o p=2 0 1 K 2 K 2 K 2 L2 =4p2 =Z Z 0  2 =41=2 X Y Z 0 in .NET

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o p=2 0 1 K 2 K 2 K 2 L2 =4p2 =Z Z 0  2 =41=2 X Y Z 0
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EFFECTS OF THE INHOMOGENEOUS IONOSPHERE ON RADIO PROPAGATION
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FIGURE 7.8. The 1D phase changing screen model.
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inhomogeneities (hF2 i ( 1), the angle of scattering of radio waves Fs $ l=l hF2 i is 1 1 small. In the coordinate system fx0 ; y0 ; z0 g with the z0 -axis directed along the ray OP, the phase uctuations F1 on the bottom boundary of the layer are (Fig. 7.9) F1 x ; y k0 L sec i
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FIGURE 7.9. Geometry of a link LEO-satellite communication with the terminal antenna placed at the Earth s surface.
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IONOSPHERIC RADIO PROPAGATION
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Then a cross-correlation function GF can be presented as GF x; Z
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7:75
where x0 x01 x02 ; Z0 y01 y02 ;  0 z01 z02 . Using Kirchoff s diffraction formulas, we can calculate the wave eld strength at the receiving point following Reference [33] & ' exp ik0 R1 R2 x02 y02 expfiF1 x0 ; y0 g exp ip dx0 dy0 7:76 Er iE0 e lR1 R2 lR
e where E0 is the amplitude of wave at a transmitting point P, R R1 R2 = R1 R2 .  2 If F1 is distributed according to hexp iF1 i exp F1 =2 , we can obtain the average eld hjEr ji at the receiving point   E0 hF2 i 1 hjEr ji exp R 2 7:77
The average eld is attenuated because part of the wave energy is transformed into the noncoherent component of the eld. When the satellite moves from point P to point P1 with coordinates {x0 , y0, z0 } and R0 R01 R02 (Fig. 7.9), the received eld equals exp ik0 R01 R02 expfiF1 x00 ; y00 g Er iE0 lR1 R2 " #9 8  > R2 0 2 02 > > > > x00 x1 y > > > = < e R dx00 dy00 exp ip e > > lR > > > > > > ; :
7:78
Here the difference between R and R is taken into account only in phase multiplication. Thus the cross-correlation function of the received eld can be presented as & 2 E0 1 GE hj Er hEr i Er1 hEr1 i ji 2 2 hexp iF1 x0 ;y0 iF1 x00 ;y00 i e R l R2 ) " !#   ip 02 R2 0 2 02 2 dx0 dy0 dx00 dy00 exp hF2 i x x00 x1 y y00 exp 1 e e lR R
7:79
EFFECTS OF THE INHOMOGENEOUS IONOSPHERE ON RADIO PROPAGATION
Using the relationship rF1 x0 ; Z0 GF1 =hF2 i, we can calculate the cross1 correlation function of the wave eld [36,37] GE   ! & ' 2 E0 R1 0 exp hF2 i x1 exp hF2 i 1 rF1 1 1 R2 R 7:80
The parameter R1 x01 =R x00 is the coordinate of ray OP along the x-axis at height Z0 (Fig. 7.9). It can be found from the speed V0 of point O when the satellite moves as x00 jV0 jt 7:81
Here, a coherent function that gives us the correlation function of the eld in a speci c plane is de ned. By using this function it is possible to obtain later the intensity of eld uctuations, I r . Spectrum of Amplitude Fluctuations. Expression (7.80) enables the relationship between the cross-correlation function of phase uctuations on the bottom boundary of the ionospheric layer and the correlation function of signal amplitude uctuations,   GE . The latter can be found for weak phase uctuations ( F2 < 1) as 1 GE
2 E0  2  F r x0 R2 1 F1 0
7:82
The time uctuations of the eld amplitude are found from the spatial phase uctuations on the bottom boundary of the ionospheric layer with small-scale inhomogeneities. Taking into account relationship (7.82), we obtain E2 =R2 k2 L sec i 0 0