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

Here we apply the renewal theory approach for analyzing aperiodic finite S-curve code-tracking loops developed by Meyr (ref. 1) to the case of a noncoherent arbitrary offset early/late delay-locked loop ("noncoherent ?-DLL"). The exact (renewal) approach is compared with the approximate (periodic extension) approach of using the periodic S-curve or phase-locked loop (PLL) theory, as well as with the linear theory developed herein for the aforementioned code-tracking loop. Finally, loop optimization with respect to the offset ? is carried out. 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. It is also shown that the optimal ? for both low and high SNR differs from the commonly accepted choice ? = ?.