Dynamic System Modelling and Adaptation Framework for Irregular Cellular Networks. Levent Kayili

Transcription

1 Dynamic System Modelling and Adaptation Framework for Irregular Cellular Networks by Levent Kayili A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto c Copyright 2015 by Levent Kayili

2 Abstract Dynamic System Modelling and Adaptation Framework for Irregular Cellular Networks Levent Kayili Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2015 In the decades since the development of the traditional cell concept, there has been much research in the field of cellular networks for greater adaptability. In particular, networks with irregular deployment of base stations (BSs) having widely different power classes, have received much attention in industry and academia alike. In such networks, BSs of both high and low power capabilities, are deployed in broad accordance with user traffic demand. In this thesis, we consider irregular cellular networks from the viewpoint of the design, adaptability and dynamism of adaptive resource allocation. Despite extensive research in the area, to our knowledge high-level system modelling for simulation purposes did not receive attention in the literature. We consider the development of such a model in this thesis. In particular, we assume a network with universal frequency allocation and power assignment. A high-level model representation and an adaptive coordinated resource allocation strategy is developed for such a network. A modified Monte Carlo simulation is proposed as a simulation model, which includes representation of BS and terminal deployments in scenarios either with or without hotspots, as well as a set of dynamics occurring at a large time scale. A representation including such dynamics is expected to be important for the consideration of adaptive resource allocation strategies and other adaptive functions such as Self Organization (SO) that operate at an assumed large time scale. A shadowing model with spatial correlation is considered as part of the system model, and is generalized for a network with an arbitrary number of distinct BS power ii

3 classes. Enhancements are then proposed to an adaptive re-configurable resource allocation framework which is based on dynamically forming scheduling cells at a large time scale. In particular, a strategy for BS power adaptation at a large time scale is proposed for improved interference mitigation. The dynamic adaptation case of BS outage compensation is additionally studied as an application of the model and adaptive resource allocation. It is believed that the high-level model with resource allocation can serve as a skeleton network model to be tailored to different purposes for more realistic network representation and design. iii

4 Acknowledgements First and foremost, I would like to begin by extending my deep gratitude to my supervisor, Professor Sousa. His guidance and support throughout my studies inspired me greatly in the pursuit of my research. I learned so much from him throughout the years, for which I am truly grateful. I would also like to thank the members of my defense committee Professor Adve, Professor Leon-Garcia, and Professor Valaee, and the external examiner, Professor Rodrigues, for their time in reading my thesis and providing many helpful comments and suggestions. I cannot overstate the value of having great colleagues throughout my years as a graduate student. For this reason, I would like to sincerely thank my fellow graduate students for their camaraderie and for providing the opportunity for many interesting conversations and discussions over the years. Finally, I would like to thank my parents, who have supported me, and encouraged me greatly throughout my Ph.D. studies. I am truly grateful for their support, and I believe that without it, the completion of my work would not have been possible. iv

5 Contents 1 Introduction Motivation Approach Contributions Scope Outline Background and Preliminaries Cellular Network Preliminaries User Scheduling Metrics Total Rate Maximization Proportional Fair Scheduling Resource Allocation Strategies Adaptive Resource Allocation Framework for Irregular BS Deployment General Slow-Time-Scale Adaptive Algorithms The ITU System Model: High-Level Reference Model for the Regular Cellular Network Channel Modelling Considerations for an Irregular Cellular Network Model Correlated Shadowing Model for Irregular BS Deployment Adaptation Case: BS Outage Compensation Relevant Work and Contribution Relevant Work Contribution Key Results Introduction Problem Statement and Proposed Algorithmic Approach v

6 3.4 Proportional Fair Compensation Algorithm Outage User Cell Re-association Generation of Compensating Cluster BS Power Adjustment Overall Algorithm Information Exchange Requirements PLM Compensation Algorithm Simulation/Evaluation Numerical Results Dynamic System Model (Single Power Class) Relevant Work Terminal and BS Deployment Models in Cellular Networks Terminal Mobility Models in Cellular Networks Approach and Contributions Introduction Drop Deployment Model Time Evolution Terminal Arrival and Departure Models BS Deployment and Outage Models Terminal Movement Model BS Movement Model Typical Parameter Values The Outline of the Network Model of the Thesis BS Power Adaptation (Single Power Class) Relevant Work: Interference Coordination Strategies for Heterogeneous Networks Contribution: Adaptive Resource Allocation Framework with Power Adaptation Key Results Introduction BS Power Adaptation Algorithm Total Rate Maximizing (TRM) Power Adaptation Proportional Fair Power Adaptation Adaptive Resource Allocation Framework with Power Adaptation Simulations vi

7 6 Static Model of Multiple Power Classes Relevant Work Contribution Introduction Deployment Model with Hotspots Distance Dependent Path Loss Model Inhomogeneous Shadowing with Correlation Generation of Shadowing for Links between BS-Terminal Pairs Shadowing Model Consistency Verification Implementation of Model in Practical Network Simulations Dynamic System Model (Multiple Power Classes) Relevant Work and Contribution Key Results Introduction Time Evolution Terminal Arrival and Departure Models BS Deployment and Outage Models Terminal Movement Model BS Movement Model Typical Parameter Values Simulations Conclusion Summary Future Work Bibliography 136 vii

8 List of Figures 2.1 Regular cellular network deployment. The black and red points represent a BS and terminals, respectively Representation of the irregular cellular network deployment. The green circles represent terminals, and the blue squares of different sizes represent BSs of different power classes Hypothetical scenario for terminal scheduling Flowchart for the adaptive resource allocation framework Algorithm for the adaptive resource allocation framework Algorithm for fast PF resource allocation for a given subframe l F The flowchart for the drop-based simulation framework based on the ITU common reference model The wireless link between a fixed base station and a moving terminal Wireless links with a common endpoint Wireless links without a common endpoint A realization of the potential field [8] BS outage scenario. The light blue square is the outage BS (BS n 0 ), the light blue circles are the outage users, dark blue squares are the candidate BSs, dark blue circles are the associated users, and the red squares and circles are the BSs and users outside the candidate set, respectively Outage user cell association update Compensating BS power update Overall iteration of the PF compensation algorithm PLM Compensation Algorithm User average spectral efficiency, in bps/hz, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks. 50 viii

9 3.7 Outage user QoS violation probability, in percent, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks Non-outage user QoS violation probability, in percent, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks Outline of the Simulation Framework Simulation area for deployment in networks with a single BS power class The terminal movement illustration Algorithm for the terminal movement at the simulation subdrop The BS movement illustration Algorithm for the BS movement at the simulation subdrop Sample realization of the evolution of the number of terminals K (b) over subdrops b, with K (0) = 25, the arrival parameter λ t = 3 terminals, and the departure parameter µ t = 5 subdrops Sample realization of the evolution of the number of BSs N (b) over subdrops b, with N (0) = 7, the arrival parameter λ bs = 0.5 BSs, and the departure parameter µ bs = 20 subdrops A realization of the potential field [8] Flowchart of the general network model in the thesis Extended adaptive resource allocation framework with power adaptation Algorithm for the adaptive resource allocation framework with TRM power adaptation Algorithm for the adaptive resource allocation framework with PF power adaptation Simulation area for cellular network Comparison of power adaptation schemes and the equal power level scenario for varying δ BS in terms of 5th percentile spectral efficiency, with K = 28 users Comparison of power adaptation schemes and the equal power level scenario for varying δ BS in terms of 50th percentile spectral efficiency, with K = 28 users Cumulative distribution functions for spectral efficiency at δ BS = 4h/3 = m, with (a) normal magnification and (b) increased magnification, with K = 28 users ix

10 5.8 Comparison of power adaptation schemes and the equal power level scenario for varying δ BS in terms of the sum log utility, with K = 28 users Comparison of power adaptation schemes and the equal power level scenario for varying δ BS in terms of the user average spectral efficiency, with K = 28 users Comparison of power adaptation schemes and the equal power level scenario for varying δ BS in terms of the user average spectral efficiency, with K = 56 users Simulation area for deployment in networks with multiple BS power classes and explicit hotspot modelling Sample radio link in an irregular cellular network. Here, L is the total length of the link path; k K is an index value for a terminal; n N and p N are index values for the BSs such that n p, n 1, n 2, p 1 and p 2; and l m is the length of path segment assigned to a BS m N Algorithm for assigning path segments to BSs Shadowing simulation scenario Comparison of normalized correlation as a function of normalized distance, d/d c,eff, Outline of the Simulation Framework The terminal movement illustration Algorithm for the terminal movement at the simulation subdrop The BS movement illustration Algorithm for the BS movement at the simulation subdrop Comparison of power adaptation schemes and the equal power level scenario for varying terminal displacement in terms of (a) 5th percentile spectral efficiency, and (b) 50th percentile spectral efficiency Comparison of power adaptation schemes and the equal power level scenario for varying terminal displacement in terms of (a) the sum log utility, and (b) the user average spectral efficiency Comparison of power adaptation schemes and the equal power level scenario for varying number of users in terms of (a) 5th percentile spectral efficiency, and (b) 50th percentile spectral efficiency Comparison of power adaptation schemes and the equal power level scenario for varying number of users in terms of (a) the sum log utility, and (b) the user average spectral efficiency x

11 Chapter 1 Introduction 1.1 Motivation The cellular concept in mobile telephone networks was developed in the late 1960s. In the original cellular paradigm, an area was divided up into cells with more or less regular sizes, with BSs placed at cell centres. A hexagonal cell model was typically used for the representation of the coverage areas in this network. In order to allocate the frequency spectrum resource efficiently to mobile users, and provide acceptable user rates, it was necessary to reduce the effects of co-channel interference. This was achieved through a static frequency allocation strategy known as classical frequency reuse, which allowed reuse of the spectrum resource at a fixed distance while keeping the co-channel interference low. The network was designed for the provision of acceptable wireless service over a given geographical area, however, it accounted for little in the form of dynamism or adaptation. In particular, the frequency allocation strategy was static, and there was no capability for organic growth of the network, in particular, from the viewpoint of adaptation of the resource allocation. Such a network shall be referred to, in this work, as a regular cellular network. The traditional cellular network with regular deployment can be said to have a highlevel reference model for the purpose of simple Monte Carlo simulation, which provides a high-level representation of the system. Such a model, that is well-known and commonly used, has been described in the International Telecommunication Union (ITU) guidelines [1] which was developed for the IMT-Advanced and is applicable to 3GPP LTE. According to the model, the BS deployment is regular and the coverage areas are represented by a regular (hexagonal) cell pattern. There is an allowance for a great amount of detail for modelling the variation of multipath fading at the small time scale, but channel modelling at the (assumed) larger time scale, in particular, the shadow fading 1

12 Chapter 1. Introduction 2 follows the classical lognormal model, which does not take into account more realistic effects like the shadowing spatial correlation. In addition, the simulation methodology for the system model does not consider the gradual evolution of the system at time scales much larger than the multipath fading, which are due to the dynamical changes in the network. Instead, independent snapshots known as simulation drops are typically used in Monte Carlo type simulation. A simulation drop, in this context, is defined as a random deployment of mobile terminals on a network area with fixed BS deployments, following the hexagonal cell pattern. Within each drop, the set of active terminals and their deployments as well as large-scale channel components such as path loss and shadowing are fixed, and there are only virtual terminal movements, which result in the multipath fading due to the Doppler effect. This high-level model can be associated with a model for the organization of resource allocation, which is the traditional scheme of classical frequency reuse, as already mentioned. Thus classical frequency reuse (CFR) is considered as part of the overall model. The system model based on the traditional cell concept with regular deployment, little large-scale dynamism as well as classical frequency reuse shall be referred to, in this thesis, as the regular cellular network model. In the decades since the development of the traditional cell concept, there has been much research in the field of cellular networks for greater adaptability. In order to meet the increasing demands from mobile users while allowing the efficient use of the frequency spectrum, BSs of different transmit power capabilities, known as power classes, have started being used. The deployment of these BSs have been in broad accordance with the user traffic demand. In particular, in areas with high density of user traffic, or local hotspots, low-power BSs with small cell sizes have started being used. In other areas with lower density of traffic, high-power BSs having large cell sizes were still utilized. The heterogeneous cellular network was therefore born as a research area and received much attention as a vast and varied field. While many definitions exist for heterogeneous networks, we consider the definition of a network with a single air interface and technology, and multiple power classes such as femto, pico, micro and macro BSs. Techniques were required for the organic growth of such networks, especially in terms of the adaptability of the resource allocation. Strategies that were much more dynamic than the classical frequency reuse were therefore proposed and adopted. In addition, much research work was done to enhance the modelling of the heterogeneous cellular network with regard to various aspects such as deployment, mobility and multipath fading channel models as well as, in a few cases, the shadowing. However, a number of unrealistic assumptions continued to be used in some of the work, mainly for the purpose of analytical tractability and simplicity of the modelling. These included, e.g., the use of the Poisson point pro-

13 Chapter 1. Introduction 3 cess (PPP) as a deployment model, which was shown to be unrealistic in real networks. They also included the use of uncorrelated lognormal shadowing and Rayleigh multipath fading models. Despite the extensive research on system modelling, to our knowledge high-level system modelling for simulation purposes, like the ITU model, did not receive attention in the literature. We consider the development of such a model in this thesis. We assume a network with universal frequency allocation and power assignment. The main motivation of such a high-level simulation model is to provide a candidate for a new high-level reference model, in the face of new research and practical developments such as heterogeneous networks as well as recent research on adaptive resource allocation strategies as well as self organization (SO) that commonly work at an assumed large time scale. The goal is to provide a high-level model representation, including an adaptive resource allocation strategy, over which new and different research efforts can then make gradual improvements driven by the need to represent the network with as much realism as required or desired for each particular situation. In our view, a benefit of the model is that researchers need not be forced to make unrealistic assumptions about deployment, shadowing, multipath fading, large time scale evolution including movement, as well as the interferers for the purpose of analysis and design. For instance, some works could provide more detail on realistic deployment and shadowing, and other works more detail on realistic multipath fading models. This contrasts with the efforts to make the models more analytically tractable using models of varying degrees of realism. Similarly, some works can focus on the aspect of resource allocation at the small time scale (or on multiple antennas), and others on making small adjustments at a larger time scale to the cellular architecture in order to adapt to the dynamism of the network. Different modifications made to such a high-level reference model by different researchers can then be compared. 1.2 Approach For the purpose of model development, we consider a network which includes BSs with multiple power classes deployed according to an irregular pattern, as in a heterogeneous cellular network. The generic type of network that is considered shall be referred to as an irregular cellular network. In this thesis, we develop a high-level model for the irregular cellular network as a modification of the regular cellular network model of the ITU. This model, which shall be referred to as the irregular cellular network model, must have characteristics that contrast with the regular cellular network model. In the new paradigm, high- and low-powered BSs are deployed in an irregular pattern in broad

