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

5-10
Propagation Effects for Vehicular and Personal Mobile Satellite Systems
5.7 Cumulative Distributions of Non-Fade Durations: Australian
Measurements
As mentioned in Section 5.2, a “non-fade duration” event of distance duration dd is
defined as the distance over which the fade levels are persistently smaller than a
prescribed fade threshold. In the example previously portrayed in Figure 5-1, the nonfade
durations distributions are derived through analysis of nfd1, nfd2, nfd3, … for the
condition that the fade is smaller than the 5 dB threshold. The authors employing the
Australian database in an analogous fashion as described above for the “fade duration”
case performed a non-fade duration analysis. The measured data were noted to fit the
power expression
−γ
P( NFD > dd | A < Aq
) = β ( dd)
, (5-6)
where P(NFD > dd| A < Aq) is the percentage probability that a continuous non-fade
distance NFD exceeds the duration distance dd (in m) given the condition that the fade is
smaller than the threshold Aq. The values of the parameters β , γ in the formulation
(5-6) are listed in Table 5-4 for road types exhibiting “moderate” and “extreme”
shadowing assuming a 5 dB fade threshold. A single best-fit power curve has been
derived for the two “moderate” runs. In Figure 5-7 are plotted the best fit curves (5-6) for
the moderate and extreme road type values of β , γ given in Table 5-4. We note nonfade
durations of 3.5 m and 0.22 m at the 10% and 90% levels, respectively, for the
“moderate” case, and 1.2 m and 0.18 m, respectively for the “extreme” case. The model
(5-6) and values β , γ in Table 5-4 were adopted by the ITU-R as the recommended
formulations describing the non-fade duration distributions for the “moderate” and
“extreme” fade cases [ITU-R, 1994].
Employing an analogous expression to (5-2), the joint absolute probability of exceeding a
non-fade duration distance dd for which the fade is smaller than Aq is given by
P( NFD > dd, A < Aq ) = P( NFD > dd| A < Aq ) P( A < Aq
) , (5-7)
where the first right hand factor is given by (5-6) and the second factor is obtained from
1 - P(A>Aq) using (5-3).
Table 5-4: Non-fade duration regression values of β , γ satisfying the power
expression (5-6) at a 5 dB threshold for road types exhibiting “moderate” and “extreme”
shadowing at a path elevation angle of 51° (f = 1.5 GHz).
Shadowing Level β γ % RMS Deviation Distance (km)
Moderate (Run 1) 20.54 0.58 33.3 33.0
Moderate (Run 2) 20.54 0.58 20.5 8.1
Extreme 11.71 0.8371 9.3 2.4