L’objectif principal de cette thèse est de développer des méthodologies statistiques adaptées au traitement de données issues de processus stochastiques et plus précisément de processus de Cox.Les problématiques étudiées dans cette thèse sont issues des trois domaines statistiques suivants : les tests non paramétriques, l’estimation non paramétrique à noyaux et l’estimation minimax.Dans un premier temps, nous proposons, dans un cadre fonctionnel, des statistiques de test pour détecter la nature Poissonienne d’un processus de Cox.Nous étudions ensuite le problème de l’estimation minimax de la régression sur un processus de Poisson ponctuel. En se basant sur la décomposition en chaos d’Itô, nous obtenons des vitesses comparables à celles atteintes pour le cas de la régression Lipschitz en dimension finie.Enfin, dans le dernier chapitre de cette thèse, nous présentons un estimateur non-paramétrique de l’intensité d’un processus de Cox lorsque celle-ci est une fonction déterministe d’un co-processus. / The main purpose of this thesis is to develop statistical methodologies for stochastic processes data and more precisely Cox process data.The problems considered arise from three different contexts: nonparametric tests, nonparametric kernel estimation and minimax estimation.We first study the statistical test problem of detecting wether a Cox process is Poisson or not.Then, we introduce a semiparametric estimate of the regression over a Poisson point process. Using Itô’s famous chaos expansion for Poisson functionals, we derive asymptotic minimax properties of our estimator.Finally, we introduce a nonparametric estimate of the intensity of a Cox process whenever it is a deterministic function of a known coprocess.

In recent years, the increase in the population of mobile users and the advances in computational capabilities of mobile devices have led to an exponentially increasing traffic load on the wireless networks. This trend is foreseen to continue in the future due to the emerging applications such as cellular Internet of things (IoT) and machine type communications (MTC). Since the spectrum resources are limited, the only promising way to keep pace with the future demand is through aggressive spatial reuse of the available spectrum which can be realized in the networks through dense deployment of small cells. There are many challenges associated with such densely deployed heterogeneous networks (HetNets). The main challenges which are considered in this research work are capacity enhancement, velocity estimation of mobile users, and energy efficiency enhancement. We consider different approaches for capacity enhancement of the network. In the first approach, using stochastic geometry we theoretically analyze time domain inter-cell interference coordination techniques in a two-tier HetNet and optimize the parameters to maximize the capacity of the network. In the second approach, we consider optimization of the locations of aerial bases stations carried by the unmanned aerial vehicles (UAVs) to enhance the capacity of the network for public safety and emergency communications, in case of damaged network infrastructure. In the third approach, we introduce a subsidization scheme for the service providers through which the network capacity can be improved by using regulatory power of the government. Finally, we consider the approach of device-to-device communications and multi-hop transmissions for enhancing the capacity of a network. Velocity estimation of high speed mobile users is important for effective mobility management in densely deployed small cell networks. In this research, we introduce two novel methods for the velocity estimation of mobile users: handover-count based velocity estimation, and sojourn time based velocity estimation. Using the tools from stochastic geometry and estimation theory, we theoretically analyze the accuracy of the two velocity estimation methods through Cramer-Rao lower bounds (CRLBs). With the dense deployment of small cells, energy efficiency becomes crucial for the sustained operation of wireless networks. In this research, we jointly study the energy efficiency and the spectral efficiency in a two-tier HetNet. We optimize the parameters of inter-cell interference coordination technique and study the trade-offs between the energy efficiency and spectral efficiency of the HetNet.

