the RMS fractional uctuation of ionization density for a series of frequencies running from 32 MHz to 60 GHz. The gures illustrate the ionospheric propagation of various wave frequencies at zenith angles of 10, 45, 60, 80 degrees, respectively. Both axes, vertical and horizontal, are plotted logarithmically. We can see that for a given frequency, an increase of ionization density causes an increase in phase uctuations. Furthermore, for a given ionization density, when we use high frequencies for the satellite communication channel (from UHF to X-band and higher), we can see a decrease in phase uctuations to values appropriate for weak scattering. Finally, for a given ionization density, when the zenith angle w becomes larger, the effect of phase uctuations becomes stronger. In fact, for a zenith angle of 60 , the phase uctuation experienced in the passage  a  2 of 32 MHz wave through the F-region with a fractional ionization density N1 of N0 10 2 is about 750 radians. But when the zenith angle is 80 , and for the same frequency and ionization density, we obtain phase uctuations of $1270 radians.  2  to be In order to obtain 750 radians, we need the ionization density N1 N0 $3:5 10 3 m 3 . To understand the role of satellite position with respect to the observer at the Earth s plane, additional analysis of the RMS uctuation of a phase as a function of the zenith angle was done and is shown for a series of frequencies running from 32 MHz to 60 GHz in Figures 7.13a,b. The gures illustrate the ionospheric propagation of various wave frequencies at ionization densities of 100%, 80%, 30%, and 1%. Again, both the vertical and horizontal axes are plotted logarithmically. As we mentioned earlier, in the following gures we can see that for a given frequency, an increase of zenith angle causes an increase in phase uctuations. Furthermore, for a given zenith angle, when we use high frequencies for the communication channel (more than 1 GHz), we can see a decrease in phase uctuations to values appropriate for weak scattering. The same features, as in Figures 7.12, are clearly seen from illustrations of Figures 7.13a,b. Frequency Dependence of Signal Intensity Fluctuation Spectrum. Above, we evaluated the expressions of the spectrum of the signal intensity uctuations de ned by (7.97). On the basis of this expression, we present in Figures 7.10 7.11 the normalized intensity uctuation as a function of the wave frequency, for various values of the spectral index, p0 . It was shown that for a given spectral index, the behavior of the intensity is an exponential type. Furthermore, for a given frequency, when the spectral index