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Resource allocation in OFDM/OFDMA cellular networks: protocol design and performance analysis

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Resource allocation in OFDM/OFDMA cellular networks: protocol design and performance analysis

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Content RESOURCE ALLOCATION IN OFDM/OFDMA CELLULAR NETWORKS: PROTOCOL DESIGN AND PERFORMANCE ANALYSIS by Yu-Jung Chang A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) December 2008 Copyright 2008 Yu-Jung Chang Dedication The dissertation is dedicated with a loving heart to my wife Yi-ping, my parents C. L. Chang and C. W. Tseng, and my brother Yu-hao. ii Acknowledgements Before I decided to pursue my Ph.D. study, I consulted a professor whom I highly trusted for his advice on making this move. He said, \There may be numerous frustrating mo- ments during the course of the study, but you will not regret it after completing the process, as none of my friends that I know did." I took the advice and that's how it all began. Five years later, I am sitting here, proud and condent to say the same: \Even though there are many moments of struggle, hesitation, and self-doubt, I don't regret that I chose to go through this process." Ph.D. study is far beyond simply a training of intellectual maturity and learning of how to conduct research. It is a test and tempering of one's determination, perseverance, and commitment. If I now possess any of this quality, it is my advisor Prof. C.-C. Jay Kuo that I am most indebted to. He constantly demonstrated himself the utmost commitment to students, to work and to excellence, which, to me, is unparalleled. The example that he sets has had immense positive in uence on everyone who works with him. I am also grateful for his continuous nancial support for me. In tough times of funding, this achievement and commitment is much rarer and more precious than it may seem. iii I would also like to thank my collaborators, notably, Prof. Feng-Tsun Chien and Dr. Jerey Z. Tao. Discussion with them led to many ideas that laid the foundation of a later publication. I have also learned many technical writing skills from them, as well as the meticulousness in proofreading and typesetting. Collaboration with them was an intellectually enjoyable event. I would like to express my deep appreciation to my thesis guidance committee mem- bers, Profs. Antonio Ortega, Michael Neely, Zhen Zhang and Ramesh Govindan, for their valuable comments and thoughts on improving the presentation and contents of the thesis. My fellow labmates have provided me with an environment in which discussion was encouraged, information was exchanged, and emotions were supported on a personal level. To name a few: Wan-Jen (Athena) Huang, Fu-Hsuan Chiu, Yu-Hao (Roger) Chang, Man- On (Simon) Pun, Usman Riaz, and Layla Tadjpour. Finally, my profound gratitude goes to my wife, Yi-ping, who is my best company, friend, and partner for life. My parents have supported me both emotionally and nan- cially throughout the study, to which I am deeply indebted. I am also grateful to my spiritual teacher Wu Jue Miao Tian for his teaching that has fostered my development of a bigger heart, a sense of responsibility as a Ph.D. for the society and people, and the inner peace and serenity that has proved instrumental during the course of the study. iv Table of Contents Dedication ii Acknowledgements iii List Of Tables viii List Of Figures ix Abstract xii Chapter 1: Introduction 1 1.1 Signicance of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Review of Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Contribution of the Research . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Outline of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter 2: Research Background 15 2.1 OFDM and OFDMA Transmission Systems . . . . . . . . . . . . . . . . . 15 2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.2 IEEE 802.16/WiMAX . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Centralized and Distributed Multiple Access . . . . . . . . . . . . . . . . . 18 2.2.1 Centralized Access . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1.1 Opportunistic Scheduling . . . . . . . . . . . . . . . . . . 19 2.2.2 Distributed Access . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.2.1 Slotted Aloha . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.2.2 802.11 Distributed Coordination Function . . . . . . . . . 21 2.2.2.3 802.16 Distributed Uplink . . . . . . . . . . . . . . . . . . 22 2.3 Markov Chain Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Modeling of Wireless Fading Channels . . . . . . . . . . . . . . . . 24 2.3.2 Modeling of Random Backo Schemes . . . . . . . . . . . . . . . . 25 2.4 Quality of Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.1 Service Dierentiation . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.2 QoS Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 Multi-cell Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.1 Cell Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 v 2.5.2 Cell Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6 Graph Theoretic Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.6.1 Classical Channel Assignment . . . . . . . . . . . . . . . . . . . . . 35 2.6.2 Reuse-One OFDMA Channel Assignment . . . . . . . . . . . . . . 36 Chapter 3: Cross-layer QoS Analysis of Opportunistic OFDM-TDMA and OFDMA Downlink Networks 39 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.1 Flow Control Regulation . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.2 Multiple Access and Scheduling . . . . . . . . . . . . . . . . . . . . 45 3.2.3 Bit Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 Performance Analysis and Comparison . . . . . . . . . . . . . . . . . . . . 49 3.3.1 Bit Rate and BER Analysis . . . . . . . . . . . . . . . . . . . . . . 49 3.3.2 Packet Average Throughput and Delay Analysis . . . . . . . . . . 51 3.3.3 Packet Maximum Delay Analysis . . . . . . . . . . . . . . . . . . . 58 3.3.3.1 OFDMA I and OFDM I . . . . . . . . . . . . . . . . . . . 59 3.3.3.2 OFDMA II and OFDMA III . . . . . . . . . . . . . . . . 62 3.3.3.3 OFDM II and OFDM III . . . . . . . . . . . . . . . . . . 65 3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Chapter 4: Opportunistic Access with Random Subchannel Backo (OARSB) for OFDMA Uplink 78 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3 Proposed OARSB Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 Delay and Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . 85 4.4.1 Markov Chain Model . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.2 Delay Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.3 Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Chapter 5: Multi-Cell OFDMA Downlink Resource Allocation Using A Graphic Framework 100 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.2 Research Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2.1 Multi-cell OFDMA Networks . . . . . . . . . . . . . . . . . . . . . 104 5.2.2 The Diversity Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2.3 Inter-cell Interference Coordination (ICIC) . . . . . . . . . . . . . 106 5.2.4 Base Station Cooperation (BSC) . . . . . . . . . . . . . . . . . . . 107 5.3 System Model and Problem Description . . . . . . . . . . . . . . . . . . . 109 5.3.1 System Model and SINR Derivation . . . . . . . . . . . . . . . . . 109 5.3.2 Multi-cell OFDMA Resource Allocation Problem . . . . . . . . . . 112 5.4 Proposed Solution Framework . . . . . . . . . . . . . . . . . . . . . . . . . 113 vi 5.4.1 The Graphic Approach . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.2 Interference Graph Construction . . . . . . . . . . . . . . . . . . . 114 5.4.3 First Phase: Interference Management . . . . . . . . . . . . . . . . 120 5.4.4 Second Phase: Channel Assignment . . . . . . . . . . . . . . . . . 121 5.5 Proposed Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.5.1 Heuristic Algorithm A1 for the First Phase . . . . . . . . . . . . . 122 5.5.2 Properties of Algorithm A1 . . . . . . . . . . . . . . . . . . . . . . 123 5.5.3 Heuristic Algorithm A2 for the Second Phase . . . . . . . . . . . . 129 5.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Chapter 6: Conclusion and Future Work 150 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 vii List Of Tables 3.1 Multiaccess OFDM modes considered in this work. . . . . . . . . . . . . . 45 3.2 The TDL Channel Model Parameters . . . . . . . . . . . . . . . . . . . . 67 3.3 Parameters of the OFDM System . . . . . . . . . . . . . . . . . . . . . . . 67 5.1 The Diversity Set of MSs in Fig. 5.4. . . . . . . . . . . . . . . . . . . . . . 116 5.2 The Algorithm to Determine the Weight of the Edge (a;b). . . . . . . . . 136 5.3 Heuristic Algorithm A1 to Solve Problem P1. . . . . . . . . . . . . . . . 137 5.4 Heuristic Algorithm A2 to Solve Problem P2. . . . . . . . . . . . . . . . 137 5.5 Simulation Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.6 Five Test Schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 viii List Of Figures 2.1 Multiple access in OFDM-TDMA and OFDMA. . . . . . . . . . . . . . . 17 2.2 Examples of (a) the reducible, (b) the periodic, (c) the irreducible and aperiodic Markov chains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 The Markov chain modeling of a Rayleigh fading channel. . . . . . . . . . 26 2.4 The Markov chain modeling of a random backo procedure. . . . . . . . . 27 2.5 An exemplary multi-cell scenario with inter-cell interference depicted by dotted lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6 A fractional frequency reuse (FFR) scheme. . . . . . . . . . . . . . . . . . 33 2.7 A simple collaboration scenario with 2 BSs and 2 MSs. . . . . . . . . . . . 34 2.8 A hexagonal graph colored by three colors [65]. . . . . . . . . . . . . . . . 36 2.9 A MS-centered graph for OFDMA cellular networks. . . . . . . . . . . . . 37 3.1 (a) A cross-layer QoS-support system model and (b) a queueing system with ow-control regulated streams and preemptive priority servicing, shown for mobile user k. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 A queueing model for OFDM-TDMA or OFDMA. . . . . . . . . . . . . . 52 3.3 A typical OFDM transmission system. . . . . . . . . . . . . . . . . . . . . 53 3.4 Illustration of the continuous-time server process for user k with a total of K users: (a) OFDMA I and (b) OFDM I. . . . . . . . . . . . . . . . . . . 60 3.5 Illustration of the discrete-time server process for user k with a total of K users: (o) OFDMA I and (x) OFDM I. . . . . . . . . . . . . . . . . . . . . 61 ix 3.6 Comparison of maximum supportable bit rates with K = 4. . . . . . . . . 68 3.7 Comparison of BER results with K = 4 and 8. . . . . . . . . . . . . . . . 69 3.8 Comparison of the packet throughput and delay results with SNR = 16 dB and K = 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.9 Illustration of the exhaustive service system and queueing in the link layer simulation in Fig. 3.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.10 Analytical delay bounds versus the number of users, K, with SNR = 16 dB. 72 3.11 The delay violation probability vs. the delay bound for OFDMA modes with SNR = 16 dB and K = 4. . . . . . . . . . . . . . . . . . . . . . . . . 74 3.12 The delay violation probability vs. the delay bound for OFDM modes with SNR = 16 dB and K = 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.13 The delay violation probability vs. the delay bound for OFDMA modes with SNR = 16 dB and K = 8. . . . . . . . . . . . . . . . . . . . . . . . . 76 3.14 The delay violation probability vs. the delay bound for OFDM modes with SNR = 16 dB and K = 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 TDD-OFDMA frame structure in IEEE 802.16e [4]. . . . . . . . . . . . . 82 4.2 An example of the proposed OARSB scheme. . . . . . . . . . . . . . . . . 84 4.3 The Markov chain description of the behavior of subchannel m of user k. 86 4.4 The Markov chain description of the three possible outcomes for a partic- ular subchannel m by jointly considering K users. . . . . . . . . . . . . . 92 4.5 Throughput vs. the number of active subchannels per user, L, for OARSB and the scheme proposed in [14], with K = 3, M = 15 and W = 3. . . . . 97 4.6 Throughput vs. the number of active subchannels per user, L, for OARSB and the scheme proposed in [14], with K = 5, M = 15 and W = 3. . . . . 98 4.7 The collision resolution delay vs. the number of active subchannels per user, L, with M = 15, K = 3 or 5, and W = 3. . . . . . . . . . . . . . . . 99 5.1 Illustration of a hexagonal multi-cell OFDMA cellular network. . . . . . . 104 x 5.2 Illustration of resource management in a multi-cell cellular network using the ICIC principle, where the same/dierent colors represent the use of the same/dierent subchannels of the band. . . . . . . . . . . . . . . . . . 107 5.3 Illustration of resource management in a multi-cell cellular network based on the BSC principle, where the same/dierent colors represent use of the same/dierent subchannels of the band. . . . . . . . . . . . . . . . . . . . 108 5.4 An example of a multi-cell multi-user scenario. . . . . . . . . . . . . . . . 115 5.5 The interference graph constructed for a multi-cell multi-user scenario. . . 115 5.6 The interference graph for the scenario given in Fig. 5.4. . . . . . . . . . . 119 5.7 Possible BSC occurrences. . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.8 A cascade topology for BSC operation. . . . . . . . . . . . . . . . . . . . . 128 5.9 The SINR distribution for dierent trac load conditions. . . . . . . . . . 140 5.10 The average SINR gains with respect to the ICI-blind scheme under dif- ferent trac loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.11 The cell-specic SINR distribution under an unequal cell load scenario (9 cells of 25 MSs, 9 cells of 5 MSs, and 1 cell of 15 MSs). . . . . . . . . . . . 142 5.12 The SINR distribution for schemes with and without power control (PC) (25 MSs per cell). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.13 The average SINR gains with respect to the ICI-blind scheme under dif- ferent trac loads for PUSC and AMC permutation schemes. . . . . . . . 144 5.14 The average SINR gains with respect to the ICI-blind scheme under dif- ferent trac loads for dierent inter-cell distance deployment. . . . . . . . 145 5.15 The contour plot of SINR (dB) in a cell, with 25-MS trac load per cell. 147 5.16 The spectrum allocation in ICI-prone areas, where each subgure shows spectrum allocation for sectors A 1 , A 4 , A 5 (top); B 1 , B 2 , B 3 (middle); and C 1 , C 6 , C 7 (bottom) depicted in Figs. 5.2 and 5.3. . . . . . . . . . . . . . 149 xi Abstract Orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) are two promising technologies adopted in the IEEE 802.16 standard to support broadband wireless access as well as multimedia quality-of-service (QoS). In this dissertation, we discuss several important topics regarding OFDM/OFDMA: cross-layer performance analysis of OFDM and OFDMA downlinks in terms of several QoS metrics; the medium access control (MAC) protocol design for the OFDMA uplink; and the inter-cell interference (ICI) management in multi-cell OFDMA networks through a systematic approach. First, performance analysis of OFDM-TDMA and OFDMA networks is performed in terms of cross-layer QoS measures which include the bit rate and the bit error rate (BER) in the physical layer, and packet average throughput/delay and packet maximum delay in the link layer. We adopt a cross-layer QoS framework similar to that in IEEE 802.16, where service classication, ow control and opportunistic scheduling with dier- ent subcarrier/bit allocation schemes are implemented. Our analysis provides important insights into the performance dierences of these two multiaccess systems. In addition, it is shown by analysis and simulation that OFDMA outperforms OFDM-TDMA in QoS xii metrics of interest. Thus, we conclude that OFDMA has higher potential in supporting multimedia services. Second, a distributed MAC algorithm for uplink OFDMA networks under the IEEE 802.16 framework is proposed and analyzed. We present a simple yet ecient algorithm to enhance the system throughput by integrating opportunistic medium access and collision resolution through random subchannel backo. Consequently, the resulting algorithm is called the opportunistic access with random subchannel backo (OARSB) scheme. OARSB not only achieves distributed coordination among users but also reduces the amount of information exchange between the base station and users. The throughput and delay performance analysis of OARSB is conducted, and the superior performance of OARSB over an existing scheme is demonstrated by analysis as well as computer simulation. Besides, the proposed OARSB scheme can be easily implemented in 802.16 due to its simplicity. Lastly, a practical and low-complexity multi-cell OFDMA downlink channel assign- ment method using a graphic framework is proposed. Our solution consists of two phases: 1) a coarse-scale inter-cell interference (ICI) management scheme and 2) a ne-scale channel-aware resource allocation scheme. In the rst phase, the task of managing the performance-limiting ICI in cellular networks is accomplished by a graphic approach, in which no ICI measurement is needed and state-of-the-art ICI management schemes such as ICI coordination (ICIC) and base station cooperation (BSC) can be incorporated easily. In the second phase, channel assignment is accomplished by taking instantaneous channel conditions into account. Heuristic algorithms are proposed to solve both phases of the problem eciently. Extensive simulation is conducted for various practical scenarios to xiii demonstrate the superior performance of the proposed solution against the conventional OFDMA allocation scheme. Thanks to its practicality and low complexity, the proposed scheme can be used in next generation cellular systems such as the 3GPP Long Term Evolution (LTE) and IEEE 802.16m. xiv Chapter 1 Introduction 1.1 Signicance of the Research Multimedia delivery is one of the key objectives of the next-generation wireless networks. From a network-centric perspective [99], its success relies on how the underlying network can support dierent quality-of-service (QoS) requirements demanded by a variety of multimedia applications. A signicant challenge is posted since multimedia applications have very diverse characteristics in terms of physical measures such as bandwidth and delay. Furthermore, it is desirable that the underlying network can serve multiple users and meet their individual QoS requirements. All of these call for a QoS-provisioning broadband network in conjunction with proper multiple access schemes such as Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA). A broadband Orthogonal Frequency Division Multiplexing (OFDM)-based network, which has been extensively investigated, serves as a strong candidate for such an endeavor. In fact, OFDM-TDMA and OFDMA (OFDM-FDMA) techniques have been adopted in the IEEE 802.16 standard [4]. Besides, a QoS framework in the medium access control 1 (MAC) layer has also been integrated with multiaccess transmission systems in the IEEE 802.16 standard [92]. The technically challenging topic of QoS provisioning has been tightly coupled with the resource allocation problem in OFDM and OFDMA. Resource allocation, which is essentially a MAC-layer problem, can be performed in two dierent ways: centralized or distributed. In the centralized approach, an arbitrator (such as the base station in an OFDM(A) network) takes full charge of resource allocation through polling, reservation, or scheduling. Notable technological advances in this regard include the proposal of opportunistic scheduling, adaptive modulation, service dierentiation, and QoS mapping. Opportunistic scheduling assigns resource to users that have better link quality. Since users' channel conditions vary independently of each other, multiuser diversity is achieved. Adaptive modulation selects modulation types according to the channel condition of each subcarrier to enhance spectrum eciency. Service dierentiation and QoS mapping are used to provide dierent levels of QoS services for dierent applications so that resources can be most eectively used. Along this research direction, we rst investigate the QoS-provisioning capability of opportunistic OFDM-TDMA and OFDMA downlink networks from the scheduling per- spective. In particular, the impact of opportunistic scheduling on QoS provisioning is examined in terms of several useful measures that are critical to multimedia services, such as the bit rate and the bit error rate (BER) in the physical layer and packet av- erage throughput/delay and packet maximum delay in the link layer. This cross-layer approach is needed to understand the QoS-provisioning wireless networks thoroughly, since QoS requirements must be treated dierently in dierent layers. With the queueing 2 and ow control techniques employed in the proposed QoS framework, we address the aforementioned QoS measures both experimentally and analytically. In contrast with the centralized scheduling scheme, the distributed resource allocation scheme relies on random access and collision avoidance/resolution schemes to coordinate users and apportion resources. Although this scenario is mostly seen in distributed net- works such as IEEE 802.11 or Wireless Local Area Networks (WLANs), it is also useful and attractive for the uplink access in a centralized system such as OFDMA due to its simplicity. The popularity of WLANs has drawn extensive attention to the design and analysis of the QoS-provisioning capability of WLANs. Its legacy collision resolution scheme via random backo has been improved and well analyzed in the literature. How- ever, there has been relatively little research devoted to the distributed uplink access for OFDMA in IEEE 802.16. We aim to address this issue and propose possible algorithmic and analytical solutions. In the second part of this dissertation, we investigate the distributed access in the OFDMA uplink. We consider a distributed scenario where uplink bandwidth allocation is performed using the slotted Aloha type of random access, which is then assisted by a collision resolution policy. A fast collision resolution algorithm, which integrates oppor- tunistic medium access and frequency-domain random backo, is devised thanks to the multiband structure of OFDMA. The analysis of this proposed scheme is then conducted. We will show that the proposed scheme not only enhances throughput, but also points out a promising direction for QoS provisioning in distributed networks. We have so far considered only the single-cell scenario of an OFDM or OFDMA network. In a typical cellular network, however, multiple cells or base stations (BSs) are 3 deployed in dierent geographical sites to cover an expansive service area. Several new issues arise in the multi-cell situation. A notable one is the management and reduction of inter-cell interference (ICI), which occurs when users or mobile stations (MSs) in adjacent cells adopt overlapping spectra. ICI is the major limiting factor on spectral eciency of wireless cellular networks. To address this issue, advanced interference management (IM) techniques such as inter-cell interference coordination (ICIC) and base station cooperation (BSC) were pro- posed to mitigate formidable ICI and improve overall system performance. Previous work concentrated on presenting the design concept of ICIC and/or BSC, justifying the use of these techniques, and obtaining the achievable performance bound. However, the problem of designing a practical algorithm to achieve the resource allocation principle suggested by ICIC or BSC has been largely overlooked. In the third part of this dissertation, a practical and low-complexity multi-cell OFDMA downlink resource allocation method using a graphic framework is proposed. Our solu- tion consists of two phases: 1) a coarse-scale ICI management scheme and 2) a ne-scale channel-aware resource allocation scheme. In the rst phase, state-of-the-art ICI man- agement techniques such as ICIC and BSC are incorporated in our framework. Specif- ically, the ICI information is acquired through inference from the diversity set of MSs and presented by an interference graph. Then, ICIC or BSC is mapped to the MAX k-CUT problem in graph theory and solved in the rst phase. In the second phase, channel assignment is accomplished by taking instantaneous channel conditions into ac- count. Heuristic algorithms are proposed to solve both phases of the problem eciently. 