Coverage Analysis and Resource Allocation in Heterogeneous Networks. Sanam Sadr

Transcription

1 Coverage Analysis and Resource Allocation in Heterogeneous Networks by Sanam Sadr 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 by Sanam Sadr, 2015.

2 Abstract Coverage Analysis and Resource Allocation in Heterogeneous Networks Sanam Sadr Doctor of Philosophy Department of Electrical and Computer Engineering University of Toronto 2015 The focus of this thesis is the analysis and design of multi-tier heterogenous networks (HetNets) with large density of access points (APs) located without a deterministic structure. We use stochastic geometry, specifically Poisson point processes (PPPs), to capture the randomness in AP locations. To differentiate their structural characteristics, APs are categorized into different tiers, each modeled by a PPP. The problem of cell association and resource allocation in a HetNet is considered from two different points of view: when the user is i)mobile and ii) stationary. To incorporate mobility in coverage analysis for mobile users, we derive the probability of handoff in an irregular multi-tier HetNet. To account for the service degradation due to handoffs, we propose a linear cost function, and use this to associate high speed users to upper tiers (e.g., macrocells) with a lower AP density. For stationary users, we first derive the statistical distribution of the load, and the minimum bandwidth required to meet an outage constraint in a multi-tier HetNet. This result is most useful for system design by relating the required spectrum to choices of network parameters. We then consider the dual problem with the objective of maximizing the overall rate coverage with orthogonal spectrum allocation across tiers given a total available bandwidth. We tackle this problem in two different phases: 1) load distribution and spectrum partitioning across tiers; 2) resource allocation across the APs and users within one tier. For analytical tractability in theformer,weapproximatethe load of each AP by its mean, and derive the optimum tier association and fraction of spectrum to be allocated to each tier. In the latter, to account for different loads at each AP, we develop ahierarchicalalgorithmtoallocatetheavailablespectrumacrosstheapsaccordingtotheir load and to users according to their data rate demand. The latter benefits from adaptive power allocation and dynamic spectrum allocation across APs. ii

3 Acknowledgements Foremost, I would like to express my special thanks to my supervisor, Prof. Raviraj S. Adve, not only for his excellent academic advice and inspiring weekly meetings but also for his continuous guidance, dedication and support during my Ph.D. studies. I feel truly honored for having the chance to work with Ravi and am hoping to have learned some of his effective problem solving and research approach, and can pass on his team spirit by treating my collaborators the way he treated me. IwouldliketothankthemembersofmyPh.D.supervisingcommittee, Prof. Alberto Leon-Garcia, and Prof. Elvino S. Sousa, for their insightful suggestions. Iwouldalsothank the external members of my final oral examination, Prof. Wei Yu andprof. ShahrokhValaee from the University of Toronto and Prof. Halim Yanikomeroglu fromcarletonuniversityfor their time and their constructive feedback. I am grateful to Diane Silva, the Administrative Coordinator, Jayne Leake at the Undergraduate Office, Judith Levene and Darlene Gorzo at the Graduate office of the Department of Electrical and Computer Engineering, and Lisa Fannin at the Doctoral Exams Office for always being helpful andforhandlingtheacademic and administrative matters within the shortest time possible. I owe special thanks to Natural Science and Engineering Research Council (NSERC) of Canada for providing financial support during my Ph.D. studies. Iamgratefulbeyondmeasurestomydearmother,Talat,andmybrother, Saman who have been my constant source of support and encouragement during difficult moments of my life. Their unconditional love has made this journey possible. This thesis is dedicated to Faady, Mamoush and Fisa. I would like to thank Andrew Corbett, for his kindness and the wonderful moments we had. Finally, I would like to thank all my friends, and fellow graduate students at the University of Toronto, particularly my colleagues, post-docs and visitors at BA7114 that I have overlapped with, for their help, friendship and support over the past several years. iii

4 Contents 1 Introduction Heterogeneous Networks Design Challenges Thesis Contributions and Organization Handoff Rate and Coverage Analysis Related Work and Motivation Contributions System Model Handoff Rate in a Single-Tier Network Coverage Probability with Handoffs Mobility-Aware Tier Association Numerical Results Handoff Rate Coverage Probability with Handoffs Summary Required Spectrum and Spectrum Partitioning in HetNets Related Work and Motivation Contributions System Model Load Distribution in The Network User Load AP Load Tier Association and Spectrum Partitioning Across Tiers Optimization Problem Equating the Two Fractions Numerical Results Summary iv

5 4 Resource Allocation in Single-Tier Small-Cell Networks Related Work and Motivation Contributions System Model Partially-Distributed Resource Allocation Numerical Results Summary Conclusion Summary Future Work Handoff Across Tiers The Minimum Required Spectrum Interference-Aware Resource Allocation within a Tier A Handoff Rate Across Tiers 96 Bibliography 103 v

