Browsing by Subject "Stochastic geometry"
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Item Analysis of blockage effects on urban cellular networks(2013-05) Bai, Tianyang; Heath, Robert W., Jr, 1973-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.Item Analysis of cellular networks : densification and data traffic dynamics(2020-12-10) Alammouri, Ahmad Mohammad; Andrews, Jeffrey G; Baccelli, F. (Francois), 1954-; de Veciana, Gustavo; Heath, Robert W; Franceschetti, MassimoWith an ever-increasing amount of deployed base stations and new types of supported devices and services, cellular networks continue to evolve and densify constantly. These changes require us to revisit and improve classical mathematical models used to assess and optimize their performance. This thesis focuses on novel modeling of cellular networks that preserve their fundamental and critical properties and account for their evolution. We focus on two aspects: scaling laws in dense cellular networks and the data traffic dynamics caused by the interactions between the wireless nodes. We first focus on the distance-based attenuation, which is a critical aspect of dense wireless communications. As opposed to the ubiquitous power-law path loss, we propose a stretched exponential path loss model that is more suitable for short-range communication. In this model, the signal power attenuates over a distance r as e[superscript minus] [superscript alpha] [superscript r][superscript beta] where [alpha],[beta] are tunable parameters. Using field measurements, we show that this model is accurate for short to moderate distances in the range r Ε (5,300) meters. We use this model to analyze downlink cellular networks. Using stochastic geometry tools, we derive expressions for the coverage probability and the average area spectral efficiency (ASE). We prove that by over-densifying the network, the coverage probability is driven to zero, and the ASE saturates to a constant, which we derive in a closed-form. Then we extend this work to study the scaling laws of signal-to-interference-plus-noise ratio (SINR) and the ASE in dense networks under fairly general assumptions regarding the signal propagation and the network operation. We start by defining a class of physically feasible path loss models characterized by three simple properties: finite transmit power, the average received power is less than the transmit power and finite network interference. We show that this class of models includes the vast majority of the bounded models used in the literature. With this class of models, we propose a new approach to analyzing cellular networks' scaling laws. This asymptotic analysis relies on three assumptions: (1) interference is treated as noise; (2) the BS locations are drawn from a Poisson point process; (3) a physically feasible path loss model. We consider three possible definitions of the average ASE, all of which give units of bits per second per unit bandwidth per unit area. When there is no constraint on the minimum operational SINR and instantaneous full channel state information (CSI) is available at the transmitter, the average ASE is proven to saturate to a constant, which we derive in a closed-form. For the other two ASE definitions, wherein either a minimum SINR is enforced or CSI is not available, the average ASE is instead shown to collapse to zero at high BS density. We provide several familiar case studies for the class of considered path loss models and demonstrate that our results cover most previous models and results on ultradense networks as special cases. Then we extend this approach to account for multi-antenna cellular networks. We show that if the number of antennas scales at least linearly with the BSs density, then the SINR approaches a constant, and we restore the desired linear scaling of the ASE with densification. We show that this conclusion holds for cellular networks operating on the traditional frequency bands (sub-6 GHz) and mmWave bands. In the final part of this thesis, we focus on data traffic dynamics in wireless systems. Precisely, we characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, where users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. Each user's service rate is based on its signal to interference plus noise ratio, where the interference is from other active users in the cell. Once the file is fully transmitted, the user leaves the cell. We derive the necessary and sufficient condition for network stability, independent of the specific bounded path loss function. A novel observation is that the network appears stable for a specific range of arrival rates for a possibly long time and then suddenly exhibits instability. This property, which is known in statistical physics but rarely observed in wireless communication, is called {\it metastability}. Finally, we propose two heuristic characterizations based on the mean-field interpretation of the network steady-state regime when it exists. The first-order approximation is very simple to compute but loose in some regimes. In contrast, the second-order approximation is more sophisticated but tight for the whole range of arrival ratesItem Analysis of millimeter wave ad hoc networks(2018-01-23) Thornburg, Andrew Scott; Heath, Robert W., Jr, 1973-; Andrews, Jeffrey; Baccelli, Francois; Hasenbein, John; de Veciana, GustavoOver the coming few years, the next-generation of wireless networks will be standardized and defined. Ad hoc networks, which operate without expensive infrastructure, are desirable for use cases such as military networks or disaster relief. Millimeter wave (mmWave) technology may enable high speed ad hoc networks. Directional antennas and building blockage limit the received interference power while the huge bandwidth enables high data rates. For this reason, understanding the interference and network performance of mmWave ad hoc networks is crucial for next-generation network design. In my first contribution, I derive the SINR complementary cumulative distribution function (CCDF) for a random single-hop mmWave ad hoc network. These