65 # [log ( fc)]2 1.3 # log( fc) A
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Log-Normal Standard Deviation
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fc(MHz)
Log-Normal Shadowing
Urban Log Normal s
Suburban Log Normal s
FIGURE 3.50 Log-normal shadowing dependency on carrier frequency.
3.7.1 Mathematical Representation
In this section we will present a method used to model the log-normal shadowing [129]. Here WGN
source is low pass filtered by a first order low pass filter (LPF) (IIR structure).
(3.84)
where n(k) the zero mean Gaussian random variable, low pass filter parameter.
x(k 1) a # x(k) (1 a) # n(k)
The LPF parameter controls the spatial decorrelation length of the log-normal shadowing.
Specifically we can write the autocorrelation of the shadowing signal as
(3.85)
where d the correlation between two samples separated by a spatial distance of D meters assuming
a vehicle speed of v m/sec, and T simulation sampling interval.
For example, in a suburban environment 7.5 dB with a correlation of approximately 0.82 at
a distance of 100 m. This was for the 900 MHz frequency band. Now for 1.7 GHz, another value
reported was 4.3 dB with a correlation of approximately 0.
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