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Scheduling and power allocation for interference mitigation in heterogeneous cellular networks Pradhan, Shristi Nhuchhe 2014

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Scheduling and Power Allocation forInterference Mitigation inHeterogeneous Cellular NetworksbyShristi Nhuchhe PradhanB.Eng., Tribhuvan University, Institute of Engineering, Pulchowk, Nepal, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)February 2014c? Shristi Nhuchhe Pradhan 2014AbstractThe wireless industry is confronted with an exponentially increasing demandfor ubiquitous wireless coverage and larger data rates. Recent studies haveshown that the spectral efficiency of a point-to-point link in cellular net-works has approached its theoretical limit. This demands an increase in thenode density in order to further improve the network capacity. However, to-day?s network already has dense deployments and high intercell interferenceseverely limits the cell splitting gains. Moreover, high capital and opera-tional expenditure associated further limit the deployment of high powermacro nodes.In this thesis, we investigate on Heterogeneous Networks (HetNets), anew paradigm for increasing cellular capacity and coverage to meet the fore-casted explosion of data traffic. HetNets consist of low power nodes suchas pico and femto overlaid over a macrocell network. Nevertheless, the de-ployment of large number of small cells overlaying macrocells presents newtechnical challenges. We focus on interference management issues in HetNetsand present user scheduling and power allocation schemes for interferencemitigation.We investigate the performance of user scheduling and power allocationtechniques for interference mitigation in HetNets. We present analyticaliiAbstractmodeling and propose improved solutions using results from the model andcomputer simulations. First, we propose a scheme to jointly minimize net-work outage probability and power consumption. Second, we propose ascheme to jointly maximize network throughput and minimize power con-sumption. Both these schemes guarantee Quality of Service (QoS) pro-visioning in HetNets. We analyze the intrinsic trade-off between networkperformance parameters, i.e., outage and power consumption; throughputand power consumption using multi-objective optimization approach. Dif-ferent user scheduling schemes have been adopted such as best user selection,proportional fairness and round-robin. Thirdly, we also propose an energyefficient power allocation method and analyze its performance with guar-anteed QoS provisioning. For all the proposed algorithms and schemes weprovide extensive simulation based results.iiiPrefaceI hereby declare that I am the primary researcher and author of this thesisas well as the related paper published [1]. I performed the majority ofwork including but not limited to conducting literature review, identifyingthe research problems, and conducting research to address these issues. Iwrote computer programs and performed simulations in order to investigatethe performance of the proposed methods. I prepared the related researchmanuscript for publication.The published conference paper that has been resulted from the researchconducted in this thesis is given below with corresponding chapters as indi-cated.? S.N. Pradhan, R. Devarajan, S.C. Jha, and V.K. Bhargava, ?Up-link power allocation schemes for heterogeneous cellular networks,? inProc. National Conference on Communications (NCC?13), Feb. 2013,pp. 1-5 (appears in Chapter 3 and Chapter 4).Rajiv Devarajan is a co-author for the contributions in Chapter 3 andChapter 4. I consulted him during formulation of optimization problemsand computer simulations.Dr. Satish C. Jha is a co-author for the contributions in Chapter 3 andivPrefaceChapter 4. I consulted him during identification of research problem.My supervisor, Professor Vijay K. Bhargava is a co-author for the con-tributions made in Chapter 3 and Chapter 4. I consulted him during iden-tification and formulation of research problems. He also provided valuablefeedback for the manuscript and this thesis.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Objectives and Motivations . . . . . . . . . . . . . . . . . . . 11.2 Technical Issues . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Research Contributions . . . . . . . . . . . . . . . . . . . . . 31.4 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . 5viTable of Contents2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Heterogeneous Networks . . . . . . . . . . . . . . . . . . . . 62.2 LTE-Advanced . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Technical Challenges . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Self-organization . . . . . . . . . . . . . . . . . . . . . 112.3.2 Backhauling . . . . . . . . . . . . . . . . . . . . . . . 122.3.3 Handover . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.4 Interference . . . . . . . . . . . . . . . . . . . . . . . 132.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Scheduling and Power Allocation Schemes . . . . . . . . . . 243.1 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 243.2 System and Channel Models . . . . . . . . . . . . . . . . . . 263.3 Joint Scheduling and Power Allocation in Multiuser per CellScenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Joint scheduling and minimizing of maximum allowedoutage probability and minimizing of total transmitpowers . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 Joint scheduling and maximizing of total throughputand minimizing of total transmit powers . . . . . . . 333.4 User Selection and Power Allocation in Each Time Slot . . . 353.4.1 User scheduling: Determining the set of users in eachtime slot . . . . . . . . . . . . . . . . . . . . . . . . . 35viiTable of Contents3.4.2 Power allocation to the selected set of users in a giventime slot . . . . . . . . . . . . . . . . . . . . . . . . . 413.5 Calculation of weights for multi-objective functions . . . . . 453.6 Scheme-3: Energy-efficient (Green) power allocation scheme 473.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . 504.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 514.2.1 Simulation analysis for Scheme-1 with user scheduling 514.2.2 Simulation analysis for Scheme-2 with user scheduling 644.3 Simulation Analysis for Scheme-3 Energy-Efficient (Green)Power Allocation Scheme . . . . . . . . . . . . . . . . . . . . 764.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Conclusions and Future Work . . . . . . . . . . . . . . . . . . 785.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Directions for Future Work . . . . . . . . . . . . . . . . . . . 79Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81AppendixA Proof of convexity of P4 . . . . . . . . . . . . . . . . . . . . . 89viiiList of Tables2.1 Specification of different nodes in HetNet . . . . . . . . . . . 84.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . 514.2 Jain?s fairness index for Scheme-1 (trade-off case) for differentscheduling policies . . . . . . . . . . . . . . . . . . . . . . . . 634.3 Jain?s fairness index for Scheme-2 (trade-off case) for differentscheduling policies . . . . . . . . . . . . . . . . . . . . . . . . 75ixList of Figures2.1 A typical heterogeneous network . . . . . . . . . . . . . . . . 72.2 Cross-tier interference scenarios in HetNets. a) Macro userjamming the UL of femtocell, b) femtocell jamming the DLof a macro user, c) macro user jamming the UL of a picocell,d) range-expanded picocell [2]. . . . . . . . . . . . . . . . . . 142.3 Illustration of ABSFs used for time-domain ICIC in Het-Nets. a) Macrocell and femtocell subframes without ICIC, b)macrocell and picocell subframes without ICIC, c) macrocelland femtocell subframes with ICIC, d) macrocell and picocellsubframes with ICIC [2]. . . . . . . . . . . . . . . . . . . . . . 183.1 HetNet system model with multiple mobile users per cellshowing an example of desired and interfering signals. . . . . 274.1 Scheme-1 using best user selection. ?min = 0.1 dB. Omax =0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Scheme-1 using proportional fairness selection. ?min = 0.1dB. Omax = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . 54xList of Figures4.3 Scheme-1 using round-robin selection. ?min = 0.1 dB. Omax= 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.4 Scheme-1: Outage minimization case (?1 = 1, ?2 = 0). ?min= 0.1 dB, 1 dB. Omax = 0.5. . . . . . . . . . . . . . . . . . . 584.5 Scheme-1: Power minimization case (?1 = 0, ?2 = 1). ?min= 0.1 dB, 1 dB. Omax = 0.5. . . . . . . . . . . . . . . . . . . 594.6 Scheme-1: Outage-Power trade-off case (?1, ?2 as in Section3.5). ?min = 0.1 dB. Omax = 0.5. . . . . . . . . . . . . . . . . 614.7 Scheme-1: Outage-Power trade-off case (?1, ?2 as in Section3.5). ?min = 1 dB. Omax = 0.5. . . . . . . . . . . . . . . . . . 624.8 Scheme-2 using best user selection. ?min = 6 dB. . . . . . . . 654.9 Scheme-2 using proportional fairness selection. ?min = 6 dB. 674.10 Scheme-2 using round-robin selection. ?min = 6 dB. . . . . . 694.11 Scheme-2: Throughput maximization case (?1 = 1, ?2 = 0).?min = 6 dB, 8 dB. . . . . . . . . . . . . . . . . . . . . . . . . 704.12 Scheme-2: Power minimization case (?1 = 0, ?2 = 1). ?min= 6 dB, 8 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.13 Scheme-2: Throughput-Power trade-off case (?1, ?2 as in Sec-tion 3.5). ?min = 6 dB. . . . . . . . . . . . . . . . . . . . . . 734.14 Scheme-2: Throughput-Power trade-off case (?1, ?2 as in Sec-tion 3.5). ?min = 8 dB. . . . . . . . . . . . . . . . . . . . . . 744.15 Variation of energy efficiency metric for different values ofmaximum UE transmit power and SINR threshold requirement. 76xiGlossary3GPP 3rd Generation Partnership ProjectABSF Almost blank subframesAWGN Additive white Gaussian noiseBER Bit error rateBS Base stationCSG Closed subscriber groupCSI Channel state informationDL DownlinkFBS Femto base stationFUE Femto user equipmentGP Geometric programHetNet Heterogeneous NetworkICIC Intercell interference coordinationLTE Long term evolutionMBS Macro base stationMUE Macro user equipmentOFDM Orthogonal frequency division multiplexingPL Path lossQoS Quality of servicexiiGlossaryRRH Remote radio headRSS Received signal strengthSON Self organizing networkSINR Signal to interference plus noise ratioUE User equipmentUL UplinkxiiiAcknowledgementsI extend my deepest thanks to my supervisor Professor Vijay K. Bhargavafor his continuous support, guidance and encouragement during my Master?sstudy and research.The work performed and documented in this thesis is supported by theNatural Sciences and Engineering Research Council (NSERC) of Canadaresearch grant. I am grateful to NSERC for their support.I am grateful to my past and present colleagues in the Information The-ory and Systems (ITS) laboratory at the University of British Columbia fortheir valuable support and feedback on my research. I would like to thankall other friends who have supported me during my Master?s study.Special thanks goes to my loving parents and family members for theirunconditional love, and support during this endeavour and in every otherphase of my life.xivTo My Parents . . .xvChapter 1Introduction1.1 Objectives and MotivationsWith unrelenting data traffic demand, wireless industry is confronted withincreasing demand for ubiquitous coverage and higher data rates [3]. Thishas urged wireless research communities to come up with better design ofcommunication networks. One of the promising concept is HeterogeneousNetworks (HetNets), which provide dual benefits of increased spatial reuseand higher link quality by bringing transmitter and receiver closer to eachother [4]. However, with great benefits, there are many challenges associatedwith the practical deployment of HetNets.This thesis investigates on the technical challenges for the implemen-tation of HetNets and focuses in combating one of the major challenges- interference mitigation. The proposed solution techniques comprise ofscheduling and power allocation for mobile users or user equipments (UEs)in the network.11.2. Technical Issues1.2 Technical IssuesHetNets recently have attracted significant research interest which involvesthe deployment of small base stations (small cells) overlaid over the macro-cell. It consists of mix of macrocells, remote radio heads, smaller and lowerpower nodes such as picocells, femtocells and relays. This increase in prox-imity between the base stations and end users has the potential to providethe next significant leap in communication networks, increase system capac-ity, enhance the indoor coverage, and boost spectral efficiency per unit area[5]. These small base stations require less or no upfront planning during de-ployment which drastically reduces the capital and operational expendituresof wireless networks [6].HetNets provide a significant paradigm shift promising excellent oppor-tunities for enhancements. However, this brings forward significant technicalchallenges and raise substantial issues for its practical implementation. Forinstance, rollouts of user deployed small cells overlying macrocells will leadto new cell boundaries. This will create substantial intercell and cross-tierinterference among the mobile users, degrading the overall performance ofthe communication network [7]. Also, within macrocells, which are oper-ator deployed cells, interference may be mitigated via frequency reuse. Inthese reuse schemes, subchannels used in a cell are prohibited in neighbour-ing cells, which lowers spatial reuse. HetNets target on universal frequencyreuse, where all the cells can use all the available resources depending ondifferent channel conditions and traffic load [2]. This nonetheless, increasesthe interference in the network.21.3. Research