• The maximum excess delay (X dB): is
define to be the time delay during which
multi path energy falls to X dB below the
maximum.
• In other words the maximum excess delay is
define as τx – τ0, where τ0 is the first arriving
signal and τx is the maximum delay at
which a multi path component is within X
dB. Of the strongest arriving multipath
signal.
• The value of τx sometimes called as a
“excess delay spread”
Doppler spread and Conference Time
Delay spread and coherence bandwidth are
parameters which describes the time dispersive
nature of the channel in local area, however they do
not offer information about the time varying nature
of the channel caused by either relative motion
between the mobile and base station or by
movement of objects in the channel.
Doppler spread : Doppler spread BD is a measure of
the spectral broadening caused by the time rate of
change of the mobile radio channel and is define as
a range of frequencies over which the received
Doppler spectrum is essentially non-zero.
• Coherence time: Coherence time TC is time
domain dual of Doppler spread and it characterize
the time varying nature of the frequency
dispersive ness of the channel in the time domain.
1
Tc ≈
fM
• Coherence time is actually a statistical measure of
the time duration over which the channel impulse
response is essentially invariant and quantifies the
similarity of the channel response at different
times.
• If the coherence time is define as the time
over which the time correlation function is
above 0.5 then thee coherence time is
approximately
9
TC =
16π f m
• In modern digital communication system
coherence time is define as a geometric
mean of equation-1 and equation-2
9
0.423
TC =
=
2
16π f m
fm
Example
• Determine the proper spatial sampling interval
required to make small scale propagation
measurements which assumes that consecutive
samples are highly correlated in time, how many
samples will be required over 10m travel distance
if fc=1900MHz and v = 50m/s, how long would it
take to make these measurements ?, what is the
Doppler spread BD for the channel?
TC ≈
9
16π f m
= 565µ s
• Taking time samples at less than half TC, at
282.5µs corresponds to a spatial sampling
interval of
vT
∆x =
C
2
= 1.41cm
• Therefore the number of samples required over
10m travel distance is
10
Nx =
= 708samples
∆x
• The time taken to make this measurement is
equal to
10m
= 0.2sec
50m / s
• The Doppler spread is
vf c
BD = f m =
= 316.66 Hz
C