The availability of location estimates of mobile devices (MDs) is vital for several important applications such as law enforcement, disaster management, battlefield operations, vehicular communication, traffic safety, emergency response, and preemption. While global positioning system (GPS) is usually sufficient in outdoor clear sky conditions, its functionality is limited in urban canyons and indoor locations due to the absence of clear line-of-sight between the MD to be localized and a sufficient number of navigation satellites. In such scenarios, the ubiquitous nature of cellular networks makes them a natural choice for localization of MDs. Traditionally, localization in cellular networks has been studied using system level simulations by fixing base station (BS) geometries. However, with the increasing irregularity of the BS locations (especially due to capacity-driven small cell deployments), the system insights obtained by considering simple BS geometries may not carry over to real-world deployments. This necessitates the need to study localization performance under statistical (random) spatial models, which is the main theme of this work. In this thesis, we use powerful tools from stochastic geometry and point process theory to develop a tractable analytical model to study the localizability (ability to get a location fix) of an MD in single-tier and heterogeneous cellular networks (HetNets). More importantly, we study how availability of information about the location of proximate BSs at the MD impacts localizability. To this end, we derive tractable expressions, bounds, and approximations for the localizability probability of an MD. These expressions depend on several key system parameters, and can be used to infer valuable system insights. Using these expressions, we quantify the gains achieved in localizability of an MD when information about the location of proximate BSs is incorporated in the model. As expected, our results demonstrate that localizability improves with the increase in density of BS deployments. / Master of Science

Exact characterization and performance analysis of wireless networks should incorporate dependencies or correlations in space and time, i.e., study how the network performance varies spatially and temporally while having prior information about the performance at previous locations and time slots. This spatio-temporal correlation in wireless networks is usually characterized by studying metrics such as joint coverage probability at two spatial locations/time slots or spatio-temporal correlation coefficient. While developing models and analytical expressions for studying the two extreme cases of spatio-temoral correlation - i) uncorrelated scenario and ii) fully correlated scenario are easier, studying the intermediate case is non-trivial. In this thesis, we develop realistic and tractable analytical frameworks based on random spatial models (using tools from stochastic geometry) for modeling and analysis of correlation in cellular networks. With an ever increasing data demand, caching popular content in the storage of small cells (small cell caching) or the memory of user devices (device caching) is seen as a good alternative to offload demand from macro base stations and reduce backhaul loads. After providing generic results for traditional cellular networks, we study two applications exploiting spatio-temporal correlation in cache-enabled cellular networks. First, we determine the optimal cache content to be stored in the cache of a small cell network that maximizes the hit probability and minimizes the reception energy for the two extreme cases of correlation. Our results concretely demonstrate that the optimal cache contents are significantly different for the two correlation scenarios, thereby indicating the need of correlation-aware caching strategies. Second, we look at a distributed caching scenario in user devices and show that spatio-temporal correlation (user mobility) can be exploited to improve the network performance (in terms of coverage probability and local delay) significantly. / Master of Science

Determining the locations of devices in mobile ad-hoc networks (MANETs), wireless sensor networks (WSNs), and cellular networks has many important applications. In MANETs, which are useful in disaster recovery, rescue operations, and military communications, location information is used to enable location-aided routing and geodesic packet forwarding. In WSNs, whose applications include environmental monitoring (e.g., for precision agriculture) and asset tracking in warehouses, not only is location information useful for the self-organization of the network, but in addition, tying locations to the sensor observations is crucial for adding meaning to the sensed data. In cellular networks, location information is used to provide subscribers with location-based services in addition to providing public service answering points with potentially life-saving location information during emergency calls. These applications are largely not new, which is evidenced by the fact that the literature is quite rich with localization studies presented over the span of many years. Because of this, it may be surprising to learn that there is a lack of analyses concerning the fundamental factors impacting localization performance. Fundamentally, localization performance depends upon three factors: (i) the number of devices participating in the localization procedure, (ii) the locations of the participating devices, and (iii) the quality of the positioning observations gathered from the participating devices. For the most part, these factors cannot reasonably be considered deterministic. Instead, at any point in time, random effects within a network and its surroundings will determine these factors for individual positioning scenarios. Unfortunately, there are currently no analytical approaches for characterizing localization performance over these random factors. Instead, researchers either provide analytical results for a deterministic set of factors or use complex system-level simulations to obtain general performance insights. While the latter certainly averages over the random factors, the validity of the results is limited by the simulation assumptions. Any change in a network parameter requires running a new time-consuming simulation. In this dissertation, we address current deficiencies in several ways. We present a new model for tractably analyzing network localization fundamentals. This is demonstrated through fundamental analyses of hearability and geometry. Further, collaboration among non-reference devices has recently garnered increasing interest from the research community as a means to (i) improve positioning accuracy and (ii) improve positioning availability. We present fundamental analyses of both of these potential benefits. As a result of our work, we not only characterize several key performance metrics, we also demonstrate that there exist new tractable ways to analyze localization performance. / Ph. D.