ContributionsPower allocation techniques are being heavily researched over for in-terference mitigation which involves controlling power transmission at thetransmitter and receiver [8],[9]. We present user selection and power controltechniques which also boosts throughput, lower outage and decrease powerconsumption in the network leading to overall performance improvement.1.3 Research ContributionsThe novel schemes and methods documented here provide promising solu-tions for the design of future HetNets. The main research contributions ofthis thesis are:? We present two problems for joint scheduling and power allocationin interference and noise limited fading macro and femtocell networks.These are formulated as multi-objective optimization problems in mixedinteger programming form. The first problem allows mobile user schedul-ing along with joint minimization of network outage probability andminimization of total power consumption. It accounts for the trade-off between outage and power consumption. The second problem al-lows mobile user scheduling along with joint maximization of networkthroughput and minimization of total power consumption of users.It accounts for the trade-off between network throughput and powerconsumption.? We investigate a two-step method to solve the optimization problems.It first involves user selection and then power allocation to the selected31.3. Research Contributionsuser in each cell on each time slot basis. Through simulation results,we show the effectiveness of the two-step algorithm by comparing itwith the exhaustive search method.? We propose methods such that users adapt their transmission accord-ing to the priority level of each objective function of the multi-objectiveoptimization problems in our schemes. It is based on changing param-eters such as users location and battery capacity. The priority level ofeach objective function is determined by the weights assigned a priorito the objective functions of our schemes.? Through simulation results, we analyze the trade-off between outageprobability and power consumption. We also study the trade-off be-tween network throughput and power consumption. Next, we com-pare the performance and user fairness using various scheduling poli-cies such as best user selection, proportional fairness and round-robin.We examine the effectiveness of the two-step method by comparingits performance with the results obtained from the exhaustive searchmethod.? We propose an energy efficient power allocation scheme to optimizethe green performance of the network. The scheme minimizes thetotal transmit power per unit system throughput with Quality of Ser-vice (QoS) guarantee. Using simulation results, we evaluate its perfor-mance for different values of maximum transmit power of mobile usersand QoS requirements.41.4. Outline of Thesis1.4 Outline of ThesisChapter 1 provides brief highlight of HetNets and its technical challengesbeing focused on the thesis. In Chapter 2, we investigate on HetNets, itsbenefits, implementation issues and research challenges. Chapter 3 explainsin detail the proposed scheduling and power allocation techniques. We pro-vide analysis of our proposed schemes through simulation results. Finally, inChapter 4, we present the major conclusions of the conducted research. Wealso present some potential future research directions in the related area.5Chapter 2BackgroundThe focus of this chapter is to explore design issues and technical challengesfor HetNets that motivated our research. We investigate on possible researchsolutions to overcome these challenges. We also provide a brief survey onrelated works available in literature.2.1 Heterogeneous NetworksCurrent cellular networks follow a macro-centric planned process and typ-ically deployed as homogeneous networks. The base stations (BS) are de-ployed in a planned manner, where they have similar transmit power levels,receiver noise floors, antenna patterns and backhaul connectivity to the datanetwork. All the macro BSs serve same number of mobile users and providethem unrestricted access in the network. Moreover, all the UEs have alikeQoS requirements and carry similar data flows [10].The macro BS settings are properly configured in order to accommodatethe traffic demand, maximize the coverage area and decrease interferencebetween signal transmissions in the network. However, with the outburst oftraffic demand, the network heavily depends on cell splitting and additionalcarriers to satisfy the capacity crunch and maintaining the QoS require-62.1. Heterogeneous Networksment of mobile users. In already dense deployments today, severe inter-cellinterference lead to drastic decrease in cell splitting gains. Moreover, inspace limited dense urban area, site acquisition cost for macro BSs can getforbiddingly high [11].As determined by the information theoretic capacity limits, current cel-lular systems have evolved to a point where a system with one BS achievesnear optimal performance. Researchers are now moving towards more ad-vanced heterogeneous network topology which will bring the network morecloser to the mobile user leading to further capacity gains [7]. HetNetswill significantly improve the spectral efficiency per unit area by utilizing adiverse set of BSs.Figure 2.1: A typical heterogeneous networkA heterogeneous cellular network is depicted in Fig. 2.1. It consists of72.1. Heterogeneous NetworksType of nodes Transmit power Coverage BackhaulMacrocell 46 dBm Few km S1 interfacePicocell 23-30 dBm <300 m X2 interfaceFemtocell <23 dBm <50 m Internet IPRelay 30 dBm 300 m WirelessRRH 46 dBm Few km FiberTable 2.1: Specification of different nodes in HetNet.small BSs like pico BS, femto BS, relays which transmit at low power levels(?250 mW - 2 W) and placed throughout macrocell, where BS transmitat substantially higher power level (?5 W - 40 W) [12]. In contrast tothe planned deployment of macro BSs, the low power BSs are placed inan unplanned or ad-hoc manner depending on the knowledge of networkcoverage requirements and traffic density. The low power nodes improvenetwork capacity in hotspots and eliminate the coverage holes in the macroonly cellular network. The low transmit power nodes are much lower incost than the macro nodes. Also, their relatively smaller physical size offerbenefit of flexible site acquisitions.A summary of specifications of different elements in HetNet is providedin Table 2.1 [2].? Macrocells comprise of network operator installed high power BSs,which emit up to 46 dBm and provide wide area coverage in the orderof kilometers. They are expected to provide QoS in terms of mini-mum data rate under constraints like outage and maximum tolerabledelay. Each macro BS has a dedicated backhaul and provide serviceto thousands of customers.82.1. Heterogeneous Networks? Picocells consist of lower power cellular tower, typically emitting at arange from 23 to 30 dBm and serving few tens of customers at rangeof 300 m or less. They are mostly installed in the areas where thereis insufficient macro penetration like office buildings. They have sameaccess features and dedicated backhaul as that in macrocells.? Femtocells consist of low power user deployed access points with trans-mit power of less than 23 dBm and covering less than 50 m. They arealso known as home BSs, which serve dozen of customers in home orenterprise buildings [6], [13]. They offload data traffic by leveragingthe user?s existing broadband connections such as digital subscriberline, cable or optical fiber which is connected to cellular operator?snetwork. Femto BSs work in open or closed subscriber group (CSG)access mode. It is speculated that they result in 70 % reductions intotal annual cost as compared to macro only network deployment [12].? Relays are access points generally deployed by the network operatorand route data to the customers from the macro BS and vice-versa.They have similar transmit power levels as picocells and coverage areaof 300 m. Relays are installed to increase signal strength and improvecoverage in poor reception areas and dead zones like tunnels and celledges. They can operate in transparent and non-transparent modesand require little or no incremental backhaul expense.? Remote Radio Head (RRH) are high power, compact, low weight unitsmounted outside the macro BSs and connected through a fiber opticcable. The central macro BS takes charge of the control and signal92.2. LTE-Advancedprocessing. RRHs reduces power consumption and eliminate powerlosses in antenna cable as some radio circuitry are moved to the re-mote antennas. It provides flexibility to the operators in deployingnetworks especially for those facing physical limitations or site acqui-sition problems.2.2 LTE-AdvancedAfter tremendous success of LTE (Long Term Evolution), researchers andindustry leaders have already started working towards the next level - LTEAdvanced to meet the ever increasing data demand. There are three majorenhancements incorporated by LTE Advanced [14]:1. Carrier aggregation that bonds multiple carriers together for increasingspectrum usage and data rates (bps).2. Advanced antenna techniques to enhance spectral efficiency (bps/Hz).3. HetNets in bringing out utmost benefit of small cells and increasingcapacity per coverage area (bps/Hz/km2).All the above mentioned enhancements play a significant role in improv-ing user experience but the most important component of LTE Advancedcome from optimizing HetNets. Densification of small cells provides pro-found increase in network capacity, but along with it generates huge amountof interference. LTE Advanced provide a interference management methodcalled Range Expansion [15], which is essentially a way to expand the reachof small cells so as to cover more and more user terminals. Range expansion102.3. Technical Challengesmakes sure that devices are connected to the small cells that can be servedbetter by the small cell rather than the macrocells. Also, more users can beoffloaded to the small cells from macrocells freeing up macro resources. Ina nutshell, LTE Advanced enhances overall network capacity with increasein the number small cells.2.3 Technical ChallengesHetNets provide excellent enhancement for next generation wireless net-works. However, with the benefits, it also introduce immense technical is-sues and raise substantial challenges for the wireless community as presentedin this section.The key technical challenges facing HetNets are identified as self-organization,backhauling, handover, and interference [2] as discussed below:2.3.1 Self-organizationSelf-organization is an important feature for HetNets since some cells likefemtocells will be deployed by the users without any assistance from thenetwork operator. It can be classified into three processes [16]:? Self-configuration: Before operating, the new cells to be deployed areconfigured automatically by the downloaded software.? Self-optimization: In order to improve the coverage and minimize in-terference, the cells continuously monitor the network status and keepoptimizing its setting.112.3. Technical Challenges? Self-healing: The cells during failure can automatically execute com-pensation process or perform failure recovery.Deploying a complete self-organizing HetNet is very challenging sinceuser arrival and their traffic load is vastly time-varying, random and uneven.2.3.2 BackhaulingThe complex network topology of HetNets exacerbate difficulties associatedwith the backhaul design. For example, picocells may require high backhaul-ing costs since it requires access to infrastructure with power supply andwired backhauling. On the contrary, femtocells have less expensive back-hauling costs since it depends on customer?s broadband connections, whichmay fail to guarantee the QoS. Therefore, operators should plan backhaulfor HetNets very carefully in order to identify the most optimized solutionin terms of cost effectiveness and maintaining QoS [17]. A better solutionmight comprise of mixture of both wired and wireless backhaul. For in-stance, some cells may have a dedicated interface to the core network, somemay count on relays to forward the traffic to the core and some cells mayform a cluster to accumulate and forward traffic to the core.2.3.3 HandoverHandovers provide seamless service without interruptions and form an in-tegral part of a communication system. Unsuccessful handovers lead to in-crease in user outage probability. It is important to provide uniform servicewhen mobile users move from one cell to another. Handovers are impor-122.3. Technical Challengestant as well for traffic load balancing, in which users at the edge of the cellare shifted from overcrowded cells to less crowded ones. Moreover, there ishuge number of signalling overhead associated due to handovers. And thisoverhead is even more significant in case of HetNets since it involves largenumber of small cells with different type of backhaul links for each cell type.2.3.4 InterferenceIn HetNets, the cross-tier and intra-tier interference problem presents a ma-jor challenge unlike the existing single-tier macro networks [18].? The cells need to have self-organizing capability, which would requirecontinuous sensing and monitoring of its surrounding environment. Itshould adapt itself dynamically in order to avoid or make interferenceless severe.? The backhaul network that connects the different type of cells to thecore network may have different bandwidth support and other con-straints. For example, in femtocells, only limited backhaul signallingis possible for interference coordination since the backhauls rely oncustomer?s broadband connection and not directly connected to thecore network.? Due to the restricted or CSG access control in some cells, mobile usersmay not handover to the cell at its closest proximity. This will lead tostrong interference in both uplink (UL) and downlink (DL) transmis-sion scenarios.132.3. Technical ChallengesInterference remain undoubtedly the major technical challenge in Het-Nets. Further, we discuss interference related issues and possible means forits mitigation.Sources of interferenceDeployment of small cells by the end users will create new cell boundaries.This will create strong intercell and intracell interference leading to degrada-tion of overall network performance. Interference in HetNets is remarkablychallenging due to the following [2]:Figure 2.2: Cross-tier interference scenarios in HetNets. a) Macro userjamming the UL of femtocell, b) femtocell jamming the DL of a macro user,c) macro user jamming the UL of a picocell, d) range-expanded picocell [2].1. Unplanned deployment: The end users deploy the low power accesspoints like femtocells in an ad hoc manner which demands a new de-142.3. Technical Challengescentralized interference avoidance scheme. Since, the operator will nolonger control the location of these cells, the scheme for HetNet shouldoperate independently using only local information.2. CSG access: When some cells work in CSG mode, non-subscribersare restricted to connect to the its nearest BS, which generates sig-nificant cross-tier interference. An interference scenario is shown inFig. 