Cryptography Reference
In-Depth Information
adequate device, it can lead to great degradation in the error rate at reception,
and therefore in the general quality of the transmission.
(a)
(b)
Figure 11.2 - Illustration of the phenomenon of ISI in the case of a
5
-path highly
frequency-selective channel, for a signal to noise ratio of 20 dB.
We now study the characteristics of a multipath channel in the frequency do-
main. We show in Figure 11.3 the frequency response of the channel generating
the constellation presented in Figure 11.2. The latter is highly perturbed by ISI.
We note that the frequencies of the signal will not be attenuated and delayed in
the same way over the whole frequency band. Thus, a signal having a band
W
between 0 and 3 kHz will be distorted by the channel. We then speak of a fre-
quency selective channel in opposition to a flat non-frequency selective channel,
for which all the frequencies undergo the same distortion. To resume, when a
multipath channel generates intersymbol interference in the time domain, it is
then frequency selective in the frequency domain.
We mainly have three different techniques to combat the frequency selectiv-
ity of transmission channels: multi-carrier transmissions, spread spectrum and
equalization. In this chapter, we deal only with the third solution, applied here
to transmissions on a single carrier frequency ("single-carrier" transmissions).
Note, however, that some of the concepts tackled here can be transposed rela-
tively easily to systems of the multi-carrier type (
Orthogonal Frequency Division
Multiplex
, or OFDM systems).
11.1.2 The equalization function
In its most general form, the purpose of the equalization function is to give an
estimation of the transmitted sequence of symbols from the sequence observed
at the output of the channel, the latter being perturbed both by intersymbol
interference and additive noise, assumed to be Gaussian. We distinguish different
equalization strategies. Here we limit ourselves to a succinct overview of the