A major component of future communication systems is vehicle-to-vehicle (V2V) communications, in which vehicles along roadways transfer information directly among themselves and with roadside infrastructure. Despite its numerous potential advantages, V2V communication suffers from one inherent shortcoming: the stochastic and time-varying nature of the node distributions in a vehicular ad hoc network (VANET) often leads to loss of connectivity and lower coverage. One possible way to improve this coverage is to allow the vehicular nodes to connect to the more reliable cellular network, especially in cases of loss of connectivity in the vehicular network. In this thesis, we analyze this possibility of boosting performance of VANETs, especially their node coverage, by taking assistance from the cellular network. The spatial locations of the vehicular nodes in a VANET exhibit a unique characteristic: they always lie on roadways, which are predominantly linear but are irregularly placed on a two dimensional plane. While there has been a signifcant work on modeling wireless networks using random spatial models, most of it uses homogeneous planar Poisson Point Process (PPP) to maintain tractability, which is clearly not applicable to VANETs. Therefore, to accurately capture the spatial distribution of vehicles in a VANET, we model the roads using the so called Poisson Line Process and then place vehicles randomly on each road according to a one-dimensional homogeneous PPP. As is usually the case, the locations of the cellular base stations are modeled by a planar two-dimensional PPP. Therefore, in this thesis, we propose a new two-tier model for cellular-assisted VANETs, where the cellular base stations form a planar PPP and the vehicular nodes form a one-dimensional PPP on roads modeled as undirected lines according to a Poisson Line Process. The key contribution of this thesis is the stochastic geometric analysis of a maximum power-based cellular-assisted VANET scheme, in which a vehicle receives information from either the nearest vehicle or the nearest cellular base station, based on the received power. We have characterized the network interference and obtained expressions for coverage probability in this cellular-assisted VANET, and successfully demonstrated that using this switching technique can provide a significant improvement in coverage and thus provide better vehicular network performance in the future. In addition, this thesis also analyzes two threshold-distance based schemes which trade off network coverage for a reduction in additional cellular network load; notably, these schemes also outperform traditional vehicular networks that do not use any cellular assistance. Thus, this thesis mathematically validates the possibility of improving VANET performance using cellular networks. / Master of Science

