Download or read book New Results on Stochastic Geometry Modeling of Cellular Networks written by Wei Lu and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing heterogeneity and irregular deployment of the emerging wireless networks give enormous challenges to the conventional hexagonal model for abstracting the geographical locations of wireless transmission nodes. Against this backdrop, a new network paradigm by modeling the wireless nodes as a Poisson Point Process (PPP), leveraging on the mathematical tools of stochastic geometry for tractable mathematical analysis, has been proposed with the capability of fairly accurately estimating the performance of practical cellular networks. This dissertation investigated the mathematical tractability of the PPP-based approach by proposing new mathematical methodologies, fair approximations incorporating practical channel propagation models. First, a new mathematical framework, which is referred to as an Equivalent-in-Distribution (EiD)-based approach, has been proposed for computing exact error probability of cellular networks based on random spatial networks. The proposed approach is easy to compute and is shown to be applicable to a bunch of MIMO setups where the modulation techniques and signal recovery techniques are explicitly considered. Second, the performance of relay-aided cooperative cellular networks, where the relay nodes, the base stations, and the mobile terminals are modeled according to three independent PPPs, has been analyzed by assuming flexible cell association criteria. It is shown from the mathematical framework that the performance highly depends on the path-loss exponents of one-hop and two-hop links, and the relays provide negligible gains on the performance if the system is not adequately designed. Third, the PPP modeling of cellular networks with unified signal attenuation model is generalized by taking into account the effect of line-of-sight (LOS) and non-line-of-sight (NLOS) channel propagation. A tractable yet accurate link state model has been proposed to estimate other models available in the literature. It is shown that an optimal density for the BSs deployment exists when the LOS/NLOS links are classified in saturate load cellular networks. In addition, the Monte Carlo simulation results of the real BSs deployments with empirical building blockages are compared with those with PPP distributed BSs with the proposed link state approximation at the end of this dissertation as supplementary material. In general, a good matching is observed.

Download or read book Stochastic Geometry Analysis of Cellular Networks written by Bartłomiej Błaszczyszyn and published by Cambridge University Press. This book was released on 2018-04-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Download or read book Analytical Modeling of Heterogeneous Cellular Networks written by Sayandev Murkherjee and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction shows how stochastic geometry techniques can be used for studying the behaviour of heterogeneous cellular networks (HCNs). The unified treatment of analytic results and approaches, collected for the first time in a single volume, includes the mathematical tools and techniques used to derive them. A single canonical problem formulation encompassing the analytic derivation of Signal to Interference plus Noise Ratio (SINR) distribution in the most widely-used deployment scenarios is presented, together with applications to systems based on the 3GPP-LTE standard, and with implications of these analyses on the design of HCNs. An outline of the different releases of the LTE standard and the features relevant to HCNs is also provided. A valuable reference for industry practitioners looking to improve the speed and efficiency of their network design and optimization workflow, and for graduate students and researchers seeking tractable analytical results for performance metrics in wireless HCNs.

Download or read book Analytical Modeling of Heterogeneous Cellular Networks written by Sayandev Mukherjee and published by . This book was released on 2014 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This self-contained introduction shows how stochastic geometry techniques can be used for studying the behaviour of heterogeneous cellular networks (HCNs). The unified treatment of analytic results and approaches, collected for the first time in a single volume, includes the mathematical tools and techniques used to derive them. A single canonical problem formulation encompassing the analytic derivation of Signal to Interference plus Noise Ratio (SINR) distribution in the most widely-used deployment scenarios is presented, together with applications to systems based on the 3GPP-LTE standard, and with implications of these analyses on the design of HCNs. An outline of the different releases of the LTE standard and the features relevant to HCNs is also provided. A valuable reference for industry practitioners looking to improve the speed and efficiency of their network design and optimization workflow, and for graduate students and researchers seeking tractable analytical results for performance metrics in wireless HCNs"--

Download or read book Stochastic Geometry and Wireless Networks written by François Baccelli and published by Now Publishers Inc. This book was released on 2009 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes.

