Stochastic Analysis of Satellite Broadband by Mega-Constellations with Inclined LEOs

As emerging massive constellations are intended to provide seamless connectivity for remote areas using hundreds of small low Earth orbit (LEO) satellites, new methodologies have great importance to study the performance of these networks. In this paper, we derive both downlink and uplink analytical expressions for coverage probability and data rate of an inclined LEO constellation under general fading, regardless of exact satellites' positions. Our solution involves two phases as we, first, abstract the network into a uniformly distributed network. Secondly, we obtain a new parameter, effective number of satellites, for every user's latitude which compensates for the performance mismatch between the actual and uniform constellations. In addition to exact derivation of the network performance metrics, this study provides insight into selecting the constellation parameters, e.g., the total number of satellites, altitude, and inclination angle.Comment: Accepted in the 31st International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 202

Modeling and Analysis of Massive Low Earth Orbit Communication Networks

Non-terrestrial networks are foreseen as a crucial component for developing 6th generation (6G) of wireless cellular networks by many telecommunication industries. Among non-terrestrial networks, low Earth orbit (LEO) communication satellites have shown a great potential in providing global seamless coverage for remote and under-served regions where conventional terrestrial networks are either not available or not economically justifiable to deploy. In addition, to the date of writing this summary, LEO communication networks have became highly commercialized with many prominent examples, compared to other non-terrestrial networks, e.g., high altitude platforms (HAPs) which are still in prototyping stage. Despite the rapid promotion of LEO constellations, theoretical methodologies to study the performance of such massive networks at large are still missing from the scientific literature. While commercial plans must obviously have been simulated before deployment of these constellations, the deterministic and network-specific simulations rely on instantaneous positions of satellites and, consequently, are unable to characterize the performance of massive satellite networks in a generic scientific form, given the constellation parameters. In order to address this problem, in this thesis, a generic tractable approach is proposed to analyze the LEO communication networks using stochastic geometry as a central tool. Firstly, satellites are modeled as a point process which enables using the mathematics of stochastic geometry to formulate two performance metrics of the network, namely, coverage probability and data rate, in terms of constellation parameters. The derivations are applicable to any given LEO constellation regardless of satellites’ actual locations on orbits. Due to specific geometry of satellites, there is an inherent mismatch between the actual distribution of satellites and the point processes that are used to model their locality. Secondly, different approaches have thus been investigated to eliminate this modeling error and improve the accuracy of the analytical derivations. The results of this research are published in seven original publications which are attached to this summary. In these publications, coverage probability and average achievable data rate of LEO satellite networks are derived for several communication scenarios in both uplink and downlink directions under different propagation models and user association techniques. Moreover, the analysis was generalized to cover the performance analysis of a multi-altitude constellation which imitates the geometry of some well-known commercial constellations with satellites orbiting on multiple altitude levels. While direct communication between the satellites and ground terminals is the main studied communication scenario in this thesis, the performance of a LEO network as a backhaul for aerial platforms is also addressed and compared with terrestrial backhaul networks. Finally, all analytical derivations, obtained from stochastic modeling of the LEO constellations, are verified through Monte Carlo simulations and compared with actual simulated constellations to ensure their accuracy. Through the numerical results, the performance metrics are evaluated in terms of different constellation parameters, e.g., altitude, inclination angle, and total number of satellites, which reveals their optimal values that maximize the capacity and/or coverage probability. Therefore, other than performance analysis, several insightful guidelines can be also extracted regarding the design of LEO satellite networks based on the numerical results. Stochastic modeling of a LEO satellite network, which is proposed for the first time ever in this thesis, extends the application of stochastic geometry in wireless communication field from planar two-dimensional (2D) networks to highly heterogeneous three-dimensional (3D) spherical networks. In fact, the results show that stochastic modeling can also be utilized to precisely model the networks with deterministic nodes’ locations and specific distribution of nodes over the Euclidean space. Thus, the proposed methodology reported herein paves the way for comprehensive analytical understanding and generic performance study of heterogeneous massive networks in the future

Downlink Coverage and Rate Analysis of Low Earth Orbit Satellite Constellations Using Stochastic Geometry

As low Earth orbit (LEO) satellite communication systems are gaining increasing popularity, new theoretical methodologies are required to investigate such networks' performance at large. This is because deterministic and location-based models that have previously been applied to analyze satellite systems are typically restricted to support simulations only. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of generic LEO networks, regardless of the actual satellites' locality and their service area geometry. Our solution stems from stochastic geometry, which abstracts the generic networks into uniform binomial point processes. Applying the proposed model, we then study the performance of the networks as a function of key constellation design parameters. Finally, to fit the theoretical modeling more precisely to real deterministic constellations, we introduce the effective number of satellites as a parameter to compensate for the practical uneven distribution of satellites on different latitudes. In addition to deriving exact network performance metrics, the study reveals several guidelines for selecting the design parameters for future massive LEO constellations, e.g., the number of frequency channels and altitude.Comment: Accepted for publication in the IEEE Transactions on Communications in April 202