14 Chapter 1. Introduction 4 accordance with the user demand. Thus a model of arbitrary BS deployment must be considered in place of the hexagonal deployment. Since the dynamics of the network at time scales other than the assumed multipath fading scale are gaining a lot of importance, the independent snapshot method of drop simulation is, inadequate, and an improved concept is needed. The set of additional dynamics in the model occurring at a slower scale can include terminal activations, deactivations and movements, BS deployments and outages, gradual changes in the large-scale channel components among others. Finally, a more realistic shadowing model is needed to reflect gradual variation of shadowing over space and the time as well as the diverse radio propagation environments in the network. Additionally, we consider and enhance a strategy for spectrum resource allocation [2] for the described irregular cellular network model. The particular resource allocation strategy is based on the idea of independent units of cells formed for coordinated resource allocation, which are known as scheduling cells or clusters. According to the framework, the scheduling cells, which represent a variation of the well-known cellular architecture, are updated dynamically with the changing network conditions at a large time scale, and the resource allocation takes place at the faster time scale of the multipath fading. Due to the existence of BSs with multiple power classes deployed in an irregular fashion, it is proposed that the adaptive resource allocation framework include large-time-scale BS power adaptation for the optimization of user performance. The parts of the work are summarized in the following: Initially, we discuss the BS outage as a type of dynamic change in the irregular cellular network, formulate a BS outage compensation problem and propose an algorithmic framework for the problem. Effectively, BS outage compensation is used as a specific case of the dynamic system model and adaptations for irregular cellular networks that are studied in the rest of the thesis. This work was published, in part, in [3]. We extend the adaptive resource allocation framework from [2], proposing BS power adaptation as an additional form of adaptation for the irregular cellular network with either a single or multiple power classes. This work is part of a journal paper [4] that will be submitted for publication. We propose BS and terminal deployment models that are appropriate for networks with either single or multiple power classes. This work is also part of the journal paper [4] that will be submitted for publication. We propose a model for large-time-scale network evolution for either a single or

15 Chapter 1. Introduction 5 multiple power classes, which consists of such dynamic changes as terminal arrival, departure and movements as well as BS deployments and outages. This contribution was published, in large part, in [5], and forms part of the contribution in [4]. We propose path loss and shadow fading models for the case of multiple power classes. This work has been accepted to be published in [6]. 1.3 Contributions The contributions of the thesis are summarized in the following. Base Station Outage: Network Model and Compensation Algorithm Most works in the literature consider the base station (or cell) outage compensation (COC) for homogeneous or regular networks. Furthermore, even works that consider irregular networks do not explicitly consider the modelling aspect of the problem. We focus on the modelling of a BS outage for an irregular network with multiple power classes in a general sense. Both the positions of BSs and the power classes are modelled. In addition, we consider the adaptive resource allocation strategy as part of the overall model. Specifically, we adopt the concept of cluster or scheduling cell for the purpose of coordinated adaptive resource allocation. To our knowledge, the use of a scheduling cell is new for the COC literature. Direct sum log utility maximization based on proportional fairness is the primary formulation used in finding a compensating cluster, outage user cell associations, and the adjusted BS power levels. The use of proportional fairness in the COC formulation is additionally different from the literature for COC. Finally, the shadowing model with spatial correlation for irregular deployment is considered for greater realism. Base station outage compensation is discussed in Chapter 3. Deployment Model The most common model in the literature for irregular deployments is the PPP model due to its simplicity and analytical tractability. However, the PPP model was shown to be unrealistic in real irregular networks. Other more realistic models exist (with the primary example being the Ginibre process [7]) however most such models have the issue of being difficult to handle. In this work, we consider the development of a baseline deployment model for Monte Carlo simulation with the primary consideration being the model simplicity and a baseline realism, which is implemented through arbitrariness or randomness of deployment with a minimum separation between the nodes and the

16 Chapter 1. Introduction 6 elements in the network. Deployment scenarios both with hotspots (multiple power classes) and without hotspots (single power class) are considered. Since this is meant as a generic model, guidelines for parameter values are provided for baseline realism of the simulation scenario. Deployment models are discussed in Chapters 4 and 6 for the case of single power class and multiple power classes, respectively. Mobility Model Most other models in the literature do not consider terminal movements over an arbitrarily large time scale as a snapshot. We propose a generic model for individual mobility (similar to the random walk model) that is meant as a generic model appropriate for a time scale that is orders of magnitude larger than the multipath fading time scale. The primary consideration for the model is its simplicity. A similar movement model is also then considered for BSs. Deployment scenarios both with hotspots (multiple power classes) and without hotspots (single power class) are considered for the movements. Since this is meant as a generic model, guidelines for parameter values are provided for the baseline realism of the simulation scenario. Mobility models are discussed in Chapters 4 and 7 for the case of single power class and multiple power classes, respectively. Shadowing Model Most of the work in the literature considers the uncorrelated lognormal shadowing model. While a few authors proposed correlated shadowing models for links with a common end and more recently, for links without a common end, to our knowledge, no work considers a theory for variation of the shadowing parameters, i.e. standard deviation and correlation distance, in a network with an arbitrary number of radio propagation environments. Such a theory is proposed based on a hypothesis for the shadowing properties, and a method of generation of shadowing for radio links is provided based on the work in [8]. Finally, model consistency is verified for a particular scenario, and the implementation in practical simulations is discussed. The model is intended for the baseline realism of the simulation scenario. The shadowing model for multiple power classes is discussed in Chapter 6. Adaptive Resource Allocation Framework with Power Adaptation An adaptive resource allocation framework based on clustering and power control at a large time scale and coordinated proportional fair resource allocation at a small time scale is proposed for a generic irregular network. Note that in heterogeneous networks, the cell

17 Chapter 1. Introduction 7 association is normally determined based on maximizing long-term received power and membership to different tiers is explicitly considered. In this work, we assume association to a cell of any tier based on maximization of long-term channel gains. The primary contribution is the power control algorithm for the purpose of adaptive resource allocation at a large time scale. While much of the literature considers power control at the multipath fading time scale, the acquisition of channel information at this scale can lead to substantial signaling requirements. In addition, much of the literature considers static or semi-static allocation of a dedicated spectrum for the purpose of resource allocation. Our contribution considers the use of the entire spectrum for greater spectral efficiency and the power adaptation at a large time scale, to reduce the signaling requirement. As the adaptive framework is to be used for a general or arbitrarily large time scale, the availability of individual QoS requirements at such periodicity are not assumed. Instead, a central entity does its best effort to maximize either the long-term sum rate or the sum log utility (based on proportional fairness) over the time scale under the modest assumption of base station power constraints. The framework is intended as a baseline adaptive resource allocation framework for an irregular network. The adaptive resource allocation framework with power adaptation is discussed in detail in Chapter Scope Multiple antenna technologies such as beamforming or MIMO are not explicitly considered. Downlink communication is exclusively considered. Orthogonal frequency division multiple access (OFDMA) scheme such as that used in 3GPP LTE is considered for the analysis. Full buffer traffic is considered for scheduling. 1.5 Outline In Chapter 2, we provide a background for resource allocation strategies and the highlevel reference model for cellular networks. We begin by giving preliminaries for the cellular network in Section 2.1. The basic definition is specialized to the cases of regular and irregular cellular networks. Finally, the computation of data rates for user scheduling in cellular networks is described. We then review the scheduling metrics and resource

18 Chapter 1. Introduction 8 allocation strategies utilized in cellular networks in Sections 2.2 and 2.3, respectively. An adaptive resource allocation framework for irregular BS deployment is discussed in detail in Section 2.4. General slow-time-scale adaptive algorithms in the literature are then reviewed in Section 2.5. In the later part of the chapter, we introduce the highlevel reference model for the regular cellular network paradigm in Section 2.6, which is represented in the ITU model. Then the considerations for the for the irregular cellular networks are summarized in Section 2.7. Finally, the literature on a model for correlated shadowing that is appropriate for irregular BS deployment is reviewed in Section 2.8. Chapter 3 presents a model for a BS outage and a framework for compensation of the outage. Section 3.1 discusses the relevant work, contribution and key results. Section 3.2 starts the chapter with an introduction. In Section 3.3, the problem statement is given and the proposed algorithmic approach is discussed. The proportional fair algorithm for BS outage compensation is developed in Section 3.4. The path loss minimizing compensation algorithm is proposed in Section 3.5. The algorithms are evaluated through numerical simulations in Section 3.6. Chapter 4 presents a system model which includes time evolution for the irregular network with a single BS power class and no power level adaptation. Sections 4.1 and 4.2 discuss the relevant work and the approach and contributions. Section 4.3 introduces the topic. The method for drop deployment is introduced in Section 4.4. The time evolution methodology is developed in Section 4.5. The typical parameter values for the system model are discussed in Section 4.6. Finally, the outline of the network model of the thesis is given in Section 4.7. Chapter 5 presents algorithms for BS power level adaptation and an extended adaptive resource allocation framework for networks with a single BS power class. Sections 5.1 and 5.2 discuss the relevant work, contributions and key results. Section 5.3 introduces the topic. The power adaptation algorithms are developed in Section 5.4. The overall adaptive resource allocation framework including the power adaptation is presented in Section 5.5. Finally, simulations are performed in Section 5.6. Chapter 6 presents the system model without time evolution for cellular networks with multiple BS power classes. Sections 6.1 and 6.2 discuss the relevant work and contributions, respectively. Section 6.3 introduces the topic. In Section 6.4, drop deployment with explicit modelling of hotspots is discussed. In Section 6.5, the distance-dependent path loss model is specialized to the network with multiple BS power classes. The model of correlated shadowing with inhomogeneous channel parameters is detailed in Section 6.6. Chapter 7 presents the final system model with time evolution for networks with

19 Chapter 1. Introduction 9 multiple BS power classes. Section 7.1 discusses the relevant work, contribution and key results. Section 7.2 begins the discussion of the chapter. The modified time evolution methodology is detailed in Section 7.3. In Section 7.4, the typical parameter values for the model are discussed. Illustrative simulations results are presented for the network with multiple power classes in Section 7.5. Chapter 8 concludes the thesis with a summary of the work and possible future research directions.

20 Chapter 2 Background and Preliminaries In this chapter, we provide a background for resource allocation strategies and the highlevel reference model for cellular networks. We begin by giving preliminaries for the cellular network in Section 2.1. We then review the scheduling metrics and resource allocation strategies utilized in cellular networks in Sections 2.2 and 2.3, respectively. An adaptive resource allocation framework for irregular BS deployment is discussed in detail in Section 2.4. General slow-time-scale adaptive algorithms in the literature are then reviewed in Sections 2.5. In the later part of the chapter, we introduce the high-level reference model for the regular cellular network paradigm in Section 2.6, which is represented in the ITU model. Then the considerations for a high-level model for the irregular cellular network are summarized in Section 2.7. Finally, the literature on a model for correlated shadowing that is appropriate for irregular BS deployment is reviewed in Section Cellular Network Preliminaries In this section, we discuss the basic cellular network model studied in the thesis. Consider a network consisting of a set of BSs N and a set of terminals K. The positions of each BS n N and each terminal k K are represented by the Cartesian coordinates (x n, y n ) and (x k, y k ), respectively. Each BS is said to belong to a power class, s, which is characterized by a distinct maximum transmit power capability, P s,max. The set of all available BS power classes is denoted by S. The power class of a given BS n is denoted by s n. By definition of a power class, BS n s operating power level, P n, must satisfy 0 P n P sn,max. Under practical network operating conditions, terminal positions, (x k, y k ), evolve due to terminal movement. Each terminal k is dynamically assigned to a single BS, denoted by n(k), for the purpose of scheduling and resource allocation. In 10

21 Regular Network (Traditiona Chapter 2. Background and Preliminaries 11 Fixed cell boundaries Cell membership straightforward Classical frequen reuse Scheduling is organized in straightforward w Figure 2.1: Regular cellular network deployment. The black and red points represent a BS and terminals, respectively. the following, the basic model introduced in this section is specialized for the cases of regular and irregular cellular networks. Regular Cellular Network Cells in the regular network are modelled with the hexagonal cell structure of Figure 2.1; therefore, the base station coordinates, (x n, y n ), coincide with the hexagon centres. The number of power classes in the regular network (or the number of elements in set S) is equal to one, that is, S S = 1, and the maximum transmit power capability of each BS is represented by a constant, P max. Finally, the operating power level, P n, of each BS is typically held constant at P max. Irregular Cellular Network The focus of this thesis is the study and modelling of the irregular network. In the irregular network, BSs are deployed in an inhomogeneous or arbitrary pattern, hence, the BS coordinates, (x n, y n ), are irregular as shown in Figure 2.2. In addition, BSs belong to a number of different power classes, which are characterized by a wide range of maximum power capabilities. Therefore, in the irregular network, S = S > 1. It will also be proposed later in the thesis that the BS power levels, P n, be dynamically adapted in the range 0 P n P sn,max, according to changing network conditions.

22 Irregular Cellular Network Chapter 2. Background and Preliminaries Dynamic BS assignments based on max channel gain 2. Dynamically form clusters (scheduling cells) Figure 2.2: Representation of the irregular cellular network deployment. The green circles represent terminals, and the blue squares of different sizes represent BSs of different power classes. 3 Computation of Transmittable Data Rates for Scheduling In this thesis, we adopt the organization of the time-frequency resource allocation from 3GPP LTE standards [9]. Terminal scheduling is performed at the LTE subframe (which corresponds to the assumed time scale of multipath fading variation) and requires the knowledge of transmittable data rates for links between all terminals and BSs. Note that computation of transmittable data rates further requires the knowledge of channel gains for all links. Let C be the set of available subcarriers in orthogonal frequency division multiplexing (OFDM). The channel power gain between BS n N and terminal k K on subcarrier c C is computed as the product of the distance-dependent path loss component, P L n,k, the large-scale shadowing component, SF n,k, and the small-scale multipath component, m n,k,c : g n,k,c = P L n,k SF n,k m n,k,c. (2.1) where the models for the channel components are elaborated later in Section 2.6. The transmittable rate, between terminal k and BS n on subcarrier c, has been approximated in [2] for the LTE system, through curve fitting of the Shannon rate formula with an SINR gap, γ:

23 Chapter 2. Background and Preliminaries 13 where r k,n,c = Bc min ( ( log SINR ) ) k,n,c, , (2.2) γ γ = 2, (2.3) p n,c g n,k,c SINR k,n,c = N 0 + j N, j n p. j,cg j,k,c (2.4) Here, B C is the subcarrier bandwidth, p n,c is the power transmitted on subcarrier c by BS n and N 0 is the noise power on each subcarrier at the receiver. 2.2 User Scheduling Metrics There has been much research by various authors [10 13] on the appropriate metric to be used for resource allocation including user scheduling. In the following, we consider full-buffer persistent data traffic conditions. Two significant scheduling metrics known as total rate maximization and proportional fair scheduling are described under such conditions Total Rate Maximization The traditional scheduling strategy has been the maximization of the total system rate in the long term [14], which shall be referred to as the total rate maximization (TRM). Under this strategy, the average rate performance of the system as a whole is optimized without regard for any single individual user s performance. The long-term TRM optimization objective is given by max k K n R k for all n N. (2.5) where K n = {k n(k) = n} is the set of terminals assigned to BS n for scheduling, and R k is the time-averaged rate for terminal k. Consider a single-frequency system. The terminal scheduled by BS n at subframe t is determined with the knowledge of the transmittable rate, r k (t), as k n(t) = arg max k K n r k (t) for all n N, (2.6) which has been shown to be equivalent to the long-term optimization of (2.5). In practice, there is a significant problem with the use of the total rate maximization of (2.5) and (2.6). Consider the simple hypothetical scenario consisting of a single BS and two