Download or read book Stochastic Geometry Analysis of Multi Antenna Wireless Networks written by Xianghao Yu and published by Springer. This book was released on 2019-03-27 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and understanding the performance of complicated multi-antenna networks, which are one of the foundations of 5G and beyond networks to meet the ever-increasing demands for network capacity. Describing the salient properties of the framework, which makes the analysis of multi-antenna networks comparable to that of their single-antenna counterparts, the book discusses effective design approaches that do not require complex system-level simulations. It also includes various application examples with different multi-antenna network models to illustrate the framework’s effectiveness.

Download or read book Stochastic Geometry Analysis of Cellular Networks written by Bartłomiej Błaszczyszyn and published by Cambridge University Press. This book was released on 2018-04-19 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Download or read book Modeling and Analyzing the Evolution of Cellular Networks Using Stochastic Geometry written by Yingzhe Li (Ph. D.) and published by . This book was released on 2017 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.

Download or read book Disruptive Events in High density Cellular Networks written by Paul Keeler and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic geometry models are used to study wireless networks, particularly cellular phone networks, but most of the research focuses on the typical user, often ignoring atypical events, which can be highly disruptive and of interest to network operators. We examine atypical events when a unexpected large proportion of users are disconnected or connected by proposing a hybrid approach based on ray launching simulation and point process theory. This work is motivated by recent results [12] using large deviations theory applied to the signal-to-interference ratio. This theory provides a tool for the stochastic analysis of atypical but disruptive events, particularly when the density of transmitters is high. For a section of a European city, we introduce a new stochastic model of a single network cell that uses ray launching data generated with the open source RaLaNS package, giving deterministic path loss values. We collect statistics on the fraction of (dis)connected users in the uplink, and observe that the probability of an unexpected large proportion of disconnected users decreases exponentially when the transmitter density increases. This observation implies that denser networks become more stable in the sense that the probability of the fraction of (dis)connected users deviating from its mean, is exponentially small. We also empirically obtain and illustrate the density of users for network configurations in the disruptive event, which highlights the fact that such bottleneck behaviour not only stems from too many users at the cell boundary, but also from the near-far effect of many users in the immediate vicinity of the base station. We discuss the implications of these findings and outline possible future research directions.

Download or read book Modeling and Analyzing Wireless Networks Using Stochastic Geometry written by Junse Lee and published by . This book was released on 2018 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 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 metrics

Download or read book Stochastic Geometry for Wireless Networks written by Martin Haenggi and published by Cambridge University Press. This book was released on 2013 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyse wireless network performance and improve design choices for future architectures and protocols with this rigorous introduction to stochastic geometry.

Download or read book Stochastic Geometry and Wireless Networks Applications written by François Baccelli and published by Now Publishers Inc. This book was released on 2010-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes.

Download or read book Heterogeneous Cellular Networks written by Rose Qingyang Hu and published by John Wiley & Sons. This book was released on 2013-04-03 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely publication providing coverage of radio resource management, mobility management and standardization in heterogeneous cellular networks The topic of heterogeneous cellular networks has gained momentum in industry and the research community, attracting the attention of standardization bodies such as 3GPP LTE and IEEE 802.16j, whose objectives are looking into increasing the capacity and coverage of the cellular networks. This book focuses on recent progresses, covering the related topics including scenarios of heterogeneous network deployment, interference management in the heterogeneous network deployment, carrier aggregation in a heterogeneous network, cognitive radio, cell selection/reselection and load balancing, mobility and handover management, capacity and coverage optimization for heterogeneous networks, traffic management and congestion control. This book enables readers to better understand the technical details and performance gains that are made possible by this state-of-the-art technology. It contains the information necessary for researchers and engineers wishing to build and deploy highly efficient wireless networks themselves. To enhance this practical understanding, the book is structured to systematically lead the reader through a series of case-studies of real world scenarios. Key features: Presents this new paradigm in cellular network domain: a heterogeneous network containing network nodes with different characteristics such as transmission power and RF coverage area Provides a clear approach by containing tables, illustrations, industry case studies, tutorials and examples to cover the related topics Includes new research results and state-of-the-art technological developments and implementation issues

Download or read book Modeling and Analysis of Wireless Networks with Correlation and Motion written by Chang-sik Choi and published by . This book was released on 2019 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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