base results are used to further give insights in mmWave ad hoc networks. The SINR distribution is used to compute the transmission capacity of a mmWave ad hoc network using a Taylor bound. The CDF of the interference to noise ratio (INR) is also derived which shows that mmWave ad hoc networks are line-of-sight interference limited. I extend my work in the second contribution to include general clustered Poisson point processes to derive insights in the effect of different spatial interference patterns. Using the developed framework, I derive the ergodic rate of both spatially uniform and cluster mmWave ad hoc networks. I develop scaling trends for the antenna array size to keep the ergodic rate constant. The impact of beam alignment is computed in the final part of the contribution. Finally, I account for the overhead of beam alignment in mmWave ad hoc networks. The final contribution leverages the first two contributions to derive the expected training time a mmWave ad hoc network must perform before data transmission occurs. The results show that the optimal conditions for minimizing the training time are different than the optimal conditions for maximizing rate.Item Analysis of millimeter wave and massive MIMO cellular networks(2016-08) Bai, Tianyang; Heath, Robert W., Jr, 1973-; Andrews, Jeffrey G; Baccelli, Francois; Qiu, Lili; Sanghavi, SujayMillimeter wave (mmWave) communication and massive multiple-input multiple-output (MIMO) are promising techniques to increase system capacity in 5G cellular networks. The prior frameworks for conventional cellular systems do not directly apply to analyze mmWave or massive MIMO networks, as (i) mmWave cellular networks differ in the different propagation conditions and hardware constraints; and (ii) with a order of magnitude more antennas than conventional multi-user MIMO systems, massive MIMO systems will be operated in time-division duplex (TDD) mode, which renders pilot contamination a primary limiting factor. In this dissertation, I develop stochastic geometry frameworks to analyze the system-level performance of mmWave, sub-6 GHz massive MIMO, and mmWave massive MIMO cellular networks. The proposed models capture the key features of each technique, and allow for tractable signal-to-interference-plus-noise ratio (SINR) and rate analyses. In the first contribution, I develop an mmWave cellular network model that incorporates the blockage effect and directional beamforming, and analyze the SINR and rate distributions as functions of the base station density, blockage parameters, and antenna geometry. The analytical results demonstrate that with a sufficiently dense base station deployment, mmWave cellular networks are capable to achieve comparable SINR coverage and much higher rates than conventional networks. In my second contribution, I analyze the uplink SINR and rate in sub-6 GHz massive MIMO networks with the incorporation of pilot contamination and fractional power control. Based on the analysis, I show scaling laws between the number of antennas and scheduled users per cell that maintain the uplink signal-to-interference ratio (SIR) distributions are different for maximum ratio combining (MRC) and zero-forcing (ZF) receivers. In my third contribution, I extend the sub-6 GHz massive MIMO model to mmWave frequencies, by incorporating key mmWave features. I leverage the proposed model to investigate the asymptotic SINR performance, when the number of antennas goes to infinity. Numerical results show that mmWave massive MIMO outperforms its sub-6 GHz counterpart in cell throughput with a dense base station deployment, while the reverse can be true with a low base station density.Item Capacity of multi-antenna ad hoc networks via stochastic geometry(2012-12) Hunter, Andrew Marcus; Andrews, Jeffrey G.; de Veciana, Gustavo; Heath, Robert W.; Stone, Peter; Haenggi, MartinThis thesis takes as its objective quantifying, comparing, and optimizing multiple-antenna (MIMO) physical layer techniques in dense ad hoc wireless networks. A framework is developed from the spatial shot noise interference model for packet radio network analysis. The framework captures the behavior of a wide variety of signal and interference distributions, which permit inspection of a number of signal processing methods including representatives from most of the major MIMO techniques. Multi-antenna systems for point-to-point are becoming mature and being developed and deployed in many wireless communication systems due to their potential to combat fading, increase spectral efficiency, and overcome interference. The framework permits an algorithm or system designer to view the network from the perspective of a typical user, to optimize performance in the midst of a given environment, or to view the network as a whole, to determine behavior that maximizes network performance. In particular, it enables questions to be answered quantitatively, such as which MIMO techniques perform best in a given environment? Or what rate and power settings should be used across the available spatial modes? Or what is the maximum benefit of channel state information? Or what gain should an individual device, or the network as a whole expect to see given a particular physical layer strategy? The dissertation begins by developing the framework for a generic set of assumptions on network behavior and signal and interference distributions. It then presents a progression of applications to representative MIMO techniques. Broad and intuitive scaling laws are developed as well as detailed exact results for careful comparison. Capacity scaling with the number of antennas is given for systems employing beamforming, selection combining, space-time block coding, and spatial multiplexing. These applications are used as the basis for developing simple distributed algorithms for optimizing MIMO settings with QoS constraints and in heterogeneous networks. Lastly, the framework is expanded to permit comparison and optimization of MIMO performance under alternative medium access strategies. In general it is found that significant