On Improving Multi-Channel Wireless Networks through ... · PDF fileAbstract On Improving Multi-Channel Wireless Networks through Network Coding and Dynamic Resource Allocation Jin

On Improving Multi-Channel Wireless Networks throughNetwork Coding and Dynamic Resource Allocation

by

Jin Jin

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Department of Electrical and ComputerEngineering

University of Toronto

Copyright c© 2011 by Jin Jin

Abstract

On Improving Multi-Channel Wireless Networks through Network Coding and

Dynamic Resource Allocation

Jin Jin

Doctor of Philosophy

Graduate Department of Department of Electrical and Computer Engineering

University of Toronto

2011

Multi-channel wireless networks represent a direction that future state-of-the-art fourth

generation (4G) wireless communication standards evolve towards. The IEEE 802.16

family of standards, or referred to as WiMAX, has emerged as one of the most important

4G networks to provide high speed data communication in metropolitan areas. There will

be huge challenges in designing the networking protocols to allow WiMAX to provide high

quality of services. How to effectively control the errors in the wireless channels and how

to efficiently manage the scarce spectrum and power resources in different communication

scenarios are crucial for network performance. This thesis aims to solve these challenges

to improve the performance of multi-channel wireless networks, using WiMAX as a rep-

resentative, through a number of techniques. First, we take advantage of the favorable

properties of network coding, and design the adaptive MAC-layer and symbol-level net-

work coding protocols. They tightly integrate with WiMAX physical and MAC layers,

effectively perform error control, and efficiently utilize scarce wireless spectrum. Second,

we investigate multicast services and the femto-cell architecture in WiMAX, and offer

a cooperative multicast scheduling protocol as well as a cognitive WiMAX architecture

with femto cells. They implement dynamic resource allocation in the networks through

techniques of cooperative communication and dynamic optimization. Evaluated with

rigorous analysis and extensive simulations, our proposed protocols are able to achieve

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substantial performance improvement over traditional protocols in the literature.

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To my parents

To my fiance, Amber

To praise God for His Love

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Acknowledgments

I started my journey of pursuing Ph.D. degree in 2006, and spent 4 years towards this

achievement, full of joy and pains. Throughout this important and precious period of

time, I received tremendous support from a lot of people, with which I am able to keep

the pace and finish the thesis smoothly.

First, I would like to express my sincere appreciation to my thesis advisor, Professor

Baochun Li, for his strong support and insightful guidance for my thesis. He lead my

research from the scratch and always encouraged me to pursue the excellence. He shared

not only his vision and dedication on research, but also the experience of intellectual

curiosity, life attitude, as well as career development, all of which have benefited me

enormously. I also thank to all the professors helping to review my thesis. They are

Professor Ben Liang, Professor Raviraj Adve, Professor Shahrokh Valaee, and Professor

Prasun Sinha. Their valuable comments and suggestions helped greatly improve the

quality of the thesis.

I owe my thanks to all the group members in iQua, who provided generous help on my

thesis. Moreover, we shared joyful and gloom time in graduate studies, and have become

life-time friends. Many thanks to Xinyu. His dedication on research and the spirit of

pursuing best have greatly encouraged me. Chen, I alway remember the delighted time

when we were roommates. We came to Canada at the same time and shared the exciting

experiences of culture shock. I greatly appreciate Henry, my “truly ally,” for his strong

support on my research with countless discussion. I feel we are alway walking side by side.

Yunfeng, I wish to express my gratitude to your kindly help and encouragement during

the time of our job hunting. Many of you, Zimu, Di, Hassan, Elias, Jiahua, Junqi, Yuan,

Professor Wang, and Mea, gave me inspiration on my thesis. Their positive attitude

and enthusiasm have opened my mind. I also wish to give my thanks to the excellent

engineers from LG Electronics Inc., especially Ronny and Taegon who visited iQua during

my Ph.D. program, when we had pleasant collaboration on research. I learned a lot from

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them on the research methodologies, and we keep long-term collaboration even after they

left Toronto.

I also met many great friends during my Ph.D. endeavor within or outside University

of Toronto who gave me great support, including Lei Duan, Lei Hua, Lei Zhou, Chen

Chen, Haifeng, Dongying, Jiang, Guoli, Raza, Weiwei, Zhengwei, Xiaojun, Fei Wei, Xiang

Cao, Fangming, Hui, and Vivia. I discussed problems, did sports, and hang out together

with them, which made the life colorful and fruitful.

I wish to send my deep love to my fiance and soul mate, Amber, for her love and

support during my journey. Her company, encouragement, understanding and commit-

ment gave me power, joy, direction, and motivation. Most importantly, I wish to express

my greatest appreciation and love to my parents in Beijing. Without their unconditional

love and continuous encouragement, I will never achieve this far. Sincerest thanks to

them from the bottom of my heart. To them this thesis is dedicated to.

Finally and importantly, I thank God for His deep love. Without His guide, I would

be like the lost lamb. I praise the Lord, and glory His name.

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Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Is Random Network Coding Helpful in WiMAX? . . . . . . . . . 5

1.2.2 Cooperative Resource Management in WiMAX . . . . . . . . . . 7

1.3 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Background Overview and Related Work 11

2.1 Introduction to WiMAX . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Network Coding in Wireless Networks . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Introduction to Random Linear Codes . . . . . . . . . . . . . . . 14

2.2.2 Random Network Coding in Wireless Networks . . . . . . . . . . 16

2.2.3 Our Work with the Use of Random Network Coding . . . . . . . 18

2.3 Resource Management in WiMAX services . . . . . . . . . . . . . . . . . 19

2.3.1 Multicast Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 Cognitive WiMAX . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Adaptive Random Network Coding in WiMAX 23

3.1 How Can Network Coding be Used in WiMAX? . . . . . . . . . . . . . . 25

3.1.1 Single-hop Transmission . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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3.1.3 Multi-hop Transmission . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 MRNC with Adaptive Algorithms . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Adaptive Block Size . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2.2 Adaptive Upstream Node . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 Single-hop transmission . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.2 Handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38


3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Drizzle: Cooperative Symbol-Level Network Coding in WiMAX 44

4.1 The Design of Drizzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.2 Adaptive Retransmission . . . . . . . . . . . . . . . . . . . . . . . 48

4.1.3 Cooperative Transmission . . . . . . . . . . . . . . . . . . . . . . 51

4.1.4 Differences from MIXIT . . . . . . . . . . . . . . . . . . . . . . . 57

4.2 Impact of Soft Decision Values . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2.1 Are Soft Values Accurate? . . . . . . . . . . . . . . . . . . . . . . 58

4.2.2 How to Use Soft Values for Error Detection? . . . . . . . . . . . . 60

4.2.3 How Do Soft Values Work in Cooperative Transmission? . . . . . 64

4.3 Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.1 Choosing the Size for Coded Blocks . . . . . . . . . . . . . . . . . 66

4.3.2 Reducing the Overhead of Carrying Coefficients . . . . . . . . . . 67

4.3.3 Computational Complexity and Protocol Overhead . . . . . . . . 69


4.4.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.4.2 Single-link Transmission . . . . . . . . . . . . . . . . . . . . . . . 71

4.4.3 Handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5 Cooperative Multicast Scheduling with Network Coding in WiMAX 80

5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.2 Multicast Scheduling Framework . . . . . . . . . . . . . . . . . . . . . . 84

5.2.1 Optimizing Multicast Scheduling . . . . . . . . . . . . . . . . . . 85

5.2.2 Protocol Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.3 Are Cooperative Communication and Random Network Coding

Helpful? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3 Cooperative Multicast Scheduling with Channel Allocation . . . . . . . . 90

5.3.1 Optimizing Performance with Limited Bandwidth . . . . . . . . . 91

5.3.2 Channel Allocation with Channel Reuse . . . . . . . . . . . . . . 94

5.3.3 How efficient are the channels allocated? . . . . . . . . . . . . . . 99

5.4 Cooperative Multicast Scheduling with Power Allocation . . . . . . . . . 100

5.4.1 Maximizing Throughput with Limited Power . . . . . . . . . . . . 100

5.4.2 What’s the Impact of Power? . . . . . . . . . . . . . . . . . . . . 102

5.5 Overhead Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Resource Management in Cognitive WiMAX with Femto Cells 106

6.1 Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2 System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2.1 Framework Formulation . . . . . . . . . . . . . . . . . . . . . . . 110

6.2.2 Models of Resource Management . . . . . . . . . . . . . . . . . . 111

6.2.3 Impact of Resource Management and Problem Hardness . . . . . 115

6.3 Resource Management With Stochastic Lyapunov Optimization . . . . . 116

6.3.1 Stochastic Network Model . . . . . . . . . . . . . . . . . . . . . . 117

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6.3.2 Resource Management Policies . . . . . . . . . . . . . . . . . . . . 118

6.3.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.4 Optimization Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.4.1 Generalized EM Algorithm . . . . . . . . . . . . . . . . . . . . . . 125

6.4.2 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 127


6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7 Concluding Remarks 132

Bibliography 134

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List of Tables

3.1 Adaptive Block Size Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Adaptive Upstream Node Algorithm. . . . . . . . . . . . . . . . . . . . . 37

4.1 Simulation parameters for evaluating Drizzle. . . . . . . . . . . . . . . . 72

6.1 Evaluation of Generalized EM algorithm. . . . . . . . . . . . . . . . . . . 127

6.2 Simulation parameters for evaluating cognitive WiMAX. . . . . . . . . . 128

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List of Figures

2.1 WiMAX works in a point-to-multipoint topology. . . . . . . . . . . . . . 12

3.1 The advantage of random network coding in a WiMAX two-way handover

procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 A two-hop transmission scenario in WiMAX. . . . . . . . . . . . . . . . . 30

3.3 The advantage of random network coding in WiMAX multi-hop transmis-

sion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 The scenario being used for simulating a WiMAX handover event. . . . . 38

3.5 MRNC vs. HARQ: throughput in a realistic handover case. . . . . . . . . 39

3.6 MRNC vs. HARQ in a large-scale handover scenario: (a) CDF of through-

put. (b) CDF of variance. . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7 Practical setting of the multi-hop scenario. . . . . . . . . . . . . . . . . . 41

3.8 MRNC vs. HARQ: throughput in a realistic multi-hop scenario. . . . . . 41

3.9 MRNC vs. HARQ in a large-scale multi-hop scenario. (a) CDF of through-

put. (b) CDF of variance. . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 A simplified block diagram showing the design of Drizzle. . . . . . . . . . 46

4.2 16-QAM (24-QAM) constellation with Gray coding and an example of

detected symbol, 1001. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3 In Drizzle, only “dirty” blocks are retransmitted to the receiver over a

single wireless link with errors. . . . . . . . . . . . . . . . . . . . . . . . . 49

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4.4 The average number of bits retransmitted in a single-link transmission,

when Drizzle is compared with HARQ and SOFT (Woo et al. [74]). Simu-

lations are performed with the environment and settings provided in Sec. 4.4. 51

4.5 Cooperative transmission of coded blocks is possible when the opportunity

of multi-path transmission arises in both handover and multi-hop modes

of WiMAX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.6 Simulating a WiMAX handover event when an MS moves across the han-

dover region with a constant speed. . . . . . . . . . . . . . . . . . . . . . 56

4.7 The throughput performance of Drizzle over time (80 seconds) in the han-

dover scenario, as a mobile station is moving around in the handover region

randomly. Simulations are performed with the settings provided in Sec. 4.4. 56

4.8 The distribution of soft decision values under BPSK modulation, which is

obtained by transmitting 200,000 bits over Rayleigh fading channel with

a speed of 30km/h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.9 The selection of SV-thresholds affects the performance of Drizzle. The per-

formance of Drizzle under 4 different SV-thresholds, 77.5%, 52.5%, 27.5%,

and 2.5%, is evaluated to show the importance of SV-threshold selection.

Values in dB are the gains that the best case outperforms the worst case

in the simulation. Simulations are performed with the settings provided

in Sec. 4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.10 The level-threshold affects the delay and throughput performance in Driz-

zle. A higher level-threshold is helpful to achieve higher throughput, but

with a larger delay. On the contrary, a lower level-threshold leads to lower

throughput, but with smaller delays. Simulations are performed with the

settings provided in Sec. 4.4. . . . . . . . . . . . . . . . . . . . . . . . . . 63

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4.11 A comparison of Drizzle’s performance with and without SV normaliza-

tion and adaptation in a cooperative transmission scenario. Two nodes are

sending coded blocks to one receiver using different modulation schemes

(QPSK and 16QAM are used on each sender respectively). The transmis-

sion is under different channel qualities (SNRs), which are generated by

varying the target BERs in a certain range. Simulations are performed

with the settings provided in Sec. 4.4. . . . . . . . . . . . . . . . . . . . . 65

4.12 The selection of block sizes impacts the performance of Drizzle. (a) The

performance of block error rates under 3 different block sizes: 4 bits, 8 bits

and 16 bits. (b) The performance of packet delivery rates (K = 2n) under

a Rayleigh fading channel. Simulations are performed with the settings

provided in Sec. 4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.13 Packet Delivery Rate and Throughput with a range of BERs. . . . . . . . 73

4.14 Throughput in a single, time-varying wireless link with mobility. . . . . . 74

4.15 Throughput comparison in the WiMAX handover scenario. . . . . . . . . 75

4.16 Throughput performance in a large-scale handover scenario. . . . . . . . 76

4.17 Throughput in a realistic multi-hop case. . . . . . . . . . . . . . . . . . . 77

4.18 Throughput performance in a large-scale multi-hop scenario. . . . . . . . 78

5.1 Illustrative examples to show the advantages of cooperative multicast

scheduling with random network coding in WiMAX. The number on each

link in (b) indicates the packet delivery rate from the BS to the MS. . . . 83

5.2 Throughput performance of four multicast scheduling protocols in a realis-

tic WiMAX MBS scenario. Cooperative multicast scheduling with random

network coding is able to achieve substantial throughput improvement by

effectively utilizing the scarce wireless bandwidth. . . . . . . . . . . . . . 90

5.3 Solving the channel allocation problem using maximum weighted bipartite

matching algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

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5.4 The performance of cooperative multicast scheduling with random net-

work coding when the number of cooperative sub-channels is limited. The

protocols with and without channel reuse algorithm are both evaluated. . 100

5.5 The performance of multicast scheduling with our power allocation algo-

rithm in a power-constrained MBS. . . . . . . . . . . . . . . . . . . . . . 103

6.1 An illustrative example of cognitive WiMAX with femto cells. . . . . . . 108

6.2 Average throughput performance of all protocols. . . . . . . . . . . . . . 129

6.3 CDF of throughput variance, which indicates fairness performance. . . . 129

6.4 Performance on the channel utilization improvement. . . . . . . . . . . . 130

6.5 Performance on the buffer backlog. . . . . . . . . . . . . . . . . . . . . . 130

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Chapter 1

Introduction

1.1 Background

The Internet has revolutionized the computer and communication world. The research

on packet switching and ARPANET [1] opened the Internet history during 1960s. Since

then, the Internet has experienced dramatic growth. With the proliferation of computer

devices and fast development of Internet applications, such as electronic mail (Email),

World Wide web (WWW), and digital audio/video, the demand on Internet speed grows

rapidly.

Nowadays, most traditional communication media, such as telephone and television

services, are reshaped or redefined using the technologies over Internet, giving rise to

the services such as Voice over Internet Protocol (VoIP) and Internet Protocol television

(IPTV). High speed Internet access is in high demand to support these applications.

Digital Subscriber Line (DSL) is a good solution by providing high speed digital data

transmission normally over a telephone line. Most of the Internet Service Providers (ISPs)

in North America provide DSL services with data throughput ranging from 384 KB/s

to 20 MB/s, depending on the line conditions and service level implementation. Similar

Internet access services can also be provided through television cables. However, such

1

Chapter 1. Introduction 2

technologies rely on the deployment of wired network infrastructure, which significantly

increases the deployment cost. In rural areas and developing countries, this is a huge

barrier to the availability of high speed Internet.

Intuitively, wireless Internet access is a solution by providing data transmission to a

mobile. WiFi, based on the IEEE 802.11 family of standards [7], was invented to provide

high speed wireless Internet access. A Wi-Fi enabled device can connect to the Internet

through an access point (AP) which normally connects to the Internet backhaul using a

wired line. In the last hop, WiFi uses shared wireless spectrum, and the speed can reach

up to 50 MB/s within the range of 100 meters in the latest standard [7]. Although this

rate is quite satisfactory, it can not fully meet the growing requirements. First, WiFi

transmission range is quite limited. The access point is normally deployed at offices, or

particular commercial areas, such as airports and cafeterias. Therefore, it is difficult to

provide ubiquitous connectivities and is not able to fully support mobility. Second, WiFi

still requires the deployment of wired backhaul networks to provide connections to the

access points. Essentially, it does not solve the problems in DSL.

How to provide high speed wireless Internet connection in a large area with full support

of mobility? The intuition is to provide Internet services via cellular networks, referred

to as mobile Internet. Mobile Internet had its beginnings around 1998 with the intro-

duction of WAP [3], then grew rapidly. Early in 2000, the wireless world caught fire with

the launch of the Internet on a mobile phone, as the traditional second generation (2G)

Global System for Mobile Communications (GSM) networks evolved to General packet

radio service (GPRS) and Enhanced Data rates for GSM Evolution (EDGE) [2]. They

are implemented in packet switch domain built on top of cellular telecom networks with

the peak data rate up to a few hundreds kilobytes per second. Starting in 2006, the

communication industry is officially in the evolution to the third generation (3G) wire-

less network technology. There are several competing 3G technologies across the world,

including CDMA2000 1xEV-DO [11], TD-SCDMA [5], HSPA [6], etc. These systems can


provide a minimum data rate of 2 MB/s for stationary or walking users, and 384 KB/s

in a moving vehicle. With such access rate, a large number of attractive applications

are developed, such as iPhone Apps, and a large amount of profit is generated in the

industry.

Is this good enough? Currently, the 3G networks still suffer from the low connection

rate with much smaller throughput compared with WiFi networks. The last hop data

rate of current mobile networks is becoming the bottleneck of the applications, such as

VoIP and IPTV on mobile devices which require data rates in megabytes per second.

The next generation (4G) wireless communication technology is proposed to replace

3G technology to provide ultra-broadband mobile Internet access. WiMAX, based on

the IEEE 802.16 family of standards [9], is one of the most important and promising

technologies for future 4G networks, aiming to provide high-rate data transmission in

the metropolitan areas by serving a large number of users. WiMAX heralds the entry of

broadband wireless access as a major new tool in the effort to link homes and businesses

to core telecommunication networks worldwide [15]. Such broadband wireless networks

represent the direction that future state-of-the-art wireless communication standards

evolve.

WiMAX essentially works in a point-to-multipoint fashion, with one base station serv-

ing a number of mobile stations in a certain area. As opposed to previous generations of

wireless Internet technologies, communication between the base station and the mobile

stations is based on the principle of orthogonal frequency division multiplexing/multiple

access (OFDM/OFDMA) [27], a digital multi-carrier modulation scheme using a large

number of closely-spaced orthogonal subcarriers. Multiple access is achieved in OFDMA

by assigning subsets of subcarriers to individual users [15]. This allows simultaneous

low data rate transmissions from several users without generating interference and col-

lision. In the meantime, it also brings lots of other benefits, such as pulsed carrier can

be avoided, shorter delay, and contention based multiple access (collision avoidance) is


simplified. Most 4G wireless communication networks adopt OFDMA which essentially

can be considered as multi-channel wireless networks. With these technologies, WiMAX

has great potentials to provide higher quality of services.

This thesis focuses on the study of multi-channel wireless communication networks,

using WiMAX as a representative. We believe the research findings on WiMAX will hold

when applied to other next generation multi-channel broadband wireless networks based

on OFDM/OFDMA, such as 3GPP Long Term Evolution (LTE) [10].

1.2 Contributions

WiMAX is a step towards achieving ultra-broadband mobile Internet in metropolitan

areas. Some desired features in the future WiMAX deployment are: high data rate

(100 MB/s mobile and 1 GB/s fixed), wide range (maximum serving range of 50 km for

each base station), resilience, and robustness [9]. There will be a number of challenges in

WiMAX designs in order to provide such performance. How to fully utilize wireless band-

width and effectively allocate the resources will be very crucial. In this thesis, we focus on

designing new algorithms and protocols to improve the performance of WiMAX systems.

In order to achieve this objective, we adopt network coding, cooperative communica-

tion, and dynamic optimization techniques to perform effective error control, resource

allocation, and communication scheduling. The highlights of the contributions in the

thesis are two folds: first on the research of the fundamental communication scenarios

and protocols by applying network coding techniques; then on the investigation of the

most important services and architectures in WiMAX. The development of these studies

constitutes the flow of the presentation in the following chapters in the thesis, reaching

a complete study on improving the performance of multi-channel wireless networks. The

research findings are summarized as follows:


1.2.1 Is Random Network Coding Helpful in WiMAX?

It is common knowledge that errors are inherently present in unreliable wireless channels.

With fixed bandwidth resource, the important challenge to maximize achievable through-

put in WiMAX is to control errors and efficiently utilize the scarce wireless spectrum in

various transmission scenarios, even when unpredictable and time-varying errors exist.

In WiMAX, Hybrid Automatic Retransmission reQuest (HARQ) has been used to pro-

vide reliable data transmission [24]. However, the built-in reliability in HARQ sacrifices

some degree of resilience and efficiency in realistic channels with varying qualities over

time. In addition, in handover and multi-hop transmission modes in WiMAX, a mobile

station is able to establish connections with two or more uplink nodes through different

sub-channels. In these cases, HARQ may not be able to fully utilize the wireless medium,

as it is designed for a point-to-point channel.

With respect to the objective of maximizing throughput and error control, network

coding has been originally proposed in information theory [12], and has since emerged

as one of the most promising information theoretical approaches to improve network

performance. It has been shown that random linear codes using a Galois field of a

limited size are sufficient to implement network coding in a practical network setting

[34]. Network coding has been successfully applied in multi-hop wireless networks to

opportunistically take advantage of multiple routes from the sender to the receiver in

unicast flows [18, 45], and soft decision values from the physical layer are utilized to

perform partial packet recovery when packets are broadcast in a shared IEEE 802.11-

based wireless channel [44]. While the benefits of network coding in 802.11-based wireless

networks are encouraging, would network coding still be helpful in WiMAX?

Unfortunately, in IEEE 802.16 WiMAX — with OFDMA at the physical layer — the

convenience of a shared wireless broadcast channel to perform opportunistic listening no

longer exists. How do we design an efficient error control protocol which tightly integrates

with WiMAX in order to fully utilize the spectrum? In this thesis, we seek to answer


these questions by proposing two protocols in WiMAX: MRNC — an adaptive MAC

layer random network coding protocol [39,42], and Drizzle — a cooperative symbol-level

network coding protocol [46].

In the study of MRNC [39,42], we investigate the benefits of random network coding

in three typical WiMAX communication scenarios: single-hop transmission, handover,

and multi-hop transmission. We observe that random network coding, with the favorable

rateless properties, fits WiMAX naturally and is able to improve the system performance

significantly. Thereafter, according to this observation, we have detailed designs on

MRNC with a random network coding algorithm as the cornerstone to optimize the per-

formance. We further tune the protocol with adaptive algorithms in order to achieve

maximum benefits. First, the network coding block size can change adaptively by tun-

ing the tradeoff between block error rate and protocol overhead. The dynamic manner

in which the block sizes are changed to match the channel conditions helps to improve

throughput over unreliable and fluctuating wireless channel conditions. Second, in han-

dover and multi-hop transmission scenarios, we design an “early brake” algorithm in order

to prematurely stop the transmissions of a subset of upstream nodes who serve the single

downstream node. By adapting the number of upstream nodes, we could reduce the over-

head, and therefore fully utilize scarce wireless bandwidth. With these well-developed

designs, we show that the performance of WiMAX can be improved enormously with

MRNC in terms of the throughput and resilience.

Although MRNC is able to provide satisfactory performance, it still suffers from low

throughput under poor channel conditions due to transient errors. In order to have

further improvement, in the next step, we extend the vision by exploring the use of

network coding in the symbol level in WiMAX and exploit the benefits of cooperative

diversity [46]. Drizzle divides each single packet into a number of physical symbols and

performs network coding across the symbols within one packet. With the rateless and

resilience properties of random network coding, Drizzle allows the sender to retransmit


a barely sufficient number of symbols that have not been successfully received at the

receiver, and the receiver is able to hold a “bucket” until it is full of correct symbols.

We take advantage of soft decision values at the physical layer to perform effective error

check. Even better, the receiver can receive these symbols from multiple senders, with

their perfect collaboration across, as multi-channel wireless networks create opportunities

of multi-path transmissions. As the size of these symbols is sufficiently small, there would

be minimal waste of wireless bandwidth provided by the physical layer. The error control

can be achieved in a finer granularity. Furthermore, with multiple senders serving a single

user via multiple channels, cooperative diversity can be exploited. The design of Drizzle

incorporates all the benefits above.

With the extensive simulation evaluation, there is no surprise in our intuition: Drizzle

is able to outperform HARQ and related work in the literature by a substantial margin.

We note MRNC and Drizzle can be readily employed in WiMAX system, and we are

able to enable MRNC and Drizzle according to the channel and networking conditions.

