Cryptography Reference
In-Depth Information
radio-mobile communication between several users based on the
Code Division
Multiple Access
technique.
11.1
Turbo equalization
Multipath channels have the particularity of transforming a transmitted signal
into a linear superposition of several different copies (or echoes) of this signal.
Turbo equalization is a digital reception technique that makes it possible to
detect data deteriorated by multipath transmission channels. It combines the
work of an equalizer and a channel decoder using the turbo principle. Schemat-
ically, this digital reception system involves a repetition of the equalization-
interleaving-decoding processing chain. First, the equalization performs an ini-
tial estimation of the transmitted data. Second, the estimation is transmitted
to the decoding module which updates this information. Then the information
updated by the decoder is sent to the equalization module. Thus, over the itera-
tions, the equalization and decoding processing operations exchange information
in order to reach the performance of a transmission on a channel with a single
path.
The purpose of this section is to present the turbo equalization principle
and its implementation in two versions: turbo equalization according to the
Maximum
A Posteriori
(MAP) criterion and turbo equalization according to
the Minimum Mean Square Error (MMSE) criterion. We will describe the algo-
rithms associated with these two techniques, as well as their respective complex-
ity. This will lead us to present the possible architectures and give examples of
implementation. Finally, potential and existing applications for these techniques
will be shown.
11.1.1 Multipath channels and intersymbol interference
This section is dedicated to transmissions on multipath channels whose partic-
ularity is to generate one or several echoes of the signal transmitted. Physically
these echoes can, for example, correspond to reflections off a building. The
echoes thus produced come and superpose themselves on the signal initially
transmitted and thus degrade the reception. The equivalent discrete channel
model allows a mathematically simple representation of these physical phenom-
ena in the form of a linear filtering of the transmitted discrete-time symbol
sequence. Let
x
i
be the symbol transmitted at discrete instant
i
,and
y
i
be the
received symbol at this same instant. The channel output is then given by
L
ā
1
y
i
=
h
k
(
i
)
x
iāk
+
w
i
(11.1)
k
=0
where
h
k
(
i
)
represents the action of the channel (echo) at instant
i
on a symbol
transmitted at instant
i
ā
k
. The impulse response of the channel at instant
i
