針對多媒體資訊在正交分頻多工寬頻無線存取系統中排程技術及子載波分配方法之研究

電 信 工 程 研 究 所

碩 士 論 文

針對多媒體資訊在正交分頻多工寬頻無線存取

系統中排程技術及子載波分配方法之研究

Scheduling and Subcarrier Allocation for OFDMA

Based Broadband Wireless Access Systems with

Multi-type Traffic

研 究 生： 林韋君

指導教授： 王蒞君 博士

在此論文中，我們針對多媒體資訊在正交分頻多工(Orthogonal

Frequency Division Multiple Access, OFDMA) 寬 頻 無 線 存 取

(Broadband Wireless Access, BWA)系統作排程技術及子載波分配方

法之研究。

首先，我們將驗證在正交分頻多工寬頻無線存取此種多載波的系

統，使用一種最簡單的最大信號干擾比(Maximum C/I)排程法，即可

同時增加系統資料流量(throughput)且維持一定的公平性。最大信號

干 擾 比 排 程 法 在 單 載 波 分 碼 多 工 存 取 (Code Division Multiple

Access, CDMA)系統可有效的增進系統資料流量，但一向被視為一種

不公平的排程方法，在此，我們重新評估最大信號干擾比排程法在多

載波的正交分頻多工存取系統中的效能。透過分析與模擬，我們發現

最大信號干擾比排程法對於正交分頻多工系統的確算是一種公平的

排程方法。因此，針對正交分頻多工系統存取，我們發展了一種以最

大信號干擾比排程法為基礎的資源分配演算法，模擬結果顯示，最大

干擾比排程法並不比比例式公平(proportional fair)排程法差很

多，總結，在正交分頻多工存取系統中，最大干擾比排程法，不但可

盡量使系統資料流量趨近最大，更可同時維持相當好的公平性。

然而，目前的通訊環境中，多媒體的資訊傳輸已成趨勢，因此如

的資源分配亦成一項重要的研究課題。我們在此針對了正交分頻多工

存取系統發展了一套滿足服務品質的排程及通道分配的演算法。即時

服務(real-time service)的使用者在意的是資料的傳輸延遲，而非

即時(non-real-time)服務的使用者則是希望資料流量盡可能的越大

越好。而在無線通訊的環境，通道狀況是隨時間改變的，因此，我們

針對在正交分頻多工存取系統中，提出了一種考慮通道狀況和服務品

質的一套排程演算法。藉著利用多載波環境中的頻率多樣性和通道變

化的效應，我們提出的排程演算法可同時滿足即時與非即時使用的的

服務品質要求。首先，我們藉著排隊理論中等待時間的分析來分配即

時使用者的無線資源，接著使用最大信號干擾比排程法來分配非即時

使用者以達最大系統流量。總而言之，我們藉著利用頻率多樣性和實

體層的通道效應作跨階層的設計，便同時滿足了不同服務品質需求的

使用者。

OFDMA Based Broadband Wireless

Access Systems with Multi-type Traffic

A THESIS Presented to The Academic Faculty

By Wei-Jun Lin

In Partial Fulfillment

of the Requirements for the Degree of Master in Communication Engineering

Department of Communication Engineering National Chiao-Tung University

July, 2004

In this thesis, we first demonstrate that the simple maximum carrier to interference ratio (C/I) scheduling can both enhance system throughput and maintain fairness performances for the orthogonal frequency division multiple access (OFDMA) sys-tem. The maximum C/I scheduling has long been recognized as an effective method to enhance throughput, but it is viewed as an unfair scheduling policy in the the single carrier code division multiple access (CDMA) system. We reassess the fair-ness performance of the maximum C/I scheduling in the context of the multi-carrier OFDMA system. Through analysis and simulations, we find that the maximum C/I scheduling is indeed an fair scheduling for OFDMA systems. Thus, with respect to the OFDMA system, we develop a maximum C/I scheduling based resource alloca-tion algorithm. Our results show that the fairness of the maximum C/I scheduling in OFDMA systems is comparable to that of the proportional fair scheduling scheme. To sum up, we conclude that in the OFDMA system, the maximum C/I scheduling not only can maximize system throughput, but simultaneously maintain very good fairness performance.

The orthogonal frequency division multiple access (OFDMA) is becoming an important technique for the future wireless systems. Through parallel multi-carrier transmissions, the inter-symbol interference (ISI) can be easily handled in transmit-ting high speed data. Furthermore, OFDMA systems bring a new dimension for allocating radio resource - subcarrier. By exploiting frequency diversity in the wide frequency spectrum, a suitable subcarrier allocation technique can further enhance throughput for the OFDMA system. This thesis addresses the issue of allocating sub-carriers for providing both real-time and non-real-time traffic in the OFDMA system. We suggest a categorized subcarrier allocation (CSA) technique to improve through-put for non-real-time traffic, while satisfying the quality of service (QoS) requirements for the real-time traffic. In the proposed CSA technique, subcarriers are categorized

into two groups based on their quality: good and fair. The real-time traffic will be assigned by the subcarrier with fair condition, while the non-real-time traffic will be assigned with good subcarriers. We find that such a subcarrier allocation method can apply the maximum carrier-to-interference (C/I) scheduling to maximize the through-put in good conditioned subcarriers, while the delay for the real-time traffic can be controlled by allocating enough fair-conditioned subcarriers through a queueing an-alytical method. Compared to dynamic subcarrier allocation (DSA) and random subcarrier allocation (RSA) methods, the CSA technique outperforms other methods in terms of throughput, blocking probability and fairness performances.

Acknowledgments

I would like to thank my family who always give me visible and invisible supports. I especially would like to appreciate Dr. Li-Chun Wang who gave me many valuable suggestions and guidance in the research during the two years. I would not finish this work without his encouragement, comments, and advice.

In addition, I deeply grateful to my laboratory mates, Chiung-Jang, Ming-Bing, Chih-Wen, Wei-Cheng, Chang-Lung, Kuan-Jiin, Shi-Yen, Shu-Yi, Ming-Chi, Ya-Wen, Lei, Yi-Cheng, Ching-Hau, Kuang-Nan, Yun-Huai, Chung-Wei and Assane at WN-LAB at the Department of Communications in National Chiao-Tung University. They provide me much assistance and share much happiness with me.

Summary . . . . v

Acknowledgements . . . . vii

List of Tables . . . . xi

List of Figures . . . . xii

1. Introduction . . . . 1

1.1 Problems and Solutions . . . 1

1.1.1 Throughput and Fairness Enhancement for OFDMA Broad-band Wireless Access Systems Using the Maximum C/I Schedul-ing . . . 2

1.1.2 Channel-aware Subcarrier Allocation and QoS Provisioning for OFDMA Systems with Multi-type Traffic . . . 3

1.2 Thesis Outline . . . 4

2. Background . . . . 6

2.1 IEEE 802.16 WMAN . . . 6

2.2 Scheduling Techniques . . . 9

2.3 Subcarrier Allocation Strategies . . . 11

2.3.1 Fixed Subcarrier Allocation (FSA) . . . 11

2.3.3 Dynamic Subcarrier Allocation (DSA) . . . 11

2.4 Quantitative Measure of Fairness . . . 13

3. Throughput and Fairness Enhancement for OFDMA Broadband Wireless Ac-cess Systems Using the Maximum C/I Scheduling . . . . 17

