Analysis and Optimization of Correlative Code-Tracking Loops in Spread-Spectrum Systems

The purpose of this paper is to apply the renewal theory approach for analyzing aperiodic finite
S
-curve code-tracking loops developed by Meyr [9] to the case of a noncoherent, arbitrary offset, early-late, delay-locked loop ("noncoherent δ-DLL"). The exact (renewal) approach is compared to the approximate (periodic-extension) approach of using the periodic
S
-curve or phase-locked loop theory, as well as to the linear theory developed herein for the aforementioned codetracking loop. Finally, loop optimization with respect to the offset δ is carried out according to certain performance criteria. The results indicate that, for low SNR, the exact and approximate theories could deviate significantly while, for high SNR, all three theories yield identical performance, as expected. Furthermore, it is shown that the optimal δ for both low and high SNR could differ from the commonly accepted choice
\delta = 1/2
.