24 Chapter 2. Background and Preliminaries 14 Terminal 1 Terminal 2 BS Figure 2.3: Hypothetical scenario for terminal scheduling. stationary terminals depicted in Figure 2.3. Terminal 1 is much closer to the BS than Terminal 2, and therefore Terminal 1 will tend to have much higher channel gain on average. We additionally assume that the channel gain fluctuations over time are small in comparison to Terminal 1 s channel gain. According to the TRM criterion of (2.6), therefore, Terminal 1 would be scheduled at all of the subframes, and Terminal 2 would not be scheduled at any of the subframes. This situation where Terminal 2 is deprived of service is commonly referred to as the fairness problem in the literature [10, 15]. Proportional fair (PF) scheduling criterion [14], which was proposed in order to overcome the fairness problem, is discussed in the next section Proportional Fair Scheduling According to the proportional fair (PF) criterion, scheduling should maximize the sum log utility (SLU) function, which is computed as the sum of the logarithm of the average user rates. Therefore, the long-term optimization objective is max log(r k ) for all n N. (2.7) k K n Since the logarithm function increases at a continually decreasing (or diminishing) rate, PF scheduling overcomes the fairness problem encountered in TRM. In particular, consider the scenario depicted in Figure 2.3. Terminal 2, i.e., the user with the weak channel, is said to be treated fairly, because a given increase in user data rate, for example, 10 kbps, for Terminal 2 (the weak user) results in a greater increase in utility than the same amount of data rate increase for Terminal 1 (the strong user). The concept of the decreasing rate of utility increase is known in economics as the law of diminishing marginal returns or law of diminishing marginal utility [16]. Under SLU maximization, Terminal 2 is therefore expected to achieve a non-zero average data rate. In fact, as discussed

25 Chapter 2. Background and Preliminaries 15 in detail in [17], both terminals achieve a long-term rate that is approximately proportional to their average transmittable rate based on the respective channel gains, which is the reason for the term proportional fairness. For more details on the properties of PF scheduling, the reader may refer to some of the many works on the topic [10 15, 17]. For a single-frequency system, the optimization of (2.7) is realized by scheduling terminal kn(t) at each subframe t, with the knowledge of instantaneous achievable rate r k (t) and time-averaged rate R k (t), that is, k n(t) = arg max k K n r k (t) R k (t) for all n N (2.8) Note that the time-averaged rate is updated at each subframe based on an exponential moving average: R k (t + 1) = ) ( ) (1 1T0 1 R k (t) + r k (t) (2.9) T 0 where T 0 is the averaging window size selected for smooth averaging. In a system with multiple frequencies, the scheduling is performed either independently in each subcarrier at the subframe or through more elaborate strategies. Note that the PF scheduling will be used in the rest of the thesis. 2.3 Resource Allocation Strategies In the traditional cellular network, the BSs are deployed according to a regular pattern, which is modeled with hexagons. The strategy of classical frequency reuse is utilized. According to this scheme, the BSs are partitioned into groups of geographically adjacent cells, known as frequency reuse clusters. The frequency reuse factor (FRF) defines the size of the clusters, and the available spectrum is distributed among the BSs according to pre-defined patterns. The FRF is said to be an indicator of the level of frequency reuse in the network. In early networks, high (or conservative) reuse factors were used for the avoidance of excessive interference. However, the scheme did not consider the variation of traffic load in the cells. In addition, the ever growing demand for capacity necessitated more aggressive frequency reuse, which would cause degraded performance for terminals at the cell edges. More recently, the fractional frequency reuse (FFR) technique was proposed as an alternative to classical frequency reuse. In this scheme (also referred to as static FFR), two different frequency reuse patterns are applied: a higher (or conservative) reuse factor for the cell-edge terminals with weak channel gains, and a lower (or aggressive) reuse

26 Chapter 2. Background and Preliminaries 16 factor for the stronger or cell-centre terminals. The drawback of the method was that the terminal partitioning was based solely on distances from the BSs, and the spectrum assignments again did not adapt to the variations of traffic load. To overcome the limitations of static FFR, techniques have recently been proposed in the literature that attempt to adapt to the variation in traffic, by using different methods to organize the frequency resource allocation. This goal is commonly achieved by coordination of resource allocation between neighboring BSs, which is also referred to in the literature as inter-cell interference coordination (ICIC). Different types of techniques are reviewed in the following. Dynamic FFR Dynamic FFR schemes attempt to adapt to variations of traffic while maintaining the general concept of FFR in the method. Boudreau et al. [18] have proposed an adaptive frequency reuse strategy for interference coordination suitable for 4G networks. The scheme switches between three different frequency-power profiles according to the traffic load in each cell. Ali and Leung [19] present an elaborate dynamic frequency allocation technique while maintaining the general idea of fractional frequency reuse. The frequency allocation is determined according to the average performance of all terminals in the network on all available frequency resources. Two-Level Resource Allocation A number of works in the literature deal with resource allocation at two levels (phases) or time scales. The common idea of these methods is that a frequency reuse pattern is decided based on slow-varying traffic distributions in the first phase, and at a faster time scale, the second phase fine-tunes the resource allocation inside each cell. Bonald et al. propose a two-level scheme for multi-cell coordination for the purpose of scheduling [20]. In the first phase, the activity of the interfering BSs is determined through interference coordination with the goal of transmission rate maximization. A TDMA transmission scheme is assumed. In the second phase, the load balancing is performed in order to divert traffic from heavily-loaded to lightly-loaded cells. Li and Liu extend the two-level resource allocation framework to a multi-cell OFDMA system [21]. In the first phase, the available spectrum is assigned to the terminals in the network by the radio network controller. In the second phase, the BSs independently modify the channel assignment in each cell according to the buffer sizes of the active

27 Chapter 2. Background and Preliminaries 17 terminals. Scheduling and resource allocation requires the knowledge of SINRs, which depend on the channel information for both the desired signal links and the interference links. It has, therefore, been noted that for ideal resource allocation, BSs need to have accurate network-wide channel information at every instant. However, acquiring the channel information from out of the cell can lead to an excessively large signalling complexity in practice. While most of the recent resource allocation techniques assume full knowledge of the channel information in the network to simplify the problem, Chang et al. [22] devise a scheme that takes this aspect into account. A two-level framework based on graph theory is proposed. In the first phase, intercell interference is reduced with no knowledge of out-of-cell interference, based solely on the geographical locations of terminals. In the second phase, the resource allocation is performed according to knowledge of instantaneous channel gains. 2.4 Adaptive Resource Allocation Framework for Irregular BS Deployment A solution for coordinated resource allocation for a network with irregular deployment, which considered the issue of channel information signaling, was developed in [2]. An important goal of the work was to design a resource allocation framework that could adapt to the variations of traffic load in the cells, which is comparable to the adaptive resource allocation strategies in the previous section. The primary design constraint was that the resource allocation was required to be flexible and adaptive enough to be suitable for irregular BS deployment. The case of a single BS power class, with BSs placed uniformly at random without restriction, was primarily considered in the work. Note that a practical application could be in a network with both small and large cells. A workable strategy to reduce the signalling requirements is to periodically group the BSs in the network into separate clusters, also referred to as scheduling cells (SCs). An OFDMA system such as the 3GPP LTE was considered. Inside each SC, channel information is exchanged and the resource allocation is coordinated. However, SCs act independently from one another during the course of scheduling at the LTE subframe level. The set of SCs is updated dynamically with the changing traffic distribution at a slower time scale. A complete adaptation framework that incorporates PF scheduling was developed. The flowchart outlining the adaptive framework is depicted in Figure 2.4. At the large time scale, terminals are assigned to BSs according to the long-term channel

28 Chapter 2. Background and Preliminaries 18 Assign terminals to BSs Form clusters (scheduling cells) Coordinated resource allocation in each cluster No l = l + 1 l mod F = 0? Yes Figure 2.4: Flowchart for the adaptive resource allocation framework. gains, and the SCs are formed based on the interference or SINR caused by each cell on every other cell. Then, at the subframe time scale, proportional fair resource allocation is performed with coordination or exchange of channel information inside each SC. The scheduling has been combined with on-off power switching and is executed in parallel in each subcarrier. Note that the power switching is designed to allow added flexibility due to finer variations of traffic distributions. The algorithmic framework for adaptive resource allocation is detailed in Figure 2.5, which lists both the slow-scale adaptation and fast-scale resource allocation steps. The details of the fast resource allocation algorithm are given in Figure 2.6. In the following, other important details are discussed in relation to (1) the clustering algorithm, (2) the fast resource allocation algorithm and (3) the requirements for channel information signalling. Clustering Algorithm The clustering algorithm specified in Figure 2.5 operates on the principle that BSs creating a lot of interference on each others terminals should be assigned to the same cluster (so that interference can then be avoided through fast scheduling). Therefore, the algorithm needs as inputs the set of BS assignments {n(k)} k K, the long-term timeaveraged channel gains, G n,k = P L n,k SF n,k, for all n and k, and the BS power level

29 Chapter 2. Background and Preliminaries 19 INPUTS: Distance-dependent path loss components, P L n,k, and shadowing components, SF n,k, for all n N and k K Vector of operating BS powers P = [P n ] = [P sn,max] Clustering algorithm parameters Q and T Proportional fair (PF) resource allocation window size parameter T 0 OUTPUTS: Set of assigned BSs {n(k)} k K Scheduling cells (SCs) N (ω) for ω = 1,..., Ω, forming a partition of the set N Optimized instantaneous BS power vectors p (ω) c (l) = [p n,c (l)] where n N (ω); and sets of scheduled users K(p (ω) c, l) = {k n,c (l)} n N (ω) ; corresponding to each SC ω = 1,..., Ω, each subframe l F, and each subcarrier c C 1: for all terminals k K do 2: for all BSs n N do 3: Compute the time-averaged channel gain according to G n,k = P L n,k SF n,k 4: end for 5: Determine the assigned BS according to n(k) = arg max n N G n,k. 6: end for 7: Form the SCs by using Algorithm 3 of [2]. 8: for SCs ω = 1 to Ω do 9: for subframes l = 1 to F do 10: Determine the optimized instantaneous power vectors and the sets of scheduled users by using the algorithm of Figure : end for 12: end for Figure 2.5: Algorithm for the adaptive resource allocation framework

30 Chapter 2. Background and Preliminaries 20 INPUTS: Set of coordinated BSs A = N (ω) Set of assigned BSs {n(k)} k K BS power level vector P = [P 1,..., P A ] Fast-changing channel gains, g k,n,c, k K, n A, c C OUTPUTS: Optimized instantaneous BS power vectors, p c(l) = [p 1,c(l),..., p A,c (l)]t, c C Sets of scheduled users, K(p c, l) = {k n,c(l)} n A, c C 1: for all subcarriers c = 1 to C do 2: Initialize maxsum to 0. 3: for all vectors p c (l) {0, P n /C} 2A 1 do 4: for all n A do 5: Set kn,c(l) r = arg max k,n,c (l) k Kn R k,n (l) 6: end for 7: Form the candidate user set K(p c, l) = {kn,c(l)} n A r k,n,c (l) R k,n (l) 8: Compute newsum = k K(p c,l) 9: if newsum > maxsum then 10: Set maxsum to newsum, p c(l) to p c (l), and K(p c, l) to K(p c, l) 11: end if 12: end for 13: end for 14: for all terminals k K do 15: Update the time-averaged user rate based on the scheduled user rates by using R k,n(k) (l + 1) = 16: end for (1 1T0 ) R k,n(k) (l) + ( 1 T 0 ) c k K(p c,l) r k,n(k),c(l) Figure 2.6: Algorithm for fast PF resource allocation for a given subframe l F.

31 Chapter 2. Background and Preliminaries 21 vector P = [P 1,..., P N ], for the computation of long-term SINRs. We let F denote the set of subframes in the analysis. According to the proposed method, the set of clusters are determined by running the K-means clustering algorithm [23] on an SINR-based BS similarity matrix. Note that the clustering algorithm requires two parameters, Q and T, as inputs: Parameter Q limits the maximum number of clusters in each iteration of the algorithm. Parameter T adjusts the tendency of BSs to join a cluster. It is, therefore, possible to adjust the cluster sizes by tuning parameters Q and T together. Detailed algorithm steps are found in [2]. Fast Resource Allocation The fast PF resource allocation specified in Figure 2.6 is performed independently at each SC ω. Note that to simplify the exposition, the set of coordinated BSs is denoted by A = N (ω), and the set of their assigned terminals by K in Figure 2.6. Additionally, the SC index ω is dropped in the rest of the variables. The algorithm steps are shown for a given subframe l F. PF scheduling discussed in Section together with binary (on or off) PF power switching is used. At the end of the power optimization and scheduling, the time-averaged rate of each user is updated with the total scheduled user rate over the subframe. Channel Information In summary, the requirements for channel information signalling is significantly reduced due to clustering. In order to perform BS assignment and clustering, the long-term channel gains, G n,k, between all BSs and terminals need to be known at a central entity at every F subframes which is a low frequency. In contrast, the estimate of fast-varying channel gains, g n,k,c, need to be exchanged at every subframe only for BSs and terminals inside the given SC. 2.5 General Slow-Time-Scale Adaptive Algorithms There has been a recent recognition in the wider community of the need for adaptation at time scales larger than the fast multipath fading time scale (i.e. at the LTE subframe). Such slowly-adaptive algorithms have prominently been studied in the context of 3GPP LTE Self Organizing Networks (SON) [24]. In Sections 2.3 and 2.4, we discussed resource allocation frameworks that commonly work at two different time scales. The adaptations at the slow time scale such as the dynamic re-organization of the frequency reuse patterns,

32 Chapter 2. Background and Preliminaries 22 and dynamic BS assignments and clustering can be considered similar to SON functions 1. More generally, the main driving force for SON has been the need to automate the configuration, optimization, maintenance, troubleshooting and recovery of the cellular system. Automation of tasks previously performed manually is expected to enable more agile adaptation in face of the greater dynamism of emerging irregular cellular networks, and simultaneously to reduce operating and other costs incurred by wireless operators. A wide variety of SON functions have been proposed in the literature [25 29]. In the most common taxonomy, the functions are classified based on the phases corresponding to the life cycle of the cellular system equipment, that is, deployment, operation, maintenance, redeployment, recovery etc. The adaptive functions and algorithms that organize these phases are classified into (a) self configuration, (b) self optimization and (c) self healing. Each of the categories is reviewed in the following, together with function and algorithm contributions from the SON literature. Self Configuration: Self configuration functions are primarily executed at the deployment and re-deployment phases of the network equipment life cycle. A number of different parameters can be configured, including radio propagation parameters such as antenna type, antenna gain, and antenna azimuth and tilt angles. The authors in [25] proposed an antenna tilt optimization method for the purpose of achieving higher system capacity and better coverage. In particular, they demonstrated an approach based on simulated annealing that uses measurements of terminal SINR information. An important aspect of the method is that it was specifically designed to utilize readily available terminal measurements in an online manner. The authors in [26] proposed an alternative game theoretic method for antenna tilt optimization. Furthermore, they proved the existence of a Nash equilibrium which can be achieved in a non-cooperative game for the optimization of system-wide utility function. Self Optimization: Self optimization is primarily executed at the operation phase of the network life cycle, and involves continuous optimization of system parameters after their initial configuration, in order to ensure efficient performance of the system. A variety of parameter optimizations for realization of distinct goals are possible. The authors in [27] proposed a scheme for balancing the load across multiple cells, and avoiding intercell interference, by performing intercell and intra-cell handovers in a partial frequency reuse (PFR) scheme for OFDMA. Authors in [28] developed a method for adaptive organization of an fractional frequency reuse (FFR) scheme for the purpose of interference control. 1 There have been few attempts to formulate a precise definition of Self Organization (SO). One such attempt [24] emphasizes the need for stability, scalability and agility of the algorithms to be considered SO, distinguishing it from the non-self-organized type of system adaptation.

