Stochastic Geometry and Wireless Networks
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.
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Contents
Preface
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1 |
Marked Point Processes and ShotNoise Fields
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43 |
Boolean Model
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71 |
Voronoi Tessellation
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91 |
Bibliographical Notes on Part I
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103 |
Interacting SignaltoInterference Ratio Cells
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131 |
SignaltoInterference Ratio Coverage
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137 |
SignaltoInterference Ratio Connectivity
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155 |
Bibliographical Notes on Part II
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165 |
Stationary Marked Point Processes
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175 |
Fairness and Optimality
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181 |
Graph Theoretic Notions
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189 |
199 | |
206 | |
Common terms and phrases
Assume assumption averages ball bond Boolean model bounded called Chapter closed sets component connected Consequently Consider constant contains convergence Corollary cover coverage process defined Definition denote density depend distribution edge equal Example exists fact fading field finite first formula fraction function geometry give given grains graph holds homogeneous independent infinite integrable intensity measure interference Lemma limit marked point process marks mean measure nodes noise Note observation obtained origin particular percolation point process Poisson p.p. positive probability Proof Proposition prove radius random variable received Remark respect result scenario Section seen sequence shot-noise simple SINR cell space square standard stationary stochastic geometry surely tessellation Theorem tion transmitters typical vector Volume Voronoi wireless