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FIGURE 3.4 Graphical representation of multipath fading with noise.
FIGURE 3.5 Rayleigh probability density function plot (normalized power 1).
3.2.2 Statistical Properties
Two quantitative metrics of interest to us in the design of wireless digital communications, deal with the
peaks and fades described above. In particular, there is interest to know the number of times per second
a fade with a certain depth (in dB) is actually encountered. Once this rate is known, the next quantity of
interest is the amount of time the signal actually spends below this null. Both of the parameters will
become more apparent and useful in the chapters that follow.
The first quantity discussed above is called the Level Crossing Rate (LCR) which is defined as the
expected rate at which the envelope crosses a specified signal level, R, in the positive direction. It is
mathematically defined as
(3.13)
where NR is the level crossing rate, R is the specified signal level, and is the time derivative of the
envelope. The results of the integration are presented below where the actual derivation can be seen
in [1], it is omitted here for sake of convenience.
(3.14)
where and fm maximum Doppler shift or frequency which is defined as
(3.
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