performance gains can be reaped with multi-antenna physical layers, provided the proper techniques are employed. It is also shown that the availability of multiple spatial channels impacts the inherent tradeoff between per-link throughput and spatial reuse.Item Design of platforms for computing context with spatio-temporal locality(2011-05) Ziotopoulos, Agisilaos Georgios; De Veciana, Gustavo; Garg, Vijay; Mok, Al; Julien, Christine; Touba, Nur; Breternitz, MauricioThis 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.Item Fractional frequency reuse for multi-tier cellular networks(2012-05) Novlan, Thomas David; Andrews, Jeffrey G.; Ghosh, Arunabha; Humphreys, Todd E.; Rappaport, Theodore S.; de Veciana, GustavoModern cellular systems feature increasingly dense base station deployments, augmented by multiple tiers of access points, in an effort to provide higher network capacity as user traffic, especially data traffic, increases. The primary limitation of these dense networks is co-channel interference. The primary source of interference is inter-cell and cross-tier interference, which is especially limiting for users near the boundary of the cells. Inter-cell interference coordination (ICIC) is a broad umbrella term for strategies to improve the performance of the network by having each cell allocate its resources such that the interference experienced in the network is minimized, while maximizing spatial reuse. Fractional frequency reuse (FFR) has been proposed as an ICIC technique in modern wireless networks. The basic idea of FFR is to partition the cell’s bandwidth so that (i) cell-edge users of adjacent cells do not interfere with each other and (ii) interference received by (and created by) cell-interior users is reduced, while (iii) improving spectral reuse compared to conventional frequency reuse. It is attractive for its intuitive implementation and relatively low network coordination requirements compared to other ICIC strategies including interference cancellation, network MIMO, and opportunistic scheduling. There are two common FFR deployment modes: Strict FFR and Soft Frequency Reuse (SFR). This dissertation identifies and addresses key technical challenges associated with fractional frequency reuse in modern cellular networks by utilizing an accurate yet tractable model of both the downlink (base station to mobile) and uplink (mobile to base station) based on the Poisson point process for modeling base station locations. The resulting expressions allow for the development of system design guidelines as a function of FFR parameters and show their impact on important metrics of coverage, rate, power control, and spectral efficiency. This new complete analytical framework addresses system design and performance differences in the uplink and downlink. Also, this model can be applied to cellular networks with multiple tiers of access points, often called heterogeneous cellular networks. The model allows for analysis as a function of system design parameters for users under Strict FFR and SFR with closed and open access between tiers.Item Fundamentals of distributed transmission in wireless networks : a transmission-capacity perspective(2011-05) Liu, Chun-Hung; Andrews, Jeffrey G.; Shakkottai, Sanjay; Arapostathis, Ari; Morton, David; Vishwanath, SriramInterference 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.Item Fundamentals of Heterogeneous Cellular Networks(2013-12) Dhillon, Harpreet Singh; Andrews, Jeffrey G.The increasing complexity of heterogeneous cellular networks (HetNets) due to the irregular deployment of small cells demands significant rethinking in the way cellular networks are perceived, modeled and analyzed. In addition to threatening the relevance of classical models, this new network paradigm also raises questions regarding the feasibility of state-of-the-art simulation-based approach for system design. This dissertation proposes a fundamentally new approach based on random spatial models that is not only tractable but also captures current deployment trends fairly accurately. First, this dissertation presents a general baseline model for HetNets consisting of K different types of base stations (BSs) that may differ in terms of transmit power, deployment density and target rate. Modeling the locations of each class of BSs as an independent Poisson Point Process (PPP) allows the derivation of surprisingly simple expressions for coverage probability and average rate. One interpretation of these results is that adding more BSs or tiers does not necessarily change the coverage probability, which indicates that fears of "interference overload" in HetNets are probably overblown. Second, a flexible notion of BS load is incorporated by introducing a new idea of conditionally thinning the interference field. For this generalized model, the coverage probability is shown to increase when lightly loaded small cells are added to the existing macrocellular networks. This is due to the fact that owing to the smaller loads, small cells typically transmit less often than macrocells, thus contributing less to the interference power. The same idea of conditional thinning is also shown to be useful in modeling the non-uniform user distributions, especially when the users lie closer to the BSs. Third, the baseline model is extended to study multi-antenna HetNets, where BSs across tiers may additionally differ in terms of the number of transmit antennas, number of users served and the multi-antenna transmission strategy. Using novel tools from stochastic orders, a tractable framework is developed to compare the performance of various multi-antenna transmission strategies for a fairly general spatial model, where the BSs may follow any general stationary distribution. The analysis shows that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Fourth, accounting for the load on the serving BS, downlink rate distribution is derived for a generalized cell selection model, where shadowing, following any general distribution, impacts cell selection while fading does not. This generalizes the