2.2a where some non-subscribers are found near houses hostingCSG femtocells. In Fig. 2.2a, a non-subscriber macro user transmitsat high power in UL to compensate for the path loss to its far serv-ing macrocell, which creates high interference and jams the UL of theclosest CSG femtocell. In Fig. 2.2b, the non-subscribed macro user isa victim in DL. Here, a femtocell working on CSG mode creates inter-ference with reception of the macro user while trying to get connectedto the far away macrocell.3. Power difference between nodes: In open access mode, all the users ofa network operator can access the cells. Usually, picocells and relaysoperate in open access mode. Open access avoids the CSG interfer-ence issue and minimizes the DL interference as the users always getconnected to the strongest cell. In HetNets, there is huge difference intransmission power between the macrocells and lower power cells likefemtocells. So, connecting users to the cell providing the strongest DLreceived signal strength (RSS) may not be a good strategy. Since theusers tend to get connected to the macrocells (due to higher trans-mission power) and not to the cell at the shortest path loss distance.152.3. Technical ChallengesThis will overload the macrocells and result in uneven traffic load dis-tribution. Moreover, users connected to the macrocells will severelyinterfere in the UL of the low power nodes. Fig. 2.2c shows how anend user connected to a macrocell (with best DL RSS) jams a nearbypicocell UL. However, if this MUE was connected to the picocell thenit would have transmitted with considerably less UL power due tolower path loss. This would benefit in terms of load balancing and ULinterference mitigation.4. Range expanded users: Due to transmission power difference of nodesin HetNets, it is important to have better cell selection methods whichallow user association with the cells that provide weaker DL pilotsignal. Range expansion is a solution to the problem (See Fig. 2.2d).In order to increase the DL coverage footprint, an offset is added tothe picocell?s or relay?s RSS. Range expansion significantly decreasesthe cross-tier interference in the UL, but this comes at the expenseof decreasing the DL signal strength to the users in the expandedregion. The users in the region may suffer from very low signal-to-interference plus noise ratio (SINR) since they are not connected tothe cells providing the best DL RSS.5. Co-channel deployment: The deployment of CSG cells exacerbates thechallenge on sharing physical resources, i.e., time and frequency withmacrocells to avoid coverage holes in the network. In co-channel de-ployment scenario, all the nodes are deployed in the same frequencylayer in order to avoid bandwidth segmentation [12]. In HetNets, co-162.3. Technical Challengeschannel deployment is attractive for numerous reasons. It is benefi-cial for any system bandwidth and does not need to depend on theavailability of wide spectrum. In addition, it does not need high costcarrier-aggregation capable UE and is suitable for low cost single car-rier low power BSs.Co-channel deployment among the low power cells and high powermacrocells presents severe interference problems especially in the caseof closed femtocells [19]. Also, in case of open access mode, the trans-mission of high-power nodes overshadow the coverage of the low powernodes. Therefore, efficient interference management techniques are re-quired to adapt to different number of low power cells and traffic loads.Intercell Interference Coordination (ICIC)HetNets demand coordination among the cells in order to manage the inter-cell interference which makes Intercell Interference Coordination (ICIC) in-dispensable for HetNet deployment [7]. A basic ICIC involves coordinationvia resource partitioning among the interfering cells. Interfering BSs cancoordinate among each other on transmission powers and/or spatial beamsin order to enable control and data transmissions to their mobile users [10].Resource partitioning can be grouped into three main categories as fol-lows:1. Time-domain techniques: In the time-domain method, transmissionof the victim users are scheduled in time-domain which mitigates theinterference from other nodes [20]. It is further classified into two172.3. Technical ChallengesFigure 2.3: Illustration of ABSFs used for time-domain ICIC in HetNets. a)Macrocell and femtocell subframes without ICIC, b) macrocell and picocellsubframes without ICIC, c) macrocell and femtocell subframes with ICIC,d) macrocell and picocell subframes with ICIC [2].categories are follows:? Subframe alignment: When the subframes of the macro nodeand femto node align, their control and data channels overlapwith each other. Therefore, control channel ICIC needs to beimplemented at the femtocells so as not to interfere with the con-trol channel of macro users. One approach to solve this is to usealmost blank subframes (ABSFs) at the femtocell. In ABSFs,182.3. Technical Challengesno control or data signals are transmitted. The macro users inthe vicinity of femtocells can be scheduled within the subframesoverlapping ABSF of femtocell. This significantly reduces thecross-tier interference. For example, macro users close to femto-cell can be scheduled in even subframes of macrocell illustratedin Fig. 2.3c. and range expanded pico users can be scheduled inthe even subframes of picocells illustrated in Fig. 2.3d.? OFDM symbol shift: In this method, to prevent overlap betweenthe control channels of femtocell and macrocell, the subframeboundary of the femto node is shifted by a number of orthogonalfrequency-division multiplexing (OFDM) symbols. The shift iswith respect to the subframe boundary of the macro node.2. Frequency-domain techniques: In frequency-domain ICIC, control andphysical channels of different cells are scheduled in reduced bandwidth[20]. This allows to have totally orthogonal signal transmission at dif-ferent cells. Frequency domain orthogonalization can be implementedin both static and dynamic manner (done using victim user detection).Macro node can determine the victim MUE by using the measurementreport of MUEs and the identity of the victim MUE may be signalledto the small node by the macro node through network backhaul. Also,small nodes may also sense the victim MUE.3. Power control techniques: Power control in HetNets has been heavilydiscussed for handling the intense interference between different nodes.For instance, the main reason for degradation for UL edge coverage is192.4. Related Workdue to interference aggregation from another layer?s UE. This causesthe received SINR to go below the minimum required. Now, the SINRof the edge UE can be enhanced by increasing the received signalpower or decreasing the interference from different layers. This can beaccomplished by adjusting the desired power received. This approachis iterative because the desired power in one level is affected by thevalue of different layer and various other factors. After some iterations,convergent result is obtained with acceptable uplink edge coverage [21].Various power control techniques can also be applied to femtocells.Reducing power at a femtocell also reduce total throughput of fem-tocell users. However, this power reduction at the femtocell causesignificant performance improvement of victim macro users. In a DLpower control approach, the received SINR of a femto user is restrictedto a target value and the transmit power at a femtocell is reduced toachieve this target SINR value. Another approach is to guarantee aminimum SINR at the macro users [2].2.4 Related WorkRecognizing the technical challenges, standard bodies and researchers haveinitiated several studies on interference management issues in HetNets. Ad-vanced methods of intercell interference management particulary for femto-cells has been a major focus for the standardization of 3GPP LTE Advanced[22].In the literature, prior works in HetNets have mostly dealt with single202.4. Related Workobjective optimization problem such as network rate maximization or powerminimization. There has been few investigations considering optimizationof multiple performance parameters. In [23] and [24], authors have consid-ered only the sum utility maximization problem. Author of [25] proposed adynamic power control algorithm for total power minimization in HetNetsin a Rayleigh fading environment. However, optimizing only one systemparameter alone may hinder the performance of other parameters. For in-stance, the effect of power minimization on network throughput and outageprobability should be considered. Therefore, it is important to study thetrade-off relation and find a balance between these system parameters.Only few researchers have addressed the system performance of HetNetsin terms of outage probability. In the literature, [26] and [27] and simi-lar works assumed perfect channel state information (CSI) and interferencemanagement algorithm was updated at fast fading time scale. However, withsuch an assumption the limitation is the requirement of very high computa-tional and signalling load, which is difficult to achieve in practice. We studythe performance of our system in terms of outage probability, where thepower updates for users are carried out on a much slower log-normal shad-owing time scale rather than fast Rayleigh fading time scale which saves oncomputational load [28]. We also exploit the trade-off relation between out-age probability and power consumption, which has not been explored muchin previous research.There has been some investigations on joint scheduling and power allo-cation for HetNets in the past. Authors in [29] analyze the upper bound ofmacro-femto hierarchical system capacity through joint power control and212.5. Summaryscheduling. They optimize the weighted sum capacity and design a localizedsub-optimal resource coordination architecture with reduced complexity. Adistributed algorithm was presented in [30] for power control and schedulingto minimize the total power consumption with QoS constraints. However,optimizing a system parameter comes at the cost of degradation of other sys-tem parameters. Therefore, it is crucial to achieve a balanced relationshipbetween the performance parameters while scheduling users in macro-femtonetworks.It is essential to design HetNets accounting to reduce transmit energyconsumption and enable energy efficient and green communications [31].[32] defines the energy efficiency as the ratio of area spectral efficiency andaverage network power consumption and proposes a method to maximizethe energy efficiency. It also investigates the trade-off associated with thedeployment of BS sleep mode strategies. We investigate energy efficiencyin terms of minimizing total mobile user transmit power per unit networkthroughput.2.5 SummaryThis chapter provided a brief introduction of HetNets along with the mainchallenges it faces for practical deployment. We argued that interferenceis the major technical challenge in HetNets and provided some examplesfor sources of interference. In literature, power control techniques havebeen largely discussed for handling the interference among the nodes inHetNets. In the following chapters, we investigate interference mitigation222.5. Summaryusing scheduling and power allocation techniques considering the trade-offbetween various network performance parameters which has not been ex-plored much in the previous research. We also explore a power allocationscheme to optimize the green performance of the network. Further, we studythe performance of our proposed schemes through extensive simulation re-sults.23Chapter 3Scheduling and PowerAllocation SchemesThe main focus of this chapter is to explore scheduling and power allocationschemes in an algorithmic and protocol design level of macro and femto-cell network. Some performance metrics that can provide a quantitativemeasure of the performance of these networks are also discussed. Novelscheduling and power allocation schemes are then introduced which over-come some of the limitation of the existing works. Since the improvement innetwork throughput and outage probability comes at the cost of increasednetwork power consumption, trade-off schemes between these performanceparameters are also analyzed using multi-objective optimization approach.3.1 Performance Metrics? Outage probability: The outage probability at the receiver is a stan-dard performance criterion of communication systems operating overfading channels. It is defined as the