Resource Allocation in Uplink OFDMA Wireless Systems E-Book

Elias Yaacoub

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on Digital & Mobile Communication
• Sprache: Englisch

Seitenzahl: 445

Veröffentlichungsjahr: 2012

Beschreibung

Tackling problems from the least complicated to the most, Resource Allocation in Uplink OFDMA Wireless Systems provides readers with a comprehensive look at resource allocation and scheduling techniques (for both single and multi-cell deployments) in uplink OFDMA wireless networks—relying on convex optimization and game theory to thoroughly analyze performance.

Inside, readers will find topics and discussions on:

• Formulating and solving the uplink ergodic sum-rate maximization problem

• Proposing suboptimal algorithms that achieve a close performance to the optimal case at a considerably reduced complexity and lead to fairness when the appropriate utility is used

• Investigating the performance and extensions of the proposed suboptimal algorithms in a distributed base station scenario

• Studying distributed resource allocation where users take part in the scheduling process, and considering scenarios with and without user collaboration

• Formulating the sum-rate maximization problem in a multi-cell scenario, and proposing efficient centralized and distributed algorithms for intercell interference mitigation

• Discussing the applicability of the proposed techniques to state-of-the-art wireless technologies, LTE and WiMAX, and proposing relevant extensions

Along with schematics and figures featuring simulation results, Resource Allocation in Uplink OFDMA Wireless Systems is a valuable book for?wireless communications and cellular systems professionals and students.

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

Preface

Acknowledgements

Acronyms

Chapter 1: Introduction

1.1 Evolution of Wireless Communication Systems

1.2 Orthogonal Frequency Division Multiple Access

1.3 Organization of this Book

Chapter 2: Background on Downlink Resource Allocation in OFDMA Wireless Networks

2.1 Centralized Single Cell Scheduling

2.2 Distributed Scheduling

2.3 Scheduling in Multicell Scenarios

2.4 Summary

Chapter 3: Ergodic Sum-Rate Maximization with Continuous Rates

3.1 Background

3.2 Problem Formulation

3.3 Problem Solution

3.4 Achievable Rate Region

3.5 Results and Discussion

3.6 Summary

Chapter 4: Ergodic Sum-Rate Maximization with Discrete Rates

4.1 Background

4.2 Problem Formulation

4.3 Problem Solution

4.4 Results and Discussion

4.5 Summary

Chapter 5: Generalization to Utility Maximization

5.1 Background

5.2 Ergodic Utility Maximization with Continuous Rates

5.3 Ergodic Utility Maximization with Discrete Rates

5.4 Summary

Chapter 6: Suboptimal Implementation of Ergodic Sum-Rate Maximization

6.1 Background

6.2 Suboptimal Approximation of the Continuous Rates Solution

6.3 Suboptimal Approximation of the Discrete Rates Solution

6.4 Complexity Analysis of the Suboptimal Algorithms

6.5 Results and Discussion

6.6 Summary

Chapter 7: Suboptimal Implementation with Proportional Fairness

7.1 Background

7.2 Proportional Fair Scheduling

7.3 Low Complexity Utility Maximization Algorithms

7.4 Proportional Fair Utilities

7.5 Results and Discussion

7.6 Summary

Chapter 8: Scheduling with Distributed Base Stations

8.1 Background

8.2 System Model

8.3 Scheduling with Distributed Base Stations

8.4 Results and Discussion

8.5 Distributed Base Stations Versus Relays

8.6 Distributed Base Stations Versus Femtocells

8.7 Summary

Chapter 9: Distributed Scheduling with User Cooperation

9.1 Background

9.2 Cooperative Distributed Scheduling Scheme

9.3 Distributed Scheduling Algorithm

9.4 Results and Discussion

9.5 Summary

Chapter 10: Distributed Scheduling without User Cooperation

10.1 Background

10.2 Noncooperative Distributed Scheduling Scheme

10.3 Comparison to Existing Schemes

10.4 Analysis of Measurement Inaccuracies

10.5 Results and Discussion

10.6 Optimization of Transmission Probabilities

10.7 Practical Considerations

10.8 Summary

Chapter 11: Centralized Multicell Scheduling with Interference Mitigation

11.1 Background

11.2 Problem Formulation

11.3 Iterative Pricing-Based Power Control Solution

11.4 Pricing Game with Centralized Control

11.5 Suboptimal Scheduling Scheme Using Pricing-Based Power Control

11.6 Suboptimal Scheduling Scheme Using Probabilistic Transmission

11.7 Results and Discussion

11.8 Summary

Chapter 12: Distributed Multicell Scheduling with Interference Mitigation

12.1 Background

12.2 System Model

12.3 Intracell Cooperation: Distributed Scheduling

12.4 Intercell Interference Mitigation/Avoidance

12.5 Results and Discussion

12.6 Practical Aspects

12.7 Summary

Chapter 13: Scheduling in State-of-the-Art OFDMA-Based Wireless Systems

13.1 WiMAX Scheduling Overview

13.2 LTE Scheduling Overview

13.2 SCFDMA Versus OFDMA Scheduling

13.4 Comparison to the LTE Power Control Scheme

14.5 Summary

Chapter 14: Future Research Directions

14.1 Resource Allocation with Multiple Service Classes

14.2 Network MIMO

14.3 Coalitional Game Theory

14.4 Resource Allocation with Femtocells

14.5 Green Networks and Self-Organizing Networks

14.6 Joint Uplink/Downlink Resource Allocation

14.7 Joint Resource Allocation in Heterogeneous Networks

14.8 Resource Allocation in Cognitive Radio Networks

Bibliography

Index

Copyright 2012 by Institute of Electrical and Electronics Engineers, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada

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Library of Congress Catalog Number: 58-9935

Resource Allocation in Uplink OFDMA Wireless Systems / Elias E. Yaacoub and Zaher H. Dawy.

p. cm.–(Wiley IEEE Series on Digital and Mobile Communication)

“Wiley-Interscience.”

Includes bibliographical references and index.

ISBN 0-471-48348-6 (pbk.)