baseline model and all its extensions, which either ignore the impact of channel randomness on cell selection or lumps all the sources of randomness into a single random variable. As an application of these results, it is shown that in certain regimes, shadowing naturally balances load across various tiers and hence reduces the need for artificial cell selection bias. Fifth and last, a slightly futuristic scenario of self-powered HetNets is considered, where each BS is powered solely by a self-contained energy harvesting module that may differ across tiers in terms of the energy harvesting rate and energy storage capacity. Since a BS may not always have sufficient energy, it may not always be available to serve users. This leads to a notion of availability region, which characterizes the fraction of time each type of BS can be made available under variety of strategies. One interpretation of this result is that the self-powered BSs do not suffer performance degradation due to the unreliability associated with energy harvesting if the availability vector corresponding to the optimal system performance lies in the availability region.Item Integrated cellular and device-to-device networks(2014-12) Lin, Xingqin; Andrews, Jeffrey G.Device-to-device (D2D) networking enables direct discovery and communication between cellular subscribers that are in proximity, thus bypassing the base stations (BSs). In principle, exploiting direct communication between nearby mobile devices will improve spectrum utilization, overall throughput, and energy consumption, while enabling new peer-to-peer and location-based applications and services. D2D-enabled broadband communication technology is also required by public safety networks that must function when cellular networks are not available. Integrating D2D into cellular networks, however, poses many challenges and risks to the long-standing cellular architecture, which is centered around the BSs. This dissertation identifies outstanding technical challenges in D2D-enabled cellular networks and addresses them with novel models and fundamental analysis. First, this dissertation develops a baseline hybrid network model consisting of both ad hoc nodes and cellular infrastructure. This model uses Poisson point processes to model the random and unpredictable locations of mobile users. It also captures key features of multicast D2D including multicast receiver heterogeneity and retransmissions while being tractable for analytical purpose. Several important multicast D2D metrics including coverage probability, mean number of covered receivers per multicast session, and multicast throughput are analytically characterized under the proposed model. Second, D2D mode selection which means that a potential D2D pair can switch between direct and cellular modes is incorporated into the hybrid network model. The extended model is applied to study spectrum sharing between cellular and D2D communications. Two spectrum sharing models, overlay and underlay, are investigated under a unified analytical framework. Analytical rate expressions are derived and applied to optimize the design of spectrum sharing. It is found that, from an overall mean-rate perspective, both overlay and underlay bring performance improvements (vs. pure cellular). Third, the single-antenna hybrid network model is extended to multi-antenna transmission to study the interplay between massive MIMO (multi-input multiple-output) and underlaid D2D networking. The spectral efficiency of such multi-antenna hybrid networks is investigated under both perfect and imperfect channel state information (CSI) assumptions. Compared to the case without D2D, there is a loss in cellular spectral efficiency due to D2D underlay. With perfect CSI, the loss can be completely overcome if the number of canceled D2D interfering signals is scaled appropriately. With imperfect CSI, in addition to pilot contamination, a new asymptotic underlay contamination effect arises. Finally, motivated by the fact that transmissions in D2D discovery are usually not or imperfectly synchronized, this dissertation studies the effect of asynchronous multicarrier transmission and proposes a tractable signal-to-interference-plus-noise ratio (SINR) model. The proposed model is used to analytically characterize system-level performance of asynchronous wireless networks. The loss from lack of synchronization is quantified, and several solutions are proposed and compared to mitigate the loss.Item Limited feedback MIMO for interference limited networks(2012-12) Akoum, Salam Walid; Heath, Robert W., Jr, 1973-; Andrews, Jeffrey G.; Sanghavi, Sujay; Debbah, Merouane; Vikalo, Haris; Kountouris, MariosManaging 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.Item Load balancing in heterogeneous cellular networks(2014-12) Singh, Sarabjot, active 21st century; Andrews, Jeffrey G.Pushing wireless data traffic onto small cells is important for alleviating congestion in the over-loaded macrocellular network. However, the ultimate potential of such load balancing and its effect on overall system performance is not well understood. With the ongoing deployment of multiple classes of access points (APs) with each class differing in transmit power, employed frequency band, and backhaul capacity, the network is evolving into a complex and “organic” heterogeneous network or HetNet. Resorting to system-level simulations for design insights is increasingly prohibitive with such growing network complexity. The goal of this dissertation is to develop realistic yet tractable frameworks to model and analyze load balancing dynamics while incorporating the heterogeneous nature of these networks. First, this dissertation introduces and analyzes a class of user-AP association strategies, called stationary association, and the resulting association cells for HetNets modeled as stationary point processes. A “Feller-paradox”-like relationship is established between the area of the association cell containing the origin and that of a typical association cell. This chapter also provides a foundation for subsequent chapters, as association strategies directly dictate the load distribution across the network. Second, this dissertation proposes a baseline model to characterize downlink rate and signal-to-interference-plus-noise-ratio (SINR) in an M-band K-tier HetNet with a general weighted path loss based association. Each class of APs is modeled as an independent Poisson point process (PPP) and may differ in deployment density, transmit power, bandwidth (resource), and path loss exponent. It is shown that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage. One of the main outcomes is demonstrating the aggressive of- floading required for out-of-band small cells (like WiFi) as compared to those for in-band (like picocells). To achieve aggressive load balancing, the offloaded users often have much lower downlink SINR than they would on the macrocell, particularly in co-channel small cells. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. As the third contribution, this dissertation proposes a tractable framework to analyze joint load balancing and resource partitioning in co-channel HetNets. Fourth, this dissertation investigates the impact of uplink load balancing. Power control and spatial interference correlation complicate the mathixematical analysis for the uplink as compared to the downlink. A novel generative model is proposed to characterize the uplink rate distribution as a function of the association and power control parameters, and used to show the optimal amount of channel inversion increases with the path loss variance in the network. In contrast to the downlink, minimum path loss association is shown to be optimal for uplink rate coverage. Fifth, this dissertation develops a model for characterizing rate distribution in self-backhauled millimeter wave (mmWave) cellular networks and thus generalizes the earlier multi-band offloading framework to the co-existence of current ultra high frequency (UHF) HetNets and mmWave networks. MmWave cellular systems will require high gain directional antennas and dense AP deployments. The analysis shows that in sharp contrast to the interferencelimited nature of UHF cellular networks, mmWave networks are usually noiselimited. As a desirable side effect, high gain antennas yield interference isolation, providing an opportunity to incorporate self-backhauling. For load balancing, the large bandwidth at mmWave makes offloading users, with reliable mmWave links, optimal for rate.Item Modeling and analysis of wireless networks with correlation and motion(2019-06-13) Choi, Chang-sik; Baccelli, F. (François), 1954-; de Veciana, Gustavo; Heath, Robert W; Andrews, Jeffrey G; Sirbu, MihaiThe use of stochastic geometry allows the analysis of the typical performance of a wireless network. Specifically, under a stationary framework, the network performance at a typical receiver represents the network performance spatially-averaged over all receivers. This approach has been applied to the Poisson point processes whose points are independently located in space. The Poisson point process expresses a total independence type randomness in network architectures. Its tractability leads to its wide use in modeling various wireless networks, e.g., cellular networks, ad hoc networks, and vehicular networks. However, a network analysis using the Poisson point process might be inaccurate when the network components are geometrically correlated or in motion, as in heterogeneous cellular networks, or vehicular networks. For instance, macro base stations are deployed far from each other. Vehicles are located on roads, i.e., lines, and they move on the lines. As a result, the analysis of these networks can be improved by new spatial models that capture these spatial and dynamic features. In my first contribution, I derive the signal-to-interference ratio (SIR) coverage probability of a typical user in heterogeneous cellular networks where base stations are modeled by the sum of a Poisson point process and a stationary square grid. In my second contribution, I develop a stationary framework based on the sum of a Cox point process and a Poisson point process to model random cellular networks with linear base stations and linear users on straight lines. I derive the SIR coverage probability of the typical user and characterize its association. In the third contribution, I investigate the statistical properties of the Cox point process, exploring the nearest distance distribution and the convergence of the Cox-Voronoi cell. In the above three contributions, I analyze the performance of wireless networks by focusing on their correlated structures, extracting results which cannot be obtained from models based only on Poisson point processes. In my fourth contribution, I propose a new technology for harvesting Internet-of-Things (IoT) data based on mesh relaying with vehicles as sinks. I derive the network capacity and compare it to the traditional approach, which is based on static base stations. In the fifth contribution, I derive the SIR distribution of direct communication from roadside devices to vehicles. By characterizing the evolution of the network snapshots, I derive the behavior of vehicles' service coverage area and the network latency. In my sixth contribution, I propose a data harvesting technology for the ground-based data devices, based on the use of unmanned aerial vehicles (UAVs). I derive the total data transmitted from a typical device by characterizing the evolution of network geometry with respect to time. These last three contributions are built on a combination of network snapshot analysis and network evolution analysis.Item Modeling and analyzing the evolution of cellular networks using stochastic geometry(2017-05) Li, Yingzhe, Ph. D.; Andrews, Jeffrey G.; Baccelli, F. (François), 1954-; de Veciana, Gustavo; Heath, Robert W; Novlan, Thomas DThe increasing complexity of cellular network due to its continuous evolution has made the conventional system level simulations time consuming and cost prohibitive. By modeling base station (BS) and user locations as spatial