This study may lead to the future deployment of random network coding at the MAC

and physical layers of real WiMAX systems.

1.2.2 Cooperative Resource Management in WiMAX

In the second half of this thesis, we study important services and architectures in WiMAX

in order to facilitate WiMAX to provide high quality of services in various working

scenarios. In order to achieve this goal, we utilize dynamic optimization as well as

network coding to perform cooperative resource allocation effectively.

First, we focus on Multicast and Broadcast Service (MBS) system, which has emerged

as the most important wireless infrastructure to broadcast data or digital video in

WiMAX. With the current mandate of MBS, the Base Station (BS) broadcasts or mul-

ticasts data in the downlink using robust modulation and coding schemes to provide

reliable transmissions for all the users, as individual feedback (such as ARQ and HARQ)


is not supported in MBS. Such a dependence on using the most robust modulation and

coding schemes to counter the most adverse channel quality among all users leads to the

under-utilization of scarce wireless bandwidth: users with good channel conditions would

not enjoy flow rates that are commensurate with their conditions, as the “least common

denominator” is used to cater to users with poor channel conditions.

In this thesis, we offer a solution of cooperative multicast scheduling by considering

the use of multiple OFDMA channels, multiple hops, and multiple paths simultaneously

[40]. Participating users in the multicast sessions are dynamically enabled as relays and

concurrently communicate with others to supply more data. During the transmission,

random network coding is adopted, which helps to significantly reduce the overhead. We

design practical scheduling protocols by jointly studying the problems of channel and

power allocation on relays. Protocols that are theoretically and practically feasible are

provided to optimize multicast rates and to efficiently allocate resources in the network.

With simulation studies, we evaluate the proposed protocols to highlight the effectiveness

of cooperative communication and random network coding in multicast scheduling with

respect to improving performance.

Second, we investigate the WiMAX architecture with femto cells and study resource

management accordingly. In WiMAX, femto cells are an important cost-effective means

of providing ubiquitous connectivity and critical for WiMAX performance. Users that

reside in femto cells experience increased throughput due to the shorter ranges. However,

traditional WiMAX architectures lack dynamic utilization of spectrum and have inherent

weakness in overlooking the special network characteristics and hence missing the bulk

of channel reuse opportunities. These problems cause the underutilization of the scarce

wireless spectrum. Therefore, there is a compelling need to re-design the resource man-

agement scheme in WiMAX with femto cells in order to achieve satisfactory performance

in WiMAX.

Cognitive radio (CR) [23] has emerged as an important technology to exploit high-


degree spectrum reuse, by allowing spectrum sensing and dynamical spectrum access.

Such a technique brings much flexibility and potentially generates benefits if employed

in WiMAX femto cell networks, especially with the proliferation of powerful cognitive

wireless devices as well as the surge of demand on service varieties and qualities in

WiMAX.

In this last part of the thesis, we propose a cognitive WiMAX architecture with femto

cells [41], where the base station and users are equipped with CRs and intelligently ad-

justs power, channel, and other resources to accommodate the entire network ecosystem.

In this new design, we develop an optimization framework for dynamic resource manage-

ment, by jointly employing multi-hop cooperative communication, power control, channel

assignment, primary user protection, buffer management, and fairness, and incorporating

user, channel, and cooperative diversities. To achieve optimality, it is designed based on

stochastic Lyapunov optimization, aiming to take advantage of the radio flexibility and

fully utilize the spectrum. Evaluated by the rigorous analysis and extensive simulations,

the proposed resource management protocol is near-optimal with closed-form bounds,

with which cognitive WiMAX achieves substantial performance improvement.

1.3 Thesis Structure

The reminder of the thesis is structured as follows. In Chapter 2, we present related

work. In Chapter 3, we examine the benefits of network coding in WiMAX and present

the design of MRNC, the adaptive MAC-layer random network coding protocol. In Chap-

ter 4, we further exploit the use of network coding, and describe Drizzle, the cooperative

symbol-level network coding protocol, to further improve the performance of WiMAX.

In Chapter 5, we study the broadcast multicast services in WiMAX, and design practical

scheduling protocols with both theoretical analysis and practical evaluation. In Chap-

ter 6, we introduce the cognitive WiMAX architecture with femto cells and develop an


optimization framework to efficiently manage the resources. Finally, we summarize the

thesis and discuss future directions in Chapter 7.

Chapter 2

Background Overview and Related

Work

In this chapter, we introduce the techniques adopted in multi-channel wireless networks

with WiMAX as the representative. We further review the related work on network

coding in wireless networks and resource management techniques in WiMAX. These

techniques serve as the cornerstones in the studies within this thesis. In the meantime,

we describe our study in brief in the context of literature.

2.1 Introduction to WiMAX

WiMAX, based on the IEEE 802.16 family of standards, aims to provide high-rate wireless

communication over wide areas to a large number of users. It not only provides the

traditional cellular network services, but also supports IP-based data communication.

WiMAX works in a point-to-multipoint fashion, where one base station (BS) serves a

number of mobile stations (MS) in a certain area. The topology is shown in Fig. 2.1.

The IEEE 802.16 standard [9] defines the air interface (physical layer) and medium

access control (MAC layer) protocols for a wireless metropolitan area network, intending

to provide high-bandwidth wireless voice and data for residential and enterprise use. In

11

Chapter 2. Background Overview and Related Work 12

Internet

Backhaul Connection

BS

MS

Femto-cell user station MS

MS

Figure 2.1: WiMAX works in a point-to-multipoint topology.

the physical layer, WiMAX is designed to work in the 2-11 GHz range. The asymmet-

rical link structure in WiMAX will enable the subscriber stations to have a handheld

form factor for PDAs, phones, or laptops. The WiMAX physical layer is based on the

OFDM/OFDMA, which is a suitable modulation/access technique for non-line-of-sight

conditions with high data rates. In practice, OFDM signals are generated and detected

using the Fast Fourier Transform (FFT). Multiple access is achieved in OFDMA by as-

signing subsets of subcarriers to individual users [15]. This allows simultaneous low data

rate transmission from several users without interference and collision.

Another important technique in the WiMAX physical layer is Adaptive Modulation

and Coding (AMC) [26]. It is the matching of the modulation, coding and other signal and

protocol parameters to the conditions on the wireless links. Intuitively, the systems turn


to use robust modulation and coding schemes when the channel quality is low. On the

other hand, aggressive modulation and coding schemes will be applied when the channel

is in relatively good condition. WiMAX defines seven combinations of modulation and

coding rates that can be used to achieve various trade-offs of data rates and robustness,

depending on channel and interference conditions.

The MAC layer of WiMAX is responsible for supporting Point-to-Multipoint (PMP)

broadband wireless access applications in the scheduling. It is designed to meet the

requirements of very-high-data rate applications with a variety of quality of service (QoS)

requirements. The signaling and bandwidth allocation algorithms in MAC layer have

been designed to accommodate hundreds of terminals per channel. MAC layer protocol

uses a scheduling service to deliver and handle different QoS requirements with different

bandwidth and latency, and thus is flexible and efficient over a vast range of different

data traffic models [15].

Currently, there are two main versions of the standards regarding WiMAX (IEEE

802.16). The early standard is 802.16-2004, which is also known as 802.16d. It refers

to the working party that has developed that standard. It is sometimes referred to as

“Fixed WiMAX,” since it has no support for mobility. The later version is 802.16e-2005,

often abbreviated to 802.16e. It is an amendment to 802.16-2004. It introduced support

for mobility and is therefore also known as “Mobile WiMAX.” Our work mainly focus

on IEEE 802.16e and later standards, which full consideration of the scenarios of user

mobility, handover, and multi-hop.

2.2 Network Coding in Wireless Networks

Ahlswede et al. originally introduced Network coding in [12], and attracted much atten-

tion in both academia and industry [47]. Network coding has become an important and

popular technique in order to improve network performance. The intuition underlying


network coding is usually illustrated using the famous butterfly example [12]. The basic

idea inside is that network coding, allowing the routers to mix the bits in forwarded

messages, can increase network throughput. Specifically, [12] showed that having the

routers mix information in different messages allows the communication to achieve mul-

ticast capacity. In recent studies on network coding that are rapidly expanding, it is

well known that random linear codes using a Galois field of a limited size are sufficient

to implement network coding in a practical network setting [34,71]. It has recently been

shown that random network coding is able to significantly improve end-to-end unicast

throughput in multi-hop wireless networks, when implemented above the MAC layer of

IEEE 802.11 [18,45].

2.2.1 Introduction to Random Linear Codes

In random linear codes [22], a data segment (also referred to as a generation or a group

in the literature) is divided into n blocks, denoted as [b1, b2, · · · , bn], each of which has a

fixed number of bytes, referred to as the block size. If the segment size is pre-determined,

the block size k can be directly computed from n. When a segment p is to be transmitted,

the sender randomly chooses a set of coding coefficients [c1, c2, · · · , cn] in the Galois field

(normally in GF(28)), and then produces one coded block x of k bytes: x =∑n

i=1 cibi.

Thus, each coded block is a linear combination of all or a subset of the original

data blocks. The n coding coefficients used to encode original blocks to x are typically

embedded in the header of the coded block [22]. If GF(28) is used, the size of each

coefficient is one byte, thus leading to a total overhead of n bytes per coded block. If the

encoder has the entire original segment when producing coded blocks, we just need to

embed the random seed used to produce the series of coefficients with a known pseudo-

random number generator. This effectively reduces the overhead to just 4 bytes for the

random seed, regardless of the number and the size of the coded block.

Such an encoding process for a coded block essentially constructs a linear equation


where the unknown variables are the source blocks, given the coding coefficients ci and

the coded block xi are known. The decoding process of random linear codes on m coded

blocks solves the m linear equations constructed by the encoding process. Clearly, m

should be larger than or equal to n in order to obtain all n source blocks. Decoding fails

if there is linear dependence among the n coded blocks used in decoding.

We also could perform a progressive decoding process using Gauss-Jordan elimina-

tion [65]. Progressive decoding has the favorable property that decoding occurs as coded

blocks are being received, which implies that the decoding time overlaps with the time

required to receive the blocks, and is hidden from the tally of overhead caused by the de-

coding complexity. Gauss-Jordan elimination is also able to immediately discard linearly

dependent blocks that are not useful for decoding, as linearly dependent blocks will lead

to a row of all zeros. Immediately after n independent coded blocks have been received

for a segment, the receiver is able to recover the entire original segment, and sends the

ACK packet back to the sender. With random network coding, the sender could virtually

produce infinite number of coded blocks, which can be referred as a “rateless” property,

which brings resilience.

Independently, there are a number of studies on rateless codes, with LT codes [53] as

a representative, to address the constraints of traditional erasure codes [55,56]. Although

the rateless properties of random network coding are utilized in the related work, it is

different from traditional rateless codes. Network coding mainly conducts recoding in

the intermediate nodes while rateless codes can not used for recoding. By relaxing the

field of operation to a larger finite field, as opposed to LT codes (where a binary field is

used for exclusive-or operations), random linear codes can generate fresh coded packets

even with a subset of data without any constraints on special degree distributions. Thus,

network coding is largely applied to complicated network scenarios, and rateless codes

are mainly used in one-hop communication, such as satellite communication. Further,

rateless codes generate more overhead compared with random linear codes.


2.2.2 Random Network Coding in Wireless Networks

The work of Li et al. [50] has shown that random linear codes are sufficient to achieve

the maximum capacity bounds for multicast traffic. Subsequently, the study of random

network coding in wireless networks has been explored in some pioneering papers [25,60].

Most of the literature exploited the benefits by applying random network coding in mul-

ticast traffic of wireless networks, and it has been shown that random network coding

could improve the throughput and minimize the communication cost in the multicast

scenarios. The benefits are mainly due to the broadcast property of the wireless chan-

nel, meaning that a transmission from a node can potentially be intercepted by all its

neighbors. Further, a few papers studied specific unicast topologies showing that random

network coding results in better throughput than pure forwarding [33,51]. These studies

of wireless network coding are mainly based on theoretical analysis.

Aiming to bridge the gap between the theory and practical network design, Katti et

al. proposed COPE [45], a forwarding architecture for wireless mesh networks by insert-

ing random network coding in a practical fashion. In addition to forwarding packets,

routers mix packets from different sources to increase the information content of each

transmission. COPE incorporates three main designs: opportunistic listening; oppor-

tunistic coding; learning neighbor state. Facilitated by these designs, COPE is able to

improve the network performance significantly.

Later on, the research interests shifted to applying network coding to opportunistic

routing in wireless networks. Opportunistic routing is a technique that achieves high

throughput in the face of lossy wireless links, and it allows any node that overhears

the transmission and the nodes which are closer to the destination to forward the re-

ceived data. The major challenge is that multiple nodes may hear a packet broadcast

and unnecessarily forward the same packet. Traditional opportunistic routing protocols,

such as ExOR [16], impose a strict schedule on routers’ access to the medium. Such

a highly structured approach does not allow spatial reuse of bandwidth. Chachulski et


al. addressed this problem by applying network coding. They proposed MORE [18], a

MAC-independent opportunistic routing protocol using random network coding running

directly on top of 802.11 without a special scheduler. The routers in MORE randomly

mix the received packets by random network coding, and then forwarded them to the

next hop. This randomness ensures that routers that hear the same transmissions do not

forward the same packets. It is the first implementation of wireless intra-flow random

network coding, demonstrating the practical benefits of mixing packets in a single flow.

With this design, random network coding is widely applied not only to traditional IEEE

802.11, but also to multi-channel wireless networks with some preliminary studies [42,75].

The network coding is mainly applied in MAC layer in these work.

Opportunistic routing capitalizes on sporadic receptions over long links. But long

links are inherently less reliable due to errors and interference, which cause the drop of

most packets in the transmission. Instead of working in the upper layers, it is envisioned

that network coding could reduce interference in wireless networks when applied in the

physical layer. Physical-layer network coding was originally proposed in [77] by Zhang et

al. In contrast to traditional network coding which performs coding on digital bit streams,

physical-layer network coding makes use of the additive nature of simultaneously arriving

electromagnetic waves for an equivalent coding operation. With physical-layer network

coding, signal scrambling due to interference which causes packet collisions in the MAC

layer protocol can be eliminated.

However, the algorithm in [77] assumes symbol-level synchronization, carrier-frequency

synchronization, and carrier-phase synchronization. In practice, it is unlikely that two

signals arrive at the exact same time at the router and incur the same distortion over

the wireless medium. In [43], Katti et al. proposes analog network coding without the

requirement of synchronization. It provides an elegant solution for physical-layer network

coding. Further, Katti et al. continue the study on physical-layer network coding, and

propose MIXIT [44], a protocol for cooperative packet recovery by performing oppor-


tunistic routing on groups of correctly received symbols in a packet. It takes advantage

of the broadcast nature of 802.11-based wireless networks and performs random network

coding across correct symbols in different packets.

As random network coding has shown its salient advantages in both physical layer

and upper layers in wireless networks, cross-layer architectures are promising to further

improve the system performance. Woo et al. proposed SOFT [74], a cross-layer design

for recovering faulty packets in WLAN. SOFT works by combining confidence values

across multiple faulty receptions to recover a clean packet using random network coding.

It is shown that SOFT is able to significantly improve the data delivery rate in 802.11-

based networks, in static wireless environments. However, the realistic channel conditions

should be time-varying and bursty. The performance of SOFT under such conditions is

unclear.

2.2.3 Our Work with the Use of Random Network Coding

There is great potential to gain benefits when applying network coding to WiMAX with

multi-channel communication. In this thesis, we seek to investigate the use of random

network coding in WiMAX. In the previous work, the network coding is basically de-

ployed in IEEE 802.11-based networks to take advantage of multiple routes and wireless

broadcast properties. Unfortunately, in multi-channel wireless networks — such as IEEE

802.16 WiMAX with OFDMA at the physical layer — the convenience of a shared wire-

less broadcast channel to perform opportunistic listening no longer exists, and Hybrid

Automatic Repeat reQuest (HARQ) is the predominant error control protocol at the

physical layer [24], rather than plain Automatic Repeat reQuest (ARQ) in IEEE 802.11

MAC. In WiMAX, with OFDMA adopted, there are abundant opportunities for concur-

rent and multi-path transmissions, such as in handover and multi-hop scenarios. The

current protocols do not fit in these scenarios and can not fully utilize the wireless spec-

trum. It is challenging to design efficient protocols to exploit the benefits of network


coding in WiMAX.

Different from previous works, in our study, we seek to solve the challenges and spe-

cially design random network coding protocols to tightly integrate with the WiMAX

architecture, by considering its communication characteristics. Specifically, we propose

and design both MAC-layer network coding and symbol-level network coding, named

MRNC and Drizzle respectively. Not only take advantage of the favorable properties

of network coding, they also enable cooperative communication to cater the multi-path

multi-channel transmission opportunities in WiMAX. They fully utilize the scarce wire-

less spectrum and are designed to adapt in realistic channel conditions with time-varying

and bursty errors. With the realistic evaluation and rigorous analysis, we show that our

proposed protocols has indeed offered important performance improvement compared

with previous work in different typical cases within the context of WiMAX.

2.3 Resource Management in WiMAX services

As stated in Chapter 1, we seek to improve WiMAX performance on its key services and

applications. In this thesis, we achieve the performance improvement through the design

of dynamic resource management in WiMAX services. Our studies mainly include the

following two parts.

2.3.1 Multicast Scheduling

IEEE 802.16 WiMAX [9] has employed the Multicast and Broadcast Service (MBS)

system/infrastructure to perform multicasting/broadcasting data or digital video. To

achieve reliability in multicast service, traditional systems in the literature enable the

Base Station (BS) broadcasts or multicasts data in the downlink using robust modulation

and coding schemes without supporting individual feedback (such as ARQ and HARQ).

The CDMA2000 1xEV-DO networks [11] adopt this multicast scheduling scheme. Ap-


parently, such a scheme under-utilizes wireless resources as the peers with higher channel

qualities do not enjoy the flow rates that commensurate with their conditions.

As a potential remedial solution, in [32], multicast members are divided into two

groups with different levels of channel qualities. The sender transmits the same copy

of each packet to two groups in two different time slots using different rates which best

fit the channel quality in each group. It has been shown to improve the throughput

performance. However, it is too conservative, especially when the number of users in

poor channel conditions is very small. The sender still has to consume more time for

multicasting the data to them. In [48], Kozat has investigated the optimal multicast rate

by focusing each transmission onto a proper subset of multicast users, rather than trying

to serve all the users at each channel use. It still works on the single-hop shared-channel

scenario, and does not exploit the cooperative diversity in the broadcasting channels.

In [38], Hou et al. attempted to utilize relays to help the users with poor channel

conditions, and the protocol is based on a two-phrase scheduling. It still suffers the same

problems in [32] and does not exploit channel and cooperative diversity in multicast

channels.

In this thesis, we study the multicast scheduling problem in WiMAX from a new

perspective of considering multiple hops, multiple paths, and multiple channels at the

same time, rather than the system models with a single shared channel. This work differs

from the literature in a number of important aspects. First, the proposed protocols rely

on concurrent cooperative transmissions among multicast users via orthogonal OFDMA

sub-channels and hence work in a substantially different system. Second, we propose to

apply random network coding to effectively reduce the overhead and perform coopera-

tive communication. Third, we design our protocols by solving optimization problems

formulated to maximize the throughput performance. Finally, we specifically study the

resource allocation problems in cooperative multicast scheduling, which are critical in

practical systems.


2.3.2 Cognitive WiMAX

Current wireless networks are governed by a fixed spectrum assignment policy. Such

an allocation is often provisioned on a long term basis and leads to under-utilization of

spectrum resources. Measurements show that only about 10 − 15% of the spectrum is

utilized in the US [4]. In contrast to the sporadic spectrum usage in licensed bands, the

recent years have witnessed a proliferation of wireless devices crowding into the unlicensed

spectrum regime. They interfere with each other and degrade the overall performance

significantly. To address this inefficiency, major efforts are undertaken to allow unlicensed

devices to operate on licensed bands that are not being used by licensed users, referred

to as “white spaces.”

Cognitive radio networks (CRNs) [23] have emerged in recent research to efficiently use

white spaces by unlicensed devices [14]. It is a revolution in radio technology to efficiently

utilize the wireless spectrum. With cognitive radio, either a network or a wireless node

can change its transmission or reception parameters to communicate efficiently avoiding

interference with licensed or unlicensed users. This alteration on the parameters is based

on the active monitoring of several factors in the external and internal radio environment,

such as radio frequency spectrum, user behavior, and network states. Such dynamic

spectrum access (DSA) technology [78] is the key function in cognitive radio. With

such convenience, the wireless nodes can dynamically adjust the frequency, power, range,

and other variables to accommodate the entire wireless ecosystem, in order to efficiently

utilize the wireless spectrum.

As we stated in Chapter 1, WiMAX is an popular technology to facilitate broadband

wireless mobile access in metropolitan area [26]. As the proliferation of WiMAX mobile

devices as well as the surge of demand of bandwidths, it is crucial to dynamically utilize

the “white spaces” in order to improve the service quality. In WiMAX, femto cells

are a cost-effective means of providing ubiquitous connectivity. At the same time, this

structure provides abundant opportunities for channel reuse. Thus, it is potential to


take advantage of the favorable properties of both WiMAX and CR techniques. In our

thesis, we investigate the benefits of their collaboration, and propose a cognitive WiMAX

architecture with femto cells as well as an optimized resource management protocol.

The related research is barely explored in the literature. The only literature we

can find is [49] which introduces the concept of Cognitive WiMAX. However, our work

radically differs from it in a number of aspects. First, we study cognitive WiMAX

with femto cells employed, which provide potential for spectrum reuse and represent

the direction that WiMAX evolves to [26]. [49] only studies regular WiMAX scenarios.

Second, we advocate cooperative and multi-path multi-channel communication, which is

more efficient and hence works in a substantially different architecture. Third, we propose

a location-aware resource management protocol with cross-layer designs, while [49] just

uses CRs to perform channel sensing without DSA. Last but not least, we specifically

provide a rigorous analysis on network performance, which is not discussed in [49].

Chapter 3

Adaptive Random Network Coding

in WiMAX

As we stated in Chapter 1 and 2, errors are inherently present in the wireless channels,

especially when unpredictable and time-varying errors exist in WiMAX. It is important

to perform error control in order to effectively maximize achievable throughput and

efficiently utilize the wireless spectrum.

In WiMAX, Hybrid Automatic Retransmission reQuest (HARQ) has been used to

provide reliable data transmission [24] with error control. It is a variation of the ARQ

error control protocol, and combines ARQ and Forward Error Correction (FEC). Its

performance, especially in the context of WiMAX, has been thoroughly investigated in

an information-theoretic fashion [20, 70]. In Type-II HARQ, its performance can be

further improved by packet soft combining, including Chase Combining (CC) [19] and

Incremental Redundancy (IR) [66], both of which help to increase the probability of

successful decoding.

Without a doubt, HARQ incurs some overhead in terms of the redundant traffic,

with its retransmissions and ACK/NACK packets. The build-in reliability in HARQ

sacrifices some degree of resilience in realistic channels with varying qualities over time.

23

Chapter 3. Adaptive Random Network Coding in WiMAX 24

Most existing literature on the performance of HARQ [17, 30, 59] has not taken such an

issue into consideration. In addition, in handover and multi-hop transmission modes in

WiMAX, a mobile station is able to establish connections with two or more uplink nodes

through different sub-channels. In these cases, HARQ may not be able to fully utilize the

wireless medium, as it is designed for a point-to-point channel. As HARQ is performed

on all the links, it may incur additional overhead and delays.

On the other hand, as we stated in Chapter 2, network coding has emerged as one of

the most promising information theoretic approaches to improve network performance,

especially in IEEE 802.11 based wireless networks. Is random network coding beneficial

in WiMAX as WiMAX works in a totally different architecture? As the first step in

the thesis, in this chapter, we investigate the deployment of random network coding

in WiMAX MAC layer. In the first half of this chapter, we evaluate the benefits of

random network coding by introducing a MAC-layer protocol, referred to as MRNC,

as compared to traditional HARQ. We show that random network coding has indeed

helped to improve the performance significantly in three typical communication scenarios

in WiMAX: single-hop transmission, handover, and multi-hop transmission.

With this observation, in the second part of this chapter, we tune the design of MRNC

by introducing two adaptive algorithms to further improve the performance. First, we

exploit the flexibility present at the MAC layer for construction and transmission of

the MAC layer packet, which is also the basic transmission unit in random network

coding, referred to as block or coded block. We seek to change the block size adaptively

by tuning the tradeoff between block error rate and protocol overhead. A heuristic

feedback-based approach is employed in the algorithm by estimating the channel quality

using average block error rate as the metric. The dynamic manner in which the block

sizes are changed to match the channel conditions helps to improve throughput over

unreliable and fluctuating wireless channel conditions.

Second, we study how to further utilize the bandwidth with network coding in han-


dover and multi-hop scenarios, where the mobile station is able to communicate with two

or more upstream nodes simultaneously. When the mobile station completely receives a

data segment, it will send the feedback to all upstream nodes to stop the current trans-

mission and invoke the transmission of the next segment. However, the upstream nodes

push redundant blocks to the receiver due to the delay of feedback transmission. We

design an algorithm for the mobile station to send the feedback even before it has com-

pletely received the segment, in order to prematurely stop the transmissions of a subset of

upstream nodes for this segment. By adapting the number of upstream nodes, we could

reduce the amount of overhead, and therefore fully utilize scarce wireless bandwidth.