6 List of Tables 4.1 Simulation Parameters vi

7 List of Figures 1.1 The hexagonal grid model for cellular networks. The desired and the interfering signals at the user are represented by solid and dashed lines respectively The PPP model for a single-tier HetNet. The red squares represent APs. The blue lines, called the Voronoi diagram, represent the coverage area of each AP Scenario where the user is initially at l 1,atconnectiondistancer from the serving AP, moving a distance v in the unit of time at angle θ with the direction of the connection; (a) handoff occurs if there is another AP closer than R to the user at the new location l 2 ;(b)theservingapremainstheclosestaptotheuserat location l 2.Hence,handoffdoesnotoccur The intersection between the two circles is the area already known to have no AP closer than AP s to the user Relation between r, v and R Handoff rate versus: (a) user displacement in a unit of time v, (b) APdensity λ k,forboththegeneralcase(θ has uniform distribution) and the special case of radial movement (θ =0) Probability of coverage versus user displacement v in a unit of time for different AP densities and τ k = 0dB: (a) the system is less sensitive to handoffs, β =0.3; (b) the probability of connection failure due to handoffs is large, β = Probability of coverage versus SIR threshold τ k for: (a) β =0.3,(b)β =0.9. v =15inbothfigures Probability of coverage in a two-tier network versus A 2. A 1 =1 A 2, {λ 1,λ 2 } = {0.1, 1}/1000, {P 1,P 2 } = {46, 20}dBm and τ 1 = τ 2 =0dB.Theoverallprobability of coverage is maximized when A 1 = A 2 = The concavity of the term f k,2 (A k )withrespecttoa k for the lower tier, i.e., k =2inatwo-tiernetwork Overall probability of coverage versus user speed.; τ 1 = τ 2 =0dB,{λ 1,λ 2 } = {0.1, 10}/(1000m 2 ), {P 1,P 2 } = {46, 20}dBm, and β = Coverage in a two-tier network with flexible tier association: (a) probability of association to the lower tier and b the bias factor for the lower tier. {λ 1,λ 2 } = {0.1, 10}/(1000m 2 ), {P 1,P 2 } = {46, 20}dBm, β =0.9 andτ 1 = τ 2 =0dB vii

8 3.1 CDF of AP load in a two-tier network with spectrum sharing (full reuse) across tiers; κ 1 = κ 2 =1Mbps,andA 2 =1 A Overall AP coverage, P A (W ), as a function of the available bandwidth for a two-tier network with spectrum sharing across tiers; κ 1 = κ 2 =1Mbps CDF of AP load in a two-tier network with orthogonal spectrum allocation across tiers; {A 1,A 2 } = {0.2, 0.8}, andκ 1 = κ 2 =1Mbps Overall rate coverage in a three-tier network with the same rate threshold for all tiers. {P 1,P 2,P 3 } = {46, 30, 20}dBm and {λ 1,λ 2,λ 3 } = {0.01, 0.05, 0.2} λ u Overall rate coverage in a three-tier network with different rate threshold across tiers, {κ 1,κ 2 } = {0.5, 1} Mbps. {P 1,P 2,P 3 } = {46, 30, 20}dBm, and {λ 1,λ 2,λ 3 } = {0.01, 0.05, 0.2} λ u Comparing the optimum tier association and spectrum partitioning for different tiers with the solution to (3.37), i.e, A k = w k. The results obtained by the interior-point method and brute force search are referred to as IP and BF respectively Random distribution of APs and users in the network A network of 3 APs. M 1 =1,M 2 = M 3 =3. Notethattherequirednumberof channels at an AP is not necessarily equal to the number of users it serves Interference graph corresponding to Fig Both APs #2 andap#3require three subchannels. Hence, they are replaced by a complete subgraph of three nodes. They only interfere with AP #1, which requires only one subchannel. Hence, there are edges between each of the complete subgraphsandthenode representing AP # Graph coloring corresponding to Fig Minimum numberofcolorsisfour, with both optimal and suboptimal coloring algorithms. This is the minimum number of channels such that no AP is interfering with another Outage rate as a function of the fixed number of PRBs assigned to each AP. λ l =1/(200m 2 ), λ u =3λ l and λ u =6λ l. R u =1.5Mbps Users at outage in both schemes versus the user demand. λ l = 1/(200m 2 ), λ u =3λ l and λ u =6λ l. M AP =18forthefixed-allocation Average minimum user achieved rate for both schemes versus the user demand. λ l =1/(200m 2 ), λ u =3λ l and λ u =6λ l. M AP =18forthefixed-allocation Total throughput of the system for both schemes versus the userdemand.λ l = 1/(200m 2 ), λ u =3λ l and λ u =6λ l. M AP =18forthefixed-allocation viii

9 A.1 Scenario where the user is initially at l 1,atconnectiondistancer k from the serving AP in tier k. AP s remains the closest AP from tier k after the user moves a distance v in the unit of time to location l 2. Triangles represent the APs in tier j. (a) handoff occurs from tier k to j since there is another AP in tier j closer than R j to the user at the new location l 2 ;(b)theservingapin tier k still provides the strongest biased average received power to the user at location l 2.Hence,handoffdoesnotoccur A.2 Scenario where the user is initially at l 1,atconnectiondistancer k from the serving AP in tier k. After the user moves a distance v in the unit of time to location l 2,anewAPisthestrongestAPintierk at connection distance z k. Triangles represent the APs in tier j. (a) handoff occurs from tier k to j since there is another AP in tier j closer than z k to the user at the new location l 2 ; (b) the new AP in tier k provides the strongest biased average received power to the user at location l 2.Hence,handoffdoesnotoccur A.3 The random variable Z k denotes the distance to the closest AP to the user after the user moves from l 1 to l ix