point processes, stochastic geometry has recently been recognized as a tractable and efficient analytical tool to quantify key performance metrics. The goal of this dissertation is to leverage stochastic geometry to develop an accurate spatial point process model for the conventional homogeneous macro cellular network, and to address the design and analysis challenges for the emerging cellular networks that will explore new spectrum for cellular communications. First, this dissertation proposes to use the repulsive determinantal point processes (DPPs) as an accurate model for macro BS locations in a cellular network. Based on three unique computational properties of the DPPs, the exact expressions of several fundamental performance metrics for cellular networks with DPP configured BSs are analytically derived and numerically evaluated. Using hypothesis testing for various performance metrics of interest, the DPPs are validated to be more accurate than the Poisson point process (PPP) or the deterministic grid model. Then the focus of this dissertation shifts to emerging networks that exploit new spectrum for cellular communications. One promising option is to allow the centrally scheduled cellular system to also access the unlicensed spectrum, wherein a carrier sensing multiple access with collision avoidance (CSMA/CA) protocol is usually used, as in Wi-Fi. A stochastic geometry-based analytical framework is developed to characterize the performance metrics for neighboring Wi-Fi and cellular networks under various coexistence mechanisms. In order to guarantee fair coexistence with Wi-Fi, it is shown that the cellular network needs to adopt either a discontinuous transmission pattern or its own CSMA/CA like mechanisms. Next, this dissertation considers cellular networks operating in the millimeter wave (mmWave) band, where directional beamforming is required to establish viable connections. Therefore, a major design challenge is to learn the necessary beamforming directions through the procedures that establish the initial connection between the mobile user and the network. These procedures are referred to as initial access, wherein cell search on the downlink and random access on the uplink are the two major steps. Stochastic geometry is again utilized to develop a unified analytical framework for three directional initial access protocols under a high mobility scenario where users and random blockers are moving with high speed. The expected delay for a user to succeed in initial access, and the average user-perceived downlink throughput that accounts for the initial access overhead, are derived for all three protocols. In particular, the protocol that has low beam-sweeping overhead during cell search is found to achieve a good trade-off between the initial access delay and user-perceived throughput performance. Finally, in contrast to the high mobility scenario for initial access, the directional cell search delay in a slow mobile network is analyzed. Specifically, the BS and user locations are fixed for long period of time, and therefore a strong temporal correlation for SINR is experienced. A closed-form expression for the expected cell search delay is derived, indicating that the expected cell search delay is infinite for noise-limited networks (e.g., mmWave) whenever the non-line-of-sight path loss exponent is larger than 2. By contrast, the expected cell search delay for interference-limited networks is proved to be infinite when the number of beams to search at the BS is smaller than a certain threshold, and finite otherwise.Item Modeling and analyzing wireless networks using stochastic geometry(2018-05) Lee, Junse; Baccelli, F. (François), 1954-; de Veciana, Gustavo; Andrews, Jeffrey; Heath, Robert; Taillefumier, ThibaudOver the past decade, stochastic geometric models, and most notably the planar Poisson point process (PPP) model, have become popular for the analysis of spectral efficiency in wireless networks, in both the D2D and the cellular contexts [1]. By modeling base station (BS) and user locations as spatial point processes, stochastic geometry has recently been recognized as a tractable and efficient analytical tool to quantify key performance metrics. This tool provides a natural way of defining and computing macroscopic properties of multiuser information theory. These properties are obtained by averaging over all node patterns found in a large random network of the Euclidean plane. For example, some key performance metrics such as signal to interference and noise ratio and data rate depend on the network geometric configurations. This tool has thus been widely adopted for analyzing the network performance and broadening network design. This thesis proposes new models to represent several new scenarios. Three main scenarios are considered: 3-D inbuilding networks, MIMO adhoc networks, and multihop communication under mmWave networks. To do so, mathematical tools such as Poisson point processes, Poisson line processes, Boolean models and Poisson bipolar models are used. Each model is 1) generative in that it has a clear physical interpretation, 2) leads to explicit analytical representations of important wireless performance metrics, and 3) highly parametric, with parameters expressing the geometric characteristic of the elements of networks. Physical interpretations from these models are quite different from previous results. The core of this thesis is focused on the effects of correlated shadowing. Shadowing is the effect that the received signal power fluctuates due to objects obstructing the propagation path. By introducing an independent shadowing term over links, it is possible to model the effect of shadow fading. Most previous papers analyzing urban networks assume that shadowing fields are independent over links. With this assumption, it is possible to derive simple closed-form expressions of important network performance metrics. However, this assumption cannot capture that shadowing fields are spatially correlated. This thesis goes beyond the independent shadowing approximation and