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无线网络的随机几何(英文版)

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作者: (美)马丁·哈恩吉
出版社: 世界图书出版有限公司北京分公司
ISBN: 9787519242107

出版时间: 2020-07
装帧: 平装
开本: 16开

作者: (美)马丁·哈恩吉
出版社: 世界图书出版有限公司北京分公司

ISBN: 9787519242107
出版时间: 2020-07

装帧: 平装
开本: 16开

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目录
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 Slivnyaks 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 ilberts 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

内容摘要
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。

主编推荐
·本书是靠前上将随机几何应用于无线网络建模研究的领军人物所著的非常不错教材。
·随机几何这一有力数学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。
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