3.1 Introduction . . . 18

3.2 Channel Models for the IEEE 802.16a System . . . 20

3.3 Problem Description . . . 22

3.3.1 Two-state Random Channel Matrix . . . 22

3.3.2 Problem Formulation . . . 23

3.4 Analysis . . . 25

3.4.1 Inclusion-Exclusion Principle . . . 25

3.4.2 Fairness Index . . . 27

3.4.3 Observation . . . 29

3.5 Resource Allocation Strategies . . . 31

3.5.1 Dynamic Power Allocation . . . 31

3.5.2 Maximum C/I Channel Allocation . . . 33

3.6 Simulation Results . . . 34

3.6.1 Simulation Methodology . . . 34

3.6.2 Effect of Multiuser Scheduling on the Fairness of Multi-carrier System . . . 36

3.6.3 System Performances Comparison of Different Resource Allo-cation Techniques . . . 36

3.6.4 System Performances Comparison of Different Scheduling Tech-niques . . . 37

3.6.5 Discussions . . . 39

4. Channel-aware Subcarrier Allocation and QoS Provisioning for OFDMA

Sys-tems with Multi-type Traffic . . . . 46

4.1 Introduction . . . 47

4.2 IEEE 802.16 Scheduling Service . . . 50

4.3 Motivation - Channel Characteristics of OFDMA Systems . . . 51

4.4 Problem Formulation . . . 52

4.5 The Proposed Categorized Subcarrier Allocation (CSA) Algorithm . . 58

4.6 Numerical Results . . . 62

4.6.1 Simulation Methodology . . . 62

4.6.2 Blocking Probability Comparison of Real-time Users . . . 64

4.6.3 Fairness Performance on Different Number of Subcarriers . . . 65

4.6.4 Throughput and Fairness Performance of Non-real-time Users 65 4.6.5 Discussions . . . 66

4.7 Conclusions . . . 67

5. Concluding Remarks . . . . 74

5.1 Throughput and Fairness Enhancement for OFDMA Broadband Wire-less Access Systems Using the Maximum C/I Scheduling . . . 75

5.2 Channel-aware Subcarrier Allocation and QoS Provisioning for OFDMA Systems with Multi-type Traffic . . . 75

5.3 Suggestion for Future Work . . . 76

Bibliography . . . . 77

2.1 Air Interface Nomenclature . . . 7

2.2 OFDMA downlink subcarriers allocation . . . 15

2.3 OFDMA uplink subcarriers allocation . . . 16

2.4 MMDS band frequency spacing (fs/BW = 8/7) OFDMA(NF F T = 2048) 16 3.1 SUI-1 Channel . . . 21

3.2 SUI-5 Channel . . . 21

3.3 Receiver SNR and Eb/N0 assumptions . . . 22

3.4 Analytical results of non-conflict condition . . . 29

3.5 Simulation Parameters . . . 36

2.1 OFDMA carrier allocation diagram . . . 7 3.1 Distribution of fairness index value for a random assignment . . . 28 3.2 Probability of the non-conflict condition with the varying number of

users and subchannels. . . 30 3.3 Fairness index with the number of subchannels varying in different

numbers of users. . . 32 3.4 Time varying with multipath fading model . . . 35 3.5 Fairness index with the number of subchannels varying in different

numbers of users when the IEEE 802.16 channel models are used. . . 41 3.6 Comparison of fairness performance of dynamic sbucarrier allocation

and power allocation (1T T I = 2048/6MHz = 341µs) . . . . 42 3.7 Comparison of throughput performance of dynamic sbucarrier

alloca-tion and power allocaalloca-tion (1T T I = 2048/6MHz = 341µs) . . . . 43 3.8 Comparison of fairness performance of max C/I and proportional

schedul-ing (1T T I = 2048/6MHz = 341µs) . . . . 44 3.9 Comparison of throughput performance of max C/I and proportional

4.1 (a) The number of users that judge the subcarrier is good for each sub-carrier; (b) The number of users that judge the subcarrier is medium for each subcarrier; (c) The number of users that judge the subcarrier

is bad for each subcarrier. . . 53

4.2 The cumulative number of subcarriers of different ratios, which is the number of good users to number of medium plus good uers for each subcarrier. . . 54

4.3 The stack presentation of OFDMA channel characterisitcs . . . 55

4.4 The stack presentation of parts of the OFDMA channel characterisitcs. We take from the 2001th to 2020th subcarriers for examples . . . 56

4.5 Proposed scheduler architecture . . . 60

4.6 Time varying with multipath fading model . . . 63

4.7 Blocking probability of real-time services when the inter-arrival rate changes. . . 68

4.8 The worst case of fairness when the number of subcarriers changes. . 69

4.9 Comparison of system throughput. . . 70

4.10 Comparison of fairness performances. . . 71

4.11 Mean throughput performances . . . 72

Introduction

With the growing demand of high data rate communication, orthogonal frequency division multiple access (OFDMA) is becoming an important technology. OFDMA has been used in many broadband wireless systems, such as the IEEE 802.16a wireless metropolitan area network (WMAN). We investigate the benefits of OFDMA systems from both frequency diversity and multiuser diversity perspectives. Frequency diver-sity inherently exists in OFDMA systems, while multiuser diverdiver-sity can be achieved by adopting scheduling algorithms. Although both diversity gains can enhance the system throughput, the challenging issue is how to select a scheduling algorithm that can achieve high system throughput and maintain the fairness among users simulta-neously.

In the traditional single carrier systems, many scheduling schemes are devel-oped. Different from single carrier systems, the channel allocation schemes in such multicarrier OFDMA systems have more dimensional consideration to support high-data-rate services. Besides, future wireless communication networks are expected to support multi-type traffic, such as voice, video and data. Therefore, allocating ra-dio resource to different types of services efficiently to meet quality of service (QoS) requirements of multi-types of services is an issue of concern.

1.1

Problems and Solutions

The objective of this thesis is to assess the performances of resource allocation schemes in the OFDMA systems. We investigate the OFDMA system from another resource

allocation viewpoint, i.e, scheduling algorithms. Wireless scheduling techniques are developed to exploit the multiuser diversity. In a multiuser wireless system, different users may have different channel responses in a time varying wireless channel. Thus, a channel may be viewed as a bad channel, but may be viewed as a good channel by other users. Consequently, if the system can first pick a user with the best channel quality among a group of users to serve in each channel , the system capacity can be improved significantly. We call this capacity improvement as the multiuser diver-sity gain. Clearly, for providing delay-tolerant data services, wireless scheduling is an inevitable technique to exploit multiuser diversity which inherently exists in the multiuser system.

1.1.1

Throughput and Fairness Enhancement for OFDMA

Broadband Wireless Access Systems Using the

Maximum C/I Scheduling

In this thesis, we first assess the fairness performance of the maximum C/I scheduling in the multi-carrier OFDMA system. The maximum C/I scheduling has long been recognized as an effective method to enhance throughput, but it is also viewed as an unfair scheduling policy in the the single carrier CDMA system. Through analysis and simulations, we will find that the maximum C/I scheduling is indeed an fair scheduling for OFDMA systems. Thus, with respect to the OFDMA system, we develop a maximum C/I scheduling based resource allocation algorithm. We show that the fairness of the maximum C/I scheduling in OFDMA systems is comparable to that of the proportional fair scheduling scheme. Hence, we conclude that the simple maximum C/I scheduling can enhance both system throughput and fairness performances for the OFDMA system.

1.1.2

Channel-aware Subcarrier Allocation and QoS

Provisioning for OFDMA Systems with Multi-type

Traffic

Future wireless communication networks are expected to support multi-type traffic, such as voice, video and data. Therefore, allocating radio resource to different types of services efficiently to meet quality of service (QoS) requirements of each service is an issue of concern. In [1], many conventional subcarrier allocation schemes are listed to try to enhance the system performances of constant data rate services. Nevertheless, in single carrier systems, if the real-time user with higher priority enters the wireless networks, the non-real-time user will delay the transmission due to lower priority. However, in multicarrier systems, the real-time users can be served by the enough good subcarriers without delay and the non-real-time users use other good subcarriers to achieve the throughput requirements at the same time.