10 Chapter 1 Introduction According to the annual visual network index (VNI) report released by Cisco (Feb. 2014), the huge growth in wireless traffic demand will continue due to the increasing number of mobile users almost always connected to a wireless network [1]. Among the possible developments to meet this huge demand for network capacity, three promising technologies stand out: densification [2], millimeter wave (mmwave) transmissions [3], and massive multiple-input multiple-output (MIMO) [4]. While the latter two technologies result in higher throughput by, respectively, increasing the bandwidth and transmitting with greater spectral efficiency per access point (AP), densification attempts to reach this goal by building a network with more active APs per unit area. This results in higher area spectral efficiency by increasing the sum throughput per unit area that the system can provide per unit bandwidth. The benefits of densification are due to: i) a smaller connection distance (hence, small cells) resulting in reduction in the transmit power [5]; ii) reuse of theavailablespectrumthroughout the network, and finally iii) fewer users competing for resources per AP. Ensuring coverage over a large geographic area with user mobility has led to a new networkarchitecturewith nested tiers of APs first introduced in [6 8]. While the APs in each tier are homogeneous, they differ across tiers in their capabilities, radio resources andradioaccesstechnology. Therateand coverage analysis in such heterogeneous networks (HetNets) whereapsareirregularlydeployed in the network is expected to be quite different from those of a regular cellular network, and is the focus in this thesis. While densification has been shown to increase the total throughput [9], it poses new chal- 1

11 Chapter 1. Introduction 2 lenges especially in terms of interference management and the increased handoffs experienced by mobile users. The large density of APs in HetNets results in alargenumberofstatistically independent interfering signals. This high level of interference in both the downlink and the uplink leads to a lower signal-to-interference-plus-noise ratio(sinr)andhenceahigheroutage rate. A measure of performance is, therefore, to characterize the distribution of the interference, and consequently SINR, in the network. For a fixed modulation and coding scheme, the outage rate is the cumulative density function (CDF) of SINR. This approach evaluates the network in terms of system-centric quantities like throughput and outage probability, and mainly depends on three factors: 1) spatial distribution of the interfering nodes (network geometry); 2) the propagation characteristics of the medium such as path loss, shadowing and fading, which determine the strength of the interfering signals, and 3) transmission characteristics of the interferers such as power and synchronization including scheduling and media access control schemes. The spatial location of the network nodes 1 can be modeled deterministically or stochastically. The deterministic approach is applicable when the locations of transmitters are known and constrained by a regular structure. Fig. 1.1 shows the traditional model of a cellular network based on deterministic base station locations and a hexagonal grid for their positions. Each base station is located at the center of the cell, and the users connect to the strongest base station, i.e., the only base station in the cell they are located in. In the grid model, the frequency reuse is determined by the reuse distance, the reuse factor and the reuse pattern. A powerful tool in assigning channels to these networks considering a certain reuse factor is graph multicoloring, e.g., refer to [10]. Besides being too idealized for HetNets, the grid-based model s analytical complexity is itself an issue and, hence, is mainly used for system-level simulations, e.g, [11]. 1.1 Heterogeneous Networks In this thesis, we consider a HetNet where a large number of APs arerandomlydeployedin a non-deterministic irregular manner[12]. On the one hand,it is impossible to completely 1 In this thesis, nodes represent APs or users.

12 Chapter 1. Introduction 3 Figure 1.1: The hexagonal grid model for cellular networks. The desired and the interfering signals at the user are represented by solid and dashed lines respectively. separate concurrent transmissions in frequency; hence, interference is considered as the main factor that limits the capabilities of such networks. On the other hand, characterizing the received and interfering signals is further complicated in HetNets due to random locations of APs. As a result, we use techniques from stochastic geometry to model and analyze the user performance in such networks. Stochastic geometry and point processes [13] have been used to derive the expressions for the connection distance, total interference and outage probability [14]. A point process is a collection of points in space the location of which are random variables. Itiscalledsimpleif two points are at the same location with zero probability. A point process is stationary if the law and relationships between the points do not change by translation. One popular 2-D spatial model is the homogeneous Poisson point process (PPP) characterized by only one parameter, λ, whichisconstantacrossa2-dspace. Thismodelisstationary and simple. In a homogeneous PPP, the number of points in area A is a Poisson random variable with mean λa; thenumber of points in disjoint regions are independent random variables, and their locations are mutually

