MonographDOI
Stochastic Geometry Analysis of Cellular Networks
TLDR
Campbell’s formula for marked point processes, Campbell-Mecke theorem, and Cox point process convergence counting measure are cited.Abstract:
Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.read more
Citations
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Journal ArticleDOI
Downlink Coverage and Rate Analysis of Low Earth Orbit Satellite Constellations Using Stochastic Geometry
TL;DR: 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 are derived from stochastic geometry, which abstracts the generic networks into uniform binomial point processes.
Journal ArticleDOI
Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association
TL;DR: This paper develops an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise ratio (SINR inline-formula> distribution, which was not possible using the existing PPP-based models.
Journal ArticleDOI
Meta Distribution of Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks
TL;DR: This work considers two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based, and shows that interference-aware UE clustering can significantly improve performance.
Journal ArticleDOI
SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion
TL;DR: In this article, the authors applied the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on $K$ -tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (PPP) model, with range expansion bias in each tier.
Book
Random Measures, Point Processes, and Stochastic Geometry
TL;DR: This book was designed to help researchers finding a direct path from the basic definitions and properties of these mathematical objects to their use in new and concrete stochastic models, with a main focus on random measures, point processes, and Stochastic geometry.
References
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Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Book
Probability, random variables and stochastic processes
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.