In [J35], 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. The usefulness of the derived results for time-delay-of-arrival estimation, synchronization, cognitive radio in the Global Navigation Satellite System context, and for anti-jamming techniques are discussed.
The effects of the relative motion between a GPS satellite and a stationary receiver on the Earth are addressed in [BC4]. An analysis of the satellite motion is carried out to justify the assumption of constant relative radial speed within observation intervals adopted in the applications. It is shown that the transmitted cyclostationary signal is still cyclostationary at the receiver but with different cycle frequencies and cyclic features. Moreover, the transmitted and received signal are not jointly cyclostationary but, rather, jointly spectrally correlated. The implications of this statistical characterization on synchronization and parameter estimation problems are discussed.
In [C50], a new synchronization technique for the coarse acquisition code is proposed, which does not assume that the so called narrow-band condition is satisfied. Thus, the Doppler effect is modeled as a frequency shift on the carrier and a stretching of the complex envelope. As a consequence, observation intervals significantly longer than those adopted in conventional techniques can be adopted leading to a higher immunity against disturbance signals. The proposed technique exploits the cyclostationarity of the received signal and the fact that transmitted and received signals are jointly spectrally correlated. Simulation results show the better performance of the proposed method with respect to the conventional technique that models the Doppler effect just as a frequency shift of the carrier.