Cyclic spectral analysis of the GPS signal

A detailed analytical model is derived for the GPS-L1 signal which is shown to be second-order cyclostationary. Closed forms for the periodically time-variant autocorrelation function and for the cyclic autocorrelation functions and cyclic spectra are derived for the complex envelope of this signal. Conjugate statistics are also derived. It is shown that different signal models must be considered for different data-record lengths of interest in the applications, including indoor ones. Numerical results are reported to corroborate the theoretical results. As example of application, a cyclostationarity-based parameter estimation method is proposed to operate with long observation intervals when the so-called narrow-band condition is not satisfied. The usefulness of the derived results for time-difference-of-arrival estimation, synchronization, cognitive radio in the Global Navigation Satellite System context, and for anti-jamming techniques is discussed.