33 Chapter 2. Background and Preliminaries 23 Table 2.1: Classification of time scales. Time Scale System Dynamics Adaptation Fastest Multipath fading User scheduling Slow terminal movements Self optimization functions Medium Terminal activation Cell assignments Terminal deactivation Clustering BS Deployments Self configuration Slowest BS Outages Self healing BS Movements Cell outage management The basic idea of the algorithm was to dynamically create efficient FFR patterns in order to adapt to the changing user traffic distributions and system conditions. Self Healing: Self healing functions are primarily executed during recovery from faults and failures that can be due to component malfunctions or natural disasters. Self healing is a systematic process which is comprised of several stages including (a) remote monitoring, (b) detection, (c) diagnosis and (d) triggering of compensation actions for the clearing of the fault or failure. The reference [29] considered the self healing for the fault referred to as a cell outage. A cell outage is defined as a rare and catastrophic failure of a BS, which results in ceasing of all signal transmission and reception at the BS. The authors in [29] provided a full description for the management of cell outages in LTE networks, reviewing both detection and compensation algorithms, and discussing the role of operator policies in the design of detection and compensation schemes. We note that self optimization functions are generally intended for execution on a relatively frequent basis during the operation of the wireless network, e.g. after a certain number of subframes. In contrast, self configuration and self healing functions are commonly executed infrequently as events such as BS deployments and outages tend to be rare. A classification of dynamism and adaptation with approximate demarcation of different time scales is provided in Table 2.1. Note that the multipath fading time scale is included in the taxonomy. Terminal movements, activations and de-activations are classified as medium scale dynamics due to their relative high frequency. BS dynamics such as outages, deployments and movements are classified as slow-scale dynamics due to the low frequency of occurrence. Note that BS movements are not common in today s cellular networks, however, they are included with the thought that they may become feasible for emerging and future networks. According to classification of the adaptation functions, user scheduling occurs at the fastest time scale, self optimization in SON oc-

34 Chapter 2. Background and Preliminaries 24 curs at the medium time scale, and self configuration and self healing at the slowest time scale. The medium- and slowest-scale dynamics can be considered as the focus of the adaptations in this dissertation. 2.6 The ITU System Model: High-Level Reference Model for the Regular Cellular Network The ITU system model [1] provides a high-level reference for the modelling of a cellular system, which was designed for the regular cellular network paradigm. The model will be used in this thesis as a starting point for developing a high-level model for the irregular cellular network. The ITU model is based, in part, on the idea of generating a large number of snapshots, known as simulation drops, for the purpose of Monte Carlo simulation. A simulation drop, in this context, is defined as a random deployment of mobile terminals on a network area with fixed BS deployments, following the hexagonal cell pattern. Within each drop, the set of active terminals and their deployments as well as large-scale channel components such as path loss and shadowing are fixed, and there are only virtual terminal movements, which result in the multipath fading due to the Doppler effect. As mentioned in Section 2.1, the time scale for multipath fading corresponds to a subframe in LTE, which is the basic time unit for user scheduling. In order to obtain statistically representative results at this time scale, a large number of LTE subframes are simulated within each simulation drop. The flowchart of the simulation methodology is given in Figure 2.7, where the number of drops used in the simulation is denoted by the variable P, and the number of LTE subframes per drop by F. Notably, the simulation drops themselves are generated independently from each other, that is, as uncorrelated snapshots of network configurations. In addition, the model uses standard large-scale channel models, in particular, for shadow fading, that are static in time and statistically uncorrelated in space. In the following, we review the channel modelling in the ITU model, considering distance-dependent path loss, shadowing and multipath fading Channel Modelling Distance-Dependent Path Loss A typical expression for the distance-dependent path loss model is given as follows: Let A be the path loss exponent parameter, B the intercept parameter, C the frequency

35 Chapter 2. Background and Preliminaries 25 Generate simulation drop i Compute path loss and shadowing for all links No i =P? Yes STOP Generate subframe j of drop i (multipath fading) Perform user scheduling i = i + 1 No j = j + 1 j mod F = 0? Yes Figure 2.7: The flowchart for the drop-based simulation framework based on the ITU common reference model. dependence parameter and X the environment-specific parameter. d n,k is the distance between BS n and terminal k in metres, and f c is the system frequency in GHz. The path loss from BS n to any terminal k is given by [30] ( ) fc P L n,k [db] = A log 10 (d n,k ) + B + C log 10 + X (2.10) 5.0 As an example, A = 20, B = 46.4, C = 20 and X = 0 are typical values for free space. Shadowing Shadowing channel gain is represented using the common log-normal model [31]. For the link between a BS n and a terminal k, log SF n,k is, therefore, generated as a Gaussian random variable with zero mean and standard deviation σ.

36 Chapter 2. Background and Preliminaries 26 Multipath Fading Modelling of fast-varying channel components m n,k,c at the subcarrier and subframe granularity is discussed in this section. Frequency variation in the wireless channel is due to the multiple path (multi-path) components with different excess propagation delays, or different echoes of the transmitted pulse. The distribution of the delay values for the echoes, weighed by signal power, is referred to as the delay spread for the channel. The delay spread affects the rate of variation of the channel response with frequency. The frequency variation due to delay spread is commonly modelled through statistical means with a frequency correlation function. The channel time variation arises due to the motion of the terminal with respect to each of the multipath channel components. In particular, the different signal multipath components undergo frequency shifts (Doppler shifts) that are proportional to the relative velocity of the terminal with respect to the angle of arrival of the component. The distribution of the Doppler shifts, weighed by signal power, is referred to as the Doppler spread for the channel. The Doppler spread is related to the rate of variation of the channel response in time. The time variation due to Doppler spread is commonly modelled through statistical means with a time correlation function. Finally, the spatial variation occurs due to the constructive and destructive interference of the electromagnetic waves for the multipath components arriving at a receiver with multiple antenna elements. Note that the situation with multiple antennas is not considered in the thesis. The literature contains many different models for time, frequency and space variation of the wireless channel [9, 32 35]. However, the joint computation of channel variation in all three variables can prove to be challenging. The ITU provides a channel model appropriate for the OFDM scheme incorporating all three types of variations, which is based on the concept known as ray clusters. Detailed explanation of the model is provided in [1]. 2.7 Considerations for an Irregular Cellular Network Model The irregular cellular network has characteristic that are very different from the regular cellular network, which has the ITU model as a high-level representation. A more appropriate high-level model would be able to provide a common network representation as a reference for the consideration of different types of dynamical changes in the network

37 Chapter 2. Background and Preliminaries 27 in the design of appropriate dynamic resource allocation and adaptation as well as SON strategies. The limitations of the existing ITU model is described in the following: First, the hexagonal deployment pattern is inadequate due to the irregular deployment of BSs in the new network paradigm. Second, more accurate channel models are needed due to irregularity of BS deployment. In particular, a more realistic shadowing model than the common lognormal model should be developed that can represent the gradual variation of shadowing over space and the time as well as the diverse radio propagation environments in the network. Third, the snapshot simulation method using simulation drops does not accurately represent the dynamism in the network. Such dynamics are important for the accurate evaluation of dynamic resource allocation frameworks, and other adaptation and SON functions that were discussed in Sections In particular, we note that in implementing slowly-adaptive functions, it is important to minimize signaling complexity and overhead resulting from, e.g., the exchange of channel information. This is especially true if centralized decision making or coordination is required for the specific implementation. The signalling complexity can potentially be reduced by considering that the evolution of the cellular channel and environment is gradual in time, meaning that each execution of the function can partially utilize the information from the previous execution. It would, therefore, be possible to design algorithms with reduced signalling complexity. To evaluate the performance of reduced-complexity adaptive algorithms, it becomes necessary to accurately model the time evolution of the cellular system and channel at such slow time scales. In this thesis, we propose a new system model framework, which is appropriate as a high-level model for the irregular network. The main considerations for the model are as follows: 1. The deployment model should reflect both the arbitrariness of deployment and the broad level of agreement between the positions of terminals and BSs (e.g. due to planning). 2. Since the original simulation drop concept of the ITU model does not allow the modelling of network time evolution at the slow time scale, an appropriate modification of the concept should be devised. 3. The shadowing model should represent the shadowing correlation as well as the diverse radio propagation environments present in the network.

38 Chapter 2. Background and Preliminaries Correlated Shadowing Model for Irregular BS Deployment The classical lognormal shadowing model gives no information on the correlation of shadowing over the network (also known as spatial correlation). Consider the special case of a link between a fixed base station and a moving terminal as depicted in Figure 2.8: Due to the inherent correlation in the topography of the physical environment, the channel gain experienced by the terminal cannot change abruptly after having traveled a relatively small distance. In 1991, Gudmundson proposed a method [36] to model the spatial correlation of shadowing. According to the Gudmundson model, the correlation between the links A-B and A-C shown in Figure 2.9, is given as a function of the distance d between the links as R(d) = σ 2 e d/dc (2.11) where σ is the shadowing standard deviation, and d c is an important parameter known as the shadowing correlation distance. Note that the Gudmundson correlation model considers the correlation between pairs of links with a common endpoint; specifically, either between a terminal and multiple BSs, or between a BS and multiple terminals. Other research in cellular networks [31, 37 39] expanded on Gudmundsons work, also focusing on the correlation between pairs of links with a common endpoint. More recent work [40] considered the mathematical feasibility of shadowing correlation models, as well as the calculation of aggregate interference in scenarios with correlated shadowing [41 43]. However, the literature in cellular networks did not report on the correlation between pairs of links with no common endpoint, illustrated in Figure 2.10, effectively neglecting such correlation. Links without a common endpoint frequently have low correlation in traditional cellular networks, due to the regular spacing and large distances between BSs. Thus it can be acceptable to neglect such correlation in the model. However, in irregular networks, BSs can, at times, be very close together. Therefore, the correlation between two links with no common end cannot be neglected in such scenarios. An appropriate correlation model incorporating non-common-endpoint links was proposed in [8], which is discussed in the following. We first define the potential field as a random process whereby each realization is a function from the plane to real numbers. Thus, if we fix a point in the plane, the result is a real random variable. According to the spatially correlated shadowing model, shadowing is computed from a Gaussian potential field generated over the network area. Note that the potential field is stored in a vector denoted by u. A homogeneous shadow fading

39 Chapter 2. Background and Preliminaries 29 BS Terminal at time t2 Terminal at time t1 Figure 2.8: The wireless link between a fixed base station and a moving terminal. B A d Figure 2.9: Wireless links with a common endpoint. C B A C D Figure 2.10: Wireless links without a common endpoint.

40 Chapter 2. Background and Preliminaries 30 Figure 2.11: A realization of the potential field [8]. scenario with fixed shadowing standard deviation, σ 0 (in db), and correlation distance, d c, is considered. The value of the potential field at point A defines the potential level of point A and is denoted by u A. For a cellular network with N BSs and K terminals, J = N + K potential levels are generated according to the following steps: Step 1: Generate a J 1 vector v whose elements are independent Gaussian random variables with zero mean and unity standard deviation. Step 2: Generate a J J correlation matrix R = [r ij ] such that where d ij is the distance between point i and point j. r ij = σ2 0 2 e d ij/d c (2.12) Step 3: Decompose the correlation matrix using Cholesky factorization such that R = BB H. Step 4: Calculate the J 1 potential level vector u according to u = Bv (2.13)

41 Chapter 2. Background and Preliminaries 31 A realization of the shadowing potential field is depicted in Figure The shadowing between point A and point B (normally, a terminal and a BS) is then computed as a function of the two potential levels according to SF [db] = f (u A, u B ) = sgn (u A + u B ) u A u B. (2.14) It was shown in [8] that the above potential field method of shadowing generation results in the correct lognormal shadowing with spatial correlation, and the resulting shadowing values satisfy a number of essential statistical properties that are detailed in the work. We note that all the correlated shadowing models discussed in this thesis will be based on the foundation of the potential field model discussed in this section. Finally, it is important to mention that different radio propagation environments would cause different radio-channel characteristics, and therefore, the values of shadowing channel parameters, σ 0, and d c, need to be different based on the environments. Typically, propagation environments are characterized by urban, suburban or rural, and indoor or outdoor scenarios. Different environments also frequently have different sizes of cells. The values of σ 0, and d c (as well as other types of channel parameters for multipath fading or distance-dependent path loss) are normally obtained by conducting channel measurements in practical propagation scenarios [1, 30, 36, 44, 45]. Note that the consideration of varying shadowing model parameter values will be important in the development and implementation of the model in this chapter.