L'analyse et l'optimisation au niveau de système sont indispensables pour la progression de performance des réseaux de communication. Ils sont nécessaires afin de faire fonctionner de façon optimale des réseaux actuels et de planifier des réseaux futurs. La modélisation et l'analyse au niveau de système des réseaux cellulaires ont été facilitées grâce à la maîtrise de l'outil mathématique de la géométrie stochastique et, plus précisément, la théorie des processus ponctuels spatiaux. Du point de vue de système, il a été empiriquement validé que les emplacements des stations cellulaires de base peuvent être considérés comme des points d'un processus ponctuel de Poisson homogène dont l'intensité coïncide avec le nombre moyen de stations par unité de surface. Dans ce contexte, des contributions de ce travail se trouvent dans le développement de nouvelles méthodologies analytiques pour l'analyse et l'optimisation des déploiements de réseaux cellulaires émergents.La première contribution consiste à introduire une approche pour évaluer la faisabilité de réseaux cellulaires multi-antennes, dans lesquels les dispositifs mobiles à faible énergie décodent les données et récupèrent l'énergie à partir d’un même signal reçu. Des outils de géométrie stochastique sont utilisés pour quantifier le taux d'information par rapport au compromis de puissance captée. Les conclusions montrent que les réseaux d'antennes à grande échelle et les déploiements ultra-denses de stations base sont tous les deux nécessaires pour capter une quantité d'énergie suffisamment élevée et fiable. En outre, la faisabilité de la diversité des récepteurs pour l'application aux réseaux cellulaires descendants est également étudiée. Diverses options basées sur la combinaison de sélection et la combinaison de taux maximal sont donc comparées. Notre analyse montre qu'aucun système n’est plus performant que les autres pour chaque configuration de système : les dispositifs à basse énergie doivent fonctionner de manière adaptative, en choisissant le schéma de diversité des récepteurs en fonction des exigences imposées.La deuxième contribution consiste à introduire une nouvelle approche pour la modélisation et l'optimisation de l'efficacité énergétique des réseaux cellulaires.Contrairement aux approches analytiques actuellement disponibles qui fournissent des expressions analytiques trop simples ou trop complexes de la probabilité de couverture et de l'efficacité spectrale des réseaux cellulaires, l'approche proposée est formulée par une solution de forme fermée qui se révèle en même temps simple et significative. Une nouvelle expression de l'efficacité énergétique du réseau cellulaire descendant est proposée à partir d’une nouvelle formule de l'efficacité spectrale. Cette expression est utilisée pour l’optimisation de la puissance d'émission et la densité des stations cellulaires de base. Il est prouvé mathématiquement que l'efficacité énergétique est une fonction uni-modale et strictement pseudo-concave de la puissance d'émission en fixant la densité des stations de base, et de la densité des stations de base en fixant la puissance d'émission. La puissance d'émission optimale et la densité des stations de base s'avèrent donc être la solution des équations non linéaires simples.La troisième contribution consiste à introduire une nouvelle approche pour analyser les performances des réseaux cellulaires hétérogènes équipés des sources d'énergie renouvelables, telles que les panneaux solaires. L'approche proposée permet de tenir compte de la distribution spatiale des stations de base en utilisant la théorie des processus ponctuels, ainsi que l'apparition aléatoire et la disponibilité de l'énergie en utilisant la théorie des chaînes de Markov. En utilisant l'approche proposée, l'efficacité énergétique des réseaux cellulaires peut être quantifiée et l'interaction entre la densité des stations de base et le taux d'énergie d'apparition peut être quantifiée et optimisée. / In communication networks, system-level analysis and optimization are useful when one is interested in optimizing the system performance across the entire network. System-level analysis and optimization, therefore, are relevant for optimally operating current networks, and for deploying and planning future networks. In the last few years, the system-level modeling and analysis of cellular networks have been facilitated by capitalizing on the mathematical tool of stochastic geometry and, more precisely, on the theory of spatial point processes. It has been empirically validated that, from the system-level standpoint, the locations of cellular base stations can be abstracted as points of a homogeneous Poisson point process whose intensity coincides with the average number of based stations per unit area.In this context, the contribution of the present Ph.D. thesis lies in developing new analytical methodologies for analyzing and optimizing emerging cellular network deployments. The present Ph.D. thesis, in particular, provides three main contributions to the analysis and optimization of energy-efficient cellular networks.The first contribution consists of introducing a tractable approach for assessing the feasibility of multiple-antenna cellular networks, where low-energy mobile devices decode data and harvest power from the same received signal. Tools from stochastic geometry are used to quantify the information rate vs. harvested power tradeoff. Our study unveils that large-scale antenna arrays and ultra-dense deployments of base stations are both necessary to harvest, with high reliability, a sufficiently high amount of power. Furthermore, the feasibility of receiver diversity for application to downlink cellular networks is investigated. Several options that are based on selection combining and maximum ratio combining are compared against each other. Our analysis shows that no scheme outperforms the others for every system setup. It suggests, on the other hand, that the low-energy devices need to operate in an adaptive fashion, by choosing the receiver diversity scheme as a function of the imposed requirements.The second contribution consists of introducing a new tractable approach for modeling and optimizing the energy efficiency of cellular networks. Unlike currently available analytical approaches that provide either simple but meaningless or meaningful but complex analytical expressions of the coverage probability and spectral efficiency of cellular networks, the proposed approach is conveniently formulated in a closed-form expression that is proved to be simple and meaningful at the same time. By relying on the new proposed formulation of the spectral efficiency, a new tractable closed-form expression of the energy efficiency of downlink cellular network is proposed, which is used for optimizing the transmit power and the density of cellular base stations. It is mathematically proved, in particular, that the energy efficiency is a unimodal and strictly pseudo-concave function in the transmit power, given the density of the base stations, and in the density of the base stations, given the transmit power. The optimal transmit power and density of base stations are proved to be the solution of simple non-linear equations.The third contribution consists of introducing a new tractable approach for analyzing the performance of multi-tier cellular networks equipped with renewable energy sources, such as solar panels. The proposed approach allows one to account for the spatial distribution of the base stations by using the theory of point processes, as well as for the random arrival and availability of energy by using Markov chain theory. By using the proposed approach, the energy efficiency of cellular networks can be quantified and the interplay between the density of base stations and energy arrival rate can be quantified and optimized.