With well-tuned designs, we show our proposed protocol tightly integrates with

WiMAX and offers salient performance improvement as evidenced in our simulation

evaluation.

3.1 How Can Network Coding be Used in WiMAX?

In order to observe how helpful random network coding can be in WiMAX, we first design

a protocol framework to employ random network coding in the MAC layer of WiMAX.

Such a MAC-layer Random Network Coding protocol, henceforth referred to as MRNC

for brevity, is designed to fairly evaluate the usefulness of random network coding in

WiMAX.

In random network coding [22], a data segment p (also referred to as a generation

or a group in the literature) is divided into n equal blocks, denoted as [bp1, b

p2, · · · , bp

n],

each of which has a fixed number of bytes, referred to as the block size. If the segment

size is pre-determined, the block size k can be directly computed from n. In MRNC,

the basic data segment can be a MAC packet (i.e., the MAC-layer Protocol Data Unit

(MPDU) in WiMAX), if the block size is sufficiently small to be accommodated. When

the segment p is to be transmitted, the sender randomly chooses a set of coding coefficients


[cp1, c

p2, · · · , cp

n] in the Galois field GF(28), and then produces one coded block x of k bytes:

x =∑n

i=1 cpi b

pi .

Thus, each coded block is a linear combination of all or a subset of the original

data blocks. The n coding coefficients used to encode original blocks to x are typically

embedded in the header of the coded block [22], leading to a total overhead of n bytes

per coded block. In MRNC, however, since the sender has the entire original segment

when producing coded blocks, we just need to embed the random seed used to produce

the series of coefficients with a known pseudo-random number generator. This effectively

reduces the overhead to just 4 bytes for the random seed. In MRNC, the sender keeps

transmitting coded blocks from the current segment, until an ACK is received from the

receiver. Upon receiving the ACK, the sender proceeds to process the next segment. In

WiMAX downlink communication, for example, the base station (BS) or relay station

(RS) serves as the sender.

For each packet it receives, the receiver uses a progressive decoding process using

Gauss-Jordan elimination [65], as we stated in Chapter 2. It helps to make the decoding

time invisible at the receiver side, and effectively check the linear dependency of all the

received blocks. Immediately after n coded blocks have been received for a segment, the

receiver is able to recover the entire original segment, and sends the ACK packet back to

the sender. In WiMAX downlink communication, for example, the receiver is typically

the mobile station (MS) or the relay station (RS).

Random network coding serves as the cornerstone in the design of MRNC, and is

instrumental towards most of its advantages over HARQ. In this section, we present

intuitive justifications with respect to how network coding is used in MRNC. We show

that random network coding is indeed helpful, as compared with HARQ in practical

WiMAX systems, in the context of three different scenarios: single-hop transmission,

handover, and multi-hop transmission.


3.1.1 Single-hop Transmission

In HARQ IR, information is first coded and punctured according to a specified punc-

turing scheme. The sender transmits only the systematic bits at first, and transmits

one redundancy packet when it receives negative feedback from the receiver. Packet soft

combining is performed upon receiving redundancy packets at the receiver side. This

procedure is continued until the packet is correctly decoded or the maximum number of

retransmissions is reached.

As described above, HARQ incurs some overhead in terms of the redundant traffic,

with its retransmissions and ACK/NACK packets. In WiMAX systems, the MS may have

high degree of mobility, leading to a fluctuating channel quality over time. ACK/NACK

packets may also incur errors and delay due to poor channel conditions. Such errors and

losses in ACK/NACK packets may lead to additional redundant packet transmissions

that may be unnecessary, triggered by the ARQ timeout. In addition to the overhead,

the build-in reliability in HARQ sacrifices some degree of resilience in realistic channels

with varying qualities over time. It may also cause the problem of transmission continuity

due to packet loss (after several retransmissions, the receiver will give up on the packet

that still could not be decoded).

In contrast, random network coding offers an elegant and simple solution to these

challenges. With the rateless property of random linear codes, MRNC is able to adapt

the rate of data transmission to coincide with the available bandwidth in time-varying

wireless channel conditions. With MRNC, the sender keeps on transmitting coded blocks,

and the receiver only needs to “hold a bucket” to “collect” sufficient number of linearly

independent blocks, such that it is able to recover the original data segment. It is not

necessary for the receiver to transmit ACK/NACK packets with each individual coded

block, and for the sender to transmit redundant packets when errors occur. Intuitively,

MRNC is able to offer resilient transmissions due to the inherent resilience to errors with

random linear codes. Should a particular coded block be lost, subsequent coded blocks


received are equally innovative and useful.

3.1.2 Handover

Handover is an essential functionality in WiMAX for dealing with user mobility, which

is a process where a mobile station migrates from the air-interface of one base station

to the air-interface provided by another base station. Recently, IEEE P802.16e/D4 [26]

adopted soft handover schemes, such as Macro Diversity Handover (MDHO).

For mobile stations that support MDHO, they maintain an active set of base stations

that are involved in MDHO. When the signal strength from a certain base station is

above a particular threshold (H Add), this base station will be added into the active set

of the mobile station. On the other hand, a base station will be removed from the active

set if the power is below the drop threshold (H Delete). With this mechanism, a mobile

station updates the active set periodically using the signal strength as the metric. In the

handover region, the mobile station associates to all base stations in the active set, and

establishes downlink connections with these base stations through separate downlink sub-

channels. Uplink communications are established through the same uplink sub-channel

to all base stations that are associated to the mobile station. Such uplink data from the

mobile station will simultaneously be relayed by the base stations to an access gateway

(AG), which connects to all base stations as a cross router.

In the traditional approach with HARQ, in the downlink, the transmission should

be synchronized by having two or more base stations sending the same MAC PDUs to

the mobile station in the same time epoch. Otherwise, diversity combining could not

be performed. Thus, the base stations that are newly involved in the active set have to

negotiate with existing base stations, with respect to which packets should be transmitted

next. To achieve this synchronization, if some packets to be sent are already in the buffer

of existing base stations, they should be shared by newly added base stations through

AG, or the new base stations have to wait until they are sent. It will delay the data


transmission from the newly involved base stations. Moreover, the requirement that

the same packets are to be transmitted by all base stations through different downlink

sub-channels will underutilize the wireless medium.

Intuitively, random network coding is helpful to take full advantage of the available

bandwidth from each base station, and to improve downlink transmission rates. With

random network coding, the synchronization efforts can be avoided, since all coded blocks

are considered equally innovative. In this mode, each sub-channel can be used separately

for transmitting different coded blocks simultaneously without collision. In this case,

all sub-channel resources can be fully utilized, which coincides with the advantage of

network coding in typical cases of multi-path communication.

We show the intuition behind the advantage of random network coding in a two-way

handover procedure with an example, shown in Fig. 3.1. After the mobile station enters

the handover region, it connects to both base stations, each through a unique sub-channel

scheduled by each base station. Encoding is implemented at AG, and different linearly

independent coded blocks are issued to the two base stations simultaneously. The base

stations then relay these coded blocks to the mobile station concurrently. The mobile

station collects these coded blocks from both base stations, and responds with an ACK

through the common uplink channel once it has received a sufficient number of linearly

independent coded blocks. In this fashion, random network coding helps to fully utilize

the downlink channels from both base stations.

3.1.3 Multi-hop Transmission

In the scope of the IEEE 802.16j standard of WiMAX, the concept of a relay station (RS)

is introduced, with a mandatory two-hop transmission mode and an optional multi-hop

mode. Fig. 3.2 shows an example of a simple two-hop relay system. When the MS moves

into the overlap region of both BS and RS, the MS is able to communicate directly with

BS, indirectly with BS via RS, or with both.


BS1 BS2MS

R1 R2 R3 R4

Access Gateway

Figure 3.1: The advantage of random network coding in a WiMAX two-way handover

procedure.

In a HARQ scheme that is proposed specifically for the multi-hop mode in WiMAX,

RS performs as an assisted relaying node, by monitoring the HARQ burst transmitted

by BS to MS. If the RS can decode the HARQ burst correctly and the MS fails to receive

the HARQ burst, the RS retransmits it to MS. The BS receives ACK/NACK packets

from RS and MS separately. If the BS receives an NACK packet from both RS and MS,

it will transmit the HARQ burst to both RS and MS again. If the BS receives an ACK

from RS and an NACK from MS, it will ask RS to retransmit the HARQ burst to MS.

In this procedure, HARQ will be performed in the transmission links between BS and

RS, BS and MS, and RS and MS, respectively.

RS

MS

BS

Figure 3.2: A two-hop transmission scenario in WiMAX.


From this description, we may observe that the retransmissions in HARQ are per-

formed on all the links among the BS, RS, and MS, which may cause additional overhead.

Similar to the case of handover, the available resources in these channels are not fully

utilized. In comparison, the multi-path advantage of random network coding is also

beneficial in this scenario. Extended from the handover case, all base stations and relay

stations with a signal strength above H Add are maintained in the active set of the mobile

station, with weaker stations eliminated from the set periodically. With random network

coding, the MS is able to receive coded blocks from different paths establishing connec-

tions with all base and relay stations with acceptable signal strengths, through which

different coded blocks are transmitted concurrently. All transmission sub-channels can

be fully utilized to increase the throughput, as all received coded blocks are equally use-

ful. Neither synchronizations nor retransmissions are required. The examples shown in

Fig. 3.2 and Fig. 3.3 explains the intuition behind such an advantage of random network

coding.

BS/RS

RS1 RS2 RS3

MS1 MS2 MS3

Figure 3.3: The advantage of random network coding in WiMAX multi-hop transmission.

3.2 MRNC with Adaptive Algorithms

The design of MRNC should take full advantage of network coding and tightly integrate

with WiMAX architecture and working scenarios. Equipped with random network cod-


ing at the core of MRNC, there are some challenges in the design, including what is an

appropriate size of a coded block as we perform network coding in the MAC layer? and

How to schedule the upstream nodes cooperatively serve the downstream nodes simulta-

neous in multi-path transmission scenarios? The solutions are critical to the protocol

efficiency. In this section, we seek to answers these questions above by tuning the design

of MRNC. We propose two adaptive algorithms — adaptive block size and adaptive up-

stream node to further improve the performance. They are based on heuristic study with

simulation analysis.

3.2.1 Adaptive Block Size

First, we study the selection of packet size, which plays a crucial role in WiMAX through-

put performance. At the MAC layer, the packet is considered as a MAC layer Protocol

Data Unit, which is also the basic transmission unit in MRNC, referred to as block or

coded block. We can simply represent the throughput under MRNC as R(1−Pe), where R

is the channel rate, and Pe denotes the block error rate, since blocks are often corrupted

during transmission in error prone wireless channels. It is noted that under the same bit

error rate, a decreasing block size would decrease the block error rate as well. Similarly,

it can be argued that if the block size increases, the resulting block error rate increases

as well.

Based on the intuition above, we can see that a smaller block is helpful to achieve

a lower block error rate. Of course, the flip side of the coin is the lower transmission

efficiency due to a lower payload to protocol overhead ratio. On the other hand, a larger

block size achieves better efficiency, but leads to a higher block error rate. Thus, we

observe that both large and small block sizes have their advantages and disadvantages

in MRNC.

The natural question that arises is: how do we adjust the block size to obtain better

performance? We propose an algorithm, referred to as adaptive block size, to dynamically


construct and transmit the blocks in MRNC. Throughout the chapter, we focus on the

throughput with only the useful bits transmitted per unit of time, excluding the protocol

overhead, which captures the throughput performance more precisely and is helpful to

show the benefits of our proposed algorithms.

Intuitively, we are able to adaptively tune the block size in response to the channel

conditions in order to improve the actual throughput. Study on dynamic block size in

sensor networks has been performed [31]. At the MAC layer, WiMAX is capable of

performing aggregation and fragmentation of MAC layer data units [26], with which we

could vary the block size in MRNC. Heuristically, when the channel quality becomes

high, we increase the block size. The larger the block size is, the less overhead the MAC

header achieves while maintaining that very few redundant coded blocks are sent. On

the other hand, we could manage to raise the throughput by decreasing the block size

under poor channel conditions. The smaller block size could help to obtain a lower block

error rate, thus fewer redundant coded blocks are required to transmit.

We design a feedback-based scheme to achieve such block size adaption. In MRNC,

after the receiver completely receives the entire segment, it will send feedback to the

sender to stop the current transmission, and invoke the transmission of the next segment.

With this feedback, the receiver could explicitly report the channel state information

based on the transmission of the coded blocks of the entire segment. We use the average

block error rate achieved in the transmission as the metric. With such knowledge, the

sender is able to dynamically adjust the block size and construct coded blocks for the

transmission of the subsequent segment.

A heuristic approach is adopted for this adaptive algorithm in our design. First, we

establish a finely tuned feedback granularity to represent different channel states which

indicate different levels of average block error rates. We propose six types of feedback,

shown in Table 3.1, each of which identifies one of the states of the transmission quality.

Upon receiving feedback from the receiver, the sender could tune the block size ac-


Table 3.1: Adaptive Block Size Algorithm.

Feedback type Block error rate Block size change

1 < 5% +75 bytes

2 < 10% & > 5% +50 bytes

3 < 20% & > 10% -25 bytes

4 < 40% & > 20% -50 bytes

5 < 90% & > 40% -75 bytes

6 > 90% -100 bytes

cording to the type of the feedback. The changes in block size accordingly are shown in

third column in Table 3.1, where for instance, “+50” implies the algorithm will increase

the block size by 50 bytes, and “-25” implies to decrease the size by 25 bytes. With this

adaptive block size algorithm, we are able to dynamically change the block size to adapt

to the fluctuating channel conditions, which will lead to higher throughput.

3.2.2 Adaptive Upstream Node

In WiMAX handover and multi-hop modes, the mobile station (MS) could build con-

nections with two or more upstream nodes through different sub-channels to enjoy the

multi-path transmission. In MRNC, random network coding is helpful to make full use

of the available bandwidth from each upstream node, and thus to improve the downlink

throughput. During the transmission, upon receiving a sufficient number of coded blocks,

MS could decode the original segment immediately, and send feedback to all upstream

nodes to stop their current transmission, and ask them to proceed to the next segment.

The problem in the current design is that the delay of feedback transmission will

cause more redundant coded blocks to be pushed to the receiver. We define the feedback

delay as the time difference between the time the last bit of the last coded block (after

receiving this block, the entire segment could be decoded correctly by the receiver) is


transmitted and the time a feedback packet is received by the senders.

Assume that at time t, the last bit of the final innovative coded block is received.

The segment could therefore be decoded at time t and all upstream nodes receive the

feedback at time t + D, with D equal to feedback delay. Without explicit knowledge,

during the time period from t to t + D, all upstream nodes continue their transmission

of the coded blocks of the segment that has already been correctly received by MS. In

the best case, the transmission of the next block is in progress while the feedback arrives.

Upon receiving it, the upstream nodes could only switch to the transmission of the next

segment after finishing the redundant transmission of the current block. We can do a

back-of-an-envelope calculation. If the block size is 256 bytes, and there are 4 upstream

nodes communicating with the MS concurrently. Thus, totally 256×4 = 1K bytes in total

will be dropped. If we further consider a large-scale WiMAX network with high speed

data transmission and with a large number of mobile nodes being served concurrently, it

becomes obvious that the scarce wireless bandwidth is under-utilized due to the deficiency

of the protocol. Moreover, the situation will be even worse when a larger feedback delay

is unavoidable. As such, mitigating the effect of feedback delay and fully utilizing the

wireless bandwidth should be critical design objectives.

To solve the above problem, we propose an algorithm by adapting the number of up-

stream nodes, referred to as adaptive upstream node, to effectively utilize the bandwidth.

This algorithm enables the MS to send feedback before it has completely received all the

coded blocks for decoding the segment. Therefore, the upstream nodes are able to pre-

maturely stop when segment downloading is almost completed. This adaptive upstream

node algorithm is designed to favor upstream nodes with better bandwidth to complete

the download, and stop the upstream nodes with lower data rates. It will gradually stop

more nodes based on the completion timing estimation in the transmission process, in

order to avoid the transmission of redundant packets.

We design a heuristic approach for such an algorithm. When 3/4 coded blocks from


a segment are successfully received, the MS could stop the upstream nodes with the

lowest throughput. The number of upstream nodes to be prevented is one half of the

nodes associated to the MS. Upon receiving the feedback, these nodes will stop the

transmission of the current segment, but start to transmit the coded blocks of the next

segment. If the entire data transmission is completed, the connections will be released,

and the bandwidth may be reallocated. Meanwhile, the remaining upstream nodes with

higher throughput shall keep transmitting the coded blocks from the current segment.

After finishing the transmission for 7/8 coded blocks, the MS will only maintain 1/4 of

the connections with the highest throughput.

We tune the design of the algorithm to further improve bandwidth utilization. At the

same time that MS sends feedback to a certain set of upstream nodes when 7/8 coded

blocks are received, the feedback is also sent to the remaining 1/4 upstream nodes to

inform them that the transmission for the current segment is almost done. Upon receiving

this signal, they take turns to transmit the coded blocks from the current segment and

from the next segment. Consider the scenario when the last coded block from the current

segment is transmitted, the following data block to be sent should be the block for the

next segment. Normally when feedback arrives after feedback delay, the transmission of

blocks from the next segment has already been started, which is useful. Thus, the wasted

bandwidth is reduced. The entire heuristic algorithm is summarized in Table 3.2.

3.3 Performance Evaluation

We are now ready to resort to extensive simulations to study the performance of MRNC

in WiMAX, as compared to HARQ. For this purpose, we implement our protocol designs

stated above in this chapter in the MAC layer of the WiMAX module, which is part

of a specific ns-2 simulator released by the WiMAX forum and is the only simulator

for WiMAX that is available to be used in both academia and industry. We have used


Table 3.2: Adaptive Upstream Node Algorithm.

Conditions Actions

received 3/4 coded blocks stop 1/2 of upstream nodes with the lowest throughput, and

ask them to transmit blocks from the next segment

received 7/8 coded blocks stop another 1/4 of upstream nodes with the lowest through-

put, and ask them to transmit blocks from the next segment

received 7/8 coded blocks the remaining 1/4 of upstream nodes take turns to transmit

blocks from two segments

received all coded blocks all upstream nodes transmit the blocks of the next segment

convolutional turbo codes (CTC), which have been employed in WiMAX. The packet

error rates in the additive white Gaussian noise (AWGN) model are obtained through

extensive simulations based on the technical specification document [26]. With respect

to parameter settings in our simulations, the ARQ retransmission timeout period is set

to be 0.05 milliseconds. In HARQ, we set the maximum number of retransmissions to be

4, and the corresponding optimal size of redundancy packets based on the results in [21].

3.3.1 Single-hop transmission

We first focus on the throughput performance in single-hop transmission. Both protocols

are used to transfer a large file in downlink over 1000 seconds between the same sender

and receiver pair. For the sake of a fair comparison, the transmission rate is set to be 25

Mbps for both MRNC and HARQ. As a starting point, we first carry out our experiments

under stable channel conditions. From the results, we observe that MRNC has managed

to achieve a higher average throughput than HARQ with margin of 18% in average.

Although the observed throughput improvement of MRNC over HARQ is quite en-

couraging under stable channel conditions, we believe that realistic channel conditions

vary over time, sometimes quite significantly. In such time-varying channel conditions, a


superior protocol needs to be resilient to channel condition fluctuations, and deliver not

only a high average throughput, but also small variance in throughput over time (referred

to as variance). To evaluate MRNC and HARQ in time-varying channel conditions, we

utilize Jakes channel files with a velocity of 40 km/h so that the received per-packet

SNR values may vary over time. We perform the simulation over 1000 seconds. The re-

sults have clearly shown that MRNC delivers 50% less variance in throughput over time

than HARQ, which is desirable in WiMAX with realistic channel conditions. We have

also calculated the average throughput, with the verdict that MRNC enjoys a 10% gain

over HARQ. These results verify the advantages of random network coding in single-hop

transmission.

3.3.2 Handover

We next try to identify the performance gain offered by random network coding in the

handover case in WiMAX, as compared to HARQ. Our evaluation is performed under

the following realistic scenarios. A total of 19 BSs are deployed in the service area. The

cell sites are layout as shown in Fig. 3.4. A constant downlink channel rate (25 Mbps) is

allocated to the MS for each sub-channel from the BSs it attaches.

A

No handover region

Handover region

B

Figure 3.4: The scenario being used for simulating a WiMAX handover event.

In the simulation, the MS is allowed to move around in the service area. Its initial


speed (in km/h) and direction (in degrees) are generated with a uniform distribution

of U [10, 50] and U [0, 360], respectively. The MS changes its speed and direction after a

certain amount of time with an exponential distribution, with a mean value of 1 minute.

The new speed is uniformly generated with U [10, 50] if the current speed is below 10

km/h; otherwise, it is obtained using U [v − 10, v + 10], where v is the current speed.

The new direction is obtained from a Gaussian distribution with the mean as the current

direction, and a standard deviation of 40 degrees. The initial location of the mobile

station is randomly chosen in the handover region.

0 500 1000 1500 20000

5

10

15

20

25

30

time (second)

thro

ughput (M

bps)

MRNC

HARQ

Figure 3.5: MRNC vs. HARQ: throughput in a realistic handover case.

Fig. 3.5 shows the downlink throughput of both protocols on the MS through a 2000-

second simulation. The improvement of the average throughput with MRNC is proxi-

mately 65%. MRNC also outperforms HARQ with respect to the throughput variance

over time with 67% gain. These improvements are more substantial than those in the

single-hop case, which coincides with our intuition that network coding fits naturally in

the handover case.

With the objective of becoming even more realistic, we seek to extend our performance

evaluation to a large scale scenario. In the cellular system described previously, we set

a large number of MSs active in the service region concurrently. The arrival process of

new MS connections in each cell is assumed to be a Poisson process with a mean of 5


connections/cell/second. The MS active time duration is exponentially distributed with

a mean of 100 seconds. Every active MS is moving around the service area using the

same way as the previous simulation. We run the simulation for 1000 seconds, and the

downlink throughput at the MS is examined. From the results, there are a total of 94880

MSs that have ever been active in the service area during the simulation time, with

450 MSs active simultaneously in each cell on average. Fig. 3.6 plots the CDF of the

average throughput and its variance, considering all active MSs in the simulation. Not

surprisingly, MRNC outperforms HARQ by 40% with respect to both average throughput

and variance, due to its effective use of bandwidth and the inherent resilience of random

network coding.

0 100 200 3000

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

MRNCHARQ

(a)

0 50 100 1500

0.2

0.4

0.6

0.8

1

Variance (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

MRNCHARQ

(b)

Figure 3.6: MRNC vs. HARQ in a large-scale handover scenario: (a) CDF of throughput.

(b) CDF of variance.


Finally, we illustrate the synergy between network coding and the WiMAX multi-hop

mode. We evaluate the performance in a practical setting of the multi-hop case, by

considering the benefit of multi-path transmission. Our simulation scenario is shown in

Fig. 3.7. In order to extend the coverage area of the cell, the RSs are placed within the

border of the radio ranges of BSs.


BS

RS

Figure 3.7: Practical setting of the multi-hop scenario.

The MS in the simulation receives downlink data either directly from RS or BS, or

from both. A similar evaluation is performed with the same setting as our simulation in

the first handover case. We observe from the results that MRNC gains a 36% throughput

improvement and a 70% variance improvement, as shown in Fig. 3.8. This coincides with

our intuition and is not a surprise: it shows the ability of random network coding to fully

utilize available wireless spectrum in the multi-hop case.

0 500 1000 1500 20005

10

15

20

25

time (second)

thro

ug

hp

ut

(Mb

ps)

HARQ

MRNC

Figure 3.8: MRNC vs. HARQ: throughput in a realistic multi-hop scenario.

Finally, we consider the case of a large-scale multi-hop network, with the same sim-

ulation setup as in the large-scale handover scenario. Fig. 3.9 presents the CDF of the

throughput and variance from a 1000-second simulation. As expected, MRNC outper-

forms HARQ in both average throughput and variance. In particular, MRNC achieves a

60% higher throughput on average, as well as a 40% gain with respect to variance over


HARQ. This confirms and highlights the benefits achieved by MRNC in the WiMAX

multi-hop mode.

0 100 200 3000

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

MRNCHARQ

(a)

0 50 100 1500

0.2

0.4

0.6

0.8

1

Variance (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

MRNCHARQ

(b)

Figure 3.9: MRNC vs. HARQ in a large-scale multi-hop scenario. (a) CDF of throughput.

(b) CDF of variance.

In closing, we would like to study the overhead of MRNC. As neither BSs nor RSs have

constraints with respect to memory and computational power, we are only concerned with

the overhead at MSs. With respect to the overhead caused by coding, we have already

employed Gauss-Jordan elimination to perform progressive decoding in MRNC, which

maximizes the timing overlap between coding and network transmission. With respect

to the overhead from packet headers, as compared to HARQ, MRNC only adds 4 bytes

to carry the random seed.