Good scheduling algorithms should have the following characteristics: (1) channel aware, (2) high throughput, (3) fair resource allocation and (4) achieving quality of service. There exist some scheduling algorithms discussed to assure QoS requirements of different types of traffic in single carrier code division multiple ac-cess (CDMA) systems [2–6]. To provide both minimum service rate guarantees and dynamic channel bandwidth allocation to all users , generalized processor sharing (GPS) [7] [8] discipline is a scheduler candidate. In [2], the author employs fair queueing algorithm to minimize queueing delays in wireless networks. In [3] and [4], the author proposes a GPS based dynamic fair scheduling scheme, called code di-vision GPS (CDGPS) for wideband direct sequence code didi-vision multiple access (DS-CDMA) networks to support multi-type traffic. Furthermore, in [3], the author develops a credit-based CDGPS (C-CDGPS) to improve capacity by trading off

short-term fairness. The CARR (channel-aware round robin) scheduler [5] utilizes channel information to increase system capacity and guarantees to allocate certain amount of time slots in an assignment round period in code division multiple access 2000 high data rate (CDMA2000 HDR) [9] or wideband code division multiple access high speed downlink packet access (WCDMA HSDPA) [10] systems. In [6], the idea of the FPLS (fair packet loss sharing) scheduling algorithm is to schedule the session of multimedia packets in the way that all the users share the packet loss fairly de-pending on their QoS requirements and to maximize the system capacity under the QoS constraints. However, in multicarrier systems, such as OFDM, if radio resource management makes use of the frequency diversity, the system performance can be im-proved. In [11], the author discusses the adaptive modulation and proposes dynamic GPS (DGPS) scheduling for OFDM wireless communication systems, which exploits both multiuser diversity and frequency diversity. Yet, in [12], the proposed propor-tional rate adaptive optimization considers subcarrier and power allocation in the multiuser orthogonal frequency division multiplexing (MU-OFDM) system. There-fore, we develop a channel-aware and quality of service (QoS) provisioning subcarrier allocation algorithm for the OFDMA systems.

1.2

Thesis Outline

The research of this thesis investigates how to exploit frequency diversity and mul-tiuser diversity by scheduling and subcarrier allocation in the multicarrier systems. We first demonstrate that the simple maximum carrier to interference ratio (C/I) scheduling can both enhance system throughput and maintain fairness performances for the orthogonal frequency division multiple access (OFDMA) system. Furthermore, we develop a new quality of service (QoS) provisioning subcarrier allocation algorithm used in the orthogonal frequency division multiple access (OFDMA) system.

The remaining chapters of this thesis are organized as follows. Chapter 2 in-troduces the background of the IEEE 802.16a wireless metropolitan area network (WMAN) and some scheduling techniques in the single carrier systems. Further-more, we discuss the subcarrier allocation approaches in the multicarrier systems and quantitative measure of fairness. Chapter 3 demonstrates that the simple maximum carrier to interference ratio (C/I) scheduling can both enhance system throughput and maintain fairness performances by exploiting frequency diversity and multiuser diversity in the OFDMA system. Chapter 4 develops a subcarrier allocation scheme that supports quality of service (QoS) requirements of multiple types of services with considering characteristics of channel. At last, Chapter 5 gives the concluding remarks and suggestions for future work.

Background

In this chapter, we introduce the background of the IEEE 802.16 WMAN and some existed resource allocation schemes.

2.1

IEEE 802.16 WMAN

In [13], an OFDMA based wireless metropolitan area network (WMAN) is specified in the IEEE 802.16a standard. In a none line of sight (NLOS) environment, WMAN in the IEEE 802.16a specification is recommended to operate in a multicarrier modu-lation mode. Each OFDMA symbol consists of various types of subcarriers, including data, pilot and null. The number of the total subcarriers is 2048, which is equal to the fast Fourier transform (FFT) size.

As shown in Fig 2.1, the carriers are grouped into subsets of carriers, which is called a subchannel. Each carrier of a subchannel is not adjacent, which can mitigate the effect of deep fading by exploiting frequency diversity.

IEEE 802.16 provides two frequency bands. One is IEEE 802.16 and the other is IEEE 802.16a [13]. The former is applied in a line of sight (LOS) The latter is operated in the frequency band of 2 to 11 GHz. In none line of sight (NLOS) channel, Table 2.1 describes the difference between IEEE 802.16 and 802.16a.

The carrier allocation condition of the uplink and the downlink in IEEE 802.16a are showed in Table 2.2 and Table 2.3. Considering downlink case, there are 173 left and 172 right guard carriers, respectively. One dc carrier and 166 pilots. Actually, only 1536 carriers are used for data transmiision. On the other hand, in

Fig. 2.1: OFDMA carrier allocation diagram

Tab. 2.1: Air Interface Nomenclature

Destination Applicability PHY MAC Duplexing

WirelessMAN-SC 10-66GHz SC Basic TDD,FDD,HFDD

WirelessMAN-SCa 2-11GHz SCa Basic,ARQ,STC,AAS TDD,FDD,HFDD WirelessMAN-OFDM 2-11GHz OFDM Basic,AAS,ARQ,Mesh,STC TDD,FDD,HFDD WirelessMAN-OFDMA 2-11GHz OFDMA Basic,ARQ,STC,AAS TDD,FDD,HFDD

uplink case, there are 176 left and 175 right guard carriers and one dc carriers. The remaining carriers are divided into 32 subchannels. Each subchannel has 53 carriers, including 48 data carriers and 5 pilots. Table 2.4 shows frequency spacing in different definition of guard time Tg in Multichannel Multipoint Distributed Service (MMDS)

band (from 2.1 to 2.7 GHz). We will adopt this to model our channel and describe the corresponding channel delay profile.

The way of allocating subcarriers is based on the following formula.

carrier(n, s) = Nsubchannels· n + {ps[nmod(Nsubchannels)] +

where

carrier(n, s) = carrier index of carrier n in subchannel s.

s = index number of a subchannel from the set [0,1,...,Nsubchannels-1].

n = carrier-in-subchannel index from the set [0,1,...,Nsubcarriers-1].

Nsubchannels= number of subchannels.

ps[j] = the series obtained by rotating {P ermutationBase0} cyclically to the left s

times.

ceil[ ] = function which rounds its argument up to the next integer.

IDcell = a positive integer assigned by the MAC to identify this particular BS sector.

Xmod(k) = the remainder of the quotient X/k (which is at most k-1).

We take an uplink example to illustrate the use of this formula. The subcarriers for subchannel s = 1 in cell IDcell = 2 are computed. The number of subchannels

Nsubchannels = 32, while the number of carriers in each subchannel Nsubcarriers = 53,

and the number of data carriers in each subchannel is 48.

P ermutationBase0 = {3, 18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21,

5, 28, 31, 23, 17, 4, 24, 0, 13, 12, 19, 14, 30}. Using equation (2.1),

1. The basic series of 32 numbers is {3, 18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21, 5, 28, 31, 23, 17, 4, 24, 0, 13, 12, 19, 14, 30}

2. In order to get 32 different permutation the series is rotated to the left (from no ro-tation at all up to 31 roro-tations). Since we have assumed s=1, (permuro-tationbases=1)

is: {18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21, 5, 28, 31, 23, 17, 4, 24, 0, 13, 12, 19, 14, 30, 3}

3. We repeat the permuted series 2 times and take the first 53 numbers only: {18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21, 5, 28, 31, 23, 17, 4, 24, 0,

13, 12, 19, 14, 30, 3, 18, 2, 8, 16, 10, 11, 15, 26, 22, 6, 9, 27, 20, 25, 1, 29, 7, 21, 5, 28, 31, 23, 17, 4, 24, 0, 13, 12, 19, 14, 30, 3}.