probability that the channel is un-able to support a given target combined SINR or instantaneous errorrate exceeds a specific value [33]. A link outage is declared when the243.1. Performance Metricsreceived SINR falls below a certain pre-specified threshold, which de-pends on acceptable bit error rate (BER), modulation/demodulationscheme, channel coding/decoding algorithm and detector structure. Itis considered as a good criterion in determining the coverage area offemtocells.? Network throughput: Throughput provides the average rate of suc-cessful data delivery over a communication channel. It is often inter-esting to know the expected performance of communication networksin terms of the throughput offered. It is an important QoS parameterto consider while designing wireless systems as it quantifies the datatransmitted in the network.We define throughput in terms of Shannon capacity formula asBlog2(1+SINR), where B is the bandwidth of the channel. Usually, it is mea-sured in bits per second (bits/s or bps). In our work, we considerthroughput normalized by bandwidth. Therefore, the unit of this met-ric is bits/s/Hz [34].? Power consumption: We consider the power consumed at the mobileusers end since we are dealing with uplink transmission. It is measuredin terms of dBm.? Energy efficiency: System performance per unit energy or power con-sumption is a major green metric at network level [34]. Power con-sumption per unit achieved system throughput (J/bit), power con-sumption per unit coverage area of a cell (W/m2), and fraction of253.2. System and Channel Modelstotal power saved by energy aware scheme are examples of green met-rics. We consider power consumption per unit system throughput(J/bit), which is expected as the basic energy efficiency metric forfourth generation cellular systems and beyond [35], [36]. Since, weare considering throughput normalized by bandwidth, the unit of thismetric is J/(bit/Hz).? Jain?s fairness index: It is important to determine whether the users inthe network are receiving a fair share of the available system resources[37]. It is defined asJ (x1, x2, ..., xn) =(?ni=1 xi)2n?ni=1 x2i, xi ? 0 (3.1)where n is the number of contending users, such that ith user receivesxi of the resources.3.2 System and Channel ModelsIn our work, we consider a network scenario having multiple mobile users ineach femtocell and macrocell. We consider the uplink of a system comprisingof a macrocell and L? 1 femtocells, i.e., total of L cells. Each cell has oneBS (receiver) and N number of UEs (transmitter) (See Fig. 3.1). Therefore,we refer to the femto transmitter as femto user equipment (FUE) and femtoreceiver as femto base station (FBS). Similarly, we refer macro transmitteras macro user equipment (MUE) and macro receiver as macro base station(MBS).263.2. System and Channel ModelsThe transmitted signal is assumed to suffer from path loss (PL), frequency-flat Rayleigh fading (conservative), interference due to co-channel transmis-sions. We consider Additive White Gaussian Noise (AWGN) at the receiver.We ignore the co-channel interference from neighbouring macrocells due toorthogonal channels. We represent the set of number of BSs (or cells) by Land set of number of users in ith cell by Ni respectively.Figure 3.1: HetNet system model with multiple mobile users per cell showingan example of desired and interfering signals.The time resource is divided into small intervals or slots. In each slot,one of the N UEs in each cell will compete for the uplink data channel.We introduce a binary variable sij(t), the user selection parameter whichdetermines whether the ith BS serves its jth UE or not at a given time slot273.2. System and Channel Modelst assij(t) =?????1 if the ith BS serves its jth UE in time slot t0 otherwiseTo simplify notations, we drop t from our expressions. However, it shouldbe noted that the variables till the end of Section 3.3 varies with each timeslot.The SINR at the ith MBS/FBS due to jth MUE/FUE is given bySINRij(s,p) =sijRijpij?Lk=1,k 6=i?Nj=1 skjRikjFikjpkj + ?ij, (3.2)where pij is the transmit power of jth UE in ith cell and pkj is the transmitpower of jth UE in kth cell. Here, in each time slot, the user selection vari-able is s , (sij)i?L,j?Ni where sij ? {0, 1} and the transmit power variableof FUEs and MUEs is p , (pij)i?L,j?Ni where pij ? R+. The numerator in(3.2) denotes the desired signal power at the BS in ith cell due to its jthUE. The denominator parameters denote the total interference from neigh-bouring cells, and noise power in the ith BS. Also, the non-negative matrixF has the following entriesFikj =?????Gikj/Gij if k 6= i0 if k = iGij is the non-negative path gain between jth UE and its BS in ithcell that is modeled as proportional to d??ij 10?ij/10, where dij is the distancebetween jth UE and BS in ith cell and ? is the PL exponent. Similarly,283.3. Joint Scheduling and Power Allocation in Multiuser per Cell ScenarioGikj is the non-negative path gain between jth UE in kth cell and BS inith cell. ?ij is a Gaussian distributed random variable with zero mean andstandard deviation of ? dB to account for log-normal shadowing between jthUE and ith BS [38]. The gain term in our analysis represents the distancedependent power attenuation. Also, we assume that the gain term does notchange much with time, i.e., the distance between transmitters and receiversdo not change, and the log normal shadowing is same. ?ij = vi/Gij wherevi is the noise power at the ith BS. In our analysis, we consider that bothdesired signals and interference signals undergo Rayleigh fading. Therefore,there is no direct line of sight signal component at the BS either from itsown UE or from neighbouring interfering UEs. Rij models Rayleigh fadingbetween jth UE and BS in ith cell, which are independent and exponentiallydistributed with unit mean. Similarly, Rikj models Rayleigh fading betweenjth UE in kth cell and ith BS.3.3 Joint Scheduling and Power Allocation inMultiuser per Cell ScenarioIn this section, we present the scheduling and power allocation problems formultiuser per cell scenario for the model discussed in Section 3.2. In orderto investigate the trade-off relation between various system parameters, weuse multi-objective optimization approach.293.3. Joint Scheduling and Power Allocation in Multiuser per Cell Scenario3.3.1 Joint scheduling and minimizing of maximum allowedoutage probability and minimizing of total transmitpowersIn our system, the outage probability at the ith BS when it serves its jthUE can be expressed in analytical form as [25]?ij(s,p) = Pr.(SINRij(s,p) < ?i)= 1? e??ij?i/pij?k?{L}\{i}(1 +N?j=1skj?iFikjpkj/pij)?1, (3.3)where ?i is the minimum SINR required at ith BS for reliable communica-tion.In such a scenario, instead of knowing the full CSI, it is enough to knowthe statistics of the channel which significantly decreases the system over-head. This allows power allocation on far longer time scale of log-normalshadowing instead of fast Rayleigh fading time scale which significantly re-duces the number of updates and computational load [28].Our objective here is to find the joint user selection and UE transmitpower variables that jointly minimizes the maximum allowed outage proba-bility and total power consumption. Power consumption and outage prob-ability are two conflicting objectives since decrease in outage probabilitygenerally comes at the cost of higher power consumption [39]. So, one orthe other objective is compromised. In order to have a trade-off balancebetween these two network parameters, we formulate a multi-objective opti-mization problem to jointly minimize the worst outage probability and total303.3. Joint Scheduling and Power Allocation in Multiuser per Cell Scenariopower consumption.The objective function for the maximum allowed outage probability canbe expressed as co(s,p) = max.i?ij(s,p). This should be transformed into anon-dimensional function to ensure consistent comparison before forming aglobal criterion function [40]. Therefore, we use normalization for transform-ing the functions. Assuming ? as the maximum possible outage probabilityat the BS, the transformed cost function is given byc?o(s,p) =max.i?ij(s,p)? . (3.4)Next, we formulate the objective function for minimizing the total powerconsumption of the selected UEs in the network. The total power consump-tion can be expressed as cp(s,p) =?Li=1?Nj=1 sijpij . The maximum possi-ble total power consumption is given as?Li=1?Nj=1 sijpmax, where pmax isthe maximum power budget of each UE. Again, after transforming it intoa non-dimensional function using normalization, the objective function isobtained asc?p(s,p) =?Li=1?Nj=1 sijpij?Li=1?Nj=1 sijpmax. (3.5)A multi-objective function can be formulated by assigning weights tothe individual transformed objective functions and taking their weightedsum. The weights are external design parameters which can be chosen apriori of executing the optimization algorithm. The weights allow to havea balance between the two objectives functions according to their relativesignificance [40]. Therefore, the multi-objective optimization problem P1313.3. Joint Scheduling and Power Allocation in Multiuser per Cell Scenariocan be formulated as followsmin.s,p?1 c?o(s,p) + ?2 c?p(s,p) (3.6)s. t. ?ij(s,p) ? (1? sij) 1 + sij?, ?j ? Ni, ?i ? L (3.7)0 ? pij ? sijpmax, ?j ? Ni, ?i ? L (3.8)N?j=1sij = 1, ?i ? L (3.9)sij = 0, ?j /? Ni, ?i ? L (3.10)sij ? {0, 1}, ?j ? Ni, ?i ? L. (3.11)The outage constraint (3.7) ensures that the maximum outage probabilityat the ith BS due to its jth selected UE is ?, such that 0 ? ? ? 1. Powerconstraint is a critical design parameter in wireless networks [41]. The powerconstraint (3.8) ensures that the transmit power of selected UEs does notexceed a practical power limit pmax assumed to be same for all UEs. Weconsider only one UE is selected in each cell given by (3.9). Also, a UE isserved by only one BS at a given time. Only the candidate UEs of ith cell(given by the set Ni) is selected in that cell denoted by (3.10). If the ithBS serves its jth UE at time slot t, then sij = 1, otherwise sij = 0 givenby (3.11). The weights ?1 and ?2 are normalized weights and predefinedsuch that ?1 +?2 = 1. P1 is clearly a mixed integer programming problem,which is generally very difficult to solve and involves high computationalcomplexity.323.3. Joint Scheduling and Power Allocation in Multiuser per Cell Scenario3.3.2 Joint scheduling and maximizing of total throughputand minimizing of total transmit powersMaximizing network throughput generally demands high power consump-tion at the transmitter. Therefore, total network throughput and the totalpower consumption at the transmitter form conflicting objectives [34]. Here,our objective is to find the joint user selection and UE transmit power vari-ables that subsequently maximizes the total throughput and minimizes thetotal power consumption.First, we formulate the objective function of maximizing the networkthroughput. Using Shannon capacity, the sum throughput can be expressedas?Li=1?Nj=1 sij log2(1 + SINRij(s,p)). Therefore, maximizing throughputis equivalent to minimizing the following cost functionct(s,p) =1?Li=1?Nj=1 sij log2(1 + SINRij(s,p)). (3.12)Next, using normalization, we transform the objective function into dimen-sionless entity. Considering the throughput threshold required at the ith BSis ?i = log2(1 + ?i). The normalized cost function is given asc?t(s,p) =?Li=1?Nj=1 sij?i?Li=1?Nj=1 sij log2(1 + SINRij(s,p)). (3.13)The second objective function of minimizing the total power consumptionhas been formulated in (3.5). Therefore, we formulate the multi-objective333.3. Joint Scheduling and Power Allocation in Multiuser per Cell Scenariooptimization problem P2 as followsmin.s,p?1 c?t(s,p) + ?2 c?p(s,p) (3.14)s. t. log2(1 + SINRij(s,p)) ? sij?i, ?j ? Ni, ?i ? L (3.15)0 ? pij ? sijpmax, ?j ? Ni, ?i ? L (3.16)N?j=1sij = 1, ?i ? L (3.17)sij = 0, ?j /? Ni, ?i ? L (3.18)sij ? {0, 1}, ?j ? Ni, ?i ? L. (3.19)Constraint (3.15) ensures QoS such that the throughput due to jth UE inith cell is at least equal to a minimum required threshold, ?i. As previously,we impose UE power limits such that the power is non-negative and does notexceed a maximum limit pmax given by (3.16). In addition, (3.17) ensuresthat only one UE is selected in each cell at a given time. Also, a UE isserved by only one BS at a given time. Only the candidate UEs in ith cellrepresented by the set Ni can be served by the BS of that cell given by(3.18). The binary variables sij indicate whether a UE is scheduled or notat a time slot.Similar to P1, P2 is a mixed integer programming problem, solvingwhich generally involves very high computational cost. In addition, userfairness cannot be achieved without considering scheduling methods. There-fore, in Section 3.4, we propose methods to solve the joint scheduling andpower allocation problems P1 and P2.343.4. User Selection and Power Allocation in Each Time Slot3.4 User Selection and Power Allocation in EachTime SlotThe optimal solution to optimization problems P1 and P2 are hard toachieve in practice and may result in poor user fairness without user schedul-ing. In this section, we investigate methods to efficiently solve P1 and P2.We separate the user selection and power allocation problem to simplify thecomputational complexity of P1 and P2. We discuss a method wherein aset of user is first selected in a given time slot. Then, power is allocatedoptimally to the set of selected users in the given time slot.Let us define a set S, which comprises of the selected users in all cellsat a given time slot. The scheduled user in ith cell is defined as Si = {j ?Ni|sij = 1}. Therefore, S =?i?L Si. S(u) denotes the uth set of useramong all possible combinations of set of user and Si(u) denotes the user inith cell for uth set