Owing to its ability to improve both spectral and energy efficiency of wireless networks, massive multiple-input multiple-output (mMIMO) has become one of the key enablers of the fifth-generation (5G) and beyond communication systems. For successful integration of this promising physical layer technique in the upcoming cellular standards, it is essential to have a comprehensive understanding of its network-level performance. Over the last decade, stochastic geometry has been instrumental in obtaining useful system design insights of wireless networks through accurate and tractable theoretical analysis. Hence, it is only natural to consider modeling and analyzing the mMIMO systems using appropriate statistical constructs from the stochastic geometry literature and gain insights for its future implementation. With this broader objective in mind, we first focus on modeling a cellular mMIMO network that uses fractional pilot reuse to mitigate the sole performance-limiting factor of mMIMO networks, namely, pilot contamination. Leveraging constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we derive analytical expressions for the uplink (UL) signal-to-interference-and-noise ratio (SINR) coverage probability and average spectral efficiency for a random user. From our system analysis, we present a partitioning rule for the number of pilot sequences to be reserved for the cell-center and cell-edge users that improves the average cell-edge user spectral efficiency while achieving similar cell-center user spectral efficiency with respect to unity pilot reuse. In addition, using the analytical approach developed for the cell-center user performance evaluation, we study the performance of a small cell system where user and base station (BS) locations are coupled. The impact of distance-dependent UL power control on the performance of an mMIMO network with unity pilot reuse is analyzed and subsequent system design guidelines are also presented. Next, we focus on the performance analysis of the cell-free mMIMO network, which is a distributed implementation of the mMIMO system that leads to the second and third contributions of this dissertation. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. This pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We study the statistical properties of this point process both in one and two-dimensional spaces by deriving approximate but accurate expressions for the density and pair correlation functions. Leveraging these new results, for a cell-free network with the proposed RSA-based pilot assignment scheme, we present an analytical approach that determines the minimum number of pilots required to schedule a user with probabilistic guarantees. In addition, to benchmark the performance of the RSA-based scheme, we propose two optimization-based centralized pilot allocation schemes using linear programming principles. Through extensive numerical simulations, we validate the efficacy of the distributed and scalable RSA-based pilot assignment scheme compared to the proposed centralized algorithms. Apart from pilot contamination, another impediment to the performance of a cell-free mMIMO is limited fronthaul capacity between the baseband unit and the access points (APs). In our fourth contribution, using appropriate stochastic geometry-based tools, we model and analyze the downlink of such a network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs in order to limit the load on fronthaul links. From our analyses, we observe that for the finite network, the achievable average system sum-rate is a strictly quasi-concave function of the number of users in the network, which serves as a key guideline for scheduler design for such systems. Further, for the user-centric architecture, we observe that there exists an optimal number of serving APs that maximizes the average user rate. The fifth and final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in citizen broadband radio service (CBRS) spectrum sharing systems. As a first concrete step, we present comprehensive modeling and analysis of this system with omni-directional transmissions. Our model takes into account the key guidelines by the Federal Communications Commission for co-existence between licensed and unlicensed networks in the 3.5 GHz CBRS frequency band. Leveraging the properties of the Poisson hole process and Matern hardcore point process of type II, a.k.a. ghost RSA process, we analytically characterize the impact of different system parameters on various performance metrics such as medium access probability, coverage probability, and area spectral efficiency. Further, we provide useful system design guidelines for successful co-existence between these networks. Building upon this omni-directional model, we also characterize the performance benefits of using mMIMO in such a spectrum sharing network. / Doctor of Philosophy / The emergence of cloud-based video and audio streaming services, online gaming platforms, instantaneous sharing of multimedia contents (e.g., photos, videos) through social networking platforms, and virtual collaborative workspace/meetings require the cellular communication networks to provide high data-rate as well as reliable and ubiquitous connectivity. These constantly evolving requirements can be met by designing a wireless network that harmoniously