Cryptography Reference
In-Depth Information
to the transmitted data, in order to simplify the computations (see Chapter 10
in [11.44], for example).
Figure 11.7 - Interference canceller.
If we assume now that we have a estimation x i + l on the transmitted data
both before ( l< 0 )andafter( l> 0 ) the symbol considered at instant i ,we
can then envisage removing the whole of the ISI at the output of the channel.
The equalization structure obtained is called an interference canceller , or IC [11-
6,11-7]. It is detailed in Figure 11.7. This structure is made up of two digital
transverse filters, with finite impulse response: a forward filter (matched to the
channel) whose aim is to maximize the signal to noise ratio before the decision,
and a canceller filter, in charge of rebuilding the ISI present at the output of the
matched filter. Note that by construction, the central coecient of the canceller
filter is necessarily null in order to avoid subtracting the useful signal. With the
reserve that the estimated data x i + l be equal to the transmitted data, we can
show that this equalizer eliminates all the ISI, without any increase in noise level.
We thus reach the matched-filter bound, which represents what we can best do
with an equalizer on a frequency selective channel. Of course, we never know a
priori the transmitted data in practice. The diculty then lies in building an
estimation of the data that is suciently reliable to keep performance close to
optimal.
None of the equalizer structures presented so far take into account the pres-
ence of a possible error correcting code on transmission. We shall now see how
we can best combine the equalization and decoding functions to improve the
global performance of the receiver.
11.1.3 Combining equalization and decoding
Most single-carrier digital transmission systems operating on frequency selective
channels incorporate an error correction coding function before the actual mod-
ulation step at transmission. The error correcting code is traditionally inserted
to combat the errors caused by the additive noise on the link. However, coupled
with a carefully built interleaving function, the encoder also offers an additional
degree of protection faced with power fading caused by the channel, when the
characteristics of the latter vary over time. We saw in the previous section that
independently of the nature of the equalizer used, the ISI systematically leads
to a loss in performance compared with a non-selective AWGN channel. The
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