analyzes the effects of correlated shadowing on various performance metricsItem Modeling, analysis, and design of collaborative services in vehicular and cloud/edge networks(2022-05-02) Kassir, Saadallah; De Veciana, Gustavo; Andrews, Jeffrey G; Caramanis, Constantine; Leibowicz, Benjamin D; Shakkottai, SanjayThe new wireless network technologies introduced in the fifth generation of cellular networks (5G) have enabled the development of various classes of mobile applications. This thesis investigates how these emerging mobile use-cases can make the most of the state-of-the-art wireless and computing technologies through effective collaborative network management and operations strategies. We study two general classes of services: (1) collaborative traffic relaying in vehicular ad-hoc networks (VANETs), aiming at providing highly available, fair and reliable connectivity/throughput to the network users; and (2) collaborative real-time services, aimed at providing devices with low-latency and high availability/reliability connectivity. In the first part of this thesis, we study VANETs and propose a novel vehicle connectivity framework wherein vehicles within communication range of each other form vehicle clusters, allowing them to opportunistically route traffic from/to each other. With the formation of these logical entities, vehicles can be viewed as mobile relay nodes, and have the potential to substantially improve the coverage and per-user throughput of the vehicular network. In this setting, we begin by presenting an analytical framework to study the performance gains enabled by this network architecture on a single road, and we show that vehicle clustering leads to considerable benefits including reduced throughput variability and improved coverage. We then look at larger-scale cellular networks and leverage results from the stochastic geometry literature to show that the proposed opportunistic vehicle clustering and relaying scheme has the potential to improve the throughput for both vehicles and non-vehicle-bound users by more than an order of magnitude through opportunistic relaying and cell load-balancing. Finally, we study wireless resource allocation mechanisms leading to improvements in shared-rate fairness among the network users. In the second part of this thesis, we study the operation of networks supporting real-time services, with a focus on devising efficient and timely information sharing mechanisms among the interconnected entities. We first examine how joint management of wireless communication and cloud/edge-computing resources can improve the timeliness of the information shared over the network, while reducing network resource provisioning costs. We investigate tradeoffs associated with status-update rate adaptation and service placement in the Cloud-to-Thing continuum for devices running real-time applications, and develop associated algorithms aiming at controlling the network congestion and improving the service availability. We argue that sending more information might be detrimental to its quality, and that various application-specific properties influence the service placement decision in the Cloud-to-Thing continuum. We then examine the performance of real-time multi-user services via the specific example of Multiplayer Cloud Gaming (MCG), and exhibit how joint rate adaptation is key to controlling congestion and providing a high quality of service in spite of spatio-temporal variations in the network delays particularly impacting massive multi-user services. Finally, we give particular attention to timely information sharing in collaborative-sensing vehicular networks. We introduce a communication-efficient information-sharing mechanism enabling vehicles to benefit from each other’s sensing capability in real-time via a centralized node (e.g., edge compute node, a cellular base station, or a road side unit). Our proposed mechanism opportunistically improves the vehicles’ situational awareness when assistance is available, allowing them, for instance, to drive at a faster speed without compromising on safety.Item On spatial birth-death and matching processes, and Poisson shot-noise fields(2019-06-18) Manjrekar, Mayank; Baccelli, F. (François), 1954-; Zitkovic, Gordon; Ward, Rachel; Arapostathis, AristotleIn this dissertation we deal with certain spatial stochastic processes that are closely related to Spatial birth-death (SBD) processes. These processes are stochastic processes that model the time-evolution of interacting individuals in a population, where the interaction between individuals depends on their relative locations in space. In this dissertaion, we consider three models of such processes with births and deaths that are amenable to long-term analysis. A common feature of all these models is that the particles in the system interact at a distance of oneItem On the Poisson Follower Model(2020-08-14) Dragović, Nataša; Baccelli, F. (François), 1954-; De Veciana, Gustavo; Zitkovic, Gordan; Tran, Ngoc; Taillefumier, Thibaud OThis dissertation presents studies of dynamics over the Poisson point process. In particular, we study a special case of Hegselmann-Krause Dynamics [1] over ℝ². Chapter 1 is a brief introduction to the thesis and its structure. Chapter 2 introduces the notation, the definitions and examples of phenomena of interest. In Chapter 3, we go deeper in analyzing the phenomena described by calculating frequency of these phenomena. A system of quadratic inequalities will be introduced to allow one to calculate the probabilities of the events pertaining to this dynamics using methods from integral geometry. Chapter 4 uses percolation arguments to prove the absence of percolation at step 1. In Chapter 5, we provide geometric results of independent interest pertaining to the Follower Dynamics. In Chapter 6, we discuss the limiting behavior of this process and include some more simulations. In Chapter 7 we propose future steps and discuss more general Hegselmann-Krause Dynamics.Item Performance analysis of mobile users in Poisson wireless