1. Surveys–Methodology. 2. Social sciences–Research–Statistical methods.

I. Groves, Robert M. II. Series.

HA31.2.S873 2007

001.4′33–dc22

2004044064

To Therese and Maria TheresaElias YaacoubTo Sanaa, Hassan, and NouraZaher Dawy

Preface

In the era of broadband wireless connectivity, users are expecting ubiquitous and seamless access to a wide range of bandwidth demanding services. Orthogonal frequency division multiple access (OFDMA) has been selected as the accessing scheme for state-of-the-art wireless communication systems. The high data rates and low latency expected from current and next generation broadband wireless access systems, such as 3GPP long-term evolution (LTE) and WiMAX (IEEE 802.16e/m), necessitate optimized and dynamic allocation of the available radio resources. In addition, the increase in demand for delay-sensitive applications with bidirectional data rate requirements such as wireless gaming, video telephony, and voice-over-IP, mandates the need for optimized uplink resource allocation algorithms.

This book treats the area of resource allocation in OFDMA wireless systems, with a focus on the uplink direction. However, the downlink direction is widely discussed, and most of the presented techniques and insights apply to the downlink. The book investigates the problems of single cell resource allocation, multicell resource allocation, centralized resource allocation, and distributed resource allocation, with/without collaboration among base stations and with/without cooperation among mobile users. Resource allocation in OFDMA wireless systems will constitute an important topic for several years to come, especially in the context of distributed and multicell scenarios. Algorithms and techniques that lead to efficient performance results, while at the same time being simple enough for practical implementation, will be of particular importance. The presented techniques in this book touch as well upon applications in cognitive radio networks, distributed base stations, heterogeneous wireless networks, and femtocells.

This book is addressed to students, professors, and researchers whose research is in the area of wireless communications with focus on resource allocation, interference mitigation, radio resource management, heterogeneous networks, and applications of game theory and convex optimization in wireless communications. The book has classroom adoption possibilities. It could be considered as a valuable supplemental reading in courses on wireless communications, cellular technologies, resource management, and network optimization. It could also serve as a supplemental reading for convex optimization and game theory courses since it presents several applications of xiii important concepts studied in these courses in a wireless communications framework. In addition, the book is addressed to research and development engineers working in the telecom industry on next generation wireless cellular technologies. In fact, the algorithms and techniques presented in the book can be customized for possible implementation in current-and next-generation LTE and WiMAX base stations. The book is also useful for telecommunications operators and vendors, service providers, consultants, research centers, and standardization bodies working on the next-generation of cellular technologies, like LTE-Advanced and WiMAX IEEE 802.16m.

A brief overview of the book organization is as follows. Chapters 1 and 2 are of introductory nature: Chapter 1 is a general introduction for the book whereas Chapter 2 presents a high-level summary of downlink OFDMA resource allocation. Centralized scheduling in a single cell scenario is studied in Chapters 3–7. Theoretical techniques based on optimization problems formulation and derivation of the optimal solutions are presented in Chapters 3–5. The reader interested in practical suboptimal schemes can skip these chapters and start reading from Chapter 6. Distributed resource allocation within a single cell scenario is investigated in Chapters 8–10, with Chapter 8 representing an intermediate step between fully centralized and fully distributed resource allocation. Multicell resource allocation is studied in Chapters 11 and 12. Practical implementation aspects of the proposed techniques and their relation to the LTE and WiMAX standards are discussed in Chapter 13. Finally, Chapter 14 discusses open research directions worthy of further investigation.

Acknowledgements

The authors would like to thank Ahmad El-Hajj for his valuable contributions and suggestions, especially during the preparation of Chapter 3. The authors are also grateful for the fruitful discussions with Profs. Mohamad Adnan Al-Alaoui, Karim Kabalan, and Ibrahim Abou Faycal from AUB, in addition to Prof. Mohamed-Slim Alouini from KAUST. The authors appreciate the encouragement of Dean Ibrahim Hajj from AUB and Dr. Adnan Abu-Dayya from QUWIC, during the preparation of this book. In addition, the authors would like to express their gratitude toward the reviewers, who contributed to shaping the final version of the book, and the team at John Wiley & Sons Inc. for their support.

The authors wish to thank the following organizations and funding sources for their support during the preparation of this book: the American University of Beirut (AUB), the AUB University Research Board, Dar Al-Handasah (Shair and Partners) Research Fund, Rathmann Family Foundation Fund, QU Wireless Innovations Center (QUWIC), Qatar National Research Fund (QNRF), and Qatar Telecom (QTel).

Acronyms

3GPPThird Generation Partnership ProjectAMCAdaptive Modulation and CodingAPAccess PointBEBest EffortBERBit Error RateBPSKBinary Phase Shift KeyingBSBase StationCBRConstant Bit RateCCDCentral Controlling DeviceCCUCentral Control UnitCDMACode Division Multiple AccessCINRChannel Gain to Interference Plus Noise RatioCNRChannel Gain to Noise RatioCPCyclic PrefixCQIChannel Quality IndicatorCRCognitive RadioCSIChannel State InformationDASDistributed Antenna SystemDBSDistributed Base StationDFTDiscrete Fourier TransformDSLDigital Subscriber LineFDDFrequency Division DuplexFDMAFrequency Division Multiple AccessFFTFast Fourier TransformGSMGlobal System for Mobile CommunicationsHIIHigh Interference IndicatorIDFTInverse Discrete Fourier TransformIFDMAInterleaved Frequency Division Multiple AccessIFFTInverse Fast Fourier TransformIIDIndependent and Identically DistributedKKTKarush–Kuhn–TuckerLFDMALocalized Frequency Division Multiple AccessLTELong-Term EvolutionMACMedium Access ControlMCSModulation and Coding SchemeMIMOMultiple Input Multiple OutputMRCMaximum Ratio CombiningNBPNash Bargaining ProblemNBSNash Bargaining SolutionNENash EquilibriumOFDMOrthogonal Frequency Division MultiplexingOFDMAOrthogonal Frequency Division Multiple AccessOIOverload IndicatorPDFProbability Density FunctionPFProportional FairPFFProportional Fair in FrequencyPFTProportional Fair in TimePFTFProportional Fair in Time and FrequencyPHYPhysical LayerQAMQuadrature Amplitude ModulationQoSQuality of ServiceQPSKQuadrature Phase Shift KeyingRBResource BlockRRRound RobinRRCRadio Resource ControllerRRHRemote Radio HeadRRMRadio Resource ManagementSCSelection CombiningSCFDMASingle Carrier Frequency Division Multiple AccessSINRSignal to Interference Plus Noise RatioSNRSignal-to-Noise RatioSRSSounding Reference SignalSSSubscriber StationTDDTime Division DuplexTDMATime Division Multiple AccessTTITransmission Time IntervalUEUser EquipmentUMTSUniversal Mobile Telecommunications SystemUTRANUMTS Terrestrial Radio Access NetworkVBRVariable Bit RateWiMAXWireless Interoperability for Microwave AccessWLANWireless Local Area Network