4 Extensive simulation is conducted for various practical scenarios to demonstrate the su- perior performance of the proposed solution against the conventional OFDMA allocation scheme. The proposed scheme can be used in next generation cellular systems such as the 3GPP Long Term Evolution (LTE) and IEEE 802.16m. 1.2 Review of Previous Work In the rst part of this dissertation, we adopt a cross-layer approach in the comparison of the QoS performance of opportunistic OFDM-TDMA and OFDMA networks. Both analytical and numerical comparisons will be provided. Related previous work on this topic is reviewed below. Cross-layer Approach A cross-layer approach to the design and analysis of wireless networks has drawn a lot of research attention lately. Generally speaking, the cross-layer approach gives new design opportunities that are not available in the layered approach. Besides, the cross-layer perspective oers a better understanding of QoS provisioning of wireless networks. For tutorials on the cross-layer design, we refer to [22,78,86]. Specic applications of the cross-layer approach will be given in the following along with our review of several related research areas. Analysis and Comparison of Multiaccess Schemes Multiaccess schemes in OFDM-TDMA and OFDMA have been compared and an- alyzed from dierent perspectives in previous work. Specically, comparison of OFDM-TDMA and OFDMA in the BER performance was studied in [76,91], where 5 OFDMA was shown to outperform OFDM-TDMA in the uncoded and the coded BER performance in [91] and [76], respectively. The link layer performance such as packet throughput and delay was studied in recent work from a cross-layer per- spective. For example, the analysis of queueing delay for 802.16 networks was conducted in [47, 66] by combining link-layer queueing with physical-layer trans- mission. A vacation queueing model was adopted in [67] to analyze the link-layer queueing performance of OFDM-TDMA systems with round-robin scheduling. A queueing model for OFDMA systems was used in [82] to design a scheduling scheme that balances multiuser diversity and queueing delay. Multimedia QoS via Service Dierentiation A common approach to Internet multimedia QoS is to use service dierentiation and QoS mapping [80]. For instance, the Dierentiated Services (DiServ) model divides trac into two classes; namely, the premium and the best eort [68]. Then, packets are labeled as either the premium or the best eort by a certain QoS map- ping strategy. Then, proper services are granted depending on the labeled class. A similar approach is used in wireless networks such as IEEE 802.16 [29,92] and IEEE 802.11 networks [62]. Here, we also consider a QoS framework where packet cate- gorization and service dierentiation are implemented, and the delay performance of the premium class is analyzed. Opportunistic Scheduling The main resource allocation issue in centralized networks is scheduling. For tutori- als on various scheduling algorithms, we refer to [21,34]. Opportunistic scheduling, 6 or channel-state-dependent scheduling, was shown to have a great value in wireless networks since it can maximize the overall system throughput [88]. A wide range of issues on opportunistic scheduling for various networks and applications has been extensively studied [12, 16, 18, 36, 61, 79, 83, 88, 93]. In this work, we investigate and compare the impact of opportunistic scheduling on the QoS provisioning of OFDM-TDMA and OFDMA networks. Adaptive Modulation Adaptive modulation (AM) has the potential to increase spectrum eciency by al- locating bits according to channel quality. Studies on the design and analysis of this technique were conducted in [13,71,91]. AM has been adopted in many industrial standards, e.g., IEEE 802.11 and 802.16. In this research, we use adaptive squared M-QAM modulation in the resource allocation of OFDM-TDMA and OFDMA. In the second part of the dissertation, we propose a distributed uplink bandwidth allocation scheme for OFDMA. Some related previous work is reviewed in the following. Multiaccess Communication Using Random Access While scheduling is used in a centralized multiaccess network, random access is the main strategy used in a distributed network. Without a central moderator, random access allows users to contend the medium by transmitting independently. A key question associated with random access is how to resolve the collision based on some collision resolution policies. One of the earliest random access schemes is the Aloha scheme [10] and its variant known as the slotted Aloha scheme [15], in which retransmission is governed by a probability. Many improvements to Aloha 7 and slotted Aloha have been proposed (e.g., [48]). Another well-known and widely used random access scheme is the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and the binary exponential backo policy used in IEEE 802.11, which has drawn a great deal of attention in devising higher throughput and lower delay improvements (e.g., [57]). An analytical framework for 802.11 MAC was rst proposed in [17]. A similar analytical approach based on Markov modeling has been used in many subsequent papers, which will also be adopted in our analysis. Distributed Access for OFDMA Uplink A distributed multiaccess strategy can be employed for OFDMA networks in uplink bandwidth allocation. The advantage of such a scheme over a centralized counter- part is its simplicity, since little information exchange is needed between the base station and users. An opportunistic multichannel Aloha scheme was proposed for OFDMA in [14] where each user requests for a set of its subchannels that is above a certain threshold in a way similar to slotted Aloha, and if the request message collides, collided subchannels are abandoned. In other words, collision resolution was not considered in [14]. A similar scheme was proposed in [89]. A fast collision resolution method was studied in [30] for OFDMA, where collided users, rather than procrastinate for a random time, switch immediately to a random subchannel so that collision may be resolved faster in the frequency domain. However, subchannel state information was not considered in the backo decision in [30]. 8 In the third part of the dissertation, we propose a high-performance yet low-complexity multi-cell OFDMA downlink resource allocation method to enable interference manage- ment techniques such as ICIC and BSC. Related previous work is reviewed in the follow- ing. Multi-Cell OFDMA Resource Allocation The multi-cell resource allocation problem can be dealt with by extending the single- cell allocation idea to the multi-cell scenario. This may be done, for instance, by considering the signal-to-interference-and-noise ratio (SINR) instead of the signal- to-noise ratio (SNR) in the problem formulation. This formulation is attractive since most of single-cell OFDMA resource allocation schemes can be directly applied to the multi-cell context. For instance, Li and Liu [60] proposed a two-level resource allocation scheme, wherein the radio network controller (RNC) coordinates multiple cells in the rst level, and performs per-cell optimization in the second level. The rst level is conducted based on perfect and predetermined knowledge of SINR for all MSs on all subchannels. A similar approach was adopted in [40] with some special treatment on ICI. Pietrzyk and Janssen [69,70] proposed heuristic algorithms for their formulated problems based on SINR, with some quality-of-service (QoS) consideration. A key assumption in this group of research work is the availability of SINR, which is however dicult to obtain a priori due to mutual dependency of ICI. In other words, a multi-cell resource allocation scheme contingent upon global and perfect knowledge of SINR is not practical. Interference Management 9 Interference management has been a focus of discussion in the industry. Many proposals were presented in the standardization meetings with an objective of en- hancing the ecacy of the next-generation cellular deployment. Most of these endeavors aim at developing systematic approaches and policies as guidelines for resource allocation. Notable proposals include inter-cell interference coordination (ICIC) [35], which suggests allocating disjoint channel resources to cell-edge MSs that belong to dierent cells; and base station cooperation (BSC) [98], which allows multiple BSs to transmit coherent signals to multiple MSs concurrently, thereby turning interference signals to useful ones. Similar mechanisms were suggested for the multi-cell scenario in 3GPP [8,9]. Recently, new improvements were proposed in 3GPP LTE (e.g., [74, 75]) and IEEE 802.16m (e.g., [43]). Most research work has concentrated on presenting the design concept of ICIC and/or BSC, justifying the use of these techniques, and obtaining the achievable performance bound. Graph Approach to Resource Allocation The channel assignment problem in cellular and mesh networks has been studied in the context of multi-coloring of a graph for decades [28,63,65]. In the traditional formulation, a graph is constructed and each node in the graph corresponds to a BS or an access point (AP) in the network to which channels are assigned. The edge connecting two nodes represents the potential co-channel interference between these two BSs or APs, which implies their geographical proximity. Then, the chan- nel assignment problem becomes the node coloring problem, where two interfering nodes should not have the same color (i.e., using the same channel). 10 1.3 Contribution of the Research Although many useful results have been presented in previous work, there are still a few open issues to be addressed. We address some of them and highlight our contributions below. As both OFDM-TDMA and OFDMA are adopted in the IEEE 802.16 standard as two transmission schemes at the 2{11 GHz band, their performance pros and cons are of great interest. However, an analytical framework that accounts for both scenarios to facilitate the comparison was missing. We propose a cross-layer analytical model in our research to achieve this goal. The latest IEEE Standard 802.16e-2005 favors OFDMA over OFDM-TDMA as the principal multiaccess scheme. We justify this choice by comparing these two systems from the scheduling perspective. Through extensive analysis and computer simula- tion, we show that OFDMA has a greater potential in meeting the requirements of multimedia delivery. The multimedia delivery capability of OFDM and OFDMA networks is investigated. To address this, we consider several physical and link layer QoS measures to capture the characteristics of multimedia applications. For instance, packet average delay and packet maximum delay are studied in this work to understand the link-layer performance of OFDM and OFDMA networks in support of non-real-time (e.g., le transfer and web browsing) and real-time (e.g., voice and video) applications, respectively. Furthermore, physical-layer measures such as BER is also considered. 11 The performance of two well known scheduling strategies (i.e., the round-robin and opportunistic scheduling) is examined analytically and empirically. The opportunis- tic scheduling is known to maximize the system throughput but may incur large delay since users could be suspended from transmission when their channels are poor. This eect is quantied and studied in the context of QoS provisioning in OFDM-TDMA and OFDMA networks. Random access schemes have been widely used in distributed networks. Its appeal- ing characteristics such as simplicity are also useful and applicable for uplink access in centralized networks such as OFDMA. This has not yet been fully studied in the past. We take on this topic by proposing a practically simple yet ecient MAC algorithm for uplink OFDMA networks. In particular, we innovatively integrate an opportunistic medium access scheme and a frequency-domain collision resolution mechanism to resolve collision eciently so as to achieve high throughput. The proposed scheme, called OARSB (opportunistic access with random subchannel backo), is simple and can be readily implemented in the IEEE 802.16 standard. The analysis of distributed MAC algorithms has always been a challenging task. To be mathematically tractable and analytically feasible, approximations or simplica- tions are often required in conducting the analysis. On the other hand, such approx- imations or simplications should not compromise analytical accuracy much. We take on this challenge, and propose an analytical method for the proposed OARSB scheme. Since the OARSB scheme employs a frequency-domain (or subchannel) backo instead of a time-domain one, our analysis is not trivially equivalent to that 12 of the random backo in IEEE 802.11, which has been studied extensively before. To the best of our knowledge, the presented analysis is new. In an interference-limited multi-cell OFDMA network, an ecient interference man- agement scheme is needed. While state-of-the-art techniques such as ICIC and BSC have been proposed, the development of a practical algorithm to achieve the re- source allocation principle suggested by ICIC or BSC has been largely overlooked. We propose a novel, high-performance yet low-complexity multi-cell OFDMA down- link channel assignment method to enable ICIC and BSC. The proposed scheme is shown to attain signicant SINR performance improvement and can be used in next generation cellular systems such as the 3GPP Long Term Evolution (LTE) and IEEE 802.16m. A fundamental challenge to the design of an interference-aware resource allocation method in a multi-cell scenario is the availability of the ICI information. Due to the mutually dependent nature of ICI, the exact SINR information prior to actual resource allocation is probably unavailable. We overcome this diculty by inferring approximate SINR from the diversity set of MSs dened in the 802.16e standard. The obstacle of SINR mutual dependency is then removed since no exact SINR information is needed for resource allocation. 1.4 Outline of the Dissertation The rest of this dissertation is organized as follows. Background material for our research is reviewed in Chapter 2. The cross-layer performance analysis of OFDM and OFDMA 13 downlinks in terms of physical and link layer QoS metrics is conducted in Chapter 3. The MAC protocol design for the OFDMA uplink by integrating opportunistic medium access and collision resolution through a random subchannel backo scheme is presented in Chapter 4. An ecient OFDMA downlink resource allocation method for the multi-cell scenario with interference management is proposed in Chapter 5. Finally, the dissertation is summarized and future research directions are pointed out in Chapter 6. 14 Chapter 2 Research Background Some background knowledge and analytical tools are reviewed in this chapter to facilitate the understanding of research results to be presented in the following chapters. 2.1 OFDM and OFDMA Transmission Systems 2.1.1 Overview Multipath fading is an inherent characteristics in almost all wireless channels. To com- pensate the channel fading eect, a channel equalization design at the receiver is often implemented. One of the main advantages and attractions of the OFDM technique is that it simplies the equalizer design signicantly. To achieve this, an OFDM system divides a wider frequency-selective band into a set of narrower frequency non-selective ( at) subcarriers. The resulting scheme allows data to be transmitted (in a lower data rate) on orthogonal subcarriers, which shortens the symbol bandwidth, or equivalently, lengthens the symbol duration. This leads to immunity against the multipath fading of a wireless channel. 15 In addition to the above physical layer benets, the OFDM structure also allows more freedom in resource allocation such as multiple access and bit allocation. Specically, thanks to the orthogonal multiband structure, multiple access may be realized in both time and frequency domains, and bit allocation may be performed separately at each subcarrier. All of the above features have created new and interesting design opportunities in both OFDM uplink and downlink transmissions. Multiple access (or multiaccess for short) is a MAC layer technique that aims to allo- cate the limited transmission medium to users properly and eciently. In the OFDM sys- tem, this task is accomplished by subcarrier/time-slot assignment and bit allocation. Two multiaccess strategies are often incorporated in OFDM, which result in OFDM-TDMA and OFDMA (OFDM-FDMA), respectively. Specically, OFDMA performs subcarrier assignment while OFDM-TDMA performs time-slot assignment. Their dierences are illustrated in Fig. 2.1. Note that both schemes may perform assignments in a static or dynamic way. The dierence between static (or round-robin) and dynamic (or oppor- tunistic) assignments lies in whether users' channel conditions are taken into account in the allocation process. 2.1.2 IEEE 802.16/WiMAX IEEE 802.16 [2] and its industrialized counterpart, WiMAX [5], have been under the spotlight in recent years. The IEEE 802.16 standard promises to provide a high data rate wireless broadband access scheme for a large number of users in a wide area, e.g., a metropolitan area. High data rates, mobility-friendly features, and low user installation costs have made IEEE 802.16/WiMAX an appealing alternative to DSL/Cable services. 16 User 1 User 2 User 3 User 4 Time Time F r e q u e n c y F r e q u e n c y OFDM-TDMA OFDMA Figure 2.1: Multiple access in OFDM-TDMA and OFDMA. The evolution of the IEEE 802.16 standard is brie y described below. The IEEE 802.16-2004 standard was published in 2004, in which OFDM was adopted to assist xed broadband wireless access. Amendments to IEEE 802.16-2004 were developed and culminated with the release of the IEEE 802.16e-2005 standard in Feb. 2006 to support mobile broadband wireless access. The main technology in support of mobility is OFDMA. OFDMA promises to deliver basic, portable and full mobility, but at the expense of more complex physical and MAC layer design. Since the developments of 802.16e, both academic and industrial attention has gradually shifted to OFDMA. Interested readers are referred to [33,39,54] for tutorial overviews and comparisons of OFDM and OFDMA in IEEE 802.16/WiMAX. Since the standardization of 802.16e, new amendments to it have been discussed in the 802.16m meetings with joint eorts from the industry to enhance the throughput performance so as to better suit the needs of next-generation 802.16 services. Suggestions 17 for standard modication include both the PHY and the MAC aspects of the OFDMA system. All proposals and contributions from industrial companies have been collected and made accessible from the IEEE 802.16 Task Group m website [3]. The standardization process of 802.16m is still in the draft stage. It involves an ongoing eort to evaluate and harmonize opinions and suggestions from dierent parties. 2.2 Centralized and Distributed Multiple Access In this section, we brie y review two main multiaccess schemes in wireless networks; namely, the centralized (or scheduling-based) and the distributed (or contention-based) schemes. Our discussion will focus on MAC protocols. 2.2.1 Centralized Access Centralized MAC protocols are mainly used in mobile cellular networks, where a central base station or an access point exists. The base station generally uses polling or reserva- tion (jointly termed \scheduling") to fulll multiple access. Since polling or reservation is periodically operated, it is known that scheduling-based MAC protocols can support predictable and guaranteed QoS. A main problem here is the design of an appropriate and eective scheduler. Design criteria for a good scheduler and many wireless schedul- ing algorithms are summarized in [21]. We examine a particular class of schedulers to be adopted in Chapter 3 below. 18 2.2.1.1 Opportunistic Scheduling A scheduler is a mechanism that manages how users share the common service opportu- nity provided by a server. When a user is in service, its servicing or transmission rate is determined by the wireless link quality of the user. Therefore, it is desirable to grant the service opportunity to users whose channels are good. This leads to the strategy of opportunistic scheduling, in which user's channel state information is taken into account in the scheduling decision. Its operation and performance advantage can be explained by the following simple example. Suppose that the user-server link is an ON/OFF channel. A server allocated to a user in the ON (or, respectively, OFF) state can serve one (or, respectively, zero) packet from this user's queue. Consider rst a round-robin scheduling where the server is allocated to K users successively regardless of their channel status. Since each user accesses to the server 1=K of time on average and with 1=2 of chance that the user is in the ON state, the average throughput for the round-robin scheduler is 1=(2K) packets per time unit. In contrast, the opportunistic scheduler allocates the server only to users who are in the ON state. If more than one user's channel is ON, the scheduler randomly picks one. The throughput of such a strategy is (1(1=2) K )=K packets per time unit, where 1(1=2) K accounts for the probability of not all K users simultaneously being in the OFF state. It can be seen that throughput is greatly enhanced by the opportunistic scheduling, and the improvement increases with the number of users, K. Thus, the resulting gain is called the multiuser diversity gain. 19 2.2.2 Distributed Access Distributed MAC protocols are mainly used in wireless ad hoc networks where no in- frastructure exists. While existing protocols for such a purpose are many (see [49] for a survey), we restrict our discussion to those which are more related to our work. 2.2.2.1 Slotted Aloha Aloha and slotted Aloha are among the earliest random access schemes. Slotted Aloha is a variant of the original Aloha, which was proposed in [10]. The dierence is that, instead of transmitting the arrived packets immediately as in Aloha, slotted Aloha waits to transmit at the beginning of the next time slot. The eciency is improved by this modication. In fact, slotted Aloha is shown to achieve twice the throughput of Aloha asymptotically [15], thanks to the reduced collision probability. In case of collisions, slotted Aloha retransmits the collided packet in the next time slot with probability p. A constant value of p, as used in the original slotted Aloha, was shown to have an unstable property with an innite number of users. Dynamic adjustment of p has been suggested to x this problem (e.g., [48]). Note that one of the main advantages of slotted Aloha is its simplicity and eectiveness in low trac load conditions. The simplicity has made slotted Aloha a useful mechanism for distributed uplink access in OFDMA, thanks to the slotted structure of OFDMA. Details will be discussed in Chapter 4. 20 2.2.2.2 802.11 Distributed Coordination Function The Distributed Coordination Function (DCF) is a contention-based MAC protocol, which is the primary scheme used in 802.11. In DCF, users sense the channel status through the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) tech- nique and, if the channel is idle, send data (in the basic access mode) or control signals (in the RTS/CTS access mode) immediately. If collision occurs, users \backo" to wait their turns of retransmission. The retransmission is dictated by the binary exponential backo mechanism. In particular, collided users are given a backo time, which is chosen uniformly and independently from the range of [0;W1], where W is the backo window size. The backo time counter decreases when the channel is sensed idle and pauses when the channel is busy. The user will retransmit when the counter reaches zero. Note that this is called the binary exponential backo since W doubles upon each collision, i.e., W = 2 i1 CW min at the i-th collision, where CW min is the initial backo window size. The reason for the increased window size is because consecutive collisions indicate that the channel is very busy, and thus no need to retry that soon. This eectively reduces the probability of re-collision. The random backo scheme has been well studied due to the popularity of IEEE 802.11 WLANs. Many improvements to the original backo scheme have also been proposed (e.g., [57, 95]). A similar random backo scheme may also be applied in the frequency domain in a multiband system (such as OFDMA), which will be discussed in Chapter 4. 21 2.2.2.3 802.16 Distributed Uplink OFDMA uplink access may be performed in a distributed fashion. In fact, the stan- dardized frame structure of OFDMA in IEEE 802.16 [4] has reserved a control channel (called the ranging subchannel) for two purposes: synchronization between users and the base station (i.e., ranging), or requests of uplink transmission from users (i.e., the uplink bandwidth request). The uplink bandwidth request can optionally be performed through a contention-based (distributed) mechanism [64]. The details of the mechanism are however left unstandardized, which provide design opportunities for researchers and developers. We will propose our solution to this problem based on slotted Aloha and random backo, in Chapter 4. 2.3 Markov Chain Techniques The purpose of this section is to summarize main results of Markov chain theory to be used in this work. We concentrate on the discrete-time Markov chain. Let A(t);t2f0;1;2;:::g be a discrete-time random process that takes on nonnegative integer values, which are called \states." Then, A(t) is called a Markov chain process if the current value (or state) of A(t) depends only on A(t 1) but not on any previous history. That is, Pr[A(t + 1) = jjA(t) = i;A(t 1) = i t1 ;::: ;A(0) = i 0 ] = Pr[A(t + 1) = jjA(t) = i] , P i;j ; (2.1) 22 0 1 2 3 0 1 2 (a) (b) 0 1 2 3 (c) Figure 2.2: Examples of (a) the reducible, (b) the periodic, (c) the irreducible and ape- riodic Markov chains. where P i;j is called the transition probability from state i to j, and is xed regardless of t. The transition probability matrix, P, is dened as having P i;j as its (i;j) entry. We dene two terms that describe a Markov chain. First, a Markov chain is called irreducible if there is a path of nonzero probability from every state to every other state, and reducible if otherwise. For instance, the Markov chain in Fig. 2.2(a) is reducible as state 2 does not reach state 1. Second, the period of any state i is dened to be the greatest common divisor (g.c.d.) of the number of hops from state i to itself considering all paths from state i to itself. Then, a Markov chain is called aperiodic if none of its states have period 2, and periodic, otherwise. A periodic chain is shown in Fig. 2.2(b) in which the period of all states is 2. It can be shown that, for an irreducible Markov chain, all states have the same period. Therefore, if an irreducible Markov chain has self transitions with any states, the chain is aperiodic, such as the one in Fig. 2.2(c). 23 We restrict ourselves to irreducible and aperiodic Markov chains with a nite number of states 0;1;::: ;m, since this is the only case to be encountered in our analysis. We dene a steady-state probability vector = ( 0 ; 1 ;::: ; m ), where j = lim t!1 Pr[A(t) = jjA(0) = i 0 ]; j = 0;1;2;::: ;m; (2.2) is the steady-state probability of being in state j, regardless of the initial state. The can be shown to uniquely exist and satisfy = P for every irreducible and aperiodic Markov chain with nite states. Note that can be found by calculating the normalized left eigenvector of P corresponding to the eigenvalue of one. We will use this technique in Chapter 4. The Markov chain technique has been widely used in many disciplines. Two applica- tions related to our work are considered in the following. 