Handbook of Propagation Effects for Vehicular and ... - Courses

Summary of Recommendations 12-17
C o
o
θ = ( θ − 7)
/ 2 for θ < 7°
( dB)
. (12-25)
Step 5: Find the mean power of sea reflected waves P r (in dB) relative to the direct
power. This is given by
Pr = Dr + Rij + Cθ ( dB)
. (12-26)
Step 6: Find the fading depth A (relative to the direct power) by substituting P r into
Pr
A = − dB
⎛ ⎞
α exp ⎜ ⎟ ( ), (12-27)
⎝ β ⎠
where the parameters α, β in (12-27) are tabulated in Table 12-5 for different fade
exceedance percentages. The expression (12-27) and the tabulated values in Table 12-5
represent “best-fit” formulations of those given by the Nakagami-Rice distributions. The
fading depth A is the dB difference between the signal of the direct incident wave and a
threshold level that the resultant signal level exceeds with a probability of P percent of
the time.
As an example, consider a receiver system with circular polarization, at a frequency
of 1.5 GHz, elevation angle of 6°, and an antenna gain of 10 dB. The fading depth at the
99% exceedance level may be shown to be –9 dB.
Table 12-5: Parameters α, β at the given probabilities that fit (12-27) representing the
Nakagami-Ricean Distribution.
Probability (%) α β
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
12.9.2 Fading Depth Dependence on Frequency and Significant Wave Height
Examples of fading depth dependence on significant wave height and frequency are given
in Figure 12-7 for the 99% probability. The curves assume the elevation angle is 5°,
circular polarization, the antenna gain is 15 dB, and wind-wave sea conditions are
dominant. A significant wave height of 2 m results in approximate fading depths of 3.5,
4.5, and 5.5 dB at frequencies of 10, 5, and 3 GHz, respectively.