4. The concatenation depends on the IDcell (which characterizes the working cell

and can range from 0 to 31). Since we have assumed s = 1 and IDcell = 2, the

last term in the equation becomes

ps[nmod(32)] + 2 · ceil[(n + 1)/32]_mod(32) with n = 0,1, ..., 52

= {20, 4, 10, 18, 12, 13, 17, 28, 24, 8, 11, 29, 22, 27, 3, 31, 9, 23, 7, 30, 1, 25, 19, 6, 26, 2, 15, 14, 21, 16, 0, 5, 22, 6, 12, 20, 14, 15, 19, 30, 26, 10, 13, 31, 24, 29, 5, 1, 11, 25, 9, 0, 3}

5. Finally adding in the first term, the set of carriers is found: carrier(n, 1) = {20, 36, 74, 114, 140, 173, 209, 252, 280, 296, 331, 381, 406, 443, 451, 511, 521, 567, 583, 638, 641, 697, 723, 742, 794, 802, 847, 878, 917, 944, 960, 997, 1046, 1062, 1100, 1140, 1166, 1199, 1235, 1278, 1306, 1322, 1357, 1407, 1432, 1469, 1477, 1505, 1547, 1593, 1609, 1632, 1667}

2.2

Scheduling Techniques

Many scheduling algorithms have been developed for the single carrier code division multiple access (CDMA) system [14–18]. First, the maximum C/I scheduling scheme allocates the channel to the user J that has the best current channel condition.

J = arg{max

i ri(t)} , (2.2)

where J is the scheduled user, i is the user index and ri is the channel response of

the user i, while t indicates time. This scheduling algorithm can exploit multiuser diversity at the expense of the fairness performance to some other users. Second, the

round-robin scheduling approach allocates resource to each user periodically, which can provide the best fairness performance, but has poor throughput because it does not take the channel information into account. We express this algorithm mathemat-ically as follow.

J = arg{max

i di(t)} , (2.3)

where di is the delay of user i. Third, the proportional fair scheduling algorithm [15]

was proposed to use the ratio of the short-term channel response to the long-term channel condition of each user as a criterion to allocate the resource. We describe the principle of the proportional fair scheduling by (2.4).

J = arg{max

i (

ri(t)

ri(t)

)} , (2.4)

where ri(t) is the long-term channel response of user i while ri(t) is the short-term

channel response of user i. Last, the exponential rule scheduling policy [16–18] further considers the service delay of each user. If the user has waited for a long time, this user will be allocated a channel with a higher priority depending on (2.5).

J = arg{max i [ ri(t) ri(t) exp (di(t) − d(t) 1 + q d(t) )]} , (2.5)

where d(t) is the average delay of all users. By (2.5), we can see the exponential term dominates that means the delay of each user can determine the priority of each user. These wireless scheduling algorithms were only evaluated in the single carrier wireless system. To our knowledge, how these scheduling algorithms perform in the multi-carrier OFDMA system is an open issue.

2.3

Subcarrier Allocation Strategies

In this section, we introduce three conventional multicarrier allocation (MCA) [1] schemes as follows.

2.3.1

Fixed Subcarrier Allocation (FSA)

Fixed subcarrier allocation means that we allocate the fixed sets of subcarriers to certain users whether the subcarriers is good or bad for these users. In other words, users use a certain set of subcarriers all the time. This scheme does not exploit multiuser diversity and frequency diversity at all. Therefore, FSA scheme is regarded as a simple but inefficient subcarrier allocation scheme.

2.3.2

Random Subcarrier Allocation (RSA)

In each time slot, users randomly select sets of subcarriers for transmission when using random subcarrier allocation (RSA) scheme. This scheme makes use of frequency diversity to avoid some unfavorable condition. If a user select a set of bad subcarriers in a time slot, he may select another better set of subcarriers for communication and does not suffer from bad communication environments all the time. In short, the RSA scheme exploit the frequency diversity to provide fairer resource allocation and this scheme do not know any channel state information.

2.3.3

Dynamic Subcarrier Allocation (DSA)

In order to enhance the system throughput performance, we prefer that each sub-carrier is allocated to the user that the subsub-carrier channel response is the best to the user among all users in each time slot. Nevertheless, it will cause unfair re-source allocation. Therefore, we allocate the rere-source from the viewpoint of users.

Furthermore, the wireless communication environments are time-varying. Hence, dynamically allocating subcarriers according to channel condition can improve the throughput performance while this resource allocation approach is called dynamic subcarrier allocation (DSA) scheme. The DSA scheme is similar to the maximum C/I (carrier-to-interference-plus-noise ratio) scheduling used in single carrier CDMA system [14] [18]. This scheme exploits both frequency diversity and multiuser diver-sity. We describe the subcarrier allocation policy as follows.

First, we define a channel matrix H in the OFDMA environment. Assume that there are N users and M subcarriers in the system.

H =         h1,1 h1,2 · · · h1,M h2,1 ... . .. hN,1 hN,2 · · · hN,M         (2.6)

where hn,mrepresents the m−th subcarrier condition to the n−th user. For example,

h3,2 means the response of subcarrier 2 observed by user 3. The DSA scheme operates

as the following procedure.

1. Give each user a priority number.

2. According to the priority of each user, the user n selects his own favorite subcar-riers for any user in order.

3. Users with lower priority do not select the selected subcarriers of the users with higher priority and they can only select the rest subcarriers.

Due to the multiuser environments, if the channel responses are independent of users, which makes the multiuser diversity exist to improve system throughput.

2.4

Quantitative Measure of Fairness

Fairness consideration is very important in the field of radio resource management. We should show the how fair resource allocation is among all users numerically. How-ever, there are many fairness measures proposed to indicate the fairness level of re-source allocation. We describe those fairness indices as follows. Define xithe resource

quantity allocated to user i, and n the number of total users. Variance V ariance = 1 n − 1 n X i=1 (xi− µ)2 where mean µ = 1 n n X i=1 xi (2.7) Coefficient of Variation

Coef f icient of V ariation (COV ) = V ariance

Mean (2.8)

Min-max Ratio

Min − max = mini {xi}

max j {xj} = min i,j xi xj (2.9)

Jain’s Fairness Index

F = (PN i=1 xi)2 N PN i=1 xi2 (2.10)

As above, all the indices can represent the degree of fairness of resource allo-cation among users. Nevertheless, in [19], we desire that the fairness index has the following properties.

(a) Population size independence: The index should be suitable for infinite or finite users. The above four indices all satisfy the requirement.

(b) Scale and metric independence: We expect that the indices are indepen-dent of scale. In other words, if users are allocated ten times quantity of resource simultaneously, the indices should be the same values. However, the variance index does not meet the goal.

(c) Boundedness: In addition to population size independence and scale in-dependence, the indices are desired to be bounded between 0 and 1. Therefore, we can judge the policy of resource allocation fair according whether the fairness index approaches 1 or not. The COV (coefficient of variation) is not bounded. Its value distributes from 0 to infinity.

(d) Continuity: The continuous index can respond the little change in allo-cation way. The min-max ratio index only take the users with best resource and with worst resource into account. Therefore, if the allocation changes among medium users, the min-max ratio index does not change.

To sum up, we observe the behaviors of the indices. We find that Jain’s fairness index satisfies all the desired properties. Consequently, we adopt the index as one of our simulation performance metric.

