Digital Signal Processing Reference
In-Depth Information
TABLE 4.2
Wiener Solutions for Different
Equalization Delays
Delay (
d
)
Wiener Solution
MSE
T
<
0
[
0,0
]
1
T
0
[
0.391,
−
0.180
]
0.609
T
1
[
0.406, 0.120
]
0.271
T
2
[−
0.271, 0.586
]
0.120
T
>
3
[
0,0
]
1
finding a two-tap equalizer using the Wiener approach. Following the proce-
dure shown in Example 3.1, we reach the solutions, and their corresponding
MSEs, shown in Table 4.2.
We can observe that each delay produces a different solution with a
distinct residual MSE. In addition to that, it is important to point out that
the values of the third column reveal a significant discrepancy between the
performances of the three nontrivial solutions. The results show that it is
also necessary to select an optimal equalization delay. This feature is to be
considered in the subsequent analysis.
4.6.1 Analysis of the Decision-Directed Criterion
As discussed in
Section 4.3.1
,
the DD algorithm deals with the following
error signal to drive an LMS-based updating:
dec
y
)
−
e
(
n
)
=
(
n
y
(
n
)
(4.77)
From this general idea, some conclusions can be immediately reached:
•
Since the estimate presented in (4.77) does not depend on the equal-
ization delay, it is possible for the DD algorithm to reach generic
solutions as far as this parameter is concerned.
•
Under the condition
dec
y
)
=
(
n
s
(
n
−
d
)
(4.78)
there is an equivalence between DD and Wiener criteria.
•
It is harder to say something about the behavior of the DD algorithm
when the above condition does not hold.
As this initial discussion indicates, the analysis of the equilibrium solu-
tions of the DD algorithm will depend on the possibility of establishing