13 Chapter 1. Introduction 4 Figure 1.2: The PPP model for a single-tier HetNet. The red squares represent APs. The blue lines, called the Voronoi diagram, represent the coverage area of each AP. independent. Fig. 1.2 shows an example of a single tier of a HetNet where the AP locations are modeled by a PPP. The popularity of the PPP model arises from the fact that it makes the analysis of large (infinite) networks with random located nodes tractable. The accuracy of this model for a two-tier cellular network was examined by Dhillon et al. [15]. Inthiswork,thedistributionof the SINR is derived at a reference user randomly located in the network. Theuserisconsidered to be in coverage if its received SINR is higher than the pre-specified threshold from at least one AP. It was shown that the probability of coverage in a real-world 4G network lies between that predicted by the PPP model (pessimistic lower bound) and thatbytheregularhexagonal grid model (optimistic upper bound) with the same AP density. Similarresultswerereported comparing the coverage predictions by the PPP and the square grid model [9]. Furthermore, the PPP model provides a tighter bound at cell edges where the probability of having a dominant interferer is closer to that found in an actual 4G network [9]. These initial results suggest that the PPP model can be a reasonably accurate model, while being tractable, in design and

14 Chapter 1. Introduction 5 analysis of HetNets. To account for different characteristics of groups of APs, e.g., macrocells, picocells, femtocells, etc., they are categorized into tiers - in general K tiers. Each tier, indexed by k, is modeled by an independent PPP, and differs in the AP transmit power P k,theapdensity λ k and the path loss exponent α k. It is assumed that all the APs in each tier have the same transmit power. The macro-cellular network would be one tier inahetnetwiththehighest transmit power and the lowest AP density; a network of small cells, on the other hand, is characterized by a much lower AP transmit power and higher AP density. We assume that the user is associated with (and serviced by) only one AP in the network at a time. As opposed to acelledgeoraninterioruser,theperformanceinthisnetwork is evaluated at a typical user. If the AP locations are modeled by a homogeneous PPP, the distance between the user (reference point of interest) and the closest point of the PPP in tier k is a random variable. If the user associated with tier k connects to the strongest (consequently, the closest) AP of the tier, the same region becomes a Voronoi tessellation an example of which is shown in Fig As opposed to the grid-based model, the distance between any two APs in the PPP model is a random variable; so are the APs coverage areas even in the sametier. Thesetofinterfering APs include either all the APs in the network or the APs in the serving tier other than the serving AP. The former applies when the spectrum is shared by all the network. In the latter, each tier is allocated an orthogonal spectrum of operation. The frequency reuse is mainly carried out through scaling the density of the interfering APs. If each AP of tier k randomly chooses 1/δ k (δ k 1) of the available bandwidth, then the set of APs in tier k transmitting on the same channel forms a new PPP with density λ k /δ k [9]. Hence, the level of interference can be controlled by thinning the interfering AP density through δ k. Adding the uncertainty due to the fading on both the desired and the interfering signals will result in an expression for the CDF of the SINR at the user [9]. It can then be used to derive the average performance of the network.

15 Chapter 1. Introduction Design Challenges There are two major challenges in HetNets: 1) cell selection, and2)resourceallocationgiven the structure of the network and the radio resources. Cell selection, hence, the coverage area of an AP highly affects the load of an AP and, therefore, should be supportedbytherequired radio sources. The statistical distribution of the coverage areaofanapinatierdependsonthe received power from the AP which, in turn, is affected by the network structure, i.e., tiers AP density, transmit power and propagation characteristics. It also can be controlled by adding a non-negative number in db, called the bias factor, to the received power from APs of a tier to favour connection to that tier. The user then connects to the tier with the maximum biased received power. In HetNet literature, this is called cell extension. Cell selection at the macroscopic level translates to tier association and tier association metric, and is mainly controlled by the tier s bias factor. Since the APs in different tiers have different transmit powers, cell extension affects the amount of load imposed on the APs of that tier, and should be supported by the available resources. Resource allocation in a multi-tier network at the macroscopic level translates to spectrum allocation across tiers in case of tiers orthogonality, or determining the effective reuse (or fractional reuse) factor in each tier in case the tiers are sharing the total available bandwidth. Hence, the joint problem of tier association and resource allocation is of great interest for offloading across tiers to be effective. These two challenges should also be considered while supporting user mobility and handoffs. In vast majority of works, the performance metric is evaluated at a stationary (but randomly located) user. With the anticipated increase in the number of applicationsavailable toahand- held device, e.g., voice, data, real-time multimedia, etc. [16,17], mobility management will play an important role in providing seamless service to the mobile usersmovingfromoneapto the other. Client-server applications such as , web browsing, etc., are amenable to shortlived connections and do not require sophisticated mobility solutions.mediastreams,however, can function normally only with a maximum interruption of 50msec; while an interruption of up to 200msec is still acceptable, any longer interruption causes perceptible and unacceptable delays [18]. Therefore, on the one hand, it is desirable to minimize handoffs between APs to avoid any excessive connection delay and call drops; on the other hand, handoffs complicate the

