TAILIEUCHUNG - Digital communication receivers P2 - P2

Baseband Communications Y(b) Timing Error Detector 4 r(t; 8 ) - x(t) ) ,+) u(t) vco 4 Figure 2-18 Error-Tracking SynchronizerStructure The timing error detector performs a suitable time-invariant nonlinear operation on the input signal and the local reference,so that its output signal z(t) gives an indication of the instantaneous timing error e = & - g. The timing error detector output signal enters a linear time-invariant loop filter. Its frequency responsein the Laplace domain is denotedby F(s) ; the frequencyresponsein the frequency domain is F(w). The loop filter output signal u(t) determinesthe instantaneous frequency of the VCO accordingto (2-31) such that the timing error e is reduced | 90 Baseband Communications Figure 2-18 Error-Tracking Synchronizer Sttucture The timing error detector performs a suitable time-invariant nonlinear operation on the input signal and the local reference so that its output signal x i gives an indication of the instantaneous timing eưor e . The timing error detector output signal enters a linear time-invariant loop filter. Its frequency response in the Laplace domain is denoted by F s - the frequency response in the frequency domain is F ư . The loop filter output signal u t determines the instantaneous frequency of the vco according to 2-31 such that the timing error e is reduced. As the input signal y t s has zero mean it does not contain a deterministic periodic component so that a conventional PLL cannot be used to estimate e. However there is still some periodicity embedded in the input signal because of its cyclostationarity with period T. This cyclostationarity is exploited by the synchronizer in order to make an estimate of . There exists a large variety of timing error detector circuits some examples are considered in Section . In spite of the many different types of timing eưor detector circuits encountered in practice it will be shown that all eưor-tracking synchronizers can be represented by the same equivalent model shown in Figure 2-19 so that they can be analyzed in a unified way. Comparing the equivalent model with the synchronizer structure shown in Figure 2-18 we see that the equivalent model replaces the timing error detector output signal by the sum KDg e N t where g e and N t are called the timing error detector characteristic and the loop noise respectively. The useful component Ki g e of the timing error detector output signal is periodic in e with period 1 also it will be shown in Section that 0 0 0 and the timing error detector gain Kd is usually chosen such that g G the timing error detector slope at the origin is normalized to 1. The loop noise N t represents the statistical .

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