Tab. 2.2: OFDMA downlink subcarriers allocation

Parameters Value

Number of DC carriers 1

Number of Guard Carriers: Left, Right 173,172

Number of Used Carriers 1702

Nused 1702

Total Number of Carriers 2048

NvarLocP ilots 142

Number of Fixed-location Pilots 32

Number of Variable-Location Pilots which 8

coincide with Fixed-Location Pilots

Total Number of Pilots 166

Number of data carriers 1536

Nsubchannels 32

Nsubcarriers 48

Number of data carriers per subchannel 48

BasicFixedLocationPilots {0,39,261,330,342,351,522,636,645,651,708,726, 756,792,849,855,918,1017,1143,1155,1158,1185, 1206,1260,1407,1419,1428,1461,1530,1545,1572, 1701} {P ermutationBase0} {3,18,2,8,16,10,11,15,26,22,6,9,27,20,25,1,29 7,21,5,28,31,23,17,4,24,0,13,12,19,14,30}

Tab. 2.3: OFDMA uplink subcarriers allocation

Parameters Value

Number of DC carriers 1

Nused 1696

Number of Guard Carriers: Left, Right 176,175

Nsubchannels 32

Nsubcarriers 53

Number of data carriers per subchannel 48

{P ermutationBase₀} {3,18,2,8,16,10,11,15,26,22,6,9,27,20,25,1,

29,7,21,5,28,31,23,17,4,24,0,13,12,19,14, 30}

Tab. 2.4: MMDS band frequency spacing (fs/BW = 8/7) OFDMA(NF F T = 2048)

T

(µ

)

BW(MHz) ∆f (kHz) T

(µ

) T

/32 T

/16 T

/8 T

/4

1.5

1194

37

74

149

298

3.0

1

597

18

37

74

149

6.0

3

298

9

18

37

74

12.0

6

149

4

9

18

37

24.0

13

74

2

4

9

18

Throughput and Fairness Enhancement

for OFDMA Broadband Wireless Access

Systems Using the Maximum C/I

Scheduling

In this chapter, we demonstrate that the simple maximum carrier to interference ratio (C/I) scheduling can both enhance system throughput and maintain fairness perfor-mances for the orthogonal frequency division multiple access (OFDMA) system. The maximum C/I scheduling has long been recognized as an effective method to enhance throughput, but it is viewed as an unfair scheduling policy in the the single carrier code division multiple access (CDMA) system. We reassess the fairness performance of the maximum C/I scheduling in the context of the multi-carrier OFDMA system. Through analysis and simulations, we find that the maximum C/I scheduling is indeed an fair scheduling for OFDMA systems. Thus, with respect to the OFDMA system, we develop a maximum C/I scheduling based resource allocation algorithm. Our re-sults show that the fairness of the maximum C/I scheduling in OFDMA systems is comparable to that of the proportional fair scheduling scheme. In short, we conclude that in the OFDMA system, the maximum C/I scheduling not only can maximize system throughput, but simultaneously maintain very good fairness performance.

3.1

Introduction

With the growing demand for high data rate communication, orthogonal frequency division multiple access (OFDMA) is becoming an important technology. OFDMA has been used in many broadband wireless systems, such as the IEEE 802.16a wireless metropolitan area network (WMAN) [13] [20]. This chapter investigates the benefits of OFDMA systems from both frequency diversity and multiuser diversity perspec-tives. Frequency diversity inherently exists in OFDMA systems, while multiuser diversity can be achieved by adopting scheduling algorithms. Although both diver-sity gains can enhance the system throughput, the challenging issue here is how to select a scheduling algorithm that can achieve high system throughput and maintain the fairness among users simultaneously.

OFDMA is not only a modulation scheme but also a multiple access technology. In an OFDMA system, each user is allocated a set of orthogonal subcarriers. In addition to overcoming the inter-symbol interference (ISI), an OFDMA system can also mitigate the multiple access interference (MAI) due to the orthogonality among subcarriers. Moreover, it can result in frequency diversity benefit with interleaving and channel coding. To further take advantage of frequency diversity [21–25], many adaptive resource allocation techniques were suggested from a view point of subcarrier power allocation [12] [26].

The goal of this chapter is to investigate the OFDMA system from another resource allocation viewpoint, i.e, scheduling algorithms. Wireless scheduling tech-niques are developed to exploit the multiuser diversity. In a multiuser wireless system, different users may have different channel responses in a time varying wireless chan-nel. Thus, a channel may be viewed as a bad channel, but may be viewed as a good channel by other users. Consequently, if the system can first pick a user with the best channel quality among a group of users to serve in each channel , the system capacity

can be improved significantly. We call this capacity improvement as the multiuser diversity gain. Clearly, for providing delay-tolerant data services, wireless scheduling is an inevitable technique to exploit multiuser diversity which inherently exists in the multiuser system.

Many scheduling algorithms have been developed for the single carrier time division multiple access (TDMA) or code division multiple access (CDMA) systems [14–18]. First, the maximum C/I scheduling scheme allocates the channel to the user that has the best channel condition [14]. This scheduling algorithm can fully exploit multiuser diversity at the expense of sacrificing the fairness performance for other users. Second, the round-robin scheduling approach allocates resource to each user periodically, which can provide the best fairness performance, but has lowest throughput because it does not take the channel information into account. Third, the proportional fair scheduling algorithm [15] was proposed to use the ratio of the short-term channel response to the long-short-term channel condition of each user to allocate the resource. Last, the exponential rule scheduling method [16–18] further considers the service delay of each user. If the user has waited for a long period of time, this user will be allocated a channel with a higher priority. These wireless scheduling algorithms were only evaluated in the single carrier wireless system. To our knowledge, how these resource management algorithms perform in the multi-carrier OFDMA system is an open issue.

There were a lot of dynamic radio resource management technologies in OFDM based multicarrier systems discussed in the literature. In traditional wired dis-crete multitone asymmetric digital subscriber lines (ADSL), a resource management method named water-filling power allocation [27] is popularly used. Therefore, a lot of papers [21] [23] [24] adopted this rule to solve the optimization problem that to maximize the system capacity under the total power constraint.

scheduling in the multi-carrier OFDMA system. The maximum C/I scheduling has long been recognized as an effective method to enhance throughput, but it is also viewed as an unfair scheduling policy in the the single carrier CDMA system. Through analysis and simulations, we will find that the maximum C/I scheduling is indeed an fair scheduling for OFDMA systems. Thus, with respect to the OFDMA system, we develop a maximum C/I scheduling based resource allocation algorithm. We will show that the fairness of the maximum C/I scheduling in OFDMA systems is comparable to that of the proportional fair scheduling scheme. Hence, we conclude that the simple maximum C/I scheduling can enhance both system throughput and fairness performances for the OFDMA system.

The rest of this chapter is organized as follows. Section 3.2 introduces the channel models for an OFDMA based IEEE 802.16a system. Section 3.3 formulates this problem. In Section 3.4, we analyze the system throughput performance with the maximum C/I scheduling algorithm in the multicarrier systems. Section 3.5 introduces the current two resource allocation strategies. Simulation results are given in Section 3.6. We give our concluding remarks in Section 3.7.

3.2

Channel Models for the IEEE 802.16a System

We will introduce more complicated but practical channel models specified in the IEEE 802.16a WMAN standard [28]. There are six typical Stanford University In-terim (SUI) channel models for three types of terrains. These SUI channels are used for the fixed broadband wireless applications (BWA) in the multichannel multipoint distributed service (MMDS) band. We will use the two SUI channel models, SUI-1 and SUI-5, in our simulations. Parameters in the two SUI channels are summarized in Tables 3.1 and 3.2.

