<s>
In	O
digital	O
communications	O
,	O
a	O
turbo	B-Algorithm
equalizer	I-Algorithm
is	O
a	O
type	O
of	O
receiver	O
used	O
to	O
receive	O
a	O
message	O
corrupted	O
by	O
a	O
communication	O
channel	O
with	O
intersymbol	O
interference	O
(	O
ISI	O
)	O
.	O
</s>
<s>
It	O
approaches	O
the	O
performance	O
of	O
a	O
maximum	B-General_Concept
a	I-General_Concept
posteriori	I-General_Concept
(	O
MAP	O
)	O
receiver	O
via	O
iterative	O
message	B-Architecture
passing	I-Architecture
between	O
a	O
soft-in	B-Error_Name
soft-out	I-Error_Name
(	O
SISO	O
)	O
equalizer	B-Algorithm
and	O
a	O
SISO	O
decoder	O
.	O
</s>
<s>
It	O
is	O
related	O
to	O
turbo	B-Error_Name
codes	I-Error_Name
in	O
that	O
a	O
turbo	B-Algorithm
equalizer	I-Algorithm
may	O
be	O
considered	O
a	O
type	O
of	O
iterative	O
decoder	O
if	O
the	O
channel	O
is	O
viewed	O
as	O
a	O
non-redundant	O
convolutional	B-Error_Name
code	I-Error_Name
.	O
</s>
<s>
The	O
turbo	B-Algorithm
equalizer	I-Algorithm
is	O
different	O
from	O
classic	O
a	O
turbo-like	O
code	O
,	O
however	O
,	O
in	O
that	O
the	O
'	O
channel	O
code	O
 '	O
adds	O
no	O
redundancy	O
and	O
therefore	O
can	O
only	O
be	O
used	O
to	O
remove	O
non-gaussian	O
noise	O
.	O
</s>
<s>
Turbo	B-Error_Name
codes	I-Error_Name
were	O
invented	O
by	O
Claude	O
Berrou	O
in	O
1990	O
–	O
1991	O
.	O
</s>
<s>
In	O
1993	O
,	O
turbo	B-Error_Name
codes	I-Error_Name
were	O
introduced	O
publicly	O
via	O
a	O
paper	O
listing	O
authors	O
Berrou	O
,	O
Glavieux	O
,	O
and	O
Thitimajshima	O
.	O
</s>
<s>
In	O
1995	O
a	O
novel	O
extension	O
of	O
the	O
turbo	O
principle	O
was	O
applied	O
to	O
an	O
equalizer	B-Algorithm
by	O
Douillard	O
,	O
Jézéquel	O
,	O
and	O
Berrou	O
.	O
</s>
<s>
In	O
particular	O
,	O
they	O
formulated	O
the	O
ISI	O
receiver	O
problem	O
as	O
a	O
turbo	B-Error_Name
code	I-Error_Name
decoding	O
problem	O
,	O
where	O
the	O
channel	O
is	O
thought	O
of	O
as	O
a	O
rate	O
1	O
convolutional	B-Error_Name
code	I-Error_Name
and	O
the	O
error	O
correction	O
coding	O
is	O
the	O
second	O
code	O
.	O
</s>
<s>
In	O
1997	O
,	O
Glavieux	O
,	O
Laot	O
,	O
and	O
Labat	O
demonstrated	O
that	O
a	O
linear	O
equalizer	B-Algorithm
could	O
be	O
used	O
in	O
a	O
turbo	B-Algorithm
equalizer	I-Algorithm
framework	O
.	O
</s>
<s>
This	O
discovery	O
made	O
turbo	B-Algorithm
equalization	I-Algorithm
computationally	O
efficient	O
enough	O
to	O
be	O
applied	O
to	O
a	O
wide	O
range	O
of	O
applications	O
.	O
</s>
<s>
Before	O
discussing	O
turbo	B-Algorithm
equalizers	I-Algorithm
,	O
it	O
is	O
necessary	O
to	O
understand	O
the	O
basic	O
receiver	O
in	O
the	O
context	O
of	O
a	O
communication	O
system	O
.	O
</s>
<s>
Next	O
,	O
the	O
symbol	O
mapper	O
maps	O
the	O
bits	O
into	O
complex	B-Application
symbols	I-Application
.	O
</s>
<s>
Typically	O
the	O
signal	O
is	O
then	O
up-converted	B-Algorithm
to	O
pass	O
band	O
frequencies	O
by	O
mixing	O
it	O
with	O
a	O
carrier	O
signal	O
.	O
</s>
<s>
This	O
is	O
a	O
necessary	O
step	O
for	O
complex	B-Application
symbols	I-Application
.	O
</s>
<s>
The	O
down-converter	B-Algorithm
mixes	O
the	O
signal	O
back	O
down	O
to	O
baseband	B-Algorithm
.	O
</s>
<s>
The	O
signal	O
is	O
what	O
would	O
be	O
received	O
if	O
were	O
transmitted	O
through	O
the	O
digital	O
baseband	B-Algorithm
equivalent	O
of	O
the	O
channel	O
plus	O
noise	O
.	O
</s>
<s>
The	O
signal	O
is	O
then	O
equalized	B-Algorithm
.	O
</s>