3.4 Summary

WiMAX employs a state-of-the-art design using HARQ Incremental Redundancy. In

comparison, the recent advances in the literature on network coding have clearly shown

the advantages that simple random linear codes may be able to bring to wireless net-

works. Is random network coding helpful at the MAC layer of WiMAX, when used

instead of traditional HARQ? In this chapter, we have designed a protocol, referred to


as MRNC, with the intention of taking full advantage of the rateless property of ran-

dom linear codes in WiMAX. We further well tune the design of MRNC by designing

two adaptive algorithms: adaptive block size and adaptive upstream node. The adaptive

block size algorithm aims to provide a more flexible scheme for data transmission by

dynamically adjusting the block size in response to the channel conditions. Meanwhile,

the adaptive upstream node algorithm could help to efficiently utilize the scarce wireless

bandwidth, particularly in multi-path transmission scenarios. With extensive studies, we

have observed that our proposed protocol based on random network coding has indeed

offered salient advantages over HARQ, especially in cases where the channel condition

varies over time, during the handover procedure, and in the multi-hop mode of WiMAX.

Chapter 4

Drizzle: Cooperative Symbol-Level

Network Coding in WiMAX

In Chapter 3, we proposed a MAC-layer random network coding protocol, MRNC, to

improve error control in WiMAX. With random network coding at the MAC layer, the

throughput performance of WiMAX improves significantly and the scope of network-

ing in WiMAX has been largely extended. However, wireless channels are inherently

unreliable, and errors occur when the signal to noise ratio (SNR) is not high enough

to decode information correctly. Since the wireless channel conditions are time-varying

and location-dependent, especially in multi-channel WiMAX, they are completely unpre-

dictable. The transient medium errors cause significant packet loss under poor channel

conditions. However, not all the bits in the packet share the same fate when packet

error occurs. Most likely, only a few bits are in error, while the rest are correct, but

lead to the drop of the entire packet in the transmission. Scarce bandwidth is wasted by

dropping the entire packet due to a few corrupted bits. Therefore, even with HARQ and

MRNC at the MAC layer, it is sometimes not sufficient to fully recover bit errors in the

unpredictable error-prone wireless channels.

44

Chapter 4. Drizzle: Cooperative Symbol-Level Network Coding in WiMAX45

Is random network coding scheme still helpful under poor channel conditions in WiMAX?

How to design finer-granularity error control protocol that tightly integrates with WiMAX?

In this chapter, we seek to answer these questions and pursue more after MRNC, by pre-

senting Drizzle, a solution at the physical layer that uses random network coding across

symbols (one symbol contains a small sequence of bits in the physical layer), rather than

using network coding at the packet level (as MRNC and previous work in IEEE 802.11

networks). It is very challenging to design such a protocol by shrinking the network

coding block to symbol level, as the extremely small size of coded blocks will generate

large amount of overhead. In order to achieve all the benefits provided symbol level net-

work coding with error control in finer granularity without generating much overhead,

we have a number of designs in Drizzle presented in this chapter. With analysis and eval-

uation, we show that Drizzle is able to fully embrace the characteristics of multi-channel

WiMAX and exploit both time and cooperative diversity, to adapt to time-varying and

bursty channel errors and thus efficiently improve throughput performance in WiMAX.

4.1 The Design of Drizzle

Drizzle is designed specifically to explore the benefits of using network coding at the

symbol level in the physical layer of WiMAX. The symbol level design of Drizzle allows

flexible and efficient operations, as compared to the rigid design of previously proposed

physical layer network coding in [43, 77]. A symbol described in this chapter refers to a

unit of data that is defined by the modulation scheme in the physical layer. For example,

one symbol represents two bits if Quadrature Phase Shift Keying (QPSK) is used, and

four bits if 16 Quadrature Amplitude Modulation (16-QAM) is used. In this section, we

first describe the basic system design of Drizzle. Then, we present two salient advantages

when Drizzle operates in the physical layer of WiMAX.


Binary Input Data Modulation

Binary Output Data De-

Modulation

Modulated Symbol

Detected Modulated Symbol

Noisy WirelessChannel

Fading

Drizzle Encoding

Drizzle Decoding

Drizzle Coded Binary Data

ACK/NACK

Generate packets(segment+CRC)

CRC Check

AWGN

x= [x1,x2,…,xn] y = [y1,y2,…,yn,…] s = [s1,s2,…,sv,…]

sr = [sr1,sr

2,…,srv,…]yr = [yr

1,yr2,…,yr

n,…]

Soft Decision Values

xr= [xr1,xr

2,…,xrn]

Figure 4.1: A simplified block diagram showing the design of Drizzle.

4.1.1 Basic Operations

In order to provide a good understanding of Drizzle, a simplified block diagram is shown

in Fig. 4.1. The transmitter divides the input bit stream into segments and adds a cyclic

redundancy check (CRC), which is used for error detection at the receiver. A CRC

appended segment is referred to as a packet. Each packet is then divided into blocks with

fixed size, each containing a certain number of physical layer symbols. We can easily

compute the number of blocks in one packet if the packet size is pre-determined, and

we denote this quantity as the batch size in network coding. Unlike MIXIT [44], Drizzle

performs random network coding upon blocks within the same packet. Let n be the

batch size, and let xi (i = 1, 2, · · · , n) be the blocks in the packet, cji (i = 1, 2, · · · , n)

be the set of random coefficients generated in a given Galois field, the size of which is

determined by the number of bits in a block (e.g., for a block with 8 bits, GF(28) would

be used). A coded block yj can then be produced as yj =n∑

i=1

cji·xi. Each generated

coded block can be mapped to one or several modulation symbols. The required number

of symbols for one coded block depends on the size of the coded block and the selected

modulation scheme. For example, a coded block with a block size of 8 bits is mapped

to four symbols for QPSK and two symbols for 16QAM. The encoder is able to generate

a virtually unlimited number of coded blocks yj (j = 1, 2, · · · ) using different sets of

coefficients, and any n of these coded blocks can be used to decode by inverting a matrix

of coding coefficients.


Demodulation in the physical layer on the receiver makes its best decision on the

received signals. Due to noise and channel fading, the demodulator may make incorrect

decisions, leading to errors. The Drizzle decoder tries to decode the received coded

blocks using “hints” from demodulation, which are referred to as soft decision values.

Soft decision values are estimates of coded bit log likelihood ratios (LLRs) [72]. In the

case of perfect channel knowledge, the estimation of code bit LLR under 2F -QAM can

be obtained by the following equation [72]:

Λ (bf ) = ln∑

s+∈{s:bf=+1}exp

(−|ys − αs+|2

σ2

)− ln

∑s−∈{s:bf=−1}

exp

(−|ys − αs−|2

σ2

)(4.1)

where f is the bit order of used 2F -QAM symbol; ys is the received QAM symbol; α

is the channel gain; s (s ∈ {s1, s2, · · · , s2F }, s = b1b2 · · · bF ) is the transmitted QAM

symbol; σ2 is the variance of noise, which is a complex Gaussian random variable with

zero mean.

Fig. 4.2 shows 16-QAM constellation with Gray coding and an example of the detected

symbol of ys (s = b1b2b3b4 = 1001). The first bit decides whether the detected symbol is

placed in the first quadrant or fourth quadrant. For the first bit of a symbol (b1 = 1),

Eq. (4.1) will return a positive value because the detected symbol is placed in the fourth

quadrant. The fourth quadrant is further divided into two spaces in the x-axis. If the

detected symbol is placed in the left half of the divided space, LLR is a negative value,

otherwise, LLR is a positive value. Through a similar approach, the third and fourth

bits can be decided. From Eq. (4.1), it is clear that the shorter the Euclidean distance

between the detected symbol and its closest constellation points is, the larger absolute

LLR value obtained.

Essentially, soft decision values represent how much confidence the demodulator has in

making the 0-1 decision on each bit. In Drizzle, the confidence level is used to estimate the

correctness of each received block using these soft decision values from the demodulation


11

10

00

01

0001 1110

b2b1

b4b3

Detected symbol

Figure 4.2: 16-QAM (24-QAM) constellation with Gray coding and an example of de-

tected symbol, 1001.

process. We will present an adaptive error detection algorithm using the confidence level

with a detailed discussion in Sec. 4.2. With such estimates, Drizzle gives priorities to

blocks with high confidence that they are correct, or “clean.” It is important to have a

sufficient number of “clean” blocks (with high probability), at least as many as the batch

size n, before decoding begins, as “dirty” blocks will lead to decoding failures, which can

be verified by checking the CRC. When an error occurs, the receiver asks the sender(s)

to retransmit additional coded blocks, until the entire packet is correctly decoded, or a

maximum number of retransmissions is reached. When the packet can not be correctly

recovered without a sufficient number of “clean” blocks until a maximum number of

retransmission is reached, the packet is discarded at the physical layer. This strategy is

employed for HARQ in various air interface standards including IEEE 802.16 WiMAX

and 3GPP LTE.

4.1.2 Adaptive Retransmission

One of the key designs in Drizzle is adaptive retransmission. The intuition is shown in an

illustrative example in Fig. 4.3. The sender first divides each single packet into a number

of small blocks, each of which contains one or a small number of physical layer symbols


A1 A2 A3 A4 A5

A1 A2 A3 A4 A5

A6 A7

A1 A2 A3A4 A5A6 A7B1 B2 B3 B4 B5

NACK

ACK

"clean" block "dirty" block

Figure 4.3: In Drizzle, only “dirty” blocks are retransmitted to the receiver over a single

wireless link with errors.

used in modulation. All blocks are encoded using random network coding [35,36], and the

sender sends the packet by transmitting n of them (n is the batch size; in the example,

5 blocks are transmitted: A1, A2, · · · , A5) to the receiver. At the receiver side, each

received packet is inspected and evaluated using confidence level as we stated above.

The blocks with lower confidence levels have lower priorities in the decoding process,

because the receiver has the lower confidence on the correctness of these blocks. The

receiver constructs a set of blocks to decode, which always includes top n blocks with the

highest confidence levels.

If decoding fails for the initial transmission, the receiver computes the number of

“dirty” blocks. This number is determined using the level-threshold, which will be dis-

cussed and elaborated in Sec 4.2. If the confidence level values of a block is below the

level-threshold, the block is marked as “dirty.” Normally, not all the bits within the

packet share the same error rate. Very often, only a small number of bits are in error;

the rest are correct. In the example, block A3 and A5 are in error, while A1, A2 and A4

are “clean.”

With this knowledge, the receiver only tries to exclude “dirty” blocks, and requests


the sender to transmit additional coded blocks (same number as the “dirty” blocks) via

NACK. In the example, the sender just needs to send two more coded blocks (A6 and

A7) to the receiver, which can then be used towards correct decoding of the packet on

the receiver. After receiving additional blocks from the sender, the receiver again tries to

decode the packet with the n (out of all the received blocks received so far) blocks with

the highest confidence levels. In the example, decoding can be successfully performed

with a total of 5 “clean” blocks (A1, A2, A4, A5, A7).

This process is referred to as adaptive retransmission, since the sender is only called

upon to retransmit a sufficient number of additional blocks for the receiver to decode,

and if blocks are sufficiently small, the available wireless bandwidth is effectively used, as

in the analogy where fine “rain drops” fill up a “bucket.” Error control in Drizzle can be

performed in fine granularity, which can be more efficient in terms of resource utilization

than traditional packet-level error control protocols and blind-push based end-to-end

error correction in [44]. In addition, thanks again to the rateless property of random

network coding, the receiver does not have to specify which blocks have errors in the

packet, and only needs to ask for an additional number of blocks. Should a particular

coded block be lost, subsequent correctly received ones are equally innovative and useful

to recover the original packet. As such, Drizzle is resilient to time-varying and bursty

channel errors, by dynamically adapting to fluctuating channel conditions in realistic

networks such as WiMAX, especially when mobility is present.

Adaptive retransmission is always performed as Drizzle is employed. How effective is

this design to saturate available wireless bandwidth from the physical layer (after demod-

ulation)? In one of our simulations, we have used a Rayleigh fading channel to simulate

time-varying channel conditions between a sender and a receiver. With this channel, we

simulated Drizzle, HARQ and SOFT [74] with WiMAX physical layer characteristics.

Fig. 4.4 shows the number of bits retransmitted for correctly recovering the error packet

over a period of time (100 seconds). We are able to observe that Drizzle consistently


0 10 20 30 40 50 60 70 80 90 100200

400

600

800

1000

1200

Time (Second)

Num

ber o

f bits

retra

nsm

itted

Drizzle HARQ SOFT

Figure 4.4: The average number of bits retransmitted in a single-link transmission, when

Drizzle is compared with HARQ and SOFT (Woo et al. [74]). Simulations are performed

with the environment and settings provided in Sec. 4.4.

uses a significantly smaller number of bits in its retransmissions (on average 403 bits for

Drizzle, 632 bits for HARQ, 835 bits for SOFT) which result in substantial throughput

enhancement, and outperforms both HARQ and SOFT by 36% and 52%, respectively.

The intuition is that, Drizzle allows the sender to retransmit a barely sufficient number

of symbols, rather than blindly retransmitting the redundancy.

In terms of delay performance, Drizzle can achieve a shorter packet delivery time

than HARQ and SOFT, since it transmits significantly smaller number of bits in its re-

transmissions, with shorter transmission delays. However, in the WiMAX Time Division

Multiplexing (TDD) mode, the only deployed mode at the time of writing this chapter,

since the receiver has to wait for an uplink transmission opportunity to send ACK/NACK

feedback to the transmitter, the gain on the transmission delay time reduction is negli-

gible. Therefore, we mainly focus on the evaluation of throughput performance in this

chapter. We will further evaluate the performance of adaptive retransmission in Drizzle

in evaluation section with more details.

4.1.3 Cooperative Transmission

Cooperative transmission is an especially effective application of Drizzle to realize the


potential benefits in multi-path transmission. Drizzle employs a typical wireless network

architecture, as shown in Fig. 4.5(a), in order to provide an efficient and cost-effective

cooperative transmission mechanism. An illustrative example of handover is shown in

Fig. 4.5(b), where a mobile node is in the handover region and connected to two upstream

nodes (base station 1 and 2). By assigning separate sub-channels on each connection

(channel 1 and 2), the receiver could communicate with all the upstream nodes con-

currently with little interference, as sub-channels are orthogonal to each other by using

OFDMA. As an opportunity for multi-path transmission is created in such scenarios,

multiple senders are able to cooperatively transmit coded blocks to a receiver.

We use the example shown in Fig. 4.5(b) to show how cooperative transmission per-

forms. In the figure, the access gateway mediates two base stations as a cross router

and serves as the sender. It generates different coded blocks and send them to the base

stations — A1, · · · , A5 to base station 1, A6, · · · , A10 to base station 2 (the batch size is

set to be 5 in the example). The base stations forward the coded blocks and the mobile

node receives them concurrently via different channels. The mobile node is able to “col-

lect” different coded blocks from all the connections simultaneously. All the correctly

received coded blocks are equally useful, due to the rateless property of random linear

codes. However, as channels are not reliable, the mobile node only receives 3 (A4, A6

and A7) “clean” blocks (the dark blocks are “dirty” blocks, and the white blocks are

“clean” ones), and thus fails to decode. It asks for retransmission, and the sender pushes

more redundancy (A11 and A12). By correctly receiving the required number of correct

blocks, the mobile node is able to successfully decode and recover the original packet.

Such cooperative transmission could also be performed at the uplink, where the mobile

node is responsible to generate distinct coded blocks, and the access gateway performs

the decoding process.

Maximum-performance cooperative transmission can be employed for the downlink,

as power is not a problem for relays and BSs. On the other hand, power-efficient co-


Mobile Node 2

Mobile Node1

Mobile Node 3

Access Gateway

Base Station 2

Base Station 1

Relay 3

Base Station 3

Relay 1

Relay 2

(a) System architecture.

Mobile NodeBase Station 1

A4 A6 A9

original packet

combining

A11

A12

A6 A9 A10A8A7A4A1 A2 A5A3

retransmission

A4 A6 A11A9 A

12

Access Gateway

channel 1 channel 2

Base Station 2

(b) Handover.

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*+'+,-./-0,1)

2-3)

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'()*)+,-./,0123

4-50,.,.6

3)4-3,.6

!% !$ !&!7!

"8

!% !$ !&!

45!7

49'..)1:"

49'..)1:#

49'..)1:%

;)1'<

(c) Two hops.

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0.1-2)*3.4)

!# !" !$!% !&

!% !$ !' !&!

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56'//)2*"

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56'//)2*8

9)2':*"

9)2':*#

*+,-,./012/3456

5.;1-/-/<

4)5.4-/<

(d) Three hops.

Figure 4.5: Cooperative transmission of coded blocks is possible when the opportunity

of multi-path transmission arises in both handover and multi-hop modes of WiMAX.


operative transmission should be employed for the uplink due to mobile node’s limited

battery power. In the downlink, each upstream node uses different coefficient matrix

to generate coded blocks and transmits generated coded blocks with different radio re-

sources. However, in the uplink, the mobile node multicasts coded blocks to different

upstream nodes. Due to different position and fading environment of different upstream

nodes, the received data experience different fading.

In addition, cooperative transmission also works well in the multi-hop mode of WiMAX

when relays are enabled. When the mobile node moves into an overlapped region covered

by both an upstream node and a relay, the sender, receiver and relay are connected to

one another via different sub-channels, where transmissions suffer little from interference.

Having more than one single wireless hop, the multi-hop mode also creates an opportunity

for multi-path transmission. The intuition is shown in Fig. 4.5(c), where the base station

serves as the sender by issuing A1, · · · , A5 directly to the mobile node and A6, · · · , A10

to the relay, which will forward the data to the mobile node. By collecting the data from

both paths concurrently, the mobile node tries to recover the original packet by decoding

the “clean” coded blocks it receives. Moreover, cooperative transmission can be easily

applied to more complicated topologies as shown in Fig. 4.5(d). Drizzle aims to take

advantage of both random network coding and the convenience of multiple channels, and

exploit the benefits of cooperation in multi-path transmission, that leads to the efficient

use of available channel bandwidth.

In the overlap serving area in the multi-path transmission scenarios shown in Fig. 4.5,

one mobile station can have multiple connections with upstream nodes. Concurrent trans-

missions can be applied and will help to increase the throughput performance, as there

are always data in the backlog for transmission. Thus, one issue we may be concerned

with is the amount of data each sender pushes to the receiver. We observe that different

channels experience different qualities, and sometimes the difference is quite significant.

Drizzle takes advantage of such channel diversity and efficiently transmits the data. At


the same time, Drizzle should provide fairness in resource allocation among users. Asking

only one sender with the best channel quality to transmit all the required data may cause

the problem of starvation of some other users due to limited resources.

With the multi-path transmission, we propose the following scheme to determine

the amount of data each sender transmits. Drizzle adopts a modified proportional rate

constraint algorithm [62,63,73]. Assume that the channel Signal to Noise Ratio (SNR) is

perfectly estimated. Denote the channel qualities of q channels, serving the same receiver,

as SNR1, · · · , SNRq. The number of coded blocks that need to be transmitted is denoted

as NR. The total number of coded blocks transmitted by each sender is denoted by Ni

(i ∈ {1, · · · , q}), i.e., Ni = dN ′ie where N ′

i is computed as follows:

N ′1

β1

=N ′

2

β2

= · · · =N ′

q

βq

NR =

q∑i=1

N ′i βk =

SNRkq∑

m=1

SNRm

q∑j=1

βj = 1.

We round up N ′i into integer values if N ′

i are fractional numbers. Though this al-

gorithm might require transmitting a few more blocks, Drizzle uses substantially less

wireless resources for error correction as compared to HARQ and SOFT. The trans-

mission of each sender is coordinated by either the access gateway or the base station,

depending on the transmission scenarios (single link transmission, handover, or multi-hop

transmission).

To show the benefits of Drizzle in cooperative transmission, we evaluate Drizzle using

simulations in the handover scenario of WiMAX, against both HARQ and SOFT [74].

A mobile node moves across the handover region, from point A to point B in Fig. 4.6,

with a constant speed. We measured the throughput on both downlink and uplink

in our simulations. The results are shown in Fig. 4.7, where it is evident that Drizzle

outperforms both HARQ and SOFT. On the downlink, Drizzle has an average throughput

gain over HARQ and SOFT of 52% and 154%, respectively. On the uplink, this margin


A

B

Region where handover is not needed

Handover region

Figure 4.6: Simulating a WiMAX handover event when an MS moves across the handover

region with a constant speed.

0 10 20 30 40 50 60 70 800

200

400

600

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT

(a) Downlink throughput

0 10 20 30 40 50 60 70 800

100

200

300

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT

(b) Uplink throughput

Figure 4.7: The throughput performance of Drizzle over time (80 seconds) in the han-

dover scenario, as a mobile station is moving around in the handover region randomly.

Simulations are performed with the settings provided in Sec. 4.4.


of improvement could reach 26% and 82%. Such substantial improvements coincide

with our intuition that cooperative transmission in Drizzle naturally takes advantage of

cooperative diversity in multi-path transmissions. We will examine the benefits of Drizzle

in more practical multi-path transmission scenarios in Sec. 4.4.

4.1.4 Differences from MIXIT

Specifically, we would like to state the differences between Drizzle and MIXIT [44] which

is also a protocol that performs random network coding across correct symbols in different

packets in the physical layer, with a brief description in Sec. 2.2.2. Our work is inspired

by MIXIT, but differs from it in a number of aspects.

First, MIXIT heavily relies on opportunistic listening and routing properties in multi-

hop 802.11 networks, and can not be effectively applied to multi-channel wireless net-

works. While, Drizzle is tightly designed for practical multi-channel wireless networks

(e.g., OFDMA based WiMAX), while providing flexibility to be applicable to other types

of wireless networks. With the design of Drizzle, we provide the answer to the question

on whether network coding would provide additional improvements in WiMAX, which is

particularly interesting since MRNC is proposed to effectively work at the MAC layer of

WiMAX and HARQ is readily used in these physical layer protocols. Second, we jointly

employ random network coding and soft decision values in Drizzle. With such a proposed

mechanism, random network coding is performed across the symbols within one packet

rather than over different packets as performed in MIXIT. Thus, the fine error control

granularity of soft decision values and the favorable rateless property of random network

coding can be both fully exploited, and are helpful to improve the performance signifi-

cantly in WiMAX. Third, MIXIT generates a large amount of overhead and is not able

to provide flexibility on feedback based on-demand retransmission due to the bounded

MRD code rates. Drizzle can be implemented with low communication costs. It employs

new techniques including inner-packet coding, pre-generated coefficient matrix, and dy-


namic retransmission, with which signaling overhead and unnecessary redundant data

transmission can be largely mitigated. According to our estimate, Drizzle is akin to a

“free lunch” with respect to the computation and communication overhead with currently

available technologies. We will elaborate the overhead analysis with the comparison of

Drizzle and MIXIT in Sec. 4.3.3.

4.2 Impact of Soft Decision Values

Soft decision values conveyed from the demodulation process in the physical layer (im-

plemented in physical chips in the real systems [28]) are used in Drizzle to detect errors

in coded blocks. As described in Sec. 4.1, we use confidence level of each coded block on

the receiver to detect errors. Is the confidence level able to fully capture the correctness

of the block? Why do we use normalized soft decision values to calculate the confidence

levels? How to take full advantage of these soft decision values in Drizzle? In this section,

we present the design and the use of soft values, serving as important cornerstones in

Drizzle.

4.2.1 Are Soft Values Accurate?

Current modulation schemes in the physical layer compute the soft decision values (SVs)

of all bits, which show the confidence of demodulation in order to make 0-1 decisions. A

bit with a negative SV is translated into 1, whereas a bit with a positive SV is translated

into 0. A larger absolute value in the SVs indicates a higher level of confidence on the

decision being made.

Unfortunately, the distribution of SVs varies depending on modulation schemes and

channel conditions. To further understand this point, we carried out a simulation. In

the simulation, a packet of 25K bytes is transmitted over Rayleigh fading channels with

a 30 km/h moving speed, and under different channel conditions. SV distributions of all


−20 −10 0 10 200

0.002

0.004

0.006

0.008

0.01

0.012

Soft Decision Value

PDF

0dB20dB

(a) SV distribution of all bits

−20 −10 0 10 200

0.05

0.1

0.15

0.2

0.25

Soft Decision Value

PDF

0dB20dB

(b) SV distribution of bad bits

Figure 4.8: The distribution of soft decision values under BPSK modulation, which

is obtained by transmitting 200,000 bits over Rayleigh fading channel with a speed of

30km/h.

received bits and error bits are shown in Fig. 4.8. As the figure shows, the SV distribution

is different as the channel quality changes. For example, if we receive a bit with SV

of -5 under the SNR of 0dB, there is still some probability that this bit is erroneous

according to the SV distribution for error bits. However, the bit with SV of -5 is 100%

“clean” under the SNR of 20dB. Also, different modulation schemes generate different

SV distributions. Thus, it is not accurate to quantitatively measure the confidence levels

without considering the impact of channel conditions and modulation schemes.

Intuitively, normalizing the soft decision values by considering different signal qualities

and modulation schemes is a good solution to this problem. In Drizzle, soft decision values

are normalized with the following formula:

NSV (s, SNR, M) =s

|s|

∫ |s|

−|s|d(s, SNR, M)ds (4.2)

where NSV denotes the normalized SV, d(s, SNR, M) denotes the probability density

function (PDF) for SV under a certain SNR and modulation (M), and s denotes the

SV variable. For example, NSV (−10, 0dB, BPSK) = −96.3%. The normalized SVs

are essentially a cumulative fraction of the absolute SV, since the SV distribution is


symmetric with respect to 0. After normalization, the range of SV resides in [−1, 1].