Chapter 1

Introduction

1.1 Evolution of Wireless Communication Systems

Wireless cellular technologies are continuously evolving to meet the increasing demands for high data rate mobile services. The design of cellular wireless communications with spectrum reuse was first developed in the 1960s. The first generation of cellular systems was based on analog frequency modulation (FM) and frequency division multiple access (FDMA) with voice traffic as the only service provided [1]. After the world's first cellular system was deployed in Japan by Nippon Telephone and Telegraph (NTT) in 1979, the Advanced Mobile Phone System (AMPS) in the United States and the European Total Access Cellular System (ETACS) in Europe followed in the 1980s [1, 2]. The design of the second generation of cellular systems moved from analog to digital communications due to the numerous advantages of the latter: support for efficient voice compression, advanced digital signal processing techniques at the transmitter and receiver, error correction coding, in addition to cheaper and faster components requiring less transmit power capabilities.

The second generation Global System for Mobile (GSM) Communications is currently the most widely deployed cellular system with more than three billion subscribers in more than 200 countries [3]. GSM is based on a hybrid time division/frequency division multiple accessing (TDMA/FDMA) air interface. The allocated spectrum for a given GSM network is divided into multiple 200 KHz frequency channels that are distributed among cells in the network based on a frequency plan in order to control the level of intercell interference in the network. In GSM, time is divided into eight time slots where each active user is allocated a time slot on a selected frequency channel. The proliferation of the Internet and the continuously escalating market demand for mobile data services necessitated the evolution of GSM by developing new enhancement technologies such as General Packet Radio Service (GPRS), enhanced data rates for GSM evolution (EDGE), and evolved EDGE that are capable of supporting packet switched mobile services with Forward-time Population Genetics Simulations: Methods, Implementation, and Applications, Bo Peng, Marek Kimmel, and Christopher I. Amos. © 2012 Wiley-Blackwell. Published 2012 by John Wiley & Sons, Inc. 3 peak data rates of 128 kbps, 384 kbps, and 1 Mbps, respectively. The enhanced data rates offered by these technologies are based on various techniques that include adaptive modulation and coding, allocation of multiple time slots per user, in addition to dual-carrier downlink and dual-antenna terminals in evolved EDGE.

In order to meet the forecasted growth of cellular subscribers and the need for faster and more reliable data services, the third generation Universal Mobile Telecommunication System (UMTS) was developed and standardized in 1999, based on a code division multiple accessing (CDMA) air interface. In a UMTS network, the frequency reuse factor is one, and thus all users in the network share the same frequency band at the same time by using different spreading/scrambling codes in order to limit the level of intracell and intercell interference in the network. The Wideband CDMA (WCDMA) mode of UMTS is currently being widely deployed by cellular operators all over the world with more than 500 million subscribers in more than 130 countries [4]. WCDMA provides higher spectral efficiency than GSM/GPRS/EDGE, with peak downlink data rates theoretically up to 2 Mbps in 3GPP Release'99, and beyond 10 Mbps in 3GPP Release 5. Practical bit rates are up to 384 kbps initially, and beyond 2 Mbps with Release 5 [5]. High Speed Packet Access (HSPA) refers to two enhancement technologies for UMTS networks: High Speed Downlink Packet Access (HSDPA) with peak bit rates up to 14.4 Mbps in the downlink and High Speed Uplink Packet Access (HSUPA) with peak bit rates up to 5.7 Mbps in the uplink. HSPA+, referred to as enhanced HSPA, can provide peak bit rates up to 84 Mbps in the downlink and 21 Mbps in the uplink. The high data rates achieved by HSPA and HSPA+ are based on various advanced features that include intelligent fast scheduling at the base station (BS), adaptive modulation and coding with high-order MQAM modulation schemes, fast data retransmission over the air interface, and multiple antenna techniques such as spatial multiplexing in addition to open loop and closed loop transmit diversity.

The 3GPP Long-Term Evolution (LTE) has been standardized as the next generation of cellular technologies following UMTS/HSPA+ on the evolution track. The LTE standard is based on an orthogonal frequency division multiple accessing (OFDMA) air interface and is capable of providing notably high peak data rates up to 75 Mbps in the uplink and 300 Mbps in the downlink. At the same time, the Wireless Interoperability for Microwave Access (WiMAX) wireless technology is being further developed as an all-IP network with an OFDMA air interface, to provide high data rate broadband wireless mobile access [6]. WiMAX evolved from a last mile wireless access technology to a broadband wireless access technology, with nomadic and mobile connectivity as standardized in IEEE 802.16d and IEEE 802.16e, respectively. Currently, standardization activities resulted in developing the technical specifications for the IMT-Advanced technologies LTE-Advanced and WiMAX IEEE 802.16m with peak bit rate capabilities exceeding 1 Gbps in the downlink.

1.2 Orthogonal Frequency Division Multiple Access

Orthogonal frequency division multiplexing belongs to the family of multicarrier modulation schemes. It is based on dividing the transmitted bitstream into multiple substreams and sending these over different orthogonal subcarriers, also called subchannels. In OFDM, the number of subcarriers is selected such that each subcarrier has a bandwidth less than the coherence bandwidth of the channel as illustrated in Fig. 1.1, in order for the subcarriers to experience relatively flat fading and, thus, avoid intersymbol interference. The subcarriers in OFDM are not required to be contiguous as in Fig. 1.1. Thus, a large continuous block of spectrum is not needed for high rate multicarrier communications, and several contiguous blocks of smaller size can be used instead. This provides flexibility in spectrum allocation and spectrum management.