networks(2019-08) Madadi, Pranav; Baccelli, F. (François), 1954-; de Veciana, Gustavo; Andrews, Jeffrey; Hasenbein, John; Shakkottai, SanjayStochastic geometry is a widely accepted mathematical tool used to analyze cellular networks, where the location of base stations are modeled by spatial point processes. It is used to derive closed-form or semi-closed-form expressions for the SINR or for the functions of the SINR which determine various network performance metrics such as coverage probability, "edge" capacity, 90% quantile rate, spectral efficiency, and connectivity without resorting to complicated simulation methods. Predominantly, it is used in deriving marginal distributions of SINR by considering a typical user assumed to be located anywhere on the plane. Models beyond the typical user approach have been proposed with the aim of analyzing QoS metrics of a population of users, and not just a single user. Most of which include considering networks at certain times by representing instances or snapshots of active users as realizations of spatial (usually Poisson) processes or users occurring at random locations that last for some random duration. Analyzing the performance of a typical mobile user on the move or that of a population of such mobile users is complicated since it requires studying not just the marginal but the spatial stochastic fields associated with wireless networks. In this thesis, we model and analyze the fields associated with wireless networks where the locations of base stations are distributed according to a homogeneous Poisson point process. We focus on characterizing the level crossings, extremes, and variability of the Shannon rate fields in noise limited (SNR based) environment by establishing a connection to queueing theory. In interference limited (SIR based) environments, we rely on the theory of Gaussian random fields which arise as natural limits of standardized interference under densification. Using this, we characterize the spatial correlations, and variability of the Shannon rate fields in the limiting regime. We leverage the spatial characterization of the fields to study the temporal variations and various Quality of Service (QoS) metrics seen by the users on the move. The quantification of such metrics as a function of a small number of network parameters, e.g., the density of base stations, path loss, should allow network operators to appropriately tune the density of the base stations to meet the demands of mobile users for a required performance level. In noise limited environments, we study the performance of mobile users in dense networks by incorporating the cost of handovers along with the temporal variability in the Shannon rate. We study the tradeoff between the cost of handover and the Shannon rate by proposing a new class of association policies. Associating with a base station that is farthest in the known users' direction of motion leads to fewer handovers but may lead to a decrease in the rate. Thus, we attribute a local association region to the mobile user to restrict the greediness in the association, which also models the constraint on the available information about the locations of the base stations. We propose a class of greedy association policies and once again leverage stochastic geometry to characterize the performance of such policies. We then optimize the shape and size of the association region by establishing a connection to the theory of Markov processes and compare the performance of this policy to traditional association policiesItem Repulsion of determinantal point processes and stationary Poisson tessellations in high dimensions(2019-09-13) O'Reilly, Elizabeth Watson; Baccelli, F. (François), 1954-; Žitković, Gordan; Ward, Rachel; Shakkottai, SanjayIn this dissertation, new results on stochastic geometric models in high dimensional space are presented. We first concentrate on a particular class of repulsive point processes called determinantal point processes (DPPs). We establish a coupling of a DPP and its reduced Palm version showing the repulsive effect of a point of the point process. This is used for discussing the degree of repulsiveness in DPPs, including Ginibre point processes and other specific parametric models for DPPs. We then study this repulsion for stationary DPPs in high dimensional Euclidean space. It is shown that for many families of DPPs, a typical point has no repulsive effect with high probability for large space dimension n. It is also proved that for some DPPs there exists an R* such that the repulsive effect occurs at a distance of [square root] nR* with high probability for large n. This R* is interpreted as the asymptotic reach of repulsion of the DPP. Examples of DPPs exhibiting this behavior are presented and an application to high dimensional Boolean models is given. The second half of this dissertation examines zero cells of stationary Poisson tessellations. First, a stationary stochastic geometric model is proposed for analyzing one-bit data compression. The data is assumed to be an unconstrained stationary set, and each data point is compressed using one bit with respect to each hyperplane in a stationary and isotropic Poisson hyperplane tessellation. Size metrics of the zero cell of the tessellation are studied to determine how the intensity of hyperplanes must scale with dimension to ensure sufficient separation of different data by the hyperplanes or sufficient proximity of the data compressed together. The results have direct implications in compressive sensing and source coding. We then study the concentration of the norm of a random vector Y uniformly sampled in the centered zero cell of a stationary random tessellation in high dimensions. It is shown that for a stationary and isotropic Poisson-Voronoi tessellation, [mathematical equation] approaches one as the dimension approaches infinity. For a stationary and isotropic Poisson hyperplane tessellation, we prove that [mathematical equation] will be within a fixed range (R [subscript ℓ], R [subscript u]) with probability approaching one as dimension n tends to infinity.