exploits the symbiotic co-existence among different types of cutting-edge wireless technologies. One such technology is massive multiple-input multiple-output (mMIMO), whose core idea is to equip the cellular base stations (BSs) with a large number of antennas that can be leveraged through appropriate signal processing algorithms to simultaneously accommodate multiple users with reduced network interference. For successful deployment of mMIMO in the upcoming cellular standards, i.e., fifth-generation (5G) and beyond systems, it is necessary to characterize its performance in a large-scale wireless network taking into account the inherent spatial randomness in the BS and user locations. To achieve this goal, in this dissertation, we propose different statistical methods for the performance analysis of mMIMO networks using tools from stochastic geometry, which is a field of mathematics related to the study of random patterns of points. One of the major deployment issues of mMIMO systems is pilot contamination, which is a form of coherent network interference that degrades user performance. The main reason behind pilot contamination is the reuse of pilot sequences, which are a finite number of known signal waveforms used for channel estimation between a user and its serving BS. Further, the effect of pilot contamination is more severe for the cell-edge users, which are farther from their own BSs. An efficient scheme to mitigate the effect of pilot contamination is fractional pilot reuse (FPR). However, the efficiency of this scheme depends on the pilot partitioning rule that decides the fraction of total pilot sequences that should be used by the cell-edge users. Using appropriate statistical constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we present a partitioning rule for efficient implementation of the FPR scheme in a cellular mMIMO network. Next, we focus on the performance analysis of the cell-free mMIMO network. In contrast to the cellular network, where each user is served by a single BS, in a cell-free network each user can be served by multiple access points (APs), which have less complex hardware compared to a BS. Owing to this cooperative and distributed implementation, there are no cell-edge users. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. Further, we show that the performance of this distributed pilot assignment scheme is appreciable compared to different centralized pilot assignment schemes, which are algorithmically more complex and difficult to implement in a network. Moreover, this pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We derive the statistical properties of this point process both in one and two-dimensional spaces. Further, in a cell-free mMIMO network, the APs are connected to a centralized baseband unit (BBU) that performs the bulk of the signal processing operations through finite capacity links, such as fiber optic cables. Apart from pilot contamination, another implementational issue associated with the cell-free mMIMO systems is the finite capacity of fronthaul links that results in user performance degradation. Using appropriate stochastic geometry-based tools, we model and analyze this network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs. As a consequence of this user-centric implementation, for each user, the BBU only needs to communicate with fewer APs thereby reducing information load on fronthaul links. From our analyses, we propose key guidelines for the deployment of both types of scenarios. The type of mMIMO systems that are discussed in this work will be operated in the sub-6 GHz frequency range of the electromagnetic spectrum. Owing to the limited availability of spectrum resources, usually, spectrum sharing is encouraged among different cellular operators in such bands. One such example is the citizen broadband radio service (CBRS) spectrum sharing systems proposed by the Federal Communications Commission (FCC). The final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in the CBRS systems. As our first step, using tools from stochastic geometry, we model and analyze this system with a single antenna at the BSs. In our model, we take into account the key guidelines by the FCC for co-existence between licensed and unlicensed operators. Leveraging properties of the Poisson hole process and hardcore process, we provide useful theoretical expressions for different performance metrics such as medium access probability, coverage probability, and area spectral efficiency. These results are used to obtain system design guidelines for successful co-existence between these networks. We further highlight the potential improvement in the user performance with multiple antennas at the unlicensed BS.

Perfect simulations are methods, which convert suitable Markov chain Monte Carlo (MCMC) algorithms into algorithms which return exact draws from the target distribution, instead of approximations based on long-time convergence to equilibrium. In recent years a lot of various perfect simulation algorithms were developed. This work provides a unified exposition of some perfect simulation algorithms with applications to spatial point processes, especially to the Strauss process and area-interaction process. Described algorithms and their properties are compared theoretically and also by a simulation study.

