Orientador: Pedro José Catuogno / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T07:50:09Z (GMT). No. of bitstreams: 1 Albuquerque_RobertaRodrigues_M.pdf: 577918 bytes, checksum: 382f6bfc15bbbcfa2efbd32b5ec398e7 (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estamos interessados no transporte paralelo da geometria diferencial no contexto do cálculo estocástico. Inicialmente resumimos os pontos fundamentais da geometria riemmaniana como as idéias de conexão, curvatura, transporte paralelo, a identidade de Bochner-Weitenböck e o mapa de desenvolvimento de Cartan, em seguida desenvolvemos alguns resultados da geometria estocástica como a fórmula geométrica de Itô, mas para isto inserimos brevemente a chamada geometria de segunda ordem. Ao final, examinaremos o transporte paralelo estocástico em algumas circunstâncias como no mapa de desenvolvimento estocástico, mapa de rolamento estocástico, construção do movimento Browniano em variedades e ainda com fluxos estocásticos na solução da equação de Stratonovich / Abstract: This dissertation is about the stochastic version of the parallel translation in the differential geometry. In the beginning it provides some basic background to Riemannian geometry, for example, the definiton of conexion, curvature, parallel translation, the Bochner-Weitenböck identity and the Cartan's rolling map theorem. After that, it is to dedicate to development of some results on stochastic geometry as the geometric Itô formula, but to do that it is important to study the second order geometry. In the end, it is essential to give attention to stochastic parallel transport in some environment as the Cartan's rolling map in the stochastic context, stochastic rolling constuctions, Brownian motion on manifolds and the stochastic flow as the solution of the Stratonovich equation / Mestrado / Geometria Estocastica / Mestre em Matemática

In this thesis, multicell coordination for wireless cellular networks is studied, whereby various approaches have been conducted to tackle this issue. Firstly, the coverage probability and e ective capacity in downlink multiple-input multiple-output (MIMO) cellular system are considered. Two scenarios are investigated; in the rst scenario, it is assumed that the system employs distance-based fractional power control with no multicell coordination. For the second scenario, it is assumed that the system implements multicell coordinated beamforming so as to cancel inter-cell interference. The base stations (BS) are modelled as randomly uniformly distributed in the area according to Poisson point process (PPP). Using tools from stochastic geometry, tractable, analytical expressions for coverage probability and e ective capacity are derived for both scenarios. Secondly, an adaptive strategy for inter-cell interference cancellation and coordination is proposed for downlink multicarrier cellular random networks. The adaptive strategy coordinates and cancels the interference on the both frequency and spatial domains. Based on this adaptive strategy, two interference management schemes have been proposed. The adaptation process is implemented based on measured instantaneous signal-to-interference and noise ratio (SINR) of the considered user. Furthermore, the locations of base stations BSs are modelled as an independent spatial PPP. Using tools from stochastic geometry, the proposed schemes have been analytically evaluated. Analytical expressions for coverage probability are derived for both schemes. In addition, an expression for average rate has been derived using the coverage probability analysis. Thirdly, low complexity algorithms for user scheduling have been proposed for coordinated MIMO multicell network. The algorithms consist of two stages: multicell scheduling stage and precoding stage. The algorithm works on sequential distributive manner. Two variants of multicell scheduling are proposed. The rst algorithm has less complexity but leads to more di erence in sum rate among cells. While the second algorithm results in better fairness in terms of system performance but causes frequent signalling among the cells. Moreover, the algorithm is extended to multimode selection in addition to the user selection. Finally, an adaptive coordination scheme for energy-effeicient resource allocation has been developed for orthogonal frequency division multiple access (OFDMA) cellular networks. The proposed scheme consists of centralised and distributed stages for allocating resources to cell-edge and cell-centre users, respectively. The optimisation problems are formulated as integer linear fractional and integer linear problems for the first stage and second stages, respectively. The spectral-energy trade-o is analysed under the constraint of fairness among users. In summary, the research work presented in this thesis reveals statistical approach to analyse the multicell coordination in random cellular networks. It also offers insight into the resource allocation and scheduling problems within multicell coordination framework, and how to solve them with a certain objective.

