无线网络的随机几何(英文版)

本书介绍无线网络性能 建模的重要数学工具——随 机几何。这一有力工具能对 无线网络性能界限做出估计 ，为未来无线网络架构和协 议设计提供帮助。本书从一 些概率论的基本知识出发， 将数学理论与实际工程应用 集成在一起讲授，易于读者 理解。书中也会讲到相关的 渗流理论和随机几何图论， 并对R统计编程语言做简要 介绍。将数学理论、动手分 析技术与实际示例和练习相 结合，本书是对无线网络性 能建模和分析来说必需的空 间随机模型的全面指南。本 书适合作为电子信息与通信 工程专业、计算机专业与应 用数学专业的高年级本科生 或低年级硕士研究生的教材 与教学参考书，也可供工程 技术人员参考。

Preface Notation Part Ⅰ Point process theory 1 Introduction 1.1 What is stochastic geometry? 1.2 Point processes as spatial models for wireless networks 1.3 Asymptotic notation 1.4 Sets and measurability Problems 2 Description of point processes 2.1 Description of one-dimensional point processes 2.2 Point process duality 2.3 Description of general point processes 2.4 Basic point processes 2.5 Distributional characterization 2.6 Properties of point processes 2.7 Point process transformations 2.8 Distances 2.9 Applications Bibliographical notes Problems 3 Point process models 3.1 Introduction 3.2 General finite point processes 3.3 Cox processes 3.4 Cluster processes 3.5 Hard-core processes 3.6 Gibbs processes 3.7 Shot-noise random fields Bibliographical notes Problems 4 Sums and products over point processes 4.1 Introduction 4.2 The mean of a sum 4.3 The probability generating functional 4.4 The Laplace functional 4.5 The moment-generating function of sums over Poisson processes 4.6 The probability generating and Laplace functionals for the Poisson point process 4.7 Summary of relationships 4.8 Functionals of other point processes Bibliographical notes Problems 5 Interference and outage in wireless networks 5.1 Interference characterization 5.2 Outage probability in Poisson networks 5.3 Spatial throughput in Poisson bipolar networks 5.4 Transmission capacity 5.5 Temporal correlation of the interference 5.6 Temporal correlation of outage probabilities Bibliographical notes Problems 6 Moment measures of point processes 6.1 Introduction 6.2 The first-order moment measure 6.3 Second moment measures 6.4 Second moment density 6.5 Second moments for stationary processes Bibliographical notes Problems 7 Marked point processes 7.1 Introduction and definition 7.2 Theory of marked point processes 7.3 Applications Bibliographical notes Problems 8 Conditioning and Palm theory 8.1 Introduction 8.2 The Palm distribution for stationary processes 8.3 The Palm distribution for general point processes 8.4 The reduced Palm distribution 8.5 Palm distribution for Poisson processes and Slivnyak's theorem 8.6 Second moments and Palm distributions for stationary processes 8.7 Palm distributions for Neyman-Scott cluster processes 8.8 Palm distribution for marked point processes 8.9 Applications Bibliographical notes Problems Part Ⅱ Percolation,connectivity,and coverage 9 Introduction 9.1 Motivation 9.2 What is percolation? 10 Bond and site percolation 10.1 Random trees and branching processes 10.2 Preliminaries for bond percolation on the lattice 10.3 General behavior of the percolation probability 10.4 Basic techniques 10.5 Critical threshold for bond percolation on the square lattice 10.6 Further results in bond percolation 10.7 Site percolation Bibliographical notes Problems 11 Random geometric graphs and continuum percolation 11.1 Introduction 11.2 Percolation on ilbert's disk graph 11.3 Other percolation models 11.4 Applications Bibliographical notes Problems 12 Connectivity 12.1 Introduction 12.2 Connectivity of the random lattice 12.3 Connectivity of the disk graph 12.4 Connectivity of basic random geometric graphs 12.5 Other graphs Bibliographical notes Problems 13 Coverage 13.1 Introduction 13.2 Germ-grain and Boolean models 13.3 Boolean model with fixed disks 13.4 Applications Bibliographical notes Problems Appendix Introduction to R Referen