Download or read book Spatial Stochastic Models for Network Analysis written by Abishek Sankararaman and published by . This book was released on 2019 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes new stochastic interacting particle models for networks, and studies some fundamental properties of these models. This thesis considers two application areas of networking - engineering design questions in future wireless systems and algorithmic tasks in large scale graph structured data. The key innovation introduced in this thesis is to bring tools and ideas from stochastic geometry to bear on the problems in both these application domains. We identify certain fundamental questions in design and engineering both wireless systems and large scale graph structured data processing systems. Subsequently, we identify novel stochastic geometric models, that captures the fundamental properties of these networks, which forms the first research contribution. We then rigorously study these models, by bringing to bear new tools from stochastic geometry, random graphs, percolation and Markov processes to establish structural results and fundamental phase transitions in these models. Using our developed mathematical methodology, we then identify design insights and develop algorithms, which we demonstrate are instructive in many practical settings. In the setting of wireless systems, this thesis studies both ad-hoc and cellular networks. In the ad-hoc network setting, we aim to understand fundamental limits of the simplest possible protocol to access the spectrum, namely a link transmits whenever it has data to send by treating all interference as noise. Surprisingly this basic question itself was not understood, as the system dynamics is coupled spatially due to the interference links cause one another and temporally due to randomness in traffic arrivals. We propose a novel interacting particle model called the spatial birth-death wireless network model to understand the stability properties of the simple spectrum access protocol. Using tools from Palm calculus and fluid limit theory, we establish a tight characterization of when this model is stable. Furthermore, we show that whenever stable, the links in steady-state exhibit a form of clustering. Leveraging these structural results, we propose two mean field heuristics to obtain formulas for key performance metrics such as average delay experienced by a link. We empirically find that the proposed formulas for delay predicts accurately the system behavior. We subsequently study scalability properties of this model by introducing an appropriate infinite dimensional version of the model we call the Interference Queueing Networks model. The model consists of a queue located at each grid point of an infinite regular integer lattice, with the queues interacting with each other in a translation invariant fashion. We then prove several structural properties of the model namely, tight conditions for existence of stationary solutions and some sufficient conditions for uniqueness of stationary solutions. Remarkably, we obtain exact formula for mean delay in this model, unlike the continuum model where we relied on mean-field type heuristics to obtain insights. In the setting of cellular networks, we study optimal association schemes by mobile phones in the case when there are several possible base station technologies operating on orthogonal bands. We show that this choice leads to a performance gain we term technology diversity. Interestingly, we show that the performance gain relies on the amount of instantaneous information a user has on the various base station technologies that it can leverage to make the association decision. We outline optimal association schemes under various information settings that a user may have on the network. Moreover, we propose simple heuristics for association that relies on a user obtaining minimal instantaneous information and are thus practical to implement. We prove that in certain natural asymptotic regime of parameters, our proposed heuristic policy is also optimal, and thus quantifying the value of having fine grained information at a user for association. We empirically observe that the asymptotic result is valid even at finite parameter regimes that are typical in todays networks. In the application of analyzing large scale graph structured data, we consider the graph clustering problem with side information. Graph clustering is a standard and widely used task which consists in partitioning the set of nodes of a graph into underlying clusters where nodes in the same cluster are similar to each other and nodes across different clusters are different. Motivated by applications in social and biological networks, we consider the task of clustering nodes of a graph, when there is side information on the nodes, other than that contained in the graph. For instance in social networks, one has access to meta data about a person (node in a social graph) such as age, location, income etc, along with the combinatorial data of who are his friends on the social graph. Similarly, in biological networks, there is often meta-data about an experiment that provides additional contextual data about a node, in addition to the combinatorial data. In this thesis, we propose a generative model for such graph structured data with side information, which is inspired by random graph models in stochastic geometry such as the random connection model and the generative models for networks with clusters without contexts, such as the stochastic block model or the planted partition model. We propose a novel graph model called the planted partition random connection model. Roughly speaking, in this model, each node has two labels - an observable R [superscript d] valued (for some fixed d) feature label and an unobservable binary valued community label. Conditional on the node labels, edges are drawn at random in this graph depending on both the feature and community labels of the two end points. The clustering task consists in recovering the underlying partition of nodes corresponding to the respective community labels better than a random assignment, when given an observation of the graph generated and the features of all nodes. We show that if the 'density of nodes', i.e., average number of nodes having features in an unit volume of space of R [superscript d] is small, then no algorithm can cluster the graph that can asymptotically beat a random assignment of community labels. On the contrary, if the density of nodes is sufficiently high, we give a simple algorithm that recovers the true underlying partition strictly better a random assignment. We then apply the proposed algorithm to a problem in computational biology called Haplotype Phasing and observe empirically, that it obtains state of art results. This demonstrates, both the validity of our generative model, as well as our new algorithm

