mohatta2015.pdf

MORE PRACTICAL ASPECTS 183
timing). Symbol timing usually refers to figuring out where to sample each symbol,
without necessarily knowing which symbol is being sampled.
The notion of symbol timing is less clear when the channel is dispersive, as there
is no one sample that corresponds to one symbol. However, we can introduce the
broader notion of sample timing. For example, the receiver may initially filter and
sample the signal four times per symbol period We may wish to use a fractionally
spaced equalizer with two samples per symbol period. Thus, we need to decide
whether to keep the even or odd samples.
Interestingly, if we use a linear, multi-tap equalizer with enough Nyquist-spaced
taps, we don't have to worry as much about sample timing, as the equalizer will
effectively interpolate the received signal and re-sample at the desired location.
We just need to have the equalizer taps roughly centered about the ideal sampling
point. The Nyquist spacing usually implies more than one sample per symbol. This
is why fractionally spaced equalization has a reputation for being robust to timing.
In wireless channels, the channel typically consists of many, closely spaced paths
(a fraction of a symbol period apart). It is usually considered impractical to estimate
all the actual path delays and path coefficients. Instead, we try to find a
simpler, equivalent channel model with a minimal number of path delays. Ideally,
this would be a fractionally spaced channel model, where the tap spacing depends
on the bandwidth of the signal. Sometimes a symbol-spaced model is used as a
reasonable approximation.
8.4.3 Doppler
The Doppler effect occurs when there is motion. For example, if a cell phone
transmitter is moving towards a cell phone tower receiver, the transmitter signal
will appear compressed in time at the receiver. One result is that the carrier
frequency appears to have shifted to a higher value. Another result is that the
symbols arrive faster than expected, so that the symbol timing shifts earlier and
earlier in time.
Fortunately, for typical cellular communication systems, the dominant effect is
the shift in frequency. As a result, the Doppler effect can be approximated as a
frequency shift or Doppler shift. The change in timing is slow enough that it can
be handled by traditional timing algorithms.
When there is multipath propagation, then the Doppler effect is different for each
path, depending on where the scatterer is relative to the moving object. This gives
rise to a range of Doppler values, called the Doppler spread. If the path delays are
all about the same, relative to the symbol period, then we can think of the channel
as having one path coefficient that is Rayleigh fading. The Doppler spread tells
us how this path coefficient changes with time. This is important when designing
channel estimation algorithms that track the channel coefficient over time.
8.4.4 Channel Delay Estimation
As discussed earlier, we can model a multipath channel, which may have a continuum
of path delays, with a sparse set of equivalent paths. Acquisition and
timing operations usually tell us roughly where the paths should be. The PDP