Cette thèse traite de la détection de zones de convergence dans une image, dans un cadre a contrario. C'est un travail théorique préliminaire qui explore différentes altérations du cadre a contrario. Elle a pour application dans le domaine médical la détection des lésions stellaires dans les mammographies, responsables de nombreux cancers du sein et qui se matérialisent par un centre intense vers lequel convergent les spicules, structures linéaires normalement présents dans le sein. Les lésions stellaires et distorsions architecturales ont suscité de nombreux travaux. La plupart des méthodes de détection sont basées sur l'extraction de caractéristiques locales de l'image (orientation du gradient, orientation des pixels, variance de l'histogramme de l'orientation...) puis utilisent une méthode de classification pour attribuer à chaque pixel une probabilité d'appartenir à une lésion stellaire. Ces méthodes nécessitent souvent l'utilisation de filtres en pré-traitement et en post-traitement afin de réduire le bruit, ou de seuiller les résultats finaux. La méthodologie a contrario offre un nouveau cadre pour la détection de structures dans les images. Elle s'appuie sur la définition d'un modèle de bruit, et sur une mesure de l'écart des observations à ce modèle. Le modèle porte sur des structures élémentaires et est souvent choisi "uniforme" : c'est-à-dire que les structures sont supposées suivre la loi uniforme et indépendantes. Or dans les mammographies on observe que les spicules ont une orientation privilégiée, et ne sont pas uniformément distribuées. Nous proposons l'utilisation de la méthode a contrario dans un cadre anisotrope pour mieux tenir compte de la distribution normale des spicules dans une mammographie. Les modèles anisotropes proposés modélisent le fait qu'une partie des structures linéaires est normalement convergentes vers un point commun. Ils portent soit sur les droites de l'image quand il s'agit de détecter les convergences globales, soit sur les segments quand on chercher les convergences locales dans une image. Concernant la détection des convergences locales, le cadre a contrario offre de nombreuses possibilités : sur le choix du nombre de fausses alarmes ou sur le choix du modèle de bruit. Ces choix sont détaillés sur des exemples synthétiques, sur des mammographies et sur des images naturelles. Les modèles a contrario que l'on étudie sont donnés sous la forme de mélanges paramétriques de deux termes : un terme uniforme et un terme "gaussien", modélisant le fait qu'une partie des structures est naturellement convergente. Pour ces différents types de modèles nous proposons d'estimer leurs paramètres. Le point de convergence globale est estimé par minimisation du nombre de fausses alarmes, et l'estimation des autres paramètres est faite par maximisation de la log-vraisemblance. Les modèles estimés sont ensuite testés en tant que modèles a contrario pour la détection des convergences et les résultats sont comparés à ceux que donnait le modèle uniforme. / This thesis deals with the detection of points of convergences in images, in an a contrario framework. This is a preliminar work which studies various alterations of the a contrario framework such as the naive model. An application in the medical field is the detection of stellate lesions in mammograms, which are highly suspicious signs of breast cancer and are characterized by a radiating pattern of spicules with a bright center. There are plenty of work regarding stellate lesions and architectural distortions. Most of them are based on the extraction of local features such as the gradient orientation, or the pixel orientation and more generally statistics of the orientation histogram. These features are then used in a classifier to assign to each pixel its probability of malignancy. The a contrario methods sets a different framework for the detection of geometric structures in images. A naïve model on line structures is defined and is often chosen as the uniform model, which is not well suited for mammograms where there is a privileged orientation of spicules. We propose in this thesis an anisotropic a contrario framework for a better description of the normal distribution of spicules in a mammogram. The designed models describe the convergence of some of the line structures to a single point. They either concern the lines or the line segments of an image wether we detect global or local convergences. In the last case we explore several definitions of the number of false alarms and several a contrario models on synthetic, natural images and mammograms. We give the a contrario models as two terms mixtures, one uniform and the other of Gaussian type. These are parametric models and we propose an algorithm to estimate their parameters (the point of convergence is estimated with an a contrario method and the other parameters are approached by maximization of the likelihood). The resulting models are used as a contrario models and the results are compared with those against the uniform model.