2.3.1 Modeling of Wireless Fading Channels In a typical non-line-of-sight (NLOS) wireless environment, it is well known that the received signal envelope has the Rayleigh distribution. With additive Gaussian noise in place, the received signal-to-noise ratio (SNR) follows the exponential distribution, i.e., g ( ) = 1 0 exp( 0 ); 0; (2.3) where 0 is the average SNR. 24 To study the packet-level performance of a Rayleigh fading channel, it is useful to model the Rayleigh fading channel by a Markov chain [90, 100]. In particular, the re- ceived SNR (which is exponentially distributed) is partitioned into m+1 disjoint regions R 0 ; ;R m by boundary points b 0 ;b 1 ; ;b m+1 , where R i is the interval [b i ;b i+1 ) for i = 0;1; ;m and b 0 < b 1 < < b m+1 with b 0 and b m+1 set to 0 and 1, respectively. The boundary points may be determined in a variety of ways, such as arbitrarily [90], by the fading speed of the channel [100], or by integrating with the adaptive modulation scheme as done in our work. Each SNR interval R i corresponds to the state i in the Markov chain, and the transition from state to state captures the time varying character- istics of the channel, specically, the Doppler spread. Assuming that the mobility-induced Doppler spread is small enough so that transitions happen only between adjacent states, the resulting Markov chain may look like the one in Fig. 2.3. The steady-state probabili- ties, i 's, can be obtained by integrating the pdf in (2.3) over disjoint regions R i 's. That is, i = Z b i+1 b i g ( )d ; i = 0;1;::: ;m: (2.4) The transition probabilities can be approximated using the level crossing rates at bound- aries b i , which have been derived in [90,100]. 2.3.2 Modeling of Random Backo Schemes The Markov chain technique can also be used to analyze the random backo procedure in the distributed access. For instance, as proposed in [17], the backo scheme in 802.11 25 0 1 2 m . . . Figure 2.3: The Markov chain modeling of a Rayleigh fading channel. can be modeled by a Markov chain with some preestablished assumptions. This approach is widely adopted by researchers in the analysis of distributed access schemes. An example is drawn in Fig. 2.4, which models a simplied 802.11 backo scheme with xed backo window size W = 5 (i.e., no exponential doubling of W is considered, for which a multistage chain is needed [17]). State 0 corresponds to \transmission" while the rest of states correspond to \backo or waiting" with the backo timer indicated by the state. (Recall that the backo timer is initially chosen uniformly from [0;W 1] and decreases afterwards.) The transition from state 0 to state i, i = 1;::: ;4, corresponds to the case where collision occurs and the backo timer is chosen to be i. The self transition from state 0 to itself corresponds to either continuous transmission or collision with the backo timer chosen to be 0 (i.e., immediate retransmission). The transition from state i to state i 1, i = 1;::: ;4, corresponds to the decrement in the backo timer, and the self-transition of state i corresponds to the situation when the channel is sensed busy and the backo timer is frozen. The transition probabilities can be obtained by analyzing the dynamics of the backo process. Fig. 2.4 can also be used to analyze the random subchannel backo process to be examined in our work. Although the states are assigned dierent physical meanings, the 26 0 1 2 4 3 Figure 2.4: The Markov chain modeling of a random backo procedure. above discussion still applies to our scheme. That is, states correspond to the positions in the subchannel backo process in our proposed scheme in Chapter 4. 2.4 Quality of Service Wireless multimedia delivery with QoS support is an important yet challenging task. The challenges come primarily from the fact that dierent applications have dierent QoS de- mands. Many approaches have been developed for multimedia delivery, and they can generally be classied as either network centric or end-system centric solutions [99]. The network centric approach aims to embed QoS support ability into the network, through methods such as service dierentiation, QoS mapping, and cross-layer channel modeling. On the contrary, end-system centric approach relies on end-user techniques such as con- gestion control, error control and power control, while assuming no QoS support from the underlying network. The network centric approach will be adopted in our work. Specically, we employ aforementioned approaches such as service dierentiation and cross-layer channel model- ing in our QoS framework. Cross-layer channel modeling is motivated by the limitation of physical-layer channel modeling in the analysis of packet-level QoS performance, which 27 is realized by the Markov chain modeling of the Rayleigh fading channel introduced pre- viously. Service dierentiation in our work is implemented in a similar fashion to those proposed for some popular networks as described below. 2.4.1 Service Dierentiation The purpose of performing service dierentiation is to provide heterogeneous services, thus providing dierentiated QoS. Service dierentiation is achieved by classifying in- coming packets into dierent priorities, or service types, in terms of, e.g. packet loss rate and/or delay [80]. (The classication itself is handled by a scheme called QoS mapping.) Some early eorts have been made in devising service dierentiation for IP and ATM net- works. The result is that IP networks based on Integrated Services (IntServ) have three service classes, while ATM networks have ve (see [68] for details). Their classications, although not exactly the same, are quite similar. Recent eorts have been dedicated to wireless networks. Dierent standard bodies have proposed their own service dierentiation design. For instance, the Third Generation Partnership Project (3GPP) has dened four QoS classes according to delay sensitivity for its cellular networks; namely, conversational, streaming, interactive, and background classes [99]. The 802.16/WiMAX standard also denes four classes in its QoS architecture, which are unsolicited grant services (UGS), real-time polling services (rtPS), non-real- time polling services (nrtPS) and the best eort (BE). They have dierent bandwidth (throughput) and delay requirements. For example, UGS demands higher and steadier bandwidth than BE, and rtPS demands more stringent delay than nrtPS. 28 Similar implementation is seen in distributed networks such as 802.11 as well. The QoS enhancement scheme to traditional DCF is dened in the 802.11e standard as EDCF (enhanced DCF). The 802.11e standard allows up to eight service classes, which dier in their backo parameters [62] such that higher-priority ones will get faster transmis- sion/retransmission in the random access process. Considering the complexity of adding multiple classes, we will examine the case of two classes, i.e. the premium and the best eort services, which is a simplied version of that in 802.16. Our framework and analysis are presented in Chapter 3. 2.4.2 QoS Metrics The characteristics of multimedia applications are quite diverse. To be mathematically tractable and analytically useful in lower layers (e.g., link and physical layers), several physical measures are often used to capture multimedia contents in the application layer. In this section, we summarize some useful QoS metrics from a layering viewpoint. In the physical layer, typical performance measures include the bit rate and the bit error rate (BER). In the link layer, the packet-level performance is of interest, such as the packet error rate (PER), the packet loss rate, average throughput, average delay, maximum delay (or delay bound), and the delay violation probability. Note that some cross layer metrics are dependent, e.g., BER and PER. In addition, some metrics are particularly useful for certain types of applications. For example, average delay is useful for delay insensitive applications such as emailing and web browsing, while maximum delay and the delay violation probability are more suitable for delay sensitive applications such as voice and video. Some (but not all) of these QoS metrics are addressed in 29 Chapter 3 to demonstrate the QoS-provisioning performance of wireless OFDM-TDMA and OFDMA networks. 2.5 Multi-cell Scenarios In a wireless cellular network, a \cell" is the coverage area of a base station. The size of the area is often limited by the power constraint of the base station and, therefore, multiple base stations are needed to cover a large geographical area. Many new design issues arise in this multi-cell scenario, which do not exist in the single-cell case. Inter-cell interference (ICI), for instance, is one of the most signicant issues. ICI occurs when transceivers or mobile stations in adjacent cells use the same spectrum so that communication signals interfere with each other. It has been shown that ICI is the predominant performance limiting factor in wireless cellular networks [52]. Fig. 2.5 shows an exemplary seven-cell setting with overlapping coverage. In general, more than seven cells can be considered, and the overlapping area may be shortened or expanded depending on the actual cell deployment considerations. In real-world cellular deployment, it is desirable to balance between the base station placement density and service quality. If very few base stations are deployed in a given region, some areas may not be covered at all. On the other hand, an overly dense base station installation will result in an increased deployment cost as well as higher ICI. Fig. 2.5 depicts the situation that results in ICI. Mobiles in the gure are near the boundary of the cell and assumed to use the same spectral resource. Since each mobile is 30 Figure 2.5: An exemplary multi-cell scenario with inter-cell interference depicted by dot- ted lines. within the transmission range of more than one base station, it will receive useful signals as well as interference, as shown by solid and dotted lines, respectively, in Fig. 2.5. To reduce ICI and, therefore, improve network performance, many interference man- agement (IM) techniques have been proposed. Three approaches have been considered [7]: interference randomization, interference cancellation, and interference coordination. We will focus on interference coordination below since it is most related to our research. We refer interested readers to [20] for interference randomization and interference cancella- tion. 2.5.1 Cell Planning Due to the large service area and the scarce frequency resource, the same frequency band is often reused in dierent geographical areas. A frequency reuse factor is used to indicate 31 how frequently (in space) the same spectrum is reused. It is dened to be K if the same spectrum is reused in every K cells. A universal frequency reuse for all geographical areas faces the challenge of choosing between spectral eciency (the advantage of a low reuse factor) and interference mitigation (the advantage of a high reuse factor), which may be dicult to determine in practice. Therefore, a exible frequency reuse, wherein the frequency reuse is not universal, is introduced to allow design exibility and better performance. The fractional frequency reuse (FFR) is one such technique supported by WiMAX. It was proposed with the goal of improving the signal strength and throughput of ICI- prone cell edge users, while achieving a better overall spectral eciency than a universal frequency reuse scheme. As shown in Fig. 2.6, FFR allows the cell center to use the entire available spectrum (provided it does not overlap with the cell edge spectrum to incur intra-cell interference) while the cell edge only a fraction of the available spectrum. It works by considering the fact that the cell center experiences high signal power and low interference, and can use a low frequency reuse factor to enhance spectral eciency. The cell edge, on the contrary, experiences low signal power and high interference so that neighboring cell edges must be partitioned into disjoint spectra for interference mitigation. The design concept for the cell edge is generally called inter-cell interference coordination (ICIC). FFR is one ICIC scheme. Along this design principle, many schemes have been proposed. For example, a cell was partitioned into several concentric regions in [42,44], where a smaller reuse factor was assigned to inner regions and a bigger reuse factor to outer regions. In order to choose a proper reuse factor for each of these regions, some measurement of ICI may be needed. 32 2 5 3 1 4 7 6 Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 Figure 2.6: A fractional frequency reuse (FFR) scheme. 2.5.2 Cell Collaboration The concept of cell collaboration was proposed in [43, 45, 46, 51, 98]. Being called Co- MIMO in [43] and base station cooperation (BSC) in [46], the collaboration takes place specically in the cell edge region. Since MSs in the cell edge are within the transmission range of multiple BSs, this technique allows multiple BSs to transmit signals to multiple cell-edge MSs concurrently with the same time and frequency resource using the MIMO technique such as beamforming. This is illustrated in Fig. 2.7 for a collaboration scenario with 2 BSs and 2 MSs. Co-MIMO or BSC can reduce ICI based on the idea that one may turn interference caused by signals transmitted by adjacent BSs into useful signals as shown by solid lines in Fig. 2.7. A more eective frequency reuse and spatial diversity can also be achieved through cooperation. Several cooperation beamforming choices were discussed in [45,51,98]. 33 BS1 BS2 MS1 MS2 Figure 2.7: A simple collaboration scenario with 2 BSs and 2 MSs. 2.6 Graph Theoretic Techniques Graph theory [19] has found its wide applications in various wireless communication environments, such as cellular, ad hoc, and sensor networks. Many design and analysis problems in the study of routing, connectivity properties, and interference modeling can all be formulated and solved in the framework of graph theory. Basically, a graph is a composition of nodes and directed or non-directed edges linking them. Nodes generally represent xed/mobile stations or terminals, such as base stations, routers or sensors, depending on the specic scenario to which the graph technique is applied. Edges describe the relationship between nodes, which can be, e.g., mutual interference in the interference modeling scenario or the bandwidth and/or cost associated with a routing path in routing decision. Our discussion will focus on the application of graphic techniques to interference characterization and channel assignment in this chapter. We rst examine the classical channel assignment problem in cellular networks, which has been studied in the past 34 several decades. Then, we consider frequency-reuse-one OFDMA networks and highlight their distinctive new features. 2.6.1 Classical Channel Assignment The classical channel assignment problem in cellular networks has been studied in the context of multi-coloring of a graph for decades, e.g., [28,63,65]. Each node in the graph represents a BS in a cell in the network, to which channels are assigned, while edges represent the potential co-channel interference between cells, which typically corresponds to the geographical proximity of cells. For instance, consider a hexagonal graph that represents a cellular network in Fig. 2.8. The objective of the channel assignment prob- lem is to assign channels to each cell such that the co-channel interference constraint is respected and the total number of used channels is minimized. This problem is translated to a graph coloring problem, as shown in Fig. 2.8, where two adjacent cells should have dierent colors (i.e., channels) and the total number of used colors (i.e., channels) is minimal. In this particular case, three colors are enough to color the graph. Besides a centralized coloring scheme with the global knowledge of the geometry and topology of networks, it is practical to consider a distributed approach to multi-coloring when such global information is unavailable. A distributed method demands only the information of neighboring cells for coloring decision. Specically, the extent of the local information is characterized by a graph distance denoted by k. That is, a cell is informed of all its neighbor cells within this distance only. A distributed algorithm under such a constraint is called a k-local algorithm, and the best channel assignment scheme is the one that uses the minimal number of channels subject to this constraint. Many 35 b r g r g b r b r g Figure 2.8: A hexagonal graph colored by three colors [65]. distributed algorithms were proposed (e.g., [28, 85]) to achieve more ecient usage of channels. Generally speaking, the more extensive the local information (i.e., bigger k), the fewer the channel number is needed for proper coloring. For distributed algorithms in the multi-coloring of general hexagonal graphs, we refer readers to [28,85] and references therein. 2.6.2 Reuse-One OFDMA Channel Assignment The classical channel assignment problem reviewed above aims to minimize the channel number (or, equivalently, to maximize spectral eciency) without any co-channel inter- ference. A dierent trade-o between co-channel (or inter-cell) interference and spectral eciency is possible; i.e., to relax the co-channel interference constraint so as to attain higher spectral eciency at the cost of some interference. Maximal spectral eciency is achieved by reusing the same set of channels (or a range of spectrum) in every cell, as in OFDMA networks with frequency reuse factor of one. However, co-channel interference 36 Figure 2.9: A MS-centered graph for OFDMA cellular networks. must be kept at a reasonably low level by the use of a proper interference management scheme. As a result, the design issue in reuse-one OFDMA networks is not to minimize the channel number as done in the classical context, but the co-channel interference with a predetermined set of channels (or a range of spectrum). This dierent problem formulation is re ected in graph coloring. Specically, the OFDMA channel assignment problem is dierent in the following three aspects. Unlike the traditional one that aims at minimizing the number of channels in use under the interference constraint, an OFDMA network has a xed and predeter- mined number of channels at disposal. Since complete avoidance of interference is not physically possible in the OFDMA case (especially in the heavy load situa- tion), a proper interference management scheme should be introduced to the graph framework. 37 Since OFDMA allows multiple users (MSs) to share frequency spectrum concur- rently as depicted in Fig. 2.1, the channel allocation problem is MS-centered, not BS-centered. In other words, nodes in the graph should denote MSs rather than BSs (see Fig. 2.9). Furthermore, unlike BSs that are still, MSs will move and the change of location will aect the interference and consequently the graph. This means that the topology of the MS-centered graph is more dynamic than the clas- sical BS-centered graph. As a result, the edge must be associated with dynamic weights to re ect the dynamics of interference between two nodes (MSs). The edge in the classical graph represents solely co-channel interference, which is determined by the proximity of cells. In the new graph in Fig. 2.9, the edge is associ- ated with a more general weight, determined by many factors such as the proximity of MSs, the residing cell of MSs, and the incorporated interference management techniques such as ICIC and BSC (see Sections 2.5.1 and 2.5.2). In light of these changes, we will use a new graphic approach, which is dierent from that of classical algorithms in [28,85], to solve the OFDMA resource allocation problem. This will be discussed in more detail in Chapter 5. 38 Chapter 3 Cross-layer QoS Analysis of Opportunistic OFDM-TDMA and OFDMA Downlink Networks 3.1 Introduction Multimedia delivery is one of the key objectives of next-generation wireless networks. Its success relies on how the underlying network can support dierent QoS requirements demanded by a variety of multimedia applications. A signicant challenge is posted since multimedia applications have very diverse characteristics in terms of physical measures such as bandwidth and delay. Furthermore, it is desirable that the underlying network can serve multiple users and meet their individual QoS requirement. All of these call for a QoS-provisioning broadband network in conjunction with proper multiple access schemes such as Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA). Recently, OFDM-based networks in combination with TDMA and FDMA have become a popular choice for such an endeavor. The IEEE 802.16 standard, for instance, has adopted OFDM-TDMA and OFDMA (OFDM-FDMA) as two transmission schemes at the 2{11 GHz band [33]. In addition, a QoS framework in the medium access control 39 (MAC) layer has also been integrated with the multiaccess transmission systems in the IEEE 802.16 standard [92]. Multiuser diversity provided by opportunistic scheduling [88] has been incorporated in multiuser OFDM-TDMA and OFDMA networks recently. Its eect on QoS-provisioning is an interesting yet challenging topic. On one hand, by allocating resources to users with better channel quality, the opportunistic scheduling scheme can maximize the overall system throughput [88]. On the other hand, it may degrade other QoS metrics such as delay, since users are suspended from transmission when their channels are poor. The impact of opportunistic scheduling on QoS provisioning is investigated in the course of comparison of OFDM-TDMA and OFDMA in this work. The bit error rate (BER) performance of OFDM-TDMA and OFDMA with multiuser diversity has been studied in previous work, e.g., [76,91]. Specically, uncoded and coded systems with opportunistic OFDMA were shown to outperform those with static OFDM-TDMA by 3 dB and 7 dB at BER = 10 3 in [91] and [76], respectively. The BER performance of OFDM-TDMA and OFDMA was also compared in [50] without considering multiuser diversity. While the BER analysis can be used to characterize the physical layer performance, it is not sucient to re ect other QoS metrics such as packet throughput and delay in the link layer. The fact that QoS requirements should be treated dierently in dierent layers suggests a cross-layer approach for QoS provisioning and analysis. In fact, the cross- layer approach has been applied to the design and analysis of QoS-featured multiaccess systems by a few researchers recently. For example, the analysis of queueing delay for 40 802.16 networks was conducted in [47,66] by combining link-layer queueing with physical- layer transmission. A vacation queueing model was adopted in [67] to analyze the link- layer queueing performance of OFDM-TDMA systems with round-robin scheduling. A queueing model for OFDMA systems was used in [82] to design a scheduling scheme that balances multiuser diversity and queueing delay. Although the packet-level analysis has been conducted for OFDM-TDMA or OFDMA in [47, 66, 67, 82], there are a few open issues to be addressed. We discuss these issues and point out our contributions below. First, an analytical framework to account for both OFDM-TDMA and OFDMA systems to facilitate their comparison is missing. By generalizing results in [23, 24], we propose a framework to achieve this goal here. Sec- ond, performance evaluation of 802.16 has been conducted primarily by simulation in the past, e.g., [41, 53]. We conduct an analysis to demonstrate that OFDMA outperforms OFDM-TDMA in terms of several QoS metrics. This is consistent with the trend of the latest IEEE Standard 802.16e-2005 [2], which adopts OFDMA as its principal multiaccess scheme. Third, although packet average delay and maximum delay are useful link-layer performance measures for non-real-time (e.g., le transfer and web browsing) and real- time (e.g., voice and video) applications, respectively, most previous work has focused on the packet average delay. The packet maximum delay and the delay violation probability will be examined in this work. Finally, the performance of two well-known scheduling strategies, namely, the round-robin scheduling and the opportunistic scheduling, is exam- ined for OFDM-TDMA and OFDMA networks so as to understand their pros and cons in the context of QoS provisioning. 41 Our approach to physical and link layer analysis is simply stated as follows. The ideal channel state information (CSI) is assumed to be available at the base station. This is often achieved by feeding the estimated channel information from the receiver back to the transmitter through a control channel. The Rayleigh fading channel is modeled by a nite-state Markov chain [100] to translate the eect of the physical layer to higher lay- ers. Specically, the channel eect is manifested in the link layer as a time-varying server with the M/G/1 queueing model for the packet throughput-delay analysis. To analyze the packet maximum delay, we adopt and implement a well-known ow control scheme [31] as part of the proposed QoS framework. With such a ow control scheme, we can derive delay bounds based on network calculus results for dierent scheduling and rate adap- tation schemes. All the aforementioned performance metrics provide valuable measures in dierentiating OFDM-TDMA and OFDMA in their QoS-provision performance. It is nally concluded that OFDMA has a higher potential in meeting the requirements of multimedia delivery. The rest of this chapter is organized as follows. The system model, which consists of the QoS-aware framework, the ow control regulation scheme, multiple access and resource allocation schemes, is discussed in Sec. 3.2. The physical and link layer analysis for OFDM-TDMA and OFDMA is presented in Sec. 3.3. Simulation results are shown and discussed in Sec. 3.4. Finally, concluding remarks are given in Sec. 3.5. 42 3.2 System Model The proposed cross-layer QoS framework is shown in Fig. 3.1(a), where QoS provision is achieved by packet categorization and service dierentiation. Specically, packets are classied into the premium and the best-eort two classes and better service is granted to the premium class. Particularly, a delay-sensitive service is oered to the premium class by the preemptive priority scheduling mechanism, where premium packets maintain a higher priority for processing in our framework. The reason to choose delay as a main performance metric for service dierentiation is that the delivery of many multimedia applications are delay-sensitive. As shown in Fig. 3.1(b), a ow control scheme is adopted on top of service dierentiation to regulate the end-to-end packet delay of the premium and the best-eort classes. The proposed QoS framework is a simplication of those used in DiServ [68] and the 802.16 MAC protocol [92]. 