The mathematical modeling and performance analysis of cellular networks have seen a major paradigm shift with the application of stochastic geometry. The main purpose of stochastic geometry is to endow probability distributions on the locations of the base stations (BSs) and users in a network, which, in turn, provides an analytical handle on the performance evaluation of cellular networks. To preserve the tractability of analysis, the common practice is to assume complete spatial randomness} of the network topology. In other words, the locations of users and BSs are modeled as independent homogeneous Poisson point processes (PPPs). Despite its usefulness, the PPP-based network models fail to capture any spatial coupling between the users and BSs which is dominant in a multi-tier cellular network (also known as the heterogeneous cellular networks (HetNets)) consisting of macro and small cells. For instance, the users tend to form hotspots or clusters at certain locations and the small cell BSs (SBSs) are deployed at higher densities at these locations of the hotspots in order to cater to the high data demand. Such user-centric deployments naturally couple the locations of the users and SBSs. On the other hand, these spatial couplings are at the heart of the spatial models used in industry for the system-level simulations and standardization purposes. This dissertation proposes fundamentally new spatial models based on stochastic geometry which closely emulate these spatial couplings and are conductive for a more realistic and fine-tuned performance analysis, optimization, and design of cellular networks. First, this dissertation proposes a new class of spatial models for HetNets where the locations of the BSs and users are assumed to be distributed as Poisson cluster process (PCP). From the modeling perspective, the proposed models can capture different spatial couplings in a network topology such as the user hotspots and user BS coupling occurring due to the user-centric deployment of the SBSs. The PCP-based model is a generalization of the state-of-the-art PPP-based HetNet model. This is because the model reduces to the PPP-based model once all spatial couplings in the network are ignored. From the stochastic geometry perspective, we have made contributions in deriving the fundamental distribution properties of PCP, such as the distance distributions and sum-product functionals, which are instrumental for the performance characterization of the HetNets, such as coverage and rate. The focus on more refined spatial models for small cells and users brings to the second direction of the dissertation, which is modeling and analysis of HetNets with millimeter wave (mm-wave) integrated access and backhaul (IAB), an emerging design concept of the fifth generation (5G) cellular networks. While the concepts of network densification with small cells have emerged in the fourth generation (4G) era, the small cells can be realistically deployed with IAB since it solves the problem of high capacity wired backhaul of SBSs by replacing the last-mile fibers with mm-wave links. We have proposed new stochastic geometry-based models for the performance analysis of IAB-enabled HetNets. Our analysis reveals some interesting system-design insights: (1) the IAB HetNets can support a maximum number of users beyond which the data rate drops below the rate of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no rate gain is observed with the addition of more SBSs. The third and final direction of this dissertation is the combination of machine learning and stochastic geometry to construct a new class of data driven network models which can be used in the performance optimization and design of a network. As a concrete example, we investigate the classical problem of wireless link scheduling where the objective is to choose an optimal subset of simultaneously active transmitters (Tx-s) from a ground set of Tx-s which will maximize the network-wide sum-rate. Since the optimization problem is NP-hard, we replace the computationally expensive heuristic by inferring the point patterns of the active Tx-s in the optimal subset after training a determinantal point process (DPP). Our investigations demonstrate that the DPP is able to learn the spatial interactions of the Tx-s in the optimal subset and gives a reasonably accurate estimate of the optimal subset for any new ground set of Tx-s. / Doctor of Philosophy / The high speed global cellular communication network is one of the most important technologies, and it continues to evolve rapidly with every new generation. This evolution greatly depends on observing performance-trends of the emerging technologies on the network models through extensive system-level simulations. Since these simulation models are extremely time-consuming and error prone, the complementary analytical models of cellular networks have been an area of active research for a long time. These analytical models are intended to provide crisp insights on the network behavior such as the dependence of network performance metrics (such as coverage or rate) on key system-level parameters (such as transmission powers, base station (BS) density) which serve as the prior knowledge for more fine-tuned simulations. Over the last decade, the analytical modeling of the cellular networks has been driven by stochastic geometry. The main purpose of stochastic geometry is to endow the locations of the base stations (BSs) and users with probability distributions and then leverage the properties of these distributions to average out the spatial randomness. This process of spatial averaging allows us to derive the analytical expressions of the system-level performance metrics despite the presence of a large number of random variables (such as BS and user locations, channel gains) under some reasonable assumptions. The simplest stochastic geometry based model of cellular networks, which is also the most tractable, is the so-called Poisson point process (PPP) based network model. In this model, users and BSs are assumed to be distributed as independent homogeneous PPPs. This is equivalent to saying that the users and BSs independently and uniformly at random over a plane. The PPP-based model turned out to be a reasonably accurate representation of the yesteryear’s cellular networks which consisted of a single tier of macro BSs (MBSs) intended to provide a uniform coverage blanket over the region. However, as the data-hungry devices like smart-phones, tablets, and application like online gaming continue to flood the consumer market, the network configuration is rapidly deviating from this baseline setup with different spatial interactions between BSs and users (also termed spatial coupling) becoming dominant. For instance, the user locations are far from being homogeneous as they are concentrated in specific areas like residential and commercial zones (also known as hotspots). Further, the network, previously consisting of a single tier of macro BSs (MBSs), is becoming increasingly heterogeneous with the deployment of small cell BSs (SBSs) with small coverage footprints and targeted to serve the user hotspots. It is not difficult to see that the network topology with these spatial couplings is quite far from complete spatial randomness which is the basis of the PPP-based models. The key contribution of this dissertation is to enrich the stochastic geometry-based mathematical models so that they can capture the fine-grained spatial couplings between the BSs and users. More specifically, this dissertation contributes in the following three research directions. Direction-I: Modeling Spatial Clustering. We model the locations of users and SBSs forming hotspots as Poisson cluster processes (PCPs). A PCP is a collection of offspring points which are located around the parent points which belong to a PPP. The coupling between the locations of users and SBSs (due to their user-centric deployment) can be introduced by assuming that the user and SBS PCPs share the same parent PPP. The key contribution in this direction is the construction of a general HetNet model with a mixture of PPP and PCP-distributed BSs and user distributions. Note that the baseline PPP-based HetNet model appears as one of the many configurations supported by this general model. For this general model, we derive the analytical expressions of the performance metrics like coverage probability, BS load, and rate as functions of the coupling parameters (e.g. BS and user cluster size). Direction-II: Modeling Coupling in Wireless Backhaul Networks. While the deployment of SBSs clearly enhances the network performance in terms of coverage, one might wonder: how long network densification with tens of thousands of SBSs can meet the everincreasing data demand? It turns out that in the current network setting, where the backhaul links (i.e. the links between the BSs and core network) are still wired, it is not feasible to densify the network beyond some limit. This backhaul bottleneck can be overcome if the backhaul links also become wireless and the backhaul and access links (link between user and BS) are jointly managed by an integrated access and backhaul (IAB) network. In this direction, we develop the analytical models of IAB-enabled HetNets where the key challenge is to tackle new types of couplings which exist between the rates on the wireless access and backhaul links. Such couplings exist due to the spatial correlation of the signal qualities of the two links and the number of users served by different BSs. Two fundamental insights obtained from this work are as follows: (1) the IAB HetNets can support a maximum number of users beyond which the network performance drops below that of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no performance gain is observed with the addition of more SBSs. Direction-III: Modeling Repulsion. In this direction, we focus on modeling another aspect of spatial coupling imposed by the intra-point repulsion. Consider a device-to-device (D2D) communication scenario, where some users are transmitting some on-demand content locally cached in their devices using a common channel. Any reasonable multiple access scheme will ensure that two nearly users are never simultaneously active as they will cause severe mutual interference and thereby reducing the network-wide sum rate. Thus the active users in the network will have some spatial repulsion. The locations of these users can be modeled as determinantal point processes (DPPs). The key property of DPP is that it forms a bridge between stochastic geometry and machine learning, two otherwise non-overlapping paradigms for wireless network modeling and design. The main focus in this direction is to explore the learning framework of DPP and bring together advantages of stochastic geometry and machine learning to construct a new class of data-driven analytical network models.

