Digital Signal Processing Reference
In-Depth Information
4
3
2
1
0
-1
σ
η
=0.05
σ
η
=0.2
σ
η
=1
-2
-3
-4
-5
-4
-3
-2
-1
0
1
2
3
4
5
y
(
n
)
FIGURE 4.3
Bussgang estimators for a 4-PAM modulation and different convolutional noise variances.
4.3.1 The Decision-Directed Algorithm
The DD algorithm can be considered as the simplest of Bussgang techniques,
since it employs the decision-device output as an estimate of the desired
response, i.e.,
dec
y
)
ψ
DD
[
y
(
n
)
]=
(
n
(4.19)
leading to an adaptation rule given by
μ
dec
y
)
−
)
x
w
(
n
+
1
)
=
w
(
n
)
+
(
n
y
(
n
(
n
)
(4.20)
In this case, the corresponding cost function being minimized by the
iterative method in (4.20) is
E
y
)
2
dec
y
J
DD
(
w
)
=
(
n
)
−
(
n
(4.21)
Intuitively, the technique is founded on the assumption that the output
of the decision-device should be a useful estimate of the signal we wish to
recover. This situation is reasonable if we begin the adaptation of the equal-
izer from a good initial condition, i.e., a condition capable of leading to a
satisfactory open-eye condition. A classical possibility to make this possible
is to employ the DD algorithm together with a supervised method. In this
case, the supervised method is responsible for using an available training
sequence to reduce as much as possible the level of intersymbol interfer-
ence (ISI) present in the received signal, which, ideally, would give rise
