Digital Signal Processing Reference
In-Depth Information
y
(
k
+
N
e
)
y
(
k
+
N
e
− 2)
y
(
k
−
N
e
)
z
−1
z
−1
z
−1
c
(-
N
e
)
c
(-
N
e
+ 1)
c
(-
N
e
+ 2)
×
×
×
×
c
(
N
e
)
(
k
)
+
+
+
FIgure 2.5
Structure of a baud-rate linear transversal equalizer.
equalizers designed on the basis of the baud-rate sampled received signal (see Figure 2.5
for a block diagram) are quite sensitive to symbol timing errors [15]. Therefore, fraction-
ally spaced linear equalizers (typically with twice the baud-rate sampling: oversampling
by a factor of two) are quite widely used to mitigate sensitivity to symbol timing errors.
A fractionally spaced equalizer (FSE) in the linear transversal structure has the output
N
N
e
∑∑
1
ˆ
()
sk
=
cnykn
() (
−
)
,
(2.46)
i
i
nN
=−
i
=
e
=
are the (2
N
e
+ 1) tap weight coefficients of the
i
t h
subequalizer. Note
that the FSE outputs data at the symbol rate. Similar to the SISO case, various crite-
ria and cost functions exist to design the linear equalizers in both batch and recursive
(adaptive) form.
Linear equalizers do not perform well when the underlying channels have deep spec-
tral nulls in the passband. Several nonlinear equalizers have been developed to deal with
such channels. Two effective approaches are:
nN
e
where {()}
cn
i
e
nN
=−
•
Decision feedback equalizer
(DFE) is a nonlinear equalizer that employs previ-
ously detected symbols to eliminate the ISI due to the previously detected sym-
bols on the current symbol to be detected. The use of the previously detected
symbols makes the equalizer output a nonlinear function of the data. DFE can
be symbol spaced or fractionally spaced.
Maximum likelihood sequence detector
•
estimates the information sequence to
maximize the joint probability of the received sequence conditioned on the
information sequence.
A detailed discussion may be found in [42].
Returning to the second-order statistical methods, for single-input multiple-output
vector channels the autocorrelation function of the observation is sufficient for the iden-
tification of the channel impulse response up to an unknown constant [51, 53], provided
that the various subchannels have no common zeros. This observation led to a number
of techniques under both statistical and deterministic assumptions of the input sequence
[50]. By exploiting the multichannel aspects of the channel, many of these techniques
lead to a constrained quadratic optimization:
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