These echoes are scaled and time-shifted versions of the transmitted pulse. This phenomenon
is also called time dispersion besides delay spread and less frequently called timing jitter [14],
since this describes the position of the start of the received pulse. The time dispersion effect is visible
in that the channel widens the time duration of the pulse so the received pulse is wider than the
transmitted one. Now the comparison of this time dispersion to the transmitted symbol time is the
same as the comparison of the channel BW (or coherence BW) relative to the occupied BW of the
modulated signal, this will be discussed in the next section.
In an effort to quantitatively compare various PDPs and provide a means to support system design
analysis, various parameters are defined, which in some extent vaguely quantify the multipath channel
of interest. The mean excess delay is defined as the first moment of the PDPand is given below [15??“17].
(3.38)
(3.39)
The root mean square (RMS) delay spread is defined as the square root of the second central moment
of the PDP and is given by
(3.40)
With the following definition
(3.41)
These parameters assume the first ray is arriving at 0 0. As we will soon see the units of these
parameters are expressed in nanoseconds (nsec) for the indoor environment and microseconds (sec)
for the outdoor environment.
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