Digital Signal Processing Reference
In-Depth Information
is, the faster the characteristics of the channel are going to change over time
and the more difficult it is for a wireless system to keep track of the channel
response. In fact, it becomes very difficult for the receiver to discern between
intentional phase changes caused by modulation of the signal-of-interest and
the modulation of a multipath component caused by the channel itself.
Definition - coherence time of a channel
The stability of a channel over time is characterized using the coher-
ence time T
c
, which is defined as the inverse of the maximum Doppler
spread frequency (4.5):
1
f
Doppler, max
T
c
=
[unit: s]
(4.5)
It is important not to confuse between the coherence time (T
c
) and
the coherence bandwidth (B
c
) of a channel. While the coherence time
points to the variation of a channel over time, the coherence bandwidth
expresses the variation of the channel over frequency and is related to
the rms delay spread of the channel.
Note: For a more extensive description of the coherence time, see
[Rap02].
From Equation (4.5), it follows that the coherence time T
c
is a statistical
measure describing the time frame over which the channel response can
be considered as invariant. Based on the ratio between the coherence time
and the symbol rate, the channel can be classified as a
slow fading
channel
(T
symbol
<
T
c
), or a
fast fading
channel (T
symbol
>
T
c
) (Figure 4.6).
Fast fading implies that the characteristics of the channel may change consider-
ably during one symbol period. Such fast changes are impossible to keep track
of in a receiver. In general, the increase of the symbol error rate due to fast fad-
ing can be modelled quite accurately by raising the noise floor of the received
signal. It follows that the best way to deal with errors introduced by fast fading
is to actually treat them as random noise and to pass the problem to the error
coding mechanism, which is optimized for this type of errors. Sometimes, the
issue of fast fading is mitigated by using a space-diversity scheme. In practice,
this means that the receiver is equipped with multiple receive antennas.
6
The
6
Note that each antenna in a multi-antenna receiver has its own analog front-end. The signals of each
antenna are only recombined later on in the receive chain, after downconversion or demodulation. Therefore,
a multi-antenna receiver is not the same as a receiver using a phased-array antenna, where the rf-outputs
of the antennas are combined with each other in analog way to produce a directive sensitivity pattern. This
does not exclude that both techniques are combined. It is perfectly possible to use a single phased array to
obtain several virtual antennas looking in different directions at the same time, and then feed the signal of
each virtual antenna into the different inputs of the multi-antenna receiver.
