inear tracking jitter performance of non-coherent DLL; two-pole Butterworth filter. pole Butterworth and ideal filters and Manchester coded data. In arriving at these results, we have made the substitution NoB1 S = No (2.33) 2.2 THE TAU-DITHER LOOP Consider the non-coherent tau-dither loop (TDL) illustrated in Figure 2.9 whose operation is described as follows. The received signal plus noise is alternately (as opposed to simultaneously) correlated with the advanced and retarded versions of the locally generated PN code (thus the name "dither" loop) to produce an error signal, which, when band-pass filtered, envelope Pseudonoise Code Tracking in Direct-Sequence Receivers E E min -10.0-9.0 Es/No.dB Figure 2.8. Linear tracking jitter performance of non-coherent DLL; ideal filter. detected, and alternately inverted by the binary signal q(t), drives the volt- age controlled clock (VCC) through the loop filter F(s). One obvious advan- tage of the TDL over the DLL is the fact that only a single input correlator is required, thus eliminating the problems of gain imbalance and other mis- matches that are present in a two-channel loop such as the DLL. 2.2.1 Mathematical Loop Model and Equation of Operation In deriving the loop model and discussing its performance, we shall draw heavily on the notation and results already presented for the DLL. For the purpose of analysis, one can show [6] that when the dither frequency fa is low relative to the noise bandwidth BH of the band-pass filter (the usual case of interest), the TDL has the equivalent loop model illustrated in Figure 2.10. Starting then when y+(t) and y_(t) as defined in (2.5), the input to the loop n;(1) SQUARE-LAW ENVELOPE DETECTOR PHASE VOLTAGE- PN CODE SHIFTER CONTROLLED FILTER GENERATOR (TC IN) CLOCK to = = DITHER FREQUENCY Figure 2.9. A non-coherent tau-dither loop. q2(i) E (f) Y (f) SQUARE-LAW y2 2 (1) ENVELOPE n;(f) DETECTOR E ( ) ) E (1) y (f) SQUARE-LAW y 2 (1) ENVELOPE DETECTOR PN CODE VOLTAGE- GENERATOR CONTROLLED FILTER CLOCK 9,(+) 92(t) Figure 2.10. A