3.2.1 Flow Control Regulation A ow control regulator [31] is adopted to process real-time multimedia data so as to keep the delay bound and arrival constraints [58]. As depicted in Fig. 3.1(b), X k1 (t) and X k2 (t) are the ow-control regulated premium and best-eort streams of user k, respectively. We write X k1 (t) (r k1 ;w k1 ) if, for any t 1 t 2 , Z t 2 t 1 X k1 (t)dt r k1 (t 2 t 1 ) + w k1 ; (3.1) where r k1 is the predened average rate of the stream and w k1 is the allowed burst degree. In other words, the input stream has to be regulated so that the output stream, 43 Premium Priority scheduling Best effort X k1 (t) ~ (r k1 , w k1 ) X k2 (t) ~ (r k2 , w k2 ) u k (t) ~ (u k , v k ) A p p l i c a t i o n P a c k e t C l a s s i f i e r F l o w C o n t r o l Premium Best effort Priority scheduling Mobile k Premium Best effort Mobile 1 Mobile K . . . Multiple access and bit allocation . . . (a) (b) App Net/Link Link (MAC) Link/PHY F l o w C o n t r o l Figure 3.1: (a) A cross-layer QoS-support system model and (b) a queueing system with ow-control regulated streams and preemptive priority servicing, shown for mobile user k. X k1 (t), can meet the imposed rate and burstiness constraints. Likewise, we have X k2 (t) (r k2 ;w k2 ). Suppose that the time-varying server process, u k (t), in Fig. 3.1(b) conforms to a similar but slightly dierent constraint. That is, we write u k (t) ( u k ;v k ) if, for any t 1 t 2 , Z t 2 t 1 u k (t)dt u k (t 2 t 1 ) v k ; (3.2) 44 where v k is the service lag and u k is the average service rate dened by u k = lim t!1 1 t Z t 0 u k ()d; (3.3) with probability one. We will show in Sec. 3.3.3 that the server process u k (t), which is prescribed by actual multiaccess and scheduling schemes, satises (3.2) asymptotically, and parameters u k and v k can be derived analytically. 3.2.2 Multiple Access and Scheduling The multiple access scheme in Fig. 3.1(a) is accomplished by OFDMA or OFDM-TDMA along with subcarrier/time slot assignment and bit allocation mechanisms. Several dif- ferent schemes to be examined are summarized in Table 3.1. Note that we use OFDM time slot and OFDM symbol interchangeably in this paper. Table 3.1: Multiaccess OFDM modes considered in this work. OFDMA Mode Subcarrier Assignment Bit Allocation OFDMA I static xed OFDMA II static adaptive modulation OFDMA III dynamic adaptive modulation OFDM-TDMA Mode Time-slot Assignment Bit Allocation OFDM I static xed OFDM II static adaptive modulation OFDM III dynamic adaptive modulation OFDMA and OFDM-TDMA perform multiple access in a frequency-sharing and a time-sharing manner, respectively. Specically, OFDMA performs subcarrier assignment while OFDM-TDMA performs time-slot assignment, both statically or dynamically. The dierence between static (or round-robin) and dynamic (or opportunistic) assignments 45 lies in whether users' channel conditions are considered. For OFDMA, static assignment allocates an equal, xed and interleaved set of subcarriers to users while dynamic as- signment allocates each subcarrier to the user with the best signal-to-noise ratio (SNR). Likewise, for OFDM-TDMA, static assignment allocates xed and alternate time slots to users (i.e., round robin) whereas dynamic assignment assigns a time slot to the user with the best channel condition. Besides, the chosen user is allocated all subcarriers exclusively in OFDM-TDMA. The subcarrier SNR distribution for each multiaccess mode can be obtained as a basis for analysis in Sec. 3.3. For a Rayleigh fading channel, the received SNR, denoted by , is exponentially distributed with the following probability density function (pdf) [100]: g ( ) = 1 0 exp( 0 ); 0; (3.4) where 0 is the average SNR. Note that Eq. (3.4) holds for subcarrier SNR in a multicar- rier system as well [84]. Eq. (3.4) applies to all modes in Table 3.1 except for OFDMA III up to a dierence in mean 0 which will be veried by simulation. In OFDMA III, recall that the dynamic assignment scheme assigns a subcarrier to the user with the best SNR at that subcarrier. Thus, when K homogeneous users are considered, the post-assignment subcarrier SNR, , is distributed according to the maximum of K independent and iden- tically distributed (i.i.d.) random variables 1 ; ; K , which represent the received SNR 46 of users 1; ;K and follow the pdf in (3.4). To derive the pdf of , we rst obtain the cumulative distribution function (cdf): Pf g = Pfmax( 1 ; ; K ) g = (1 exp( 0 )) K ; 0: Then, by dierentiating the cdf, we have g ( ) = K 0 exp( 0 )(1 exp( 0 )) K1 ; 0: (3.5) 3.2.3 Bit Allocation The multiaccess scheme apportions resource among users while the bit allocation scheme chooses the type and order of modulation for each user. We consider squared M-QAM modulations with M = 2 2r , r = 1; ;r m , where r m determines the highest modulation allowed. Both xed and (discrete-rate) adaptive modulation (AM) methods are consid- ered, where only the AM methods take channel conditions into account in adaptive bit allocation [13]. The AM methods are described below. A tight BER approximation for squared M-QAM is given by [13]: P b = 0:2exp( 3 2(M 1) ); (3.6) 47 where is the channel SNR. With continuous-rate adaptation, bit rate R c b is given by the following capacity expression: R c b = log 2 M = log 2 (1 + 1:5 ln5P b ): (3.7) Note that (3.7) is obtained directly by the rearrangement of (3.6). Discrete-rate adaptation connes the bit rate to integer values (more precisely to 2r, r = 0; ;r m ), which is described as follows. First, the set of possible received SNR (i.e., the nonnegative real line) is partitioned into r m +1 disjoint regions R 0 ; ;R rm by boundary points b 0 ;b 1 ; ;b rm+1 ; where R r is the interval [b r ;b r+1 ) for r = 0;1; ;r m and b 0 < b 1 < < b rm+1 with b 0 and b rm+1 set to 0 and 1, respectively. Second, the boundary points are determined by b r = 2 3 (ln5P b )(2 2r 1); r = 1;2; ;r m : (3.8) Last, when the received SNR falls in R r and the information is successfully fed back to the transmitter, 2r bits are loaded to the corresponding subcarrier. Note that the channel is too poor to support any order of modulation when the SNR falls in R 0 . This leads to the following bit rate expression of discrete-rate adaptation: R d b = 8 > > < > > : 2b 1 2 log 2 (1 + 1:5 ln 5P b )c; if < b rm , 2r m ; if b rm , (3.9) 48 wherebxc represents the largest integer that is less than or equal to x. Note that for any P b and , R d b R c b . 3.3 Performance Analysis and Comparison Multiaccess schemes in Table 3.1 are analyzed in this section based on the system model introduced in Sec. 3.2. The physical layer performance is considered in Sec. 3.3.1 while the link layer performance metrics are examined in Secs. 3.3.2 and 3.3.3. 3.3.1 Bit Rate and BER Analysis For the bit rate and BER analysis, we focus on AM-based modes (e.g., OFDMA II{III, OFDM II{III) since non-AM modes are trivial special cases. The theoretical bit rate upper bounds are derived under the assumption of continuous-rate adaptation. However, such bounds also hold for the discrete-rate adaptation case. For xed P b and , the bit rate per subcarrier with continuous-rate adaptation is given in (3.7). With the distribution of shown in (3.4) for OFDMA II and OFDM II{III, the bit rate corresponding to these modes is bounded by R b1 = E [log 2 M()] log 2 E [M()] (3.10) = log 2 Z 1 0 M( )g ( )d = log 2 (1 + 1:5 ln5P b 0 ): 49 The total bit rate R t1 (in the unit of bits/sec) can be obtained by scaling with the total number of subcarriers N and OFDM symbol time T s as R t1 N T s log 2 (1 + 1:5 ln5P b 0 ): (3.11) Similarly, the total bit rate for OFDMA III, R t2 , is obtained by replacing by in (3.10) and using (3.5). That is, we have R t2 N T s log 2 1 + 1:5 ln5P b 0 ( K X k=1 1 k ) : (3.12) For the BER analysis, note that the AM scheme described in Sec. 3.2.3 will lead to comparable BER performance for all OFDMA and OFDM modes due to the predeter- mined P b in place. A more informative comparison in BER can be achieved by xing a target bit rate for all modes. Towards this end, we adopt a method based on [32] to add and subtract bits from proper subcarriers successively until the target bit rate is achieved. That is, when the actual bit rate is smaller (or larger) than the target bit rate, additional bits are added to (or subtracted from) subcarriers such that the error proba- bility is increased as small as possible (or decreased as far as possible). In other words, additional bits are successively added to (or subtracted from) the subcarrier where the dierence between capacity (R c b in (3.7)) and assigned discrete-rate bits (R d b in (3.9)) is maximal (or minimal). The equivalence between \maximizing the dierence between capacity and the as- signed bits" and \minimizing the bit error rate" is intuitive and it can be formally proved. 50 The proof is however omitted here due to the space limit. This operation to increase (or decrease) the BER when bits are added (or subtracted) will be conrmed by simulation in Sec. 3.4. Furthermore, the proposed bit rate adjustment method may not be the best solution due to its computational complexity. The main purpose for us to adopt this method is to demonstrate a more meaningful BER comparison by xing the bit rate. In a realistic system design, if no target bit rate is established as a requirement, such a manipulation is unnecessary. 3.3.2 Packet Average Throughput and Delay Analysis The packet-level average throughput and delay performance is analyzed in this subsection. By delay, we refer exclusively to queueing delay. To complete the delay analysis, and for fair comparison, a common queueing model for both OFDM-TDMA and OFDMA is adopted. We simplify Fig. 3.1(a) by merging the premium and the best eort in one single queue 1 . Specically, we consider the model shown in Fig. 3.2, where user data are queued separately with one congregated Poisson arrival of rate . The server rate is determined by the opportunistic (dynamic) OFDM-TDMA or OFDMA scheme. We assume that user i's packets may be transmitted over links i = 1;2;::: ;K. In other words, when the opportunistically selected link has an empty queue, the server will continue to process the next queue as long as not all queues are empty. This simplication facilitates the analysis as we need not deal with the dynamics of each individual queue (such as 1 ; 2 ;::: ; K ) while solely focusing on the dierentiation of OFDM and OFDMA as 1 This simplication does not compromise our comparison. In fact, the results presented here are readily extensible to priority queues. 51 : : Mobile 1 Mobile 2 Mobile K u(t) l 1 l 2 l K l Figure 3.2: A queueing model for OFDM-TDMA or OFDMA. dierent server processes. The resulting model for the average delay analysis is therefore a single composite queue with Poisson arrival rate and service rate , which will be modeled by the M/G/1 queueing system [15]. We consider a fast fading channel where fading coecients are i.i.d. over OFDM symbols. This provides a good approximation for i.i.d. service times considered in the M/G/1 model when each packet's service time spans over many independent OFDM symbols. Besides, correlations in the channels associated with an OFDM symbol at the end of one packet and at the beginning of another are negligible transients when the packet service time spans many OFDM symbols so that the ergodic average is reached. The average delay W in the M/G/1 model is given by [15]: W = E[S 2 ] 2(1 E[S]) ; (3.13) where S is the packet service time and is the Poisson packet arrival rate. Note that in the case of innite-sized queues as assumed in this work, the throughput is proportional 52 S/P Adaptive modulation IFFT P/S GI insertion : : : Channel P/S Symbol detection FFT S/P GI removal : : : Parallel Serial Serial Data from link layers Figure 3.3: A typical OFDM transmission system. to the value. Therefore, we only need to determine S up to the second moment to complete the throughput-delay relation in (3.13). We consider the service time S being measured in the unit of the number of subcar- riers. The idea can be explained by the fact that the \service" of an OFDM/OFDMA system is conducted by loading bits to subcarriers to process packets. Besides, an OFDM transmission system (Fig. 3.3) matches the number of subcarriers with the number of samples in an OFDM symbol through the parallel-to-serial (P/S) and serial-to-parallel (S/P) conversions (the overhead of guard intervals, or GI, is considered negligible here). Thus, the conventional notion of delay measured by time samples can also be equivalently measured by subcarriers. The discussion above can be described mathematically as follows. Service time S is dened to be the smallest N s that satises S , ( N s Ns X i=1 I i ) ; (3.14) 53 where I i is the number of bits loaded to subcarrier i, which is identically (but not nec- essarily independently) distributed over all i, and is the xed packet size in bits. For convenience, we dene a random variable U such that U , P Ns i=1 I i , and a positive valued \overshoot" variable . Then, (3.14) can be rewritten as S , N s U = + : (3.15) We evaluate the rst two moments of S in the following. First, we dene an indicator function, 1 n , to be 1 n = 8 > > < > > : 1; if N s n; 0; else: (3.16) That is, 1 n is the indicator function of the event fN s ng. Second, while I i 's may be correlated which depends on the coherence bandwidth 2 of the fading channel, we consider an approximation where I n is independent of all I i 's before U = + is reached, i.e., E[I n 1 n ] = E[I n ]E[1 n ]. The approximation becomes more accurate when the coherence bandwidth is relatively small compared to a service time duration. Thus, random variable N s in (3.14) satises the \stopping rule" [37, p. 66] for the set of random variablesfI i ;i 1g. That is, the eventfN s ng, conditional on the I i 's before U = + is reached, is independent of those afterwards, i.e.,fI n ;I n+1 ;:::g. The rst moment can 2 The coherence bandwidth is a statistical measure of the range of frequencies (or subcarriers) over which the channel can be considered of equal gain. 54 be derived by following this property and the Wald's equality [37, p. 66], as well as using the fact that I i 's are identical random variables each of mean value E[I]. Thus, we have E[U] = E " Ns X i=1 I i # = E[N s ] E[I]: Then, by the denition of S in (3.15) we have E[S] = E[ + ] E[I] : Note that the \overshoot" is bounded above by the maximum value of I i , i.e., the maximum possible number of bits loaded to a subcarrier, which is usually negligibly small compared to the xed size of a packet, . Therefore, we can obtain a good approximation for E[S], i.e., E[S] = E[I] : (3.17) The second moment of S can be derived similarly. Using the indicator function in (3.16) we have E[U 2 ] = E " ( Ns X i=1 I i ) 2 # = E " ( 1 X i=1 I i 1 i ) 2 # = E " 1 X i=1 (I i 1 i ) 2 # + E 2 6 42 1 X i=1 i<j 1 X j=1 (I i 1 i I j 1 j ) 3 7 5 : (3.18) 55 The rst term above can be further simplied by using the fact that 1 i is independent of fI i ;I i+1 ;:::g (\stopping rule"), i.e., E " 1 X i=1 (I i 1 i ) 2 # = 1 X i=1 E[I 2 i ]E[1 2 i ] = E[I 2 ]E " 1 X i=1 1 2 i # = E[I 2 ] E[N s ]: (3.19) The nal step above follows from the denition of the indicator function in (3.16). To proceed on the second term of (3.18), we rst observe that, for i < j, 1 i is independent of fI i ;I j g. The same is not true for 1 j , which is independent of I j but not of I i . To make further simplication possible, however, we approximate E[I i I j 1 i 1 j ] = E[I i I j ]E[1 i 1 j ] so that the second term of (3.18) can become more tractable. That is, E 2 6 42 1 X i=1 i<j 1 X j=1 (I i 1 i I j 1 j ) 3 7 5 = 2 1 X i=1 i<j 1 X j=1 E[I i I j ]E[1 i 1 j ] E[I 2 ] 2E 2 6 4 1 X i=1 i<j 1 X j=1 1 i 1 j 3 7 5 = E[I 2 ] 2E N s (N s 1) 2 = E[I 2 ] E[N 2 s ] E[N s ] : (3.20) The rst step above follows from the approximation. The second step uses an upper bound drawn on E[I i I j ], which is explained further below. E[I i I j ] represents the cross- correlation among subcarriers, which depends on the coherence bandwidth of the channel. 56 Without exact knowledge about the channel, we may proceed by deriving an upper bound by using the Schwartz inequality and the fact that I i and I j are nonnegative. That is, E[I i I j ] q E[I 2 i ]E[I 2 j ] = E[I 2 ]; i6= j: Substituting (3.19) and (3.20) into (3.18), we obtain E[U 2 ] E[N 2 s ] E[I 2 ]: Again, by the denition of S in (3.15) we have E[S 2 ] E[( + ) 2 ] E[I 2 ] 2 E[I 2 ] : (3.21) To complete the analysis in (3.17) and (3.21), we need to obtain the rst two moments of I i , i.e., the number of bits loaded to subcarrier i. Apparently, I i depends on the AM scheme in (3.9), the subcarrier channel condition given in (3.4) or (3.5), and the selected multiaccess mode. Based on the AM method described in Sec. 3.2.3 and the SNR distribution given in (3.4) and (3.5), we rst obtain the probability of the subcarrier SNR falling into SNR interval R r , which is denoted by r . By integrating pdfs in (3.4) or (3.5) over disjoint regions R r 's we have r = Z b r+1 br g ( )d or Z b r+1 br g ( )d ; (3.22) 57 where r = 0;1; ;r m . Then, with these r 's, the rst and second moments of I i can be obtained by E[I] = rm X r=0 r (2r); E[I 2 ] = rm X r=0 r (2r) 2 : (3.23) Finally, by substituting (3.23) in (3.17) and (3.21), and then (3.17) and (3.21) in (3.13), we obtain the theoretical throughput-delay lower bound curves. This result will be veried by computer simulation in Sec. 3.4. 3.3.3 Packet Maximum Delay Analysis We obtain analytical packet delay bounds for all modes listed in Table 3.1 in this subsec- tion. A result from network calculus is described below, which will be used in analysis later. The delay for the premium stream in Fig. 3.1(b) is bounded by [31] d pm w k1 + v k u k ; (3.24) if queues are stable (i.e., r k1 +r k2 u k ) and the rst-in-rst-out (FIFO) service strategy is employed for each queue. Note that only the delay performance of the premium stream is of our interest. Also, the delay bound in (3.24) refers to delay experienced by the regulated streams. The waiting time inside the ow control regulator as analyzed in [81] is not of our concern. 58 Recall that the denition in Sec. 3.2.1 is tied with continuous processes. However, the slotted structure of OFDM/OFDMA suggests that the server process be represented by a discrete-time random process u k [n], where n is the OFDM time slot index. This change turns all integrations into summations in Sec. 3.2.1 while leaving ow control parameters unchanged but in dierent units. That is, w k1 , w k2 and v k are in the unit of bits and rates r k1 , r k2 and u k are in the unit of bits per time slot. Then, the delay bound in (3.24) is in the unit of the number of OFDM time slots. Note that there is no discrepancy between the units used in this subsection and those in Sec. 3.3.2, where the number of subcarriers is used, since the number of subcarriers can be translated to an equivalent number of OFDM symbols, and vice versa. The most remarkable dierence is that, instead of averaging over all users and packets in presenting the average delay results in Sec. 3.3.2, we must treat each packet and each user individually here since the measure of delay bounds is not an average. In the following, we obtain deterministic delay bounds for static modes such as OFDMA I and OFDM I, and then derive probabilistic delay bounds for the remain- ing modes that use dynamic allocation. Note that a smaller delay bound guarantees better worst-case delay performance. 3.3.3.1 OFDMA I and OFDM I These two modes employ static multiple access and bit allocation yet in a dierent fashion. Recall from Fig. 3.1 that the server process u k (t) is prescribed by actual multiaccess and bit allocation, thus resulting dierent server processes of OFDMA I and OFDM I as 59 server process u k (t) ... Ts 2Ts KTs (K+1)Ts 0 2KTs ... time t t 1 t 2 (b) (a) ... t 2 ' Figure 3.4: Illustration of the continuous-time server process for user k with a total of K users: (a) OFDMA I and (b) OFDM I. depicted in Fig. 3.4 for the continuous-time representation and Fig. 3.5 for the discrete- time representation. From these gures, we observe that the server rate of OFDMA I is a constant, since subcarriers are divided evenly among users in each OFDM time slot. In contrast, in OFDM I, user k's server rate peaks at time slots when user k is in service and remains zero during periods in which other users are served. To obtain the delay bound in (3.24), our task is to nd the pair ( u k ;v k ) that denes the server process (w k1 is controlled and known in the design of a ow-control regulator). Let N be the total number of subcarriers and r the (xed) number of bits loaded to each 60 server process u k [ n] ... 1 2 K K+1 2K ... OFDM symbol n ... 2K+1 ... ... ... Figure 3.5: Illustration of the discrete-time server process for user k with a total of K users: (o) OFDMA I and (x) OFDM I. subcarrier. Therefore, in each OFDM time slot N r bits are served. OFDMA I has a constant server rate, i.e., u k [n] = u k = N r=K and v k = 0: Consequently, we have d pm w k1 u k : (OFDMA I) (3.25) For OFDM I, the average server rate u k is the same as that in OFDMA I according to (3.3). To obtain v k , we need to examine (3.2) carefully. First, we observe that a suciently large v k in the RHS will make (3.2) always hold since the LHS of (3.2) is non-negative. However, an arbitrarily large value of v k is not useful in deriving the delay bound in (3.24). Thus, we want to nd a smallest v k for which (3.2) is satised for any 61 choice of t 1 and t 2 . As depicted in Fig. 3.4, our choice of t 1 and t 2 is the pair that spans the widest among any t 1 and t 2 values that enclose a \peak-rate" time slot of OFDM. Since t 2 t 1 = 2k 1 is the largest in this case, the associated v k will guarantee that (2) holds also for any other choices of t 1 and t 2 . With such t 1 and t 2 and (3.2), we have N r u k (2K 1) v k : By arranging the terms and the fact that N r = K u k , we have the smallest v k as v k = u k (K 1): (3.26) Substituting u k and v k into (3.24) yields d pm w k1 u k + (K 1); (OFDM I) (3.27) where u k = Nr=K. By comparing (3.25) and (3.27), we see that OFDMA I has a smaller delay bound than OFDM I by a xed amount of K 1. The physical interpretation of this result is that the K1 idle time slots in OFDM I account for the K 1 extra delay bound. 3.3.3.2 OFDMA II and OFDMA III To obtain delay bounds for OFDMA III and, as a special case, OFDMA II, we make two assumptions in the asymptotic analysis. The number of subcarriers, N, is large, and the subcarrier channel coecients are i.i.d. These may be regarded as an ideal approximation 62 to real-world situations. However, as will be demonstrated by simulation in Sec. 3.4, the theoretically derived delay bounds coincide well with experimental results in both the i.i.d. and the real-world channel setups. Thus, our analysis does provide insights into performance dierences among dierent modes. OFDMA III, unlike OFDMA I, has a time-varying server process due to the uctuation of user channels. Specically, the server process u k [n] is a discrete-time random process dened by u k [n] = X i2D k [n] I i [n]; (3.28) where I i [n] is the number of bits loaded onto subcarrier i, and D k [n] is the set of sub- carriers assigned to user k, both at OFDM time slot n. I i [n], i 2 D k [n], are i.i.d. by our aforementioned assumption. Besides, due to opportunistic selection of users, the probability of each user \winning" a particular subcarrier is 1=K, which leads to the binomially-distributed jD k [n]j, denoted by jD k [n]j B(N;1=K), where jxj is the cardi- nality of set x. Given u k [n] as the summation of jD k [n]j i.i.d. random variables, along with the assumption of big N, we have (as N !1 and consequently jD k [n]j!1) u k [n] E[u k [n]] p V ar(u k [n]) !N(0;1); (3.29) whereN(0;1) is the standard Gaussian distribution according to the Central Limit The- orem, and E[u k [n]] = N K E[I i [n]]; V ar(u k [n]) = N K V ar(I i [n]) + N K (1 1 K )(E[I i [n]]) 2 ; 63 which can be obtained by applying the standard conditional mean and variance procedures to (3.28) (conditioned on D k [n]). Furthermore, by ergodicity (which can be shown by the Law of Large Numbers) we have u k = E[u k [n]] = N K E[I i [n]]: (3.30) To obtain v k , we resort to the denition in (3.2) and a proper choice of t 1 and t 0 2 in Fig. 3.4. Then, (3.2) reduces to u k [n] u k v k : (3.31) Second, we dene the delay violation probability P dv as the probability that the delay bound in (3.24) is violated. Since w k1 and u k are known or derived in (3.30), the violation in (3.24) may only occur when v k is violated, i.e., (3.31) fails to hold. Then, with P dv being the outage probability in (3.31) and by plugging the asymptotic distribution of u k [n] into (3.31), it is straightforward to show Q( v k (P dv ) p V ar(u k [n]) ) = 1 P dv ; or, equivalently, v k (P dv ) =Q 1 (1 P dv ) p V ar(u k [n]): (3.32) Finally, by substituting (3.30) and (3.32) into (3.24), we obtain d pm w k1 + v k (P dv ) u k : (OFDMA III) (3.33) 64 OFDMA II, which is a special case with xed jD k [n]j = N=K, has the same u k in (3.30) but a dierent V ar(u k [n]) = N K V ar(I i [n]): Substituting V ar(u k [n]) into (3.32) and then (3.33) yields the delay bound for OFDMA II. 3.3.3.3 OFDM II and OFDM III We rst obtain results for OFDM III and then OFDM II as a special case. The server process in OFDM III can be written as u k [n] = 8 > > < > > : u k;b [n] = P N i=1 I i [n]; n2 C(k); 0; otherwise; (3.34) where C(k) is the set of time slots assigned to user k. The average server rate is easily obtained by the denition in (3.3) as u k = E[u k [n]] = N K E[I i [n]]: (3.35) To nd v k , we follow the analysis for OFDM I with one additional assumption; namely, there exists C idle such that any idle period (when u k [n] = 0 for user k) is, up to a negligible violation probability, of length no greater than C idle K1 time slots. The value of C idle is chosen empirically to ensure the statistics associated with the opportunistic assignment is unchanged. 