The purpose is to introduce the estimator categories to the system designer.
6.4.1 Data Aided
This first form of timing error estimation is termed data aided since the output of the decision device
is used to determine the timing adjustment. The basic premise of operation is that the samples entering
the decision device are compared to the samples output by the decision device and the timing
instance is varied in order to minimize this difference. This assumes a timing instance was chosen
prior to performing these operations. A simplified block diagram of a data-aided technique is provided
in Fig. 6.26.
The symbol timing estimator is mathematically represented as
(6.97) e(k) Re5r(k 1) # a*(k) r(k) # a*(k 1)6
320 CHAPTER SIX
??“2
??“1.5
??“1
??“0.5
0
0.5
1
1.5
2
0 8 12 16
Normalized Symbol Time (Ts/8)
Eye Value
Optimal Sampling Point
Possible Sampling Points
4
??“1.5
??“1
??“0.5
0
0.5
1
1.5
0 8 12 16
Normalized Symbol Time (Ts/8)
Eye Value
Optimal Sampling Point
Possible Sampling Points
4
FIGURE 6.24 QPSK eye diagram with roll-off factor 0.22.
FIGURE 6.25 QPSK eye diagram with roll-off factor 0.9.
Continuing with the assumption that the data symbols are complex valued we have
(6.
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