Doppler Effect in Non-gso Satellite Propagation

Recent technological advances have accelerated a renaissance in usage of non-geostationary (non-GSO) communication satellites in provision of various services domestically and globally. Early ventures into communication satellites have used satellites in low Earth orbits. The main reasons for this mode of operation were that the booster technology was not available to lift satellites into a higher orbit, the satellite technology was not sufficiently mature to achieve higher performance such as power generation and signal bandwidth. Also, there was a problem with reliability due to operation in hostile space environment. After that early stage, more than 30 years the most dominant domain of communication using satellites has been in circular geostationary equatorial Earth synchronous orbit. As the satellite system technology developed, it became possible to provide services by the use of satellites in various orbital regimes like low Earth orbit (LEO at about 1000 km altitude), medium Earth orbit (MEO at about 10000 km altitude), geostationary orbit (GSO) and the highly elliptical orbit satellites (HEO). One of the problems ground transceivers are facing when communicating with non-GSO satellites is significant Doppler frequency shift. This time varying phenomenon is caused by the line of sight (LOS) component of the relative velocity vector evolving from the rapid movement of the satellite in its orbit relative to the ground transceiver including satellite velocity and the relative velocity due to the Earth’s rotation. This paper deals with analytic derivation of the Doppler frequency shift observed by a user on the surface of the Earth as a function of time. Previous researches in this area mainly focused on efficient methods for compensation of this effect. Expression for obtaining radial velocity of the satellite using measurement of Doppler frequency shift is derived in [1]. In [2] the authors study Doppler frequency shift at the point of the Earth equator from the non-GSO satellite using circular equatorial orbit. The LEO satellites Doppler estimation algorithm for implementation in the terminal phase-lock loop, compensating frequency shift have been studied in [3]. This paper gives mathematical derivation of the trajectory coordinates of non-GSO satellites using inclined circular orbits. Based on this, LOS relative velocity component is deduced giving explicit equations for the frequency shift observed by a transceiver situated anywhere on the Earth. Furthermore S-shaped Doppler frequency shift – time curves are derived (with maximum elevation angle as parameter). Possible applications of Doppler frequency shift for satellite navigation and positioning system, compensation of time varying frequency shift in terminal PLL processor and aircraft monitoring, positioning, search and rescue are proposed and analysed.