Improving spectral-utilization is a core focus to cater the ever-increasing demand in data rate and system capacity required for the development of 5G. This dissertation focuses on three spectrum-reuse technologies that are envisioned to play an important role in 5G networks: device-to-device (D2D), full-duplex (FD), and nonorthogonal multiple access (NOMA). D2D allows proximal user-equipments (UEs) to bypass the cellular base-station and communicate with their intended receiver directly. In underlay D2D, the D2D UEs utilize the same spectral resources as the cellular UEs. FD communication allows a transmit-receive pair to transmit simultaneously on the same frequency channel. Due to the overwhelming self-interference encountered, FD was not possible until very recently courtesy of advances in transceiver design. NOMA allows multiple receivers (transmitters) to communicate with one transmitter (receiver) in one time-frequency resource-block by multiplexing in the power domain. Successive-interference cancellation is used for NOMA decoding. Each of these techniques significantly improves spectral efficiency and consequently data rate and throughput; however, the price paid is increased interference. Since each of these technologies allow multiple transmissions within a cell on a time-frequency resource-block, they result in interference within the cell (i.e., intracell interference). Additionally, due to the increased communication, they increase network interference from outside the cell under consideration as well (i.e., increased intercell interference). Real networks are becoming very dense; as a result, the impact of intercell interference coming from the entire network is significant. As such, using models that consider a single-cell/few-cell scenarios result in misleading conclusions. Hence, accurate modeling requires considering a large network. In this context, stochastic geometry is a powerful tool for analyzing random patterns of points such as those found in wireless networks. In this dissertation, stochastic geometry is used to model and analyze the different technologies that are to be deployed in 5G networks. This gives us insight into the network performance, showing us the impacts of deploying a certain technology into real 5G networks. Additionally, it allows us to propose schemes for integrating such technologies, mode-selection, parameter-selection, and resource-allocation that enhance the parameters of interest in the network such as data rate, coverage, and secure communication.

Wireless coverage becomes one of the most significant needs of modern society because of its importance in various applications such as health, distance education, industry, and much more. Therefore, it is essential to provide wireless coverage worldwide, including remote areas, rural areas, and poorly served locations. Recent advances in Low Earth Orbit (LEO) satellite communications provide a promising solution to address these issues in poorly served locations. The thesis studies the performance of a multi-level LEO satellite communication system. More precisely, we model the LEO satellites’ location as Binomial Point Process (BPP) on a spherical surface at n different altitudes given that the number of satellites at each altitude ak is Nk where 1 ≤ k ≤ n and study the distance distribution. The distance distribution is characterized in two categories depending on the location of the observation point: contact distance and the nearest neighbor distance. For that proposed model, we study the user coverage probability by using tools from stochastic geometry for a scenario where satellite earth stations (ESs) with two antennas are deployed on the ground where one of the antennas communicates with the user while the other communicates with LEO satellite. Additionally, we consider a practical use case where satellite communication systems are deployed to increase coverage in remote and rural areas. For that purpose, we compare the coverage probability of the satellite-based communication system in such regions with the coverage probability in case of relying on the nearest anchored base station (ABS), which is usually located at far distances from rural and remote areas.

