Since the channel is time-varying, the adaptive filter coefficients should also be time-varying in
order to track the temporal variations. This is accomplished by the decision-directed mode where
detected symbols are used to update the coefficients. The update is accomplished by creating an error
signal, e(k). Hence the coefficient update algorithm aims to minimize the error between the adaptive
filter and detector outputs.
294 CHAPTER SIX
Equalization
Linear
FIR Lattice
Nonlinear
DFE MLSE
FIR/CIR
Estimate FIR Lattice
FIGURE 6.1 Outline of equalization methods.
T/2
Detector
Decision
Directed Mode
T/2 r(k)
+
X
Coefficient
Adaptation Algorithm
X X
+
Training
Mode
??“
b0(k)
b0(k)
b2(k)
b2(k)
b1(k)
b1(k)
x(k) x???(k)
e(k) = x(k) ??“ x???(k)
FIGURE 6.2 Linear equalizer structure.
The received signal is mathematically represented below assuming the channel response has a
time duration of N samples.
(6.1)
Which can be written in vector form as
(6.2)
where k denotes the time index, _h is the channel vector of size N 1, and is the desired signal vector
of size N 1.
(6.3)
Next we can write the equalizer output assuming K taps are used. Here we collect K samples of
the input sequence
(6.
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