Tab. 3.1: SUI-1 Channel

Tap 1 Tap 2 Tap 3 Units Delay 0 0.4 0.8 µs

power (omni. ant) 0 -15 -20 dB power (30◦ _{antenna) 0 -21 -32 dB}

K Factor 18 0 0

Maximum Doppler frequency 0.4 0.4 0.4 Hz

Tab. 3.2: SUI-5 Channel

Tap 1 Tap 2 Tap 3 Units

Delay 0 5 10 µs

power (omni. ant) 0 -5 -10 dB power (30◦ _{antenna) 0 -11 -22 dB}

K Factor 0 0 0

Maximum Doppler frequency 2 2 2 Hz

to Rician fading. On the other hand, SUI-5 is close to Rayleigh fading channel and it is exposed severe multipath fading effect. Moreover, the channel response value “1” is defined to be the state that received signal-to-noise ratio (SNR) can be satisfied. If the value is above 1, the channel is in good condition. In our simulation, we evaluate the system capacity by using the QPSK with coding rate 1/2 case [13]. The channel response “1” corresponds to the received SNR 9.4 dB. The receiver with SNR values in Table 3.3 can achieve BER less than 10−6_.

Tab. 3.3: Receiver SNR and E_b/N0 assumptions

Modulation coding rate Receiver SNR QPSK 1/2 9.4 QPSK 3/4 11.2 16QAM 1/2 16.4 16QAM 3/4 18.2 64QAM 2/3 22.7 64QAM 3/4 24.4

3.3

Problem Description

3.3.1

Two-state Random Channel Matrix

A simple channel model is adopted to describe the impact of the number of subchan-nels when using the maximum C/I scheduling algorithm. We assume that there are N users requiring the same data rate. Each subchannel has two states: good and bad [29]. Good state means that the channel could bear 1 + δ times of the required rate rate, while the bad state means that the channel only could transmit 1 − δ times of the normal data rate. We also assume that the channel condition on which each user observed is independent. In other words, the same channel may be viewed as a good channel for a user, but a bad one for others.

different users. Consequently, we can form a channel matrix H : H =user index subcarrier index z }| {                        h1,1 h1,2 · · · h1,M h2,1 ... . .. hN,1 hN,2 · · · hN,M         (3.1)

where hn,m represents the m−th subchannel condition to the n−th user. For example,

h3,2 means the response of subchannel 2 observed by user 3. Each element can be in

two states, good or bad with equal probability 1

2. This model will be used for only

analysis.

3.3.2

Problem Formulation

For simplicity, we adopt the two-state channel model to analyze both the throughput and fairness performance of multicarrier systems. We first assume that each user uses just one subchannel. Next, we will calculate the probability that all users are allocated with good subchannels. This is an issue of permutation and combination in mathematics. As the numbers of users and subchannels increase, the process of permutation and combination calculation becomes very complicated. Therefore, we propose a systematic analytical approach. Owing to too many possibilities in permutation and combination as the numbers of users and subchannels increase, we will apply the Inclusion-Exclusion Principle to analyze system performance.

We define a permutation matrix P, which contains all permutations of 1,2,3,...,N. Take N=3 as an example. P =      1 1 2 2 3 3 2 3 1 3 1 2 3 2 3 1 2 1      (3.2)

where P is an N × N! matrix. This matrix will be used to permutate all conditions that all users have observed good channel conditions. The value x of each entry in the i − th row of the permutation matrix P represents the entry located at the i − th row and the x − th column of the channel matrix H in a good condition. In other words, the x − th subchannel is in a good condition for the i − th user. For example, if the second column vector of P, [1, 3, 2]T_{, this means that h}

11, h23 and h32 are in the

good state. Then the channel matrix becomes

H =      ∨ f ree f ree f ree f ree ∨ f ree ∨ f ree      , (3.3)

where the elements labelled ”∨” in the i − th row and the j − th column in channel matrix H mean that the j − th subchannel is in a good state for the i − th user. The elements labelled ”f ree” mean that the subchannel conditions responding to some users can be either good or bad. Thus, all users can use good subchannel without conflicts. Consider both the second and fourth columns of P in (3.2), i.e. [1, 3, 2]T

and [2, 3, 1]T_{, simultaneously. Then the channel matrix becomes}

H =      ∨ ∨ f ree f ree f ree ∨ ∨ ∨ f ree     . (3.4)

Since there are at least N good subchannels in different rows and different columns, each user can have a good subchannel for transmissions. In the following, we introduce a systematic approach to analyze the impact of the maximum C/I scheduling algo-rithm in the multicarrier systems by applying the Inclusion-exclusion principle [30].

3.4

Analysis

3.4.1

Inclusion-Exclusion Principle

Our goal is to calculate all conditions that all users can use good subchannels. Con-sider N users and N subchannels. We count the number of cases that the good subchannels can distribute in N different rows and different columns in the channel matrix HN ×N. First, we will use the parameter, permutation matrix P . Any

combi-nations of the columns in matrix P corresponds to a channel matrix H. It is possible that different combinations of columns in P map to the same channel matrices H. Our objective is to calculate the number of matrices H in which all users can find a good subchannel without conflicts. For example,

H =      ∨ bad bad bad ∨ bad bad bad ∨      (3.5)

represents a case that all users can have good subchannels without conflicts. By contrast, H =      ∨ bad bad ∨ bad bad bad ∨ bad      (3.6)

represents a case that users 1 and 2 compete for subchannel 1. Next, we apply the Inclusion-Exclusion Principle to calculate the number of all users having good channels.

Lemma To calculate the size of A1

S

A2

S

. . .SAn, calculate the sizes of all

by intersecting an odd number of the sets and then subtract the results obtained by intersecting an even number of the sets [30].

For example, if we will calculate the number of multiples of 2 and 3 from 1 to 100, we will first count the number of multiples of 2, then we add the number of multiples of 3; and finally we subtract the number of multiples of 6.

We define F (k) as the number of matrices H for selecting k columns from the permutation matrix P . For an even number of k, F (k) is denoted as Fe_{(k), whereas}

for an odd number of k, F (k) is represented by Fo_{(k). Note that k is ranged from 1}

to N! and P is an N × N! matrix. By applying the Inclusion-Exclusion Principle, we can calculate the number of the non-conflict conditions as

X

k=1,3,...,N !−1

Fo_{(k) −} X k=2,4,..,N !

Fe_{(k) (3.7)}

For example, if N = 3, then the permutation matrix P

P =      1 1 2 2 3 3 2 3 1 3 1 2 3 2 3 1 2 1      (3.8)

For Fo_{(1), there are six (C}3!

1 ) selections, which corresponds to the case that {1}, {2},

{3}, {4}, {5} and {6} columns in permutation matrix P are selected individually. In

this case, each Fo_{(1) corresponds to 2}6 _{channel matrices H because there are six free}

elements in H. (see (3.3) as an example). For Fe_{(2), there are C}3!

2 combinations,

which means that we choose {1,2}, {1,3},{1,4},...{4,5},{4,6} and {5,6} columns from the permutation matrix P . Fe_{(2) may be either 2}3 _{(e.g. {1,4}) or 2}4 _{(e.g. {2,4}).}

When N increases, the permutation and combination conditions becomes huge. The systematic approach based on (3.7) can solve the complex permutation and combi-nation problems.

3.4.2

Fairness Index

According to [31] [19], we define a fairness index F in the multiuser systems as follows:

F = (PN i=1 ri)2 NPN i=1 ri2 , (3.9)

where ri is the transmission data rate of the i − th user, and N is the number of total

users. For F = 1, it is the fairest condition between users, and it is not fair as F < 1. For example, if there are two users transmitting data, one is transmit at 1.2 times of the required data rate, and the other transmit at 0.8 times of the required data rate. Then the fairness index F is about 0.96. If the transmission data rate of one user is 1.5, and the other is 0.5, the fairness index is 0.8. Thus the former example is fairer than the latter.