42 Chapter 3 Adaptation Case: BS Outage Compensation 3.1 Relevant Work and Contribution Relevant Work A cell outage is defined as a rare and catastrophic failure of a BS, which results in ceasing of all signal transmission and reception at the BS. Following the outage, the users assigned to the outage BS lose service and adaptation of the network needs to be performed. The type of adaptation has been referred to, in the context of 3GPP LTE SON, as cell outage compensation (COC). A small number of works in the literature have explored the COC problem. In homogeneous networks, the literature [29, 46 48] focused on the development of algorithms for cell outage compensation by tuning of various control parameters in different types of systems, including antenna tilt, pilot power and uplink target received power, in order to mitigate the performance effects due to the outage in accordance with operator policy. In the area of heterogeneous networks, the authors in [49] and [50] studied the cell outage compensation problem and offered algorithm solutions based on the adjustment of antenna gains and transmission powers Contribution Most works in the literature consider the base station (or cell) outage compensation (COC) for homogeneous or regular networks. Furthermore, even works that consider irregular networks do not explicitly consider the general modelling aspect of the problem. 32

43 Chapter 3. Adaptation Case: BS Outage Compensation 33 We focus on the modelling of a BS outage for an irregular network with multiple power classes in a general sense. Both the positions of BSs and the power classes are modelled. In addition, we consider the adaptive resource allocation strategy as part of the overall model. Specifically, we adopt the concept of cluster or scheduling cell for the purpose of coordinated adaptive resource allocation. To our knowledge, the use of a scheduling cell is new for the COC literature. Direct sum log utility maximization based on proportional fairness is the primary formulation we used in finding a compensating cluster, outage user cell associations, and the adjusted BS power levels. The use of proportional fairness in the COC formulation is additionally different from the literature for COC. Finally, the shadowing model with spatial correlation, discussed in Chapter 2, is considered for greater realism especially of the irregularly deployed network Key Results The results indicate that both COC algorithms show robustness toward cell outage in terms of user average spectral efficiency, and outage user and non-outage user QoS violation probabilities for both a regular and an irregular network. In particular, the COC algorithms are shown to achieve a large percentage (nearly 75%) of the user spectral efficiency of the no outage scenario in both network types. In addition, the proportional fairness-based COC algorithm is shown to allow the tuning, or trading off, of the average number of BSs with raised power which is a measure of the algorithm cost against different measures of performance including user spectral efficiency. 3.2 Introduction Chapter 2 discussed adaptive resource allocation strategies that respond to network variations (such as due to traffic changes) for cellular networks. In addition, more general adaptive functions in the 3GPP LTE SON literature were reviewed. The focus of the discussion in this thesis is slow- and medium-time-scale adaptations. Typical adapted parameters include transmit power, antenna gain, antenna tilt and other parameters related to the adaptive frequency re-use scheme that is employed. This thesis focuses on dynamic adaptations with the final aim of improved spectral resource allocation, that is appropriate for the irregular cellular network paradigm. In particular, BS assignments, clustering and power adaptation (power control) will be mainly considered in the development of the schemes. In this chapter, we study BS (or cell) outage compensation as a specific case of

44 Chapter 3. Adaptation Case: BS Outage Compensation 34 dynamic adaptation for the irregular cellular network. A BS outage is defined as a rare and catastrophic failure of a BS, which results in ceasing of all signal transmission and reception at the BS. Following the outage, the users assigned to the outage BS lose service and adaptation of the network needs to be performed. The type of adaptation has been referred to, in the context of 3GPP LTE SON, as cell outage compensation (COC). Several works [29, 46 48] studied the concept of COC and proposed algorithms for its implementation. In summary, the proposed COC algorithms aim to mitigate the effects of the cell outage without the requirement for manual intervention. Particularly, the users assigned to the BS that have lost service which shall be referred to as outage users have their cell assignments switched to physically nearby BSs, known as compensating BSs or cells. Adjustments are also made to a selected control parameter (e.g. BS transmit power) in the compensating BSs. In this thesis, a distinct approach for outage compensation is proposed, partially based on concepts studied throughout the thesis, such as BS assignments, power adaptations and scheduling clusters. The authors of [46 48] showed that, in attempting to compensate for the outage, there exists the risk of sacrificing the performance in terms of data rate in the nearby compensating cells. For this reason, the concept of compensating cells is refined in this work as follows: Instead of being classified, merely, as a group of cells assisting in compensation, compensating cells explicitly form the compensating cluster with resource allocation coordination similar to the clustering concept discussed in Chapter 2. In addition, the methods for outage user cell association and BS power adjustment in existing COC algorithms are typically based on traditional criteria, including total rate maximization (TRM) or path loss minimization (PLM). Note that the path loss minimization means the maximization of the long-term average (or expected value) of the channel power gain between a BS and a user. However, for resource allocation, proportional fairness (PF) (equivalent to maximization of the sum-log utility (SLU)) was established to be a better criterion than TRM, as it has the property of achieving a balance between two conflicting goals: the maximization of total rate (TRM) and the maintenance of perfect fairness among users. In this work, we, therefore, propose a COC algorithm based on the PF criterion, as the final aim of the work is the PF resource allocation under the cell outage scenario. The chapter first considers a model of the BS outage in a network with irregular BS deployment and distinct power levels. Then methods are developed for BS outage compensation, with an emphasis on the variation of architecture resulting from the use of the compensating cluster. The rest of this chapter is organized as follows: The COC problem formulation and proposed algorithmic approach is described in Section 3.3. The

45 Chapter 3. Adaptation Case: BS Outage Compensation 35 BS n0 d0 Figure 3.1: BS outage scenario. The light blue square is the outage BS (BS n 0 ), the light blue circles are the outage users, dark blue squares are the candidate BSs, dark blue circles are the associated users, and the red squares and circles are the BSs and users outside the candidate set, respectively. COC algorithm based on the PF criterion is developed in Section 3.4. The simplified COC algorithm based on PLM is discussed in Section 3.5. Finally, the numerical evaluations are presented in Section Problem Statement and Proposed Algorithmic Approach We consider that a BS n O has experienced an outage. Let K O be the set of users currently associated with BS n O otherwise known as outage users. Let N C be the set of candidate BSs, which are specified as those BSs located within a pre-determined distance, d O, from BS n O (based on the channel power). The BS outage is illustrated for a sample scenario in Figure 3.1. The COC problem consisting of joint cell association, cluster formation and power adaptation is stated in terms of the following three questions: 1. Which BSs should be in the compensating cluster? Determine the set of BSs comprising the compensating cluster, denoted as N CO, such that N CO N C N.

46 Chapter 3. Adaptation Case: BS Outage Compensation What are the compensating BS power levels? For each BS n N CO, determine the operating power level, P n. 3. Which BSs should be associated with the outage users? For each outage user, k K O, find the associated BS n(k) N C. In relation to point 3, we form the set of BSs newly associated with any of the outage users: N AS = {n K n,o }, (3.1) where K n,o = {k n(k) = n; k K O } is the set of all outage users assigned to BS n. As the goal of a utility maximizing algorithm (such as a PF or TRM procedure) is to maximize the utility function over all outage users and the relevant non-outage users, the resource allocation must be coordinated among some (or all) of the BSs in N AS. Equivalently, the associations set N AS and the coordination set N CO must not be disjoint, which is expressed mathematically as: N AS N CO. (3.2) Note that the condition of (3.2) will be useful in the development of COC algorithms later in this chapter. We emphasize that the COC problem statement of this section considers the clustering, user cell associations and BS power levels in a limited geographic area, within a distance d O from the outage BS. According to the adaptive resource allocation framework of Chapter 2, however, the same type of adaptations should also typically be performed elsewhere in the network, which can have an effect on the COC solution inside the area of question. The effect of BSs outside the candidate BS area are neglected in the present contribution, as interference received from BSs at a sufficiently large distance tends to be small, and the research s primary aim is to develop an approximate, tractable algorithm for compensation. Our detailed study of the stated COC problem based on utility maximization (such as PF or TRM procedures) has shown that difficulty arises in finding an optimal solution to the COC problem, even in a limited physical area, due to the mutual dependence of individual problem parts. In particular, the key mutual dependencies are listed in the following: As per (3.2), the best choice for compensating cluster, N CO, is dependent on the outage user cell associations, n(k). The best choice for N CO is, in general, dependent on the BS power levels, P n, as shown in the clustering algorithm development of [2].

47 Chapter 3. Adaptation Case: BS Outage Compensation 37 The actual measured other-cell interference will tend to reduce with increased cluster size, which will affect the optimal choice for BS power levels P n. Thus, the optimal choice for P n is itself dependent on the choice of compensating cluster, N CO. The best cell association, n(k), for each outage user is, in general, dependent on the choice of P n as discussed in [27, 51]. We conclude from the discussion that it is not straightforward to solve all three parts of the COC problem directly. Therefore, we take the approach of decoupling the problem parts, and providing low-complexity heuristic solutions. In particular, the main proposed solution, which is based on the proportional fair criterion, will consist of iteration between the following steps: 1. Fixing BS power levels, P n, and solving for the updated outage user cell associations, n(k). 2. Fixing the BS power levels, P n, and the user cell associations, n(k), and solving for the compensating cluster set, N CO. 3. Fixing the user cell associations, n(k), and the compensating cluster set, N CO, and solving for the updated BS power levels, P n. Additionally, the secondary COC solution method will be a further simplified algorithm based on the TRM and PLM criteria referred to as the PLM COC algorithm. Details of the PF COC and PLM COC algorithms are discussed in the following sections. 3.4 Proportional Fair Compensation Algorithm In the previous section, it was mentioned that adaptations are considered for a limited geographic area, and the effect of BSs outside the candidate set, n / N C, and their terminals, k such that n(k) / N C, are neglected. Consequently, certain assumptions are needed for the BS power levels and cell associations for cells outside the candidate BS set, which will be applied to both the PF and the PLM compensation algorithms. Let E[g n,k ] be the long-term average (or expected value) of the channel power gain between BS n and user k, P 0n the maximum allowed power level based on the transmission capability of BS n and α n a power multiplier constant which depends on the BS index n. It is assumed that 1. The BSs n / N C operate at a constant power setting P n = P 0n /α n.

48 Chapter 3. Adaptation Case: BS Outage Compensation The associated BS for non-outage users (both within and outside the candidate cells) is determined according to the traditional method of maximizing E[g n,k ]: n(k) = arg max E[g n,k ], (3.3) n which shall be referred to as the path loss minimization (PLM) method. Note that it was explained in Chapter 2 that the maximum allowed BS power level, P 0n, is normally determined based on the BS power class, s. In particular, P 0n is equal to the distinct maximum power capability, P sn,max, of the power class s n. However, the present chapter uses a simplified model of BS deployment for the irregular network, which does not consider the complete realistic modelling of hotspot deployment. Such a model will be developed in detail in Chapter 6. In this chapter, individual maximum BS power capabilities, P 0n, will be determined through a heuristic optimization method, to provide a form of realism to the analysis. Section 3.6. The power capability optimization is discussed in In this section, the PF outage compensation algorithm is discussed, which consists of the steps of: 1. Outage user cell re-association 2. Compensating cluster generation 3. BS power adjustment Outage User Cell Re-association The cell re-association of outage users is discussed in this section. Denote the vector of associated BSs for outage users as n KO = [n(k 1 ), n(k 2 ), n(k 3 ),..., n(k KO )]. The proportional fair outage user cell association problem is given by max S CO (3.4) n KO subject to n(k) N C, k K O where S CO is the sum-log utility for the compensating cluster users and is computed by S CO = k K CO log R k,n(k) (3.5)

49 Chapter 3. Adaptation Case: BS Outage Compensation 39 Here, K CO = {k n(k) = n; n N CO } is the set of users assigned to the BSs in the compensating cluster (which is as yet undetermined), and R k,n(k) is the long-term average rate for user k from BS n(k). Note that the use of the PF scheduling strategy at the subframe time scale is assumed throughout the analysis. Under the assumption, R k,n(k) is approximated as [27]: R k,n(k) = G(K n(k)) K n(k) E[r k,n(k) ] (3.6) Here, K n(k) is the number of terminals assigned to BS n(k), G(y) is a quantity known as the multiuser diversity scheduling gain, expressed in terms of the number of assigned users, and E[r k,n(k) ] is the long-term average of the instantaneous achievable rate of user k from BS n, where r k,n, the instantaneous rate over the entire frequency band, is given by r k,n = c C r k,n,c. The derivation in [27] showed that the multiplicative factor, G(K n(k) )/K n(k), in (3.6) accounts for the PF scheduling in the system. In particular, the numerator G(K n(k) ) the scheduling gain accounts for the multiplicative increase in the average rates due to the diversity from scheduling multiple users. The denominator K n(k) accounts for the relative reduction in the average rates due to division of the timefrequency resource among the users assigned to BS n(k). It was shown in [27] that under an easily satisfiable set of conditions, PF scheduling results in equal division of resources among the users. Furthermore, the scheduling gain, G(y), was approximated as G(y) = y i=1 1 i (3.7) Finally, we approximate E[r k,n(k) ] as a function of total bandwidth, B T and the average SINRs, SINR k,n(k), which in turn depend on the power levels and the channel gains: E[r k,n(k) ] = B T log 2 ( = B T log 2 ( SINR k,n(k) 2 ) P n(k) E[g n(k),k ] 2(N 0 C + j n(k) P je[g k,j ]) ) (3.8) Thus, by substitution of (3.7) and (3.8) into (3.6), the expression for R k,n(k) is evaluated as R k,n(k) = Kn(k) i=1 1 i K n(k) B T log 2 ( 1 + ) P n(k) E[g n(k),k ] 2(N 0 C + j n(k) P je[g k,j ]) (3.9)

50 Chapter 3. Adaptation Case: BS Outage Compensation 40 Finally, the substitution of (3.9) into (3.4) yields the optimization: max n KO subject to S CO n(k) N C, k K O S CO = log R k,n(k) k K CO R k,n(k) = Kn(k) i=1 1 i K n(k) B T log 2 ( 1 + (3.10) ) P n(k) E[g n(k),k ] 2(N 0 C + j n(k) P, k K CO je[g k,j ]) The authors in [27] show that the direct solution of the optimization problem of (3.10) is highly complex computationally. To reduce algorithmic complexity, they take the approach of determining the initial cell associations offline by using a direct solution, and periodically updating the associations using a simpler heuristic online solution. For this purpose, an efficient cell association update technique is proposed, which is based on the following property: Proposition 3.1 [27] Assume that a user k is initially associated with BS n. Then, under a set of modest assumptions, switching the association of user k to another BS j will result in an increase in the overall network-wide sum-log utility if R k,j > R k,n. (3.11) In this section, we propose a heuristic iterative cell association update technique for outage users, inspired by Proposition 3.1 and the solution approach of [27]. The detailed algorithm is given in Figure 3.2. Note that the method requires an initial set of cell associations, n(k), for outage users, k K O, which are typically computed according to PLM: n(k) = arg max n N C E[g n,k ] (3.12) The optimal BS for switching is then computed for each user based on maximizing the increase in R k,n. In addition, a single outage user is selected for switching at each iteration in order to avoid oscillatory behaviour of the algorithm.

