Digital Signal Processing Reference
In-Depth Information
density function of the power delay profile [Dev87]. In more familiar and com-
prehensive terms, the rms delay spread is given by the standard deviation of
f
pdp
(τ )
, as shown in (4.2):
∞
f
pdp
(τ ) dτ
1
2
)
2
τ
rms
=
(τ
−
τ
·
[unit: s]
0
∞
with
τ
=
τ
·
f
pdp
(τ ) dτ
(4.3)
0
In practice, the rms delay spread is calculated from statistical data obtained by
real-life measurements of the delay profile of the channel (Figure 4.1). Some
typical measurement results for different environments are shown in Table 4.1
[Skl01].
Environment
Frequency
rms delay spread
Notes
Urban
910 MHz
avg. 1
.
3
μ
s
NY City [Cox75]
0
.
2-0
.
3
μ
s
Suburban
910 MHz
Typical avg. [Cox72]
μ
Indoor
850 MHz
<
0
.
27
s
Office building [Dev90]
Table 4.1.
Typical values of delay spread in the 900 MHz band.
A very important side note here is that the power delay profile can indeed be
used as a measure for the
average
combined signal power available from all
multipath components. However, as a result of destructive interference, it will
not always be possible for a receiver to extract all of the available signal power
from the channel at any moment in time. This statement is valid for any single-
antenna receiver setup, no matter how complex the receiver architecture may
be. A well-known example of this is the fading experienced by the narrowband
broadcast fm radio service.
1
Interference between two multipath components
of the same signal will cause considerable variations in the available signal
power. For a mobile fm receiver, such as a car radio, the listener will experi-
ence fading as periodic audio drop-outs, caused by the squelch
2
circuit of the
receiver. In a stationary receiver, simply moving the antenna over a small dis-
tance can solve the problem most of the time. Fortunately, fading very rarely
poses a real problem in the fm broadcast service: broadcast fm features a suf-
ficiently high transmission power (up to more than 100 kW
3
), as a result of
which the average rf signal power at the client side is at least an order of
magnitude higher than the sensitivity level of the receiver. As a result of this,
1
The term 'narrowband' refers to the 150 kHz wide channel of a commercial fm broadcast station. It should
not be confused with the narrowband fm (n-fm) modulation method.
2
A 'carrier squelch' or 'noise squelch' mutes the audio output in case of an insufficient signal strength.
3
One nasty (but amusing) side-effect: the excessive transmission power of a nearby radio station can desen-
sitize the rf front-end of a receiver over its entire frequency band [Han67, Gav84a, Gav84b].
