Code and Carrier Tracking for Spectrally Asymmetric Signals

Abstract

Standard GNSS signals like binary phase shift keying (BPSK) or binary offset carrier (BOC) signals exhibit a spectrum symmetric with respect to the nominal center frequency. The corresponding signal tracking theory is well established and describes the noise performance of code and carrier tracking in terms of 1-sigma values for delay, frequency and phase lock loops (DLL, FLL or PLL) tracking errors plus the corresponding Cramer-Rao lower bounds. Recently more generalized GNSS signals have been either proposed or constructed from existing signals. Their spectrum is not symmetric anymore, which impacts code and carrier tracking. Examples for those signals are the introduction of a possible third signal component to an existing open service signal with a frequency offset, the combined coherent tracking of two legacy GNSS signals (e.g. L5+L2C) known as metasignal concept [4], or the intentional offset of the nominal frequency of a legacy signal to sharpen the correlation peak known as variable IF tracking loop (VITAL) concept [2]. Within this paper we apply the standard tracking theory for spectrally asymmetric signals. Spectral asymmetry should result in a generally increased code tracking accuracy as the spectral energy is located near to one or the other edge of the signal bandwidth yielding sharper correlation peaks. This is nicely exploited in the VITAL scheme. An implementation of the VITAL concept within a MATLAB-based software receiver demonstrates that the increased code tracking accuracy transfers also to increased positioning results for real-world GPS C/A signals. The correlation depends on the spectral asymmetry and in a sense the VITAL concept can be seen as a gradual way to include carrier accuracy into the code tracking. A more detailed single channel analysis with two different software receiver shows, however, a discrepancy between expected accuracy gain and true accuracy gain. This could be due to a drawback of spectrally asymmetric signals, that is, code phase and carrier phase estimates become correlated and cycle slips or carrier tracking errors in general affect the code tracking loop. This is shown analytically and by processing simulated GNSS signals with software receivers.