16 Chapter 1. Introduction 7 resource allocation problem. Therefore, in the move towards multi-tierheterogeneousnetworks, the issues of cell association and handoffs must be addressed in an effective manner. 1.3 Thesis Contributions and Organization Throughout the thesis, we use the maximum biased average received power as the connection metric. Therefore, a user is associated with and serviced by one AP of only one tier at a time. The mathematical analysis of a multi-tier HetNet in the downlink is presented in Chapter 2 and Chapter 3, whereas Chapter 4 presents a resource allocation algorithm within a single tier of a HetNet. We analyze the downlink of a multi-tier network from two different points of view: when a user is i) mobile (Chapter 2) and ii) stationary (Chapter 3). For both analyses, we use PPPs to model AP locations in the HetNet. The main difference between the two is that in Chapter 2, the focus is on handoff and coverage analysis for a mobile user in a multi-tier network with the received SIR as the coverage metric. Each tier is characterized by an SIR threshold and the user is considered to be in coverage if its downlink SIR is higher than the pre-specified SIR threshold of the serving tier. The focus in Chapter 3 is on load distribution across tiers in a multi-tier network where each tier is characterized by a data rate threshold. For a user connected to a tier, this threshold becomes the user s target data rate and is used as the coverage metric. The user is then considered to be in coverage (referred to as data rate coverage) if its achieved data rate from the serving tier is higher than the target data rate. The mathematical expressions derived for SIR or data rate coverage is the complementary CDF of the received SIR or data rate experienced by the reference user located at the origin. Finally, in all the analyses provided in this thesis, we assume an open-access network, where in serving the reference user, there is no restriction or constraint on the serving tier or AP other than the biased average received power in the downlink. Eachtopic,listedbelow,isthe whole or part of a chapter. Given the variety of issues being considered, we include a relevant literature review in each chapter. Handoff rate. In a dense network of APs, the capacity increase is due to the smaller connection distance between the user and the serving AP despite the simultaneous increase in

17 Chapter 1. Introduction 8 the level of interference. It has been shown in [9] that in a single-tier network where each user connects to the closest AP, and AP locations are modeled by a PPP, the level of change in the desired and the interfering signals is on the same order. In other words, the statistical distribution of SIR does not change with AP density or transmit power; hence, the overall capacity increases linearly with the AP density. Increasing the density of APs, however, increases the handoff rate and might negatively affect the quality-of-user (QoS) at the user. We analyze the impact of user mobility in a multi-tier HetNet where APs are distributed according to independent homogeneous PPPs. In an irregular network, where the user connects to the strongest AP, we define handoff as the event where the initial serving AP does not remain the strongest AP as the user moves and hence, a handoff occurs. We derive the handoff rate as the probability of this event. In a multi-tier network with cell extension, if handoffs across tiers are allowed, a handoff occurs if, as the user moves, the serving APdoesnotremaintheonewith the strongest biased average received power. The handoff rate inasingletierispresentedin Chapter 2, with the probability of handoff across tiers presented in the appendix for reference. Mobility-aware tier association. To capture potential connection failures due to mobility, we propose a linear cost model assuming that a fraction of handoffs result in such failures. The rationale is that even if the user might be in coverage both beforeandafteritmoves,its received service is degraded due to the handoff. Since the probability of handoff, as defined above, is a function of the AP density, the serving tier is crucial. Here, we allow only for handoffs within a tier and focus on tier association to minimize the negative effects of such handoffs. Considering a multi-tier network with orthogonal spectrum allocation across tiers and the maximum biased average received power as the tier association metric, we derive the probability of coverage for two cases: 1) the user is stationary (i.e., handoffs do not occur, or the system is not sensitive to handoffs); 2) the user is mobile, and the system is sensitive to handoffs. Optimizing the bias factor for maximum coverage in both cases, we show that when the user is mobile, and the network is sensitive to handoffs, both the optimum tier association and the probability of coverage depend on the user s speed; a speed-dependent bias factor can then adjust the tier association to effectively improve the coverage, and hence system performance in a fully-loaded network. This work is presented in Chapter 2. It is worth emphasizing that

18 Chapter 1. Introduction 9 there may be other definitions of handoffs. Our analysis technique would be applicable if the handoff rate could be related to tier density and the association bias factor. Load distribution in the network. An important characteristic of a multi-tier HetNet is its flexibility in tier association, hence, load distribution across tiers. A measure of how load is distributed in the network is the average number of users per AP in each tier which is linearly proportional to the tier s association probability. Another measure to capture the load distribution across the network is the CDF of the spectrum required by a typical AP in each tier. In a network with AP locations modeled by PPPs, the coverage area of an AP is acontinuousrandomvariable;soistheuser sreceivedsinr,hence,itsloadimposedonthe serving AP to achieve its data rate demand. To characterize it, we derive the CDF and the moment generating function (MGF) of the user s load considering fading on both the desired and the interfering signals. Modeling user locations by another independent PPP, we derive the MGF of the AP load in a multi-tier network. Defining the AP outage rate as the probability of the event that the AP s load exceeds its allocated bandwidth, this metric can then be used to derive the minimum required spectrum in the network. This work is presented in the first part of Chapter 3. Tier association and spectrum partitioning across tiers. The dual problem of minimizing the required spectrum is to maximize the user s QoS given the available bandwidth. Constrained on each user being serviced by only one AP at a time, this, in general, is an NP hard problem stating which user should be associated with which AP (among all tiers) and how much of the available radio resources should be allocated to it. To reach an optimal solution, acentralcoordinatorrequiresperfectknowledgeofthechannel gains from all the APs to all the users. Furthermore, this information must be updated regularly. We break down this problem as follows: i) tier association and spectrum partitioning across tiers; ii) resource allocation across the APs and the users within each tier. We first consider the problem of tier association and spectrumpartitioningacrosstiers. For analytical tractability, we assume every AP serves an equal number of users determined by the AP and user density and the tier association probability. Each user is associated with the tier offering the maximum biased average received power. It, however, is considered to be in coverage only if it receives the data rate threshold set by the tier. We then formulate an