of user. In Section 3.4.1, we discuss various schemes forscheduling users. Next, in Section 3.4.2, we discuss different power allocationschemes.3.4.1 User scheduling: Determining the set of users in eachtime slotWe determine the set of users S to be scheduled for transmission in eachtime slot based on different user selection policies as described below. Foreach cell at a given time slot, only one UE located inside its coverage areais selected for transmission.353.4. User Selection and Power Allocation in Each Time SlotBest user selection: Exhaustive search methodIn this scheme, the set of users S that provide the best performance inminimizing the cost functions are scheduled at the given transmission timeslot. It provides the best value of network parameters but performs worstin terms of user fairness. It provides the optimal value at each time slot andrequires exhaustive search over all the possible combination of set of users.The optimization problem P4 or P5 discussed in Section 3.4.2 is solvedfor all the possible set of user combinations and the set of users giving thethe lowest value of cost function is selected in each time slot. Clearly, thisapproach entails significant computational cost as well as feedback overhead.Best user selection: Two-step methodIn the two-step method, the optimization problems P1 or P2 are solved intwo steps namely scheduling and power allocation. First, the set of user tobe scheduled is selected and second, power is allocated to the selected setof users in each time slot basis. Similar to the exhaustive search method, itdoes not consider fairness among the users.We determine the user for transmission in each cell depending on whichset of users provide the lowest cost function or highest cost saving. Further,we consider an iterative process such that there are power updates from thepower allocation algorithm while selecting the set of users for scheduling.This algorithm is depicted in Algorithm 1. The superscript m indicates theassociated variable is produced after the mth iteration.Since, actual power is allocated after user selection, we initially con-363.4. User Selection and Power Allocation in Each Time SlotAlgorithm 1 Determining set of users for scheduling: Best user selection1: Initialize: m = 0 and compute p02: repeat3: u?? argminuC(S(u))4: Solve P4 or P5 to find the optimal powers p(Smi (u?)) to the selectedusers, i.e., Smi (u?) and assign it to p(Sm+1i (u?))5: m = m+ 16: until |?i p(Smi )??i p(Sm?1i )| ? ? or m = M7: Output: Ssider random power allocation to each user in each cell at each time slot.Let C(Sm(u)) denote the value of cost function of P1 or P2 when uth setof user is selected at the mth iteration. At each iteration, the u?th set ofuser providing the lowest cost function is selected. Then, using the pro-posed power allocation schemes discussed in Section 3.4.2, optimal powersis allocated to each selected user in each cell Smi (u?) in mth iteration. Thisallocated power is then used for these users in the (m+ 1)th iteration, i.e.,p(Sm+1i (n?)) = p(Smi (n?)) . For the users not selected in the previous itera-tion, the random power assigned initially is used in the next iterations. Asthe number of iterations progress, powers may be allocated to those usersunassigned in previous iterations.We stop the iteration when |?i p(Smi )??i p(Sm?1i )| is smaller than aprescribed small positive value ? or when the number of iterations exceed aprescribed value M . The set of users produced by the last iteration may beadopted as the set of users to be scheduled at the given time slot. However,in some cases, we may observe oscillations between two or more set of usersduring the iterations. In such a case, we may use some decision criteria toselect the desired set of users at the given time slot.373.4. User Selection and Power Allocation in Each Time SlotAfter a set of user, S is selected in each time slot, the information ispassed to the centralized node through feedback channel. Power is thenallocated to these selected UEs based on P4 (Scheme-1) or P5 (Scheme-2).Proportional fairness scheme: Exhaustive search methodIn order to have a balance between the competing interest of improvinguser fairness and minimizing the cost functions in our proposed schemes,we investigate the popular proportional fairness scheduling algorithm [42].The conventional proportional fairness scheme is based on the current andmoving average throughput of the users. To suit our multi-objective problemformulation, we transform the proportional fairness scheme [42] to considerthe cost functions of P4 and P5. Let us consider C(t,S) and C?(t,S) as theinstantaneous and exponential moving average value of the cost functionrespectively for a set of user S scheduled at time slot t.The moving average value of cost function for the set of users S is up-dated asC?(t,S) = (1? 1? ) C?(t? 1,S) +1? C(t,S), (3.20)where ? is the time interval over which fairness is achieved. Also, ? is themaximum number of time slots for which the set of users can be starved ornot receive service. C?(t,S) is the sliding window average estimated over thepast ? time slots. Note that C(t,S) = 0 if S is not scheduled at time slott. The cost saving for set of user S at a given time slot t is calculated asCsav(t,S) = Cmax(t,S)? C(t,S), where Cmax(t,S) is the maximum trans-mission cost affordable. Here, we assume Cmax(t,S) = 1. The decision383.4. User Selection and Power Allocation in Each Time Slotmetric is defined as the cost saving per moving average cost i.e.,Csav(t,S)C?(t,S).At the beginning of each time slot, the algorithm checks for the numberof starved time slots for each user combination i.e. ?(t,S). If any set ofuser is starved for ? or more time slots, then that particular user set isselected at the current time slot. In case of two or more starved users, auser is selected randomly among the starved ones. Otherwise, the set ofusers which gives maximum decision metric shall be selected. It should benoted that the initial value of moving average for the objective function iszero, i.e. C?(0,S) = 0. When a set of users is not selected at a given timeslot, its average value decreases, which increases the probability of that setof user being scheduled in the next time slots.Proportional fairness scheme: Two-step methodSimilarly, as in the case of best user selection, we investigate the two-stepmethod using proportional fairness scheduling policy. The algorithm isshown in Algorithm 2. Here, we adopt the similar expression for movingaverage value of cost function and other initializations as was considered inthe exhaustive search method for proportional fairness.At the beginning of each time slot, if any set of user is starved for ? ormore time slots then that particular user set u? is selected for transmission.Ties are broken randomly in case there are two or more set of users starvingfor ? or more time slots. Otherwise, in order to select the set of users, weconsider the iterative process as depicted in Algorithm 2. Here, in the givenmth iteration, the set of user u? is selected providing the highest value ofdecision metric defined as the ratio of cost saving and moving average cost393.4. User Selection and Power Allocation in Each Time Slotof the set of user, i.e., Csav(t,S(u))C?(t,S(u)). After u? is selected, power p(Smi (u?)) isoptimally allocated to each user belonging to the user set, i.e., Smi (u?). Thepower obtained in the mth iteration is then assigned to these users in the(m + 1)th iteration, i.e., p(Sm+1i (u?)) = p(Smi (u?)), which can be used tocalculate the cost function in next iterations. We terminate the iterationwhen |?i p(Smi )??i p(Sm?1i )| is smaller than a prescribed small positivevalue ? or when the number of iterations exceed a prescribed value M . Theset of users produced in the last iteration may be adopted as the set of usersto be scheduled in the given transmission time slot.Algorithm 2 Determining set of users for scheduling: Proportional fairness1: Initialize: m = 0, compute p02: u?? argmaxu?(t,S(u))3: if ?(t,S(u?)) ? ? then4: S = S(u?)5: else6: repeat7: u?? argmaxuCsav(t,S(u))C?(t,S(u))8: Solve P4 or P5 to find the optimal powers p(Smi (u?)) to the selectedusers, i.e., Smi (u?) and assign it to p(Sm+1i (u?))9: m = m+ 110: until |?i p(Smi )??i p(Sm?1i )| ? ? or m = M11: S = Sm(u?)12: end if13: Output: SAfter the set of user S to be selected in each time slot is determined, theinformation is passed to the centralized node through the feedback channel.Finally, optimal powers are allocated to these selected users based on P4(Scheme-1) or P5 (Scheme-2).403.4. User Selection and Power Allocation in Each Time SlotRound-robin schemeIn round-robin scheduling scheme [43], the set of users are assigned the timeslots in a cyclic fashion and in equal number. It does not give priority toany particular set of users. This scheme is easy to implement and performsbest in terms of providing user fairness.3.4.2 Power allocation to the selected set of users in agiven time slotP1 and P2 are reduced to problems when there exists only one UE in eachcell at a time slot using user scheduling methods discussed in Section 3.4.1.Our proposed power allocation schemes presented here can be solved todetermine the transmit powers for S.Scheme-1: Multi-objective optimization for minimization ofworst outage probability and minimization of total transmitpowers (in a given time slot)Using the scheduling methods, P1 is reduced to a single user per cell scenarioat each time slot that makes it easier to solve it. Since a UE is alreadyselected in each cell, we can use i to index both BS and selected UE inthat cell. We no longer need to consider the user selection constraints inour problem formulation. The outage probability at ith BS can now be413.4. User Selection and Power Allocation in Each Time Slotexpressed as?i(p) = Pr.(SINRi(p) < ?i)= 1? e??i?i/pi?k?{L}\{i}(1 + ?iFikpk/pi)?1. (3.21)Then, problem P1 is simplified to equivalent problem P3 as given belowmin.?,p?1( ?Omax)+ ?2(?Li=1 piL ? pmax)(3.22)s. t. ?i(p) ? ?, ?i ? L (3.23)0 ? pi ? pmax, ?i ? L (3.24)0 ? ? ? Omax, (3.25)where the first objective function is the normalized maximum outage prob-ability in the network. Omax is the maximum possible outage probability.Here, we have used epigraph form [44] by introducing ?. The second ob-jective function denotes the normalized sum of UE powers. Since, each cellhas only one UE connected to its BS, we have total of L UEs connectedto its BS in the network in each time slot. We assume ? to vary withincertain acceptable limits, i.e., 0 ? ? ? Omax given by (3.25). This alsoaddress the feasibility conditions for (3.22) since depending on the valueof Omax, the optimization problem may or may not be feasible. P3 canbe converted into an equivalent convex optimization problem P4 by letting? = ?log(1??), and making a logarithmic change of variable in p [44], i.e.,p?i = log pi for all i. Therefore, ? varies in the range 0 ? ? ? ?max, where423.4. User Selection and Power Allocation in Each Time Slot?max = ? log(1?Omax). Since, ? is a monotonically increasing function of?, minimizing ? is equivalent to minimizing ?. Thus, P4 is given as followsmin.?, p??1( ??max)+ ?2(?Li=1 ep?iL ? pmax)(3.26)s. t. fi(p?) ? ?, ?i ? L (3.27)0 ? ep?i ? pmax, ?i ? L (3.28)0 ? ? ? ?max, (3.29)where fi(p?) = ?i?ie?p?i +?k?{L}\{i} log(1 + ?iFikep?k?p?i). As shown in Ap-pendix A, P4 is a convex optimization problem. Therefore, existing numer-ical solvers can be used to find the optimal solution of P4.Scheme-2: Multi-objective optimization of total throughput andminimization of total transmit powers (in a given time slot)Since we assume that users are already selected using different methodsdiscussed in Section 3.4.1, P2 is reduced to the case of single user per cellscenario at each time slot. The network throughput can now be expressedas ?Li=1 log2(1 + SINRi(p)). We approximate the throughput based onhigh SINR assumption [45] given as log2(1 + SINR(p)) ' log2(SINR(p)).Therefore, the sum throughput can be expressed as log2(?Li=1 SINRi(p))).Next, we reduce P2 to the equivalent multi-objective optimization prob-433.4. User Selection and Power Allocation in Each Time Slotlem P5 as followsmin.p?1L?i=1?iSINRi(p)+ ?2(?Li=1 piL ? pmax)(3.30)s. t. SINRi(p) ? ?i, ?i ? L (3.31)0 ? pi ? pmax, ?i ? L. (3.32)The first objective denotes maximizing the total system throughput. Sincelog(?) is a monotonically increasing function, maximizing log(?) is equivalentto maximizing (?). Therefore, maximizing log2(?Li=1 SINRi(p))) is equiva-lent maximizing (?Li=1 SINRi(p)) which is further equivalent to minimizing1/?Li=1 SINRi(p). The second objective function denotes minimizing the to-tal UE transmit power. As previously, we normalize each objective to haveconsistent comparison. 1/SINRi(p) is a posynomial in p and the productof posynomial is again a posynomial. The sum of power terms also form aposynomial. Hence, the objective function is a posynomial in p. In addition,the SINR constraint SINRi(p) ? ?i is equivalent to 1/SINRi(p) ? 1/?i for?i ? 