Download or read book Stochastic Geometry Analysis of LTE A Cellular Networks written by Peng Guan and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this thesis is on performance analysis and system optimization of Long Term Evolution - Advanced (LTE-A) cellular networks by using stochastic geometry. Mathematical analysis of cellular networks is a long-lasting difficult problem. Modeling the network elements as points in a Poisson Point Process (PPP) has been proven to be a tractable yet accurate approach to the performance analysis in cellular networks, by leveraging the powerful mathematical tools such as stochastic geometry. In particular, relying on the PPP-based abstraction model, this thesis develops the mathematical frameworks to the computations of important performance measures such as error probability, coverage probability and average rate in several application scenarios in both uplink and downlink of LTE-A cellular networks, for example, multi-antenna transmissions, heterogeneous deployments, uplink power control schemes, etc. The mathematical frameworks developed in this thesis are general enough and the accuracy has been validated against extensive Monte Carlo simulations. Insights on performance trends and system optimization can be done by directly evaluating the formulas to avoid the time-consuming numerical simulations.

Download or read book A Non Uniform User Distribution and Its Performance Analysis on K tier Heterogeneous Cellular Networks Using Stochastic Geometry written by Chao Li and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the cellular networks, to support the increasing data rate requirements, many base stations (BSs) with low transmit power and small coverage area are deployed in addition to classical macro cell BSs. Low power nodes, such as micro, pico, and femto nodes (indoor and outdoor), which complement the conventional macro networks, are placed primarily to increase capacity in hotspots (such as shopping malls and conference centers) and to enhance coverage of macro cells near the cell boundary. Combining macro and small cells results in heterogeneous networks (HetNets). An accurate node (BS or user equipment (UE)) model is important in the research, design, evaluation, and deployment of 5G HetNets. The distance between transmitter (TX), receiver (RX), and interferer determines the received signal power and interference signal power. Therefore, the spatial placement of BSs and UEs greatly impacts the performance of cellular networks. However, the investigation on the spatial distribution of UE is limited, though there is ample research on the topic of the spatial distribution of BS. In HetNets, UEs tend to cluster around BSs or social attractors (SAs). The spatial distribution of these UEs is non-uniform. Therefore, the analysis of the impact of non-uniformity of UE distribution on HetNets is essential for designing efficient HetNets. This thesis presents a non-uniform user distribution model based on the existing K-tier BS distribution. Our proposed non-uniform user distribution model is such that a Poisson cluster process with the cluster centers located at SAs in which SAs have a base station offset with their BSs. There are two parameters (cluster radius and base station offset) the combination of which can cover many possible non-uniformity. The heterogeneity analysis of the proposed nonuniform user distribution model is also given. The downlink performance analysis of the designed non-uniform user model is investigated. The numerical results show that our theoretical results closely match the simulation results. Moreover, the effect of BS parameters of small cells such as BS density, BS cell extension bias factor, and BS transmit power is included. At the same time, the uplink coverage probability by the theoretical derivation is also analyzed based on some simplifying assumptions as a result of the added complexity of the uplink analysis due to the UEs' mobile position and the uplink power control. However, the numerical results show a small gap between the theoretical results and the simulation results, suggesting that our simplifying assumptions are acceptable if the system requirement is not very strict. In addition to the effect of BS density, BS cell extension bias factor, and BS transmit power, the effect of fractional power control factor in the uplink is also introduced. The comparison between the downlink and the uplink is discussed and summarized at the end. The main goal of this thesis is to develop a comprehensive framework of the non-uniform user distribution in order to produce a tractable analysis of HetNets in the downlink and the uplink using the tools of stochastic geometry.