51 Chapter 3. Adaptation Case: BS Outage Compensation 41 Require: The candidate set N C. Initial cell associations, n(k), for each outage user, k K O. 1: repeat 2: for all outage users k K O do 3: Initialize the flag: γ(k) 0 4: for all BSs j N C do 5: Compute R k,j according to (3.6), with values of K j and E[r kj ] adjusted as appropriate. 6: end for 7: if R k,j R k,n(k) > 1 for some j N C then 8: Find jk, the optimal BS to switch to, from j k = arg max R k,j j N C R k,n(k). 9: else 10: Raise the flag: γ(k) 1 11: end if 12: end for 13: if γ(k) = 0 for some value of k K O then 14: Find user k that will have its cell association switched as k R k,j = arg max k k KO R k,n(k). 15: Execute the switch: n(k ) j k 16: end if 17: until no more cell association switches are possible, i.e. γ(k) = 1, k K O. Figure 3.2: Outage user cell association update Generation of Compensating Cluster Let SINR th be a pre-determined threshold for long-term average SINRs, SINR k,n(k). We determine the set of BSs comprising the compensating cluster as: N CO = {n K n,o ; NOT ( ) SINR k,n(k) < SINR th, k K n,o } (3.13) where the condition, NOT ( ) SINR k,n(k) < SINR th, k K n,o, serves to exclude those BSs that provide low average SINR for outage users. This can serve to restrict the size of the compensating cluster. Note that from (3.1), N AS = {n K n,o }. Therefore, N CO computed according to (3.13) satisfies N CO N AS and the required condition of (3.2): N AS N CO (3.14) In the remainder of this chapter, SINR th is set to 0 as a specialization of (3.13), that is,

52 Chapter 3. Adaptation Case: BS Outage Compensation 42 the second condition in (3.13) is not utilized. Therefore, N CO = {n K n,o } N AS (3.15) which also satisfies (3.2) BS Power Adjustment We consider the optimization of the BS power levels, P n, based on the maximization of a weighted sum-log utility function over all the users in the compensating cluster. Let P NCO = [P n1, P n2, P n3,..., P nnco ] be the compensating cluster BS power vector. The BS power optimization problem is expressed as max S β,co (3.16) P NCO subject to S β,co = β log R k,n(k) + (1 β) log R k,n(k) k K O k K CO,k / K O 0 P n P 0n, n N CO where S β,co is the weighted sum-log utility, R k,n(k) is computed from (3.9), β is the weight assigned to the contribution of outage users to S β,co, chosen in the range 0 β 1, and (1 β) represents the weight assigned to the contribution of non-outage users to S β,co. Due to the non-convexity of (3.16) and the anticipated solution complexity [52], a simple heuristic greedy power increase method is proposed as an approximate solution. It is assumed that each BS n N CO is initially operating below its maximum power level at P 0n /α n 1. Details of the algorithm are given in Figure 3.3. Note that S β,co (P n = P n) represents the S β,co value computed after modification of a single BS s power level, where P n is a temporary variable. According to the method, a single BS is selected at each step for power increase in greedy fashion. The step is then repeated iteratively until no more power increases are possible. 1 The reduction factor of SINR, the long-term SINR, due to operating below P 0n is given by α n N 0C+ j n,j N CO P 0nE[g k,j ]/α n+ j n,j / N CO P 0nE[g k,j ] N 0C+ j n P0nE[g k,j]. While this may be significant, especially for a rare event like a cell outage, the concern of the thesis is not on the rarity of the event. The focus of the thesis is on providing a model for a change in the network configuration and the corresponding adaptation.

53 Chapter 3. Adaptation Case: BS Outage Compensation 43 Require: Initial power levels, P n = P 0n /α n, for each BS, n N CO. 1: repeat 2: Form the candidate BS set for power increase according to N CP I = {n P n = P 0n /α n, n N CO }. 3: for all BSs n N CP I do 4: Assign temporary variable: P n α n P n = P 0n 5: Compute S β,co (P n = P n). 6: end for 7: Find optimum power increase BS, n = arg max n NCP I S β,co (P n = P n) 8: Implement power increase: P n α n P n = P 0n 9: until N CP I =. Figure 3.3: Compensating BS power update. Require: Maximum power level, P 0n and power multiplier, α n, n N. Candidate set N C. 1: for all n N do 2: P n P 0n /α n. 3: end for 4: for all k K do 5: n(k) arg max n E[g n,k ] 6: n(k) (0) n(k) 7: end for 8: repeat 9: for all k K O do 10: n(k) n(k) (0) 11: end for 12: Use Algorithm 1 to update the cell association, n(k), for each outage user, k K O. 13: Use eq. (3.15) to update the compensating cluster N CO. 14: Use a single iteration of Algorithm 2 to find the optimum power increase BS n and increment its power. 15: until N CP I = Figure 3.4: Overall iteration of the PF compensation algorithm Overall Algorithm The overall algorithm relies on fixing any two of cell association, clustering and power levels, and solving for the other through the methods described in this section. The iteration steps are shown in Figure 3.4.

54 Chapter 3. Adaptation Case: BS Outage Compensation Information Exchange Requirements The information exchange required is similar to that of the clustering and BS assignment procedure of [2], which was discussed in Chapter 2. In particular, the long-term average channel gains, E[g n,k ], between BSs and users need to be known at a central node. Additionally, the central node needs to know the traffic load information for the BSs, i.e., the number of users, K n, assigned to each BS, for the execution of cell re-association and BS power adjustment steps. Note that the channel and load information exchange occurs on an infrequent basis due to the rare nature of the BS outage occurrences. In contrast, fast-varying channel gains, g n,k,c, need to be exchanged for the purpose of fast scheduling at the subframe time scale, for BSs inside the compensating cluster. 3.5 PLM Compensation Algorithm A simplified PLM compensation procedure is discussed in this section. In the particular algorithm realization, the outage user cell associations are determined according to the PLM method: n(k) = arg max n N C E[g n,k ], k K O (3.17) The set of BSs comprising the compensating cluster is computed from (3.13), with SINR th set to zero: N CO = {n K n,o } N AS (3.18) Finally, we consider the power optimization problem based on maximization of a weighted sum rate function, denoted by S β,co : max S β,co (3.19) P NCO subject to S β,co = β R k,n(k) + (1 β) k K O 0 P n P 0n, n N CO k K CO,k / K O R k,n(k) In order to reduce algorithm signalling complexity, S β,co is replaced by a simplified sum rate function S β,co, which is defined in terms of E[r k,n(k)] in place of R k,n(k). The

55 Chapter 3. Adaptation Case: BS Outage Compensation 45 optimization becomes max S β,co (3.20) P NCO subject to S β,co = β E[r k,n(k) ] + (1 β) E[r k,n(k) ] k K O k K CO,k / K O 0 P n P 0n, n N CO We note that the computation of outage user cell associations, n(k), from (3.17) does not require knowledge of the rates R k and, hence is not dependent on the power levels P n. Similarly, the computation of compensating cluster N CO from (3.18) only requires the knowledge of cell associations from (3.17), and not the power levels. In contrast, the power level optimization of (3.20) requires knowledge of both the cell associations and the compensating set. As a consequence, the outage user cell associations, n(k), the compensating cluster, N CO, and the power levels, P n, can be found sequentially rather than in iterative fashion. The heuristic greedy method of the previous section is again used for the power level adjustments. The overall PLM algorithm is detailed in Figure 3.5. The requirements for information exchange are similar to those of the PF compensation algorithm. In particular, the long-term average channel gains, E[g n,k ], need to be known at a central node. However, one advantage is that the exchange of load information, K n, for each BS is not required. 3.6 Simulation/Evaluation We simulate both a regularly-deployed and an irregularly-deployed cellular network for the evaluation of the COC algorithms. In each case, the network is composed of 19 BSs, and the outage BS is located at the centre of the circular simulation area. The simulation methodology and parameters are largely based on the ITU recommendations. Note that a single subcarrier has been assumed for the evaluation. In the irregular network deployment, the BSs are positioned according to the uniform statistical distribution over the network area. In addition, the spatially correlated shadowing model of [8] detailed in Chapter 2, which considers correlation for irregular deployment, is utilized. A summary of the model parameters is provided in Table 3.1. As indicated in Table 3.1, the initial BS power levels are all equal to P 0 /α for the regular network. In this simulation, the initial power levels for the irregular network are computed by means of a fast heuristic optimization. In particular, we consider the total

56 Chapter 3. Adaptation Case: BS Outage Compensation 46 Require: Maximum power level, P 0n and power multiplier, α n, n N. Candidate set N C. 1: for all n N do 2: P n P 0n /α n. 3: end for 4: for all k K, k / K O do 5: n(k) arg max n E[g n,k ] 6: end for 7: for all k K O do 8: n(k) arg max n NC E[g n,k ] 9: end for 10: N CO {n K n,o } N AS 11: repeat 12: Form the candidate BS set for power increase according to N CP I = {n P n = P 0n /α n, n N CO }. 13: for all BSs n N CP I do 14: Assign temporary variable: P n α n P n = P 0n 15: Compute S β,co (P n = P n). 16: end for 17: Find optimum power increase BS, n = arg max n NCP I S β,co (P n = P n) 18: Implement power increase: P n α n P n = P 0n 19: until N CP I =. Figure 3.5: PLM Compensation Algorithm. rate maximization problem: max P R n (3.21) n N P n G nn subject to R n = B T log 2 (1 + N 0 C + j N,j n P jg nj 0 P n P 0 α, n N. ), n N where the set of users associated with each BS was replaced by a virtual representative user indexed by n, P n is the BS power level, R n is a rate computed for virtual user n and G nj is a channel gain for the link between virtual user n and the BS j, which is generated as the geometric mean of user channel gains: G nj = ( k K n E[g k,j ] ) 1/Kn. (3.22) Note that the powers are bounded by P 0 /α as the BSs are assumed to be operating

57 Chapter 3. Adaptation Case: BS Outage Compensation 47 Parameter Bandwidth per subcarrier BS power budget per subcarrier, P 0 The factor α Table 3.1: Simulation parameters. Value 15 khz dbm 10 Initial BS powers for regular network P 0 /α Noise figure at terminal Background noise power spectral density Distance-dependent path-loss (carrier frequency = 2 GHz) Shadowing standard deviation, σ 0 Shadowing correlation distance, d c Inter-site distance 7 db -174 dbm/hz P L = log 10 (d)[db], d in km 8 db 50 m 500 m Total number of cells 19 Number of Users in Centre Cell 66 Number of Users per Cell in the Other Cells Number of subcarriers 1 Subframe size (= time slot size) PF scheduling window size, T ms 5 subframes below their maximum power capabilities. The optimization of (3.21) can be thought of as a fast way to estimate realistic BS power capabilities for a given random distribution of users and BSs. It was shown in [53] that under the assumption of high SINR (i.e. if (P n G nn )/(N 0 C + j N,j n P jg nj ) 1), (3.21) reduces to a convex geometric program a type of problem easily solved through interior-point methods. For the current problem, the solution is obtained by using CVX, a package for solving convex programs [54] Numerical Results In evaluating the COC algorithms, the following performance metrics are considered: User Average Spectral Efficiency: The total spectral efficiency (or the rate per total bandwidth) of the users in the compensating cluster normalized by the total number of users in the compensating cluster.

58 Chapter 3. Adaptation Case: BS Outage Compensation 48 Table 3.2: N P I and N CO as a function of β for the COC algorithms in the regular network. β N P I for PLM N P I for PF N CO for PLM N CO for PF Outage User QoS violation probability: The proportion of outage users in the compensating cluster whose average spectral efficiency is lower than a threshold, η t. Non-Outage User QoS violation probability: The proportion of non-outage users in the compensating cluster whose average spectral efficiency is lower than η t. The Average Number of BSs in the Compensating Cluster: Since N CO denotes the set of BSs in the compensating cluster, we let N CO be a particular realization of the number of elements in N CO. The average number of BSs in the compensating cluster, is thus denoted as N CO. The Average Number of BSs with Raised Power: Similarly, let N P I be the set of BSs with raised power. A realization of the number of elements in N P I is denoted by N P I, and the average number of BSs with raised power, is denoted as N P I. The performance of the proposed PF COC and PLM COC techniques are evaluated for various values of the parameter β and compared to a coordination scenario in the absence of cell outage, or the no outage scenario. The value of η t is set to 0.02 bps/hz. For a fair comparison, it is assumed that the cluster and BS power levels obtained through COC are also used for the analysis of the no outage scenario 2. Note that the results will only show the no outage scenario corresponding to the COC scheme with the best spectral efficiency and QoS violation probability, thereby serving as an upper bound on performance. The variation in N CO and N P I is illustrated for regular and irregular networks in Tables 3.2 and 3.3, respectively. For both regular and irregular deployment, as the parameter β increases, N P I decreases for the PF algorithm. Simultaneously, N P I is reduced slightly for the PLM algorithm. N CO stays approximately constant with changes 2 In the no outage scenario, the centre BS is also included in the cluster.

59 Chapter 3. Adaptation Case: BS Outage Compensation 49 Table 3.3: N P I network. and N CO as a function of β for the COC algorithms in the irregular β N P I for PLM N P I for PF N CO for PLM N CO for PF in β in all cases. In summary, the PF algorithm allows for significant adjustment of N P I which can be thought of as the cost of the compensation algorithm implementation by variation of β. The range of adjustment is generally larger for regular deployment. The user average spectral efficiency, outage user QoS violation probability and non-outage user QoS violation probability are plotted as functions of N P I in Figures , respectively. Figures 3.6a and 3.6b indicate that approximately 75% of the user spectral efficiency of the no outage scenario is achieved by both COC algorithms for regular and irregular deployment, with N P I at a maximum (corresponding to β = 0.1). However, if a slightly smaller user spectral efficiency is sufficient, β can be set higher, resulting in lower N P I for the PF algorithm. Effectively, the PF algorithm allows for a trade-off between low compensation cost (N P I ) and high user spectral efficiency. Figure 3.7a indicates that outage user QoS violation rate for the PF algorithm is around 6-9% under regular deployment, compared to approximately 4.5% for the no outage scenario which represents a modest increase. In addition, the violation rate for the PLM COC algorithm is close to 8%. Effectively, the PF algorithm is shown to achieve a trade-off between QoS violation rate and compensation cost (N P I ) under the regular deployment scenario. Similarly, Figure 3.7b indicates for irregular deployment that the QoS violation rate for the PF algorithm is around 10-12%, compared to approximately 7% for the no outage scenario. The violation rate for the PLM COC algorithm is close to 11.5%. The PF algorithm also achieves a trade-off between QoS violation rate and N P I under the irregular deployment scenario. Similar trends as Figure 3.7 are shown for the non-outage user QoS violation probability in Figure 3.8. In particular, a modest increase in violation rates compared to the no outage scenario is obtained. The PF algorithm achieves a trade-off between violation rate and N P I. Additionally, the non-outage user QoS violation rate stays below about 2% for both COC algorithms in the two deployment scenarios.

60 Chapter 3. Adaptation Case: BS Outage Compensation 50 (a) (b) Figure 3.6: User average spectral efficiency, in bps/hz, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks.

61 Chapter 3. Adaptation Case: BS Outage Compensation 51 (a) (b) Figure 3.7: Outage user QoS violation probability, in percent, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks.

62 Chapter 3. Adaptation Case: BS Outage Compensation 52 (a) (b) Figure 3.8: Non-outage user QoS violation probability, in percent, as a function of the average number of BSs with raised power for (a) regular and (b) irregular networks.

63 Chapter 3. Adaptation Case: BS Outage Compensation 53 In summary, both the PF and PLM COC algorithms show robustness toward cell outage. Specifically, they achieve a large percentage of the user spectral efficiency of the no outage scenario and result in only a modest increase in the QoS violation rates. In addition, the PF COC algorithm is tunable and allows for trading off N P I, which is related to algorithm cost, against various measures of user performance.

