## Stochastic Geometry Analysis of Cellular NetworksAchieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results. |

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### Contents

Introduction | 3 |

The Role of Stochastic Geometry in HetNet Analysis | 13 |

Statistics of Received Power at the Typical Location | 42 |

Fundamental Results | 73 |

Advanced Results | 97 |

Further Extensions | 128 |

Extensions to NonPoisson Models | 144 |

Concluding Remarks | 168 |

Appendix B Timeline of Cellular Technology Generations | 175 |

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### Common terms and phrases

approximation assume Baccelli base station locations Błaszczyszyn CCDF cellular networks coverage probability Cox process defined DEFINITION denote deployment determinantal point process determinantal process distance EFIR equivalent Example exponential expression factorial moment factorial moment measure Haenggi HetNet independent intensity measure k-coverage Keeler Laplace transform Lemma M-matrix macro base station macrocell mean meta distribution MISR multitier network network model number of points order statistics Palm measure parameter path loss exponent path loss function path loss model Poisson model Poisson network Poisson point process Poisson process probability density Proposition random variable Rayleigh fading receive antenna received power scenarios Section serving base station shot noise simulation single-tier network SINR threshold SIR distribution spectral efficiency stationary point process STINR process stochastic geometry Theorem tier tractable transmission transmit power typical cell typical location user terminal wireless networks