65 Similarly to the analysis for OFDM I, v k is derived with judicious choice of t 1 and t 2 applied to (3.2), i.e., u k;b [n] u k [2(C idle K 1) + 1] v k : Then, due to the asymptotic distribution of u k;b [n], u k;b [n] N E[I i [n]] p N V ar(I i [n]) !N(0;1); (3.36) we have v k (P dv ) =Q 1 (1 P dv ) p N V ar(I i [n]) +(2C idle 1 1 K )N E[I i [n]]: (3.37) Substituting (3.35) and (3.37) into (3.24) gives the delay bound d pm w k1 + v k (P dv ) u k : (OFDM III) (3.38) All the above derivation also applies to OFDM II by setting C idle = 1 due to the static round-robin time-slot assignment in OFDM II. 66 Table 3.2: The TDL Channel Model Parameters rms delay spread ( rms ) 1 s tap spacing (T) 175 ns number of taps (L) 20 max delay spread ( max ) 3.325 s (= 175 ns (20-1)) Table 3.3: Parameters of the OFDM System OFDM symbol time (T s ) 100.8 s useful symbol time (T b ) 89.6 s guard time (T g ) 11.2 s FFT size (N FFT ) 512 sample time (T) 175 ns (= 89.6 s/512) 3.4 Simulation Results In this section, we perform computer simulation to verify the analysis given in Sec. 3.3 and make an extensive comparison of the link and the physical layer performance of OFDM- TDMA and OFDMA. The Rayleigh fading channel is adopted and generated by a tapped delay line (TDL) channel model with equally-spaced taps and an exponential power delay prole. The parameters for the TDL channel model are given in Table 3.2. We consider homogeneous users whose channel coecients are i.i.d. A practical framed structure is considered where, unless otherwise noted, each frame contains ten OFDM symbols. A fast fading channel based on the method described in [88] is implemented. We restrict the squared M-QAM modulations to 4-, 16-, 64- and 256-QAM (i.e., r m = 4). Besides, although OFDMA may have a larger number of subcarriers than OFDM in real-world applications, we use an identical set of parameters for both systems for fair comparison. The parameters of the OFDM system are borrowed from [94] and summarized in Table 3.3. 67 4 6 8 10 12 14 16 18 20 22 24 10 5 10 6 10 7 10 8 SNR (dB) Bit Rate (bits/sec) OFDMA II, OFDM II (ana. upper bound) OFDMA II (sim.) OFDM II (sim.) OFDM III (ana. upper bound) OFDM III (sim.) OFDMA III (ana. upper bound) OFDMA III (sim.) Figure 3.6: Comparison of maximum supportable bit rates with K = 4. We rst examine the total bit rate that can be supported by each mode. Both ana- lytical upper bounds from (3.11) and (3.12) and empirical results are shown in Fig. 3.6. Note that target BER P b = 10 3 is set for bit allocation. We observe that, among these four modes, OFDMA III achieves the best performance due to multiuser diversity and frequency diversity that arise from dynamic allocation. Likewise, OFDM III outperforms OFDMA II and OFDM II due to dynamic time-slot allocation. Both OFDMA II and OFDM II perform static multiple access which leads to the same share of resource of each user on the average. Consequently, we observe comparable curves in Figs. 3.6 and 3.7 68 4 6 8 10 12 14 16 18 20 10 −6 10 −5 10 −4 10 −3 10 −2 10 −1 10 0 SNR (dB) Bit Error Rate OFDM II (sim. K=4) OFDMA II (sim. K=4) OFDM III (sim. K=4) OFDM III (sim. K=8) OFDMA III (sim. K=4) OFDMA III (sim. K=8) Figure 3.7: Comparison of BER results with K = 4 and 8. for OFDMA II and OFDM II, where the dierence is contributed by randomness in bit allocation. Fig. 3.7 shows the uncoded BER performance when the bit rate is xed at 4 bits/subcarrier (or roughly 20 Mbits/sec). For K = 4, we see that OFDMA III outperforms OFDM III by 3.5 dB, and OFDM III outperforms OFDMA II and OFDM II by 2 dB when BER = 10 3 . This result is slightly dierent from that of [91] due to dierent settings. We also observe an additional multiuser diversity gain contributed by more users with K = 8. Note that 69 0 1 2 3 4 5 6 0 5 10 15 20 average throughput (packets/frame) average delay (time slots) OFDMA II, OFDM II (ana. lower bound) OFDM II (sim.) OFDMA II (sim.) OFDM III (ana. lower bound) OFDM III (sim.) OFDMA III (ana. lower bound) OFDMA III (sim.) Figure 3.8: Comparison of the packet throughput and delay results with SNR = 16 dB and K = 4. the bit adding and subtracting operations described in Sec. 3.3.1 renders BER above P b at the low SNR region since extra bits are added to make up 4 bits/subcarrier. We choose a xed packet length of = 3000 bits and SNR = 16 dB in presenting the packet throughput-delay performance curves shown in Fig. 3.8. We see that the performance dierences are translated from the physical-layer transmission schemes and they are consistent with the results in Figs. 3.6 and 3.7. In particular, given a xed 70 Frame i . . . . . . Packet arrival N i N i+1 N i+2 Frame i+1 Frame i+2 Queue status time Figure 3.9: Illustration of the exhaustive service system and queueing in the link layer simulation in Fig. 3.8. delay, OFDMA III achieves the largest throughput and, consequently, the best packet- level throughput-delay performance. As the throughput value approaches capacity, all schemes suer from a signicant amount of delay. Note that although there is no notion of frames in the analytical M/G/1 model, a frame should be considered in the nite granularity implementation. In the simulation, we consider a practical exhaustive service system where only packets that arrive before or during the current frame can be served in the current frame as shown in Fig. 3.9. Packets are multiplexed and served in the frame sequentially in both time and frequency. Besides, the number of packets in a queue is counted frame by frame and averaged to give a nite granularity approximation of N, the time-average number of packets in the queue. With N and throughput controlled to get dierent points in the plot, we calculate the average delay by Little's Law [15]: W = N=. Due to the exhaustive service assumption and nite granularity approximation, N is nearly zero at a low throughput value, resulting W 0. This accounts for the fact that the simulation curve does not obey the analytical lower bound curve when the throughput 71 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 120 number of users delay bound (time slots) OFDMA I OFDM I OFDMA II OFDM II OFDMA III OFDM III Figure 3.10: Analytical delay bounds versus the number of users, K, with SNR = 16 dB. is low. It is worthwhile to point out that the throughput-delay result here is an average over all users and packets. The result of the individual delay incurred to each user packet is presented next. We implement the ow control regulator by the \leaky bucket" scheme in [81]. We choose a token pool of size of 3000 tokens. Each token can serve 1 bit of data, from which the burst sizes w k1 and w k2 can be calculated to be 3001 bits. The token arrival rates, which determine the average regulated rates r k1 and r k2 , are chosen such that queues are stable. Moreover, C idle is found empirically to ensure the violation probability less 72 than 10 2 ; for example, C idle = 4 (or, respectively, 5) for K = 4 (or, respectively, 8). We x user channel SNR = 16 dB and P dv = 10 4 to obtain the analytical delay bounds in Sec. 3.3.3, which, after rounded up to the nearest integer number of time slots, are drawn in Fig. 3.10 for the premium stream. We see from Fig. 3.10 that OFDMA modes generally have better worst-case delay performance than OFDM modes. The idle periods introduced by round-robin or opportunistic time-slot assignments in OFDM account for the performance gap. The opportunistic assignment, in particular, creates the possibility of a long idle period which explains for the largest delay bounds of OFDM III. Note that, when K = 1, all modes degenerate to the same scheme. As K increases, the delay bound increases because the same resources are shared among an increasing number of competitors. In Figs. 3.11 and 3.12, we draw the Monte Carlo simulation curves when SNR = 16 dB and K = 4. We see that the analytical delay bounds, obtained from Fig. 3.10 by xing K = 4 and shown in the legend of both plots, agree well with the actual packet maximum delay performance. Figs. 3.11 and 3.12 provide knowledge of the packet delay distribution by presenting the percentage of packets (y-axis) that experience delay higher than a particular value (x-axis). It is observed that OFDM schemes generally have higher delay variation than OFDMA. For example, OFDM III in Fig. 3.12 has a large dynamic range in the packet delay while OFDMA III has a much smaller range as shown by the sharper slope of curves in Fig. 3.11. This observation suggests that OFDMA is more suitable for supporting real-time trac, since real-time trac is vulnerable to large delay. Figs. 3.11 and 3.12 also show simulation results under the setting of i.i.d. subcarrier channels. The results of the i.i.d. case are very close to its non-i.i.d. counterparts. This 73 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 delay bound (time slots) delay violation probability OFDMA I (sim.), ana. bound=12 OFDMA II (sim.), ana. bound=12 OFDMA II (sim., iid) OFDMA III (sim.), ana. bound=8 OFDMA III (sim., iid) Figure 3.11: The delay violation probability vs. the delay bound for OFDMA modes with SNR = 16 dB and K = 4. may be explained as follows. Although these two settings produce dierent bit allocation results on individual subcarriers, the dierence is mitigated by a number of summations in the process of calculating the overall packet delay. To conclude, as far as the link layer delay analysis is concerned, the i.i.d. assumption facilitates the derivation of analytical delay bounds that work well for both i.i.d. and real-world setups as conrmed by Figs. 3.11 and 3.12. Simulation results for SNR = 16 dB and K = 8 are shown in Figs. 3.13 and 3.14 to demonstrate the eect of user number K. As compared with the case of K = 4 in 74 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 delay bound (time slots) delay violation probability OFDM I (sim.), ana. bound=15 OFDM II (sim.), ana. bound=15 OFDM II (sim., iid) OFDM III (sim.), ana. bound=38 OFDM III (sim., iid) Figure 3.12: The delay violation probability vs. the delay bound for OFDM modes with SNR = 16 dB and K = 4. Figs. 3.11 and 3.12, an increased individual delay is observed due to a larger number of users. Overall, we observe consistent results for K = 4 and K = 8, and the discussion made for K = 4 holds for K = 8 in Figs. 3.13 and 3.14 as well. 3.5 Conclusion Performance analysis and comparison of OFDM-TDMA and OFDMA centered on schedul- ing with cross-layer consideration were conducted. Several OFDM/OFDMA modes with 75 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 delay bound (time slots) delay violation probability OFDMA I (sim.), ana. bound=24 OFDMA II (sim.), ana. bound=23 OFDMA II (sim., iid) OFDMA III (sim.), ana. bound=13 OFDMA III (sim., iid) Figure 3.13: The delay violation probability vs. the delay bound for OFDMA modes with SNR = 16 dB and K = 8. dierent multiaccess and resource allocation schemes were considered along with an an- alytical framework based on the QoS architecture of IEEE 802.16. The analysis and simulation oered a thorough understanding of the system's capability of supporting multimedia delivery from a cross-layer viewpoint involving both link and physical layers. The analytical and empirical results suggest that dynamic OFDMA has a stronger poten- tial to support multimedia transmission than dynamic OFDM-TDMA. It is also observed that the opportunistic assignment can be employed more eectively in OFDMA. 76 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 delay bound (time slots) delay violation probability OFDM I (sim.), ana. bound=31 OFDM II (sim.), ana. bound=31 OFDM II (sim., iid) OFDM III (sim.), ana. bound=92 OFDM III (sim., iid) Figure 3.14: The delay violation probability vs. the delay bound for OFDM modes with SNR = 16 dB and K = 8. 77 Chapter 4 Opportunistic Access with Random Subchannel Backo (OARSB) for OFDMA Uplink 4.1 Introduction Orthogonal Frequency Division Multiple Access (OFDMA) is a physical-layer technology adopted by the IEEE 802.16e standard [4] to support broadband wireless access. One of the main characteristics of OFDMA is that it allows multiple users to transmit si- multaneously on orthogonal subcarriers in both downlink and uplink transmissions. In the downlink direction, which is a point-to-multipoint communication, the base station (BS) allocates the channel to users through scheduling. On the other hand, in the uplink direction, the multiple access nature demands not only communications between users and the BS but also coordination among independent users. Coordination among users in OFDMA uplink may be done in two dierent ways, i.e. a centralized scheme or a distributed scheme. An arbitrator takes full charge of channel allocation by scheduling users in the centralized approach. In contrast, in the distributed scheme users share subchannels in a random access fashion, which is then assisted by a 78 collision-avoidance mechanism. In particular, users operate and coordinate themselves according to short feedback messages (e.g., ACK or NACK) received from the BS indi- cating the status (e.g., success or collision) of previous requests. The main advantage of a distributed scheme is its simplicity since little information exchange is required between BS and users. For this reason, distributed channel allocation is appealing for uplink OFDMA, and it has been adopted by the 802.16e standard as an option for the uplink bandwidth request [4]. Distributed access in OFDMA networks has been studied in previous work, e.g. [14, 30,89]. In the scheme proposed by Wang et al. in [89], each user determines the quality of its subchannels by a common set of centrally-optimized thresholds and sends requests of transmission in a way that allows better subchannels to \win" more likely during the contention period. If two or more request messages collide, the corresponding subchannel is not used. An opportunistic multichannel Aloha was proposed for OFDMA by Bai and Zhang in [14], where each user contend for a set of its subchannels that is above a certain threshold and, if the request message collides, the collided subchannels are not used. In other words, collision resolution was not considered. Choi et al. [30] proposed a fast retrial method for OFDMA where collided users, rather than procrastinate for a random time, switch immediately to a random frequency band so that collision may be resolved in the frequency domain. However, opportunistic allocation is not studied in [30]. Being motivated by [30], we consider a frequency-domain collision resolution mech- anism but in the context of opportunistic access in this work. A simple yet ecient algorithm is proposed to enhance the system throughput by integrating opportunistic 79 medium access and collision resolution through random subchannel backo [26]. Conse- quently, it is called the opportunistic access with random subchannel backo (OARSB) scheme. The proposed OARSB scheme is a purely distributed uplink scheme with no common thresholds employed. By leveraging the multiuser diversity and resolving colli- sions eciently, OARSB not only achieves distributed coordination among users but also reduces the amount of information exchange between the base station and users. The throughput and delay performance analysis of OARSB is conducted using a Markov chain model. The superior performance of OARSB over an existing scheme is demonstrated by analysis as well as computer simulation. The rest of this chapter is organized as follows. The system model is discussed in Sec. 4.2. The OARSB scheme is presented in Sec. 4.3. The throughput and delay performance of the OARSB scheme is analyzed in Sec. 4.4. Simulation results are shown in Sec. 4.5. Finally, concluding remarks are given in Sec. 4.6. 4.2 System Model The frame structure of a time-division duplex (TDD)-OFDMA scheme dened in IEEE 802.16e [4] is depicted in Fig. 4.1, which shows the time-frequency resource planning for both uplink and downlink communications. In the uplink section, a ranging subchannel is reserved for the purpose of either synchronization between users and the BS (i.e., ranging) or requests of sending uplink data from users to the BS (i.e., the uplink bandwidth request). 80 The uplink bandwidth request is of our main interest in this work. It may be done in two dierent ways: polling-based (centralized) or contention-based (distributed). In the polling scheme, the BS polls each user alternately for its intent to transmit, which is suitable for the rtPS service [64]. In the contention scheme, users contend for the transmission opportunity via random access, which is suitable for the nrtPS service [64]. Regardless of the scheme adopted, the bandwidth request process is completed in the uplink section, and results are broadcasted to users through the UL-MAP messages in the downlink. Then, users will use the uplink subchannels according to the assignment information in UL-MAP as shown in Fig. 4.1. We consider the contention-based uplink channel allocation in this work, which is a distributed scheme by nature. The medium access is performed on ranging subchannels. The available subchannels are divided into logical subgroups that correspond one-to-one to the remaining uplink data subchannels. Thus, a user who plans to use a particular data subchannel will contend for its usage on the corresponding ranging subchannels. Note that a subchannel (SC) is a clustering of serveral adjacent subcarriers [54]. 4.3 Proposed OARSB Scheme The distributed uplink channel allocation for OFDMA may be performed using the slotted Aloha scheme [14] due to the slotted structure of OFDMA. A collision resolution policy may also be incorporated to regulate the packet retransmission as well as enhance the throughput. Thanks to the multiband structure of OFDMA, a fast collision resolution scheme can be performed in the frequency domain as well [30]. That is, collided packets 81 Ranging subchannel UL burst #1 UL burst #2 UL burst #3 UL burst #4 UL burst #5 DL burst #2 DL burst #5 DL burst #6 DL burst #4 DL burst #3 D L b u r s t # 1 ( U L - M A P ) P r e a m b l e D L - M A P FCH Ranging subchannel UL burst #1 UL burst #2 UL burst #3 UL burst #4 UL burst #5 Uplink Downlink Uplink S u b c h a n n e l l o g i c a l n u m b e r OFDMA symbol number Downlink ... Figure 4.1: TDD-OFDMA frame structure in IEEE 802.16e [4]. \backo" to random subchannels in the immediate next time slot instead of waiting for a certain number of time slots for retransmission. In other words, the frequency-domain backo replaces the traditional time-domain backo. Since the waiting time is greatly reduced, this method is also called \fast retrials" [30]. We call it the opportunistic access with random subchannel backo (OARSB) scheme in this work. Due to fading in a wireless environment, backo to a subchannel in deep fade is not desirable. In other words, subchannel gains of each user should be taken into account in the backo decision. Hence, the proposed OARSB not only resolves the collision in the frequency domain but also exploits multiuser diversity, since subchannel gains tend to vary from one user to the other. 82 The proposed OARSB algorithm can be described in detail as follows. Suppose that we have K contending users and a total of M uplink data subchannels. Each user is allowed to request (contend) L subchannels, where L M. With knowledge of its own channel (but no others), each user can rank its subchannels in the descending order in gains and request for its best L subchannels initially (See Fig. 4.2(a) for the case of K = 2, M = 7 and L = 3). The subchannels currently in request are called active, while the rest are inactive and queued. Thus, each user has L subchannels in the active region and M L subchannels in the inactive queue during the negotiation. The active region is denoted by S 0 while each position in the inactive queue is represented by S i , i = 1;::: ;M L, as shown in Fig. 4.2(a). The frequency-domain backo collision resolution is realized in the following way. We assume that users know the feedback messages (success or collision) within one time slot. Upon collision (i.e., two or more users request for the same subchannel), the collided subchannel is \backoed" to the inactive queue in a random position S a , which is de- termined by a random number, a, chosen uniformly and independently from [0;W 1], where W is the backo window size. All the subchannels in original S 1 ; ;S a positions will be shifted one position toward the active region, and the front one will become active to substitute for this collided subchannel. For example, with W = 3 in Fig. 4.2(a), the collided SC 2 of user 1 is assigned a = 2 at t = 1 and thus backoed to position S 2 at t = 2. Besides, the front one of the inactive queue, SC 4, becomes active to replace SC 2. Note that if a = 0, the collided subchannel will \backo" to S 0 , i.e., remain active. For example, user 2's SC 2 from t = 1 to t = 2 in Fig. 4.2(a). 83 OFDM symbol time s u b c h a n n e l s SC 1 SC 2 SC 3 SC 4 SC 5 SC 6 SC 7 User 1: SC2 > SC5 > SC7 > SC4 > SC6 > SC1 > SC3 User 2: SC7 > SC2 > SC6 > SC1 > SC3 > SC4 > SC5 active region inactive queue U1 U1 U2 U2 U1 t=1 t=2 t=3 U2 U1 U1 U1 U2 U2 U2 S 0 t=1 (initial) User 1: 4 5 7 6 2 1 3 User 2: 7 2 6 1 3 4 5 User 1: 4 5 6 7 2 1 3 User 2: 1 2 6 3 7 4 5 User 1: 4 5 7 6 2 1 3 User 2: 1 2 6 3 7 4 5 t=2 t=3 a =2 a =0 a =1 a =2 a =1 a =0 (a) (b) S 1 S 2 S 3 S 4 Figure 4.2: An example of the proposed OARSB scheme. When multiple collisions happen, as shown in t = 1 of the example, the same process will be performed for each collided subchannel sequentially, as seen in t = 2 of the example. The step-by-step backo process is shown in Fig. 4.2(a) and its corresponding \subchannel switching" is shown in Fig. 4.2(b). It is worthwhile to point out that one major dierence between the proposed OARSB algorithm and fast retrials in [30] is that OARSB switches to good subchannels instead of random subchannels. This is realized by a frequency-domain backo design where collided good subchannels are not discarded 84 but retained for possible future retrials. With help of randomness, the backo design also reduces the likelihood of re-collision. 4.4 Delay and Throughput Analysis The delay (due to collision resolution) and throughput for the proposed OARSB scheme are analyzed in this section. Understanding the delay and throughput helps in choosing proper parameters for the algorithm given the ranging period length and throughput requirements. To facilitate the analysis, we make the following three assumptions. A1) Channel fading is independent across subchannels and users. That is, subchannel gains are i.i.d. for all users. This is achievable if the subchannel bandwidth is bigger than the coherence bandwidth, and users act independently. A2) For a particular time t, subchannels of users are equally likely to be active, i.e., k;m (t) = PrfSC m of user k is active at time tg , ; k = 1;::: ;K;m = 1;::: ;M: (4.1) Furthermore, the state of activeness is independent across subchannels and users. A3) The timeline of the ranging period is partitioned into initial (t = 1) and backo (t = 2;3;:::) two stages. For the initial stage, we can obtain explicitly k;m (1) , 1 = L=M; k = 1;::: ;K;m = 1;::: ;M: (4.2) 85 active 0 1 2 W-1 W . . . M-L inactive . . . Figure 4.3: The Markov chain description of the behavior of subchannel m of user k. For the backo stage, we assume the probability values remain constant over time. Thus, along with assumption A2 we have k;m (t) , ; k = 1;::: ;K;m = 1;::: ;M; and t = 2;3;::: ; (4.3) where will be derived in Sec. 4.4.1. 4.4.1 Markov Chain Model We use a Markov chain model to describe the transition dynamics of a subchannel, through which we can obtain steady state probabilities and transition probabilities that will be used in the delay and throughput analysis as given in Secs. 4.4.2 and 4.4.3, re- spectively. The dynamic of a particular subchannel, m, of a particular user, k, of the proposed OARSB is depicted in Fig. 4.3, where state i corresponds to position S i in Fig. 4.2(a). We drop \S" for the notational convenience. The transitions shown in Fig. 4.3 have ruled 86 out unlikely transitions for the sake of analytical tractability. For example, the transition from state W 1 to 0 implies at least W 1 SCs in the active region of this user collide, which is unlikely to happen. For this reason, backward transitions only occur in adjacent states. Besides, if a subchannel falls initially in states W; ;M L, it will stay in the same state. Let q m be the probability that an active SC m sees no collision. By the assumption of independent subchannels and users and the fact that an active SC m sees no collision when the rest K 1 SC m's are all inactive, we have q m = q = (1 ) K1 : (4.4) Let A(t) represent the state at time t. Then, the transition probabilities are dened by P i;j = Pr[A(t + 1) = jjA(t) = i]; i;j = 0;1;::: ;W 1: (4.5) In the following, we will obtain all non-zero transitions in Fig. 4.3 in terms of q. First, we look at the self transition of state 0, which is the probability that an active SC at time t remains active at time t + 1. This may occur in two possible cases; namely, this SC does not collide or it collides but backos to the active region again (i.e., when a = 0). Since a takes on value 0 with probability 1=W, we have P 0;0 = q + (1 q) 1 W : (4.6) 87 The outgoing transitions from state 0 to state i correspond to the case where this SC collides and backos to state i (i.e., when a = i). As a result, we have P 0;i = (1 q) 1 W ; i = 1;2;::: ;W 1: (4.7) Then, we derive the transitions for the remaining states. The self transitions of state i, i = 1;::: ;W1, may occur in two possible ways: no collisions in user k's active region (of size L), or l collisions, 1 l L, which all backo to positions in front of state i. By summing these two cases, we have P i;i = q L + L X l=1 L l (1 q) l q Ll ( i W ) l ; i = 1;2;::: ;W 1: (4.8) The outgoing transition probabilities are simply one minus the self transition probabilities, i.e., P i;i1 = 1 P i;i ; i = 1;2;::: ;W 1: (4.9) Let P denote the transition matrix of this Markov chain model with P i;j as the (i;j) entry, and = ( 0 ; 1 ; ; W1 ) be the steady-state probabilities. Then, can be uniquely obtained by solving the following equations: = P; (4.10) W1 X i=0 i = L + W 1 M : (4.11) 88 By the denition of in (4.1), we have = 0 : (4.12) Note that in (4.12) is a function of q (because P is a function of q), and q in (4.4) is a function of . This nonlinear system can be solved using numerical methods and can be shown to have an unique solution set. 4.4.2 Delay Analysis The delay is dened as the time it takes for the collision to resolve, i.e. d ,ft d j collision is resolved at time t = t d g: (4.13) For example, we have d = 3 in Fig. 4.2. In general, we have d = 1;2;::: ;D, where D is the maximum allowed delay, which can be viewed as the nite length of the ranging period. If the collision is not resolved at the end of the ranging period, we set d = D. If no initial collision occurs so that no collision resolution takes place, we have d = 1. For the special case of no collision resolution scheme as that given in [14], we get d = 1 always. Let P c0 be the initial collision probability (i.e., collision occurs at t = 1), and P c be the collision probability for all subsequent time slots (i.e., collision occurs at t = 2;3;:::) 89 with assumption A3. Note that the delay is equal to n if collision occurs in consecutive time slots t = 1;::: ;n 1 and resolves at t = n. Thus, we obtain Prfd = ng = 8 > > > > > > < > > > > > > : 1 P c0 ; n = 1; P c0 P n2 c (1 P c ); 1 < n < D; P 1 i=D P c0 P i2 c (1 P c ); n = D: (4.14) The expected delay can be calculated as E[d] = 1 P c0 + P c0 2 + P c (1 P D2 c ) 1 P c : (4.15) The value of P c0 can be obtained as follows. We rst observe that \no initial collision" is equivalent to \all active SCs are successful at t = 1". An SC m is successful if one and only one SC m is active. With the independent assumption across subchannels and users, the probability of no initial collision is the number of permutations that involve no duplicate subchannels in the active region divided by the number of total possible permutations. This yields P c0 = 8 > > < > > : 1 M(M1)(MLK+1) (M(M1)(ML+1)) K ; if LK M; 1; else; (4.16) where we use the fact that, when LK > M, at least one SC appears in the active region more than once. The value of P c may be approximated with assumptions A2{A3. Note that the proba- bility of no collision, 1P c , is equal to the probability that all active SCs see no collision. 