S.B. Boloshin, D.V. Gayvoronsky, V.P. Ipatov, I.M. Samoilov, B.V. Shebshaevich

Applications of the space-based navigation are currently ubiquitous. In addition to the GPS and GLONASS in operation deployment of a number of new systems like Galileo, Beidou/Compass or QZSS is a matter of few years. One of the most critical issues in satellite navigation system designing is an appropriate choice of the set of signals emitted by space vehicles, or, putting it another way, optimizing a system-s user interface. In the course of accomplishing it such a factor cannot be ignored as statistics of the relative Doppler shifts of different satellite signals, since the level of cross-correlations between the latter ones depends on their frequency mismatch. The paper first discusses theoretical approach to deriving probability density function (pdf) of both individual signal Doppler frequency and differential Doppler shift of two signals, the analysis basing on the assumption of uniform and independent distribution of space vehicles on the orbit sphere. With some reasonable approximation it is demonstrated that in such a scenario the relative Doppler frequency is rather close to triangular with the maximum at zero point. To analyze to what degree this theoretical result remains valid against deterministic pattern of space constellation a computer verification was undertaken applied to the realistic orbit parameters of GLONASS satellites for an arbitrary position of user on the Earth surface. The simulation has fully corroborated the analytical prediction as for the shape of the relative Doppler pdf. In the light of the conclusion arrived at it appears adequate to recommend for the future FDMA user interface (if this multiple access mode is decided to be saved) to set frequency space between different vehicle signals being multiple of the ranging code repetition frequency. Along with this the results obtained have an impact on designing CDMA user interfaces, too, justifying widely practiced preference of signal sets with low correlation level at zero frequency shift.