19 Chapter 1. Introduction 10 optimization problem with the objective of maximizing the user s rate coverage constrained by the available bandwidth. We assume an orthogonal spectrum allocation across tiers. For each tier, its association probability and its ratio of the allocated spectrum are the optimization variables. The tier s allocated bandwidth is available to all the APs of the tier with reuse- 1. We show that, equating the two fractions for each tier (i.e., equating the tier s association probability with its allocated share of the total spectrum) essentially results in zero performance loss and can be used for spectrum allocation and load distribution across tiers. This work is presented in the second part of Chapter 3. Resource allocation within a tier. In Chapter 3, we derive the fraction of the total bandwidth to be allocated to a tier assuming a biased average number of users per AP. Furthermore, all the APs within a tier share the spectrum available to the tier with no interference management scheme. Due to random (and unequal) distribution of the load across the tier, each AP supports not a constant but a random number of users; this might result in overloaded APs. Given the total spectrum available to a tier, we consider the problem of resourceallocationacrosstheaps within a tier and propose a hierarchical low-complexity resource allocation algorithm. In the proposed algorithm, each user is serviced by one AP at a time. To avoid rapid changes in the serving AP, each user connects to the AP offering the strongest received power, i.e., the closest AP to the user. Each user has a specific data rate demand, which imposes a specific load on its serving AP. The objective of the algorithm is to maximize the sum of the achieved data rate across all users in the tier normalized by their data rate demand. To tackle the complexity involved, our proposed algorithm has four steps, three of which are carried out at the APs with only the spectrum allocation across the APs carried out at a central co-ordinator. The algorithm is considered dynamic in the sense that each AP requests a share of the bandwidth available to the tier depending on its load. Hence, as the users move from one AP to another, so would the allocated spectrum. Another advantage of the proposed algorithm is its low complexity due to its hierarchy. This work along with the complexity analysis of the algorithm is presented in Chapter 4. The dissertation concludes in Chapter 5. We summarize the key resultsandproposeextensions to the analyses and the algorithm presented in this thesis to further improve their

20 Chapter 1. Introduction 11 applicability in modeling and design of real networks.

21 Chapter 2 Handoff Rate and Coverage Analysis The objective of this chapter is to derive the handoff rate for amobileuserinanirregular cellular network as a function of system parameters and the user speed. Our goal is to analyze the impact of mobility, and to use this analysis in deriving effective tier association rules and, hence, load distribution in a multi-tier network to minimize this(negative)impact. 2.1 Related Work and Motivation In the context of cellular networks, there is a large body of literature studying the delays caused due to handoffs [18 20], protocols and effective handoff algorithms [21 24], and multi-tier system design with microcells overlayed by macrocells [7,25]. If there are enough resources, the classic handoff algorithms in a multi-tier network assign users to the lowesttier(e.g.,themicrocells) thereby increasing system capacity [22]. To account for mobility, based on an estimated sojourn time compared to a threshold, the user is classified as slow or fast, and is assigned to the lower or the upper tier respectively [26, 27] (these works assume a two-tier network). The estimated sojourn time depends on the cell dimensions as well as user information such as the point of entry and user trajectory [28]. Similarly, velocity adaptive algorithms use the mobility vector, including both the estimated velocity and the direction, to perform the handoff [21]. To avoid the ping-pong effect due to unnecessary inter-tier handoffs, once the user is classified as fast, it remains connected to the upper tier regardless of any changes in its speed [29]. Another alternative is to introduce a dwell-time threshold to take into account the history of the user 12

