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Stochastic Geometry for Wireless Networks

Book Description

Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.

Table of Contents

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