Abstract
Providing truly ubiquitous connectivity requires development of low Earth orbit (LEO) satellite Internet, whose theoretical study is lagging behind network-specific simulations. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of a massive inclined LEO constellation in terms of total interference power’s Laplace transform in the presence of fading and shadowing, ergo presenting a stochastic geometry-based analysis. We assume the desired link to experience Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading, which serves to represent different fading scenarios by varying integer <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , while the interfering channels can follow any fading model without an effect on analytical tractability. To take into account the inherent non-uniform distribution of satellites across different latitudes, we model the LEO network as a nonhomogeneous Poisson point process with its intensity being a function of satellites’ actual distribution in terms of constellation size, the altitude of the constellation, and the inclination of orbital planes. From the numerical results, we observe optimum points for both the constellation altitude and the number of orthogonal frequency channels; interestingly, the optimum user’s latitude is greater than the inclination angle due to the presence of fewer interfering satellites. Overall, the presented study facilitates general stochastic evaluation and planning of satellite Internet constellations without specific orbital simulations or tracking data on satellites’ exact positions in space.
Highlights
Recent advances towards 6th generation (6G) wireless networks require progression and development of non-terrestrial networks to provide seamless connections with high transmission capacity [1]–[4]
Downlink coverage probability and average data rate of inclined low Earth orbit (LEO) constellations are analyzed under general shadowing and fading propagation models
The satellites’ positions are assumed to be distributed as a nonhomogeneous Poisson point process (NPPP), which models the satellites distribution across varying latitudes precisely by setting the intensity function to be the actual density of satellites in an actual constellation
Summary
Recent advances towards 6th generation (6G) wireless networks require progression and development of non-terrestrial networks to provide seamless connections with high transmission capacity [1]–[4]. Among non-terrestrial networks, low Earth orbit (LEO) satellite Internet constellations have gained increasing popularity as they provide global connectivity for unserved or underserved regions, where the deployment of terrestrial networks is not feasible or economically reasonable [5], [6]. Conventional simulation-based studies are restricted to few number of satellites with deterministic locations which is not capable of evaluating the general performance of a massive satellite network consisting of thousands of satellites. In most of the literature, the coverage regions are assumed to have fixed circular footprints, while selecting smaller inclination angles and simultaneous consolidated operation of several LEO networks render a notso-regular Voronoi tessellation. Downlink coverage probability and average data rate of inclined LEO constellations are analyzed under general shadowing and fading propagation models. The satellites’ positions are assumed to be distributed as a nonhomogeneous Poisson point process (NPPP), which models the satellites distribution across varying latitudes precisely by setting the intensity function to be the actual density of satellites in an actual constellation
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