64 Chapter 4 Dynamic System Model (Single Power Class) 4.1 Relevant Work Terminal and BS Deployment Models in Cellular Networks A number of spatial point processes have been used to model the deployment of BSs and terminals in multi-tier or heterogeneous cellular networks. Spatial point processes are the generalization of point processes indexed by time to the higher dimensions, in particular, two-dimensional space. Among the point processes, the simplest and most popular is the Poisson Point Process (PPP). In the PPP model, each node is placed independently over area A with the density of nodes given by λ. The probability that there are n nodes in area A is thus given by the Poisson distribution and is equal to (λa) n e λa /n! The procedure to generate the PPP is to first draw Poisson distributed number n and then to place n points uniformly at random in A. The PPP is suitable to model a network composed of a large number of nodes randomly and independently existing in some area. In the cellular networks, it has been commonly used to model the terminal deployments [55] as well as BS deployments [56,57]. Typically, the nodes in different tiers are modelled via independent homogeneous PPPs. Similar to PPP as far as the independent and identically distributed node locations, the Binomial Point Process (BPP) has the only distinguishing feature that it generates a fixed number of nodes in a given area. It has been used to model deployment of a known number of mobile users in a cell of known size [58]. 54

65 Chapter 4. Dynamic System Model (Single Power Class) 55 More general models have also been considered in the literature. The Poisson Cluster Process (PCP), in particular, models the random patterns produced by random clusters. A PCP is constructed from a parent PPP by replacing each point with a cluster of points where the points are independently and identically distributed in the spatial domain. The PCP has commonly been used to model a network where nodes occur in clusters e.g. according to certain social behaviour such as users gathered around Wi-Fi hotspots. In cellular networks, the combination of a PPP and a PCP has been applied in the heterogeneous networks [59] where the PPP represents the mobile users in a macrocell and the PCP represents femtocells or hotspots. Although the distance among BSs are random in a cellular network, we cannot find two BSs owned by the same provider that are arbitrarily close to each other. Thus research has considered the Matern hard core point process (MHCPP) which imposes a minimum distance, d min between nodes. The MHCPP is obtained by starting from a PPP. A random score uniformly distributed in [0, 1] is assigned to each point in the PPP, then all the points that fall within a distance less than d min from another point with a lower score is deleted. This results in a minimum separation between any points of d min. MHCPP has been used in place of the basic PPP process to model BS deployments in a cellular network where there is a restriction on BS separation due to such constraints as geographical constraints as well as network planning or due to the MAC protocol that avoids nearby simultaneous transmissions [60 62]. However, dealing with MHCPPs is relatively more complicated compared to the PPP. Therefore, the PPP model remains appealing partially due to its simplicity and analytical tractability [63 65]. Recent research has also considered more realistic point processes that capture the cellular network characteristics with greater accuracy. Gibbs family of processes, in particular, model the repulsion between the BS nodes, making it less likely that BSs are located close to each other. Gibbs processes belong to the category of Soft Core point processes (SCPP) as they do not impose a hard minimum distance between nodes. Research in [65, 66] has shown that the Gibbs processes model BS spatial locations in real networks more accurately compared to PPP models. Ginibre process is another point process that can be used to model the repulsion between BSs. Deng et al [7] consider and study the Ginibre point process as a model for wireless networks. They introduce the β-gpp as an intermediate process between PPP and GPP through consideration of the accuracy, tractability and practicality tradeoffs. They derive the coverage probability of a typical user in a cellular network and show that it compares well with actual base station deployments. The authors in [67] investigate the spatial modelling issue. Both the deterministic,

66 Chapter 4. Dynamic System Model (Single Power Class) 56 hexagonal model at one end and the random deployment following a Poisson point process (PPP) at the other extreme are considered. The authors utilize a modified perturbed hexagonal lattice model that lies in between the PPP and the hexagonal model in terms of irregularity. A frequency reuse-1 interference network is then assumed and an upper bound on the average total interference as a function of distance is provided. The paper specifies the loss in coverage probability when moving from a perfect lattice to the random BS deployment Terminal Mobility Models in Cellular Networks There exist a number of statistical models to represent movement in cellular networks. The most widely-used is the random walk model [68, 69], which is sometimes referred to as Brownian motion. According to this model, a terminal moves by choosing an arbitrary direction and speed from the given ranges [v min, v max ] and [0, 2π], respectively. Each movement in the model is performed either for a constant time or for a constant distance travelled. Then a new speed and direction are selected. The random walk model represents a memoryless mobility pattern as the current speed and direction are independent of past speeds and direction. However, this model can result in unrealistically sudden turns and stops. A similar model as the random walk model is the random waypoint model, which is also widely used [70,71]. According to the model, a terminal chooses a random destination in the simulation area and a speed that is uniformly distributed between [v min, v max ]. It then moves to the destination at the chosen speed. After arrival at the destination, the terminal pauses for a predetermined length of time before repeating the process. Gauss-Markov mobility model was introduced to improve the realism of the random walk model [72, 73]. In this model, a nodes next location is generated by its current location and velocity. The variation of one tuning parameter allows the variation of the degree of randomness in the mobility pattern. At one extreme of the parameter value, the random walk model is obtained and the other extreme results in linear motion. Intermediate values of randomness are obtained between the two extremes. Another category of mobility models known as group mobility models represent particular types of user movement as a group [74], such as a group of young children walking in a single file (column mobility model), a group of students touring a museum (nomadic community mobility model) or police officers pursuing an escaped criminal (pursue mobility model).

67 Chapter 4. Dynamic System Model (Single Power Class) Approach and Contributions System Model Approach of the Thesis A system model for an irregular cellular network is considered, which is based on the concept of Monte Carlo simulations. The model explicitly specifies the representations of terminal and BS deployments, shadow fading as well as the large-time-scale evolution model of the system. Scenarios with either a single or multiple BS power classes are considered. Much of the literature considers classical models particularly for the deployment (e.g. PPP), and the shadowing (e.g. lognormal shadowing) for the purpose of simplicity and analytical tractability despite their lack of realism. Our primary contributions include the deployment models for BSs and terminals, terminal movement (mobility) models, and shadowing model with correlation for multiple power classes. The model is considered primarily as a generic reference model for the purpose of the design of resource allocation with adaptation at a large time scale, for an irregular cellular network. The goal of developing the model is that it can be used along with any modifications as desired, in order to model the cellular network as realistically as desired in terms of the interference, deployment positions, movement and channel models (shadowing and multipath fading) among other elements. Deployment Model The most common model in the literature for irregular deployments is the PPP model due to its simplicity and analytical tractability. However, the PPP model was shown to be unrealistic in real irregular networks. Other more realistic models exist (with the primary example being the Ginibre process [7]) however most such models have the issue of being difficult to handle. In this work, we consider the development of a baseline deployment model for Monte Carlo simulation with the primary consideration being the model simplicity and a baseline realism, which is implemented through arbitrariness or randomness of deployment with a minimum separation between the nodes and the elements in the network. Deployment scenarios both with hotspots (multiple power classes) and without hotspots (single power class) are considered. Since this is meant as a generic model, guidelines for parameter values are provided for baseline realism of the simulation scenario. Note that this chapter deals with the deployment model without hotspots or the single power class scenario. The deployment model including hotspots and multiple BS power classes is elaborated in Chapter 6.

68 Chapter 4. Dynamic System Model (Single Power Class) 58 Mobility Model Most other models in the literature do not consider terminal movements over an arbitrarily large time scale as a snapshot. We propose a generic model for individual mobility that is meant as a generic model appropriate for a time scale that is orders of magnitude larger than the multipath fading time scale. The primary consideration for the model is its simplicity. A similar movement model is also then considered for BSs. Deployment scenarios both with hotspots (multiple power classes) and without hotspots (single power class) are considered for the movements. Since this is meant as a generic model, guidelines for parameter values are provided for the baseline realism of the simulation scenario. Note that this chapter deals with the movement (mobility) model without hotspots or the single power class scenario. The mobility model including hotspots and multiple BS power classes is elaborated in Chapter Introduction In Chapter 3, we studied the BS outage as a specific case of a dynamic change occurring in the irregular cellular network, and BS outage compensation as an adaptation in response to the particular type of dynamic change. In Chapters 4 through 7, we propose a full system model that incorporates a wide array of dynamic changes occurring in the irregular network, and study an algorithmic framework for system adaptation. The resource allocation framework of [2] was shown to have the capability to adapt to the slow traffic variations, and the clustering concept was designed for the irregular deployment of BSs. The case of a single BS power class was primarily considered. The scheduling and on-off power switching at the subcarriers further adjusts to the variations in the traffic and channel conditions at a finer level. The adaptive resource allocation framework has thus been adopted in this chapter for the model with network time evolution. In the following, the system model of the ITU will be modified as needed to meet the requirements of the irregular network with a single BS power class. Recall that the original drop-based simulation method of the ITU model does not allow the modelling of network evolution at the slow time scale (i.e. the time scale of the simulation drop). Therefore, we propose a modified method of drop-based simulation, which is summarized as follows: First, we re-define the simulation drop as an independent deployment of both terminals and BSs. Second, we define a new term subdrop as a modified version of a given simulation drop, which is obtained by making small step-

69 Chapter 4. Dynamic System Model (Single Power Class) 59 wise changes to the initial drop configuration. Time evolution at the slow scale is thus obtained by implementing a series of subdrops for each drop, which consist of gradual dynamic changes. The dynamics studied include terminal arrivals and departures, BS deployments and outages as well as terminal movements. In this thesis, BS movements are also considered as they provide a way to represent the arbitrariness or time variation of the BS locations with respect to the terminals in the model, and are believed to be plausible in emerging and future networks. The system model is developed in stages in Chapters 4 through 7. In this chapter, the system simulation model with network time evolution is considered for the irregular network with a single BS power class and constant BS power levels. Adaptation of BS power levels (power control) will be discussed in Chapter 5. The static system model and the time evolution model for a network with multiple power classes will be examined in Chapters 6 and 7, respectively. In the current model, the simulation proceeds as summarized in Figure 4.1. Both the generation of drops, subdrops and subframes, together with slow-scale time evolution, as well as the execution of slowly-adaptive functions and fast resource allocation are shown. The framework requires details of channel models, methods of drop deployment and time evolution as well as slow adaptation and fast resource allocation algorithms. Note that the multipath, correlated shadowing and path loss channel models, described in Chapter 2, are used in the current model. The rest of the chapter details the proposed drop deployment and time evolution models. The methodology of simulation drop deployment is developed in Section 4.4. The time evolution model is discussed in Section 4.5. Finally, typical parameter values for the models are detailed in Section Drop Deployment Model Realistic modelling of simulation drop deployment is considered in this section. Recall that a drop is defined as the independent and mathematically random deployment of a number of terminals and BSs in a network simulation area. In practical irregular networks, variety of restrictions are typically imposed on the positioning of BSs due to various reasons, including broad-level deployment planning by wireless operators, and public and private property considerations. Therefore, it is essential that the proposed random deployment model have certain mathematical restrictions to reflect the practical constraints of deployment. Note that the imposed restrictions are parametrized so that they can be adapted to a large number of practical situations by the tuning of parameters. A circular area as shown in Figure 4.2 is utilized in the deployment of the network

70 Chapter 4. Dynamic System Model (Single Power Class) 60 Generate simulation drop i Generate subdrop j of drop i No Compute path loss and shadowing for all terminal-bs links i = P? Yes STOP Check arrivals, departures and movements Execute slowly adaptive algorithms No i = i + 1 j mod B = 0? Yes Generate subframe l of subdrop j Perform coordinated resource allocation in each cluster j = j + 1 No l = l + 1 l mod F = 0? Yes Figure 4.1: Outline of the Simulation Framework. shadowing potential field realization as discussed in Section 3.2 is fixed. In other words, the dynamism in subdrops results solely from gradual changes relating to BSs and terminals on a given and fixed topography. Let N (b) and K (b) be the set of BSs and terminals active at subdrop b, respectively. Specifically, N (0) and K (0) denote the set of BSs and terminals active at subdrop 0. At each subsequent subdrop 1 b B, ΔK (b) a terminals arrive at uniform randomly distributed locations according to the standard Poisson distribution f(i; λ t ) = Pr(ΔK (b) a = i) = λ t i e λ t, where f( ) denotes the probability mass function, and λ t > 0 is the Poisson parameter. Each terminal departs the i!

71 Chapter 4. Dynamic System Model (Single Power Class) 61 with a single BS power class. Let R be the radius of the simulation area. N BSs are dropped with uniform random distribution onto the circular simulation area. The twodimensional (2-D) uniform random distribution for the BSs on the circle is obtained by first generating the position in polar coordinates a, the radius, and φ, the angle with respective probability densities given by f A (a) and f Φ (φ): 2a for 0 a R, R f A (a) = 2 (4.1) 0 otherwise, f Φ (φ) = 1 for 0 φ 2π, (4.2) 2π and later converting the results into rectangular coordinates x and y by using x = a cos φ (4.3) y = a sin φ (4.4) In order to reflect the restrictions due to network planning and property considerations, it must be ensured that the distances between BSs are not smaller than the minimum allowed separation parameter, δ BS, as illustrated in Figure 4.2. If the distance between any generated pair of BSs is less than δ BS, the coordinates of one of the affected BSs must be re-computed according to (4.1)-(4.4). Finally, the coordinates of K terminals on the circular area are also generated randomly by using (4.1)-(4.4). If any terminal is found to have the same coordinates as any of the BSs 1, the coordinates of the terminal must be re-computed. 4.5 Time Evolution Time evolution in irregular networks for each simulation drop is obtained through the generation of multiple subdrops. The list of modelled network dynamics includes gradual terminal arrivals and departures, BS deployments and outages, terminal and BS movements as well as changes in the large-scale channel parameters. A detailed time evolution methodology is discussed in this section. Let P be the set of drops used in the simulation, B p the set of subdrops associated with each drop p P, and F b the set of subframes associated with each subdrop b B p, for p P. As the Times New Roman large letters indicate the cardinality of sets, P is 1 In practice, this condition is implemented by imposing a restriction on the minimum distance between the terminals and the BSs.

72 Chapter 4. Dynamic System Model (Single Power Class) 62 BS R Figure 4.2: Simulation area for deployment in networks with a single BS power class. the total number of simulation drops, B p is the number of subdrops associated with drop p, and F b is the number of subframes associated with subdrop b. The number of subdrops used in each drop is equal, that is, B p is equal to a constant B for all p P. Similarly, an equal number of subframes is utilized in each subdrop, or F b = F for all b B p, p P. For consistency of notation, the initial deployment of a drop before any time evolution is referred to as subdrop 0. The remaining subdrops associated with the drop are numbered from 1 to B 1. It is important to note the relationship between the drop, subdrop and the shadowing model random potential field [8] discussed in Chapter 2. In particular, for all subdrops b B p associated with a given simulation drop p P, the realization of the random potential field is modelled to be constant. In other words, the physical topography can be conceptualized as fixed within each simulation drop, and the changes in shadowing over the subdrops result solely from BS and terminal movements on the fixed topography. The detailed modelling of the dynamics is discussed in the following Terminal Arrival and Departure Models Let K (b) be the set of terminals active at subdrop b. In particular, K (0) denotes the set of terminals that are active at the initial subdrop, indexed by 0. At each subsequent subdrop 1 b B 1, [ K a ] (b) terminals arrive to the system according to the Poisson distribution: f(i; λ t ) = P r ( [ K a ] (b) = i ) = λi te λt, i = 0, 1, 2,... (4.5) i!