Figure 1.1 Channel variation over the different subcarriers.

Multicarrier modulation schemes using overlapping but orthogonal subcarriers were investigated since the 1960s [7, 8]. However, the use of such schemes at the time was practically difficult due to the large number of filters and modulators required [9]. A major reduction in the implementation complexity of OFDM transmitters and receivers was achieved by using discrete Fourier transform (DFT) operations to modulate and demodulate OFDM signals [10]. With the DFT implementation, frequency division is achieved by baseband processing instead of bandpass filtering. An OFDM transmitter and receiver implementation using fast Fourier transform (FFT) blocks is shown in Fig. 1.2. OFDM modulation is used in cable access networks, such as Asymmetrical Digital Subscriber Lines (ADSL) and Hybrid Digital Subscriber Lines (HDSL) [11–13], in addition to several wireless communication systems, such as Wireless LANs (WLANs) [14], Digital Video Broadcasting (DVB) [15], LTE, and WiMAX. A historical overview of OFDM can be found in Ref. [16].

Figure 1.2 OFDM with IFFT/FFT implementation.

The main advantages of OFDM include robustness against multipath fading, exploitation of frequency diversity, facilitation of advanced multiple input multiple output (MIMO) techniques, in addition to adaptive loading per subcarrier and efficient multiple accessing. The basic idea of adaptive loading is to vary the data rate and power assigned to each subcarrier depending on its channel gain. Hence, the power and rate associated with each subcarrier can be optimized to maximize the rate for a given maximum transmit power or to minimize the transmit power for a given target rate. This can be achieved by using a variable-rate variable-power modulation scheme like MQAM. The power loading on the different subcarriers was first investigated in Ref. [17]. Orthogonal frequency division multiple access (OFDMA) is an extension of OFDM based on dividing the subcarriers among users in order to exploit multiuser diversity gains, which made it an attractive choice for cellular broadband wireless access systems such as LTE and WiMAX. A major challenge to exploit the advantages of OFDMA in wireless broadband communication systems is the efficient joint allocation of subcarriers and powers among users in the uplink and downlink in order to meet target quality of service objectives such as target bit rate, latency, and/or fairness constraints. This requires the design of dynamic and optimized resource allocation schemes that can adapt based on varying channel and interference conditions and that can be enhanced to exploit cooperation opportunities among base stations and users while maintaining relatively low complexity suitable for practical implementation.

To this end, this book presents a comprehensive study of resource allocation and scheduling techniques in OFDMA wireless networks (the terms “resource allocation” and “scheduling” are used interchangeably throughout the book). Although the investigation of both the uplink and downlink directions is of equal importance, the main focus in this book will be on the uplink. In fact, the increase in demand for mobile applications with bidirectional rate and delay requirements has mandated the need for efficient uplink scheduling algorithms in OFDMA wireless systems. This book treats the area of uplink OFDMA resource allocation from various perspectives that include the following: centralized and distributed, instantaneous and ergodic, optimal and suboptimal, single cell and multicell, cooperative and noncooperative, in addition to different combinations of these variants.

1.3 Organization of this Book

An overview of the book outline is shown in Fig. 1.3. Chapter 2 is a background chapter that presents a survey of downlink resource allocation and scheduling techniques in OFDMA wireless networks. In Chapter 3, the problem of ergodic sum-rate maximization with continuous rates in OFDMA uplink is formulated and solved. Power and rate constraints are considered, and the achievable rate region is investigated. Chapter 4 presents the formulation and solution of the ergodic sum-rate maximization problem with discrete rates. This represents an extension of Chapter 3 to a scenario where a limited number of achievable rates are available due to a predefined set of modulation and coding schemes. In Chapter 5, the solutions of Chapters 3 and 4 are extended to general utility maximization, where the utility of a user is a function of its rate. Chapter 6 presents suboptimal scheduling algorithms that overcome the practical limitations of the optimal solutions derived in Chapters 3 –5. The suboptimal algorithms are shown to achieve a close performance to the optimal solutions, with a considerably reduced complexity. In Chapter 7, the suboptimal algorithms are applied with various utility functions. An emphasis is given to utilities ensuring proportional fairness in order to provide fair access to the resources among the users.

Figure 1.3 Book outline.

Chapters 3–7 deal with fully centralized scheduling. Chapter 8 discusses the implementation of the algorithms in a distributed base station scenario. This chapter constitutes an intermediate step between centralized scheduling where full control is given to the BS, and distributed scheduling where users take part in scheduling decisions. Chapter 9 treats the scenario of distributed resource allocation with user cooperation. Users are assumed to be able to successfully exchange information. Hence, this represents a scenario with a limited coverage area, for example, the area covered by a single remote radio head (RRH) in a distributed base station system. The users implement the algorithms of Chapters 6 and 7 in a distributed way, and achieve results close to centralized scheduling with a limited amount of exchanged information. Chapter 10 consists of investigating distributed resource allocation without user collaboration. The proposed approach is based on channel sensing and probabilistic transmission. It consists of a scheduling phase followed by a transmission phase. The approach leads to complete avoidance of collisions during transmission, while reducing the collision probability during the scheduling phase.

Chapter 11 treats the problem of centralized scheduling in a multicell scenario. The resource allocation problem is formulated as a pricing game between BSs and the convergence to a Nash equilibrium is shown. Enhancements in the presence of a central controller are demonstrated. Suboptimal scheduling techniques are presented to overcome the limitations of the game theoretic model. The suboptimal techniques rely on pricing-based power control in the presence and absence of BS collaboration, in addition to probabilistic scheduling in the latter case. Chapter 12 investigates the problem of distributed scheduling in a multicell scenario. Techniques derived in Chapter 11 are applied to the distributed scheduling scenario presented in Chapter 9. In addition, a transparent pricing scheme is presented in the case with BS collaboration, where the prices are completely oblivious to the users.

Chapter 13 presents an overview of resource allocation in the state-of-the-art wireless systems LTE and WiMAX, and describes the applicability of the presented resource allocation techniques in these systems. Finally, open research directions in the area of OFDMA resource allocation are outlined in Chapter 14.