Instantaneous and ergodic rates are two of the most commonly used metrics to characterize throughput of wireless networks. Roughly speaking, the former characterizes the rate achievable in a given time slot, whereas the latter is useful in characterizing average rate achievable over a long time period. Clearly, the reality often lies somewhere in between these two extremes. Consequently, in this work, we define and characterize a more realistic N-slot average rate (achievable rate averaged over N time slots). This N-slot average rate metric refines the popular notion of ergodic rate, which is defined under the assumption that a user experiences a complete ensemble of channel and interference conditions in the current session (not always realistic, especially for short-lived sessions). The proposed metric is used to study the performance of typical nodes in both ad hoc and downlink cellular networks. The ad hoc network is modeled as a Poisson bipolar network with a fixed distance between each transmitter and its intended receiver. The cellular network is also modeled as a homogeneous Poisson point process. For both these setups, we use tools from stochastic geometry to derive the distribution of N-slot average rate in the following three cases: (i) rate across N time slots is completely correlated, (ii) rate across N time slots is independent and identically distributed, and (iii) rate across N time slots is partially correlated. While the reality is close to third case, the exact characterization of the first two extreme cases exposes certain important design insights. / Master of Science / Choice of an appropriate metric is essential for accurate design and analysis of wireless networks. The two most popular metrics used to characterize data rate or throughput of wireless networks are instantaneous and ergodic rates. While instantaneous rate characterizes the throughput achievable in a given time slot, the ergodic rate characterizes the average achievable throughput over a long period of time. But often, the real-world scenarios fall in between these two extremes, where the network performance is to be characterized over a given finite number of time slots. Hence, we define and characterize a new suitable metric <i>N-slot average rate</i>, which is the achievable rate averaged over <i>N</i> time slots. Using this metric, we develop an analytical framework to study the performance of typical nodes in both ad hoc and downlink cellular networks. We model these networks using homogeneous Poisson point processes and characterize the <i>N</i>-slot average throughput using the tools of stochastic geometry. Accounting for the prominent cases of network mobility, we derive the distribution of <i>N</i>-slot average rate in the following three scenarios: rate is completely correlated across <i>N</i> time slots, rate is independent and identically distributed across N time slots, and rate is partially correlated across <i>N</i> time slots. We studied the impact of various system parameters on our metric and also discussed key insights from our results.

Managing interference is the main technical challenge in wireless networks. Multiple input multiple output (MIMO) methods are key components to overcome the interference bottleneck and deliver higher data rates. The most efficient MIMO techniques require channel state information (CSI). In practice, this information is inaccurate due to errors in CSI acquisition, as well as mobility and delay. CSI inaccuracy reduces the performance gains provided by MIMO. When compounded with uncoordinated intercell interference, the degradation in MIMO performance is accentuated. This dissertation investigates the impact of CSI inaccuracy on the performance of increasingly complex interference limited networks, starting with a single interferer scenario, continuing to a heterogeneous network with a femtocell overlay, and finishing with a clustered multicell coordination model for randomly deployed transmitting nodes. First, this dissertation analyzes limited feedback beamforming and precoded spatial multiplexing over temporally correlated channels. Assuming uncoordinated interference from one dominant interferer, using Markov chain convergence theory, the gain in the average successful throughput at the mobile user is shown to decrease exponentially with the feedback delay. The decay rate is amplified when the user is interference limited. Interference cancellation methods at the receiver are shown to mitigate the effect of interference. This work motivates the need for practical MIMO designs to overcome the adverse effects of interference. Second, limited feedback beamforming is analyzed on the downlink of a more realistic heterogeneous cellular network. Future generation cellular networks are expected to be heterogeneous, consisting of a mixture of macro base stations and low power nodes, to support the increasing user traffic capacity and reliability demand. Interference in heterogeneous environments cannot be coordinated using traditional interference mitigation techniques due to the on demand and random deployment of low power nodes such as femtocells. Using tools from stochastic geometry, the outage and average achievable rate of limited feedback MIMO is computed with same-tier and cross-tier interference, and feedback delay. A hybrid fixed and random network deployment model is used to analyze the