Digital Signal Processing Reference
In-Depth Information
ν(
n
)
s
(
n
)
˜
x
(
n
)
y
(
n
)
s
(
n
)
ˆ
x
(
n
)
h
Σ
w
Dec (·)
FIGURE 4.1
Unsupervised equalization scheme.
•
The transmitted signal
s
(
n
)
belongs to a finite symbol alphabet
A
.
•
The transmitted signal is composed of a sequence of independent
and identically distributed (i.i.d.) random variables.
The first assumption comes directly from the nature of the application,
since we necessarily employ some kind of digital modulation scheme. In
practice,
y
(
n
)
does not belong to
A
, which explains the need for a nonlinear
ˆ
device to map
y
.
In a way, the aim of the equalizer is to provide a signal
y
(
n
)
to
s
∈
A
(
n
)
whose values
are close to the symbol levels associated with
A
. The more the equalizer com-
pensates the channel distortions, the more
y
is concentrated around the
symbol levels. A classical and ingenious technique to evaluate this perfor-
mance in digital communication is the
eye pattern
[28,245]. Figure 4.2 shows,
for a binary transmission scheme, the eye pattern before and after an opti-
mized equalizer. The name “eye pattern” comes from the peculiar shape of
the diagram, and the two illustrated conditions are referred to as
closed-eye
and
open-eye
conditions, respectively. In supervised equalization, as men-
tioned in Section 3.1.2, the role of the training period is to allow an open-eye
condition to be reached in order that the system may safely work in the infor-
mation transmission mode. In this mode, the equalizer is optimized using
an unsupervised technique, the aim of which is to preserve the open-eye
condition. In the absence of a training procedure, the unsupervised equalizer
must be optimized from an initial closed-eye condition.
(
n
)
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
0
0.2 0.4 0.6 0.8 1
Time (ms)
1.2 1.4 1.6 1.8
2
0
0.2 0.4 0.6 0.8 1
Time (ms)
1.2 1.4 1.6 1.8
2
(a)
(b)
FIGURE 4.2
Eye pattern before and after an optimized equalizer: (a) closed-eye condition and (b) open-eye
condition.
