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., Ph. D.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 millimeter wave and massive MIMO cellular networks(2016-08) Bai, Tianyang; Heath, Robert W., Ph. D.; 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., Ph. D.; 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 A stochastic geometry analysis of cooperative wireless networks powered by energy harvesting(2015-05) Khan, Talha Ahmed; Heath, Robert W., Ph. D.; Orlik, Philip VEnergy harvesting technology is essential for enabling green, sustainable and autonomous wireless networks. In this report, a large-scale wireless network with energy harvesting transmitters is considered, where a group of transmitters forms a cluster to cooperatively serve a desired user in the presence of co-channel interference and noise. Using stochastic geometry, simple closed-form expressions are derived to characterize the outage performance at the user as a function of important parameters such as the energy harvesting rate, the energy buffer size and the cluster size for a given cluster geometry. The analysis is further extended to characterize the delay due to transmission failure. The developed framework is flexible in that it allows the in-cluster transmitters to have possibly different energy harvesting capabilities. The analytical expressions are first validated using simulations and then used for investigating the impact of different parameters such as cluster and buffer size on outage performance. The results suggest that substantial outage performance can in fact be extracted with a relatively small energy buffer. Moreover, the utility of having a large energy buffer increases with the cluster size as well as with the energy harvesting rate.