Digital Signal Processing Reference
In-Depth Information
standard deviation of the combined signal power (not magnitude) at the output
of a rake combiner holds (4.6):
σ
1
n
2
σ
2
n
2
σ
n
n
2
σ
n
=
+
+···+
1
√
n
σ
Rayleigh
,
≈
(4.7)
where
n
is the number of independently Rayleigh fading multipath streams that
are being resolved in the receiver and
σ
i
is the standard deviation of the power
of the
i
-th multipath component.
It follows that the deviation from the mean power that can be extracted from
the channel becomes smaller when the number of resolved paths is increased.
In other words, the number of occasions where the signal power drops below a
certain minimal level is drastically reduced. This is great news for the reliabil-
ity of the wireless link in a static environment.
For example, suppose that the design specifications of a certain wireless link
prescribe a 90% uptime guarantee, while the remaining 10% outage time is
absorbed by the time-domain diversity of the error coder. Figure 4.8 shows the
cumulative distribution function (cdf) of the power distribution for different
numbers of resolved paths in a nlos channel. A receiver unaware of the 'mul-
tipath' concept shows a crossover value of 0
.
01. This actually boils down to
Cumulative distribution function
1 resolved NLOS path
std deviation: 1.39 P
avg
CT
90%
: P
avg
-20dB
1.0
2 resolved paths
0.8
std deviation: 0.98 P
avg
CT
90%
: P
avg
-10dB // CT
95%
: P
avg
-14dB
1
resolved
path
0.6
3 resolved paths
std deviation: 0.80 P
avg
CT
90%
: P
avg
-7dB // CT
95%
: P
avg
-9.2dB
0.4
4 resolved paths
5 resolved
paths
std deviation: 0.70 P
avg
CT
90%
: P
avg
-5.9dB // CT
95%
: P
avg
-7.4dB
0.2
CT
90%
CT
95%
5 resolved paths
std deviation: 0.63 P
avg
CT
90%
: P
avg
-4.9dB // CT
95%
: P
avg
-6.2dB
0
0.5
1
1.5
2
instantaneous received power
normalized to P
avg
Figure 4.8.
Confidence thresholds (ct
90%
and ct
95%
)foranlos channel and
one to five resolved multipath components. For example, in case
of five resolved paths, the instantaneous power available to the re-
ceiver is higher than P
avg
−
4
.
9 dB for 90% of the time.