<s>
The	O
equalizer	B-Algorithm
attempts	O
to	O
unravel	O
the	O
ISI	O
in	O
the	O
received	O
signal	O
to	O
recover	O
the	O
transmitted	O
symbols	O
.	O
</s>
<s>
If	O
the	O
equalizer	B-Algorithm
makes	O
soft	O
decisions	O
,	O
it	O
outputs	O
information	O
relating	O
to	O
the	O
probability	O
of	O
the	O
bit	O
being	O
a	O
0	O
or	O
a	O
1	O
.	O
</s>
<s>
If	O
the	O
equalizer	B-Algorithm
makes	O
hard	O
decisions	O
on	O
the	O
bits	O
,	O
it	O
quantizes	O
the	O
soft	O
bit	O
decisions	O
and	O
outputs	O
either	O
a	O
0	O
or	O
a	O
1	O
.	O
</s>
<s>
In	O
this	O
diagram	O
,	O
the	O
channel	O
is	O
the	O
equivalent	O
baseband	B-Algorithm
channel	I-Algorithm
,	O
meaning	O
that	O
it	O
encompasses	O
the	O
D/A	O
,	O
the	O
up	O
converter	O
,	O
the	O
channel	O
,	O
the	O
down	O
converter	O
,	O
and	O
the	O
A/D	O
.	O
</s>
<s>
The	O
block	O
diagram	O
of	O
a	O
communication	O
system	O
employing	O
a	O
turbo	B-Algorithm
equalizer	I-Algorithm
is	O
shown	O
below	O
.	O
</s>
<s>
The	O
turbo	B-Algorithm
equalizer	I-Algorithm
encompasses	O
the	O
equalizer	B-Algorithm
,	O
the	O
decoder	O
,	O
and	O
the	O
blocks	O
in	O
between	O
.	O
</s>
<s>
The	O
difference	O
between	O
a	O
turbo	B-Algorithm
equalizer	I-Algorithm
and	O
a	O
standard	O
equalizer	B-Algorithm
is	O
the	O
feedback	O
loop	O
from	O
the	O
decoder	O
to	O
the	O
equalizer	B-Algorithm
.	O
</s>
<s>
This	O
extrinsic	O
information	O
is	O
then	O
mapped	O
back	O
into	O
information	O
about	O
the	O
transmitted	O
symbols	O
for	O
use	O
in	O
the	O
equalizer	B-Algorithm
.	O
</s>
<s>
These	O
extrinsic	O
symbol	O
likelihoods	O
,	O
,	O
are	O
fed	O
into	O
the	O
equalizer	B-Algorithm
as	O
a	O
priori	O
symbol	O
probabilities	O
.	O
</s>
<s>
The	O
equalizer	B-Algorithm
uses	O
this	O
a	O
priori	O
information	O
as	O
well	O
as	O
the	O
input	O
signal	O
to	O
estimate	O
extrinsic	O
probability	O
information	O
about	O
the	O
transmitted	O
symbols	O
.	O
</s>
<s>
The	O
a	O
priori	O
information	O
fed	O
to	O
the	O
equalizer	B-Algorithm
is	O
initialized	O
to	O
0	O
,	O
meaning	O
that	O
the	O
initial	O
estimate	O
made	O
by	O
the	O
turbo	B-Algorithm
equalizer	I-Algorithm
is	O
identical	O
to	O
the	O
estimate	O
made	O
by	O
the	O
standard	O
receiver	O
.	O
</s>
<s>
The	O
turbo	B-Algorithm
equalizer	I-Algorithm
repeats	O
this	O
iterative	O
process	O
until	O
a	O
stopping	O
criterion	O
is	O
reached	O
.	O
</s>
<s>
In	O
practical	O
turbo	B-Algorithm
equalization	I-Algorithm
implementations	O
,	O
an	O
additional	O
issue	O
need	O
to	O
be	O
considered	O
.	O
</s>
<s>
The	O
channel	O
state	O
information	O
(	O
CSI	O
)	O
that	O
the	O
equalizer	B-Algorithm
operates	O
on	O
comes	O
from	O
some	O
channel	O
estimation	O
technique	O
,	O
and	O
hence	O
un-reliable	O
.	O
</s>
<s>
Firstly	O
,	O
in	O
order	O
to	O
improve	O
the	O
reliability	O
of	O
the	O
CSI	O
,	O
it	O
is	O
desirable	O
to	O
include	O
the	O
channel	O
estimation	O
block	O
also	O
into	O
the	O
turbo	B-Algorithm
equalization	I-Algorithm
loop	O
,	O
and	O
parse	O
soft	O
or	O
hard	O
decision	O
directed	O
channel	O
estimation	O
within	O
each	O
turbo	B-Algorithm
equalization	I-Algorithm
iteration	O
.	O
</s>
<s>
Secondly	O
,	O
incorporating	O
the	O
presence	O
of	O
CSI	O
uncertainty	O
into	O
the	O
turbo	B-Algorithm
equalizer	I-Algorithm
design	O
leads	O
to	O
a	O
more	O
robust	O
approach	O
with	O
significant	O
performance	O
gains	O
in	O
practical	O
scenarios	O
.	O
</s>
