Digital Signal Processing Reference
In-Depth Information
4.4
Multipath resolvability and link reliability
Whether the issue of multipath is approached from the side of the frequency
domain or from a time-domain point of view, the outcome will always be the
same: if several signal components arrive within a single sample period,
8
the
receiver will not be able to discern between these individual multipath compo-
nents. In more general terms: the multipath resolvability - which is the number
of different paths
n
that a generalized, ideal receiver can distinguish - is de-
fined by the number of symbol periods over which a multipath channel spreads
the energy of a single transmitted symbol (4.6):
round
τ
rms
T
s
n
=
+
1
(4.6)
It is very important to realize that the superposition of signal components that
arrive within the time frame of a single symbol still causes constructive or
destructive interference. In the frequency domain, this finding manifests itself
as a flat fading component that is superimposed on the frequency-selective
nature of the channel (which is caused by isi). Averaged over a sufficiently
long period of time,
9
no additional power is lost due to the effects of this flat
fading component. However, under static channel conditions, this will cause
unacceptable long outages of the link, something that cannot be solved by the
time-diversity of error coding.
A generalized rake receiver architecture increases the reliability under static
channel conditions by combining the energy of the resolved multipath compo-
nents.
10
Seen over a longer period of time, the individual paths that can be re-
solved by the receiver experience - independently from each other - Rayleigh
or Rician frequency flat fading.
11
While the reliability of a single resolved path
is not better than what is achieved in a non frequency-selective flat fading chan-
nel, combining the energy of several of such independently fading multipaths
increases the reliability of a communication link. It follows that intersymbol
interference is a necessary evil for a reliable wireless link in the multipath
environment.
8
If
τ
rms
<
10
·
T
s
, then we have a flat fading channel.
9
This depends on the coherence time T
c
of the channel.
10
There are several ways to combine the energy of multiple symbol streams. The most common technique
is
selection diversity combining
(sdc). A good example of sdc is switching between two antennas and
selecting only the antenna which offers the best signal quality. More advanced techniques combine the
energy of multiple resolved streams before the demodulator takes a decision about the value of the received
symbol. These techniques are known as
maximum ratio combining
(mrc)or
equal gain combining
(egc).
The latter one is in fact a simplified version of mrc, but ignores the signal-to-noise ratio of the different
multipath components. More information on this topic can be found in [Fuj01].
11
Rician fading is the model for line-of-sight (los) fading, while Rayleigh fading if the stochastic model
for non-los fading [Pro00].