Chapter 2

Background on Downlink Resource Allocation in OFDMA Wireless Networks

This chapter is a background chapter that presents a survey of downlink resource allocation and scheduling techniques in OFDMA wireless networks. In the subsequent chapters of this book, background on relevant resource allocation techniques for both OFDMA uplink and downlink will be presented and analyzed. However, the main focus will be on the uplink, while noting that several of these techniques can be applied to the downlink direction also.

In this chapter, the main aspects of downlink resource allocation are summarized, and the interested reader can find an overview of various OFDMA downlink resource allocation and scheduling scenarios: centralized and distributed, instantaneous and ergodic, optimal and suboptimal, single cell and multicell, cooperative and noncooperative, in addition to different combinations of these variants. Applications to the LTE system are presented, and the additional constraints imposed by the LTE standard are outlined.

The chapter is organized as follows. Centralized scheduling techniques within a single cell are described in Section 2.1. Scenarios with distributed scheduling are presented in Section 2.2. Section 2.3 surveys scheduling techniques in a multicell scenario where intercell interference represents a major challenge to be addressed. The chapter is summarized in Section 2.4.

2.1 Centralized Single Cell Scheduling

In centralized scheduling, both in the downlink and uplink, the base station (BS) is responsible for the scheduling process. Decisions are made at the BS and communicated to mobile users. Centralized single cell downlink resource allocation in cellular OFDMA systems has been widely investigated in the literature [18, 19], Forward-time Population Genetics Simulations: Methods, Implementation, and Applications, Bo Peng, Marek Kimmel, and Christopher I. Amos. © 2012 Wiley-Blackwell. Published 2012 by John Wiley & Sons, Inc. 11 [20–27]. Topics investigated include sum-rate maximization, general utility maximization, achieving a desired quality of service (QoS) with minimum power, and ergodic sum-rate maximization. In sum-rate maximization, which could be considered as an extension of the centralized maximum C/I scheduling scheme [28], it was shown that the optimal solution is to separate subcarrier allocation from power allocation: each subcarrier is allocated to the user with the best channel condition and power is allocated by water-filling over the subcarriers [19, 20, 24]. To provide more fairness, utility maximization is investigated, where the utility could be a function ensuring more fairness than using only the rate [19, 20, 24]. The logarithm of the rate, for example, is shown in Refs [19, 20] to achieve proportional fairness (PF) [29]. These works make use of the classical Shannon capacity (or some formula derived from it) to model the rate. Instead of trying to achieve the maximum capacity, another objective is to achieve a desired QoS while minimizing the required transmit power. This is done by bit loading over the allocated subcarriers [18, 21, 25, 30]. Most of the existing work focuses on channel aware resource allocation assuming the channel state information (CSI) is known at the scheduler, and that there is always data to transmit. However, some existing work deals with channel-aware queue-aware algorithms where the buffer lengths and the queue states of each user are taken into account [23].

In centralized instantaneous scheduling, a certain utility (e.g., sum-rate) is maximized at each scheduling instant. The BS takes advantage of the random variations of the channel states of the various users over the OFDMA subcarriers in order to perform efficient resource allocation. This way, the BS takes advantage of the frequency and multiuser diversity dimensions [18–20]. Ergodic scheduling uses an additional degree of freedom. With ergodic scheduling, the time dimension is used in addition to the frequency and multiuser diversity dimensions [26, 27, 31], and hence the interest is in long-term performance. In both the instantaneous and ergodic scheduling scenarios, the utility maximization is used either using continuous rates (Shannon capacity), or a discrete set of rates corresponding to a finite number of modulation and coding schemes (MCS).

The scheduling problem in the uplink is more challenging than that in the downlink due to the distributed power constraint: in the downlink, the power has a centralized nature because power allocation is done at a central entity, the BS, which is the single power source in a single cell. In the uplink, each user is a power source by itself. Hence, the power has a distributive nature and should be considered on a per-user basis.

The optimal solution in instantaneous sum-rate maximization in OFDMA uplink requires the computation of Lagrangian parameters enforcing the power constraint for each user being scheduled. In the downlink, a single Lagrangian parameter is needed since only one power constraint is available, the power constraint for the BS [26]. These parameters are generally computed using subgradient techniques [27, 32]. The convergence of subgradient iterations for a large number of users at each scheduling interval leads to a considerable complexity. This complexity can be reduced significantly by resorting to ergodic scheduling and taking advantage of the time dimension as an additional degree of freedom in the scheduling process.

Ergodic weighted sum-rate maximization in downlink OFDMA systems is considered in Refs [26, 27], subject to maximum power constraints. Ergodic weighted sum-rate maximization is also considered in Ref. [33] in the context of an ad hoc cognitive radio (CR) network. In Ref. [33], additional minimum rate constraints are added, in order to ensure fairness for users by allowing them to achieve a minimum target rate. The solution approach in Refs [26, 33, 27] consists of transforming the weighted sum-rate maximization problem into a convex utility maximization problem, formulating and solving the dual problem, and proving that the duality gap is zero. Hence, the solution of the dual problem corresponds to the solution of the primal problem [34]. To enforce the maximum transmit power constraint, in addition to the minimum rate constraint in Refs [33, 27], the Lagrangian parameters are computed via subgradient iterations as described in Ref. [35].

To perform these iterations with ergodic scheduling, if the fading probability distribution function (pdf) is known, enough samples can be generated offline to be used in the iterations of these Lagrangian parameters. The obtained Lagrangians can then be used in instantaneous resource allocation without recomputation as long as the fading pdf remains unchanged. In case the pdf is unknown and offline training is not possible, convergence can be obtained online by using running averages over the instantaneous fading realizations. In this case, it is not required that the BS knows the fading pdf, as long as it is aware of the instantaneous fading realizations. Such an online training approach is shown in Ref. [36] to lead to the same solution as the offline case in the context of ad hoc peer-to-peer cognitive radio networks. However, in instantaneous utility maximization, the Lagrangians have to be computed at each scheduling instant. This requires subgradient iterations in order to compute these parameters at every transmission time interval (TTI). Ergodic utility maximization allows to avoid this overhead. It should be noted that in both ergodic and instantaneous scheduling, the rate, subcarrier, and power allocations are performed at every fading state. The difference is in computing the Lagrangians: With ergodic scheduling, the optimal rate, subcarrier, and power allocations are computed at each fading state using the current Lagrangian parameters, acting as power prices in order to regulate the transmit power; at a slower timescale, the power prices are adjusted to meet the average power constraints, similarly to the approach described in Ref. [37]. However, with instantaneous scheduling, the power prices are adjusted at every fading state.