It is straightforward that larger absolute values of the normalized SVs indicate higher

confidence levels on the correctness of demodulation.

SV distributions under different channel qualities and modulation schemes are ob-

tained from a large number of simulations. Normalized SVs are able to reflect relative

characteristics of SVs, as they are tightly integrated with fluctuating channels and the

adaptive modulation scheme adopted in the physical layer of WiMAX. SVs in the re-

mainder of the chapter are normalized values if not noted otherwise.

4.2.2 How to Use Soft Values for Error Detection?

In Drizzle, soft decision values have two main functions. First, they are used to construct

the set of coded blocks used for decoding. To determine the confidence level of a coded

block, Drizzle uses the absolute value of the normalized SV of each bit, and then computes

the average of all bits in the coded block. A smaller average represents a lower confidence

level that the block is correct, whereas a larger average shows a higher confidence level.

As we have shown, blocks with higher confidence levels will be given higher priorities to

be included in the set of blocks for decoding.

Unfortunately, confidence levels of coded blocks directly computed from the average

may not be sufficiently accurate, since very often there exists a large variance on the

absolute SVs of bits within one block (a block contains a small number of bits). A few

bits with low absolute SVs may not effectively reduce the confidence level of the entire

block, provided that there are much higher absolute SVs on some of the bits in the

block. As such, it is necessary to penalize the blocks with one or a few “dirty” bits with

low absolute SVs. The existence of even one block that is not correctly received will

contaminate the entire decoding process.

In Drizzle, we check the SVs for all bits in a block. If any of the bits has an absolute

SV that is below a certain threshold, we will set the confidence level of the entire block


to the absolute SV with the lowest value. In this way, priorities of blocks with just a

few error bits will be reduced, which provides a more accurate measure with respect to

the confidence level of each coded block. It is important to set such a threshold in order

to rule out the blocks with a small number of “bad” bits. We refer this threshold as

SV-threshold.

It is non-trivial to make the selection of SV-threshold value. If a SV-threshold is se-

lected too aggressively (overly high), the priorities of “clean” blocks would be incorrectly

reduced. On the other hand, if it is set to be too low, it would not be sufficiently powerful

to detect blocks that are received in error. In order to study the optimal SV-threshold

that achieves maximized throughput performance, we evaluate the impact of the selec-

tion of SV-threshold via simulations. Fig. 4.9 shows the performance of Drizzle with

different SV-thresholds under different bit error rates of the wireless channel. We use 4

different SV-thresholds to check how SV-threshold selection affects the performance. As

shown in the figure, choosing a threshold as 27.5% gives the best performance among

the four choices we have simulated. When higher thresholds are used (such as 52.5%, or

77.5%), the throughput is reduced, which indicates that overly aggressive screening may

incorrectly reduce the priorities of “clean” blocks. On the other hand, we observe that a

threshold that is too low (such as 2.5%) also negatively affects throughput performance,

as “dirty” blocks remain in the set used for decoding. This observation shows that we

should carefully tune the SV-threshold. Heuristically, 22% is used in Drizzle based on a

large number of simulations that we have performed.

The second function of soft decision values in Drizzle is to count the number of “dirty”

blocks in the set used for decoding. When the decoding fails after each transmission, the

receiver will count the number of “dirty” blocks in the decoding set, and ask the sender

to transmit the same number of additional coded blocks. This number will determine

the number of blocks retransmitted, and will directly affect the performance of Drizzle.

As such, a threshold must be set in Drizzle (referred to as level-threshold), so that blocks


0.02 0.04 0.06 0.08 0.1 0.12 0.140

200

400

600

Bit Error Rate

Thro

ughp

ut (K

bps)

77.5% 52.5% 27.5% 2.5%0.76dB

1.50dB2.81dB

2.02dB

Figure 4.9: The selection of SV-thresholds affects the performance of Drizzle. The per-

formance of Drizzle under 4 different SV-thresholds, 77.5%, 52.5%, 27.5%, and 2.5%,

is evaluated to show the importance of SV-threshold selection. Values in dB are the

gains that the best case outperforms the worst case in the simulation. Simulations are

performed with the settings provided in Sec. 4.4.

with confidence levels lower than this threshold will be counted as “dirty” ones.

It is a tradeoff to set the value of level-threshold. If a high level-threshold is selected,

correctly received blocks could be counted as error blocks and extra retransmissions will

be requested, which will consume more bandwidth. Since more redundant retransmission

blocks are transmitted, it is with a higher possibility to correctly recover the packet in

the receiver at the next retransmission (a small number of retransmissions). On the

other hand, if a low level-threshold is selected, error blocks could not be detected. It will

also cause extra retransmission for error correction after the failure of network decoding

(large number of retransmissions). In this case, whereas barely required blocks are re-

transmitted, more retransmission requests are required, which cause delays.

Drizzle is designed to be able to adjust the level-threshold depending on specific

requirements of the applications. If the application is delay sensitive (such as voice), the

level-threshold should be set to be high in order to conservatively request more coded

blocks at the following transmission. Otherwise, if the application requires a higher


0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.1450

100

150

200

250

300

Bit Error Rate

Thro

ughp

ut (K

bps)

12% Level Threshold75% Level Threshold

(a) Throughput

0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.148

10

12

14

16

Bit Error Rate

Dela

y (m

sec)

12% Level Threshold75% Level Threshold

(b) Delay

Figure 4.10: The level-threshold affects the delay and throughput performance in Drizzle.

A higher level-threshold is helpful to achieve higher throughput, but with a larger delay.

On the contrary, a lower level-threshold leads to lower throughput, but with smaller

delays. Simulations are performed with the settings provided in Sec. 4.4.


throughput, the level-threshold could be set to be lower, to request a barely sufficient

number of additional coded blocks, so that available bandwidth can be most efficiently

used. Fig. 4.10 shows the delay and throughput tradeoff of two different level-thresholds,

with the values of 12% and 75% are used in this simulation. A level-threshold of 12%

shows 14% higher throughput on average, whereas a level-threshold of 75% is 39% better

with respect to delays on average.

Theoretically, SV-threshold and level-threshold can be dynamically adjusted to adapt

to the network environment, including channel quality, mobility, and the transmission

mode. Another potential solution for threshold selection can be obtained by historical

data learning. In our future work, we will further study the optimal thresholds for Drizzle

using learning techniques.

4.2.3 How Do Soft Values Work in Cooperative Transmission?

By applying normalized SV and adaptive threshold described above, Drizzle is able to

check the correctness of each coded block it collects, no matter where the block comes

from and which modulation scheme is used on it. Normalized SV and adaptive threshold

techniques in Drizzle are essentially a way to perform link adaptation by tightly inte-

grating with the adaptive modulation scheme adopted in the physical layer of WiMAX.

They are especially helpful to achieve cooperative transmission in Drizzle as described in

Sec. 4.1.3. Although, in the multi-path transmissions, different senders may use different

modulation schemes to transmit coded blocks to the same receiver, as channel conditions

are different on each path (adaptive modulation is applied), the receiver could check the

correctness of all the blocks effectively by applying normalized SV and adaptive threshold.

Drizzle makes it possible for the receivers to correctly select clean blocks and decode the

original packets successfully.

We perform simulations to examine the effectiveness of Drizzle in such a multi-path

transmission scenario. In the simulation, two upstream nodes serve as senders and trans-


mit data to the same receiver via two separate sub-channels, and QPSK and 16QAM

are used on each path respectively. By applying adaptive modulation, the modulation

schemes are determined to meet the target Bit Error Rate (BER) based on the estimated

SNR. For example, if the target BER is 10−3, 16QAM is used at a SNR of 8dB and

64QAM is used at a SNR of 12dB. Now, we set the modulation schemes as QPSK and

16QAM in the simulation. Then, we calculate the SNRs on each channel according to

the target BERs (by adopting the solution in [28]). By varying the target BERs, we

examined the downlink throughput at the receiver under different channel conditions

(with different SNRs). Fig. 4.11 shows the simulation results, where a 3.24dB gain can

be achieved on average by applying normalized SV and adaptive threshold. This shows a

significant benefit when link adaptation in Drizzle is applied.

10−5 10−4 10−3 10−20

100

200

300

400

500

Bit Error Rate

Thro

ughp

ut(K

bps)

with SV normalizationand adaptationwithout SV normalizationand adaptation

Figure 4.11: A comparison of Drizzle’s performance with and without SV normalization

and adaptation in a cooperative transmission scenario. Two nodes are sending coded

blocks to one receiver using different modulation schemes (QPSK and 16QAM are used on

each sender respectively). The transmission is under different channel qualities (SNRs),

which are generated by varying the target BERs in a certain range. Simulations are

performed with the settings provided in Sec. 4.4.


4.3 Implementation Issues

As Drizzle uses network coding at its core, we are aware of a few implementation issues

that, if not appropriately addressed, may affect the performance.

4.3.1 Choosing the Size for Coded Blocks

As we have shown, each packet is divided into a number of blocks, on which random

network coding is performed. At a glance, it may appear that a smaller block is always

preferable, as a smaller block lead to less overhead when retransmissions are made, and

more accurate confidence levels as the normalized SVs of bits are averaged.

Unfortunately, a block that is too small will lead to an inherent problem that is hard

to address. A block with m bits has to use at least GF(2m) to perform random network

coding, and a smaller number of bits in a block leads to a smaller size of the Galois

Field with a smaller degree of freedom when coefficient vectors are randomly chosen.

This leads to a higher probability of producing linearly dependent blocks with random

network coding.

It is therefore important to choose an appropriate size for coded blocks, so that a block

is sufficiently small, but supports a sufficient degree of freedom to generate randomized

coefficient vectors that are linearly independent of one another.

In order to show the effect of different block sizes to the packet delivery rate, we

consider a packet with a size of 512 bits which is divided into 128, 64, 32 blocks for

m = 4, 8, 16, respectively. Block error rates and packet delivery rates are shown in

Fig. 4.12. We can clearly see that as the block size increases, the block error rate also

increases. However, due to the high decoding error probability with small block sizes, its

packet delivery rate, which is a ratio of the number of error-free packets over the total

transmitted packets, suffers from poor performance.

Considering the tradeoff between the block error rate and the decoding error proba-


bility generated by blocks with different sizes, we select 8 bits as the best tradeoff. Thus,

we adopt GF(28) to perform random network coding. In this case, a block may contain

multiple symbols when a symbol is smaller than 8 bits. For example, a block contains 4

symbols with QPSK modulation, where a symbol has 2 bits. In 16QAM modulation, a

block includes 2 symbols. Our simulation results shown in Sec. 4.4 have further verified

the effectiveness of our choice of the block size.

4.3.2 Reducing the Overhead of Carrying Coefficients

In Drizzle, it is important to reduce the overhead of communicating random coefficients

from the sender to the receiver for each coded block. Since the size of the block is

small, the number of blocks in a packet will be large (64 blocks in a 512-bit packet, for

example) with a large number of corresponding coefficients. Regardless of how we carry

these coefficients, the overhead over wireless channels will be prohibitive.

Our solution is to avoid the communication of coefficients between the receivers and

senders. In Drizzle, the random coefficient matrix is pre-generated and kept at both

the senders and the receivers. In WiMAX, each sender-receiver pair needs to negotiate

parameters such as modulation, coding, and transmission power, before the actual data

transmission. In Drizzle, the sender transmits the index of the pre-generated random

coefficients matrix that is used for encoding to the receiver, as a part of the session control

information (in HARQ, the session number is also communicated as a part of the session

control information). In order to reduce the overhead of storing different coefficient

matrices for different batch sizes and different maximum number of retransmission blocks,

only one coefficient matrix with a minimum sufficient size is stored and used for encoding

and decoding. Let us denote the maximum batch size as N , the maximum number of

retransmission blocks as D, and the maximum number of cooperating upstream nodes

as C. Then the dimension of the stored matrix is N ×M , where M = N + D × C. To

guarantee successful decoding, any N ×N sub-matrix is produced to be nonsingular.


0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

SNR (dB)

Bloc

k Er

ror R

ate

4 bits8 bits16 bits

(a) Block Error Rate

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.2

0.4

0.6

0.8

1

Bit Error Rate

Pack

et D

elive

ry R

ate

4 bits 8 bits16 bits4.5dB

3.6dB

3.4dB

(b) Packet Delivery Rate

Figure 4.12: The selection of block sizes impacts the performance of Drizzle. (a) The

performance of block error rates under 3 different block sizes: 4 bits, 8 bits and 16 bits.

(b) The performance of packet delivery rates (K = 2n) under a Rayleigh fading channel.

Simulations are performed with the settings provided in Sec. 4.4.


How can the reliability of index negotiation be ensured? Wireless systems like WiMAX

and 3GPP employ a reliable management/control message transmission mechanism. Ses-

sion control information is conveyed using management/control messages, which are pro-

tected by the modulation and coding scheme (MCS) level, which is more robust than

regular data burst transmission, or reliable error control schemes using HARQ or MAC

level ARQ. The Multiple-input and multiple-output (MIMO) antenna scheme and low

density parity check (LDPC) codes use the same concept to transmit the index for pre-

coding matrix and matrix H, respectively, which are pre-generated and kept in the trans-

mitters and receivers. Therefore, the coefficient index can be effectively protected and

guaranteed to be successfully distributed to both receivers and senders.

Upon receiving such an index, the receiver has full knowledge of all coefficient vectors

used in future coded blocks from the sender, by looking up the pre-generated matrix. It

is also possible to use a seed of a pseudo-random number generator instead of the index

to specify a future sequence of coefficient vectors to be used by the sender.

4.3.3 Computational Complexity and Protocol Overhead

As neither base stations nor relay stations have constraints with respect to the energy

and computational power, we are only concerned with the computation overhead at

mobile stations. Modern mobile devices, such as smartphones, have abundant memory

and computational power. According to the results in [65], random network coding is

almost “free” with modern mobile processors. The coding speed could reach 1248 Mbps

for 16 blocks of 32 KB each and 348 Mbps for 64 blocks of 32 KB each. As our block

size is as small as a few bits, encoding and decoding are even much faster. Although

it indeed incurs additional computation to some extent, it keeps the overhead within

practical limits.

Specifically, Drizzle has a much smaller overhead compared with MIXIT [44]. In

MIXIT, blocks are coded across packets and only on the correct symbols. Thus, the


header has to include several runs of random coefficients, which generates a large amount

of overhead. Assume that the packet size is 1500 bytes (a typical size in IEEE 802.11

networks) and the batch size is 32 (typical number), with 4 runs. For each coded block, a

8.5% overhead is incurred, which is rather substantial. Usually, with 400 symbols, there

are dozens of runs at the least, regardless of dynamic programming schemes used in

MIXIT. Assume that there are 20 runs, leading to a completely unacceptable overhead

of 42%. Moreover, if the header is not correctly received, the decoding can not be

performed (with most of the packets discarded). In contrast, Drizzle adopts a totally

different approach by using a pre-defined codebook, which is only transmitted to the

receivers once. There is no header overhead when coded blocks are transmitted.

Another problem in MIXIT is that the feedback (ACK/NACK) has to be reported to

the sender via multiple hops through a shared channel, which may generate large delays,

especially when the number of hops is large and the batch size is small. In Drizzle, the

feedback information are transmitted via separate channels (control channels). Thus, the

feedback messages are transmitted in parallel with the data, which do not generate any

delay at all.


We are now ready to resort to extensive simulations to study Drizzle’s performance.

For this purpose, we take advantage of the latest communication toolbox in MATLAB

for simulation implementation. MATLAB is efficient for evaluating the performance

of physical-layer protocols, and it is well designed to simulate physical layer designs in

multi-channel wireless networks with fading channel characteristics, modulation, and soft

decision values. To be realistic, we evaluate Drizzle’s performance in WiMAX networks,

where the practical settings of a real-world WiMAX network configuration are adopted.


4.4.1 Simulation Settings

Similar to the simulation evaluation in Chapter 3, in this chapter, WiMAX networks

are simulated according to typical parameters defined in the IEEE 802.16 standard [9]

and WiMAX system evaluation methodology released by WiMAX forum [8]. The sim-

ulation parameter settings according to these two documents are listed in Table 4.4.1.

In particular, we have used mobility patterns that reflect realistic parameter settings

in a practical wireless environment. To evaluate the performance, we compare Drizzle

with HARQ, and SOFT from previous work [74] proposed in the setting of IEEE 802.11

networks. With respect to HARQ, we adopt the type-II HARQ which performs Packet

Soft Combining in transmissions and employs Viterbi Soft Decision Decoding using soft

decision values. In the multi-path transmission scenarios, maximal ratio combining is

performed in HARQ. With respect to SOFT, we have simulated the protocol to the best

of our knowledge according to all the available details presented in [74]. We focus on

three typical communication scenarios of WiMAX: single-link transmissions, handovers

and multi-hop transmissions on both uplink and downlink.

4.4.2 Single-link Transmission

As a starting point, we first evaluate the performance of Drizzle in a basic, single-link

transmission scenario. We perform the simulation that all three protocols are used to

transfer a large file between a base station (BS) and a mobile station (MS) in the down-

link. In this experiment, we are interested in two performance metrics: the packet

delivery rate (calculated as the fraction of transmitted packets that are correctly deliv-

ered to the receiver), and the throughput. Fig. 4.13 shows a performance comparison

among Drizzle, HARQ and SOFT under various BERs. The performance with respect to

packet delivery rates is shown in Fig. 4.13(a), and Fig. 4.13(b) shows the corresponding

throughput for all three protocols. From the results, we could easily observe that Driz-


Table 4.1: Simulation parameters for evaluating Drizzle.

Channel Type Rayleigh fading channel and AWGN

Path loss Model COST-HATA-231a

Sampling time 0.1 second

Transmitter Power (Base Station) 25 dBm

Transmitter Power (Mobile Station) 20 dBm

Noise Power -129.5 dBW

Packet Size 512 bits

Number of Blocks in a segment 64

Adaptive Modulation used

OFDMA used

aThe extended HATA model to 2GHz by the European Cooperative for Scientific and Technical

(COST) research.

zle’s packet delivery rate (average: 0.99) is higher than both HARQ (average: 0.97) and

SOFT (average: 0.91) by 1.89% and 9.14% respectively. The performance gain becomes

more substantial when throughput is considered. Drizzle outperforms HARQ and SOFT

by 33.6% and 55.8%, respectively. This is because Drizzle is designed to tightly integrate

with the WiMAX physical layer for efficient bandwidth utilization. Due to the fact that

Drizzle utilizes scarce bandwidth very efficiently by transmitting a barely sufficient num-

ber of symbols to recover the error packet, as discussed in Sec. 4.1.2, a small performance

gain in packet delivery rate can result in a large throughput performance gain. These

improvements are supported by the efficient use of available wireless bandwidth, due to

adaptive retransmissions in Drizzle.

Although the observed performance improvement is quite encouraging under stable

channel conditions, we focus more on the performance under realistic wireless environ-

ments with fluctuating channel conditions. To evaluate the performance of all three


0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.0650.75

0.8

0.85

0.9

0.95

1

Bit Error RatePa

cket

Del

ivery

Rat

e

Drizzle HARQ SOFT

(a) Packet Delivery Rate

0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065100

200

300

400

500

Bit Error Rate

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT

(b) Throughput

Figure 4.13: Packet Delivery Rate and Throughput with a range of BERs.

protocols, we run the simulation under the same mobility simulation scenarios as in

Sec. 3.3. One MS moves around the service area of a cell randomly. Its initial speed (in

km/h) and direction (in degrees) are generated with a uniform distribution of U [10, 80]

and U [0, 360], respectively. The MS will change its speed and direction after a certain

amount of time with an exponential distribution, with a mean value of 10 seconds. The

new speed is uniformly generated with U [10, 80] if the current speed is below 10 km/h;

otherwise, it is obtained using U [v − 10, v + 10], where v is the current speed. The new

direction is obtained from a Gaussian distribution with the mean as the current direction,

and a standard deviation of 40 degrees. The initial location of MS is randomly chosen

in the service region. The design of this simulation scenario aims to provide realistic

time-varying channel conditions. Moreover, we apply multi-path Rayleigh fading in the

transmission, since the MS keeps on moving.


0 10 20 30 40 50 60 70 80 90 100200

300

400

500

600

Time (Second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT

Figure 4.14: Throughput in a single, time-varying wireless link with mobility.

Fig. 4.14 shows the downlink throughput performance of all three protocols. We

observe from the results that Drizzle’s throughput (average: 485.95 Kbps) performs

substantially better than both HARQ (average: 381.27 Kbps) and SOFT (average: 336.95

Kbps). This observation coincides with our intuition and is not a surprise: it shows

Drizzle’s ability to adaptively match its transmissions to the available bandwidth in

time-varying channels, which helps in maintaining higher throughput.

4.4.3 Handover

We next try to identify the potential performance gain offered by cooperative transmis-

sions in Drizzle in the WiMAX handover scenario, as compared to HARQ and SOFT.

Our evaluation is performed under the same scenarios as in Sec. 3.3. A total of 19

BSs are deployed in the service area. The cell sites are laid out as shown in Fig. 3.4,

in which the MS is allowed to move around in the service area as the same fashion in

the single-link case. At the handover region, the MS is able to enjoy the multi-path

communication and perform cooperative transmission. Fig. 4.15 shows both uplink and

downlink throughput at the destination for all protocols from 1000-second simulations.

The average throughput results are: 505 Kbps (downlink) and 352 Kbps (uplink) for

Drizzle, 351 Kbps (downlink) and 303 Kbps (uplink) for HARQ, 259 Kbps (downlink)

and 237 Kbps (uplink) for SOFT. In this scenario, the improvement with Drizzle reaches


0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT


0 100 200 300 400 500 600 700 800 900 1000100

200

300

400

500

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT


Figure 4.15: Throughput comparison in the WiMAX handover scenario.

44% and 95% over HARQ and SOFT, respectively, on downlink transmissions. At the

same time, Drizzle outperforms HARQ and SOFT by 38% and 50% on the uplink. Such

a throughput advantage should be considered substantial by any standard.

With the objective of becoming even more realistic, we seek to extend our performance

evaluation to a large scale scenario. In the cellular system described previously, we set

a large number of MSs active in the service region concurrently. The arrival process of

new MS connections in each cell is assumed to be a Poisson process with a mean of 5

connections/cell/second. The MS active time duration is exponentially distributed with

a mean of 100 seconds. Every active MS is moving around the service area using the

same way as the previous simulation. We run the simulation for 1000 seconds, and the

downlink throughput at the MSs is examined. From the results, there are a total of

95,010 MSs that have ever been active in the service area during the simulation time,


0 20 40 600

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cumu

lative

Fra

ction

of M

Ss

DrizzleHARQSOFT

(a) Downlink

0 10 20 30 400

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

DrizzleHARQSOFT

(b) Uplink

Figure 4.16: Throughput performance in a large-scale handover scenario.

with 460 MSs active simultaneously in each cell on average. Fig. 4.16 plots the CDF

of the average throughput for both uplink and downlink transmissions, considering all

active MSs in the simulation. Not surprisingly, Drizzle outperforms HARQ and SOFT

by 50% and 100% respectively on the downlink with respect to the average throughput,

due to its effective use of bandwidth and the advantages of random network coding in

cooperative transmission. Further, Drizzle beats HARQ and SOFT by 56% and 62%

respectively on uplink transmissions.


Finally, we illustrate the performance advantage of Drizzle, generated by both adaptive

retransmission and cooperative transmission, in a WiMAX multi-hop transmission sce-

nario. In order to extend the coverage area of a cell, relay stations (RSs) are placed

within the border of the radio ranges of BSs. The simulation scenario is the same as

in Sec. 3.3 and shown in Fig. 3.7, where a relatively large multi-hop network is con-

sidered. A similar evaluation is performed with the same setting as our simulation in

the first handover case, where an MS randomly moves around and performs adaptive

retransmission and cooperative transmission as long as such opportunities are explored.


0 100 200 300 400 500 600 700 800 900 10000

200

400

600

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT


0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

Time (second)

Thro

ughp

ut (K

bps)

Drizzle HARQ SOFT


Figure 4.17: Throughput in a realistic multi-hop case.

As shown in Fig. 4.17, we observe from the results that Drizzle obtains 32% and 77%

average throughput improvement over HARQ and SOFT respectively on the downlink.

The performance gains reach to 56% and 85% on the uplink. This demonstrates the

ability of Drizzle to fully utilize available wireless spectrum in the multi-hop case.

Finally, we consider the case of a large-scale multi-hop network, with the same sim-

ulation setup as in the large-scale handover scenario. The maximum number of hops is

limited to be 3. Fig. 4.18 presents the CDF of the throughput from 1000-second simula-

tions. As expected, Drizzle outperforms HARQ and SOFT, and again by a substantial

margin. In particular, Drizzle achieves a 80% higher throughput on average over HARQ,

as well as a 1.8x gain over SOFT in the downlink. Further, Drizzle performs better than

HARQ and SOFT by 62% and 100%, respectively, in uplink transmissions. This confirms

and highlights the benefits achieved by Drizzle in the multi-hop scenario, which is one of


0 20 40 600

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

DrizzleHARQSOFT

(a) Downlink

0 20 40 60 800

0.2

0.4

0.6

0.8

1

Throughput (Kbps)

Cum

ulat

ive F

ract

ion

of M

Ss

DrizzleHARQSOFT

(b) Uplink

Figure 4.18: Throughput performance in a large-scale multi-hop scenario.

its design objectives.