performance in a fixed cell of interest. The maximum density of transmitting femtocells is derived as a function of the feedback rate and delay. The detrimental effect of same-tier interference is quantified, as the mobile user moves from the cell-center to the cell-edge. The third part of this dissertation considers limited coordination between randomly deployed transmitters. Building on the established degrading effect of uncoordinated interference on practical MIMO methods, and the analytical tractability of random deployment models, interference coordination is analyzed. Using multiple antennas at the transmitter for interference nulling in ad hoc networks is first shown to achieve MIMO gains using single antenna receivers. Clustered coordination is then investigated for cellular systems with randomly deployed base stations. As full coordination in the network is not feasible, a random clustering model is proposed where base stations located in the same cluster coordinate. The average achievable rate can be optimized as a function of the number of antennas to maximize the coordination gains. For multicell limited feedback, adaptive partitioning of feedback bits as a function of the signal and interference strength is proposed to minimize the loss in rate due to finite rate feedback. / text

Interference is a defining feature of a wireless network. How to optimally deal with it is one of the most critical and least understood aspects of decentralized multiuser communication. This dissertation focuses on distributed transmission strategies that a transmitter can follow to achieve reliability while reducing the impact of interference. The problem is investigated from three directions : distributed opportunistic scheduling, multicast outage and transmission capacity, and ergodic transmission capacity, which study distributed transmission in different scenarios from a transmission-capacity perspective. Transmission capacity is spatial throughput metric in a large-scale wireless network with outage constraints. To understand the fundamental limits of distributed transmission, these three directions are investigated from the underlying tradeoffs in different transmission scenarios. All analytic results regarding the three directions are rigorously derived and proved under the framework of transmission capacity. For the first direction, three distributed opportunistic scheduling schemes -- distributed channel-aware, interferer-aware and interferer-channel-aware scheduling are proposed. The main idea of the three schemes is to avoid transmitting in a deep fading and/or sever interfering context. Theoretical analysis and simulations show that the three schemes are able to achieve high transmission capacity and reliability. The second direction focuses on the study of the transmission capacity problem in a distributed multicast transmission scenario. Multicast transmission, wherein the same packet must be delivered to multiple receivers, has several distinctive traits as opposed to more commonly studied unicast transmission. The general expression for the scaling law of multicast transmission capacity is found and it can provide some insight on how to do distributed single-hop and multi-hop retransmissions. In the third direction, the transmission capacity problem is investigated for Markovain fading channels with temporal and spatial ergodicity. The scaling law of the ergodic transmission capacity is derived and it can indicate a long-term distributed transmission and interference management policy for enhancing transmission capacity. / text

As the trends towards decentralization, miniaturization, and longevity of deployment continue in many domains, power management has become increasingly important. In this work, we develop power-aware control strategies for wireless sensor networks to improve the lifetime of the network and to ensure that the desired performance is guaranteed. For the case of static networks (networks of agents with no mobility), we identify the problem of the effects of power variations on the performance of an individual sensing device and on the entire network. To address this problem in a randomly deployed sensor network comprising of sensing devices whose sensing range is a function of transmitted power, we propose power-aware controllers to compensate for the variations in available power and maintain desired performance. We also propose a novel energy-efficient sleep-scheduling scheme that is random in nature and allows limited coordination among neighboring sensors for making switching decisions. This scheme is based on the concept of a hard-core point process from stochastic geometry, in which neighboring points are allowed to interact with each other through some predefined interaction laws. For the case of mobile networks (networks of agents with mobility), we propose a solid framework for distributed power-aware mobility strategies that can achieve any desired global objective while minimizing total energy consumption. This goal is achieved by first exploring fundamental trade-offs among various modes of operations of mobile devices and then exploiting these trade-offs for minimizing energy consumption. Through this framework, a whole class of decentralized power-aware controllers emerge for solving canonical problems in multi-agent systems like connectivity maintenance, rendezvous, and coverage control.

