Characterization of Doppler shift in inter-satellite laser link between LEO, MEO, and GEO orbits

Over the past few decades, the development of optical wireless communications (OWC) has led to its application in a wide range of environments, including indoor, outdoor, and space. Optical carriers offer advantages such as high bandwidth, security, and directivity, making it a suitable technology for applications in radio astronomy, remote sensing, cellular networks, high-speed train communications, last-mile access, underwater/terrestrial communications, and satellite communications employing laser links. However, laser links between satellites experience Doppler shift due to their relative motion, and this effect should be taken into account from a system design perspective. This paper presents a study of the Doppler shift characterization in laser links for circular Keplerian orbits. An analytical derivation establishes the relationship between the Keplerian orbital elements and the Doppler shift in laser links. The derived equations provide a more comprehensive understanding of the impact of these orbital elements on the Doppler shift in laser links. Additionally, equations have been derived for the Doppler shift rate and the visibility window condition during satellite communication. Furthermore, we conducted a link failure analysis using simulations to evaluate the effects of the Doppler shift, also identifying the worst-case scenarios for orbits most significantly impacted by this shift. The results showed that among the six Keplerian orbital elements, the semi-major axis, inclination, and right ascension of ascending node contribute to the Doppler shift in circular orbits. While the Doppler shift impact is less significant for laser communication systems employing intensity modulation/direct detection, it can degrade the communication system performance for coherent detection. This work contributes to the effective estimation of Doppler shift from a system design perspective.