0. P5 is a geometric program (GP) [46], which can be solved efficientlyand globally using interior point methods [44]. ?1 and ?2 can be determinedas discussed in Section 3.5.443.5. Calculation of weights for multi-objective functions3.5 Calculation of weights for multi-objectivefunctionsIn this section, we propose a method for determining the weights of ourmulti-objective optimization problems. The weights, ?1 and ?2 in our multi-objective functions determine the priority level for each objective function.Varying weights is useful in considering various cases with different prioritiesassigned to the objectives. We consider PL between the BS and UE forvarying the weight for the case of outage probability minimization and totalthroughput maximization. When the PL for a UE is higher, correspondingly,the outage probability is higher and throughput is lower. Therefore, PL canbe used to analyze the cost of outage probability and network throughput.When the PL becomes high, we assign high priority or weight, ?1 to outageprobability minimization in Scheme-1 and total throughput maximizationin Scheme-2. We use the Keenan Motley PL model to account for indoorpropagation loss due to walls and floors [47]. The PL between ith BS andjth UE is given asPLij = 32 + 10?log(dij) +NfATf +NwATw (dB), (3.33)where Nf is the number of floors traversed, ATf is the attenuation per floor,Nw is the number of walls traversed and ATw is the attenuation per wall.The floor and wall attenuation factors vary greatly depending on featuresspecific to buildings such as wall thickness, floor thickness, construction453.5. Calculation of weights for multi-objective functionsmaterial, floor and ceiling material [48]. Further, we normalize (3.33) as??1 =PLijPLmax, (3.34)where PLmax is the maximum PL that a signal can undergo in our networkand occurs at the edge of the femtocell/macrocell, which is found usingthe maximum coverage radius, dmax in (3.33). ?1 at any time instant t isselected based on the average distance between BS and UE in the network.We vary the weight for the total power consumption minimization ac-cording to the UE?s remaining battery capacity ?rem. If ?rem of an UE ishigh then ?2 is lower and if ?rem is low then ?2 is higher. For instance,when UEs do not have enough battery capacity, the weights are adjustedsuch that the total power minimization receives higher priority. The valueof weight corresponding to the sum power minimization objective can bechosen as??2 =1?( 1?rem?1?max), (3.35)where ?rem is the UE?s remaining battery capacity such that ?0 ? ?rem ??max. ?max is the UE?s maximum battery capacity and ?0 is the minimumpossible battery capacity (?0 > 0). Here, ? = 1?0 ?1?max. ?rem of jth UE inith cell at time slot t is calculated as?rem,ij(t) = ?max ?t?1?n=0pij(n) ? T, (3.36)where T is the Transmission Time Interval (TTI) of physical resource blocks,n is the discrete time index. To select ?2 at a time slot t, we consider the463.6. Scheme-3: Energy-efficient (Green) power allocation schemeuser in the network with least value of ?rem. Therefore, using normalization,the weights ?1 and ?2 are calculated from (3.34) and (3.35)?1 =??1??1 + ??2, ?2 =??2??1 + ?2?. (3.37)3.6 Scheme-3: Energy-efficient (Green) powerallocation schemeIn this section, we propose an energy-efficient (green) power allocation schemefor our single user per cell network model. To optimize the green per-formance of the network, the scheme minimizes the total transmit powerper unit network throughput (J/bit). It also guarantees QoS in terms ofSINR required at each BS. The effect of power saving on the overall systemthroughput is being considered with this scheme.We follow similar approach as in the case of Scheme-2 (multi-objectiveoptimization of total throughput and minimization of total transmit pow-ers). Based on high SINR assumption, we approximate the network through-put. Therefore, the sum throughput can be expressed as log2(?Li=1 SINRi(p))).Since log(?) is a monotonically increasing function, maximizing log(?) isequivalent to maximizing (?). Therefore, maximizing log2(?Li=1 SINRi(p)))is equivalent to minimizing 1/?Li=1 SINRi(p). Next, we formulate the prob-lem P6 for minimizing total power consumption per unit throughput given473.7. Summaryas followsmin.p?Li=1 pi?Li=1 SINRi(p)(3.38)s. t. SINRi(p) ? ?i, ?i ? L (3.39)0 ? pi ? pmax, ?i ? L. (3.40)The QoS requirement is fulfilled such that SINR received at the BS satisfiesthe minimum threshold ?i. In addition, we consider the power constraintssuch that the transmit power of UE is non-negative and does not exceedpmax. The total transmit power form a posynomial and the inverse of prod-uct of SINRs is also a posynomial. Therefore, the objective function is aposynomial as the product of posynomials is again a posynomial. Also, theSINR constraint is equivalent to 1/SINRi(p) ? 1/?i for ?i ? 0, which formposynomial. Therefore, P6 is a geometric program (GP) [46] that can besolved optimally using interior point methods [44].3.7 SummaryIn this chapter, we introduced the system and channel model for our net-work. We investigated two joint scheduling and power allocation problemswhich can be formulated as multi-objective optimization problems. The firstproblem accounted for the trade-off balance between outage probability andtotal transmit power whereas the second problem accounted for the trade-offbalance between network throughput and total transmit power. We exploreda method to solve the joint scheduling and power allocation wherein we sep-483.7. Summaryarated the problem into two steps: first, selecting the users in each cell andsecond, allocating powers to the selected users. We discussed different meth-ods of user scheduling such as best user selection, proportional fairness andround-robin. We also proposed a method to vary the weights of the multi-objective problems depending on the network transmission scenario. As anapproach to optimize the green performance of the network, we introduceda scheme to minimize the power consumption per network throughput.49Chapter 4Performance AnalysisIn this chapter, we evaluate the performance of the proposed scheduling andpower allocation schemes based on results obtained from computer simula-tions.4.1 Simulation SetupWe consider a network with a macrocell overlaid by femtocells. UEs areplaced randomly in each cell and fixed over the time. Gij is modeled as beingproportional to (d?ij ? a ? b ? c)?110?ij/10. a = 1032/10, b = 10NfATf/10 and c =10NwATw/10. ?ij is a Gaussian distributed random variable with zero meanand standard deviation of 4 dB to account for log-normal shadowing effects[49]. We consider 1000 time slots where a user is scheduled simultaneouslyin each cell at each time slot and ? is assumed to be 80. We assume SINRthreshold requirement equal for all the BSs denoted by ?min. Further, someother simulation parameters are listed in Table 4.1.504.2. Simulation ResultsSimulation Parameters ValuesNumber of macrocell 1Number of femtocells 3Number of UEs per cell 2Femtocell radius 40 mMacrocell radius 800 mPath loss exponent 3Number of floors (Nf ) 2Number of walls (Nw) 2Attenuation per floor (ATw) 15 dBAttenuation per wall (ATw) 4 dBReceiver noise figure -60 dBmTransmission Time Interval (T) 10 msTable 4.1: Simulation Parameters4.2 Simulation ResultsIn this section, we analyze the performance of proposed Scheme-1 andScheme-2 for various user scheduling policies, i.e., best user selection, pro-portional fairness and round-robin.4.2.1 Simulation analysis for Scheme-1 with user schedulingHere, we study the simulation results for Scheme-1 of minimizing the out-age probability and minimizing the power consumption for different userselection methods.Figs. 4.1, 4.2 and 4.3 show the performance of Scheme-1 for best user se-lection, proportional fairness and round-robin selection respectively. Figs. 4.1(a),4.2(a), 4.3(a) show the variation of outage probability per time slot with in-creasing value of UE maximum power budget, pmax for each of these selec-tion methods. Figs. 4.1(b), 4.2(b), 4.3(b) show the variation of total power514.2. Simulation Resultsconsumption per time slot with increasing pmax for each of these selectionmethods. For these scheduling policies, we compare the performance fordifferent cases of weights ?1 and ?2 in P4, namely outage minimization,outage-power trade-off and power minimization at ?min = 0.1 dB. It shouldbe noted that results for outage minimization can be achieved from P4 bysetting ?1 = 1 and ?2 = 0. Outage-Power trade-off case can be obtainedby varying ?1, ?2 according to the method proposed in Section 3.5. Powerminimization case can be achieved with ?1 = 0 and ?2 = 1 in P4. We thenevaluate the effectiveness of the trade-off schemes based on the comparisonof the results obtained.Let us consider best user selection at pmax = 30 dBm. For outageminimization case, the outage probability is 0.047 (Fig. 4.1(a)) and to-tal power consumption is 32.18 dBm (Fig. 4.1(b)). For power minimiza-tion case, the outage is 0.5 (Fig. 4.1(a)) and power consumption in 5.493dBm (Fig. 4.1(b)). Moreover, we observe that power consumption is veryhigh while minimizing outage probability whereas outage is very high whileminimizing the power consumption. Therefore, to reduce the power con-sumption, system outage needs to be compromised and vice-versa. As ob-served from the outage-power trade-off results, we obtain better balancewith respect to these parameters. We see the outage probability is 0.071(Fig. 4.1(a)) and power consumption is 19.55 dBm (Fig. 4.1(b)). Hence, theproposed trade-off scheme provides a significant power saving of 12.63 dBmat the cost of small increase in outage probability of 0.024 compared to theoutage minimization case.Next, consider proportional fairness selection at pmax = 20 dBm. For524.2. Simulation Results20 21 22 23 24 25 26 27 28 29 3000.050.10.150.20.250.30.350.40.450.5Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1 with Best User Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(a)20 21 22 23 24 25 26 27 28 29 305101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1 with Best User Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(b)Figure 4.1: Scheme-1 using best user selection. ?min = 0.1 dB. Omax = 0.5.534.2. Simulation Results20 21 22 23 24 25 26 27 28 29 300.050.10.150.20.250.30.350.40.450.5Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1 with Proportional Fairness Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(a)20 21 22 23 24 25 26 27 28 29 305101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1 with Proportional Fairness Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(b)Figure 4.2: Scheme-1 using proportional fairness selection. ?min = 0.1 dB.Omax = 0.5.544.2. Simulation Resultsoutage minimization, the outage is 0.11 (Fig. 4.2(a)) and total power con-sumption is 22.55 dBm (Fig. 4.2(b)). For power minimization case, the out-age is 0.5 (Fig. 4.2(a)) and the power consumption is 9.359 dBm (Fig. 4.2(b)).For the trade-off case, the outage is 0.287 (Fig. 4.2(a)) and power consump-tion is 13.03 dBm (Fig. 4.2(b)). Therefore, we see that the outage-powertrade-off case provides good balance between the outage and power con-sumption. It provided significant decrease in outage probability of 0.213 atthe cost of small increase in power of 3.671 dBm as compared to the powerminimization case. The data points for Figs. 4.1 and 4.2 are obtained usingexhaustive search method.Similarly, for the round-robin selection, we achieve a good balance throughthe trade-off case. For instance at pmax = 30 dBm, for outage minimiza-tion case, the outage is 0.182 (Fig. 4.3(a)) and the power consumption is32.31 dBm (Fig. 4.3(b)). For power minimization case, the outage is 0.5(Fig. 4.3(a)) and the power consumption is 12.59 dBm (Fig. 4.3(b)). Fortrade-off case, the outage is 0.196 (Fig. 4.3(a)) and the power consumptionis 26.26 dBm (Fig. 4.3(b)). Therefore, having the right trade-off balanceresults in 6.05 dBm decrease in power consumption at the cost of slightincrease in outage of 0.014 as compared to the outage minimization case.Further in Figs. 4.4, 4.5, 4.6, and 4.7, we depict the results for outageminimization, power minimization and outage-power trade-off (for SINRthreshold, ?min = 0.1 dB and 1 dB) cases respectively. For these threecases, we compare the results for best user selection, proportional fairnessand round-robin user selection scheme. We also compare the trends fortwo values of SINR threshold, ?min = 0.1 dB and 1 dB. In the trade-off554.2. Simulation Results20 21 22 23 24 25 26 27 28 29 300.20.250.30.350.40.450.5Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1 with Round-Robin Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(a)20 21 22 23 24 25 26 27 28 29 30101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1 with Round-Robin Selection  Outage Minimization, ?min = 0.1 dBOutage-Power Trade-off, ?min = 0.1 dBPower Minimization, ?min = 0.1 dB(b)Figure 4.3: Scheme-1 using round-robin selection. ?min = 0.1 dB. Omax =0.5.564.2. Simulation Resultsresults, we compare the results obtained from the two-step method and thatobtained using exhaustive search method. We analyze the effectiveness ofthe two-step method for the best user selection and proportional fairnessselection.For outage minimization case, i.e., when ?1 = 1 and ?2 = 0 in P4, theoutage probability decreases with increasing pmax as depicted in Fig. 4.4(a),as higher power availability at UE would mean higher probability of success-ful signal transmission to its BS. Also, as more power is available at the UE,the power consumption in the network increases. For various user selectionpolicies, best user selection gives the least outage probability followed by pro-portional fairness and round-robin scheme. Among the analyzed schedulingschemes, the round-robin selection algorithm perform the worst in termsof both throughput and power consumption because it does not seek anynetwork or user related information for its selection decision. The usersare simply chosen in cyclic order in a given time slot for data transmissionand provides highest fairness among the given scheduling algorithms. Thesystem suffers less outage probability when ?min = 0.1 dB as compared tothat when ?min = 1 dB. This is because higher SINR threshold requirementat the BS will degrade the performance as some transmissions may not beable to satisfy the QoS requirement. Fig. 4.4(b) shows increasing networkpower consumption with increasing UE power budget. As more power isavailable at the UE, higher power is consumed in the network. The totalpower consumption seems close for ?min = 0.1 dB and 1 dB.In case of power minimization case, i.e., ?1 = 0 and ?2 = 1 in P4, theoutage probability remains invariant with different pmax because the outage574.2. Simulation Results20 21 22 23 24 25 26 27 28 29 3000.050.10.150.20.250.30.35Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1: Outage Minimization Case  Best-User, ?min = 0.1 dBProp-Fair, ?min = 0.1 dBRound-Robin, ?min = 0.1 dBBest-User, ?min = 1 dBProp-Fair, ?min = 1 dBRound Robin, ?min = 1 dB(a)20 21 22 23 24 25 26 27 28 29 3022242628303234Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1: Outage Minimization Case  Best-User, ?min = 0.1 dBProp-Fair, ?min = 0.1 dBRound-Robin, ?min = 0.1 dBBest-User, ?min = 1 dBProp-Fair, ?min = 1 dBRound Robin, ?min = 1 dB(b)Figure 4.4: Scheme-1: Outage minimization case (?1 = 1, ?2 = 0). ?min =0.1 dB, 1 dB. Omax = 0.5. 