The demand for wireless communication is ceaselessly increasing in terms of the number of subscribers and services. Future generations of cellular networks are expected to allow not only humans but also machines to be immersively connected. However, the radio frequency spectrum is already fully allocated. Therefore, developing techniques to increase spectrum efficiency has become necessary. This dissertation analyzes two spectrum sharing techniques that enable efficient utilization of the available radio resources in cellular networks. The first technique, called full-duplex (FD) communication, uses the same spectrum to transmit and receive simultaneously. Using stochastic geometry tools, we derive a closed-form expression of an upper-bound for the maximum achievable uplink ergodic rate in FD cellular networks. We show that the uplink transmission is vulnerable to the new interference introduced by FD communications (interference from the downlink transmission in other cells), especially when the disparity in transmission power between the uplink and downlink is considerable. We further show that adjusting the uplink transmission power according to the interference power level and the channel gain can improve the uplink performance in full-duplex cellular networks. Moreover, we propose an interference management technique that allows a flexible overlap between the spectra occupied by the downlink and uplink transmissions. The flexible overlap is optimized along with the user-to-base station association, the power allocation and the channel allocation in order to maximize a network-wide utility function. The second spectrum sharing technique, called non-orthogonal multiple access (NOMA), allows a transmitter to communicate with multiple receivers through the same frequency-time resource unit. We analyze the implementation of such a scheme in the downlink of cellular networks, more precisely, in the downlink of fog radio access networks (FogRANs). FogRAN is a network architecture that takes full advantage of the edge devices capability to process and store data. We propose managing the interference for NOMA-based FogRAN to improve the network performance by jointly optimizing user scheduling, the power allocated to each resource block and the division of power between the multiplexed users. The simulation results show that significant performance gains can be achieved through proper resource allocation with both studied spectrum sharing techniques.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22589号 / 情博第726号 / 新制||情||124(附属図書館) / 京都大学大学院情報学研究科通信情報システム専攻 / (主査)教授 守倉 正博, 教授 原田 博司, 教授 大木 英司 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The ever-growing demands for wireless technologies necessitate the evolution of next generation wireless networks that fulfill the diverse wireless users requirements. However, upscaling existing wireless networks implies upscaling an intrinsic component in the wireless domain; the aggregate network interference. Being the main performance limiting factor, it becomes crucial to develop a rigorous analytical framework to accurately characterize the out-of-cell interference, to reap the benefits of emerging networks. Due to the different network setups and key performance indicators, it is essential to conduct a comprehensive study that unifies the various network configurations together with the different tangible performance metrics. In that regard, the focus of this thesis is to present a unified mathematical paradigm, based on Stochastic Geometry, for large-scale networks with different antenna/network configurations. By exploiting such a unified study, we propose an efficient automated network design strategy to satisfy the desired network objectives. First, this thesis studies the exact aggregate network interference characterization, by accounting for each of the interferers signals in the large-scale network. Second, we show that the information about the interferers symbols can be approximated via the Gaussian signaling approach. The developed mathematical model presents twofold analysis unification for uplink and downlink cellular networks literature. It aligns the tangible decoding error probability analysis with the abstract outage probability and ergodic rate analysis. Furthermore, it unifies the analysis for different antenna configurations, i.e., various multiple-input multiple-output (MIMO) systems. Accordingly, we propose a novel reliable network design strategy that is capable of appropriately adjusting the network parameters to meet desired design criteria. In addition, we discuss the diversity-multiplexing tradeoffs imposed by differently favored MIMO schemes, describe the relation between the diverse network parameters and configurations, and study the impact of temporal interference correlation on the performance of large-scale networks. Finally, we investigate some interference management techniques by exploiting the proposed framework. The proposed framework is compared to the exact analysis as well as intensive Monte Carlo simulations to demonstrate the model accuracy. The developed work casts a thorough inclusive study that is beneficial to deepen the understanding of the stochastic deployment of the next-generation large-scale wireless networks and predict their performance.

The Internet of Things (IoT) is a foundational building block for the upcoming information revolution. Particularly, the IoT bridges the cyber domain to anything within our physical world which enables unprecedented monitoring, connectivity, and smart control. The utilization of Unmanned Aerial Vehicles (UAVs) can offer an extra level of flexibility which results in more advanced and efficient connectivity and data aggregation. In the first part of the thesis, we focus on the optimal IoT devices placement and, the spectral and energy budgets management for accurate source estimation. Practical aspects such as measurement accuracy, communication quality, and energy harvesting are considered. The problem is formed such that a set of cheap and expensive sensors are placed to minimize the estimation error under limited system cost. The IoT revolution relies on aggregating big data from massive numbers of devices that are widely scattered in our environment. These devices are expected to be of low- complexity, low-cost, and limited power supply, which impose stringent constraints on the network operation. Aerial data transmission offers strong line-of-sight links and flexible/instant deployment. The UAV-enabled IoT networks can, for instance, offer solutions to avoid and manage natural disasters such as forest fire. We investigate in this thesis the aerial data aggregation for field estimation, wildfire detection, and connection coverage enhancement via UAVs. To accomplish the network task, the field of interest is divided into several subregions over which the UAVs hover to collect samples from the underlying nodes. To this end, we formulate and solve optimization problems to minimize total hovering and traveling times. This goal is fulfilled by optimizing the UAV hovering locations, the hovering time at each location, and the trajectory traversed between hovering locations. Finally, we propose the utilization of the tethered UAV (T-UAV) to assist the terrestrial network, where the tether provides power supply and connects the T-UAV to the core network through a high capacity link. The T-UAV however has limited mobility due to the limited tether length. A stochastic geometry-based analysis is provided for the optimal coverage probability of T-UAV-assisted cellular networks.