90 Let us rst consider a particular user k. The probability that an active SC of user k sees no collision is (1 ) K1 , i.e., when none of the remaining K 1 same SC's is active. This probability applies to user k's all L active SCs. Then, we examine another user k 0 6= k. Its active SC sees no collision with probability (1 ) K2 , i.e., with one less interfering user. This yields P c = 1 (1 )(1 ) 2 (1 ) K1 L : (4.17) Note that replacing by 1 in (4.17) gives an approximation to the exact P c0 in (4.16). Finally, substituting (4.16) and (4.17) in (4.15) yields the analytical delay result. 4.4.3 Throughput Analysis The throughput T is dened as the total information rate (in bits/sec) supported by all successful subchannels at the end of collision resolution, i.e., at t = d. We are interested in nding the average number of successful subchannels, E[N], and the average supportable information rate of each successful subchannel, E[R]. Then, with these two, the average throughput is given by [14]: E[T] = E[N] E[R]: (4.18) The average number of successful subchannels, E[N], can be derived as follows. We dene m (t) = Pr[SC m is successful at time t] = (t); (4.19) 91 successful S U 2 U 0 unsuccessful Figure 4.4: The Markov chain description of the three possible outcomes for a particular subchannel m by jointly considering K users. which leads to E[N] = M (d): (4.20) To obtain (d), we observe that the OARSB scheme relies on the interaction between users to resolve collision eectively. In other words, all K SC m's should be considered jointly. Besides, the OARSB scheme operates sequentially to create inter-dependence between times t + 1 and t in terms of an SC being successful or not. As a result, (t + 1) and (t) are dependent. In light of these two observations, we resort to a Markov chain that jointly considers K users and traces all the history up to t = d (such as steps shown in Fig. 4.2(a)). As shown in Fig. 4.4, the Markov chain for a particular SC m has three possible states: successful (denoted by state S); unsuccessful when no SC m is active (denoted by state U 0 ); and unsuccessful when two or more SC m's are active (denoted by state U 2 ). The transition probability Q i;j is dened as Q i;j = Pr[B(t + 1) = jjB(t) = i]; i;j = S;U 2 ;U 0 ; (4.21) 92 where B(t) represents the state at time t. We can derive all Q i;j by scrutinizing the interaction between subchannels of all K users. First, we examine state S. Since an active subchannel will become inactive only upon collision, a successful subchannel can either remain successful (S) or collide with others (U 2 ). Thus, Q S;U 0 = 0. To obtain Q S;U 2 , we use the fact that the transition from S to U 2 takes place when at least one of the K1 inactive SC m's become active, i.e., from state 1 to 0 in Fig. 4.3. This leads to Q S;U 2 = Pr[B(t + 1) = U 2 and B(t) = S] Pr[B(t) = S] = P K1 j=1 K K1 j j 1 (1 1 ) K1j 1 P j 1;1 K(1 ) K1 : (4.22) Since the sum of transition probabilities of a state is equal to one, we have Q S;S = 1 Q S;U 2 : (4.23) The same analysis applies to state U 0 . The transition probability Q U 0 ;S accounts for the probability that exactly one out of K inactive SC m's becomes active. That is, Q U 0 ;S = Pr[B(t + 1) = S and B(t) = U 0 ] Pr[B(t) = U 0 ] = P K i=1 K i ( 1 ) i (1 1 ) Ki i(1 P 1;1 )P i1 1;1 (1 ) K : (4.24) 93 Likewise, we have Q U 0 ;U 0 = Pr[B(t + 1) = U 0 and B(t) = U 0 ] Pr[B(t) = U 0 ] = P K i=0 K i ( 1 ) i (1 1 ) Ki P i 1;1 (1 ) K (4.25) and Q U 0 ;U 2 = 1 Q U 0 ;S Q U 0 ;U 0 (4.26) for state U 0 . Transitions of state U 2 can be derived in a similar way as shown below. QU 2 ;S = P K i=2 P Ki j=0 K i i Ki j (1) j (1 1) Kij i 1 W (1 1 W ) i1 P j 1;1 + (1 1 W ) i j(1 P1;1)P j1 1;1 1 (1 ) K K(1 ) K1 ; (4.27) Q U 2 ;U 0 = P K i=2 P Ki j=0 K i i Ki j ( 1 ) j (1 1 ) Kij (1 1 W ) i P j 1;1 1 (1 ) K K(1 ) K1 ; (4.28) Q U 2 ;U 2 = 1 Q U 2 ;S Q U 2 ;U 0 : (4.29) Let Q be the transition probability matrix, i.e., Q = 2 6 6 6 6 6 6 4 Q S;S Q S;U 2 Q S;U 0 Q U 2 ;S Q U 2 ;U 2 Q U 2 ;U 0 Q U 0 ;S Q U 0 ;U 2 Q U 0 ;U 0 3 7 7 7 7 7 7 5 : (4.30) 94 Then, (d) can be obtained as (d) = the rst element of Q d1 ; (4.31) where = ( S ; U 2 ; U 0 ) is the initial state probability vector with S = K 1 (1 1 ) K1 ; U 0 = (1 1 ) K ; U 2 = 1 S U 0 : Note that the scheme in [14] is a special case of the proposed OARSB with (1) = K 1 (1 1 ) K1 and E[N] = M (1). Now, we are ready derive E[R] to complete the throughput analysis. The average rate of each successful subchannel is the average rate of all potentially successful subchannels, i.e., the best L+W1 subchannels of each user (Fig. 4.3). Furthermore, the SNR of the i-th best subchannel follows the probability distribution function (pdf) of the i-th largest exponential order statistics for the Rayleigh fading channel. With a discrete adaptive modulation scheme and given pdfs, the average rate of i-th best subchannel, r i , can be easily obtained. We refer to [25] for more details. Finally, we have E[R] = 1 L + W 1 L+W1 X i=1 r i ; (4.32) and substituting E[R] and E[N] into (4.18) gives the desired throughput result. 95 4.5 Simulation Results Computer simulation is performed in this section to demonstrate the performance of the proposed OARSB scheme and verify the analysis given in Sec. 4.4 numerically. An OFDMA system is implemented with parameters specied in [94]. We choose an FFT size of 512, which is divided into 16 subchannels, each of which has 32 subcarriers. One subchannel is dedicated for the ranging purpose. Thus, we have M = 15 data subchan- nels for contention. The Rayleigh fading channel is adopted in the simulation and its parameters are chosen such that the assumption A1 in Sec. 4.4 is met. The throughput performance of the proposed OARSB scheme is shown in Figs. 4.5 and 4.6 for K = 3 and 5, respectively, with the OMC-Aloha scheme [14] as the performance benchmark. Both schemes allow an equal number of requested (active) subchannels, L, from each user for fair comparison. W = 3 is considered for the OARSB scheme. We see that the throughput of both schemes is lower when L is too small or too big due to low channel utilization and intense collision, respectively. The best throughput is achieved around operational points of L = M=K or M=K 1. It is observed that the adoption of collision resolution in OARSB greatly improves its throughput for the region centered around operational points. This can be explained by the fact that random subchannel backo judiciously switches to other subchannels so that collision is eciently resolved among users. Moreover, OARSB gives a higher priority to better subchannels so that multiuser diversity is exploited accordingly. Figs. 4.5 and 4.6 compare the analytical and simulation results. We see that they agree well for L M=K, which is the typical operational region. However, the discrepency 96 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 10 12 x 10 6 number of active subchannels per user, L bits/sec OMC−Aloha (K=3, sim.) OMC−Aloha (K=3, ana.) OARSB (K=3, sim.) OARSB (K=3, ana.) Figure 4.5: Throughput vs. the number of active subchannels per user, L, for OARSB and the scheme proposed in [14], with K = 3, M = 15 and W = 3. becomes bigger when L is larger due to the approximations used in the Markov chain analysis in Sec. 4.4. The collision resolution delay result is shown in Fig. 4.7 for OARSB. Generally, the bigger the L, the longer the delay due to more contending subchannels in place. Likewise, the bigger the K, the longer the delay due to more contending users in place. Note that we set the maximum allowable delay (i.e., the ranging period length), D, to 15. Thus, for L > M=K the collision tends to persist after the ranging period and, thus, the delay is D = 15. In contrast, when L M=K, all collisions can mostly be resolved during the ranging period. 97 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 10 12 x 10 6 number of active subchannels per user, L bits/sec OMC−Aloha (K=5, sim.) OMC−Aloha (K=5, ana.) OARSB (K=5, sim.) OARSB (K=5, ana.) Figure 4.6: Throughput vs. the number of active subchannels per user, L, for OARSB and the scheme proposed in [14], with K = 5, M = 15 and W = 3. 4.6 Conclusion A distributed channel allocation scheme for uplink OFDMA called OARSB was proposed. The advantage of opportunistic assignment and the eciency of the frequency-domain collision resolution strategy are integrated in OARSB. The proposed OARSB scheme can easily be implemented in 802.16 due to its simplicity. It was shown by analysis and simulation that the throughput is enhanced signicantly. 98 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 number of active subchannels per user, L time slots OARSB (K=3, sim.) OARSB (K=3, ana.) OARSB (K=5, sim.) OARSB (K=5, ana.) Figure 4.7: The collision resolution delay vs. the number of active subchannels per user, L, with M = 15, K = 3 or 5, and W = 3. 99 Chapter 5 Multi-Cell OFDMA Downlink Resource Allocation Using A Graphic Framework 5.1 Introduction Orthogonal Frequency Division Multiple Access (OFDMA) is a widely adopted technology in many next generation cellular systems such as the 3GPP Long Term Evolution (LTE) [1] and IEEE 802.16m [3] due to its eectiveness and exibility in radio resource allocation, as well as the capability of combating frequency selective fading. The radio spectrum is a scarce resource in wireless communications and, therefore, its ecient use is critical. The rapid growth of wireless applications and subscribers have called for a good radio resource management (RRM) scheme that can increase the network capacity and, from a commercial point of view, save the deployment cost. Consequently, developing an eective radio resource allocation scheme for OFDMA is of signicant interest to academia as well as industry. The fundamental challenge of resource allocation lies in the scarcity of the available spectrum, the expansive servicing area and the large user number. As a result, the same 100 frequency spectrum has often to be reused in multiple geographical areas or cells. This will incur inter-cell interference (ICI) when users or mobile stations (MSs) in adjacent cells use the same spectrum. In fact, ICI has been shown to be the predominant performance- limiting factor in wireless cellular networks [52]. A signicant amount of research has been devoted to ICI-aware radio resource allocation in cellular networks [52]. While techniques surveyed in [52] are useful in some application scenarios, many (such as channel borrowing) cannot be directly applied to networks using a frequency reuse- 1 in cell deployment (i.e., the same spectrum is reused in each and every cell). Since reuse-n (n > 1) systems tend to lose more bandwidth than what can be gained from less interference (and better link quality), reuse-1 has been generally considered as the preferred scheme for modern cellular systems such as OFDMA. Despite the lucrativeness of better spectral eciency, reuse-1 OFDMA networks are also subject to severer ICI. Thus, a good ICI management scheme on top of OFDMA is needed. Research endeavors on multi-cell OFDMA resource allocation with ICI consideration can be classied into two categories. The rst category extends the single-cell alloca- tion experience [59, 91, 96] to the multi-cell scenario, mainly by considering the signal- to-interference-and-noise ratio (SINR) instead of the signal-to-noise ratio (SNR). This formulation is handy as most of the single-cell OFDMA resource allocation schemes can be directly applied to the multi-cell context. For instance, Li and Liu [60] proposed a two- level resource allocation scheme, wherein the radio network controller (RNC) coordinates multiple cells in the rst level, and performs per-cell optimization in the second level. The rst level is conducted based on perfect and predetermined knowledge of SINR for all MSs on all subchannels. In [40], a similar approach was adopted with some special treatment 101 on ICI. Pietrzyk and Janssen [69,70] proposed heuristic algorithms for their formulated problems based on SINR, with some quality-of-service (QoS) consideration. Abrardo et al. [11] proposed a centralized and a distributed method for multi-cell OFDMA resource allocation based on the measurement of ICI. Note that a key assumption in this category of research is the availability of SINR. This may be dicult to obtain a priori, however, since the interference depends on the distance, location, and occupied channel status of interferers, which are unknown before resource allocation. In other words, it is the mutual dependency of ICI that complicates the problem. Thus, a multi-cell resource allocation scheme contingent upon global and perfect knowledge of SINR may not be practical. The second category of work aims at developing systematic RRM techniques and policies as guidelines for resource allocation. For instance, advanced techniques such as inter-cell interference coordination (ICIC) [35] and base station cooperation (BSC) [98] were proposed to mitigate formidable ICI and improve overall system performance. Similar RRM mechanisms were suggested for the multi-cell scenario in the 3GPP [8,9]. Recently, new improvements were also proposed in 3GPP LTE (e.g., [74,75]) and IEEE 802.16m (e.g., [43]) standardization activities. Some of the ICIC schemes (e.g., [75]) were designed based on the concept of soft reuse; i.e., asymmetric reuse factors are applied to cell-center and cell-edge regions. Specically, cell center is allowed to use smaller reuse factor to enhance the spectral eciency since cell-center MSs, with reduced transceiving power, will cause less interference to neighbors (i.e., downlink power control). The issues of downlink power control and soft reuse are further studied in [72, 73]. Most research work in this category has concentrated on presenting the design concept of ICIC and/or BSC, justifying the use of these techniques, and obtaining the achievable performance 102 bound. The problem of designing a practical algorithm that actually achieves the resource allocation principle suggested by ICIC or BSC has been largely overlooked. Based on this observation, we are motivated to propose a novel, high-performance yet low-complexity multi-cell OFDMA downlink channel assignment method to enable ICIC and BSC in the reuse-1 deployment. In the proposed framework [27], the problem of ICI reduction is rst addressed using a graphic approach, where no precise SINR information is required. Then, the task of channel assignment is conducted by taking instantaneous channel conditions into account. In order to strike a balance between performance optimality and practicality, heuristic algorithms are further proposed to simplify the solution of ICI reduction and channel assignment. It is demonstrated by extensive simulation that the proposed scheme can oer substantial SINR improvements in the reuse-1 deployment. The rest of this chapter is organized as follows. After a brief background review in Sec. 5.2, we describe our system model and the resource allocation problem in Sec. 5.3. Our solution framework is presented in Sec. 5.4. Two heuristic algorithms to facilitate the solution framework are discussed in Sec. 5.5. The performance advantage of our proposed solution is demonstrated by computer simulation in Sec. 5.6. Finally, concluding remarks are given in Sec. 5.7. 103 BS4 BS3 BS1 BS2 BS5 BS6 BS7 Figure 5.1: Illustration of a hexagonal multi-cell OFDMA cellular network. 5.2 Research Background 5.2.1 Multi-cell OFDMA Networks A hexagonal multi-cell OFDMA cellular network is considered in this work. An example network with seven cells is drawn in Fig. 5.1. Each cell is served by a base station (BS) located at the center of the cell, and there are several MSs within each cell. Each MS is classied by its proximity to the BS as either in the cell center or the cell edge area. The boundary that separates the cell center and the cell edge can be a design parameter. In OFDMA systems, the radio resource to be allocated to users is the subchannel. A subchannel is a group of subcarriers, which may or may not be contiguous. This depends on the specic permutation scheme used, which determines the mapping from physical subcarriers to logical subchannels. As specied in the IEEE 802.16e standard [4], PUSC 104 (partial usage of subchannels) and AMC (adaptive modulation and coding) are permuta- tion schemes that dene non-adjacent and adjacent subcarrier groupings for a subchannel, respectively. 5.2.2 The Diversity Set In regular operation, each MS is registered at and communicates with a single BS, which is called the anchor (or serving) BS. However, in some scenarios (e.g., soft handover or, as will be introduced later in this section, base station cooperation), simultaneous communication with more than one BS may take place. A diversity set is dened in the 802.16e standard [4] to serve this purpose. It keeps track of the anchor BS and neighboring BSs that are within the communication range of an MS. This information is maintained at the MS as well as the BS. The diversity set of MS m is denoted by D m = A m [B m , where A m is the anchor BS set which has only one element (i.e. anchor BS A m ) and B m is the neighbor BS set which may have zero, one or multiple BSs. Note that the number of elements in set B m depends on the geographic location of MS m in relation to its neighboring BSs, as well as on some path loss threshold. Property: (Forming the Diversity Set) It is assumed that each MS, besides its own serving BS, has at most two neighbor BSs in its diversity set. That is, for any MS m, jD m j 3, where jj is the cardinality of a set. The above property follows from the observation about a hexagonal network that the dominant signal comes from the nearest three BSs. Signal from farther BSs will undergo severer path loss degradation before it reaches the MS and thus is assumed below the path loss threshold used to determine the diversity set. Note that, however, when dening 105 the SINR we take all BSs in the network into consideration as the potential interfering source. This will be presented in Sec. 5.3.1. 5.2.3 Inter-cell Interference Coordination (ICIC) Since ICI dominates the performance of interference-limited cellular networks, proper ICI management is needed. Inter-cell interference coordination (ICIC) was proposed in [35,74] to eectively reduce ICI in cell-edge regions. It is achieved by allocating disjoint channel resources to cell-edge MSs that belong to dierent cells. Since cell-edge MSs are most prone to high ICI, the overall ICI can be reduced by judicious coordination between cell- edge MSs in channel allocation. This idea is illustrated in Fig. 5.2. MS 1 has anchor BS 1 and MS 2 has anchor BS 2. A i , B i and C i refer to the three sectors 1 in the cell-edge area, and D i refers to the cell-center area, i = 1;::: ;7. Non-overlapping channel resources as shown by dierent colors are allocated to MS 1 and MS 2 located in neighboring B 1 and B 2 sectors, respectively. Therefore, the potential interference caused by downlink signals to each other, shown by dotted lines, is avoided. In general, ICIC suggests allocation of disjoint channel resources to neighboring cell-edge regions (i.e., A 1 , A 4 and A 5 ; B 1 , B 2 and B 3 ; C 1 , C 6 and C 7 ) to mitigate ICI. In other words, ICIC reduces the number of interferers and/or the \damage" of each interferer. The latter can be achieved by, for instance, allocating the same resource to MSs that are geographically farther apart from each other so that the interference is mitigated due to the increased path loss. 1 Sectorization shown in Figs. 5.2 and 5.3 serves only to illustrate the relationship between the geo- graphical location of MSs and resource management. We will focus on the discussion of non-sectorized cell deployment in the rest of this chapter. Nevertheless, the framework established hereafter can be readily applied to sectorized systems. 106 BS1 BS2 BS7 BS3 BS6 BS4 BS5 MS1 MS2 A 1 A 2 A 3 A 4 A 5 A 6 A 7 B 1 B 2 B 3 B 4 B 5 B 6 B 7 C 1 C 2 C 3 C 4 C 5 C 6 C 7 D 1 D 2 D 3 D 4 D 5 D 6 D 7 Figure 5.2: Illustration of resource management in a multi-cell cellular network using the ICIC principle, where the same/dierent colors represent the use of the same/dierent subchannels of the band. However, while ICIC solely based on cell-edge resource collision avoidance is benecial to the uplink, it oers only a limited performance gain in the downlink scenario since it overlooks the interference caused by transmission from the BS to cell-center MSs [74]. This motivates us to develop a holistic channel assignment framework where all MSs, cell-center and cell-edge alike, are taken into account in ICIC management. 5.2.4 Base Station Cooperation (BSC) Proposed in [51, 98], base station cooperation (BSC) is another eective ICI manage- ment scheme. BSC allows a group of BSs to send signals concurrently to a group of MSs each served by a BS from this group of BSs using the same time and frequency resource. It can essentially be considered as a combination of Space Division Multiple 107 BS1 BS2 BS7 BS3 BS6 BS4 BS5 MS1 MS2 A 1 A 2 A 3 A 4 A 5 A 6 A 7 B 1 B 2 B 3 B 4 B 5 B 6 B 7 C 1 C 2 C 3 C 4 C 5 C 6 C 7 D 1 D 2 D 3 D 4 D 5 D 6 D 7 Figure 5.3: Illustration of resource management in a multi-cell cellular network based on the BSC principle, where the same/dierent colors represent use of the same/dierent subchannels of the band. Access (SDMA) [56,97] and Macro Diversity HandOver (MDHO) [4], where multiple BSs communicate simultaneously to MSs specically residing in the cell-edge area and within the transmission range of the cooperating BSs. The concept of BSC is illustrated in Fig. 5.3. MS 1 has anchor BS 1 and MS 2 has anchor BS 2. The same channel resource (e.g., subchannels) represented by the same color is allocated to both MS 1 and MS 2 lo- cated in cell-edge areas B 1 and B 2 of the neighboring base stations BS 1 and BS 2. Then, BS 1 and BS 2 transmit signals jointly to MS 1 and MS 2 in the same frequency band. Thus, the potential interference that would otherwise be caused by downlink signals to each other is now turned into useful signals as shown in Fig. 5.3 by solid lines. Besides ICI reduction this also achieves spatial diversity. In general, BSC suggests allocation of 108 overlapping channel resources to neighboring cell-edge regions (i.e., A 1 , A 4 and A 5 ; B 1 , B 2 and B 3 ; C 1 , C 6 and C 7 ) to allow cooperation. 5.3 System Model and Problem Description 5.3.1 System Model and SINR Derivation We consider a downlink hexagonal cellular network as described in Sec. 5.2.1 with L base stations (BSs), each with N T antennas, and M l MSs, each with N R antennas, served by the l-th BS. The total number of MSs in the entire network is therefore M = P L l=1 M l . Each MS is labeled as either a cell-center or a cell-edge user, depending on its proximity to the BS. Assume a set of N subchannels is available for resource allocation, and the frequency reuse factor is one, i.e., each BS will use all N subchannels. Note that due to the intra-cell allocation constraint in OFDMA networks, which restricts the use of a subchannel by at most one MS within the same cell, the number of served MSs in cell l must be less than or equal to the number of subchannels, i.e., M l N for all l's. Signal transmission in the multi-cell OFDMA system is modeled as follows. We con- sider an arbitrary symbol in an OFDMA frame for the interference study in the ensuing discussion. Let the N R N T matrix H (l) mn represent the channel from BS l to MS m in the subchannel n, which has complex Gaussian elements. Let the L mn 1 vector s mn be the transmitted data intended for MS m using subchannel n, which has zero mean and normalized power, i.e., E[s mn s H mn ] = I Lmn . The data vector s mn is precoded by an N T L mn precoding matrix, T mn , which also has normalized power, i.e., jjT mn jj 2 F = 1, where jjjj 2 F is the Frobenius norm of a matrix. 109 Suppose downlink power control (PC) is employed to reduce ICI caused to neighbor cells. That is, the downlink signal for MS m is sent with power P m depending on its proximity to the BS. Specically, we have P m = 8 > > < > > : P 0 ; if MS m is in the cell center; P 1 ; if MS m is in the cell edge; (5.1) where P 0 < P 1 . In the ICIC operation, each MS is communicating with one BS. Thus, the received baseband discrete-time signal at MS m using subchannel n after matched ltering and sampling is comprised of useful signal part from the serving BS A m , and the interference from the corresponding serving BS A v of the interfering MS v plus noise. That is, r mn = p P m H (Am) mn T mn s mn + X v2Im p P v H (Av) mn T vn s vn + n mn ; (5.2) where I m is the set of interfering MSs for MS m, and n mn is the additive white Gaussian noise with noise power E[n H mn n mn ] = N 0 . The signal-to-interference-and-noise ratio (SINR) is used to evaluate the performance of a multi-cell wireless cellular network. It is a more accurate measure than SNR in interference-limited cellular networks. From (5.2), the SINR (in the linear scale) of the received signal at MS m using subchannel n is given by SINR mn = P m jjH (Am) mn T mn jj 2 F P v2Im P v jjH (Av) mn T vn jj 2 F + N 0 : (5.3) 110 Since H (l) mn captures both slow fading (due to path loss) and fast fading (due to the Rayleigh fading) eects, it is convenient to consider the following equivalent form SINR mn (ICIC) = P m (Am) mn ' (Am) m P v2Im P v (Av) mn ' (Av) m + N 0 ; (5.4) where (l) mn is the fading channel power in subchannel n from BS l to MS m, and ' (l) m is the path loss attenuation factor from BS l to MS m, independent of n. Note that ICIC aims to reduce the size of I m (i.e., the number of interferers) and/or the \damage" of each interferer as re ected by the term P v (Av) mn ' (Av) m in the denominator of (5.4). To obtain the SINR expression for BSC, note that in the BSC operation, each MS is communicating with more than one BS. Thus, the SINR expression for the BSC scheme involves an additional term as compared to (5.4). For simplicity, we assume that the transmitting power of each cooperating base station is equally split among MSs involved in the cooperation, which can be achieved by a proper design of precoding matrices 2 . Let C m be the set of other MSs that engage in BSC with MS m. Then, the received SINR (in the linear scale) at MS m using subchannel n is in the form of SINR mn (BSC) = 1 1+jCmj P m (Am) mn ' (Am) m + P u2Cm P u (Au) mn ' (Au) m P v2I 0 m P v (Av) mn ' (Av) m + N 0 ; (5.5) where jC m j is the cardinality of the set C m , and I 0 m is the set of interfering MSs for MS m. More specically, the downlink transmission from the corresponding serving BS to the MS in the set I 0 m will cause interference to MS m. 2 The precoding matrix design is beyond the scope of this research work. We refer interested readers to [51] and references therein. 