In this thesis, new methods for proving concentration inequalities for Poisson functionals are developed. The focus is on techniques that are based on logarithmic Sobolev inequalities, but also results that are based on the convex distance for Poisson processes are presented. The general methods are applied to a variety of functionals associated with random geometric graphs. In particular, concentration inequalities for subgraph and component counts are proved. Finally, the established concentration results are used to derive strong laws of large numbers for subgraph and component counts associated with random geometric graphs.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Atualmente, a tecnologia celular està presente em todos os aspectos da vida cotidiana: lares, escritÃrios, indÃstrias, etc. Tal tecnologia teve um rÃpido crescimento durante as duas Ãltimas dÃcadas tentando acompanhar o aumento do volume de trÃfego nas redes de comunicaÃÃo sem-fio. Naturalmente, ao propor modelos mais realistas possÃveis, com o propÃsito de caracterizar fenÃmenos que afetam a qualidade do sinal ou o desempenho do sistema, novas ideias, concepÃÃes e outras ferramentas surgem para descrever tais situaÃÃes. Este à o caso da Geometria EstocÃstica ou, particularmente, o processo pontual de Poisson, o qual vem sendo frequentemente utilizado como um modelo de rede celular, a partir da localizaÃÃo aleatÃria dos nÃs na rede. Diante desta ferramenta matemÃtica, à possÃvel implantar estaÃÃes rÃdio base na rede externa celular, bem como pontos de acesso baseados em picocÃlulas, femtocÃlulas, etc. AlÃm disso, permite-se quantificar a interferÃncia, Ãrea de cobertura, probabilidade de outage, dentre outros. Estes resultados tambÃm levam em consideraÃÃo o impacto de mobilidade no desempenho de tais redes. Nesse contexto, este trabalho analisarà redes ad-hoc sem-fio propondo expressÃes analÃticas para as seguintes mÃtricas de caracterizaÃÃo de desempenho: interferÃncia e conectividade de transmissÃo. Essas mÃtricas levam em consideraÃÃo tanto a razÃo sinal-ruÃdo mais interferÃncia (signal-to-interference-plus-noise ratio (SINR)) como a razÃo sinal-interferÃnca (signal-to-interference ratio (SIR)), em que neste caso, a potÃncia de ruÃdo à considerada nula. Especificamente, o fenÃmeno interferÃncia serà caracterizado via modelo shot-noise segundo um processo pontual chamado de processo pontual marcado (marked point process (MPP)), sendo este mais realista do que o tradicional modelo de Poisson. AlÃm disso, este tipo de modelo incorpora os efeitos de propagaÃÃo de rÃdio de pequena e larga escala e sobretudo as diferentes tecnologias de detecÃÃo e tratamento de sinal. Paralelamente, adotaremos um canal de rÃdio com desvanecimento Nakagami-m. Por fim, o tratamento matemÃtico para o modelo proposto torna-se um fator desafiador deste trabalho, visto que, tais resultados generalizam alguns jà publicados na literatura, os quais adotam alguns parÃmetros menos realistas. / Currently, cellular technology is present in all aspects of everyday life: homes, offices, industries, etc. Such technology had grown rapidly over the last two decades trying to follow up with the increased traffic volume on the networks of wireless communication. Naturally, to propose possible more realistic models, with the purpose of characterizing phenomena that affect the signal quality or performance system, new ideas, concepts and other tools to describe such situations arise. This is the case of Stochastic Geometry or, particularly, the point process Poisson, which has been often used as a model for cellular network from the random node locations in the network. Faced with this mathematical tool, it is possible deploy base stations in cellular external network and access points based picocells, femtocells, etc. Moreover, it allows to quantify the interference, coverage area, outage probability, among others. These results also consider the impact of mobility on the performance of such networks. In this context, this thesis will analyze ad-hoc wireless networks offering analytical expressions for the following metrics of performance characterization: interference and transmission connections. These metrics take into account both signal-to-interference-plus-noise ratio (SINR) and signal-to-interference ratio (SIR), in which case, the noise power is considered null. Specifically, the interference phenomena will be characterized via shot-noise model according to a point process called marked point process (MPP), this being more realistic than the traditional Poisson model. Furthermore, this type of model incorporates effects of radio propagation small and large scale, mainly the different technologies for the detection and signal processing. In parallel, we will adopt a radio channel with Nakagami-m fading. Finally, the mathematical treatment for the proposed model becomes a challenging factor in this work, since such results generalize some already published in the literature, which adopt some less realistic parameters.

Large-scale blockages like buildings affect the performance of urban cellular networks, especially in the millimeter-wave frequency band. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages, and quantifies their effects on the performance of cellular networks. Specifically, random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane, which is called a Boolean scheme. The distribution of the number of blockages in a link is proven to be Poisson with parameter dependent on the length of the link, which leads to the distribution of penetration losses of a single link. A path loss model that incorporates the blockage effects is proposed, which matches experimental trends observed in prior work. The blockage model is applied to analyze blockage effects on cellular networks assuming blockages are impenetrable, in terms of connectivity, coverage probability, and average rate. Analytic results show while buildings may block the desired signal, they may still have a positive impact on network performance since they also block more interference. / text