We will illustrate that a random assignment method cannot easily achieve high value of the fairness index. We illustrate this point as follows. We generate a set of random variables. Each random variable represents the resource allocated to each user. We assume the random variables are uniformly distributed in the interval (0,1). Fig. 3.1 shows the cumulative distribution function (CDF) of the value of the fairness index. From Fig. 3.1, we find that the more the users, the harder the fairness is achieved. When there are 8 users, the probability that the fairness index is larger than 0.8 is 38%. However, if 32 users exist in the system, the probability that the fairness index is greater than 0.8 is smaller than 20%. From this example, we know that a random assignment approach can not easily achieve the fairness index higher than 0.8 or 0.9. Thus, it is not trivial to design a resource allocation scheme achieving the fairness index higher than 0.9.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Value of fairness index

CDF

8 users 32 users 56 users 80 users

3.4.3

Observation

By applying the Inclusion-Exclusion Principle, we can systematically calculate prob-ability that all users can use good subchannels when N is not too large. We list the results in Table 3.4.

Tab. 3.4: Analytical results of non-conflict condition

Number of users (sub-channels) Probability 2 7/16 = 0.4375 3 247/512 = 0.4824 4 37823/65536 = 0.5771

From Table 3.4, we observe that the probability of the non-conflict condition (i.e., all users can use good subchannels.) increases with the number of users (sub-channels) increasing apparently. By increasing the number of subchannels and users, we find that system throughput performance can be improved even without other complicated scheduling algorithms, such as proportional fairness scheduling or even exponential rule scheduling algorithms.

Furthermore, we observe the effect of the number of subcarriers on the fair-ness when the maximum carrier-to-interference scheduling algorithm is used in the multicarrier systems.

Due to the complexity, we obtain the numerical results by programming when N is larger than 5. We find that we can further achieve good fairness performance between users by efficiently exploiting both multiuser diversity and frequency diver-sity. For the case of N = 7 in Fig. 3.2, one can find that with 90% probability, all

5 10 15 20 25 30 0 0.5 0.65 0.85 0.9 0.93 0.96 0.99 0.995 0.999 0.9999 number of subcarriers(users)

probability that all users use good subcarrier

Fig. 3.2: Probability of the non-conflict condition with the varying number of users and

subchannels.

the seven users can have the good subchannels and the fairness index F = 1.

Figure 3.3 shows the effect of increasing number of the subcarriers on fairness performance with different numbers of users in a two-state random channel model. We can easily see that the more the number of subcarriers, the better the system fairness performance. However, as the number of users increases, the required number of subcarriers to provide satisfying fairness performance increases. Observing Fig. 3.3, if we require the system fairness index has to be larger than 0.9 when there are

24 users in the system, we should divide available total bandwidth into at least 22 subcarriers.

3.5

Resource Allocation Strategies

Besides some scheduling algorithms mentioned in Section 2.2, we will describe some other resource allocation approaches mathematically in the multicarrier OFDMA sys-tem.

3.5.1

Dynamic Power Allocation

The dynamic power allocation is commonly used in traditional wired discrete multi-tone (DMT) [27] systems, such as ADSL. We allocate power in different multi-tones with different channel condition. The goal is to maximize the system capacity. Conse-quently, this issue becomes an optimization problem under total power constraint. We describe this problem by the following equations.

max Pn,m N X n=1 M X m=1 ρn,m M log2{1 + Pn,mh2n,m N0_MB } (3.10) subject to N X n=1 M X m=1 Pn,m ≤ Ptotal (3.11) Pn,m ≥ 0 ∀n, m (3.12) ρn,m = {0, 1} ∀n, m (3.13) N X n=1 ρn,m = 1 ∀m (3.14)

5 10 15 20 25 30 0 0.1 0.3 0.5 0.6 0.7 0.8 0.9 0.95 0.98 0.99 number of subcarriers fairness index 8 users 16 users 24 users 32 users

Fig. 3.3: Fairness index with the number of subchannels varying in different numbers of

where ρn,m = 1 means that the m-th subchannel is assigned to the n-th user, n is the

user index while m is the subcarrier index, and B denotes the total bandwidth. In this case, ρn,m is fixed with time. The dynamic power allocation algorithm can solve

such optimization problem under several constraints.

3.5.2

Maximum C/I Channel Allocation

We see this problem from another scheduling viewpoint. Instead of power allocation, we schedule users with best channel response for each subcarrier. In order to maxi-mize the system capacity, we can regard the maximum C/I channel allocation as to apply water-pouring principle to the dimension of multiple users. The following equa-tions describe the principle of maximum C/I channel allocation to maximize system throughput. max ρn,m N X n=1 M X m=1 ρn,m M log2{1 + h2 n,m N0_MB } (3.15) subject to ρn,m = {0, 1} ∀n, m (3.16) N X n=1 ρn,m = 1 ∀m (3.17) M X m=1 ρn,m = M N ∀n (3.18)

where (4.2) and (4.3) mean that each subchannel is allocated to only one user, and (4.4) means that each user can use a certain number of subcarriers, respectively.

3.6

Simulation Results

Besides numerical results described in Section 3.4, we will show some simulation results to illustrate the benefits of multicarrier system when using the maximum C/I scheduling scheme. Furthermore, we will compare both system throughput and fairness performances of different resource management approaches in the multicarrier systems.

3.6.1

Simulation Methodology

Then, we apply the two practical IEEE 802.16 channel models, SUI-1 and SUI-5, to our simulation. In [28], six SUI channel delay profiles are specified. For the multicar-rier OFDMA system, we first take the appropriate 2048 samples of the channel delay profiles where the sample time

Ts =

1

B , (3.19)

where B is total bandwidth and 2048 is FFT size corresponding to the number of subcarriers. And then we use the fast Fourier transform (FFT) technique [32] to transform from time domain to frequency domain. Hence, we can observe the multi-path fading effect in the frequency domain, (see Fig. 3.4). Finally, observing a long time period of this frequency domain channel models, we pick different time points to represent the channel response of different users. Therefore, we can form a practical channel matrix for simulation to evaluate the system performance. The simulation parameters are listed in Table 3.5.

Tab. 3.5: Simulation Parameters

No. of user 32 FFT size 2048 Total bandwidth 6 MHz

Channel model SUI-1 and SUI-5

3.6.2

Effect of Multiuser Scheduling on the Fairness of

Multi-carrier System

Figure 3.5 shows the fairness by using the IEEE 802.16a SUI-5 channel models in simulation. For the sake of fitting in with IEEE 802.16a OFDMA physical layer standard, 2048 FFT size used, we divide the total bandwidth into 2,4,8,16 and 32 subchannels. We still observe that when the number of subcarriers increases, the system fairness performance becomes better even in the SUI-5 channel model.

3.6.3

System Performances Comparison of Different

Resource Allocation Techniques

Figures 3.6 and 3.7 compares the fairness and throughput performances of different resource management algorithms in SUI-1 and SUI-5 channel models, respectively. In SUI-1 channel model, the fairness performance can be maintained easily. However, SUI-5 channel suffer from more severe fading.

Figure 3.6 shows that dynamic power allocation and maximum C/I scheduling policies do not have obvious difference in fairness performance in SUI-1 channel mod-els. Because frequency and multiuser diversity exist in the multiuser multi-carrier environment, fairness performance is very good. However, the fairness performance

of the maximum C/I scheduling is worse than that of the power allocation scheme about 3.5%. Nevertheless, the value about 0.96 of the fairness index of the maximum C/I scheduling algorithm still means it is a fair resource allocation.