2.1.1 Continuous Versus Discrete Rates

The Shannon capacity formula for Gaussian channels, log 2(1 + SNR), where SNR denotes the signal-to-noise ratio, is widely used in the literature, for example [19, 20, 24, 27, 26, 33]. This capacity expression is based on the assumption of infinite length codewords generated according to a normal distribution [38]. However, in a practical system, only a discrete set of rates are achievable due to a fixed number of MCS.

Most of the algorithms in the literature that use discrete rates treat the problem of the transmit power minimization given per user minimum rate constraints [18, 39, 30, 25]. This problem is the dual formulation of the sum-rate maximization problem, which consists of maximizing the sum-rate given a maximum power constraint. In Ref. [40], an algorithm proposed for power minimization is extended to the case of sum-rate maximization. The main focus in the literature is on downlink resource allocation [18, 39, 25, 40] with a few papers treating the uplink problem [30], where the power minimization problem is considered. These algorithms follow a three-steps approach to resource allocation with discrete rates: estimating the number of subcarriers to be allocated to each user, selecting and allocating the appropriate subcarriers, and using bit loading to allocate the power on these subcarriers. A comprehensive survey of existing algorithms is presented in Ref. [9]. Selecting the best subalgorithm in the literature for each of the three steps, a new algorithm is developed in Ref. [9], where the focus is on the downlink power minimization problem. However, indications on extending the algorithm to the sum-rate maximization case are discussed based on the approach of Ref. [40].

The algorithms in Refs [18, 39, 30, 25, 40, 9] correspond to instantaneous scheduling with discrete rates. The problem of ergodic sum-rate maximization with discrete rates is investigated in Ref. [26] for the downlink in addition to the continuous rates scenario. Due to the discontinuity of the maximization function, the problem becomes harder to solve due to the loss of convexity. However, it is shown in Ref. [26] that the maximization problem with discrete rates is quasiconcave and the optimal dual solution can be reached with zero duality gap as in the continuous rates scenario.

2.1.2 Optimal Versus Suboptimal Scheduling

Although the ergodic sum-rate maximization solutions are simpler to implement than the optimal instantaneous sum-rate maximization solutions, they require an initiation phase to compute the Lagrangians via iterative subgradient iterations, and a tracking of the channel probability density function to repeat the calculations when necessary. The computational load increases at the BS with the number of users, since the optimal solution necessitates that the transmit power dedicated to each user on each allocated subcarrier be computed every TTI, because the optimal solution is determined by water-filling. Hence, the investigation of suboptimal algorithms that achieve a good performance has received considerable attention in the literature [19, 20, 24, 25, 40].

It should be noted that when the number of subcarriers increases, the scheduling complexity increases, even with linear complexity algorithms. In practice, the signaling load will also increase with the number of subcarriers. Hence, resource allocation is not performed on a subcarrier by subcarrier basis in state-of-the-art OFDMA-based systems. Instead, subcarriers are assembled into groups of consecutive subcarriers, called subchannels in WiMAX or resource blocks (RB) in LTE for example, and allocation is performed on an RB basis. In LTE, the available spectrum is divided into RBs consisting of 12 adjacent subcarriers [41]. In WiMAX, 192 data OFDM subcarriers are distributed in 16 subchannels of 12 subcarriers each. Each subchannel is made of four groups of three adjacent subcarriers each [42]. An example of grouping subcarriers into blocks is shown in Fig. 2.1.

Figure 2.1 Adjacent subcarriers grouped into blocks.

As stated previously, utility maximization is widely investigated [19, 20]. In addition to sum-rate maximization, where the utility of a user is its achieved rate, proportional fair scheduling is widely investigated in the literature, where the utility is the logarithm of user rate. The importance of proportional fair scheduling in providing fairness is explained in Ref. [43] by resorting to a game theoretical interpretation. The Nash bargaining problem (NBP) [44] is a well-known scenario in game theory. Players in the NBP negotiate to maximize their payoffs, given a set of shared resources. The optimal solution of the NBP, the Nash bargaining solution (NBS), consists of distributing the resources in a way to maximize the product of the payoffs [45]. It was shown that PF scheduling is equivalent to the implementation of the NBS in the resource allocation of wireless communication systems, the payoff of each user being its rate [43, 46]. PF scheduling is widely investigated in the literature, mainly in the framework of centralized resource allocation [29, 19]. With OFDMA adopted as the accessing scheme of next generation cellular systems, for example, 3GPP LTE and mobile WiMAX (IEEE 802.16e), several applications of PF to OFDMA have been studied [47–49].

2.2 Distributed Scheduling

In centralized scheduling, resource allocation decisions are made at a central entity, the base station. In current and future broadband wireless access systems, users are expecting ubiquitous and seamless access to a variety of bandwidth demanding services. Mobile devices capable of supporting multiple standards are becoming more common in the market. Current research is not only ongoing on enhancing scheduling techniques within a given network, but also on optimizing the resource allocation in heterogeneous networks. This involves selecting the best network to serve a mobile user, among several networks with different access technologies such as GSM/EDGE, UMTS/HSPA, WiMAX, and WLAN [50–52].

Conversely to centralized resource allocation, mobile devices have more autonomy in making transmission decisions in distributed schemes. Distributed scheduling is usually studied in the context of ad hoc networks, relay-based networks, and sensor networks [53–55]. Distributed channel allocation schemes for wireless local area networks (WLANs) are also an active topic of current research [56, 57]. In addition, CR networks have gained increasing importance, and the problem of resource allocation in CR networks is being widely investigated [58–63]. CR, ad hoc, and sensor networks are distributed in nature. However, distributed resource allocation has also been implemented in infrastructure-based networks where users are connected to a central BS [64, 65].