111 5.3.2 Multi-cell OFDMA Resource Allocation Problem Here we describe the multi-cell OFDMA channel allocation problem in the reuse-1 net- work. Let Y = [y mn ] be the channel assignment matrix whose entry y mn is equal to one if subchannel n is assigned to MS m and zero, otherwise. Then, the centralized multi-cell OFDMA resource allocation problem can be formulated as follows. P: Find an assignment matrix, denoted by Y (P) opt , that maximizes the total capacity, i.e., Y (P) opt = arg max Y M X m=1 N X n=1 log 2 (1 + SINR mn ) y mn ; (5.6) subject to the following two constraints 8 > > < > > : C1: 8n2f1;2;::: ;Ng;if y m 0 n = 1;then y mn = 0;for all m for which A m = A m 0; C2: 8m2f1;2;::: ;Mg;R m = P N n=1 y mn : (5.7) Note that constraint C1 guarantees that a subchannel is used by at most one MS in each cell, i.e., no intra-cell interference. Constraint C2 states that the resource block demand 3 of MS m, namely R m , is met for all m. Note that constraints C1 and C2 are to be met simultaneously. Thus, if all served MSs in a particular cell l have an equal resource block demand of R > 1, the number of served MSs in cell l can be at most N=R, i.e., M l N=R. Any attempt to solve Problem P directly would encounter two challenges. First, SINR mn is unavailable before actual resource allocation since the interference for MS 3 The number of subchannels will be equal to the throughput if all subchannels are statistically equal. Although the SINR of each subchannel is likely statistically unequal in the multi-cell scenario, in light of the complex inter-dependency of SINR and the diculty to obtain exact statistics, we use C2 to approximate the throughput requirement. 112 m in subchannel n depends on the utilization of subchannel n by other MSs, which is unknown until P is solved. Second, Problem P is an NP-hard combinatorial optimization problem with nonlinear constraints. In other words, nding an optimal solution directly is computationally prohibitive and no polynomial-time algorithm can solve P optimally. In the next section, we address these challenges by proposing a new solution frame- work, where the obstacle of SINR mutual dependency is removed as no exact SINR information is needed prior to the resource allocation and the complexity is reduced by adopting heuristic algorithms. 5.4 Proposed Solution Framework 5.4.1 The Graphic Approach The channel assignment problem in cellular and mesh networks has been studied in the context of multi-coloring of a graph for decades (see, e.g., [28,63,65]). In the traditional formulation, each node in a graph corresponds to a BS or an access point (AP) in the network to which channels are assigned. The edge connecting two nodes represents the potential co-channel interference in between, which typically corresponds to the geograph- ical proximity of these two nodes. Then, the channel assignment problem becomes the node coloring problem, where two interfering nodes should not have the same color, i.e., use the same channel. Our current problem, however, diers from the conventional problem fundamentally in three aspects. First, while the traditional one aims at minimizing the number of chan- nels (colors) in use under the interference constraint, we have a xed and predetermined 113 number of (sub)channels (colors) at disposal in the OFDMA network. Besides, since complete avoidance of interference is often not physically possible in the reuse-1 deploy- ment, a proper compromise has to be considered. Second, nodes in the graph of our case should denote MSs rather than BSs, because channels are allocated to MSs in OFDMA networks. Furthermore, the location and movement of MSs will change the interference and consequently the graph. Third, while the conventional graph of base stations con- tains edges that represent solely the co-channel interference, the edge of our graph should be associated with a more general weight since we incorporate technologies such as ICIC and BSC. In the following, we introduce the graph-based resource allocation framework for multi-cell OFDMA. First, a method to construct the interference graph is presented. Then, the two phases of the resource allocation problem are conducted upon the inter- ference graph. 5.4.2 Interference Graph Construction The rst step of the graphic approach to OFDMA resource allocation is to construct the interference graph corresponding to the network topology. Consider an illustrative example with 3 BSs and 5 MSs as shown in Fig. 5.4. Our objective is to construct a corresponding undirected interference graph as shown in Fig. 5.5. In this graph, which is denoted by G = (V;E), each node (from set V ) represents an MS and each edge (from set E) contains an integer \cost" or weight that characterizes the potential interference between two MSs. The weight of the edge (a;b) is denoted by w ab and w ab = w ba . 114 1 BS 1 2 4 5 3 BS 2 BS 3 Figure 5.4: An example of a multi-cell multi-user scenario. We propose a method to determine the edge weight without accurate SINR measure- ments since the measurement of SINR can be dicult in practice. The basic idea is to infer the interference intensity from MS's geographic location. Specically, the weight associated with edge (a;b) is determined based on the diversity set maintained at the 1 2 4 5 3 w 12 w 23 w 34 w 13 w 15 w 45 w 35 w 25 w 24 w 14 Figure 5.5: The interference graph constructed for a multi-cell multi-user scenario. 115 Table 5.1: The Diversity Set of MSs in Fig. 5.4. Anchor BS set Neighbor BS set MS 1 A 1 =f1g B 1 =f3g MS 2 A 2 =f3g B 2 = MS 3 A 3 =f2g B 3 =f3g MS 4 A 4 =f3g B 4 =f1g MS 5 A 5 =f2g B 5 =f1;3g BSs for MSs a and b. The diversity set contains useful geographical information that is related to the interference between MSs. To give an example, the diversity set for the scenario in Fig. 5.4 is given in Table 5.1, where each row indicates the diversity set maintained for the corresponding MS. Each MS has an anchor BS (a.k.a. serving BS) and possibly several neighbor BSs if it is located at the cell edge. For instance, MS 5 belongs to BS 2 but detects signals from BS 1 and BS 3 above the path loss threshold so that the diversity set identies them as the neighbor BSs. Thus, we have A 5 =f2g and B 5 =f1;3g for MS 5, as shown in Table 5.1. Given the diversity set information in Table 5.1, we can infer the interference intensity between any two MSs as discussed below. (Intra-cell interference) MS 2 and MS 4 have the same anchor BS and are thus within the same cell. Therefore, they will have intra-cell interference to each other. (ICI and optional BSC) MS 1 and MS 4 each has an anchor BS that falls in each other's neighbor BS set. This suggests that the downlink signal for MS 1 can reach MS 4, and vice versa. For this reason, transmission to MS 1 and MS 4 will cause ICI to each other. Meanwhile, this is also the precise condition under which BSC communication that involves MS 1 and MS 4 may be established. 116 (ICI but no optional BSC) MS 3 and MS 4 will have ICI, as the element of A 4 is in the set B 3 (the downlink signal for MS 4 from BS 3 will reach MS 3). However, BSC communication that involves MS 3 and MS 4 cannot be established as the element of A 3 is not in the set B 4 . (No interference) MS 1 and MS 3 will not interfere with each other, as the anchor BS of neither MS is in the neighbor BS set of the other MS. The above analysis is performed for every pair of nodes followed by a proper weight assignment. There are six possible weight values between any two nodes, w B ; w N ; w 0 ; w 1 ; w 2 ; w A ; (5.8) where w B , w N and w A correspond to weights associated with BSC, no-interference, and intra-cell interference, respectively, and w 0 ;w 1 ;w 2 are ICI weights at various levels de- pending on the geographic location of the two MSs. More specically, the mutual ICI is the weakest if the two MSs are in the center of two dierent cells (denoted by w 0 ), medium if one MS is in the cell edge and the other in the cell center of two dierent cells (denoted by w 1 ), and strongest if the two MSs are in the edge of two dierent cells (denoted by w 2 ). The no-interference weight, w N , is set to zero to conform to the convention of \no edge" in the graph. The intra-cell interference weight, w A , should be assigned with a very large value as the intra-cell interference must be avoided. To support techniques such as BSC, which achieves interference management by allo- cating the same, rather than dierent, subchannel to interfering cell-edge MSs, we should 117 assign the corresponding weight w B a very small value. Thus, in addition to the phys- ical meaning of interference, where bigger weight value represents stronger interference between MSs, the weight is also associated with the general meaning of functionality. Overall, the six weight values can be ranked as w B w N (= 0) < w 0 < w 1 < w 2 w A ; (5.9) and jw B j w A : (5.10) Note that since BSC is an optional mechanism while the intra-cell interference must be avoided, we have the weight relationship in (5.10). More specically, w A should be signicantly large such that (L 1)w 2 + 2jw B j < w A : (5.11) This will guarantee that the intra-cell interference can be avoided, as will be veried in Sec. 5.5.2. The complete algorithm to determine the edge weight is summarized in Table 5.2. In Table 5.2, the anchor BS of MS a and MS b are rst examined. If they are the same, the weight decision can be made directly; that is, we assign w ab with value w A (Step 1). If they are not the same, then further procedures are needed. Specically, depending on whether the anchor BS of MS a is in the neighbor BS set of MS b, the temporary weight (w 0 ;w 1 ;w 2 ) or w N is assigned to w (1) ab accordingly (Step 2). Likewise, depending 118 1 2 4 5 3 w 1 w 1 w 2 w N w 2 w 2 w A w 1 w 2 / w B w A Figure 5.6: The interference graph for the scenario given in Fig. 5.4. on whether the anchor BS of MS b is in the neighbor BS set of MS a, the temporary weight (w 0 ;w 1 ;w 2 ) or w N is assigned to w (2) ab accordingly (Step 3). If the anchor BS of each MS is in the neighbor BS set of each other MS, BSC may be performed. If the system determines that BSC will be used for these two MSs, assign w B (Step 4); otherwise, assign max(w (1) ab ;w (2) ab ) (Step 5). The resulting interference graph with assigned weight for Fig. 5.4 is illustrated in Fig. 5.6, where there might be two possible weights for some edge depending on the actual conguration of MSs. It is assumed that the conguration choice is predetermined before the allocation process. For example, if MS 1 and MS 4 are both pre-congured to perform BSC whenever feasible, edge (1;4) will be assigned with weight w B ; otherwise, it will be assigned with weight w 2 . Since BSC is not establishable between the rest node pairs in the graph, they are left with only one option and proper weights are assigned according to the algorithm in Table 5.2. Once the interference graph is constructed, our solution to the resource allocation problem follows a two-phase approach on the graph. That is, 1) the coarse-scale inter-cell 119 interference management and 2) the ne-scale channel assignment. These are described in the following. 5.4.3 First Phase: Interference Management There is a close relationship between the MAX k-CUT problem [77] in general graph theory and the interference management problem in OFDMA networks. In graph theory, a cut is a partition of the vertices of the graph into multiple sets or clusters. The size of a cut is the total number of edges crossing the cut. In our weighted graphs, the size of the cut is the sum of weights of the edges crossing the cut. A cut is maximal (max) if the size of the cut is not smaller than the size of any other cut. By generalizing a cut to k cuts, the MAX k-CUT problem is to nd a set of k cuts that is not smaller in size than any other k cuts. Given N subchannels and M MSs, our interference management problem is a MAX N-CUT problem on the interference graph and is formally stated as follows. P1: Given an interference graph G = (V;E) with M nodes and edge weight w ab for each edge (a;b), nd a partition of the graph into N (N 2) disjoint clusters R i ;i = 1;::: ;N, such that S N i=1 R i = V and P a2R i ;b2R j ;i<j w ab is maximized. Here, each cluster corresponds to a subchannel. Nodes (or MSs) in the same cluster will be assigned with the same subchannel. In the goal of maximizing the inter-cluster edge weight in Problem P1, the result will tend to place strong interferers into dierent clusters or equivalently, separate them on dierent subchannels, which helps to reduce ICI. If BSC is supported, the clustering result will tend to place BSC-feasible MSs into the same cluster to allow cooperation, due to the small BSC weight value w B . 120 Both constraints C1 and C2 of Problem P in (5.7) are readily addressed in this graphic framework. The very large intra-cell interference weight w A will ensure the com- plete avoidance of intra-cell interference as stated in C1. To meet the resource block demand R m = P N n=1 y mn in C2, we can duplicate the node corresponding to MS m for R m times in the interference graph and assign a very large weight (e.g., w A ) to edges that connect these duplicate nodes. This way, these duplicate nodes will be placed into dierent clusters and consequently, R m subchannels will be assigned to MS m to meet the resource block demand. 5.4.4 Second Phase: Channel Assignment After the rst-phase partition, MSs are grouped into N clusters for subchannel allocation. In the second phase, we should decide which subchannel to allocate to which cluster. Among N! possible subchannel assignment choices, the second-phase assignment aims to nd the one that best leverages the instantaneous channel quality. The problem is formulated as follows. P2: Let J be the set formed by N! valid subchannel assignment choices after the rst phase. Find an assignment matrix Y (P2) opt such that Y (P2) opt = arg max Y2J M X m=1 N X n=1 log 2 (1 + SNR mn ) y mn ; (5.12) where SNR mn is the instantaneous channel quality between MS m and its serving BS on subchannel n, which is proportional to (Am) mn . 121 Note that, since ICI is dealt with in the rst phase, the second phase considers SNR only, which avoids the inter-dependency issue. 5.5 Proposed Algorithms In this section, we present heuristic algorithms for the two phases of the resource allocation problem presented in Sec. 5.4. 5.5.1 Heuristic Algorithm A1 for the First Phase Problem P1 is an NP-hard problem for a graph with a large number of nodes [55]. That is, the optimal solution for P1 is computationally prohibitive for large graphs. Consequently, we apply the simple heuristic algorithm described in [77] on Problem P1, which can eciently produce an approximate solution. It is proved in [77] that, given all weights in the graph are nonnegative integers, the heuristic algorithm achieves an absolute ratio of (1 1=k) for a general MAX k-CUT problem. That is, the algorithm can yield a clustering in which the inter-cluster weight sum is at least (1 1=k) times of the optimal cut. In our case of k = N, with some weight being negative, the algorithm can produce (1 1=N) times of the optimal solution on the shifted version of weights, i.e., after the absolute value of the most negative weight is added to all weight values to make all weights nonnegative. The idea of the algorithm is to iteratively assign nodes to the cluster such that at each step the increased intra-cluster weight is minimized. The detailed description of the algorithm is given in Table 5.3 for a practical scenario with M > N. The clustering problem becomes trivial when M N, because the amount of OFDMA resource available 122 for allocation (i.e., N) is greater than or equal to what is needed by the MSs (i.e., M number of MSs), so that we can just give each MS its own subchannel. In this case, the algorithm terminates at Step 2 with the optimal solution. If M > N, the algorithm proceeds by rst assigning N arbitrarily chosen nodes to N clusters, one in each cluster (Step 2). Then, the rest MN nodes are iteratively assigned at each step to the cluster for which the increased intra-cluster weight is minimized (Steps 3 & 4). Once the new assignment is done, the intra-cluster weight of the cluster is updated (Step 5). The iteration repeats until all nodes are assigned into a cluster (Step 6). The complexity of this heuristic method is proportional to the sum of the number of edges, nodes and clusters in the graph. For our particular case with M nodes and N clusters, this heuristic method is of complexity O(M 2 =2 + M=2 + N). 5.5.2 Properties of Algorithm A1 Some discussions on the properties of the clustering algorithm A1 are presented here. The objective is to show that algorithm A1 along with the weight assignment in Sec. 5.4.2 will indeed produce desirable results. Property 1: (BSC-weight Assignment) An MS node can be connected by a BSC (w B ) weighted edge with other MSs in at most two neighbor cells. Proof: (Property 1) First, we note that BSC weight is assigned to the edge between two MSs when each MS's anchor BS is in each other MS's neighbor BS set (Sec. 5.4.2). Second, by the Property of Forming the Diversity Set in Sec. 5.2.2, an MS has at most two neighbor BSs in its diversity set (denoted here for convenience by BS a and BS b). 123 Thus, an MS will have a BSC-weighted edge only with MSs that are served by either BS a or BS b, but no others. Property 2: (Intra-cell Interference Avoidance) Any two intra-cell MSs will be placed into two dierent clusters by algorithm A1. Proof: (Property 2) Denote any two intra-cell MSs by MS a and MS b. According to our weight assignment rule, w ab = w ba = w A . If at Step 2 of A1, MS a and MS b are assigned into dierent clusters, we are done. If not, MS a and MS b are clustered at dierent iterations. Assume without loss of generality that MS a is clustered before MS b is clustered. Consider at some iteration when MS b is selected for clustering decision and MS a has already been placed in cluster R i , and all previous iterations did not place intra-cell MSs, if any, into the same cluster. We intend to show that the current iteration will not place intra-cell MSs into the same cluster either, or specically, MS b will be clustered into a dierent cluster than R i at this iteration, to complete the proof. The clustering decision for MS b starts with Step 3 of A1 where the increased intra- cluster weight is calculated for all clusters, i.e., W a i 0 = X v2R i 0 w bv ;i 0 = 1;::: ;N: Note that the summing terms in calculating W a i contain one w A as MS a is in cluster R i , and at most two w B 's due to Property 1 and the fact that intra-cell MSs, if any up to this iteration, are in dierent clusters. Thus, we have W a i w A + 2w B . On the other hand, since the number of intra-cell MSs in any cell l is no greater than the number of subchannels, i.e., M l N, MS b is connected by at most N 1 intra-cell (w A ) weighted 124 edges. Since we have N clusters, there must exist some cluster R j ;j 6= i, for which the summing terms in calculating W a j do not include w A . As w 2 is the next largest weight to w A , and since the maximum number of nodes currently in cluster R j is L 1 (we have L cells), we have W a j (L1)w 2 . By the fact that w A is signicantly large and specically by (5.11), we are led to W a j < W a i . Thus, Step 4 of A1 will place MS b into a dierent cluster than R i , which completes the proof. Property 3: (Feasibility of BSC) Dene the number of distinct MSs and BSs that involve in the same BSC event on a particular subchannel to be M BSC and L BSC , re- spectively. A BSC event is \feasible" if M BSC L BSC , i.e., the virtual operation of BSC can be supported realistically. Algorithm A1 will always produce feasible BSC. Proof: (Property 3) Assume M BSC > L BSC . Since BSC is established between BSs and MSs served by these BSs, there must be at least two MSs that are served by the same BS if M BSC > L BSC , i.e., they are intra-cell MSs. By Property 2, these two MSs will be placed into dierent clusters. But by denition all M BSC MSs involve in the same BSC event and therefore are placed in the same cluster. By contradiction we have M BSC L BSC . Note that some BSC operations may be feasible, but not necessarily ecient. In particular, a BSC operation that involves many geographically far apart BSs is, although feasible by Property 3, not an ecient way to leverage the advantage of performing BSC. In the following we aim to show that, by rst stating a property that follows directly from our interference graph construction method and next proposing a method to treat a complex BSC scenario, algorithm A1 will produce a BSC event that involves at most three (geographically close) BSs and three MSs. 125 Property 4: (Clustering of BSC) Algorithm A1 will yield a clustering result where an MS node is connected by at most two BSC-weighted edges that are intra-cluster edges (i.e., edges that have two ends within the same cluster). Proof: (Property 4) This result follows directly from Property 1 and Property 2. Following the result in Property 4, BSC events may occur in one of the three possible scenarios shown in Fig. 5.7. All MS nodes in each scenario are placed in the same cluster for BSC to take place, and each MS node is connected by at most two BSC-weighted edges due to Property 4. The scenarios in Figs. 5.7(a){5.7(b) are \BSC cliques" 4 and a proper degree of BSC will be performed accordingly (i.e., 2-MS, 2-BS or 3-MS, 3-BS BSC). A BSC clique can be of size no greater than three due to Property 4. The third scenario where BSC events might occur is the \BSC cascade" scenario in Fig. 5.7(c). Edges not shown here are not BSC weighted. Note that two end nodes in this scenario do not link (by a BSC-weighted edge) unless the number of nodes is less than or equal to three, which degenerates to the scenarios in Figs. 5.7(a){5.7(b) 5 . In other words, in the cascade scenario, no three MSs are pairwise connected by BSC weights (i.e., no BSC cliques of three) but any MS except for the end nodes is connected by two BSC- weighted edges to another two MSs. A possible topology corresponding to Fig. 5.7(c) is drawn in Fig. 5.8. It it seen that due to the geographical location and the diversity set, MS 1 and MS 3 do not have a BSC-weighted edge in between, but each of them has a BSC-weighted edge with MS 2. The solid arrows in Fig. 5.8 show the downlink transmission in a potential BSC operation in the cascade setting. However, as is seen in 4 A BSC clique is a graph in which every node is connected by a BSC-weighted edge to every other node. 5 It can easily be veried that the scenario of four or more nodes that form in a circle is not possible due to the hexagonal network topology and the diversity set property used to determine BSC relations. 126 1 2 w B (a) BSC clique of two 1 2 w B 3 w B w B (b) BSC clique of three 1 2 w B 3 w B 4 5 6 w B w B w B . . . . . . (c) BSC cascade Figure 5.7: Possible BSC occurrences. Fig. 5.8, dierent BSC transmissions may cause interference to each other (e.g., consider a BSC event among MS 1, MS 2 and MS 3, and another BSC event among MS 2, MS 3 and MS 4). To address this issue, we propose a method to break up the cascade into multiple BSC cliques of two when algorithm A1 produces one. Method: (Treating the BSC Cascade) It is assumed that after clustering achieved by algorithm A1, the radio network controller (RNC) can identify the physical challenge of performing some BSC events yielded by A1, such as the cascade scenario. Then, a negotiation will take place between BSs and MSs such that the edge weight between some MSs is changed from BSC weight (w B ) to ICI weight (w 0 , w 1 , or w 2 ) to break up the 127 1 2 3 4 5 6 . . . . . . Figure 5.8: A cascade topology for BSC operation. cascade. For example, if the BSC weights between nodes 2 and 3, and nodes 4 and 5 in Fig. 5.7(c) are changed to ICI weights, the cascade is broken up into three BSC cliques of two. In general, for a cascade that contains M cas distinct MSs, where M cas 3,b Mcas1 2 c changes of weight are needed. Then, algorithm A1 is run again with the new set of weights. Note that the BSC cascade scenario is however rare in practice. In fact, the cascade scenario will occur only when all the following conditions are met simultaneously. 1. There must be some MSs that are located within the three-cell overlapping coverage area. For long cascade to happen, there must be a \string" of MSs each located in a dierent (and nearby) three-cell overlapping area. 2. Some MSs in the cascade may have other BSC choices (\partners") that will not result in any cascade. Among these choices, algorithm A1 chooses one that produces a cascade. 