Study on the cross-correlation of GNSS signals and typical approximations

In global navigation satellite system (GNSS) receivers, the first signal processing stage is the acquisition, which consists of detecting the received GNSS signals and determining the associated code delay and Doppler frequency by means of correlations with a code and carrier replicas. These codes, as part of the GNSS signal, were chosen to have very good correlation properties without considering the effect of a potential received Doppler frequency. In the literature, it is often admitted that the maximum GPS L1 C/A code cross-correlation is about -24 dB. We show that this maximum can be as high as -19.2 dB when considering a Doppler frequency in a typical range of [-5, 5] kHz. We also show the positive impact of the coherent integration time on the cross-correlation and that even a satellite with Doppler outside the frequency search space of a receiver impacts the cross-correlation. In addition, the expression of the correlation is often provided in the continuous time domain, while its implementation is typically made in the discrete domain. It is then legitimate to ask the validity of this approximation. Therefore, the purpose of this research is twofold: First, we discuss typical approximations and evaluate their regions of validity, and second, we provide characteristic values such as maximums and quantiles of the auto- and cross-correlation of the GPS L1 C/A and Galileo E1 OS codes in the presence of Doppler, for frequency ranges up to 50 kHz and for different integration times.