CentraleSupelec , bâtiment Bréguet, L2S, 3, rue Joliot-Curie, 91190 Gif-sur-Yvette,salle D2.06

Soutiendra publiquement ses travaux de thèse intitulés

**Modeling and performance evaluation of spatial/y-correlated cellular networks**

dirigés par

**Monsieur Marco DIRENZO**

**Composition du jury:**

M. Marco DIRENZO |
L2S, CNRS | Directeur de thèse |

M. Marcelo DIAS DE AMORIM |
Sorbonne Université, LIP6 | Rapporteur |

M. Philippe MARY |
NSA Rennes, Laboratoire IETR | Rapporteur |

M. Marceau COUPECHOUX |
LTCI, Telecom ParisTech | Examinateur |

Mme Inbar FIJALKOW |
ENSEA, Laboratoire ETIS | Examinateur |

M. Philippe MARTINS |
Telecom ParisTech | Examinateur |

Mme Lina MROUEH |
ISEP | Examinateur |

**Résumé:**

In the modeling and performance evaluation of wireless cellular networks, stochastic geometry is widely applied to provide efficient and accurate solutions. Homogeneous Poisson point process (H-PPP) is the most widely used point process to model the spatial locations of base stations (BSs) due to its mathematical tractability and simplicity. For BSs with spatial correlations, only non-Poisson point processes can help. However, the long simulation time and weak mathematical tractability make non Poisson PPs not suitable. Therefore, to overcome mentioned problems, we have the following contributions in this thesis: First, we introduce a new methodology for modeling and analyzing downlink cellular networks, where the BSs constitute a motion-invariant point process that exhibits correlations among the points, i.e., spatial repulsion or spatial clustering. The proposed approach is based on the theory of inhomogeneous Poisson PPs (I-PPPs) and is referred to as inhomogeneous double thinning (IDT) approach. The proposed approach consists of approximating the original motion invariant PP with an equivalent PP that is made of the superposition of two conditionally independent 1- PPPs. A tractable expression of the coverage probability is obtained. Sufficient conditions on the parameters of the thinning functions that guarantee better or worse coverage compared with the baseline homogeneous PPP model are identified. Then, based on the IDT approach, a new tractable analytical expression of MISR of cellular networks where BSs exhibits spatial correlations is introduced. For homogeneous PPP, MISR is proved to be constant under network densification. For non-Poisson PPs, we apply proposed IDT approach to approximate the performance of non-Poisson point process. Taking beta-Ginibre point process (beta-GPP) as an example, we successfully prove that MISR for beta-GPP is constant under network densification with our proposed approximation functions. We prove that of MISR performance for beta-GPP case only depends on the degree of spatial repulsion, i.e., beta, regardless of different BS densities. Third, following the extension and application of !DT approach, we further study meta distribution of the SIR, which is the distribution of the conditional success probability given the point process. We derive and compare the closed-form expressions of the b-th moment function for homogeneous PPP and IDT approach. We propose a simple and accurate numerical method based on numerical inversion of Laplace transforms to compute CCDF through moments. The proposed method is more efficient and stable than the conventional approach. Furthermore, the proposed method is compared be more accurate than sorne other approximations and bounds. Ali the proposed approaches are substantiated with the aid of empirical data for the spatial distribution of the BSs.

**Mots-clés: **HetNets, stochastic geometry, point processes,

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