La tâche de répondre à une demande croissante pour une meilleure qualité de l'expérience utilisateur dans les communications sans fil, est contestée par la quantité d'énergie consommée par les technologies concernées et les méthodes employées. Sans surprise, le problème de la réduction de la consommation d'énergie doit être abordé à diverses couches de l'architecture de réseau et de diverses directions. Cette thèse traite de certains aspects cruciaux de la couche physique de l'architecture de réseau sans fil afin de trouver des solutions efficaces d'énergie. Dans la première partie de cette thèse, nous explorons l'idée de l'efficacité énergétique à un niveau fondamental. A commencer par répondre aux questions telles que: - Qu'est-ce que la forme physique d'information ?, nous construisons un dispositif de communication simple afin d'isoler certaines étapes clés dans le processus physique de la communication et nous dire comment elles affectent l'efficacité énergétique d'une communication système. Dans la deuxième partie, nous utilisons des outils de la géométrie stochastique pour modéliser théoriquement réseaux cellulaires afin d'analyser l'efficacité énergétique du système. L'exploitation de la traçabilité d'une telle modélisation mathématique, nous explorons les conditions dans lesquelles la consommation d'énergie peut être réduite. En outre, dans cette partie, nous introduisons le concept de la mise en cache des données des utilisateurs à la périphérie du réseau (à savoir le final ac BS qui est en contact avec l'utilisateur) et de montrer quantitativement comment la mise en cache peut aider à améliorer l'efficacité énergétique d'un cellulaire réseau. Nous tenons également à ce traitement à un ac Hetnet scénario (à savoir quand il y a plus d'un type de glspl déployé BS) et étudions divers indicateurs de performance clés. Nous explorons également les conditions où l'efficacité énergétique d'un tel système peut être améliorée. Les résultats de thèse fournissent quelques idées clés pour améliorer l'efficacité énergétique dans un réseau cellulaire sans fil contribuant ainsi à l'avancement vers la prochaine génération (5 G) des réseaux cellulaires. / The task of meeting an ever growing demand for better quality of user experience in wireless communications, is challenged by the amount of energy consumed by the technologies involved and the methods employed. Not surprisingly, the problem of reducing energy consumption needs to be addressed at various layers of the network architecture and from various directions. This thesis addresses some crucial aspects of the physical layer of wireless network architecture in order to find energy efficient solutions.In the first part of this thesis, we explore the idea of energy efficiency at a fundamental level. Starting with answering questions such as - emph{What is the physical form of `information'?}, we build a simple communication device in order to isolate certain key steps in the physical process of communication and we comment on how these affect the energy efficiency of a communication system.In the second part, we use tools from stochastic geometry to theoretically model cellular networks so as to analyze the energy efficiency of the system. Exploiting the tractability of such a mathematical modeling, we explore the conditions under which the consumption of energy can be reduced. Further in this part, we introduce the concept of caching users' data at the edge of the network (namely the final ac{BS} that is contact with the user) and show quantitatively how caching can help improve the energy efficiency of a cellular network. We also extend this treatment to a ac{HetNet} scenario (namely when there are more than one type of glspl{BS} deployed) and study various key performance metrics. We also explore the conditions where energy efficiency of such a system can be improved.The results in thesis provide some key ideas to improve energy efficiency in a wireless cellular network thereby contributing to the advancement towards the next generation (5G) cellular networks.