128 3. Step 2 of algorithm A1 does not break up the cascade initially by assigning some MSs in the cascade into dierent clusters. The likelihood of condition 1 above being met is little in a typically large cell coverage area with a relatively small three-cell overlapping area, as will be veried in the simulation. The likelihood of condition 2 being met is reduced when more MSs in the potential cascade have some other BSC choices so that simultaneous selection of particular BSC pairs to result in a cascade is less likely. While condition 3 being met or not is totally random, the likelihood is generally reduced in lighter load networks (i.e., smaller M). After the discussion above on the possible BSC occurrences, we are led to the nal property below. Property 5: (Degree of BSC) Algorithm A1 will produce BSC events that involve at most three MSs and their corresponding three (geographically close) anchor BSs. That is, BSC operation will be both feasible and ecient. Proof: (Property 5) This result follows directly from the discussion on the possible BSC scenarios given above. Specically, for BSC cliques of two, BSC cliques of three, and BSC cascade scenarios after properly treated, it is easily seen that the produced BSC events will involve at most three MSs and the corresponding three anchor BSs. 5.5.3 Heuristic Algorithm A2 for the Second Phase Exhaustive search through all N! choices to solve Problem P2 is also computationally infeasible. We propose a heuristic suboptimal algorithm that iteratively assigns sub- channels to clusters as described in Table 5.4. We call this method max-SNR channel assignment. 129 In Table 5.4, the initial subchannel pool is f1;::: ;Ng. N clusters are ordered from small to large in size in terms of the number of nodes contained in the cluster (break ties arbitrarily). Smaller clusters are examined rst, because the choice of subchannels makes more impact to smaller clusters. For each particular cluster, the subchannel for which the sum capacity is maximum for this cluster is assigned to this cluster (Steps 1 & 2). The procedure continues on the next cluster with the subchannel pool of one less entry, i.e., the subchannel that has already been assigned is removed from the pool (Step 3). The iteration repeats until all clusters are assigned with one subchannel (Step 4). This heuristic method that iteratively assigns subchannels to clusters is of complexity O(N 2 ). An alternative method, called random channel assignment, can also be used here to solve the second-phase problem. In this method, one assignment out of N! choices is randomly picked as the solution. The complexity of this random assignment method is O(1). However, the performance of the random channel assignment may not be as good as that of the heuristic method described above, as it does not take channel condition into consideration when performing the channel assignment. 5.6 Simulation Results In this section, we study the performance of the proposed schemes by computer simula- tion. The simulation setup follows closely the IEEE 802.16m evaluation methodology [6] and is summarized in Table 5.5. The ve schemes to be investigated and compared are shown in Table 5.6. ICI-blind is the traditional OFDMA scheme where no ICI-aware mechanism is employed; i.e., each 130 cell performs its own channel allocation independently without intra-cell interference. The rest are our proposed schemes, which dier in the interference management mechanism in the rst phase (ICIC or ICIC+BSC) and in the second phase (random or max-SNR assignments). The graph edge weights are chosen to be (w B ;w N ;w 0 ;w 1 ;w 2 ;w A ) = (10 3 ;0;50;100;200;10 5 ): It is worthwhile to note that the performance of our proposed graph-based scheme is not sensitive to the chosen weight values, which is another highly desirable feature of this solution approach. Indeed, as revealed by the simulation, as long as the inter-relationship of weights in (5.9){(5.11) is respected, a small variation in the weight does not change the nal channel assignment decision yielded by the proposed algorithm. Figs. 5.9(a){5.9(c) show the cumulative distribution function (CDF) of SINR for ve test schemes under dierent trac load conditions (with 25, 15 and 5 uniformly dis- tributed MSs per cell, respectively). It is evident that both ICIC and BSC schemes have a remarkable improvement on the SINR performance as compared to the ICI-blind scheme. This demonstrates the eectiveness of proposed ICI-reduction schemes. We also see a higher additional gain of ICIC2 (BSC2) compared to ICIC1 (BSC1) in lower load conditions. This is because interference dominates in higher load conditions, and the channel-aware resource assignment makes a diminishing impact in the second phase. Be- sides, due to fewer interferers, the average SINR increases for all schemes as the trac load decreases as shown in Figs. 5.9(a){5.9(c). 131 The average SINR gains of proposed schemes with respect to the ICI-blind scheme under various trac loads are compared in Fig. 5.10. Several observations can be drawn from this gure. First, as discussed previously, we see a more signicant gain of ICIC2 and BSC2 in low load situations. Second, the ICIC gain drops signicantly in very high load situations. This is because the inevitable channel collision in the presence of a large number of MSs has rendered the ICIC strategy ineective, if still feasible at all. In contrast, BSC retains the gain as trac load increases, and experiences only minor degradation in very high load situations. This is explained by the fact that, while a high load creates a high interference environment, it also creates more BSC opportunities. As BSC can only be established among MSs that are \geographically tting", a higher load increases the number of MSs that can be engaged in BSC, and consequently the number of actual events of BSC. This eect counteracts the degradation caused by more interferers. The eect of unequal cell loading on the SINR performance is examined in Fig. 5.11. We simulate an unequal load scenario with randomly selected nine cells of 25 MSs, nine cells of 5 MSs, and one cell of 15 MSs to make an average of 15 MSs per cell in our 19-cell simulator. Cell-specic SINR performance is shown in Fig. 5.11(a) for heavy load cells (25 MSs) and Fig. 5.11(b) for light load cells (5 MSs). We see that both gures have performance close to the uniform 15-MS-per-cell scenario in Fig. 5.9(b). However, heavy load cells achieve slightly better performance than light load ones. This is due to the slightly lighter trac in the neighboring cells \seen" by a heavy load cell, which leads to less ICI and better performance. Fig. 5.12 shows the eect of downlink power control (PC) on the SINR performance. We compare the case with PC (P 0 = 40 dBm and P 1 = 46 dBm) and without PC 132 (P 0 = P 1 = 46 dBm). It is observed from Fig. 5.12(a) that PC improves the low SINR performance as the reduced transmission power to cell-center MSs causes less interference to neighboring cells. This inevitably compromises the SINR performance of the MSs in the cell center, as revealed in Fig. 5.12(b), since a reduction in transmission power for cell center users will decrease their received signal strength. Nevertheless, these gures still justify the use of power control from the system capacity point of view, as the performance improvement in low SINR regime is far more important than the minor SINR degradation in the high SINR regime. Moreover, a reasonable degree of SINR deterioration for these cell-center users normally does not cause an immediate drop in their modulation coding scheme (MCS) level, and therefore will not entail a decrease in the throughput perceived by these MSs in the cell center. Fig. 5.13 compares two permutation schemes, namely PUSC and AMC, dened in the IEEE 802.16e standard. PUSC scrambles subcarriers before grouping them into a subchannel and, thus, the quality of subchannels is expected to be statistically alike. Therefore, performing the second-phase task yields a smaller gain. In contrast, AMC maps physically contiguous subcarriers to a logical subchannel. Thus, the disparity be- tween subchannels is anticipated to be higher due to frequency-selective fading across subcarriers. This contributes to a higher performance gain associated with ICIC2 and BSC2 with AMC permutation. In real-world cellular deployment, it is desirable to balance between the BS placement density and service quality. If too few BSs are deployed in a given region, some areas are not covered. On the other hand, an overly dense BS installation will not only result in increased deployment cost but also lead to aggravated ICI. We examine this issue in 133 Fig. 5.14, by adjusting a parameter called inter-cell distance ratio () dened in Table 5.5. Three dierent cell deployment schemes ( = 1, 0.9, and 0.8) are compared. When cells are closer to each other (smaller ), ICI is higher and consequently, employment of an ICI management scheme is more benecial, as revealed by the higher gain in Fig. 5.14. In addition, smaller also provides more coverage overlapping areas in which BSC can be performed by MSs located in these areas. In other words, denser deployment of cells provides an extra advantage for the BSC scheme, which accounts for the 6 dB gain of BSC2 when = 0:8. Fig. 5.15 draws the contour plot of the SINR level in a cell plane as shown by the circle to represent the coverage. The \heights" in the plot represent the SINR in dB. Each concentric circle shows an SINR value after averaging over several MSs located at that particular distance away from the BS. Three schemes are compared under the same trac load of 25 MSs per cell. We see from Figs. 5.15(a){5.15(c) that ICI-blind, ICIC1 and BSC1 achieve equally high SINR in the cell center but dier in the cell edge. In particular, the cell-edge SINR value is the lowest for ICI-blind, medium for ICIC1, and highest for BSC1. This shows that ICI management is particularly helpful to cell-edge MSs. In addition, BSC1 observes an SINR increase towards the cell edge because of the use of BSC in the cell edge. This gure also reveals the geographical relationship of the SINR distribution. Fig. 5.16 shows the spectrum usage in specic cell-edge areas to demonstrate how our proposed algorithms achieve the bandwidth allocation depicted in Figs. 5.2 and 5.3. In each gure, a marker indicates an MS in the corresponding sector (the y-axis) using the corresponding subchannel (the x-axis). Each subgure shows spectrum allocation 134 for sectors A 1 , A 4 , A 5 (top); B 1 , B 2 , B 3 (middle); and C 1 , C 6 , C 7 (bottom). The reuse of the same subchannel in physically close areas is viewed as a collision, drawn by connecting lines. A comparison between Fig. 5.16(a) and Fig. 5.16(b) readily suggests that our algorithms achieve ICI reduction by lowering the number of collided subchannel assignment. BSC is interesting in that it purposefully allocates the same subchannels to adjacent areas as depicted in Fig. 5.3. In fact, the \collisions" of subchannels in Fig. 5.16(c) are for the BSC purpose. Thus, instead of impairing the performance, such \collisions" enhance the overall performance. 5.7 Conclusion A downlink multi-cell OFDMA resource allocation framework was proposed in this work. A two-phase approach consisting of coarse-scale ICI management and ne-scale channel- aware allocation was presented. In particular, the main task of managing the performance- limiting ICI in cellular networks is accomplished by a graphic approach, in which state- of-the-art ICI management schemes such as ICIC and BSC can be incorporated easily. A separate handling of interference management and network capacity maximization in the proposed graph framework can deliver a substantial SINR performance improvement, which is conrmed by the extensive computer simulation. Thanks to its practicality and low complexity, the proposed scheme can be used in next generation cellular systems such as 3GPP Long Term Evolution (LTE) and IEEE 802.16m. 135 Table 5.2: The Algorithm to Determine the Weight of the Edge (a;b). Initialize: If MSs a and b are congured to perform BSC whenever feasible, B = 1; otherwise, B = 0. If MS a (or b) is in cell edge, a (or b ) = 1; otherwise, a (or b ) = 0. I BSC = 0. 1. If A a \A b 6= , w ab = w A . Go to 6. 2. If A a \B b 6= , w (1) ab = w a+ b . I BSC = I BSC + 1. Else, w (1) ab = w N . 3. If A b \ B a 6= , w (2) ab = w a+ b . I BSC = I BSC + 1. Else, w (2) ab = w N . 4. If I BSC = 2 and B = 1, w ab = w B . Go to 6. 5. w ab = max(w (1) ab ;w (2) ab ). 6. Output w ab . 136 Table 5.3: Heuristic Algorithm A1 to Solve Problem P1. Initialize: Let W i = P u2R i ;v2R i w uv be the intra-cluster weight of cluster R i ;i = 1;::: ;N. Initially, since clusters have not yet been assigned with nodes, W i = 0;8i = 1;::: ;N. 1. Arbitrarily order M nodes. 2. Assign the rst N nodes to N clusters, one in each cluster. 3. Take the next node from the ordered nodes. Let this node be node m. Let W a i be the increased intra-cluster weight to cluster R i if node m is assigned to cluster R i . Specically, W a i is the sum of edge weights between node m and all nodes that have already been assigned to cluster R i , i.e., W a i = P v2R i w mv . Collect W a i for all i = 1;::: ;N. 4. Assign node m to cluster R i , where i = arg min i W a i . If there is more than one minimum, break the tie randomly. 5. Update the intra-cluster weight of cluster R i such that W i = W i + W a i . 6. Repeat Steps 3{5 for all nodes. Table 5.4: Heuristic Algorithm A2 to Solve Problem P2. Initialize: Let = f1;::: ;Ng be the subchannel pool. Order N clusters in size from the smallest to the largest (break the tie arbitrarily). 1. Examine clusters in order, one at a time. Let the selected cluster be R i . Calculate the sum capacity T n = P m2R i log 2 (1 + SNR mn ) for all n2 . 2. Assign subchannel n to cluster R i , where n = arg max n T n . 3. Update subchannel pool to exclude n , i.e., = nfn g. 4. Repeat Steps 1{3 for all clusters. 137 Table 5.5: Simulation Setup. Cell Parameters Number of Cells, L 19, wrap-around Cell Radius 750 m Cell-center Radius 500 m Inter-cell Distance Ratio, a 0.9 Antennas N T , N R 4, 2 Frequency Reuse Factor 1 OFDMA Parameters FFT size 1024 Carrier Frequency 2.5 GHz Sampling Frequency 11.2 MHz Number of Subchannels, N 30 Number of Subcarriers Per Subchannel 28 DL Permutation Type PUSC Channel Model Path Loss (dB) 130:62 + 37:6 log 10 (d), (d in km) Fast Fading ITU Pedestrian B Power Control Parameters Cell-center Trans. Power, P 0 40 dBm Cell-edge Trans. Power, P 1 46 dBm Thermal Noise Power, N 0 -119 dBm a Inter-cell distance may be shortened or expanded to control cell over- lapping area. The ratio shown here is relative to the back-to-back hexagon cell deployment. Table 5.6: Five Test Schemes. Scheme First Phase: Second Phase: Interference Management Channel Assignment ICI-blind no ICI consideration random ICIC1 ICIC random ICIC2 ICIC max-SNR BSC1 ICIC+BSC random BSC2 ICIC+BSC max-SNR 138 −10 −5 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SINR (dB) CDF ICI−blind ICIC1 ICIC2 BSC1 BSC2 (a) 25 MSs per cell −10 −5 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SINR (dB) CDF ICI−blind ICIC1 ICIC2 BSC1 BSC2 (b) 15 MSs per cell 139 −10 −5 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SINR (dB) CDF ICI−blind ICIC1 ICIC2 BSC1 BSC2 (c) 5 MSs per cell Figure 5.9: The SINR distribution for dierent trac load conditions. 140 5 10 15 20 25 30 0 1 2 3 4 5 6 7 8 9 10 Traffic load (MSs per cell) Gain in average SINR (dB) ICIC1 ICIC2 BSC1 BSC2 Figure 5.10: The average SINR gains with respect to the ICI-blind scheme under dierent trac loads. 141 −10 −5 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SINR (dB) CDF ICI−blind ICIC1 ICIC2 BSC1 BSC2 (a) Heavy load cells (25 MSs) −10 −5 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SINR (dB) CDF ICI−blind ICIC1 ICIC2 BSC1 BSC2 (b) Light load cells (5 MSs) Figure 5.11: The cell-specic SINR distribution under an unequal cell load scenario (9 cells of 25 MSs, 9 cells of 5 MSs, and 1 cell of 15 MSs). 142 −15 −10 −5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 SINR (dB) CDF ICI−blind without PC ICI−blind with PC ICIC1 without PC ICIC1 with PC BSC1 without PC BSC1 with PC (a) Low SINR region 0 5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 SINR (dB) CDF ICI−blind without PC ICI−blind with PC ICIC1 without PC ICIC1 with PC BSC1 without PC BSC1 with PC (b) High SINR region Figure 5.12: The SINR distribution for schemes with and without power control (PC) (25 MSs per cell). 143 5 10 15 20 25 30 0 1 2 3 4 5 6 7 8 9 10 Traffic load (MSs per cell) Gain in average SINR (dB) ICIC2, PUSC ICIC2, AMC BSC2, PUSC BSC2, AMC Figure 5.13: The average SINR gains with respect to the ICI-blind scheme under dierent trac loads for PUSC and AMC permutation schemes. 144 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 Traffic load (MSs per cell) Gain in average SINR (dB) ICIC2, r=1 ICIC2, r=0.9 ICIC2, r=0.8 BSC2, r=1 BSC2, r=0.9 BSC2, r=0.8 Figure 5.14: The average SINR gains with respect to the ICI-blind scheme under dierent trac loads for dierent inter-cell distance deployment. 145 −20 −10 0 10 20 30 40 50 (a) ICI-blind −20 −10 0 10 20 30 40 50 (b) ICIC1 146 −20 −10 0 10 20 30 40 50 (c) BSC1 Figure 5.15: The contour plot of SINR (dB) in a cell, with 25-MS trac load per cell. 147 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors A 1 , A 4 , A 5 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors B 1 , B 2 , B 3 0 5 10 15 20 25 30 2 4 6 subchannel index cell index spectrum use by sectors C 1 , C 6 , C 7 (a) ICI-blind 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors A 1 , A 4 , A 5 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors B 1 , B 2 , B 3 0 5 10 15 20 25 30 2 4 6 subchannel index cell index spectrum use by sectors C 1 , C 6 , C 7 (b) ICIC1 148 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors A 1 , A 4 , A 5 0 5 10 15 20 25 30 2 4 6 cell index spectrum use by sectors B 1 , B 2 , B 3 0 5 10 15 20 25 30 2 4 6 subchannel index cell index spectrum use by sectors C 1 , C 6 , C 7 (c) BSC1 Figure 5.16: The spectrum allocation in ICI-prone areas, where each subgure shows spectrum allocation for sectors A 1 , A 4 , A 5 (top); B 1 , B 2 , B 3 (middle); and C 1 , C 6 , C 7 (bottom) depicted in Figs. 5.2 and 5.3. 149 Chapter 6 Conclusion and Future Work 6.1 Conclusion In this dissertation, we have addressed both centralized and distributed access problems in OFDM/OFDMA networks, for single-cell and multi-cell scenarios. The protocol design and performance analysis were conducted, and several main results are summarized below. In Chapter 3, performance analysis and comparison of OFDM-TDMA and OFDMA downlinks centered on scheduling with cross-layer considerations were conducted. Sev- eral OFDM/OFDMA modes with dierent multiaccess and resource allocation schemes were considered along with an analytical framework based on the QoS architecture of IEEE 802.16. The analysis and computer simulation oered a thorough understanding of system's capability of supporting multimedia delivery from a cross-layer viewpoint in- volving both link and physical layers. The analytical and simulation results reveal that dynamic OFDMA has a greater potential to support multimedia QoS delivery than dy- namic OFDM-TDMA. It was also observed that the opportunistic assignment can be employed more eectively in OFDMA. 150 In Chapter 4, a distributed channel allocation scheme for uplink OFDMA called \op- portunistic access with random subchannel backo" (OARSB) was proposed. The ad- vantage of opportunistic assignment and the eciency of the frequency-domain collision resolution strategy were integrated in OARSB. The proposed OARSB scheme can be conveniently implemented in 802.16 due to its simplicity. It was shown by analysis and computer simulation that the throughput is enhanced signicantly. In Chapter 5, a downlink multi-cell OFDMA resource allocation framework was pro- posed. A two-phase approach consisting of coarse-scale ICI management and ne-scale channel-aware allocation was presented. In particular, the main task of managing the performance-limiting ICI in cellular networks is accomplished by a graph method, in which state-of-the-art ICI management schemes such as ICIC and BSC can be incor- porated easily. To handle interference management and network capacity maximization separately in the graph framework leads to substantial SINR performance improvement, which is conrmed by extensive computer simulation. Thanks to its practicality and low complexity, the proposed scheme can be used in next generation cellular systems such as 3GPP Long Term Evolution (LTE) and IEEE 802.16m. 6.2 Future Work The OARSB scheme was proposed for distributed uplink OFDMA in Chapter 4. More studies are needed to understand its values and applications more thoroughly. We point out one possible extension on the OARSB algorithm below, pertaining to its more gen- eralized forms and possible applications. 151 Hybrid of time- and frequency-domain backo design The OARSB scheme proposed in Chapter 4 is a novel combination of opportunis- tic access and the frequency-domain backo mechanism. It can be further gen- eralized to contain both time- and frequency-domain backo options along with opportunistic access. This generalization may be useful in service dierentiation for distributed networks, and thereby provide QoS in distributed networks. For instance, delay-insensitive and delay-sensitive applications can be coupled with the time- and frequency-domain backo mechanism, respectively, as frequency-domain backo can provide faster collision resolution and thus smaller delay. In addition, if complexity is of concern, the scheme can be simplied to consist of one backo type only (i.e., either time- or frequency-domain backo). These design issues worth our further studies. A multi-cell OFDMA downlink resource allocation scheme using a graph framework was proposed in Chapter 5. Many potential future research topics can be built upon this work. We describe some of them in the following. Distributed multi-cell coordination Multi-cell network control can be accomplished in a centralized or distributed fash- ion. We considered a centralized approach in Chapter 5, where a graph is con- structed and algorithms are employed in a centralized way with a radio network controller (RNC). In contrast, distributed coordination does not demand such a central controller. Each cell performs its own resource allocation based on local in- formation and/or message exchange with other cells [38]. The distributed approach 152 has drawn a signicant amount of attention in the industry such as the 3GPP LTE community. Suggestions such as exchanging the high interference indicator (HII) and the overload indicator (OI) signaling among cells have been discussed, e.g., [74]. These messages are used to inform neighboring cells of certain resource blocks (e.g., time and frequency) in use and, thus, subject to high interference. Neighboring cells receiving such signaling can take proper action, e.g., not allocating its own users to these high-interference resource blocks. This idea encounters some practical chal- lenges, including a fair yet ecient way to resolve the con ict between cells, exact signaling to support the operation, and the resulting performance in comparison with a centralized approach. They all deserve further studies. Multi-cell time and frequency domain resource allocation OFDMA PHY consists of resources in both time and frequency. We considered the frequency domain (subchannels) allocation only in Chapter 5. New design issues and opportunities for interference management may arise when the time dimension is also incorporated. For instance, interference among dierent cells may be lowered under a light trac condition if the data mapping to the physical resource is oset in time and frequency. Dierent scanning and mapping schemes used for uplink and downlink may oer opportunities for interference management as well. Implementation details of this idea need further investigation. Application of the graph framework to relay networks IEEE 802.16j proposes the deployment of both base stations (BSs) and relay stations (RSs) for mobile multihop relay (MMR) to amend the legacy 802.16e standard. One 153 BS and several RSs form a multi-level tree topology to expand cell coverage, where mobile users can communicate directly with BSs or, when being outside the BS range, with RSs [87]. The application of the proposed graph framework to this scenario is an interesting topic. How would the interference between MSs and, consequently, the interference graph change, from the all-BS scenario to the BS- and-RS scenario? How would the resource allocation problem change? Can the interference management schemes (ICIC and BSC) be applied directly to this new scenario? Or some modications are needed? These issues should be studied so as to understand the potential of the proposed graph framework in the relay network. 154 Bibliography [1] 3GPP Long Term Evolution (LTE). [Online]. Available: http://www.3gpp.org/Highlights/LTE/LTE.htm [2] 802.16 Working Group. [Online]. Available: http://www.ieee802.org/16 [3] IEEE 802.16 Task Group m. [Online]. Available: http://ieee802.org/16/tgm/ [4] Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems. IEEE Std 802.16e-2005. [5] WiMAX Forum. [Online]. Available: http://www.wimaxforum.org [6] Draft IEEE 802.16m Evaluation Methodology. IEEE 802.16 Broadband Wireless Access Working Group, 2007. 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Abstract (if available)

Abstract Orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) are two promising technologies adopted in the IEEE 802.16 standard to support broadband wireless access as well as multimedia quality-of-service (QoS). In this dissertation, we discuss several important topics regarding OFDM/OFDMA: cross-layer performance analysis of OFDM and OFDMA downlinks in terms of several QoS metrics

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Asset Metadata

Creator Chang, Yu-Jung (author)

Core Title Resource allocation in OFDM/OFDMA cellular networks: protocol design and performance analysis

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 10/29/2008

Defense Date 09/09/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag cellular networks,IEEE 802.16,interference management,MAC protocol design,OAI-PMH Harvest,OFDM,OFDMA,performance analysis,resource allocation

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kuo, C.-C. Jay (committee chair), Govindan, Ramesh (committee member), Neely, Michael J. (committee member)

Creator Email yjrchang@gmail.com,yujungc@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1704

Unique identifier UC1289299

Identifier etd-Chang-2392 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-118908 (legacy record id),usctheses-m1704 (legacy record id)

Legacy Identifier etd-Chang-2392.pdf

Dmrecord 118908

Document Type Dissertation

Rights Chang, Yu-Jung

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

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