22 Chapter 2. Handoff Rate and Coverage Analysis 13 before any handoff decision [22]. This technique is based on speed estimation at each cell border. Whether the handoff is performed solely by the network controller [30], or autonomous decisions by the user equipment are taken into account [31], it is desirable to reduce the signalling overhead due to unnecessary or frequent handoffs between the tiers or among the APs within one tier. The proposed algorithms mentioned above are mainlyapplicableinlargecells. Importantly, the handoff rate, sojourn time or dwell time analysis provided in the literature consider deterministic AP locations and a regular grid for the positions of the base stations. With the increasing deployment of multi-tier networks, especially small cells in an irregular, non-deterministic manner [12], handoff analyses for HetNets mustnowtakeintoaccountthe randomness of the AP locations by using random spatial models [32],themostcommonof which is Poisson point processes. The first work that applied a mobility model in the context of a PPP network was by Lin et al. [33]. The authors proposed a modified random waypoint (RWP) model 1 in a single-tier irregular network, and derived an analytical expression forthehandoffrateandsojourntime. This work defines handoff rate as the ratio of the average number ofcellsamobileusertraverses to the average transition time (including the pause time) and showsthatthehandoverrateis proportional to the square root of the AP density. The sojourn timeistheamountoftimea user spends in a cell. Their analysis predicts a slightly higher handover rate and lower sojourn time (overall, a pessimistic prediction) compared to an actual 4G network. The handover rate and sojourn time predictions in this work, along with the coverage predictions in [9, 15], imply that the PPP model provides a slightly pessimistic but sufficiently accurate analysis while being analytically tractable. A similar relation between the handoff rate and AP density was reported in [35] in a multi-tier network. The authors in [35], however, showalinearrelationbetween the handoff rate and the user velocity. Attracted by its applicability and tractability, we use the PPP model for handoff analysis in an irregular multi-tier network. Similar to [33], we consider the handoff rate during one movement period. However, differing from both works [33] and [35], we use a different mobility 1 The RWP model [34] is one of the most commonly used mobility models for evaluating the performance of a protocol in ad hoc networks. In this model, each node picks a random destination uniformlydistributedwithin an underlying physical space, and travels with a speed uniformly chosen from an interval. Upon reaching the destination, the process repeats itself (possibly after a random pause time).

23 Chapter 2. Handoff Rate and Coverage Analysis 14 model (as opposed to e.g., the modified RWP), and a different definition for handoff rate to include the connection metric and incorporate mobility in coverage analysis [36]. 2.2 Contributions Handoff rate. We define handoff as the event that the user associated with onecell crosses over to the next cell in one movement period. We refer to the probability of this event as the handoff rate. It can also be interpreted as the probability that the serving AP does not remain the best candidate in one movement period. Using this definition, we derive the handoff rate in a network where AP locations are modeled by a homogeneous PPP. Based on some mild approximations, we simplify this expression; our numerical simulations show that our theoretical expression provides reliable results over abroadrangeofsystemparameters. We note that other handoff metrics may be used, such as a handoff being initialized only if the received signal power falls below a threshold. However, these schemes seem better suited for the traditional cellular network and not our reuse-1 HetNet. Probability of coverage with handoffs. In order to derive the probability of coverage in a network for mobile users, we assume that a certain fraction of handoffs result in connection failure; in other words, the outage probability is linearly related to the handoff rate derived earlier through a cost factor. We use the biased average received power as the connection metric, and a pre-specified SIR threshold in an interference-limited network to define coverage at a reference user. We, then, derive the probability that a mobile user, initially in coverage, remains so despite its motion. This approach provides a tractable model to analyze the impact of mobility; specifically, we do not attempt to derive a joint coverage probability distribution across the locations of a specific mobile user. The cost function mainly characterizes the cost of handoff for a mobile user, even if the user is considered in coverage from the SIR point of view. Mobility-aware tier association. Weextendtheseresultstoderivecoverageforamobile user in a multi-tier irregular network considering handoffs. We assume orthogonal spectrum allocation among tiers; however, the results can be easily extended to include spectrum sharing across tiers [37]. The expression for the probability of coverage with mobility is not in closed

24 Chapter 2. Handoff Rate and Coverage Analysis 15 form but is readily computable involving an integral. Using this expression, the overall network coverage can be improved by adjusting the tier association through the correspondingbias factor in a mobility-aware manner, hence, improving system performance in a fully-loaded network. Key results. Itwasshownin [9], thatthecapacityofanetworkincreaseslinearly with the number of the APs if the average received power is used as the connection metric, and that the path loss exponent is the same for all tiers. This, however, is not true for a mobile user if ahandoffoccurswhenevertheusercrossesthecellboundaries. Hence, the fast moving users should be offloaded to upper tiers to avoid frequent handoffs. This supports the belief that the lower tiers are to provide the main portion of the network capacity (serving slow-moving users) whereas the upper tiers provide (SIR) large-scale coverage. Anotherinterestingobservationwas made from the probability of coverage in a single tier as a function of the tier s SIR threshold. Our results show that the degradation in service (mentioned above) - even for a fast moving user in a network where most handoffs result in outage - decreases with the increase in the SIR threshold. 2.3 System Model We consider the downlink of a heterogeneous network comprising K tiers of APs where each tier models the base stations of a particular group, such as those of macrocells, picocells, femotcells, etc. Each tier, indexed by k, is defined by the tier s base station transmit power. In other words, an AP belongs to tier k, ifitstransmitpowerisp k. The tier is characterized as a homogeneous Poisson point process Φ k with a tuple {P k,λ k,τ k } denoting the transmit power, the AP density and the SIR threshold respectively. The tiers are organized in increasing order of density i.e., λ 1 λ 2 λ K.Furthermore,Φ 1 and Φ K,respectively,denotethehighestand the lowest tiers with the highest and the lowest transmit power respectively. Given the density λ k,thenumberofapsbelongingtotierk in area A is a Poisson random variable, with mean Aλ k,whichisindependentofothertiers. Needlesstosay,alltheAPsintierk have the same transmit power P k.notethatwhilewehavemodeledeachtierofahetnetbyanindependent PPP, the model is more accurate for tiers with large density of APswithrandomlocations;in other words, this model better suits small cells than macrocells.