584.2. Simulation Results20 21 22 23 24 25 26 27 28 29 300.450.460.470.480.490.50.510.520.530.540.55Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1: Power Minimization Case  Best-User, ?min = 0.1 dBProp-Fair, ?min = 0.1 dBRound-Robin, ?min = 0.1 dBBest-User, ?min = 1 dBProp-Fair, ?min = 1 dBRound-Robin, ?min = 1 dB(a)20 21 22 23 24 25 26 27 28 29 30681012141618Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1: Power Minimization Case  Best-User, ?min = 0.1 dBProp-Fair, ?min = 0.1 dBRound-Robin, ?min = 0.1 dBBest-User, ?min = 1 dBProp-Fair, ?min = 1 dBRound Robin, ?min = 1 dB(b)Figure 4.5: Scheme-1: Power minimization case (?1 = 0, ?2 = 1). ?min =0.1 dB, 1 dB. Omax = 0.5.594.2. Simulation Resultsprobability constraint becomes tight. Therefore, the outage approaches itsmaximum allowed value i.e., Omax = 0.5 and stays constant and does notdepend on how the users are scheduled. The power consumption remainsconstant for different values of pmax as shown in Fig. 4.5(b). However,the power consumption is found to be highest for round-robin scheme withhigher ?min requirements. The data points in Figs. 4.4 and 4.5 for outageminimization and power minimization are obtained using exhaustive searchfor both best user selection and proportional fairness scheme.For the outage-power trade-off cases as shown in Fig. 4.6 (?min = 0.1dB) and 4.7 (?min = 1 dB), the outage probability decreases with increasingpmax for the same reasons explained earlier for outage minimization case.Moreover, as discussed earlier, the trade-off scheme provides a good balancebetween the outage probability and power consumption. The outage per-formance is best for best user selection, followed by proportional fairnessand round-robin selection. Even though the outage performance of pro-portional fairness is worse than the best user selection, it provides betteruser fairness as shown later in Table 4.2. We also compare the performanceof our proposed scheme under different user selection algorithms. For thebest user selection policy, we see that the outage and power consumptionperformance is almost equal using the exhaustive search and the two-stepalgorithm for both the values of SINR threshold. In case of proportional fair-ness scheduling, the performance of two-step algorithm follows very close tothat obtained using exhaustive search method. At pmax = 30 dBm, thetwo-step method gave only 0.04 higher outage and 0.39 dBm higher powerconsumption compared to the exhaustive search method. This shows the604.2. Simulation Results20 21 22 23 24 25 26 27 28 29 300.050.10.150.20.250.30.350.4Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1: Outage-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 0.1 dBBest User Selection (Two-Step), ?min = 0.1 dBProportional Fairness (Exhaustive), ?min = 0.1 dBProportional Fairness (Two-Step), ?min = 0.1 dBRound Robin, ?min = 0.1 dB(a)20 21 22 23 24 25 26 27 28 29 30810121416182022242628Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1: Outage-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 0.1 dBBest User Selection (Two-Step), ?min = 0.1 dBProportional Fairness (Exhaustive), ?min = 0.1 dBProportional Fairness (Two-Step), ?min = 0.1 dBRound Robin, ?min = 0.1 dB(b)Figure 4.6: Scheme-1: Outage-Power trade-off case (?1, ?2 as in Section3.5). ?min = 0.1 dB. Omax = 0.5.614.2. Simulation Results20 21 22 23 24 25 26 27 28 29 300.050.10.150.20.250.30.350.4Power budget of user equipment, pmax (dBm)OutageprobabilityScheme-1: Outage-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 1 dBBest User Selection (Two-Step), ?min = 1 dBProportional Fairness (Exhaustive), ?min = 1 dBProportional Fairness (Two-Step), ?min = 1 dBRound Robin, ?min = 1 dB(a)20 21 22 23 24 25 26 27 28 29 30810121416182022242628Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-1: Outage-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 1 dBBest User Selection (Two-Step), ?min = 1 dBProportional Fairness (Exhaustive), ?min = 1 dBProportional Fairness (Two-Step), ?min = 1 dBRound Robin, ?min = 1 dB(b)Figure 4.7: Scheme-1: Outage-Power trade-off case (?1, ?2 as in Section3.5). ?min = 1 dB. Omax = 0.5.624.2. Simulation ResultsScheduling method, pmax = 30 dBm ?min = 0.1 dB ?min = 1 dBBest user selection (exhaustive) 0.0625 0.0711Best user selection (two-step) 0.0625 0.0625Proportional fairness (exhaustive) 0.5040 0.4072Proportional fairness (two-step) 0.4682 0.4550Round-robin 0.9999 0.9999Table 4.2: Jain?s fairness index for Scheme-1 (trade-off case) for differentscheduling policiesefficiency of the two-step method considering Scheme-1.User fairness comparison for Scheme-1Next, we explore the user fairness for different scheduling policies for Scheme-1. We consider Jain?s fairness index [37], which is a standard performanceparameter to quantify the user fairness. We estimate the index in terms ofthe time slot resource allocated to each set of users in 1000 time slots. Table4.2 shows the fairness index for Scheme-1 at pmax = 30 dBm, and ?min =0.1 dB, 1 dB. As expected, the best user selection provides worst user fair-ness and round-robin selection provides the best user fairness. For example,at ?min = 0.1 dB, the fairness index for best user selection using two-stepmethod was 0.0625 and fairness index for round-robin scheme was 0.9999.Moreover, proportional fairness algorithm performs between these two ex-treme cases and hence provides a balanced user fairness. For proportionalfairness using two-step method, the index is obtained as 0.4682 for ?min =0.1 dB. We also compare the user fairness between exhaustive search andthe two-step algorithm. At both the values of SINR threshold, the Jain?sfairness index using two-step algorithm is close to that of exhaustive search634.2. Simulation Resultsmethod. Therefore, the two-step method performs well in providing userfairness among the users.4.2.2 Simulation analysis for Scheme-2 with user schedulingIn this section, we study the simulation results for Scheme-2 of maximizingthe network throughput and minimizing the power consumption for thevarious user selection methods.Figs. 4.8, 4.9 and 4.10 show the performance of Scheme-1 for best user se-lection, proportional fairness and round-robin selection respectively. Figs. 4.8(a),4.9(a), 4.10(a) show the variation of total network throughput per time slotwith increasing value of maximum UE power budget, pmax. Figs. 4.8(b),4.9(b), 4.10(b) shows the variation of total power consumption per time slotwith increasing pmax. Similar to Scheme-1, for each of these user schedulingmethods, we compare the performance for different cases of weights ?1 and?2 in P5, namely throughput maximization, throughput-power trade-offand power minimization at ?min = 6 dB. Note that results for through-put maximization can be achieved from P5 by setting ?1 = 1 and ?2 = 0.Throughput-Power trade-off case can be obtained by varying ?1, ?2 basedon Section 3.5. Power minimization case can be achieved with ?1 = 0 and?2 = 1 in P5. We also investigate the effectiveness of the trade-off casebased on the obtained results.First, we discuss the performance of Scheme-2 with best user selec-tion at a particular value of maximum UE power budget, say pmax =30 dBm. For throughput maximization case, the network throughput is22.48 bits/s/Hz (Fig. 4.8(a)) and total power consumption is 34.06 dBm644.2. Simulation Results20 21 22 23 24 25 26 27 28 29 30681012141618202224Power budget of user equipment, pmax (dBm)Networkthroughput(bits/s/Hz)Scheme-2 with Best User Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off, ?min = 6 dBPower Minimization, ?min = 6 dB(a)20 21 22 23 24 25 26 27 28 29 30101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2 with Best User Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off, ?min = 6 dBPower Minimization, ?min = 6 dB(b)Figure 4.8: Scheme-2 using best user selection. ?min = 6 dB.654.2. Simulation Results(Fig. 4.8(b)). For power minimization case, the network throughput is7.973 bits/s/Hz (Fig. 4.8(a)) and total power consumption is 10.65 dBm(Fig. 4.8(b)). Clearly, the power consumption is very high while maxi-mizing throughput and network throughput is very low while minimizingthe power consumption. Therefore, high network throughput comes at thecost of very high power consumption and low power consumption comes atthe cost of significant decrease in network throughput. This demands fora right balance between these network performance parameters. For thethroughput-power trade-off case, the network throughput is 17.47 bits/s/Hz(Fig. 4.8(a)) and power consumed is 18.72 dBm (Fig. 4.8(b)). We observesignificant power saving of 15.34 dBm at the cost of reasonable decrease inthroughput of 5.01 bits/s/Hz as compared to the throughput maximizationcase. Hence, the proposed trade-off scheme provide a good balance betweenthe network throughput and power consumption.Second, let us consider proportional fairness selection at pmax = 20dBm. For throughput maximization case, the network throughput is 18.46bits/s/Hz (Fig. 4.9(a)) and power consumption is 25.22 dBm (Fig. 4.9(b)).For power minimization case, the network throughput is 7.973 bits/s/Hz(Fig. 4.9(a)) and total power is 13.35 dBm (Fig. 4.9(b)). For trade-off case,the network throughput is 11.61 bits/s/Hz (Fig. 4.9(a)) and power con-sumption is 15.28 dBm (Fig. 4.9(b)). Therefore, the trade-off results showincrease in throughput of 3.64 bits/s/Hz at the cost of small increase inpower of 1.93 dBm. Therefore, the trade-off results provide a balance be-tween these two performance parameters. Here, the data points for Figs. 4.8and 4.9 are obtained using exhaustive search.664.2. Simulation Results20 21 22 23 24 25 26 27 28 29 3068101214161820Power budget of user equipment, pmax (dBm)Networkthroughput(bits/s/Hz)Scheme-2 with Proportional Fairness Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off,?min = 6 dBPower Minimization, ?min = 6 dB(a)20 21 22 23 24 25 26 27 28 29 30101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2 with Proportional Fairness Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off,?min = 6 dBPower Minimization, ?min = 6 dB(b)Figure 4.9: Scheme-2 using proportional fairness selection. ?min = 6 dB.674.2. Simulation ResultsThird, we study the benefits of trade-off scheme for round-robin selec-tion. Considering pmax = 30 dBm, for throughput maximization case, thenetwork throughput is 13.32 bits/s/Hz (Fig. 4.10(a)) and power consump-tion is 32.25 dBm (Fig. 4.10(b)). For power minimization case, the networkthroughput is 5.358 bits/s/Hz Fig. 4.10(a)) and power consumption is 12.52dBm (Fig. 4.10(b)). For trade-off case, the throughput is 10.95 bits/s/HzFig. 4.10(a)) and power consumption is 20.12 dBm (Fig. 4.10(b)). Thus,we see a good power saving of 12.13 dBm at the cost of small decrease inthroughput of 2.37 bits/s/Hz.Next, we compare the performance of Scheme-2 for different schedulingmethods. We also investigate the results for two values of SINR threshold,?min = 6 dB and 8 dB. In addition, we evaluate the effectiveness of the two-step method by comparing the results with that obtained using exhaustivesearch method.Let us consider the throughput maximization case, i.e., when ?1 = 1and ?2 = 0 in P5. In Fig. 4.11(a), we see the network throughput increaseswith increasing pmax, as higher power available at UE will increase theSINR at the respective BSs. The throughput is highest for the best userselection followed by proportional fairness and round-robin scheme. For bestuser selection scheme, each cell selects the user with highest throughput.The throughput is least for round-robin selection which is expected since itdoes not follow any parameter maximization criterion during user selection.The proportional fairness scheme achieves lower throughput as comparedto the throughput maximization case. The throughput obtained for ?min= 8 dB is found to be lower than when ?min = 6 dB since higher SINR684.2. Simulation Results20 21 22 23 24 25 26 27 28 29 30567891011121314Power budget of user equipment, pmax (dBm)Networkthroughput(bits/s/Hz)Scheme-2 with Round-Robin Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off, ?min = 6 dBPower Minimization, ?min = 6 dB(a)20 21 22 23 24 25 26 27 28 29 30101520253035Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2 with Round-Robin Selection  Throughput Maximization, ?min = 6 dBThroughput-Power Trade-off, ?min = 6 dBPower Minimization, ?min = 6 dB(b)Figure 4.10: Scheme-2 using round-robin selection. ?min = 6 dB.694.2. Simulation Results20 21 22 23 24 25 26 27 28 29 301012141618202224Power budget of user equipment, pmax (dBm)Networkthroughput(bits/s/Hz)Scheme-2: Throughput Maximization Case  Best-User, ?min = 6 dBProp-Fair, ?min = 6 dBRound-Robin, ?min = 6 dBBest-User, ?min = 8 dBProp-Fair, ?min = 8 dBRound-Robin, ?min = 8 dB(a)20 21 22 23 24 25 26 27 28 29 302224262830323436Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2: Throughput Maximization Case  Best-User, ?min = 6 dBProp-Fair, ?min = 6 dBRound-Robin, ?min = 6 dBBest-User, ?min = 8 dBProp-Fair, ?min = 8 dBRound-Robin, ?min = 8 dB(b)Figure 4.11: Scheme-2: Throughput maximization case (?1 = 1, ?2 = 0).?min = 6 dB, 8 dB. 704.2. Simulation Resultsthreshold demand at BS degrades the system performance. The total powerconsumption trend is depicted in Fig. 4.11(b), which shows that the networkdemands for higher power in order to maximize throughput.For power minimization case, i.e., when ?1 = 0 and ?2 = 1 in P5,the SINR constraints are active at each time slot. Therefore, the networkthroughput at all time slots is constant for a given value of ?min. The powerconsumption for ?min = 8 dB is higher than that for ?min = 6 dB, as thesystem tries to achieve the demanded ?min by allocating higher power to theusers. Here, the results in Figs. 4.11 and 4.12 for throughput maximizationand power minimization cases are obtained using exhaustive search methodfor both best user selection and proportional fairness scheme.Figs. 4.13 and 4.14 depict the results for throughput-power trade-offcase for SINR threshold values of 6 dB and 8 dB respectively. The bestuser selection performs best in terms of both throughput and power saving.The proportional fairness algorithm provides higher throughput than theround-robin selection. As we see later in Table 4.3, the proportional fairnessscheme provides a balanced user fairness compared to the best user selectionand round-robin selection. Both throughput and power consumption arehigher for higher ?min since the power consumption increases with increasein ?min as users may need higher power to satisfy higher ?min. Moreover,higher ?min, i.e., higher SINR means higher throughput. In case of best userselection for both values of SINR threshold, the throughput and power valuesobtained from the exhaustive search and two-step method are the same.For proportional fairness selection policy, the results obtained from the two-step method is very close to that using exhaustive search method. For714.2. Simulation Results20 21 22 23 24 25 26 27 28 29 30567891011Power budget of user equipment, pmax (dBm)Networkthroughput(bits/s/Hz)Scheme-2: Power Minimization Case  Best-User, ?min = 6 dBProp-Fair, ?min = 6 dBRound-Robin, ?min = 6 dBBest-User, ?min = 8 dBProp-Fair, ?min = 8 dBRound-Robin, ?min = 8 dB(a)20 21 22 23 24 25 26 27 28 29 301011121314151617Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2: Power Minimization Case  Best-User, ?min = 6 dBProp-Fair, ?min = 6 dBRound-Robin, ?min = 6 dBBest-User, ?min = 8 dBProp-Fair, ?min = 8 dBRound-Robin, ?min = 8 dB(b)Figure 4.12: Scheme-2: Power minimization case (?1 = 0, ?2 = 1). ?min =6 dB, 8 dB.724.2. Simulation Results20 21 22 23 24 25 26 27 28 29 30681012141618Power budget of user equipment, pmax (dBm)Networkthroughput(bps/Hz)Scheme-2: Throughput-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 6 dBBest User Selection (Two-Step), ?min = 6 dBProportional Fairness (Exhaustive), ?min = 6 dBProportional Fairness (Two-Step), ?min = 6 dBRound Robin, ?min = 6 dB(a)20 21 22 23 24 25 26 27 28 29 3013141516171819202122Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2: Throughput-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 6 dBBest User Selection (Two-Step), ?min = 6 dBProportional Fairness (Exhaustive), ?min = 6 dBProportional Fairness (Two-Step), ?min = 6 dBRound Robin, ?min = 6 dB(b)Figure 4.13: Scheme-2: Throughput-Power trade-off case (?1, ?2 as in Sec-tion 3.5). ?min = 6 dB.734.2. Simulation Results20 21 22 23 24 25 26 27 28 29 308101214161820Power budget of user equipment, pmax (dBm)Networkthroughput(bps/Hz)Scheme-2: Throughput-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 8 dBBest User Selection (Two-Step), ?min = 8 dBProportional Fairness (Exhaustive), ?min = 8 dBProportional Fairness (Two-Step), ?min = 8 dBRound Robin, ?min = 8 dB(a)20 21 22 23 24 25 26 27 28 29 301415161718192021222324Power budget of user equipment, pmax (dBm)Totalpowerconsumption(dBm)Scheme-2: Throughput-Power Tradeoff Case  Best User Selection (Exhaustive), ?min = 8 dBBest User Selection (Two-Step), ?min = 8 dBProportional Fairness (Exhaustive), ?min = 8 dBProportional Fairness (Two-Step), ?min = 8 dBRound Robin, ?min = 8 dB(b)Figure 4.14: Scheme-2: Throughput-Power trade-off case (?1, ?2 as in Sec-tion 3.5). ?min = 8 dB.744.2. Simulation ResultsScheduling method, pmax = 30 dBm ?min = 6 dB ?min = 8 dBBest user selection (exhaustive) 0.1236 0.1230Best user selection (two-step) 0.0625 0.0625Proportional fairness (exhaustive) 0.7689 0.7430Proportional fairness (two-step) 0.7390 0.6637Round-robin 0.9999 0.9999Table 4.3: Jain?s fairness index for Scheme-2 (trade-off case) for differentscheduling policiesexample, at pmax = 30 dBm, the two-step method gave only 0.09 bits/s/Hzlower throughput and 0.17 dBm higher power as compared to the exhaustivesearch method. Therefore, the results show the effectiveness of the two-stepmethod for our proposed Scheme-2.User fairness comparison for Scheme-2Similar to Scheme-1, we investigate user fairness for Scheme-2. We againconsider Jain?s fairness index [37] and estimate the index in terms of thetime slot resource allocated to each set of users in 1000 time slots. Table 4.3shows the fairness index for pmax = 30 dBm and ?min = 6 dB and 8 dB. Thebest user selection provides the least user fairness and round-robin selectionprovides the highest user fairness. However, we observe that proportionalfairness algorithm provides a balanced user fairness. For example, at pmax= 6 dB, the best user selection using two-step method provides user fairnessof 0.0625 and round-robin method provides fairness of 0.9999. The pro-portional fairness method provides balanced user fairness of 0.7390 (usingtwo-step). We also compare the user fairness between exhaustive search andthe two-step method. The user fairness from the two-step method is close754.3. Simulation Analysis for Scheme-3 Energy-Efficient (Green) Power Allocation Schemeto that obtained using the exhaustive search method. Thus, the two-stepmethod is efficient in terms of providing good user fairness.4.3 Simulation Analysis for Scheme-3Energy-Efficient (Green) Power AllocationScheme20 21 22 23 24 25 26 27 28 29 300.0130.0140.0150.0160.0170.0180.019Power budget of user equipment, pmax (dBm)Powerperunitthroughput(J/(bit/Hz))Scheme-3: Green Power Allocation  ?min = 6 dB?min = 6.5 dB?min = 7 dB?min = 7.5 dB?min = 8 dBFigure 4.15: Variation of energy efficiency metric for different values ofmaximum UE transmit power and SINR threshold requirement.Fig. 4.15 shows the variation of energy efficiency metric against pmaxfor different values of SINR threshold, ?min. We observe increasing power764.4. Summaryper unit throughput with increasing pmax. The reason is that the proposedscheme tries to achieve the given ?min by allocating higher power to the UEswith bad channel conditions. This increases the overall power consumptionthat may adversely affect the energy efficiency. The power consumptionper unit system throughput also increases with higher ?min requirements.This is because high QoS demand makes the scheme allocate high powerto the users. Also, with higher QoS requirement, the power consumptionrequirement is higher for the users with bad channel conditions.4.4 SummaryIn this chapter, we argued that achieving trade-off balance between the per-formance parameters is beneficial in HetNets. Through simulation results,we investigated the performance of our proposed trade-off schemes. We an-alyzed how the proposed scheme provided a good balance between outageprobability and power consumption. Also, a good trade-off balance wasachieved between network throughput and power consumption. In addi-tion, we investigated the performance using different user selection policiessuch as best user selection, proportional fairness and round-robin. We alsostudied the effectiveness of the two-step method of solving our optimiza-tion problems by comparing it with the results obtained through exhaustivesearch method. Finally, we investigated the performance of the green powerallocation scheme for different values of maximum UE transmit power andSINR threshold.77Chapter 5Conclusions and FutureWork5.1 ConclusionsIn this thesis, we studied joint user scheduling and power allocation tech-niques for interference mitigation and enhancing the performance of Het-Nets. These were presented as multi-objective optimization problems, whichprovided trade-off balance between network parameters such as networkthroughput, outage probability and power consumption. In order to solvethe multi-objective optimization problems, we investigated a two-step method,where the user selection and power allocation were accomplished separatelyin two steps at a given time slot. In addition, we proposed methods tovary the weights which determine the relative importance of each objectivedepending on the network transmission scenario at a given instant. Wealso investigated the performance of our schemes with various user selectionpolicies like best user selection, proportional fairness and round-robin.The simulation results showed that the proposed schemes are very ef-ficient in attaining trade-off balance between different conflicting system785.2. Directions for Future Workparameters. The performance of the two-step method was found to be veryclose to that obtained using exhaustive search method. The performancecomparison was based on best user selection and proportional fairness se-lection policies. Jain?s fairness index obtained through simulation resultsprovided a good comparison for the trade-off between user fairness for vari-ous user selection policies.Finally, we presented an energy efficient power allocation scheme to opti-mize the green performance of the network. The scheme minimized the totalUE transmit power per unit throughput while guaranteeing QoS. Throughsimulation results, we studied its performance for different values of transmitpower of mobile users and QoS requirement.5.2 Directions for Future WorkThe research carried out in this thesis has exposed us to various interestingresearch challenges for the future wireless systems. Some of the possiblefuture research work that can follow from the important findings of thiswork are briefly described below.? Analysis with larger HetNet: In our work, we have considered smallnetwork with few femtocells, macrocells and users per cell. Analysis ofour proposed schemes with much larger network could be carried out.? Cell association and load balancing: It is beneficial to offload mobileusers from heavily loaded macrocells to lightly loaded small cells. Thiscan provide higher data rate by offering mobile users many more re-795.2. Directions for Future Worksource blocks than the macrocell. Strategies based on traffic transfer tolightly loaded cells include mobile assisted call admission algorithms(MACA) [50], cell breathing techniques [51]. Cell range expansionis an effective method to balance load among high and lower powernodes, which is enabled through cell biasing and adaptive resourcepartitioning [52].? Self organizing network (SON) architecture: The work in our thesisdoes not consider the self-organization and self-optimization featuresof HetNets. SON architectures like centralized, distributed or hybridcould be implemented depending on the application cases [53].? Admission control: Advanced admission control mechanisms is neededto reduce network congestion, call dropping probabilities. It providesusers with guaranteed QoS and more efficient utilization of resources.For instance, determining the characteristics of an ongoing session,such as its type, bandwidth requirement, and delay sensitivity. Basedon these characteristics, assigning a priority to the session taking intoaccount various constraints [54].? Energy saving: It is important to minimize energy consumption asso-ciated with the operation of a cellular network. One approach is toswitch on/off small cells depending on the traffic which varies signifi-cantly with time and geographic locations. This tackles the problemof inefficient resource utilization during off-peak time [53].80Bibliography[1] S. Pradhan, R. Devarajan, S. Jha, and V. Bhargava, ?Uplink powerallocation schemes for heterogeneous cellular networks,? in Proc. Na-tional Conference on Communications (NCC?13), Feb. 2013, pp. 1?5.[2] D. Lopez-Perez, I. Guvenc, G. De la Roche, M. Kountouris, T. Quek,and J. 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We defineg(?, p?1, ...p?i, ...p?L) = fi(p?)? ?= ?i?ie?p?i +?k?{L}\{i}log(1 + ?iFikep?k?p?i)? ? (A.4)Here, we want to show that g is jointly convex with respect to ? and p?. TheHessian matrix of g is given byH(g) =????????????????????2g??2?2g???p?1. . . ?2g???p?i. . . ?2g???p?L?2g?p?1???2g?p?21. . . ?2g?p?1?p?i. . . ?2g?p?1?p?L... ... . . . ... . . . ...?2g?p?i???2g?p?i?p?1. . . ?2g?p?2i. . . ?2g?p?i?p?L... ... . . . ... . . . ...?2g?p?L???2g?p?L?p?1. . . ?2g?p?L?p?i. . . ?2g?p?2L???????????????????. (A.5)Now,?2g?p?2i= ?i?ie?p?i +?k?{L}\{i}?iFikep?i?p?k(ep?i?p?k + ?iFik)2= A (A.6)?2g?p?2k???k 6=i= ?iFikep?i?p?k(ep?i?p?k + ?iFik)2= B (A.7)?2g?p?i?p?k???k 6=i= ?2g?p?k?p?i???k 6=i= ??iFikep?i?p?k(ep?i?p?k + ?iFik)2= C (A.8)90Appendix A. Proof of convexity of P4The Hessian matrix can now be expressed asH(g) =????????????????0 0 . . . 0 . . . 00 B . . . C . . . 0... ... . . . ... . . . ...0 C . . . A . . . C... ... . . . ... . . . ...0 0 . . . C . . . B????????????????. (A.9)We observe that|Hii| ??j 6=i|Hij | ?i. (A.10)Therefore, H is a diagonally dominant matrix with non-negative diagonalentries. This means that H is positive semidefinite. Hence, constraint (3.27)is convex.Also, (3.28) is a set of exponential inequality constraints and (3.29) is alinear inequality constraint. Hence, P4 is a convex optimization problem.91

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