Stochastic Geometry and Wireless Networks, Part I: Theory

✍ Scribed by Francois Baccelli, Bartlomiej Blaszczyszyn

• Publisher: Now Publishers Inc
• Year: 2009
• Tongue: English
• Leaves: 164
• Category: Library

✦ Synopsis

Stochastic Geometry and Wireless Networks, Part I: Theory first provides a compact survey on classical stochastic geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on signal to interference noise ratio (SINR) stochastic geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Stochastic Geometry and Wireless Networks, Part II: Applications. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Parts I and II.

✦ Table of Contents

Preface......Page 6
Preface to Volume I......Page 10
Contents of Volume I......Page 12
I Classical Stochastic Geometry......Page 15
1.1 Definition and Characterizations......Page 17
1.2 Laplace Functional......Page 20
1.3 Operations Preserving the Poisson Law......Page 22
1.4 Palm Theory......Page 27
1.5 Strong Markov Property......Page 31
1.6 Stationarity and Ergodicity......Page 32
1.7 Extensions......Page 36
2.1 Marked Point Processes......Page 37
2.2 Shot-Noise......Page 43
2.3 Interference Field as Shot-Noise......Page 46
2.4 Extremal Shot-Noise......Page 54
3.1 Boolean Model as a Coverage Process......Page 57
3.2 Boolean Model as a Connectivity Model......Page 65
4.1 Introduction......Page 71
4.2 The Inverse Formula of Palm Calculus......Page 72
4.3 The Neveu Exchange Formula......Page 74
4.4 Neighbors in the Voronoi Tessellation, Delaunay Triangulation......Page 77
4.5 The Voronoi Tessellation Model for Cellular Access Networks......Page 78
Bibliographical Notes on Part I......Page 81
II Signal-to-Interference Ratio Stochastic Geometry......Page 83
5.1 Introduction......Page 85
5.2 The Signal-to-Interference Ratio Cell is Well-Defined......Page 86
5.3 Standard Stochastic Scenario and First Order Cell Characteristics......Page 87
5.4 Fading in Signal-to-Interference Ratio Cell and Higher Order Characteristics......Page 90
5.5 Noise or Interference Limited Cell: Towards a Boolean or Voronoi Shape......Page 91
6.1 Introduction......Page 103
6.2 Constraints on Cell Intersections......Page 104
6.4 Joint Point-Coverage Probability......Page 105
7.1 Introduction......Page 107
7.2 Typical Cell of the Coverage Process......Page 108
7.3 Nearest Transmitter Cell......Page 109
7.4 SINR as a Random Closed Set......Page 110
7.5 The Coverage Process Characteristics......Page 113
8.2 Signal-to-Interference Ratio Graph......Page 119
8.3 Percolation of the Signal-to-Interference Ratio Connectivity Graph......Page 120
Bibliographical Notes on Part II......Page 125
III Appendix: Mathematical Complements......Page 127
9.1 Higher Order Moment Measures......Page 129
9.2 Palm Measures......Page 130
10.1 Marked Point Processes......Page 133
10.2 Palm--Matthes Distribution of a Marked Point Process......Page 134
11 Fairness and Optimality......Page 137
12.2 Lemmas......Page 139
13.1 Minimum Spanning Tree......Page 145
14.1 Bond percolation on Zd.......Page 149
14.2 Independent Site Percolation......Page 152
Bibliography......Page 155
Table of Notation......Page 159
Index......Page 161