Abstract The aim of this thesis is to devise new paradigms on radio resource sharing including cache-enabled virtualized large cellular networks for mobile network operators (MNOs). Also, self-organizing resource allocation for small cell networks is considered. In such networks, the MNOs rent radio resources from the infrastructure provider (InP) to support their subscribers. In order to reduce the operational costs, while at the same time to significantly increase the usage of the existing network resources, it leads to a paradigm where the MNOs share their infrastructure, i.e., base stations (BSs), antennas, spectrum and edge cache among themselves. In this regard, we integrate the theoretical insights provided by stochastic geometrical approaches to model the spectrum and infrastructure sharing for large cellular networks. In the first part of the thesis, we study the non-orthogonal multi-MNO spectrum allocation problem for small cell networks with the goal of maximizing the overall network throughput, defined as the expected weighted sum rate of the MNOs. Each MNO is assumed to serve multiple small cell BSs (SBSs). We adopt the many-to-one stable matching game framework to tackle this problem. We also investigate the role of power allocation schemes for SBSs using Q-learning. In the second part, we model and analyze the infrastructure sharing system considering a single buyer MNO and multiple seller MNOs. The MNOs are assumed to operate over their own licensed spectrum bands while sharing BSs. We assume that multiple seller MNOs compete with each other to sell their infrastructure to a potential buyer MNO. The optimal strategy for the seller MNOs in terms of the fraction of infrastructure to be shared and the price of the infrastructure, is obtained by computing the equilibrium of a Cournot-Nash oligopoly game. Finally, we develop a game-theoretic framework to model and analyze a cache-enabled virtualized cellular networks where the network infrastructure, e.g., BSs and cache storage, owned by an InP, is rented and shared among multiple MNOs. We formulate a Stackelberg game model with the InP as the leader and the MNOs as the followers. The InP tries to maximize its profit by optimizing its infrastructure rental fee. The MNO aims to minimize the cost of infrastructure by minimizing the cache intensity under probabilistic delay constraint of the user (UE). Since the MNOs share their rented infrastructure, we apply a cooperative game concept, namely, the Shapley value, to divide the cost among the MNOs. / Tiivistelmä Tämän väitöskirjan tavoitteena on tuottaa uusia paradigmoja radioresurssien jakoon, mukaan lukien virtualisoidut välimuisti-kykenevät suuret matkapuhelinverkot matkapuhelinoperaattoreille. Näiden kaltaisissa verkoissa operaattorit vuokraavat radioresursseja infrastruktuuritoimittajalta (InP, infrastructure provider) asiakkaiden tarpeisiin. Toimintakulujen karsiminen ja samanaikainen olemassa olevien verkkoresurssien hyötykäytön huomattava kasvattaminen johtaa paradigmaan, jossa operaattorit jakavat infrastruktuurinsa keskenään. Tämän vuoksi työssä tutkitaan teoreettisia stokastiseen geometriaan perustuvia malleja spektrin ja infrastruktuurin jakamiseksi suurissa soluverkoissa. Työn ensimmäisessä osassa tutkitaan ei-ortogonaalista monioperaattori-allokaatioongelmaa pienissä soluverkoissa tavoitteena maksimoida verkon yleistä läpisyöttöä, joka määritellään operaattoreiden painotettuna summaläpisyötön odotusarvona. Jokaisen operaattorin oletetaan palvelevan useampaa piensolutukiasemaa (SBS, small cell base station). Työssä käytetään monelta yhdelle -vakaata sovituspeli-viitekehystä SBS:lle käyttäen Q-oppimista. Työn toisessa osassa mallinnetaan ja analysoidaan infrastruktuurin jakamista yhden ostaja-operaattorin ja monen myyjä-operaattorin tapauksessa. Operaattorien oletetaan toimivan omilla lisensoiduilla taajuuksillaan jakaen tukiasemat keskenään. Myyjän optimaalinen strategia infrastruktuurin myytävän osan suuruuden ja hinnan suhteen saavutetaan laskemalla Cournot-Nash -olipologipelin tasapainotila. Lopuksi, työssä kehitetään peli-teoreettinen viitekehys virtualisoitujen välimuistikykenevien soluverkkojen mallintamiseen ja analysointiin, missä InP:n omistama verkkoinfrastruktuuri vuokrataan ja jaetaan monen operaattorin kesken. Työssä muodostetaan Stackelberg-pelimalli, jossa InP toimii johtajana ja operaattorit seuraajina. InP pyrkii maksimoimaan voittonsa optimoimalla infrastruktuurin vuokrahintaa. Operaattori pyrkii minimoimaan infrastruktuurin hinnan minimoimalla välimuistin tiheyttä satunnaisen käyttäjän viive-ehtojen mukaisesti. Koska operaattorit jakavat vuokratun infrastruktuurin, työssä käytetään yhteistyöpeli-ajatusta, nimellisesti, Shapleyn arvoa, jakamaan kustannuksia operaatoreiden kesken.