In OFDMA distributed scheduling in the presence of a certain infrastructure, distributed antennas are placed throughout the cell area while being connected to a central BS. This corresponds to a distributed BS scenario. The concept of distributed base stations (DBSs) and remote radio heads (RRHs) emerged to increase the coverage and capacity of wireless networks in a cost-effective way. It consists of a centrally located BS enclosure connected to RRHs via fiber optic cables [66]. In the existing literature, the terms distributed base station and distributed antenna system (DAS) are used interchangeably. DBSs were initially proposed to enhance indoor coverage of cellular systems where a building is treated as a single cell with several distributed antennas rather than either multiple pico cells each with a dedicated antenna or as a single cell with one central antenna [67]. The DBS approach allows avoiding excessive handovers in the first case and significant fading in the latter. The coverage and capacity of DBSs in an indoor WCDMA system was investigated in Ref. [68] for several types of antennas. In a multicell system with DBSs, it was shown that maximum ratio combining (MRC) in the uplink achieves a considerable capacity and coverage enhancement, but simultaneous transmission in the downlink reduces performance since it increases the intercell interference [69]. A solution for this problem was proposed in Ref. [70], where it was found that selecting only the RRH with best channel to the user ensures the best downlink performance with DBSs. A similar conclusion was reached in Ref. [71] where transmitting from the RRH with the best channel was shown to outperform the case of using the RRH as a relay while transmitting the signal directly from the BS. These results are validated from an information theoretic standpoint in Refs [72, 73], where selective transmission (from only the RRH with best channel to user) in the downlink was compared to maximum ratio transmission (using all the RRHs).

It should be noted that, in a practical scenario, installing RRHs at desired locations (e.g., equidistant along the cell boundary) might not be possible. Therefore, the performance of random placement of RRHs throughout the cell is investigated in Refs [74, 75], in terms of outage probability, as a lower bound on the actual performance. Interestingly, it is found that as the number of RRHs increases, the performance converges to that of regularly deployed RRHs. In fact, in the case of both fixed and random RRH locations, the gains achieved by a DBS system are shown to increase with the number of RRHs up to a certain limit where the gain obtained after using an additional RRH is negligible. This limit is considered to be four and seven RRHs per cell in Refs [70] and [72], respectively, for the regular RRH positions, and seven in Ref. [75] for the random RRH positions.

2.3 Scheduling in Multicell Scenarios

In Sections 2.1 and 2.2, the main focus is on a single cell scenario and hence intercell interference is not considered. The emphasis is on mitigating intercell interference, since intracell interference is not an issue in OFDMA due to the orthogonality of the subcarriers and the exclusivity of subcarrier allocations in each cell. To limit the effects of interference in multicell scenarios, several techniques for reusing the radio frequencies are investigated in the literature. Static reuse schemes are based on fractional frequency reuse (FFR) where a cell is divided into an inner area with the same frequencies reused in all cells and an outer area where a subset of the frequencies is reused [76]. Such an FFR scheme is illustrated in Fig. 2.2, where the entire bandwidth is divided into four segments. Part of the RBs is used with reuse of 1 in the cell center region, whereas reuse 3 is applied in regions A, B, and C [77]. An extension of the FFR reuse scheme for multicell scheduling in OFDMA networks is presented in Ref. [78], where each cell is subdivided into three regions: an inner region with the same frequencies reused in all cells (reuse 1), a middle region with an FFR with reuse 3, and an outer region with an FFR with reuse 9. Better interference mitigation is shown to be achieved with the enhanced FFR scheme of Ref. [78].

Figure 2.2 Fractional frequency reuse.

More efficient schemes consist of dynamic frequency reuse where all the frequencies are allowed to be used in all cells and elaborate techniques are applied for interference mitigation or avoidance. In Ref. [79], downlink scheduling in OFDMA is used with each BS randomly turning on or off certain subcarriers to mitigate interference. In Ref. [80], downlink transmit power allocation in a multicell wireless network under a sum-capacity maximization criterion and peak power constraints at each BS is investigated. It is shown that the optimal power control is binary (on–off) for two cells, and that binary power control yields a negligible capacity loss for more than two cells. However, scheduling is not used with power control in Ref. [80]. This has been explored in Ref. [81], where a distributed algorithm for power allocation and scheduling in multicell networks is proposed. Intercell coordination is applied to maximize the overall system capacity by deactivating cells that do not offer enough capacity to outweigh interference caused to the network. A single frequency is considered in Ref. [81], and the application of the approach to OFDMA networks necessitates the use of subcarrier allocation to exploit the frequency diversity gain. In Ref. [82], resource allocation is considered in the downlink of multicell OFDMA systems without BS cooperation. A price that increases with the transmit power is used in order to reduce the interference. The prices are used as a sort of power control scheme to reduce transmission power.

2.3.1 Multicell Scheduling in LTE

LTE performs interference mitigation using power control. The LTE power control scheme is detailed in Ref. [83], and its evaluation via simulations is described in Ref. [84]. LTE power control does not necessitate coordination between BSs for the purpose of interference mitigation. However, LTE allows communication between BSs over the X2 interface [85]. Intercell interference coordination (ICIC) between LTE BSs can be performed using the overload indicator (OI) and the high interference indicator (HII). The OI indicates the interference level received on each RB in the cell sending the OI, whereas the HII indicates the occurrence (or not) of high interference on each RB [85]. The BS receiving the OI and HII would then try to perform scheduling while avoiding allocation on the RBs subjected to high interference in its neighbor cells.

In the current LTE standard, the minimum latency for the exchange of information between BSs is 20 ms, whereas RBs are allocated on a 1 ms basis (duration of one TTI). This makes real-time processing of interference cancellation data from adjacent BSs unfeasible [86]. In Ref. [87], LTE resource allocation is performed in two levels: a fast (1 ms TTI) intracell level that does not involve ICIC, and a slow intercell level (duration of several TTIs) involving ICIC. The HII indicator is used in a proactive way in order to signal “protected bands” not to be allocated in neighbor cells. When the proactive scheme fails to select perfectly nonoverlapping protected bands, the OI indicator is used to request neighbor cells to refrain from scheduling UEs detected causing high interference. This scheme is shown in Ref. [87] to lead to enhanced performance. However, it assumes that all RBs are allocated to a single user per cell at a given TTI.