Dans cette thèse, nous analysons les performances des réseaux de communication à l'aide d’approches issues de la théorie des jeux. Cette thèse se présente en deux parties. La première partie étudie la performance des réseaux ad-hoc, cellulaires et de transport en tenant compte d’effets spatiaux. La deuxième partie adresse des problématiques économiques dans les réseaux de communications, liées à la réglementation de la «neutralité du réseau». Ici, nous étudions la concurrence des prix ainsi que des mécanismes de partage des revenus entre fournisseurs de services réseau.Dans la première partie, nous utilisons des modèles de jeu d’accès canal (MAC) et jeu de brouillage pour étudier les performances d'un réseau mobile ad hoc (MANET), et de jeux de routage afin d'étudier les performances d'un réseau de transport. Dans les réseaux cellulaires, nous étudions l'effet de la réduction de la densité spatiale des stations de base sur la quantité de rayonnement au corps humain (réseau vert).Les considérations géométriques jouent un rôle important dans les performances des réseaux sans fils. Par exemple, la position des nœuds affecte le niveau des interférences. Dans les MANETS, la mobilité des nœuds conduit à une observation différente du niveau d’interférences provenant de leurs voisins, et aussi due à la nature décentralisée du réseau, les utilisateurs peuvent adopter un comportement égoïste dans le partage des ressources. Afin de modéliser les propriétés géométriques du réseau ainsi que le comportement égoïste des utilisateurs, nous utilisons la géométrie stochastique et la théorie des jeux. Notre travail a développé un mécanisme de tarification et a montré qu’en définissant un prix approprié, tous les utilisateurs pouvaient être amenés à recevoir une part équitable des ressources conduisant à un optimal global des performances du réseau. Nous considérons aussi une configuration antagoniste où certain nœuds tendent à dégrader les performances du réseau en brouillant les communications des autres nœuds du réseau. Dans la deuxième partie de la thèse, nous étudions des aspects économiques dans les réseaux communication. Les représentants de plusieurs fournisseurs d'accès Internet (ISP) ont exprimé leur souhait de voir un changement important dans les politiques de tarification de l'Internet. En particulier, ils aimeraient voir les fournisseurs de contenu (CP) payer pour l'utilisation du réseau, compte tenu de la grande quantité de ressources qu'ils utilisent. Ce qui serait une violation flagrante du «principe de neutralité des réseaux» qui a caractérisé le développement de l'Internet filaire. La thèse a étudiée la possibilité de l’introduction d’un régulateur facilitant les interactions monétaires entre les ISP et les CP dans un régime non neutre. En utilisant des outils issus de la théorie des jeux et de la conception de mécanismes, nous avons développé deux mécanismes de négociation décidant des paiements entre les ISPs et CPs. Nous montrons que si les joueurs négocient avant de fixer les prix d’accès des utilisateurs finaux, ceci conduit à un équilibre favorable où tous les joueurs ressortent gagnant. Nous considérons également le cas où certains CPs établissent des contrats d’exclusivités avec les ISP afin d’obtenir des traitements préférentiels et en étudions l’impact sur les fournisseurs d’accès et les utilisateurs finaux. Avec la croissance du commerce de l’internet, la régulation des interactions monétaires entre différents fournisseurs de services est inévitable. Notre travail fournit des lignes directrices importantes sur la façon dont l'Internet doit être réglementé de telle sorte que les intérêts des utilisateurs finaux sont protégés / In this thesis we analyze the performance of communication networks using game theoretic approaches. The thesis is in two parts. The first part studies the performance of Ad hoc, cellular and transportation networks taking into consideration spatial effects. The second part studies economic issues in the communication networks related to the `net neutrality' regulations. Here we study price competition and revenue sharing mechanisms between the network service providers.In the first part, we use Medium Access Control (MAC) game and Jamming game models to study the performance of a Mobile Ad hoc NETwork (MANET), and