We call this unidirectional since the adaptive
equalizer operation traverses the same direction throughout its operation.
a(k) b(k)
x(k) bT(k) # r(k) aT(k) # xr(k 1)
296 CHAPTER SIX
Detector
Decision
Directed Mode
+
Training
Mode
??“
x(k) x???(k)
+
T
x a0(k)
??“
T/2 T/2 r(k)
+
X
Coefficient
Adaptation Algorithm
X X
b0(k)
b0(k)
b2(k) a0(k)
b2(k)
b1(k)
b1(k)
e(k) = x(k) ??“ x???(k)
e(k) = x(k) ??“ x???(k)
FIGURE 6.3 Decision feedback equalizer structure.
Depending on the wireless system of interest this a priori information is continually transmitted
independent of the number of users in the system. It is important to make total use of the system in
order to capitalize on receiver performance. With this assumption the receiver can utilize the pilot
information in the adjacent time slots. And then train the equalizer in the reverse direction. This is
shown in Fig. 6.5 by the dashed lines. This form of equalization is called bidirectional since the
RECEIVER DIGITAL SIGNAL PROCESSING 297
Pilot Pilot Data Data
Time Slot Time Slot
Train Decision Directed Train Decision Directed
FIGURE 6.4 Unidirectional training.
FIGURE 6.5 Bidirectional training.
Pilot Pilot Data Data
Time Slot Time Slot
Train Decision Directed
Train
adaptive weights are being updated from both directions in time.
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