4.5 Summary

In this chapter, we have explored the use of network coding in the physical layer of

multi-channel WiMAX, where it is challenging to effectively perform error control with

transient bit errors. The highlight of this chapter is our conclusion that, when network

coding is used at the symbol level, Drizzle is able to provide high and resilient throughput

in WiMAX by outperforming HARQ (not to mention existing work in 802.11-based

networks) and other state-of-the-art protocols in the literature.

The intuition that Drizzle improves WiMAX performance is quite simple to narrate:

as its name implies, Drizzle allows the sender to retransmit a barely sufficient number

of symbols that have not been successfully received at the receiver, and the receiver is

able to hold the “bucket” until it is full of coded blocks, as if they are very fine “rain

drops.” Even better, the receiver can receive these blocks from more than one sender, with

perfect collaboration across different senders, as multi-channel wireless networks create a

large number of opportunities on multi-path transmissions. Since these “rain drops” are

sufficiently small, there would be minimal waste of wireless bandwidth provided by the


physical layer. As our extensive simulation results have shown, there is no surprise in our

intuition: Drizzle is able to outperform both HARQ and related work in the literature

by a substantial margin.

Chapter 5

Cooperative Multicast Scheduling

with Network Coding in WiMAX

In this chapter, we shifted our study from the fundamental communication protocols to

the networking services in WiMAX, and first investigate multicast scheduling which is

important to the quality of services in WiMAX. Data and video multicasting has become

an extremely important service/application in WiMAX through Multicast and Broadcast

Service (MBS) system. With the current mandate of MBS, the Base Station broadcasts or

multicasts data in the downlink using robust modulation and coding schemes to provide

reliable transmissions for all the users, as individual feedback (such as ARQ and HARQ) is

not supported in MBS. However, such a dependence on using the most robust modulation

apparently under-utilizes the scarce wireless bandwidth. The main difficulty of multicast

scheduling is caused by the diverse channel conditions of users in the multicast session.

How to properly select a multicast rate in WiMAX MBS? Our research on multicast

scheduling is from a perspective by considering the use of multiple ODFMA channels,

multiple hops, multiple paths, and random network coding simultaneously. The highlight

of our contributions is a multicast scheduling framework that exploits potential benefits

made possible by cooperative communication in the realistic context of MBS in WiMAX.

80

Chapter 5. Cooperative Multicast Scheduling with Network Coding in WiMAX81

The framework is formulated as a set of optimization problems, by jointly considering

relay assignment, channel allocation and power control, which are very critical for efficient

cooperative communication. Both theoretical and practical solutions are provided, and

then evaluated in extensive simulations. Corroborating our intuition, our protocols are

able to improve multicast throughput substantially. With the support of effective MBS,

WiMAX improves its performance.

5.1 Problem Formulation

In the network, the Base Station (BS) multicasts data and Mobile Stations (MSs) collect

the data in the downlink. According to the conventional multicast scheduling as shown

in Fig. 5.1(a), the BS has to multicast data using robust modulation and coding schemes

to ensure the reliable transmissions to all MSs. In the example in Fig. 5.1(a), we assume

the multicast rate is 5 packets per second. Thus, the total throughput at MS1 and MS2

is 10 packets per second. However, this reliability under-utilizes the wireless bandwidth,

as the MSs in good channel conditions (MS2 in this example) get data in a conservative

low rate.

For a given multicast session, different downlink users actually experience different

channel conditions, and the same channel experiences different gains on different trans-

mission links, especially when user mobility is considered. This diversity may become

a positive factor in multicast sessions, if we exploit its potential advantages by allowing

users to cooperatively contribute to each other as relays. Such cooperative communication

has been shown to improve throughput of multiple unicast sessions by simultaneously

exploring the broadcast nature of a shared wireless channel and the cooperation among

multiple users [54], but not fully explored and employed in multicast scheduling yet,

especially in WiMAX MBS.

As we stated in Chapter 3 and Chapter 4, the adoption of OFDMA in WiMAX


makes the use of multiple orthogonal sub-channels realistic, which allows for the ad-

ditional convenience of supporting concurrent transmissions via different sub-channels

without interference. However, multicast protocols that are currently proposed in MBS

are primitive in nature, as they fail to embrace this unique advantages of WiMAX, and

to take advantage of both channel and cooperative diversity to improve the multicast

performance.

In order to take advantage of all the benefits stated above and improve the per-

formance in MBS of WiMAX, we study multicast scheduling problem by considering

multiple hops, multiple paths, and multiple channels at the same time, rather than the

system models with a single shared channel. The potential protocols are able to dy-

namically assign multicast users as relays, and ask them to cooperatively transmit data

to other peers. The basic idea, explained intuitively, is that users with good channel

conditions can forward the received data to the remaining users who need help.

In this case, the Base Station may use a much higher rate to multicast data to all

users, leading to more efficient use of bandwidth. As shown in Fig. 5.1(b), the BS

multicasts data with 10 packets per second, with much higher rate than the conventional

multicast scheduling in Fig. 5.1(a). Under this rate, MS2 still reliably receives all the

packets due to its good channel condition, while MS1 only receives 70% as it is farther

from the BS. Taking advantage of relays which are enabled in WiMAX, we ask MS2

who is close to MS1 to cooperatively transmit data to it through a separate sub-channel,

aiming to compensate its loss. Via different paths, MS1 receives data simultaneously

from both BS and MS2 and is able to collect 10 packets per second. Benefited from

this cooperative communication, the total throughput on MS1 and MS2 dramatically

increases to 20 packets per second. To get more gains, the BS even can use higher

multicast rate. Although none of MSs is able to correctly receive all the data reliably

(In the example, MS5, MS6 and MS7 get data directly from BS by 90%, 50% and 80%

respectively), they could contribute to each other to achieve reliable transmissions with


MS1 MS2

MS3

MS5 MS6

MS7

BS

MS4

(a) Conventional multicast scheme

0.8

0.5

1

0.9

1

10.7

1

MS1

MS2

MS5

MS6MS7

MS4

MS3

BS

1

1

(b) Cooperative multicast scheme

Figure 5.1: Illustrative examples to show the advantages of cooperative multicast schedul-

ing with random network coding in WiMAX. The number on each link in (b) indicates

the packet delivery rate from the BS to the MS.

higher throughput, as shown in Fig. 5.1(b).

The bad news, however, is that it is challenging to schedule transmissions in a coop-

erative fashion. Relays do not have sufficient knowledge on which packets their neighbors

need. Blindly “pushing” packets that are not needed to other peers will incur a substan-

tial degree of overhead. To address this challenge, we again may take advantage of the

favorable rateless properties of random network coding. With random network coding, all

packets are encoded with random linear codes, and all coded data blocks could be consid-

ered equally useful and innovative. With the data fully mixed, relays can freely “push”

innovative blocks to their downlink multicast members. Without dictating which packet

is from which source, receivers only need to “hold” a “bucket” and collect a sufficient

amount of data from their upstream nodes. With the help of random network coding,

the overhead can be substantially mitigated in cooperative communication. The Base

Station only needs to multicast coded blocks in a rateless fashion, until all users are able

to reconstruct the original data by receiving a sufficient number of linearly independent


coded blocks, regardless of their channel conditions.

The design objective of multicast scheduling with cooperative communication and

random network coding in WiMAX is to realize all the potential benefits described in

these intuitive examples. To achieve such an objective, there are a number of practical

challenges:

B How to dynamically assign multicast users as relays and apply random network

coding in cooperative communication to tightly fit in the design of WiMAX MBS?

B How to optimally allocate channels for cooperative communication to obtain max-

imum benefits on multicast performance even with limited amount of bandwidth?

B How to efficiently allocate power for cooperative communication when the energy

on relays is highly constrained?

Our responses to these challenges constitute the flow of presentation in this chapter.

5.2 Multicast Scheduling Framework

We concentrate on the multicast scheduling in the time-slotted WiMAX MBS, where

the Base Station (BS) serves as the multicast sender and keeps on broadcasting a big

file, and the Mobile Stations (MSs) (also referred to as nodes) are the participating

users in multicast sessions. Throughout the chapter, we assume quasi-stationary channel

conditions: any node’s channel condition remains the same during a given time slot, and

it varies independently from one time slot to another. The channel quality information on

each link can be effectively estimated [61] and fully captured by the BS through Channel

State Information (CSI) messages exchanged between the BS and each MS periodically

in WiMAX [9]. The objective is to find the optimal multicast rate, as well as the most

efficient cooperative communication schedule, to maximize the aggregate throughput on

all users under a proportional fairness criteria which is able to strike a good balance


between utilization and fairness and its robustness with respect to changes in topology

and power constraints [67]. We perform scheduling at each time slot, thus the overall

performance will be optimized in the long term [67].

5.2.1 Optimizing Multicast Scheduling

The objective of the multicast scheduling can be stated as,

maxR(t)

∑i∈ζ

Ui(t)

ri(t)(5.1)

where R(t) denotes the multicast rate at time slot t. If modulation and coding scheme m

(index) is used, R(t) = Rm(t), where m ∈ {1, 2, · · · , 6}, as there are mainly six schemes

according to IEEE 802.16 standard [9]. ri(t) denotes the average throughput at node

i over time horizon [1, t], which is kept track at each node and reported to the BS. It

shows the consideration of proportional fairness on multicast users. ζ is the set of nodes

in MBS, and the total number is G.

Ui(t) is the throughput on node i at time slot t in Eq. (5.1), taking account for

the transmissions both from BS directly, and from cooperative communication. At the

starting point, we assume there is a channel pool with sufficient number of sub-channels,

and each link can be assigned one sub-channel for cooperative communication if there

exists such opportunities. We will study more complicated and realistic cases on channel

and power allocation for cooperative communication in the following sections. All nodes

work in the full-duplex mode and are equipped with multiple radios which support con-

current communication with multiple nodes in both downlink and uplink via separate

sub-channels. Random network coding is applied in the transmissions, with which all the

packets are considered to be fully random and linearly independent with high probability.

Thus, we calculate Ui(t) by,

Ui(t) = Sm,i(t)Rm(t) +∑g∈ζ

Rgi(t) (5.2)


Sm,i(t) ∈ [0, 1] is the packet deliver rate from the BS to node i when modulation and

coding scheme m is used at time slot t. Exact closed-form packet deliver rate under coded

modulations is not available, and we calculate it by using an accurate approximation for

packet error rate in [52]. Note we specifically denote the multicast rate at time slot t as

Rm(t) (m ∈ {1, · · · , 6}) to indicate that Sm,i(t) depends on the multicast rate selection.

Rgi(t) (∀g, i ∈ ζ) is the maximum transmission rate that can be achieved on the link

from node g to node i under certain channel conditions. It is subject to the following

constraints:

0 ≤ Rgi(t) ≤ Cgi(t) (5.3)

Rgi(t) ≤ max{0, Bg(t)−Bi(t)

T} (5.4)

(5.3) shows that the cooperative transmission rate is bounded by the capacity on the

link (denoted as Cgi(t)). At the same time, this rate is limited by the amount of innovative

data that node g is able to contribute to node i. As random network coding is employed,

a packet is innovative (or referred to as useful or new) if it is linearly independent from

the other packets from the same segment. Checking for independence can be done using

simple Gaussian Elimination. As we assume the packets are fully random and linearly

independent with high probability, we can use (5.4) to describe this constraint, where

Bg(t) denotes the amount of innovative data buffered at node g at time slot t, and Bi(t)

indicates the same information at node i. T is the duration of one time slot. It is easy

to get from this constraint: Rgi(t) = 0, if g = i.

Now we can see from Eq. (5.2) that Sm,i(t)Rm(t) represents the throughput from BS,

and∑

g∈ζ Rgi(t) describes the cooperative throughput. The total throughput Ui(t) is also

constrained as the total data that each node receives can not exceed the amount the BS


is able to provide,

Ui(t) ≤t∑

h=1

R(h)− Bi(t)

T⇒

∑g∈ζ

Rgi(t) ≤t−1∑h=1

R(h)− Bi(t)

T+ (1− Sm,i(t))Rm(t) (5.5)

Overall, the multicast scheduling can be formulated as the optimization problem with

the objective of (5.1), subject to (5.2) - (5.5). As there are six modulation and coding

schemes, we can solve it using exhaustive search for all six possible schemes to get the

optimal solution.

5.2.2 Protocol Design

We design the multicast scheduling protocol based on the optimization above and by

applying random network coding in the transmission. The BS holds all the original data,

and separates the data into segments. Random network coding is performed within the

segment as the same fashion of MRNC presented in Chapter 3. The BS multicasts the

coded blocks in a rateless fashion, using the rate determined by solving the optimization

problem we formulated above at each time slot. When a node receives a packet (coded

block), it checks whether it contains new information, and ignores non-innovative packets.

When performing cooperative communication, the node produces new coded blocks by

creating random linear combinations of the coded blocks it has correctly received from

the same segment and transmits them to its neighbors (the nodes within the sender’s

transmission range). Note the recoded blocks are still the linear combination of the

original data blocks.

All the nodes collect the data and perform decoding, with which the node is able to

recover the entire original segment immediately after sufficient number of independent

coded blocks have been received for a segment, and sends the ACK back to the BS. When

the BS receives the ACKs from all the nodes, it first multicasts a message to inform all


nodes that the transmission for current segment is finished, and then starts to proceed

the next segment. Upon receiving such message, all nodes flush the buffer and reset the

time slot index t = 0, and also start the cooperative transmission for the next segment

instead of the transmissions for the current segment.

5.2.3 Are Cooperative Communication and Random Network

Coding Helpful?

We now resort to extensive simulations to evaluate the usefulness of cooperative commu-

nication and random network coding. To be realistic, the simulations are performed by

emulating WiMAX MBS with typical parameters according to IEEE 802.16 standard [9]

and WiMAX system evaluation methodology released by WiMAX forum. The evaluation

is performed under the following scenario. The BS multicasts a large file to all MSs. To

provide realistic time-varying channel conditions, each MS is allowed to move randomly

in the service area of the BS, and its initial location is randomly chosen in the service

region. We apply multi-path Rayleigh fading in the transmission, since the MS keeps on

moving.

To evaluate the performance, we compare four multicast scheduling protocols: co-

operative multicast scheduling with random network coding (denoted as “COOP-NC”),

cooperative multicast scheduling without random network coding (denoted as “COOP”),

optimal multicast scheduling (denoted as “OPT”), and optimal multicast scheduling

with cooperative bandwidth (denoted as “OPT-M”). “COOP-NC” is performed under

the design described in this section. “COOP” also follows this design, but without ran-

dom network coding. MSs just randomly send the data in the buffer to their neighbors.

“OPT” is the optimal scheduling protocol without applying cooperative communication

and random network coding. We adopt the protocol in [48] and have simulated it to

the best of our knowledge according to all the available details presented in the chapter.

“OPT-M” is also based on “OPT”, but the BS uses more bandwidth by applying all the


sub-channels assigned for cooperative communication in “COOP-NC” in multicasting.

Thus, “COOP-NC” and “OPT-M” consume the same amount of bandwidth, with which

the comparison is more fair.

Fig. 5.2(a) shows the performance on average throughput over time (1000-second

simulation) of all protocols as a function of increasing number of MSs active in MBS.

We observe from the results that “COOP-NC” performs best. Compared with “OPT”,

a 72% gain is achieved. For more fair comparison, “COOP-NC” shows its advantages by

outperforming “OPT-M” with a margin of 58%. Such a throughput advantage should

be considered substantial by any standard. It coincides with our intuition that multicast

scheduling with cooperative communication and random network coding naturally fits in

the design of WiMAX MBS and is able to achieve significant throughput improvement due

to its effective use of wireless spectrum. Specifically, we examine the usefulness of random

network coding. Evident from the results, “COOP-NC” outperforms “COOP” by 20%

as random network coding effectively reduces the overhead. Another interesting result

we get is the margin that “COOP-NC” and “COOP” outperform “OPT-M” and “OPT”

becomes more substantial with increasing number of MSs. This observation indicates

more MSs create higher degree of cooperation which is able to benefit more on throughput

performance.

To further explore the advantages of cooperative communication and random network

coding in multicast scheduling, we examine the performance on average multicast rate at

the BS with the results shown in Fig. 5.2(b). When the number of MSs increases, the BS

gradually uses higher multicast rates to transmit data when cooperative communication

and random network coding are applied, which exactly shows the multicast bandwidth

at the BS is more efficiently utilized. This result verifies and confirms — from a different

aspect — the advantages of our protocol in WiMAX MBS.


0 10 20 30 40 50150

200

250

300

350

Number of MSs

Aver

age T

hrou

ghpu

ts (K

bps)

COOP-NCCOOPOPT-MOPT

(a) Throughput vs. Number of MSs

0 10 20 30 40 50200

250

300

350

400

Number of MSs

Mult

icast

Rate

(Kbp

s)

COOP-NCOPT-MOPT

(b) Multicast rate vs. Number of MSs

Figure 5.2: Throughput performance of four multicast scheduling protocols in a realistic

WiMAX MBS scenario. Cooperative multicast scheduling with random network coding

is able to achieve substantial throughput improvement by effectively utilizing the scarce

wireless bandwidth.

5.3 Cooperative Multicast Scheduling with Channel

Allocation

In practical systems like WiMAX, the OFDM channels are scarce resources and the

number of channels to support cooperative communication is limited. Thus, it is very

critical to efficiently allocate the channels for cooperative communication in the schedul-

ing. Moreover, there are potential channel diversity gains in the networks, as sub-channel

experiencing gain could vary from one link to another, allowing for the cooperate links to

be assigned their best channels. In this section, we study the optimal multicast scheduling

with constrained bandwidth resources, exploiting all the benefits provided by multi-user,

multi-channel and cooperative diversity.


5.3.1 Optimizing Performance with Limited Bandwidth

Under limited resources, the scheduling turns to be a joint optimization problem (denoted

as COOP-CA-NC), whose objective is to find not only the optimal multicast rate Rm but

also efficient centralized channel allocation scheme to maximize overall throughput under

the fairness criteria. To study it, we set a binary function K(n)gi ∈ {0, 1} to capture the

assignment of sub-channel n to the cooperative transmission link from node g to node

i, where n ∈ χ and χ denotes the set of sub-channels that are available for cooperative

communication. The set of feasible assignments is denoted as K. To avoid interference

in the cooperative communication, we set one sub-channel only can be assigned to one

link,

∑g∈ζ

∑i∈ζ

K(n)gi ≤ 1 ∀n ∈ χ (5.6)

By considering the channel allocation, the throughput on each user (Eq. (5.2)) should

be updated as follows,

Ui = Sm,iRm +∑g∈ζ

∑n∈χ

K(n)gi R

(n)gi (5.7)

where R(n)gi is the maximum rate that can be achieved when sub-channel n is assigned to

the link from node g to node i.

Now we are ready to state the optimization objective as,

maxR,K

∑i∈ζ

Ui

ri

=∑i∈ζ

Sm,iRm

ri

+∑i,g∈ζ

∑n∈χ

K(n)gi

R(n)gi

ri

(5.8)

As studied in the previous section, we use exhaustive search to get the optimal mul-

ticast rate. When we fix Rm in the search each time, Sm,i can be determined. ri is

pre-determined since it is the average throughput before time slot t. Thus, the joint

optimization problem can be decomposed, and the scheduling is reduced to the channel

allocation problem for each search as stated in the following (denoted as CA-NC),

maxK

∑i,g∈ζ

∑n∈χ

K(n)gi ω

(n)gi (5.9)


where

ω(n)gi =

R(n)gi

ri

(5.10)

subject to (5.6), and following constraints (updating (5.3) - (5.5)):

0 ≤ ω(n)gi ≤

C(n)gi

ri

∀g, i ∈ ζ, n ∈ χ (5.11)∑n∈χ

K(n)gi ω

(n)gi ≤ max{0, Bg −Bi

Tri

} ∀g, i ∈ ζ (5.12)

∑g∈ζ

∑n∈χ

K(n)gi ω

(n)gi ≤

t−1∑h=1

R(h)

ri

− Bi

Tri

+(1− Sm,i)Rm

ri

(5.13)

Overall, we can get the optimal solution of joint optimization problem by exhaustive

search and solving channel allocation problem. The procedure is stated in Algorithm 1.

However, the main problem of Algorithm 1 is the difficulty of solving channel alloca-

tion problem CA-NC. It is a mixture integer program (MIP) which is NP hard in general.

We formulate it to a maximum weighted bipartite matching (WBM) problem which is

equivalent to the original problem and can be solved optimally with polynomial time

complexity in terms of the number of MSs. Construct a bipartite graph A = (Φ× χ, E).

The vertices in Φ denote all the possible cooperative links (e.g. (1, 2) indicates the trans-

mission link from node 1 to node 2. Note it is different from (2, 1) which represents

the transmission link from node 2 to node 1). The set of sub-channels for cooperative

transmissions is denoted by the vertex set χ.

The edge set E corresponds to |Φ|×|χ| edges connecting all possible pairs. The weight

of each edge carries ω(n)gi as we defined in Eq. (5.10), which represents the maximum

cooperative transmission rate that can be achieved if sub-channel n is assigned to link

(g, i) subject to the proportional fairness criteria. In WBM, we initially set ω(n)gi =

1ri

min{R(n)gi , max{0, Bg−Bi

T}}. We exclude all links from Φ whenever ω

(n)gi = 0. |Φ| may

be not equal to |χ|. Thus we patch void vertices to χ or Φ to make |Φ| = |χ|. If a edge

connects any void node, its weight is also set to be zero.


Algorithm 1 Multicast scheduling with channel allocation1. Set Q = 0.

2. for m = 1 to 6 do

3. Set QMR =∑

i∈ζSm,iRm

ri.

4. Solve CA-NC. The optimal objective value is denoted as QCA and the optimal

channel allocation is KCA.

5. if QMR + QCA > Q then

6. Q = QMR + QCA.

7. ROPT = Rm.

8. KOPT = KCA.

9. end if

10. end for

11. ROPT is the optimal multicast rate and KOPT is the optimal scheme for channel

allocation.

Given the above graphical setup, channel allocation problem can be solved by solving

a WBM problem. The intuition is shown in Fig. 5.3. If vertex (g, i) in Φ and vertex n

in χ are matched, we assign sub-channel n to link (g, i) and set K(n)gi = 1. The WBM

problem can be solved using existing network flow algorithms such as the cost scaling

algorithm [13].

Solving the WBM problem above may violate a few constraints. First, we consider

constraint (5.12). The violation may happen when more than one sub-channels are

assigned to one cooperative link, and the link capacity via multiple sub-channels may be

over large. To solve this problem, we assign sub-channels by performing WBM in rounds.

In each round, we remove the sub-channels that are already assigned in the previous round

from set χ. Particularly, we update the weight on each edge by considering the constraint

(5.12). Then, we solve the WBM problem in a new round.

Another constraint may be violated is (5.13). To solve this problem, we check whether


(1,2)

(2,1)

(1,3)

... ...

1

2

3

... ...

! !

"(n)gi = 0"(n)

gi

Void Vertices

Regular Vertices

Figure 5.3: Solving the channel allocation problem using maximum weighted bipartite

matching algorithm.

the throughput of cooperative communication on each node i exceeds the upper limit

at each round. If so, we favor the cooperative links with highest rates where efficient

transmissions can be achieved. We assign sub-channels to those links and release the

sub-channels assigned to other links. It is easy to find the solution by a simple search.

After that, we have to omit all the links from Φ which cooperatively contribute to node i,

since the maximum throughput on this node has already been reached. We can not assign

any more sub-channels to these links in the following rounds. Overall, the approach is

summarized in Algorithm 2.

5.3.2 Channel Allocation with Channel Reuse

To fully utilize the available resources, we further exploit the advantages provided by the

spatial reuse in the cooperative communication. It is straightforward that two links which

do not include each other in the interference region could use the same sub-channels for

communication without interference. The interference information in the network can be

collected in a distributed fashion. If two nodes could correctly overhear the frequently

exchanged handshake messages with each other (the transmission power is assumed to


Algorithm 2 Channel allocation algorithm using maximum weighted bipartite matching

1. Initiate K(n)gi = 0, ∀(g, i) ∈ Φ,∀n ∈ χ.

2. Define Bgi := max{0, Bg−Bi

Tri},∀(g, i) ∈ Φ.

3. repeat

4. Construct the bipartite graph, and patch the void nodes to make |Φ| = |χ|.

5. Solve the WBM problem, and get the solutions as K(n)gi .

6. for each i ∈ ζ do

7. if (5.13) is violated then

8. Define Tg :=∑

n∈χ K(n)gi ω

(n)gi ,∀g ∈ ζ.

9. Define D1, D2, · · · , DG to be the sorted array of Tg (∀g ∈ ζ) in descending

order.

10. for v = 1 to G do

11. if∑

g′≤v Dg′ ≥

∑t−1h=1

R(h)ri

− Bi

Tri− (1−Sm,i)Rm

rithen

12. Define ξ := {g|∃g′> v, st. Tg = Dg

′}.

13. Release channel assignment on (g, i),∀g ∈ ξ.

14. Exclude links (g, i) ∀g ∈ ζ from Φ .

15. break

16. end if

17. end for

18. end if

19. end for

20. for each (g, i) ∈ Φ do

21. Bgi = Bgi −∑

n∈χ K(n)gi ω

(n)gi .

