Digital Signal Processing Reference
In-Depth Information
is that whenever the decision device performs a correct estimate, no noise
parcel is fed back, which decisively contributes to mitigate any enhancement
effect.
Several learning strategies can be applied to adapt the parameters of
a DFE. It is possible to implement both supervised algorithms, as those
presented in Chapter 3 [30], and unsupervised techniques, like Bussgang
algorithms [234].
In the supervised context, it is possible to perform parameter adaptation
by employing a standard LMS algorithm for both filters:
w
f
(
n
+
1
)
=
w
f
(
n
)
+
μ
e
(
n
)
x
(
n
)
(7.2)
w
b
(
n
+
1
)
=
w
b
(
n
)
+
μ
e
(
n
)
ˆ
y
(
n
−
1
)
(7.3)
e
being a standard error signal. Notice that the algorithm
treats the past decisions as conventional input signals, without highlighting
any dependence with respect to the equalizer weights, which evokes ideas
underlying equation-error methodologies in IIR filtering [249,274].
An analogous approach can be followed to apply an unsupervised algo-
rithm. The expressions, for instance, for the constant modulus algorithm
(CMA) are similar to those presented in Section 4.3 [121]:
(
n
)
=
d
(
n
)
−
y
(
n
)
2
w
f
(
n
+
1
)
=
w
f
(
n
)
+
μ
y
(
n
)
[
R
2
−|
y
(
n
)
|
]
x
(
n
)
(7.4)
2
w
b
(
n
+
1
)
=
w
b
(
n
)
+
μ
y
(
n
)
[
R
2
−|
y
(
n
)
|
]ˆ
y
(
n
−
1
)
(7.5)
Finally, it is important to remark that the performance of these algo-
rithms, as well as of the structure itself, is strongly related to the error prop-
agation phenomenon. As the name indicates, error propagation takes place
when wrong symbol estimates are generated by the decision device, which
means that the process of interference intersymbol removal via feedback
loop that characterizes the DFE is compromised [121].
7.1.1 Predictive DFE Approach
As discussed in Chapter 3, the prediction-error filter (PEF) is able to provide
equalization if the channel is minimum-phase. For general phase responses,
the PEF only equalize the magnitude response of the channel, and an
additional processing is required to compensate the phase distortions.
In order to extend the use of the predictive approach to nonminimum-
phase channels, Rocha et al. proposed in the structure presented in
In this figure, a forward PEF, which is always minimum-phase as already
discussed in Section 3.7, is used as a magnitude equalizer. The proposal