25 Chapter 2. Handoff Rate and Coverage Analysis 16 We use the maximum biased average received power as the tier association metric where the received power from all the APs of different tiers are multiplied by the corresponding bias factor B k,andtheuserisassociatedwiththetierwiththelargestproduct. Let r j denote the distance between a typical user and the nearest AP in the jth tier. In this setup, the user connects to tier k if: k =argmaxp j L 0 (r j /r 0 ) α B j, (2.1) j {1,,K} where B j is the bias factor associated with tier j, L 0 is the path loss at reference distance r 0. α is the path loss exponent for all tiers. We use r 0 =1andL 0 =(4π/ɛ) 2 where ɛ denotes the wavelength at 2GHz. Since all the APs in each tier have the same transmit power and bias factor, the best candidate from each tier is the AP closest to the user. Without loss of generality, we set B 1 =1. Ifallthetiershavethesamebiasfactor(orsimply,B j =1, j), the tier association metric is the maximum received power, hence, maximum SIR criterion. Here, we refer to it as max-sir. Compared to using max-sir, when B j > 1, it results in an increased coverage area, hence, a larger number of users connecting to tier j. We use the notation introduced in [37] where P j = P j P k, B j = B j B k, λ j = λ j λ k power, bias factor and AP density with respect to tier k. denoting tier j s relative transmit In our model, the channel between APs and users suffers from path loss,withpath-loss exponent α, and small-scale Rayleigh fading with unit average power. Since networks such as those under consideration here are interference-limited, we ignore thermal noise. Also, for tractability, we ignore shadowing. Log-normal shadowing can be accounted for in tier association by adjusting the tier s AP density [38]. We use the received SIR as the coverage metric. More precisely, a mobile user connected to tier k is considered to be in coverage if its downlink SIR with respect to the serving AP from that tier is greater of the serving tier s SIR threshold, τ k.anytierassociationotherthanmax-sirresultsinahigherlevel of interference. Due to this increase in the level of interference, it has been shown, e.g., in [39], that orthogonal spectrum allocation or partial fractional reuse across tiers can increase the total (sum over all users) utility, and reduce the outage area in a multi-tier network. Hence, In the coverage analysis, we assume orthogonal spectrum allocation across tiers and a reuse factor of one within each tier. Therefore, at a typical user connected to tier k, thesetofinterferingapsincludeallthe

26 Chapter 2. Handoff Rate and Coverage Analysis 17 APs in tier k except the serving AP 2.Theexpressionsderivedinthischaptercanbegeneralized to allow for spectrum sharing across tiers [37], and any arbitrary fading distribution for the interfering signals [9]. Within the serving tier, the user connects to the nearest AP in thattier. Iftheuseris initially in coverage, when it moves, it might fall into the coverage area of another AP at a shorter distance, and a handoff occurs. Although the user might be in coverage at both locations, rapid changes in the serving AP increases the possibility of connection failure. Fig. 2.1 shows the scenario under consideration. l 1 is the user s initial location at connection distance r from the serving AP denoted by AP s. The user moves a distance v in a unit of time, at angle θ with respect to the direction of the connection, to a new location l 2 at distance R from AP s. This model is most suitable for a scenario where the user moves ataconstantspeedorithas small variations such that it can be approximated by its mean. Whether the handoff occurs (Fig. 2.1(a)) or not (Fig. 2.1(b)) depends on the existence of anotherapinthecirclewiththe user at the center and radius R. 2.4 Handoff Rate in a Single-Tier Network In Fig. 2.1, C denotes the circle with its center at l 1 and radius r; A denotes the circle with its center at l 2 and radius R. The two circles intersect in at least one point which is AP s. The excess area swiped by the user moving from l 1 to l 2 is denoted by A\A C.Forthemostpart, we assume that the user can move in any direction with equal probability. We will show later that due to symmetry, the probability of handoff for the user moving at angle (2π θ) isthe same as that for the user moving at angle θ with the direction of the connection. Denoting the corresponding random variable as Θ, the probability distribution function (PDF) of Θ is then set to be non-zero in [0,π); here, we assume a uniform distribution given by f Θ (θ) =1/π. Let H k denote the event that a handoff occurs for a user connected to tier k. Throughout this chapter, we denote the complementary event that a handoff doesnotoccurfortheuser connected to tier k as H k. Furthermore, let random variable R k denote the distance between the user and the closest AP in tier k. Modeling AP locations by a homogeneous PPP with 2 AreusefactorofgreaterthanonecanbeaccountedforbyusingareducedAPdensityincalculatingthe interference [9], but will not change the handoff rate.