Thermal Noise Performance of Early–Late Code Tracking With Finite Sampling Frequency

Early–late (E-L) code tracking accuracy in thermal noise is an important metric of receiver performance assessment and has been investigated extensively. However, most of the existing theoretical studies are based on the assumption of continuous signals, neglecting the effects of finite signal sampling frequencies. Taking a finite sampling frequency into account, this article extends the theory of E-L code tracking accuracy to a more generalized case. Theoretical expressions are derived for thermal noise performance of digital E-L code tracking loops for arbitrary signal spectra, incorporating a noncommensurate sampling frequency employed in commonly used digital receivers. Both the coherent and noncoherent processing structures are considered. Numerical results of binary phase shift keyed signals with rectangular chip shapes and binary offset carrier signals are presented, revealing some notable differences in code tracking errors between the finite sampling and continuous signal cases. Moreover, results of both the simulation and experimental test further verify the correctness of the proposed theoretical expressions. These results improve the theory of E-L code tracking accuracy and provide useful insights for the performance evaluation and parameter design of commonly used digital receivers.