At the same time, we observe Fig. 3.7. We find that the throughput per-formances of the maximum C/I scheduling policy always better than that of the power allocation scheme whether in the SUI-1 channel model or in the SUI-5 channel model. In the SUI-1 channel model, the difference of the throughput performances of the maximum C/I scheduling algorithm and the power allocation scheme is very small. The maximum C/I performs better than the dynamic power allocation about 5%. On the other hand, the throughput performance of the maximum C/I schedul-ing policy is better than that of the power allocation algorithm about 13%. In short, we observe that the system performances of the maximum C/I scheduling algorithm and the power allocation policy are similar in the SUI-1 channel model. However, in the SUI-5 channel model, the maximum C/I scheduling enhance the system through-put about 13% more than the power allocation at the expense sacrificing 3.5% of the fairness performance. Therefore, we concludes that good fairness performance is easily achieved in the multiuser multi-carrier system even when the maximum C/I scheduling adopted.

3.6.4

System Performances Comparison of Different

Scheduling Techniques

In addition to comparing the system performance of the power allocation and the maximum scheduling schemes, we compare the system performances of the maximum C/I and proportional scheduling algorithms in this subsection.

Figure 3.8 compares the fairness performance of the maximum C/I scheduling and the proportional fair scheduling in the IEEE 802.16 SUI-1 and SUI-5 channel

models. In the IEEE 802.16 SUI-1 channel model, the fairness performance can be easily maintained. However, because of more severe fading, it is more difficult to maintain the short-term fairness performance in the IEEE 802.16 SUI-5 channel than that in the IEEE 802.16 SUI 1 channel. The proportional fair scheduling takes the great part of frequency diversity and multiuser diversity when the channel variation is not severe, so it also performs well. Furthermore, from the figure, we see that in the IEEE 802.16 SUI-1 channel model, the difference of fairness performance between the maximum C/I and the proportional fair scheduling is insignificant. Even in the IEEE 802.16 SUI-5 channel model, although the fairness of the proportional fair scheduling scheme is still better than the maximum C/I scheduling scheme, the difference of the fairness index between the two scheduling algorithms is less than 3.5%.

Figure 3.9 shows that main advantage of using maximum C/I in a multiuser multi-carrier system. In Fig. 3.9, we compare the throughput performance of both scheduling schemes. In the SUI-1 channel, the throughput performances of the two algorithms are about the same. Interestingly, when consider the SUI-5 channel model with more severe fading, Fig. 3.9 indicates that maximum C/I can take advantage of severer fading and maximize the system throughput. Summarizing from Figs. 3.8 and 3.9, we find that the maximum C/I scheduling can improve the throughput performance by 20% over the proportional fair scheduling at the cost of degrading the fairness index by only 3.5%.

Consequently, the maximum C/I is sufficiently used in the OFDMA system. We do not need other complicated resource allocation algorithms, such as proportional fair scheduling or power allocation method, to achieve good fairness performance at the expense of throughput. By adopting this simple maximum C/I scheduling schemes, we can obtain good fairness performance and the best throughput perfor-mance simultaneously. In SUI-5 channel model, the maximum C/I improves total system throughput about 13% compared to the power allocation without dynamic

subcarrier allocation. Moreover, the maximum C/I scheduling algorithm even in-crease more than 20% of system throughput than that using the proportional fair scheduling policy.

3.6.5

Discussions

In the scenario described above, we should decide to whom all subcarriers belong every transmission time interval (TTI). It is impractical to do this in such a short time. In fact, because IEEE 802.16a is a fixed wireless application, the channel does not change frequently. Hence, we do not need to schedule users every TTI. Considering the coherence time of the system, the maximum Doppler frequency is 20Hz (SUI-5 channel), and then we will calculate the coherence time based on (3.20) [33]. Coherence time is the time duration over which two received signals have a strong potential for amplitude correlation. The Doppler spread and coherence time are inversely proportional to one another. The equation (3.20) is defined as the time over which the time correlation function is above 0.5. For example, when the maximum Doppler shift fd = 2Hz, and the coherence time Tc is about 90 ms. Therefore, the

maximum C/I scheduling approach is practical in the system.

Tc =

9 16πfd

(3.20)

3.7

Conclusions

In this chapter, we have demonstrated that the simple maximum carrier-to-interference scheduling scheme can be a fair scheduler in the OFDMA system, although it is viewed as an unfair scheduling scheme in the single carrier TDMA/CDMA systems. Using this simple maximum C/I scheduling algorithm in the OFDMA system can exploit

multiuser diversity and frequency diversity thoroughly, thereby achieving both high throughput and good fairness performances. Moreover, using this simple maximum C/I scheduling algorithm can combat the worse channel effect and observe the good fairness performance in a multiuser OFDM system.

5 10 15 20 25 30 0 0.1 0.3 0.5 0.6 0.7 0.8 0.9 0.95 0.98 0.9998 # of subchannels Fairness index 8 users 16 users 24 users 32 users

Fig. 3.5: Fairness index with the number of subchannels varying in different numbers of

5 10 15 20 25 30 0.8 0.95 0.96 0.99 0.995 0.996 0.997 0.998 0.999 0.9995 time fairness index

Max C/I in SUI−1 Max C/I in SUI−5 PA in SUI−1 PA in SUI−5

Fig. 3.6: Comparison of fairness performance of dynamic sbucarrier allocation and power

0 5 10 15 20 25 30 35 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 time (TTI)

Normalized System Throughput

Max C/I in SUI−1 Max C/I in SUI−5 PA in SUI−1 PA in SUI−5

Fig. 3.7: Comparison of throughput performance of dynamic sbucarrier allocation and

5 10 15 20 25 30 0.8 0.95 0.96 0.99 0.995 0.996 0.997 0.998 0.999 0.9995 0.9999 time fairness index

Max C/I in SUI−1 Max C/I in SUI−5 Prop fair in SUI−1 Prop fair in SUI−5

Fig. 3.8: Comparison of fairness performance of max C/I and proportional scheduling

0 5 10 15 20 25 30 35 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 time (TTI)

Normalized System Throughput

Multicarrier Max C/I and Proportional Fair Scheduling Algorithms Simulation−−Throughput

Max C/I in SUI−1 Max C/I in SUI−5 Prop fair in SUI−1 Prop fair in SUI−5

Fig. 3.9: Comparison of throughput performance of max C/I and proportional scheduling

Channel-aware Subcarrier Allocation and

QoS Provisioning for OFDMA Systems

with Multi-type Traffic

The orthogonal frequency division multiple access (OFDMA) is becoming an impor-tant technique for the future wireless systems. Through parallel multi-carrier trans-missions, the inter-symbol interference (ISI) can be easily handled in transmitting high speed data. Furthermore, OFDMA systems bring a new dimension for allocat-ing radio resource - subcarrier. By exploitallocat-ing frequency diversity in the wide frequency spectrum, a suitable subcarrier allocation technique can further enhance throughput for the OFDMA system. This chapter addresses the issue of allocating subcarriers for providing both real-time and non-real-time traffic in the OFDMA system. We sug-gest a categorized subcarrier allocation (CSA) technique to improve throughput for non-real-time traffic, while satisfying the quality of service (QoS) requirement for the real-time method. In the proposed CSA technique, subcarriers are categorized into two groups based on their quality: good and fair. The real-time traffic will be assigned by the subcarrier with fair condition, while the non-real-time traffic will be assigned with good subcarriers. We find that such a subcarrier allocation method can apply the maximum carrier-to-interference (C/I) scheduling to maximize the throughput in good conditioned subcarriers, while the delay for the real-time traffic can be con-trolled by allocating enough fair-conditioned subcarrier through a queueing analytical method. Compared to other methods, such as dynamic subcarrier allocation (DSA)