22. for each n ∈ χ do

23. ω(n)gi = min{R

(n)gi

ri, Bgi}.

24. end for

25. end for

26. Exclude the assigned channels in χ.

27. until All channels or all links are excluded


be equal for all nodes), we mark out that they are within each other’s interference zone.

An “interference table” I is defined as follows,

Iki =

1 If node i is in interference zone of node k

0 Otherwise

where k, i ∈ ζ. Nodes will periodically update this table and send interference information

to the BS. To prevent collision, channel reuse is not allowed in the interference zone. Thus,

the channel assignment should follow the following constraints,

∑i∈ζ,i6=k

Iki

∑g∈ζ

K(n)gi ≤ 1 ∀n ∈ χ, ∀k ∈ ζ (5.14)∑

g∈ζ

K(n)gi ≤ 1 ∀n ∈ χ, ∀i ∈ ζ (5.15)

Thus, the channel allocation problem should be updated with the consideration of

channel reuse, which can be stated as (denoted as CA-NC-reuse),

maxK

∑i∈ζ

ai (5.16)

where

ai =∑n∈χ

∑g∈ζ

K(n)gi ω

(n)gi (5.17)

subject to (5.11) - (5.15)

It is also a MIP, and we use the randomized rounding procedure (Algorithm 3) to

solve it with polynomial time complexity in terms of the number of MSs.

As designed in Algorithm 3, the rounding procedure ensures that all constraints are

satisfied. We note (5.12), (5.13) and (5.14) are satisfied with high probability in practice,

since the rate of cooperative communication is relatively much lower than the multicast

rate and the transmission range of MSs is relatively much smaller than the serving area

of the BS due to the power and bandwidth constraints. Thus, we can ignore them in the


Algorithm 3 Randomized rounding algorithm for channel allocation with channel reuse

1. Solve its relaxation (convex) with K(n)gi being relaxed to [0,1]. Let the optimal frac-

tional solutions be K∗(n)gi (∀g, i ∈ ζ, ∀n ∈ χ).

2. Initiate K(n)gi = 0 (∀g, i ∈ ζ, ∀n ∈ χ).

3. for each g, i ∈ ζ, n ∈ χ do

4. Round K(n)gi = 1 with probability K

∗(n)gi .

5. if K(n)gi = 1 then

6. if (5.12) or (5.13) or (5.14) is violated then

7. Set K(n)gi = 0.

8. else

9. Set K(n)ji = 0, ∀j 6= g.

10. end if

11. end if

12. end for

13. The optimal rounding solutions are K(n)gi .


rounding procedure (line 6 in Algorithm 3). Now, we give the approximation factor for

this randomized rounding algorithm under this assumption.

Lemma 5.1 f1jY1 +f2j(1−Y1)Y2 + · · ·+flj(∏l−1

i=1(1−Yi))Yl ≥ (1− (1− 1l)l)∑

1≤i≤l fijYi

whenever Yi ≥ 0 for all i and∑

i Yi ≤ 1 and f1j ≥ f2j ≥ · · · ≥ flj ≥ 0.

Proof: refer to [29]. ut

Theorem 5.1 Algorithm 3 provides an approximation guarantee of at least (1−(1− 1G)G),

where G is the number of multicast users.

Proof: Without loss of generality, for each i ∈ ζ, n ∈ χ, assume that the sorted users

are 1, 2, · · · , G with ω(n)1i ≥ ω

(n)2i ≥ · · · ≥ ω

(n)Gi ≥ 0. The probability that sub-channel n

is assigned to the link (u, i) in randomized rounding algorithm is∏u−1

j=1 (1−K∗(n)ji )K

∗(n)ui ,

∀u ∈ ζ. Thus, the expected throughput contribution on node i to the objective function

(5.16) can be stated as,G∑

u=1

(u−1∏j=1

(1−K∗(n)ji )K

∗(n)ui )ω

(n)ui

Using Lemma 5.1, we have,

∑n∈χ

G∑u=1

(u−1∏j=1

(1−K∗(n)ji )K

∗(n)ui )ω

(n)ui ≥

∑n∈χ

(1− (1− 1

G)G)∑j∈ζ

K∗(n)ji ω

(n)ji =

(1− (1− 1

G)G)∑n∈χ

∑j∈ζ

K∗(n)ji ω

(n)ji =

(1− (1− 1

G)G)a∗i ∀i ∈ ζ

a∗i is the throughput contribution of node i to the objective function (5.16) in the

optimal fractional solution. Thus, we have the expected contribution of node i to the

objective function in the rounding solution E[ai] as:

E[ai] ≥ (1− (1− 1

G)G)a∗i


Thus, we have, ∑i∈ζ

E[ai] ≥ (1− (1− 1

G)G)∑i∈ζ

a∗i

ut

5.3.3 How efficient are the channels allocated?

To study the impact of the channel allocation and identify the performance gains offered

by cooperative communication and random network coding with limited bandwidth re-

sources, we perform a set of simulations under the same scenario in the previous section.

Fig. 5.4(a) shows the average throughput over time (1000 seconds) as the function of

increasing number of active MSs when the number of sub-channels is limited as 100.

“COOP-CA-NC” which performs the multicast scheduling protocol with channel allo-

cation as we designed in this section beats the same protocol without random network

coding (“COOP-CA”) by 19%, and outperforms “OPT-M” and “OPT,” by delivering

65% and 94% improvement respectively. It demonstrates: by efficiently allocating sub-

channels, cooperative communication with random network coding is helpful to achieve

significant throughput improvement with very limited amount of bandwidth resources. Fur-

ther, we perform the simulations with fixed number of MSs, but with increasing number

of sub-channels. Shown in Fig. 5.4(b), “COOP-CA-NC” outperforms others by a sub-

stantial margin. This improvement becomes more salient as the number of sub-channels

increases. The intuition is: more bandwidth resources for cooperative communication will

benefit more on multicast performance.

To evaluate the performance gains provided by channel reuse, we specifically con-

duct simulations by performing multicast scheduling with the design of channel reuse.

From Fig. 5.4, we observe that multicast scheduling with channel reuse under randomized

rounding algorithm (denoted as “Reuse-rounding”) performs close to the optimum (de-

noted as “Reuse-optimal”) within 95%. Moreover, “Reuse-rounding” further improves

the throughput by 8% in average compared with “COOP-CA-NC” which already pro-


10 20 30 40 50100

150

200

250

300

350

400

Number of MSs

Aver

age T

hrou

ghpu

ts (K

bps)

Reuse-optimalReuse-roundingCOOP-CA-NCCOOP-CA

OPT-MOPT

(a) Throughput vs. No. of MSs

20 40 60 80 100100

150

200

250

300

350

400

Number of Sub!channels

Aver

age T

hrou

ghpu

ts (K

bps)

Reuse-optimalReuse-roundingCOOP-CA-NCCOOP-CA

OPT-M

OPT

(b) Throughput vs. No. of channels

Figure 5.4: The performance of cooperative multicast scheduling with random network

coding when the number of cooperative sub-channels is limited. The protocols with and

without channel reuse algorithm are both evaluated.

vides very satisfactory performance as we evaluated above. These results highlight the

benefits achieved by our proposed protocols.

5.4 Cooperative Multicast Scheduling with Power

Allocation

One of the most critical problems in the practical systems is that the MS is very energy-

constrained. Thus, the cooperative communication may not be fully performed with

limited power on relays. In this section, we study the multicast scheduling from a different

aspect, aiming to maximize the throughput by effectively allocating power on relays.

5.4.1 Maximizing Throughput with Limited Power

Let S(n)gi denote the power that node g transmits data to node i if channel n is assigned

on this link. S denotes the set of feasible power allocation schemes. As we note, the


power for cooperative communication on each node is limited,

∑n∈χ

∑i∈ζ

S(n)gi ≤ Pg ∀g ∈ ζ (5.18)

where Pg is the power limit on each node.

Under the power constraint, we update constraint (5.11):

0 ≤ ω(n)gi ≤ C

(n)gi = BW/ri · log2(1 + S

(n)gi /σ

(n)gi ) (5.19)

where BW denotes the channel bandwidth (the sub-channels are with equal bandwidth)

and σ(n)gi is the noise on the link.

Instead of only considering channel allocation in multicast scheduling as we designed

in the previous section (CA-NC and CA-NC-reuse), we aim to optimize the performance

by jointly accounting for both channel and power allocation. We state this new problem

(denoted as CA-PA) as follows,

maxK,S

∑g,i∈ζ

∑n∈χ K

(n)gi ω

(n)gi (5.20)

subject to (5.12) - (5.15), (5.18) and (5.19)

We take dual problem by introducing a set of dual variables λg ≥ 0, g ∈ ζ. Thus, the

objective (5.20) can be rewritten as,

maxK,S

∑g,i∈ζ

∑n∈χ K

(n)gi ω

(n)gi +

∑g∈ζ λg(Pg −

∑n∈χ

∑i∈ζ S

(n)gi ) (5.21)

subject to (5.12) - (5.15), and (5.19)

As proved in [76], the original optimization problem (5.20) can be solved by solving

its dual (5.21) with nearly zero duality gap when G is sufficiently large. We use the dual

update method to solve the problem as shown in Algorithm 4.

The hard part is to solve CA-PA even under fixed λ which is obviously nonconvex

(MIP). Here, we adopt a heuristic approach with polynomial time complexity in terms

of the number of MSs as given in Algorithm 5. This algorithm gives a good solution

and λ always can be converged in various set-ups we tested.


Algorithm 4 Dual update method to solve joint channel and power allocation problem

Initialize λ (vector of the dual variables).

repeat

Solve CA-PA with fixed λ.

Update λ using the ellipsoid method [76].

until λ is converged.

Algorithm 5 Heuristic algorithm to solve joint channel and power allocation problem

under fixed λ

Step 1: For the fixed λ, solve its relaxation (convex) with K(n)gi being relaxed to [0,1].

Let the optimal channel allocation solutions be K∗(n)gi (∀g, i ∈ ζ, ∀n ∈ χ).

Step 2: Round K(n)gi = 1 with probability K

∗(n)gi (∀g, i ∈ ζ, ∀n ∈ χ). If K

(n)gi = 1, check

whether all constraints are satisfied. Set K(n)gi = 0 if not.

Step 3: Solve the convex optimization problem with fixed K(n)gi , by taking S

(n)gi (∀g, i ∈

ζ, ∀n ∈ χ) as the variables. Let the optimal power allocation solutions be S∗(n)gi .

5.4.2 What’s the Impact of Power?

Finally, we evaluate the performance of our protocol with power allocation. The sim-

ulations are performed under increasing power limit at MSs, and Fig. 5.5(a) shows the

average throughput across time and 50 MSs with same power limit. “COOP-CA-PA-

NC” represents our cooperative multicast scheduling with random network coding, and

especially applies both channel and power allocation algorithms as we designed in this

section. It is not a surprise that “COOP-CA-PA-NC” outperforms all other protocols

(“COOP-CA-PA” is the protocol with the same design as “COOP-CA-PA-NC” but with-

out random network coding) with substantial gains. By efficient power allocation, coop-

erative communication with random network coding could be well performed and achieve

significant performance improvement, even with highly limited power on relays. We ob-

serve from the results that the throughput increases dramatically as the transmission


power rises up, which shows more power the MSs use for cooperative communication

could achieve more gains.

0 5 10 15 20 25150

200

250

300

350

Transmission Power (dBm)

Aver

age T

hrou

ghpu

ts (K

bps)

COOP-CA-PA-NCCOOP-CA-PAOPT-MOPT

(a) Throughput vs. Power Limit

2 4 6 8 10160

180

200

220

240

260

280

Power Variance (dBm)

Aver

age T

hrou

ghpu

ts (K

bps)

COOP-CA-PA-NCCOOP-CA-PAOPT-MOPT

(b) Throughput vs. Standard Variance of

Power Limit

Figure 5.5: The performance of multicast scheduling with our power allocation algorithm

in a power-constrained MBS.

Another set of simulations specifically study the impact of power on multicasting.

We examine the throughput under increasing standard variances of power used for co-

operative communication across different MSs. Fig. 5.5(b) shows that the throughput

decreases as the variance increases. We can intuitively conclude from this observation:

maximum throughput performance gains can be obtained if each node performs coopera-

tive communication by equally using its maximum power. In our future work, we may

study how to motivate MSs to make contributions to the networks for multicasting.

5.5 Overhead Analysis

In closing, we study the protocol overhead. Base stations in the real systems can be

considered as server-level computers, thus have no power and computation constraints.

Nowadays, the mobile devices, like a cell phone, normally have sufficient memory cache

and strong computing ability. The new generation iPhones are equipped with micropro-


cessors and can even run 3-D computer games smoothly. Although our protocol may

consume some computation power and memory if deployed in the mobile devices, the

generated delay should be sufficiently small that can be neglected. Verified by our sim-

ulations, our protocols have an average running time of less than 5 ms (over Intel Core

Duo machine running at 1.83 GHz and a memory of 2 GB), and are therefore suitable

for typical WiMAX with scheduling durations of 5–10 ms. With respect to the commu-

nication overhead, the protocols require MSs to report the channel quality information

(normally 5 bits per message) to the BS. This communication can be performed over the

fast feedback channel in WiMAX and this channel state reporting is originally required

in WiMAX standards [9]. Overall, our proposed protocols generate little communication

overhead within practical limits.

5.6 Summary

In this chapter, we have studied the multicast scheduling service problem, which is one of

the most important issues in WiMAX regarding the quality of services. Previous schedul-

ing protocols in the literature — almost without an exception — has solved the problem

based on a shared-channel single-hop transmission model, which ignores the advantages

provided by both channel and cooperative diversity in WiMAX where multiple chan-

nels are used. In contrast, we consider multicast scheduling with multi-hop multi-path

transmissions over multiple OFDMA channels to fully exploit the advantages provided

by cooperative communication and random network coding. The intuition is that co-

operative communication with random network coding could favor the users with good

channel conditions to enjoy high multicast flow rates from the source and cooperatively

help others with poor channel conditions simultaneously with little overhead. We design

multicast scheduling protocols which are tightly integrated with the design of WiMAX

MBS, and study the critical problems of channel and power allocation for cooperative


communication. Theoretical and practical solutions based on optimization are provided

and further evaluated in extensive simulations. The highlight of this chapter is our con-

clusion: multicast performance can be significantly improved by applying cooperative

communication and random network coding with effective use of wireless spectrum.

Chapter 6

Resource Management in Cognitive

WiMAX with Femto Cells

In the last chapter of technical part in this thesis, we extend our study to the communi-

cation architecture level in WiMAX and seek to improve its performance in the scenario

of femto cells. Femto cells are an important cost-effective architecture in WiMAX. With

the proliferation of wireless devices and the surge of demand of various applications sup-

ported in WiMAX, the requirement of bandwidth increases dramatically. Therefore, it

is important to fully utilize the wireless spectrum with femto cells in the networks.

However, traditional WiMAX architectures lack dynamic utilization of spectrum and

have inherent weakness on overlooking the special network characteristics and hence

missing the bulk of channel reuse opportunities. On the other hand, cognitive radio (CR)

[23] has emerged as an important technology to exploit high-degree spectrum reuse, by

allowing spectrum sensing and dynamical spectrum access. Such a technique brings much

flexibility and potentially generates benefits if employed in WiMAX femto cell networks.

However, the collaboration of WiMAX, femto cells, and CRs is barely investigated in the

literature.

In this chapter, we specifically propose a cognitive WiMAX architecture with femto

106

Chapter 6. Resource Management in Cognitive WiMAX with Femto Cells107

cells, where the base station and users are equipped with CRs and intelligently adjusts

power, channel, and other resources to accommodate the entire network ecosystem. In

this design, we develop an optimization framework for location-aware cooperative resource

management, by jointly employing multi-hop cooperative communication, power control,

and fairness, and incorporating user, channel, and cooperative diversities. Evaluated

by the rigorous analysis and extensive simulations, our protocol is near-optimal with

closed-form bounds, achieving substantial performance improvement.

6.1 Network Architecture

WiMAX network architecture with femto cells can be illustrated using the example shown

in Fig. 6.1, where a typical WiMAX network consisting of one macro base station (BS)

and six femto cells, serving two classes of users: primary user (PU) and secondary user

(SU). PUs are fixed inside a certain femto cell and communicate with the corresponding

femto BSs with dedicated channels, enjoying guaranteed quality of services (QoS). SUs

are highly dynamic (can move randomly in the entire area) and communicate directly

with macro BS with best effort services.

As the power used by femto BSs is an order of magnitude less than macro BS, the

serving area of each femto cell is quite limited (shown by shadow circle areas). The smaller

size of femto cells creates abundant opportunities for spatial reuse: the transmissions

outside the femto cells are able to be executed over the same channels used inside femto

cells. Thus, they work in a completely distributed fashion, and the channel availability

in the network is location-dependent and dynamic for SUs due to the bursty channel use

by PUs and SU mobility.

However, traditional WiMAX architectures and MAC-layer protocols are hobbled by

the holdover from cellular networks: they lack dynamic utilization of spectrum holes

and are essentially based on single-hop transmissions, requiring globally available channel


resources. The existing state-of-the-art resource management protocols have to carefully

coordinate the transmissions of macro and femto cells in a time-sharing mode [68], which

have inherent weakness on overlooking the special network characteristics and hence

missing the bulk of channel reuse opportunities. For example shown in Fig. 6.1, channel

1 is used by PU 1. Macro BS then can not use this channel to transmit data to SU 2 in

order to avoid interference to PU 1, although SU 2 resides outside the interference region

of PU 1. This is due to the single-hop transmission schedule with a fixed power, leading

to resource under-utilization.

C2

C1

C2C3

C3

C2

Femto Cell 1

Femto Cell 3

Femto Cell 2

Femto Cell 6

1

2

4

5

4

3

2

1

Macro BS

Femto Cell 4

Femto Cell 5

9

7

Femto BS

X

Primary User

Y

Secondary User

8

10

C1

C3

C2

C3

C1

C1

C2

Figure 6.1: An illustrative example of cognitive WiMAX with femto cells.

To solve the problem above, cognitive radio technique can be applied in WiMAX

to form a novel architecture of cognitive WiMAX with femto cells in order to further

improve the performance of WiMAX, with the important and promising femto cell de-

ployment. Different from traditional architectures, wireless devices in cognitive WiMAX

are equipped with frequency-agile CRs that bring convenience for spectrum sensing and


adjusting the frequency, power, range, and other variables to accommodate the entire

wireless ecosystem accordingly. With such a flexible radio, rather than confining to a

single-hop transmission, we are able to perform multi-hop cooperative communication,

aiming to fully exploit the spectrum holes. The key observation is that, the set of accessi-

ble channels for different users are different depending on their locations. The requirement

for globally available channels is relaxed, and users use locally accessible channels within

one hop to perform communication, providing abundant transmission opportunities with

channel reuse, and thus substantially improving the channel utilization.

The intuition is shown in Fig. 6.1, where the transmission from macro BS to SU 2 is

not feasible if all channels are occupied in femto cells. With CRs, the macro BS carefully

adjusts its transmission power. In the consequentially tuned transmission range (the

inner circle from macro BS in Fig. 6.1), the macro BS sends data to SU 1 via channel

2 without generating interference to PUs. In tandem, SU 1 relays data to SU 2 using

cooperative transmissions performed on channel 3 which is commonly available for both

the sender and receiver. Similarly, the original infeasible communication from the macro

BS to SU 4 can be performed in two-hop transmission with SU 3 as the relay. Essentially,

we take advantage of the location-dependent characteristics of WiMAX femto cell, and

data issued from BS are propagated via multiple paths and hops over spectrum holes

supported by CRs. Intuitively, wireless channels are effectively utilized by incorporating

user, channel, and cooperative diversities. Such an architecture naturally fits WiMAX

femto cell networks: PUs can use dedicated resources to enjoy guaranteed QoS, while

SUs opportunistically take advantage of spectrum holes to get best effort services without

generating interference to PUs.

In cognitive WiMAX, it is critical to design a efficient resource management frame-

work to accommodate this new designed architecture. Further, it is desirable to im-

plement all the benefits stated above in the resource management protocol by jointly

considering power control, flow routing, cooperative scheduling, interference avoidance,


and buffer management. To achieve this objective, we have the following designs:

B We advocate a cognitive WiMAX architecture with femto cells, and provide the

corresponding system models.

B We design a location-aware cooperative resource management protocol, including

flow control policy, buffer management strategy, and channel and power alloca-

tion scheme. It is based on stochastic Lyapunov optimization with performance

guarantees.

B We apply generalized expectation maximization algorithm to efficiently solve the

optimization problems required in the resource management protocol, by fully ex-

ploiting the unique problem structure and network characteristics.

The development of these designs constitutes the flow of presentation in this chapter.

6.2 System Models

6.2.1 Framework Formulation

In cognitive WiMAX with femto cells, both macro BS and SUs are equipped with ultra-

sensitive cognitive radios to perform spectrum sensing and power and frequency adjust-

ment. The network consists of one macro BS and F femto cells with A PUs and N SUs,

sharing C orthogonal channels supported by OFDMA. Each PU resides in a dedicated

femto cell and communicates with the corresponding femto BS over one pre-allocated

channel to support guaranteed QoS. SUs are fully mobile and served opportunistically

by the macro BS without generating interference to PUs. The entire network operates

in a time-slotted fashion, where channel conditions and user actions remain the same

during a given time slot, and vary independently from one time slot to another. Without

loss of generality, we set the time slot duration as 1.


Let S(t) = {Sca(t)}A×C represent the channel states on each time slot t. Sc

a(t) = 0

means PU a is using channel c. Otherwise, Sca(t) = 1. We assume the channel availability

state process evolves according to a finite state ergodic Markov chain. Within a time slot,

a SU can access a subset of the channels, potentially depending on its current location

and channel state S(t). This channel accessibility information is concisely represented

by H(t) = {hcn(t)}N×C . hc

n(t) = 1 if SU n can access channel c. Otherwise, hcn(t) = 0.

Macro BS obtains the channel availability information in the entire network via chan-

nel sensing with CRs, and the channel state information can be expressed by a probability

vector Y(t) = {Y ca (t)}A×C according to the sensing results. Each element captures the

probability that channel c is not occupied by PU a at time slot t. Intuitively, the closer

Y(t) is to S(t) (better sensing techniques employed), the smaller interference that can

be potentially generated to PUs.

CRs make it possible for the macro BS and SUs to adaptively use network resources.

We denote the macro BS’s transmission power on each channel as PBS(t) = {P cBS(t)}C .

UBS(t) = {µcn(t)}N×C represents the channel allocation to SUs in a macro cell, where

µn(t) is the binary variable capturing the assignment of channel c to SU n for the trans-

mission from macro BS. We denote SU power allocation using PSU(t) = {P cn(t)}N×C ,

where P cn(t) is the amount of power that SU n uses on channel c. The cooperative trans-

mission scheduling is described by USU(t) = {µcmn(t)}NN×C , each element of which is

a 0 − 1 variable to capture the allocation of channel c to the cooperative transmission

from SU m to SU n. We assume the location of PUs are fixed while the SUs are mobile.

SUs can self-locate themselves using popular techniques applied in mobile phones, such

as GPS.

6.2.2 Models of Resource Management

Spectrum and power resources can be finely tuned and dynamically allocated to macro

and cooperative transmissions, in order to fully utilize the spectrum and take advantage


of channel reuse and diversity. According to the network model given above, we have the

following four groups of constraints for resource management.

Power Constraints:

C∑c=1

P cBS(t) ≤ Pmax (6.1)

C∑c=1

P cn(t) ≤ Pmax

n ∀n (6.2)

P cBS(t) · gc

a · Sca(t) ≤ β ∀a, c (6.3)

Inequality (6.1) shows that the total transmission power of the macro BS has an upper

bound Pmax. The power constraints on SUs are represented by (6.2). To avoid interfer-

ence to PUs, the power received by PUs on each channel should not exceed the tolerable

level β, if the corresponding channel is being used. Inequality (6.3) describes this set of

constraints, where gca is the propagation gain from macro BS to PU a at channel c and

it can be calculated by gca = d−j

a . da ≥ 1 is the distance between BS and PU a, where j

is the path loss index [64].

Channel Constraints:

0 ≤N∑

n=1

µcn(t) ≤ 1 ∀c (6.4)

µcmn(t) ≤ hc

m(t), µcmn(t) ≤ hc

n(t) ∀m, n, c (6.5)

µcmn(t) ≤ lcm(t), µc

mn(t) ≤ lcn(t) ∀m, n, c (6.6)

Inequality (6.4) indicates that the macro BS can not use the same channel to transmit

data to multiple SUs. (6.5) shows that cooperative communication is constrained by the

channel accessibility represented by H(t) with the dynamic spectrum access technique.

(6.6) shows the constraint imposed by the channel availability on each SU with regards

to the transmission from macro BS to SUs. Similar to H(t), we use L(t) = {lcn(t)}N×C

to capture this information:

lcn(t) =

1 If P c

BS(t) · gcn(t) ≤ γ

0 Otherwise

(6.7)


The definition of L(t) indicates whenever the multicast power received by a SU exceeds

the threshold γ on a channel, this channel should be considered to be unavailable, and

can not be assigned for cooperative transmission. gcn(t) in (6.7) is the propagation gain

from BS to SU n on channel c at time t.