Downlink and Uplink Low Earth Orbit Satellite Backhaul for Airborne Networks

Providing backhaul access for airborne networks ensures their seamless connectivity to other aerial or terrestrial users with sufficient data rate. The backhaul for aerial platforms (APs) has been mostly provided through geostationary Earth orbit satellites and the terrestrial base stations (BSs). However, the former limits the achievable throughput due to significant path loss and latency, and the latter is unable to provide full sky coverage due to existence of wide under-served regions on Earth. Therefore, the emerging low Earth orbit (LEO) Internet constellations have the potential to address this problem by providing a thorough coverage for APs with higher data rate and lower latency. In this paper, we analyze the coverage probability and data rate of a LEO backhaul network for an AP located at an arbitrary altitude above the ground. The satellites' locality is modeled as a nonhomogeneous Poisson point process which not only enables tractable analysis by utilizing the tools from stochastic geometry, but also considers the latitude-dependent density of satellites. To demonstrate a compromise on the backhaul network's selection for the airborne network, we also compare the aforementioned setup with a reference terrestrial backhaul network, where AP directly connects to the ground BSs. Based on the numerical results, we can conclude that, for low BS densities, LEO satellites provide a better backhaul connection, which improves by increasing the AP's altitude.acceptedVersionPeer reviewe

Coverage and Rate Analysis of Mega-Constellations Under Generalized Serving Satellite Selection

The dream of having ubiquitous and high-capacity connectivity is coming true by emerging low Earth orbit (LEO) Internet constellations through several commercial plans, e.g., Starlink, Telesat, and Oneweb. The analytical understanding of these networks is crucial for accurate network assessment and, consequently, acceleration in their design and development. In this paper, we derive the coverage probability and the data rate of a massive LEO network under arbitrarily distributed fading and shadowing. The conventional user association techniques, based on the shortest distance between the ground terminal and the satellite, result in a suboptimal performance of the network since the signal from the nearest server may be subject to severe shadowing due the blockage by nearby obstacles surrounding the ground terminal. Thus, we take into account the effect of shadowing on the serving satellite selection by assigning the ground terminal to the satellite which provides the highest signal-to-noise ratio at the terminal's place, resulting in a more generalized association technique, namely the best server policy (BSP). To maintain tractability of our derivations and consider the latitude-dependent distribution of satellites, we model the satellites as a nonhomogeneous Poisson point process. The numerical results reveal that implementing the BSP for serving satellite selection leads to significantly better performance compared to the conventional nearest server policy (NSP).acceptedVersionPeer reviewe

Stochastic Analysis of Satellite Broadband by Mega-Constellations with Inclined LEOs

acceptedVersionPeer reviewe

Nonhomogeneous Stochastic Geometry Analysis of Massive LEO Communication Constellations

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-m fading, which serves to represent different fading scenarios by varying integer m, 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.publishedVersionPeer reviewe

Modeling and Analysis of LEO Mega-Constellations as Nonhomogeneous Poisson Point Processes

Requirements and technological advancements towards 6th generation (6G) wireless networks lead to enabling and development of massive low Earth orbit (LEO) satellite constellations to provide ubiquitous and high-capacity connectivity, particularly for maritime and airborne platforms. Consequently, new methodologies to study the performance of LEO networks are of great importance. In this paper, we derive both downlink and uplink analytical expressions for coverage probability and data rate of a massive inclined LEO constellation under general shadowing and fading. We model the LEO satellite network as a nonhomogeneous Poisson point process with general intensity in order to take into account uneven distribution of satellites along the latitudes. The results provided in this study facilitate the stochastic evaluation and design of the future massive LEO networks, regardless of satellites' exact trajectories in orbits.acceptedVersionPeer reviewe

Numerical Approximations for the Gaussian Q-Function by Sums of Exponentials

The accurate prediction of wireless systems’ performance is a key factor in the timely adoption of new technologies and systems’ design. In many cases, when evaluating the performance measures of a communication system with additive white Gaussian noise, integrals involving the Gaussian Q-function appear and closed-form solutions cannot be expressed in terms of elementary functions. This has motivated researchers to propose approximations and bounds for the Gaussian Q-function to facilitate expression manipulations. This paper gives a brief overview about the existing approximations of the Q-function. In addition, it summarizes and compares the different quadrature numerical integration techniques that can be applied in approximating the Gaussian Q-function in a tractable form as a weighted sum of exponentials.publishedVersio

On routing protocols in inter-satellite communications

Low earth orbit (LEO) satellite networks offer broadcasting to remote places or places at the time of natural or human-caused calamities. LEO satellites are preferable in a real-time communication compared to e.g. geostationary satellites due to smaller propagation delay and packet loss. Inter-satellite communication may further reduce the end-to-end delay between two terrestrial nodes. Routing of the networks will play a crucial role in optimizing the potential capacity of the network. We present and analyze a simple ALOHA type routing protocol for inter-satellite links in a satellite network.publishedVersio