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9.3.3 Example Calculation

Consider the following example:
equation09-26a.gif
equation09-26b.gif
equation09-26c.gif
Polarization = Circular 
(9-26)

It is desired to find the signal level variation (relative to the direct power) at the 99% exceedance probability level. For circular aperture antennas, the half power beamwidth BW in (9-15) is approximately given by
equation09-27.gif, 
(9-27)
where rho.gif is the antenna efficiency factor (between 0 and 1). Assuming a nominal value of 0.6 for , BW  44°. Hence (9-15) is satisfied. We tacitly assume the conditions (9-16) and (9-17) are also satisfied. Injecting  and  into (9-20), we obtain Dr = -0.29 dB. Substituting Image58.gif into (9-23) results in Image59.gif dB. The reflection coefficient for circular polarization is given by RCC = -6.19 dB from Table 9-1 at Image60.gif. Substituting the above values into (9-24) gives the mean power of sea reflected waves Pr = -6.98 dB. Finally, substituting =-24.8271, =-6.9088 from Table 9-2 (P = 99%) into (9-25) results in a fading depth relative to the direct signal of A = -9.0 dB. Figure 9-1 at  gives the same value for the fading depth at the 99% level.

Table 9-1: Fresnel reflection coefficient values of the sea
at 1.5 GHz for various polarizations

Elevation, theta.gif (deg)
Polarization
Horiz.,  (dB)
Vertical,  (dB)
Circular,  (dB)
1
-0.03
-2.86
-1.34
2
-0.06
-5.83
-2.52
3
-0.09
-9.05
-3.57
4
-0.12
-12.58
-4.52
5
-0.15
-16.01
-5.39
6
-0.18
-17.41
-6.19
7
-0.21
-16.01
-6.94
8
-0.24
-13.95
-7.64
9
-0.27
-12.19
-8.3
10
-0.30
-10.81
-8.92
11
-0.33
-9.7
-9.52
12
-0.36
-8.81
-10.09
13
-0.39
-8.07
-10.64
14
-0.42
-7.46
-11.16
15
-0.45
-6.93
-11.67
16
-0.48
-6.48
-12.17
17
-0.51
-6.09
-12.65
18
-0.54
-5.74
-13.12
19
-0.57
-5.44
-13.58
20
-0.60
-5.16
-14.03

Table 9-2: Parameters ,  at the given probabilities
that fit (9-25) derived from the Nakagami-Rice distribution.

Probability (%)
1
9.5414
-10.3467
10
6.7844
-9.0977
50
2.9286
-3.5705
90
-8.1119
-8.6521
99
-24.8271
-6.9088

 

Figure 9-3: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 0 dBi, 1.5 GHz and circular polarization.
 
 

Figure 9-4: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 5 dBi, 1.5 GHz, and circular polarization.
 
 

Figure 9-5: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 10 dBi, 1.5 GHz, and circular polarization.
 
 

Figure 9-6: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 15 dBi, 1.5 GHz, and circular polarization.
 
 

Figure 9-7: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 18 dBi, 1.5 GHz, and circular polarization.
 
 

Figure 9-8: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 20 dBi, 1.5 GHz, and circular polarization.
 
 

Figure 9-9: Fading depth versus path elevation angle at different exceedance probabilities assuming an antenna gain G0 = 25 dBi, 1.5 GHz, and circular polarization.

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