Digital Signal Processing Reference
In-Depth Information
Of course, the channel must offer a sufficient amount of resolvable multipath
components. In the heavy multipath indoor channel, increasing the multipath
resolvability simply comes down to the point that the symbol duration must be
chosen sufficiently shorter than the rms delay spread of the channel. If the cor-
relation between the resolved paths is sufficiently low, the individual symbol
streams can be assumed to have independent fading characteristics [Cha79].
While the total signal power integrated over all resolved components still has a
statistical time-varying fading profile, the reliability under static channel con-
ditions is improved. This statement can be proven as follows.
Figure 4.7 shows the simulated pdf of the received signal power in case of a
single resolved Rayleigh fading nlos path. First, note that the signal envelope
of a Rayleigh distributed nlos channel has a large peak at lower values and
a long tail for higher signal magnitudes. Relative to the average power that is
available from the channel, this means that the link suffers from destructive in-
terference during considerable periods of time. However, how does this finding
fit with the previous conclusion that no power (and as a consequence also no
Shannon capacity) is lost when the channel is evaluated over a longer period
of time? The answer here is given by the long tail of the Rayleigh distribution:
from time to time, it happens that a considerable number of multipath compo-
nents interferes in a constructive manner. At such occasions, a very high signal-
to-noise ratio will temporarily boost the information capacity of the channel.
At least theoretically though. In any real-world receiver implementation, the
Probability density function
1 resolved NLOS path
mean rx power: P
avg
std deviation: 1.39 P
avg
0.04
3 resolved paths
mean power: P
avg
std deviation: 0.81 P
avg
0.03
0.02
5 resolved paths
mean power: P
avg
std deviation: 0.63 P
avg
0.01
0
0
0.5
1
1.5
instantaneous received power
normalized to P
avg
Figure 4.7.
Simulated probability density for the instantaneous received power
with respect to the average received power (P
avg
) in a Rayleigh-
fading nlos channel. A higher number of resolved multipath com-
ponents results in a reduced standard deviation.
