Cryptography Reference
In-Depth Information
on an additive white Gaussian noise (AWGN) channel. This equalizer, shown
in Figure 11.5, is called a
linear equalizer
or LE.
Figure 11.5 - Linear equalizer.
We distinguish several optimization criteria to define the coecients of the
transverse filter. The optimal criterion involves minimizing the symbol error
probability at the output of the filter, but its application leads to a system of
equations dicult to solve. In practice, we prefer criteria sub-optimal in terms
of performance, but leading to solutions easily implementable, like the
Minimum
Mean Square Error
or MMSE criterion [11.44]. The linear MMSE equalizer is an
attractive solution due to its simplicity. However, this equalizer suffers from the
problem of amplification of the noise level on highly selective channels having
strong attenuations at certain points in the frequency spectrum.
Figure 11.6 - Decision-feedback equalizer.
Examining the diagram of the principle of the linear equalizer, we can note
that when we take a decision on symbol
x
i
at instant
i
,wehaveanestimation
on the previous symbols
x
i−
1
,
x
i−
2
, . . . We can therefore envisage rebuilding
the (causal) interference caused by these data and therefore cancel it, in order to
improve the decision. The equalizer which results from this reasoning is called a
Decision-Feedback Equalizer
or DFE. The diagram of the principle of the device
is illustrated in Figure 11.6. It is made up of a forward filter, in charge of
converting the impulse response of the channel into a purely causal response,
followed by a decision device and a feedback filter, in charge of estimating the
residual interference at the output of the feedback filter in order to cancel it via
a feedback loop.
As a general rule, the DFE provides performance higher than that of the lin-
ear equalizer, particularly on channels that are highly frequency selective. How-
ever, this equalizer is non-linear in nature, due to the presence of the decision
device in the feedback loop, which can give rise to an error propagation phe-
nomenon (particularly at low signal to noise ratio) when some of the estimated
data are incorrect. In practice, the filter coecients are generally optimized
following the MMSE criterion, by assuming that the estimated data are equal