This dissertation is in the area of pervasive computing. It focuses on designing platforms for storing, querying, and computing contextual information. More specifically, we are interested in platforms for storing and querying spatio-temporal events where queries exhibit locality. Recent advances in sensor technologies have made possible gathering a variety of information on the status of users, the environment machines, etc. Combining this information with computation we are able to extract context, i.e., a filtered high-level description of the situation. In many cases, the information gathered exhibits locality both in space and time, i.e., an event is likely to be consumed in a location close to the location where the event was produced, at a time whic h is close to the time the event was produced. This dissertation builds on this observation to create better platforms for computing context. We claim three key contributions. We have studied the problem of designing and optimizing spatial organizations for exchanging context. Our thesis has original theoretical work on how to create a platform based on cells of a Voronoi diagram for optimizing the energy and bandwidth required for mobiles to exchange contextual information t hat is tied to specific locations in the platform. Additionally, we applied our results to the problem of optimizing a system for surveilling the locations of entities within a given region. We have designed a platform for storing and querying spatio-temporal events exhibiting locality. Our platform is based on a P2P infrastructure of peers organized based on the Voronoi diagram associated with their locations to store events based on their own associated locations. We have developed theoretical results based on spatial point processes for the delay experienced by a typical query in this system. Additionally, we used simulations to study heuristics to improve the performance of our platform. Finally, we came up with protocols for the replicated storage of events in order to increase the fault-tolerance of our platform. Finally, in this thesis we propose a design for a platform, based on RFID tags, to support context-aware computing for indoor spaces. Our platform exploits the structure found in most indoor spaces to encode contextual information in suitably designed RFID tags. The elements of our platform collaborate based on a set of messages we developed to offer context-aware services to the users of the platform. We validated our research with an example hardware design of the RFID tag and a software emulation of the tag's functionality. / text

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Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / Triggered by the popularity of smart devices, wireless traffic volume and device connectivity have been growing exponentially during recent years. The next generation of wireless networks, i.e., 5G, is a promising solution to satisfy the increasing data demand through combination of key enabling technologies such as deployment of a high density of access points (APs), referred to as ultra-densification, and utilization of a large amount of bandwidth in millimeter wave (mmWave) bands. However, due to unfavorable propagation characteristics, this portion of spectrum has been under-utilized. As a solution, large antenna arrays that coherently direct the beams will help overcome the hostile characteristics of mmWave signals. Building networks of directional antennas has given rise to many challenges in wireless communication design. One of the main challenges is how to incorporate 5G technology into current networks and design uniform structures that bring about higher network performance and quality of service. In addition, the other factor that can be severely impacted is interference behavior. This is basically due to the fact that, narrow beams are highly vulnerable to obstacles in the environment. Motivated by these factors, the present dissertation addresses some key challenges associated with the utilization of mmWave signals. As a first step towards this objective, we first propose a framework of how 5G mmWave access points can be integrated into the current wireless structures and offer higher data rates. The related resource sharing problem has been also proposed and solved, within such a framework. Secondly, to better understand and quantify the interference behavior, we propose interference models for mmWave networks with directional beams for both large scale and finite-sized network dimension. The interference model is based on our proposed blockage model which captures the average number of obstacles that cause a complete link blockage, given a specific signal beamwidth. The main insight from our analysis shows that considering the effect of blockages leads to a different interference profile. Furthermore, we investigate how to model interference considering not only physical layer specifications but also upper layers constraints. In fact, upper network layers, such as medium access control (MAC) protocol controls the number of terminals transmitting simultaneously and how resources are shared among them, which in turn impacts the interference power level. An interesting result from this analysis is that, from the receiving terminal standpoint, even in mmWave networks with directional signals and high attenuation effects, we still need to maintain some sort of sensing where all terminals are not allowed to transmit their packets, simultaneously. The level of such sensing depends on the terminal density. Lastly, we provide a framework to detect the network regime and its relation to various key deployment parameters, leveraging the proposed interference and blockage models. Such regime detection is important from a network management and design perspective. Based on our finding, mmWave networks can exhibit either an interference-limited regime or a noise-limited regime, depending on various factors such as access point density, blockage density, signal beamwidth, etc.