Other interference coordination and cancellation techniques applicable to the current LTE standard are surveyed in Ref. [86] (applicable to both uplink and downlink, unless otherwise specified): power control, static and adaptive fractional frequency reuse, MIMO (LTE downlink), multiuser MIMO (LTE uplink), space division multiple access (SDMA), interference cancellation (LTE uplink), opportunistic spectrum access, organized beamforming, sphere decoding (LTE uplink), and dirty paper decoding (LTE uplink). It should be noted that scheduling algorithms in general, including ICIC algorithms, are out of the scope of the LTE standard. The LTE standard has been developed to support a wide range of interference coordination approaches while allowing various types of scheduler operation, including channel state dependent (opportunistic) schedulers [87]. However, the benefits of channel aware scheduling discussed in Sections 2.1 and 2.2 tend to limit the additional benefits of ICIC [87], and the benefits of ICIC may not justify the added complexity of intercell communications [77].

In LTE, although the standard does not explicitly prescribe the timescale at which ICIC should operate, ICIC is currently performed on a scale of tens to hundreds of milliseconds, whereas fast scheduling is performed each millisecond [87]. Fast ICIC performed on the millisecond scale is beyond the current LTE standard and may be applicable to LTE-Advanced, where faster ICIC control is considered.

In Ref. [88], a beam coordination approach is proposed for LTE-Advanced, where each BS groups users served by the same beam in a way to reduce interference and enhance cell rate and edge users rate. The approach of Ref. [88] is based on feedback from users in each cell, and does not require inter-BS communication. It can be considered to be at the low end of coordinated multipoint (CoMP), which is a form of network MIMO. Major research is ongoing for network MIMO within the framework of LTE-Advanced, such as [89–92]:

Synchronization of jointly processed terminals in time and frequency, and detection under synchronization offsets.Multisector channel estimation, feedback of CSI to BSs, and impact of imperfect CSI on network MIMO.Performance of network MIMO under a limited backhaul infrastructure between cooperating BSs.Cooperative scheduling for network MIMO.

It should be noted that in the CoMP and network MIMO literature [93,94], sometimes a central control unit is assumed to coordinate the actions of BSs. This corresponds to a hierarchical level higher than the BSs in the network organization. In this case, the centralized approach corresponds to a scenario where the user equipment (UE) estimates the channel information from all the cooperating BSs and feeds it back to the central control unit, where scheduling operations are performed accordingly [93,94]. The scenario where BSs take actions without the presence of a central control unit is referred to as “decentralized.” In a decentralized scenario, the UE feeds back the channel information to all the cooperating BSs. Therefore, each BS gathers all the available feedback information, including those related to other BSs [93,94].

2.4 Summary

In this chapter, a survey of downlink resource allocation in OFDMA systems was presented. Three major topics were studied. The first is related to centralized scheduling within a single cell. Solutions based on instantaneous and ergodic scheduling were presented, in addition to a discussion of suboptimal scheduling techniques. The second topic is related to distributed scheduling where the subject of distributed antenna systems in OFDMA was analyzed. The third topic corresponds to multicell scheduling, where efficient interference mitigation techniques are needed in order to reduce the impact of intercell interference on the resource allocation process. Applications of the multicell scheduling schemes to LTE were presented, and the additional constraints imposed by the LTE standard were outlined.

Chapter 3

Ergodic Sum-Rate Maximization with Continuous Rates

In this chapter1, the problem of uplink resource allocation in single cell OFDMA networks is discussed. In particular, the focus is on ergodic sum rate maximization and on deriving its optimal solution subject to per-user power and rate constraints. The presented optimal solution provides a bound on performance for practical resource allocation algorithms. In addition, the characteristics of the achievable rate region are determined. The chapter is structured as follows. Section 3.1 presents a review of the related literature and outlines the main topics of this chapter. The problem is formulated in Section 3.2 and the solution is presented in Section 3.3. The achievable rate region is determined in Section 3.4. Numerical results are presented and analyzed in Section 3.5. Finally, Section 3.6 summarizes the chapter.

3.1 Background

Resource allocation in OFDMA has been widely investigated in the downlink both in the case of instantaneous rate maximization (e.g., [18-20, 23, 24]) and ergodic rate maximization (e.g., [27, 26]). The solution is generally divided into two parts: subcarrier allocation and power allocation. The solution described in Ref. [19] consists of allocating each subcarrier to the user with the best channel condition on that subcarrier and allocating power by water-filling over the subcarriers.

The scheduling problem in the uplink is more challenging than that in the downlink due to the distributed power constraint: in the downlink, the power has a centralized nature because power allocation is done at a central entity, the base station (BS), whereas in the uplink, the power has a distributive nature and should be considered on a per-user basis. Instantaneous scheduling in the uplink was investigated in Refs [95, 96, 47, 97]. The allocation problem is divided into two subproblems in Ref. [95]. A greedy algorithm is proposed with water-filling used to allocate power for each user on its allocated subcarriers. Then using the marginal functions, an optimal (user, subcarrier) pair is found. Steps are repeated until all subcarriers are allocated. In Ref. [96], fairness is added to the approach of Ref. [95] by allocating subcarriers to a given user until its required rate is reached then the user is excluded from the allocation of the remaining subcarriers. The algorithm proposed in Ref. [47] has similar steps to that of Ref. [95], but differs in that it performs water-filling for each user on all unallocated subcarriers in addition to the subcarriers allocated to that user before searching for the optimal (user, subcarrier) pair. The algorithms in Refs [95, 47, 96] are suboptimal. In Ref. [97], instantaneous sum-rate maximization is formulated into a convex optimization problem and solved using a dual decomposition approach, then a set of suboptimal algorithms are presented and compared, due to the prohibitive complexity of implementing the optimal solution.

In this chapter, maximization of weighted uplink ergodic sum-rate in OFDMA systems is considered. In weighted ergodic sum-rate maximization, advantage is taken of the time dimension in the optimization in addition to the frequency and multiuser diversity dimensions [26]. Ergodic maximization was considered in Ref. [33] in the context of an ad hoc cognitive radio network. The total weighted rate in the system was considered with rate constraints on the primary users.

The main topics discussed in this chapter are summarized as follows:

1.