routing games to study the performance of a transportation network. In the cellular networks, we study the effect of reducing the spatial density of base stations on the amount of radiation to human body (green networking). Geometric aspects play an important role in the performance of wireless networks. For example, node locations affect the amount of interference. In MANETs, the mobility results in users experiencing different amount of interference from their neighbors, and also due to decentralized nature of the network the users can be selfish in sharing the resources. To model the geometrical properties of the network and selfish behavior of the users we used stochastic geometry and game theory. Our work developed a pricing mechanism and showed that with an `appropriate' price all the users can be made to get a fair share of the resources resulting in global optimal network performance. We also considered an adversarial setting where some of the nodes aim to degrade the performance of the network by jamming other nodes’ transmissions.In the second part of the thesis, we study economics aspects in communication networks. Representatives of several Internet access providers (ISPs) have expressed their wish to see a substantial change in the Internet pricing policies. In particular, they would like to see content providers (CPs) pay for use of the network, given the large amount of resources they use. This would be in clear violation of the ``net neutrality'' principle that had characterized the development of the wireline Internet. The thesis explored possibility of a regulator facilitating monetary interactions between the ISPs and CPs in a nonneutral regime. Using tools from game theory and mechanism design we developed two bargaining mechanisms to decide payments between the ISPs and CPs. We showed that if the players bargain before they set the access prices for end users, it results in a favorable equilibrium where every player benefits. We also considered the case where some of CPs make exclusive contracts with the ISPs to get preferential treatment and studied its impact on both the service providers and the end users.As the Internet commerce grows, regulation of the monetary interaction between various service providers is unavoidable. Our work provides important policy guidelines on how the Internet should be regulated such that the end users' interests are protected

Orientador: Paulo Regis Caron Ruffino / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T23:01:19Z (GMT). No. of bitstreams: 1 Costa_PauloHenriquePereirada_M.pdf: 875708 bytes, checksum: 8862a1813f1bb85b5d0269462a80501e (MD5) Previous issue date: 2009 / Resumo: O objetivo desse trabalho é estudar as equações de Hamilton no contexto estocástico. Sendo necessário para tal um pouco de conhecimento a cerca dos seguintes assuntos: cálculo estocástico, geometria de segunda ordem, estruturas simpléticas e de Poisson. Abordamos importantes resultados, dentre eles o teorema de Darboux (coordenadas locais) em variedades simpléticas, teorema de Lie-Weinstein que de certa forma generaliza o teorema de Darboux em variedades de Poisson. Veremos que apesar de o ambiente natural para se estudar sistemas hamiltonianos ser variedades simpléticas, no caso estocástico esses sistemas se adaptam bem em variedades de Poisson. Além disso, para atingir a nossa meta, estudaremos equações diferenciais estocásticas em variedades de dimensão finita usando o operador de Stratonovich / Abstract: This dissertation deals with transfering Hamilton's equations in stochastic context. This requires some knowledge about the following: stochastic calculus, second order geometry and Poisson and simplectic structures. Important results that will be discussed in this theory are Darboux's theorem (local coordinates) for simplectic manifolds, and Lie-Weintein's theorem that is in a certain way of Darboux's theorem on Poisson manifolds. We will see that although the natural environment for studying hamiltonian systems is symplectic manifolds, if we have a Poisson structure we will still be able to study them. Moreover, to achieve our goal, we will study stochastic differential equations on finite dimensional manifolds using the Stratonovich operator / Mestrado / Geometria Estocastica / Mestre em Matemática