Latency Analysis of LEO Satellite Relay Communication: An Application of Conditional Contact Angle Distribution

This article investigates the transmission delay of a Low Earth Orbit (LEO) satellite communication system in a bent pipe structure. By employing a stochastic geometry framework, satellites are modeled as spherical binomial point processes (BPP). A suboptimal satellite relay selection strategy is proposed, which achieves optimal conditions through theoretical analysis and numerical exploration. We derive the distance distributions for the uplink and downlink links, and provide corresponding analytical expressions for the transmission delays

Conditional Contact Angle Distribution in LEO Satellite-Relayed Transmission

This letter characterizes the contact angle distribution based on the condition that the relay low earth orbit (LEO) satellite is in the communication range of both the ground transmitter and the ground receiver. As one of the core distributions in stochastic geometry-based routing analysis, the analytical expression of the \ac{CDF} of the conditional contact angle is derived. Furthermore, the conditional contact angle is applied to analyze the inaccessibility of common satellites between the ground transmitter and receiver. Finally, with the help of the conditional contact angle, coverage probability and achievable data rate in LEO satellite-relayed transmission are studied

Stochastic Geometry-Based Low Latency Routing in Massive LEO Satellite Networks

In this paper, the routing in massive low earth orbit (LEO) satellite networks is studied. When the satellite-to-satellite communication distance is limited, we choose different relay satellites to minimize the latency in a constellation at a constant altitude. Firstly, the global optimum solution is obtained in the ideal scenario when there are available satellites at all the ideal locations. Next, we propose a nearest neighbor search algorithm for realistic (non-ideal) scenarios with a limited number of satellites. The proposed algorithm can approach the global optimum solution under an ideal scenario through a finite number of iterations and a tiny range of searches. Compared with other routing strategies, the proposed algorithm shows significant advantages in terms of latency. Furthermore, we provide two approximation techniques that can give tight lower and upper bounds for the latency of the proposed algorithm, respectively. Finally, the relationships between latency and constellation height, satellites' number, and communication distance are investigated

Coverage Analysis for UAV-Assisted Cellular Networks in Rural Areas

Despite coverage enhancement in rural areas is one of the main requirements in next generations of wireless networks (i.e., 5G and 6G), the low expected profit prevents telecommunication providers from investing in such sparsely populated areas. Hence, it is required to design and deploy cost efficient alternatives for extending the cellular infrastructure to these regions. A concrete mathematical model that characterizes and clearly captures the aforementioned problem might be a key-enabler for studying the efficiency of any potential solution. Unfortunately, the commonly used mathematical tools that model large scale wireless networks are not designed to capture the unfairness, in terms of cellular coverage, suffered by exurban and rural areas. In big cities, in fact, cellular deployment is essentially capacity driven and thus cellular base station densities are maximum in the town centers and decline when getting far from them. In this paper, a new stochastic geometry-based model is implemented in order to show the coverage spatial variation among urban, suburban, and exurban settlements. Indeed, by implementing inhomogeneous Poisson point processes (PPPs) it is possible to study the performance metrics in a realistic scenario where terrestrial base stations (TBSs) are clustered around the urban center while outer aerial base stations (ABSs) are uniformly distributed outside an urban exclusion zone. Based on this, our simulation results can quantify the improvement, in terms of coverage probability, that even a surprisingly low density of ABSs can bring to peripheral regions depending on the extension of the exclusion zone, enabling us to draw insightful considerations

Multi-connectivity between terrestrial and non-terrestrial MIMO Systems

Communicating in a non-terrestrial network (NTN) has recently emerged as a promising technology to provide global seamless connectivity. Although low earth orbit (LEO) satellites in an NTN have been employed for providing ubiquitous coverage and high data rates for ground users, especially in emergent outdoor scenarios, NTN has not been integrated into the design of multi-connectivity for users in a terrestrial network (TN). Inspired by the 3rd Generation Partnership Program (3GPP) suggestion, this paper investigates TN-NTN-combined multi-connectivity downlink multiple-input multiple-output (MIMO) communication system, where each user may simultaneously connect to a base station (BS) in a TN and an LEO satellite in an NTN. Specifically, each user may have four different downlink access modes: served by both an LEO satellite and a BS, served by a BS, served by an LEO satellite, and not scheduled. Zero-forcing beamforming is employed at each LEO satellite to reduce the mutual interference among the satellite’s served users, and maximum ratio transmission beamforming is used at each terrestrial BS to enhance the downlink signal strength. By deriving the probability of each access mode and modeling the interference in such a TN-NTN-combined multi-connectivity MIMO system, we obtain a typical user’s downlink coverage probability and average achievable data rate. Extensive Monte Carlo simulations are conducted to validate our analytical derivations. Simulation results demonstrate that the user’s coverage probability and average achievable data rate can be significantly improved by realizing multi-connectivity with both TN and NTN compared to pure TN or NTN

Unmanned Aerial Vehicle (UAV)-Enabled Wireless Communications and Networking

The emerging massive density of human-held and machine-type nodes implies larger traffic deviatiolns in the future than we are facing today. In the future, the network will be characterized by a high degree of flexibility, allowing it to adapt smoothly, autonomously, and efficiently to the quickly changing traffic demands both in time and space. This flexibility cannot be achieved when the network’s infrastructure remains static. To this end, the topic of UAVs (unmanned aerial vehicles) have enabled wireless communications, and networking has received increased attention. As mentioned above, the network must serve a massive density of nodes that can be either human-held (user devices) or machine-type nodes (sensors). If we wish to properly serve these nodes and optimize their data, a proper wireless connection is fundamental. This can be achieved by using UAV-enabled communication and networks. This Special Issue addresses the many existing issues that still exist to allow UAV-enabled wireless communications and networking to be properly rolled out

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

Stochastic Geometry-Based Analysis of LEO Satellite Communication Systems

— This letter studies the performance of a low-earth-orbit (LEO) satellite communication system where the locations of the LEO satellites are modeled as a binomial point process (BPP) on a spherical surface. In particular, we study the user coverage probability for a scenario where satellite gateways (GWs) are deployed on the ground to act as a relay between the users and the LEO satellites. We use tools from stochastic geometry to derive the coverage probability for the described setup assuming that LEO satellites are placed at n different altitudes, given that the number of satellites at each altitude ak is Nk where 1 ≤ k ≤ n. To resemble practical scenarios where satellite communication can play an important role in coverage enhancement, we compare the performance of the considered setup with a scenario where the users are solely covered by a fiber-connected base station (referred to as anchored base station or ABS in the rest of the letter) at a relatively far distance, which is a common challenge in rural and remote areas. Using numerical results, we show the performance gain, in terms of coverage probability, at rural and remote areas when LEO satellite communication systems are adopted. Finally, we draw multiple system-level insights regarding the density of GWs required to outperform the ABS, as well as the number of LEO satellites and their altitudes