73 Chapter 4. Dynamic System Model (Single Power Class) 63 where f( ) denotes the probability mass function, and λ t > 0 is the Poisson parameter, expressed in terms of the number of terminals. The coordinates of the arriving terminals are determined according to the random deployment procedure of Section 4.4. Each terminal must depart the system after a survival time, τ k, expressed in terms of the number of subdrops. τ k is generated according to the following steps: Step 1: Virtual survival time, χ, is generated as a temporary variable according to the exponential probability mass function with mean parameter, µ t > 0 (expressed in terms of the number of subdrops): 1 µ f(χ) = t e χ µ t if χ 0, (4.6) 0 if χ < 0. Step 2: The actual survival time, τ k, is computed according to τ k = χ (4.7) The number of terminals that depart at subdrop b, [ K d ] (b), is determined with the knowledge of terminal survival times, τ k. The total number of terminals remaining at subdrop b is thus given by K (b) = K (b 1) + [ K a ] (b) [ K d ] (b) (4.8) BS Deployment and Outage Models Similar to the terminal model, the simulation framework has the option for modelling BS deployments and BS outages. Let N (b) be the set of BSs active at subdrop b. The BS deployment is modelled as an arrival and the BS outage is modelled as a departure process. Let I bs be an indicator parameter which is set to 0 if BSs are not allowed to be deployed (i.e. arrive) and have an outage (i.e. depart). This means that the set N (0) is fixed over the duration of the drop. If the BSs are allowed to have both deployments and outages, I bs is then set to 1. For I bs = 1, the number of BSs, [ N a ] (b), arriving to the system at subdrops 1 b B 1 follow the Poisson distribution: f(i; λ bs ) = P r ( [ N a ] (b) = i ) = λi bs e λ bs, i = 0, 1, 2,... (4.9) i! where f( ) denotes the probability mass function, and λ bs > 0 is the Poisson parameter, expressed in terms of the number of BSs. The coordinates of the arriving BSs are

74 Chapter 4. Dynamic System Model (Single Power Class) 64 determined according to the random deployment procedure of Section 4.4. Each BS departs the system after a survival time, τ n, (expressed in number of subdrops), which is generated according to the following steps: Step 1: Virtual survival time, χ, is generated according to the exponential probability mass function with mean parameter µ bs > 0: 1 µ f(χ) = bs e χ µ bs if χ 0, (4.10) 0 if χ < 0. Step 2: The actual survival time, τ n, is computed according to τ n = χ (4.11) Similar to the terminals, the number of BSs that depart at subdrop b, [ N d ] (b), is determined with the knowledge of BS holding times, τ n. The total number of BSs remaining at subdrop b is given by N (b) = N (b 1) + [ N a ] (b) [ N d ] (b) (4.12) Terminal Movement Model Terminals are moved at every subdrop through a randomly generated displacement in a random direction. The movement model is illustrated in Figure 4.3. The full algorithm for the terminal movement at the subdrop is given in Figure 4.4. Direction of movement over the xy-plane is represented by angle θ k,b, which is drawn from a uniform random distribution in the interval [0, 2π]. The displacement, denoted as d k,b, is drawn from a uniform random distribution in [ d t,min, d t,max ], where d t,min and d t,max are model parameters. Terminals are moved at each subdrop through the displacement d k,b in the direction represented by angle θ k,b. However, it is ensured that terminals do not go out of the bounds of the circular simulation area of radius R illustrated in Figure 4.2. Consequently, a check condition is utilized in the realization of the terminal movements 2. As long as a terminal would remain within the simulation area, i.e., if (x k + d k,b cos θ k,b ) 2 + (y k + d k,b sin θ k,b ) 2 R 2, its coordinates (x k, y k ) are updated 2 While terminals going out of bounds could be treated as a departure, the check condition is used to represent the departures and movements separately.

75 Chapter 4. Dynamic System Model (Single Power Class) 65 y (x k + dk,bcosθk,b, y k + dk,bsinθk,b) dk,b θ k,b (xk, yk) x Figure 4.3: The terminal movement illustration. according to: x k x k + d k,b cos θ k,b (4.13) y k y k + d k,b sin θ k,b (4.14) If the full movement would place the terminal out of the simulation area, i.e., if (x k + d k,b cos θ k,b ) 2 + (y k + d k,b sin θ k,b ) 2 > R 2 ; terminal is first moved through a partial displacement α < d k,b, it is then placed at a position at 180 degrees from its position in the circular simulation area, and finally, the remainder of the movement is completed at its new location. The updated coordinates of the terminal are therefore given by x k (x k + α cos θ k,b ) + ( d k,b α) cos θ k,b (4.15) y k (y k + α sin θ k,b ) + ( d k,b α) sin θ k,b (4.16) where α is determined by solving α 2 + 2α(x k cos θ k,b + y k sin θ k,b ) + (x 2 k + y 2 k R 2 ) = 0 (4.17) BS Movement Model Similar to the terminals, the proposed simulation framework has the option for modelling BS movements. Let π bs be a fixed probability of BS movement. At each subdrop, BSs

76 Chapter 4. Dynamic System Model (Single Power Class) 66 Require: x k, y k, for terminals k K, and parameters d t,min and d t,max 1: for all terminals k K do 2: Generate d k,b U [ d t,min, d t,max ], and θ k,b U [0, 2π]. 3: if (x k + d k,b cos θ k,b ) 2 + (y k + d k,b sin θ k,b ) 2 R 2 then 4: x k x k + d k,b cos θ k,b 5: y k y k + d k,b sin θ k,b 6: else 7: Solve for α in α 2 + 2α(x k cos θ k,b + y k sin θ k,b ) + (x 2 k + y2 k R2 ) = 0 8: x k (x k + α cos θ k,b ) + ( d k,b α) cos θ k,b 9: y k (y k + α sin θ k,b ) + ( d k,b α) sin θ k,b 10: end if 11: end for Figure 4.4: Algorithm for the terminal movement at the simulation subdrop. are moved with probability π bs through a random displacement in a random direction. The movement model is illustrated in Figure 4.5. The detailed algorithm is described in Figure 4.6. The direction of movement over the xy-plane, represented by angle θ n,b, is drawn from a uniform distribution in the interval [0, 2π]. The displacement, denoted as d n,b, is drawn from a uniform distribution in [ d bs,min, d bs,max ]. As long as a BS would remain within the simulation area, i.e., if (x n + d n,b cos θ n,b ) 2 +(y n + d n,b sin θ n,b ) 2 R 2, its coordinates (x n, y n ) are updated according to: x n x n + d n,b cos θ n,b (4.18) y n y n + d n,b sin θ n,b (4.19) If the movement would place the BS out of the simulation area, the coordinate update is given by x n (x n + α cos θ n,b ) + ( d n,b α) cos θ n,b (4.20) y n (y n + α sin θ n,b ) + ( d n,b α) sin θ n,b (4.21) where α is determined by solving α 2 + 2α(x n cos θ n,b + y n sin θ n,b ) + (x 2 n + y 2 n R 2 ) = 0 (4.22)

77 Chapter 4. Dynamic System Model (Single Power Class) 67 y (x n + dn,bcosθn,b, y n + dn,bsinθn,b) dn,b θ n,b (xn, yn) x Figure 4.5: The BS movement illustration. Require: x n, y n, for BSs n N, and parameters π bs, d bs,min and d bs,max 1: for all BSs n N do 2: Generate γ such that P r(γ = 1) = π bs and P r(γ = 0) = 1 π bs. 3: if γ = 1 then 4: Generate d n,b U [ d bs,min, d bs,max ], and θ n,b U [0, 2π]. 5: if (x n + d n,b cos θ n,b ) 2 + (y n + d n,b sin θ n,b ) 2 R 2 then 6: x n x n + d n,b cos θ n,b 7: y n y n + d n,b sin θ n,b 8: else 9: Solve for α in α 2 + 2α(x n cos θ n,b + y n sin θ n,b ) + (x 2 n + yn 2 R 2 ) = 0 10: x n (x n + α cos θ n,b ) + ( d n,b α) cos θ n,b 11: y n (y n + α sin θ n,b ) + ( d n,b α) sin θ n,b 12: end if 13: end if 14: end for Figure 4.6: Algorithm for the BS movement at the simulation subdrop.

78 Chapter 4. Dynamic System Model (Single Power Class) 68 Table 4.1: Typical parameter values. Parameter Typical Range and/or Value Minimum BS separation, δ BS δ BS R Numbers of subdrops, B typical value of 20 Numbers of drops, P P B, typical value of 300 Scheduling average window size, T 0 typical value of 5 Numbers of subframes, F F T 0, F P, typical value of 100 Terminal arrival parameter, λ t typical value of 3 terminals BS arrival parameter, λ bs λ bs λ t, typical value of 0.5 BSs Terminal departure parameter, µ t typical value of 5 subdrops BS departure parameter, µ bs µ bs µ t, typical value of 20 subdrops Maximum terminal displacement, d t,max Minimum terminal displacement, d t,min Maximum BS displacement, d bs,max 0.1d c d t,max 10d c 0 d t,min 1 4 d t,max 0.1d c d bs,max 10d c Minimum BS displacement, d bs,min 0 d bs,min 1 d 4 bs,max BS movement probability, π bs π bs Typical Parameter Values In this section, we discuss typical values for the time evolution and drop deployment model parameters. Although there may be many ways to set some of the parameters, a few important suggestions will be made. Recommended values and ranges for the parameters are summarized in Table 4.1. Justification for the recommendations are discussed in the following. We first consider the minimum BS separation parameter, δ BS, in the drop deployment model. Note that if δ BS were on the order of the simulation area radius R, that is, δ BS R, the number of BSs fitting in the simulation area would be severely limited. Therefore, it is recommended that δ BS be small in comparison to R, or satisfy δ BS R, so that a large number of BSs can be used in the system simulation while the practical separation constraints are still satisfied. In the time evolution model, we begin by considering the setting of the total number of drops, P, the number of subdrops, B, and the number of subframes, F, as well as the scheduling averaging window size, T 0. The primary consideration is that a sufficiently large number of drops, subdrops and subframes be used in the simulation so that the simulation results will be representative (in a statistical sense) of the different types of

79 Chapter 4. Dynamic System Model (Single Power Class) 69 possible network configurations and slow and fast network evolutions. A secondary and competing consideration is that P, B, and F must be small enough that the simulations can be completed on a given computer system in a desirable amount of time. (Note that the program execution times can vary greatly depending on the system; therefore, the issue is not considered in detail here.) In order to balance the two competing factors, we propose the strategy of setting P as high as possible while setting B and F at a moderate value to keep the computational complexity sufficiently low. There is an expectation that even if the values B and F are relatively low, the values P B and P BF (i.e. the total number of subdrops and subframes, respectively) will be high enough to be statistically representative of evolution scenarios. A P value of 300 (which is high) and a B value of 20 (which is moderately low) are suggested and seem to work well in practice. Note that the P value can also be set higher for greater accuracy. The setting of the F value must be done in conjunction with the T 0 value. In the exponential averaging of (2.9) in Chapter 2, the setting of T 0 affects the response of the average rates, R, to the instantaneous rates, r. Small T 0 values result in fast but not instantaneous response times; and conversely, large T 0 values result in slow response times, but smoother averaging. We recommend a typical low T 0 value of T 0 = 5 from the literature [75], which results in a relatively fast response time. In order to ensure adequate statistical averaging of results with exponential averaging, the value of F is recommended to be higher than the B value. Setting F = 100 is shown to work well in practice. The setting of terminal arrival and departure, and BS deployment and outage parameters are considered next. It is important to note that in realistic networks, the BS deployments and outages occur much less frequently compared to terminal arrival and departure events. It is, therefore, suggested that BS and terminal model parameters, λ bs, λ t, µ bs and µ t, satisfy the relations: λ bs λ t (4.23) µ bs µ t (4.24) Setting of the actual parameter values are expected to depend on many other factors, including the subdrop time duration and initial number of terminals, K (0), and number of BSs, N (0) used in the model. However, nominal settings of λ bs = 0.5 BSs, λ t = 3 terminals, µ bs = 20 subdrops and µ t = 5 subdrops are suggested, and are shown to work well in practice. Figures 4.7 and 4.8 illustrate sample realizations of the evolution of the number of terminals and BSs, respectively, with the suggested model values. We finally discuss the parameter settings for the terminal and BS movement models.

80 Chapter 4. Dynamic System Model (Single Power Class) 70 Figure 4.7: Sample realization of the evolution of the number of terminals K (b) over subdrops b, with K (0) = 25, the arrival parameter λ t = 3 terminals, and the departure parameter µ t = 5 subdrops. Since subdrops are designed to model small gradual changes over the network configuration, we suggest setting the maximum terminal displacement parameter, d t,max, large enough to cause a small but noticeable change in shadowing over one subdrop. It is known from correlated shadowing theory that movement on the order of correlation distance, d c, results in a noticeable change in shadowing. Therefore, d t,max needs to satisfy 0.1d c d t,max 10d c. (4.25) Furthermore, it is recommended that the minimum displacement parameter, d t,min, be set as low as possible, and possibly set to zero, to allow a wide random variation of terminal displacement. Hence, it should satisfy 0 d t,min 1 4 d t,max. (4.26) Similar to BS arrivals and departures, BS movements are expected to occur very infre-

81 Chapter 4. Dynamic System Model (Single Power Class) 71 Figure 4.8: Sample realization of the evolution of the number of BSs N (b) over subdrops b, with N (0) = 7, the arrival parameter λ bs = 0.5 BSs, and the departure parameter µ bs = 20 subdrops. quently. Thus it is suggested that π bs satisfy π bs 1. (4.27) Finally, for the same reasons as terminal models, it is recommended that the values of maximum and minimum BS displacements, d bs,max and d bs,min, satisfy similar inequality relations: 0.1d c d bs,max 10d c (4.28) 0 d bs,min 1 4 d bs,max. (4.29)

82 Chapter 4. Dynamic System Model (Single Power Class) The Outline of the Network Model of the Thesis The basic structure of the general network model in the thesis is outlined in block diagram form in Figure Note that this is a more detailed version of the block diagram of Figure 4.1. However, note that the model of Figure 4.10 does not include all of the details discussed in the full model of the thesis. For instance, there is much more detail in terms of hotspot deployment, and shadowing with multiple propagation environments (Chapter 6); BS dynamics (Chapters 4 and 7); and the BS power adjustment algorithms (Chapter 5) in the complete model. Figure 4.9: A realization of the potential field [8].