Analysis of noncommensurate sampling effects on the performance of PN code tracking loops

Abstract

Noncoherent early-late processing (NELP) code tracking loops are often implemented using digital hardware for digital global positioning system (GPS) receivers. Noncommensurate sampling technology is widely used because it is viewed as an effective solution to cope with the drawback of digital effects. However, the relationship between the sampling rate and auto-correlation function (ACF) is not adequately characterized by traditional analysis. The principles for selecting the sampling rate are still not apparent. In order to solve this problem, we first analyzed the effects of different sampling rates on ACF and obtained the analytical form of a discrete auto-correlation function (DACF) for a noncommensurate sampling rate. Based on the result, the relationship between the step variation in DACF and NELP parameters such as sampling rate, integration time, and correlator spacing was determined. The maximum step variation size of DACF was also determined. However, considering the actual situation, additional factors such as code Doppler shift, precorrelation filter, and thermal noise may degrade the step variation of DACF. The relationship between the step variation and these factors was analyzed separately. An appropriate sampling rate and appropriate correlator spacing were proposed to achieve the typical accuracy of measurement. The numerical simulation verified the validity of the above theoretical analyses, and finally, the conclusions and design constraints for the digital GPS receiver are summarized.