Cooperative Constraints:

0 ≤N∑

m=1

µcmn(t) ≤ 1 ∀c, n (6.8)

0 ≤ µcn(t) +

N∑m=1

µcnm(t) ≤ 1 ∀c, n (6.9)

0 ≤C∑

c=1

µcmn(t) +

N∑m′=1

µcnm′ (t) ≤ 1 ∀n, m (6.10)

Inequality (6.8) shows that one SU can not be helped by multiple SUs via the same

channel. (6.9) indicates the incoming and outgoing transmissions on each SU can not be

performed on the same channel. With respect to the multi-hop mode of transmission, we

constrain it in two hops described by (6.10). Cooperative communication is performed

concurrently via multiple channels, which is supported by multiple radios equipped on

SUs. Only a small number of radios are requires which is practically feasible, as the

distribution of SUs is sparse and dynamic, and the probability that multiple SUs are

within the interference region of each other is very low.

Flow Constraints:

With relays enabled, we perform multi-path transmission with perfect flow splitting

at the relays, due to its ability for load balancing and flexibility. Denote f cn[m](t) as the

flow rate that the macro BS transmits to SU n over channel c with the data destined for

SU m in time slot t, which means SU n should relay the data to SU m. If m = n, SU n

gets its own data. Similarly, let f cmn(t) be the flow rate of the cooperative transmission

from SU m to SU n at channel c in time period t. Thus, we have the throughput on each

SU as:

Un(t) =C∑

c=1

µcn(t)f c

n[n](t) +C∑

c=1

N∑m=1

µcmn(t)f c

mn(t) (6.11)


U = (U1, · · · , UN) denotes the throughput vector.

The flow routing is subject to the following constraints:

C∑c=1

µcnm(t)f c

nm(t) =C∑

c=1

µcn(t)f c

n[m](t) ∀m 6= n (6.12)

N∑m=1

f cn[m](t) ≤ µc

n(t)ωcn(t) ∀n (6.13)

f cnm(t) ≤ ωc

nm(t) ∀n, m, c (6.14)

Eq. (6.12) shows the flow balance requirement. The flow rate should be scheduled

and optimized at the macro BS, and be guaranteed to be feasible. (6.13) and (6.14)

indicates that the aggregate flow rate on each link can not exceed the link capacity.

ωcn(t) and ωc

nm(t) denote the capacities of macro transmission link (macro BS to SU n)

and cooperative transmission link (SU n to SU m) on channel c, respectively:

ωcn(t) = B · log2(1 +

P cBS(t)gc

n(t)

N0

) ∀n, c (6.15)

ωcnm(t) = B · log2(1 +

P cn(t)gc

nm(t)

N0

) ∀n, m, c (6.16)

where gcnm(t) is the propagation gain from SU n to SU m and B is the channel bandwidth.

We denote the upper bound of the channel capacity as ωmax due to the power constraint

and noise (denoted as N0).

It is easy to prove that the capacity of each channel is achieved for macro transmis-

sions. Otherwise, the macro BS can transmit more data to SUs to increase the aggregate

throughput. Thus, the inequality in (6.13) can be turned to equality. In the network,

the relays fully utilize the cooperative links if channel resources are allocated, and the

cooperative link capacity is much smaller than the transmission link from the macro BS

due to highly constrained power on SUs. Hence, the capacities of cooperative links are

achieved as well in (6.14).


6.2.3 Impact of Resource Management and Problem Hardness

The resource management protocol should be tightly integrated with the architecture of

cognitive WiMAX with femto cells. The objective is to maximize the aggregate through-

put on all SUs under a fairness criteria while keeping the interference to PUs within a

tolerable level. Three design factors are taken into consideration as follows.

Power Control. Essentially, the power control scheme is to tune the transmission

and interference ranges, making high-degree spatial reuse and spectrum hole utilization

in the location-dependent WiMAX femto cells. In the absence of adjustable power,

there is hardly much we can do once we encounter an infeasible transmission scenario in

scheduling. In our network, we seek the optimal power allocation for both the macro BS

and SUs that can be continually tuned.

Multi-hop Channel Allocation. Multi-hop transmission significantly reduces the

transmission requirement on global spectrum availability, making resource allocation fea-

sible with locally available channel resources when direct single-hop transmission is infea-

sible. In tandem, cooperative communication [54] exploits user, channel, and cooperative

diversities that benefit the network performance.

Flow Routing. Multi-path transmission makes the problem more challenging as the

transmitter has to schedule which packet is sent to which node via which relay. The

allocation of data flows should not cause channel overflow and packet loss, and at the

same time fully consider the efficiency of resource utilization.

To achieve an optimal resource management, we first consider a greedy centralized

optimization framework to maximize the aggregate throughput utilities at each time

slot:

maxPBS(t),PSU(t),UBS(t),USU(t)

N∑n=1

θnUn(t)

subject to: (6.1)− (6.16).

where θn > 0 describes the SU priority (fairness).


Derived from (6.13), we have the following fact:

N∑m=1

f cn[m](t) = µc

n(t)ωcn(t) ⇒

C∑c=1

N∑m=1

µcn(t)f c

n[m](t) =C∑

c=1

µcn(t)ωc

n(t) ⇒

∑c,m

µcnm(t)f c

nm(t) =C∑

c=1

µcn(t)ωc

n(t)−C∑

c=1

µcn(t)f c

n[n](t) ⇒

N∑n=1

Un =N∑

n=1

C∑c=1

ωcn(t)µc

n(t) (6.17)

Thus, the greedy optimization can be rewritten to be:

maxPBS(t),PSU(t),UBS(t),USU(t)

N∑n=1

θnUn(t)

subject to: (6.17) and U ∈ Λ

where Λ represents the achievable throughput region of SUs. It is easy to solve the

optimization problem if the set Λ is known in advance. However, in practice, this region

is unknown. Blindly transmitting data will lead to channel overflow or under-utilization,

and flow routing for each SU will be out of control. Moreover, greedy optimization can

not guarantee the optimality in the long term. To address these challenges, we next

present our online resource management protocol.

6.3 Resource Management With Stochastic Lyapunov

Optimization

In this section, we propose an online location-aware cooperative resource management

protocol, based on stochastic Lyapunov optimization without the requirement of the

knowledge on SU throughput region. With rigorous proof, we show that it is able to

achieve near-optimal throughput performance over time. We also provide deterministic

worst case bounds of the interference to PUs and the maximum data buffer backlog.


6.3.1 Stochastic Network Model

The macro BS maintains a data buffer for each SU, and Bn(t) denotes the buffer backlog.

In each time slot, new packets are admitted into the buffer with a rate of Rn(t) and the

macro BS transmits the data buffered to the corresponding SU (directly or via relay) as

long as channel resources are allocated. Essentially, Rn(t) reflects the throughput per-

formance if we carefully tune this rate and manage resources to make the buffer backlog

bounded and stable. Rmax is the achievable maximum rate due to the computation and

bandwidth limit of SUs. Then, we have the following data buffer dynamics:

Bn(t + 1) = max{Bn(t)− Un(t), 0}+ Rn(t) (6.18)

Let rn denote the time average rate of SU n. We have,

rn = limt→∞

1

t

t−1∑τ=0

Rn(τ) (6.19)

r = (r1, · · · , rN) denotes the rate vector on all SUs.

In cooperative communication, relays may generate interference to PUs due to sensing

errors. If one cooperative transmission link causes interference to a PU, we count it as

one collision of the PU. We use Eca(t) to capture the total number of such collisions for

PUs as defined:

Eca(t) =

N∑m=1

N∑n=1

µcmn(t)Ia

m(t)

(1− Sc

a(t)

)(6.20)

where Iam(t) is the binary variable indicating whether the cooperative communication

issued by SU m possibly generate interference to PU a. This information can be captured

according to location information (if PU a is in the transmission range of SU m, then

Iam(t) = 1). It is intuitive that the more interference incurred, the more severely PUs

would suffer from the packet losses. Let eca denote the time average rate of collisions:

eca = lim

t→∞

1

t

t−1∑τ=0

Eca(τ) (6.21)

In the network, this interference information of each PU can be tracked using an

interference buffer, and all SUs are aware of it. The buffer backlog, denoted as Xca(t),


reflects the interference level, which can not exceed a time average tolerable rate ρca.

Thus, we have the following interference buffer dynamics:

Xca(t + 1) = max{Xc

a(t)− ρca, 0}+ Ec

a(t) (6.22)

Overall, we aim to maximize the aggregate throughput of SUs under the fairness

criteria (consistent with the centralized greedy optimization problem):

maxN∑

n=1

θnrn

subject to: (6.1)− (6.22). (6.23)

6.3.2 Resource Management Policies

We design the online resource management protocol based on stochastic optimization to

solve the problem (6.23). It includes three policies stated as follows:

(i) Flow Control: At each time slot t, the macro BS controls the data rate admitted

to the data buffer of each SU as the solution to the following problem:

min Rn(t)

(Bn(t)− V θn

)subject to: 0 ≤ Rn(t) ≤ Rmax (6.24)

where V ≥ 0 is a constant parameter, which can be tuned according to the system

requirement. The above problem has the threshold-based solution:

Rn(t) =

0, if Bn(t) > V θn,

Rmax, otherwise.

(ii) Macro Allocation: At each time slot t, the power and channel allocation for the

macro transmissions issued by the macro BS to SUs should follow the policy by solving

the following problem:


maxN∑

n=1

C∑c=1

Bn(t)ωcn(t)µc

n(t)

subject to: (6.1), (6.3), (6.4), (6.15) (6.25)

This allocation policy reflects two intuitive designs: (a) The link with a higher capacity

has a higher priority to get channel resources, which is helpful to achieve higher aggregate

throughput (represented by ωcn(t)). (b) Resource allocation favors SUs with a large data

buffer backlog (represented by Bn(t)). More data in the buffer implies higher urgency

to transmit the data to avoid buffer overflow. From the fairness point of view, a larger

backlog also indicates the SUs have obtained a smaller share of channel resources to

transmit data in the previous time slots. Thus, they should be given a higher priority to

obtain channel resources in the current time slot.

(iii) Cooperative Allocation: At each time slot t, the power and channel allocation

for cooperative communication should follow the policy by solving the following problem:

max∑

a,m,n,c

µcmn(t)

{(Bn(t)−Bm(t)

)ωc

mn(t)−Xca(t)I

am(t)

(1− Y c

a (t)

)}subject to: (6.2), (6.5)− (6.7), (6.16) (6.26)

Three factors are taken into account for cooperative allocation. (a) Buffer backlog.

More buffered data of SU n than SU m implied higher urgency to transmit the data

of SU n than m, leading to a higher priority that SU m helps SU n via cooperative

communication (represented by Bn(t) − Bm(t)). (b) Channel rate. The higher rate a

cooperative link is able to achieve (represented by ωcmn(t)), the higher chance channel

resources are allocated on the link. (c) Interference level. The channel allocation favors

cooperative transmissions that will not potentially generate interference to PUs (repre-

sented by Iam(t)(1−Y c

a (t))), especially the ones who already have high interference levels

(represented by Xca(t)). Note that cooperative allocation is performed after the macro

allocation with a fixed power and channel allocation for macro transmissions.


6.3.3 Performance Analysis

We now characterize the performance of our scheduling policies with the following bounds.

(i) Backlog Performance. Initialize Bn(0) = 0. The data buffer backlogs are

bounded as:

Bn(t) ≤ Bmax , V θmax + Rmax ∀n, t (6.27)

Proof: Bn(0) = 0 < Bmax. Now, suppose that Bn(t) ≤ Bmax. We show the same holds

for Bn(t+1). We have two cases. (a) Bn(t) ≤ Bmax−Rmax. Obviously, Bn(t+1) ≤ Bmax

according to Eq. (6.18). (b) Bn(t) > Bmax − Rmax, then Bn(t) > V θn − Rmax + Rmax =

V θn. Thus, we will choose Rn(t) = 0 according to our macro allocation policy, so that

Bn(t + 1) ≤ Bn(t) ≤ Bmax. Overall, (6.27) is proved. ut

(ii) Interference Performance. Initialize Xca(0) = 0. ∀t > 0, if Y c

a (t) < 1, set

0 < ε < 1 and Y ca (t) ≤ 1− ε. Then the worst case of the interference buffer backlogs for

all PUs is upper bounded by:

Xca(t) ≤ Xmax ,

Bmaxωmax

ε+ bN

2c ∀c, a, t (6.28)

Proof: Xca(0) = 0 < Xmax. Now, suppose that Xc

a(t) ≤ Xmax. We show the same holds for

Xca(t+1). First, suppose Y c

a (t) = 1. Then, there will be no interference to PU a as it does

not occupy channel c. Thus, we get Xca(t+1) ≤ Xmax according to (6.22) with Ec

a(t) = 0.

Next, suppose Y ca (t) < 1, and we have two cases. (a) Xc

a(t) ≤ Xmax − bN2c. Note that

bN2c represents the maximum number of cooperative transmission links (SU pairs) in the

network, which is also the maximum value of Eca(t). Obviously, Xc

a(t + 1) ≤ Xmax under

this case. (b) Xca(t) > Xmax − bN

2c = Bmaxωmax

ε. Then, Xc

a(t)ε > Bmaxωmax. Thus, we

have Xca(t)(1− Y c

a (t)) > (Bn(t)− Bm(t))ωcmn. If Ia

m(t) = 1, according to our cooperative

allocation policy, choose µcmn(t) = 0, which means there is no cooperative communication

on channel c. If Iam(t) = 0, the transmissions issued by all SUs can not reach PU a. Thus,

Xca(t + 1) ≤ Xc

a(t) ≤ Xmax. Overall, (6.28) is proved. ut

(iii) Utility performance. Initialize Bn(0) = 0, Xca(t) = 0. The time average


throughput utility achieved by our protocol is within B/V of the optimal value:

limt→∞

inf1

t

t−1∑τ=0

N∑n=1

θnE{

Rn(τ)

}≥

N∑n=1

θnr∗n −

B

V(6.29)

where r∗n is the optimal achievable rates of problem (6.23), and V, B > 0 are constants.

We use the technique of Stochastic Lyapunov Optimization to prove it. Let Q(t) =

(Q1(t), · · · , QK(t)) be a vector of queue lengths for a discrete time stochastic queueing

network. Let W (Q) be any non-negative scalar valued function of the queue lengths,

called a Lyapunov function. Define the Lyapunov drift ∆(t) as follows:

∆(t) , E{

W (Q(t + 1))−W (Q(t))

}(6.30)

The network accumulates utility every time slot with bounded value. We have the

stochastic process f(t) to represent the utility earning with over-time optimum f ∗.

Theorem 6.1 Suppose there exist V > 0, B > 0, d > 0, and a non-negative function

W (Q) such that E{W (Q(d))} < ∞. For t > d, if the Lyapunov drift satisfies:

∆(t)− V E{f(t)} ≤ B − V f ∗ (6.31)

then we have:

limt→∞

inf1

t

t−1∑τ=0

E{

f(τ)

}≥ f ∗ − B

V(6.32)

Proof: Refer to [69]. ut

In our resource management problem, we set:

Q(t) = (B1(t), · · · , BN(t), X11 (t), · · · , XC

1 (t), · · · , X1A(1), · · · , XC

A (t)) (6.33)

Define f(t) ,∑N

n=1 θnRn(t) as the aggregated throughput utility earning at each time

slot according to (6.23), and thus f ∗ ,∑N

n=1 θnr∗n as the over-time optimal utility ac-

cordingly. We further define the Lyapunov function as follows:

W (Q(t)) ,1

2

A∑a=1

(N∑

n=1

(Bn(t))2 +C∑

c=1

(Xca(t))

2

)


Now, we calculate the Lyapunov drift as follows:

∆(t) ≤ B − E

{A∑

a=1

N∑n=1

{Bn(t)

(Un(t)−Rn(t)

)}}− E

{A∑

a=1

C∑c=1

Xca(t)

(ρc

a − Eca(t)

)}(6.34)

where B , 12

(A ·N · (Bmax)

2 +∑A

a=1

∑Cc=1(ρ

ca)

2 + A · C)

.

Now we subtract V E{∑N

n=1 θnRn(t)} from both sides of the drift inequality (6.34)

and substitute (6.20) into (6.34). We have:

∆(t)− V E

{N∑

n=1

θnRn(t)

}≤ B −

A∑a=1

C∑c=1

ρcaE

{Xc

a(t)

}+ A · E

{N∑

n=1

Rn(t)

(Bn(t)− V θ

)}

−E

{A∑

a=1

N∑n=1

Bn(t)Un(t)−A∑

a=1

C∑c=1

Xca(t)E

ca(t)

}(6.35)

We then derive the following equation by substituting (6.11), (6.13), and (6.20) into

the last term of (6.35).

E

{A∑

a=1

N∑n=1

Bn(t)Un(t)−A∑

a=1

C∑c=1

Xca(t)E

ca(t)

}= E

{∑a,n,c

Bn(t)f cn[n](t)µc

n(t)

}+

E

{ ∑a,n,m,c

µcmn(t)Bn(t)ωc

mn

}− E

{ ∑a,n,m,c

µcmn(t)Xc

a(t)Iam(t)(1− Sc

a(t))

}(6.36)

Further, we have the following fact (derived from Eq. (6.13)):

N∑m=1,m6=n

f cn[m](t) + f c

n[n](t) = ωcn(t)µc

n(t) ⇒

f cn[n](t)µc

n(t) = ωcn(t)µc

n(t)−N∑

m=1,m6=n

f cn[m](t)µc

n(t) (6.37)

Using (6.37) and (6.12), we have:

E

{∑a,n,c

Bn(t)f cn[n](t)µc

n(t)

}= E

{∑a,n,c

Bn(t)ωcn(t)µc

n(t) +∑

a,n,m,c

Bn(t)µcnm(t)ωc

nm(t)

}(6.38)


Substitute (6.38) into (6.36) and put (6.36) into (6.35). We have:

∆(t)− V E

{N∑

n=1

θnRn(t)

}≤ B −

A∑a=1

C∑c=1

ρcaE

{Xc

a(t)

}

+A · E

{N∑

n=1

Rn(t)

(Bn(t)− V θ

)}− A · E

{N∑

n=1

C∑c=1

Bn(t)ωcn(t)µc

n(t)

}

−E

{ ∑a,m,n,c

µcmn(t)

{(Bn(t)−Bm(t)

)ωc

mn(t)−Xca(t)I

am(t)

(1− Sc

a(t)

)}}(6.39)

The last three terms in the right side of (6.39) are exactly our resource management

policies (replace Sc(t) as Yc(t) by considering the sensing errors on the macro BS). Note

that the macro transmission is dominant in the aggregate throughput on SUs according to

(6.17). Thus, we can optimize the last two terms separately although they have common

constraints (6.7) and (6.9). Then, it is clear to see that our management policies minimize

the right side of (6.39) over all alternate feasible scheduling policies at each time slot.

We now define the stationary, randomized policy SR, that chooses a feasible resource

allocation at every time slot as a function of only the channel state information S(t) and

P(t), which will yield the following steady state values [58]:

E{RSRn (t)} = r∗n (6.40)

ec,SRa , lim

t→∞

t−1∑τ=0

E{Ec,SRa (τ)} ≤ ρc

a (6.41)

Note that our policies minimize the right side of (6.39) including the SR policy [58].

Thus, we can show (from (6.34)):

∆(t)− V E{f(t)} ≤ B − E

{A∑

a=1

C∑c=1

Xca(t)

(ρc

a − Ec,SRa (t)

)}

−A · E

{N∑

n=1

{Bn(t)

(Un(t)−RSR

n (t)

)}− V f ∗ (6.42)

Now, we aim to prove of inequality (6.31) from (6.42), by getting the constant lower

bounds of the second and third last terms in (6.42). First, as Bn(t) ≥ 0 and Un(t) ≥ 0,

we have E{∑N

n=1 Bn(t)Un(t)

}≥ 0. Further, 0 ≤ Bn(t) ≤ Bmax and 0 ≤ RSR

n ≤ Rmax.


Thus, (6.42) turns to be:

∆(t)− V E{f(t)} ≤ B + A ·N ·BmaxRmax − V f ∗ − E

{A∑

a=1

C∑c=1

Xca(t)

(ρc

a − Ec,SRa (t)

)}(6.43)

We then use “delayed” queue backlogs to formulate it. Clearly, for t > d, we have:

Xca(t− d) + d · bN

2c ≥ Xc

a(t) ≥ Xca(t− d)− dρc

a (6.44)

Now, we substitute Xca(t) in (6.42) with (6.44):

∆(t)− V E{f(t)} ≤ B + A ·N ·BmaxRmax + Z − V f ∗

−E{∑A

a=1

∑Cc=1 Xc

a(t− d)(ρc − Ec,SRa (t))

}(6.45)

where Z , d∑A

a=1

∑Cc=1

(bN

2c+ (ρc

a)2

).

Using iterative expectations, we have the following:

E{ C∑

c=1

Xca(t− d)Ec,SR

a (t)

}= E

{ C∑c=1

Xca(t− d) · E{Ec,SR

a (t)|T(t− d)}}

(6.46)

T represents the system state at time slot t on the primary channel availability H(t)

and Y(t), which can be considered as a Markov process. By the property of Markov

processes, any functions of these states H(t) and Y(t) converge exponentially fast to

their steady state values. Recall that the stationary, randomized policy is only based

on the system states. Thus, there exists α > 0, 0 < σ < 1 such that (using (6.40) and

(6.41)):

E{

Ec,SRa (t)|T(t− d)

}≤ ec,SR

a + ασd ≤ ρca + ασd (6.47)

Now, substitute (6.47) into (6.45), then (6.42) finally can be expressed as follows,

which fits to the form of (6.31):

∆(t)− V E{f(t)} ≤ B − V f ∗

B = B + A ·N ·BmaxRmax + Z + A · C ·Xmaxασd.

Thus, by applying Theorem 6.1, we are able to prove (6.29).


6.4 Optimization Solution

It is noted Lyapunov optimization stands and thus we can generate the favorable per-

formance studied above as long as we can optimally solved the optimization problems

stated in our three resource allocation policies. However, we observe Macro and coopera-

tive allocation policies in Sec. 6.3.2 require us to solve optimization problems (6.25) and

(6.26), which are non-linear integer programming (NIP) and thus without polynomial-

time solution. We can use traditional branch-and-bound algorithm to solve these prob-

lems optimally. However, it does not exploit the special structure of these optimization

problems, and has a high complexity due to LP relaxation and inefficient search. In

this section, we propose to apply the Generalized Expectation Maximization (EM)

algorithm [57] to our problems, which specifically exploits special problem structures

and cognitive WiMAX network characteristics, and reduces the complexity. We note, in

practice, the approximation would help to achieve good tradeoff between complexity and

optimality.

6.4.1 Generalized EM Algorithm

Generalized EM is an iterative method to optimize two sets of variables (λ, θ). We obtain

the optimal solutions by iteratively updating the variables via two steps:

E step: θ(k+1) = arg maxθ F(θ, λ(k))

M step: λ(k+1) = arg maxλF(θ(k+1), λ(k))

Successive application of generalized EM maximizes the lower bound of F , i.e.,

F(θ(k+1), λ(k)) ≥ F(θ(k), λ(k))

F(θ(k+1), λ(k+1)) ≥ F(θ(k+1), λ(k))

Accordingly, in the macro allocation problem (6.25), we divide the variables into two

sets: PBS(t) and UBS(t). We iteratively solve the problem with two steps. First, take


PBS(t) as the variable and UBS(t) as a fixed value (referred to as the BS Power Opti-

mization step). Then, take UBS(t) as the variable but UBS(t) as a fixed value (referred

to as the Macro Channel Assignment step). The optimal solution can be obtained by

repeating these two steps until convergence.

Surprisingly, by separating the problem into two steps, the complexity of the opti-

mization problem is largely reduced due to the special problem structure. With a fixed

channel allocation, the BS Power Optimization step is actually a LP. The macro Chan-

nel Assignment step, with a fixed power allocation, can be considered as a maximum

weighted bipartite matching (WBM) problem, which can be solved optimally with poly-

nomial time complexity in terms of the number of users. Construct a bipartite graph

A = (Φ × χ, E). The vertices in Φ denote all SUs, and the vertices in χ denote all

channels. The edge set E corresponds to |Φ| × |χ| edges connecting all possible pairs,

with weight Bn(t)ωcn(t). Run the WBM algorithm to obtain the matched pairs, providing

corresponding channel assignment. The WBM problem can be solved in a centralized

fashion using network flow algorithms such as the cost scaling algorithm [13], and can

also be solved in distributed approximation algorithms [37].

In the cooperative allocation problem (6.26), we can also divide the variables into two

sets: PSU(t) and USU(t). Then, the problem is separated into two steps: the SU Power

Allocation step and the Cooperative Channel Allocation step. The SU Power Allocation

step is a LP. The Cooperative Channel Allocation step can be formulated into a similar

WBM, where Φ includes all cooperative links 1 and χ contains all available channels,

excluding the ones that can not be used according to the constraints. The weight of each

edge in E carries

(Bn(t) − Bm(t)

)ωc

mn(t) − Xca(t)I

am(t)

(1 − Y c

a (t)

). With this graph

setup, the problem can be solved optimally.

1For example, (1, 2) indicates the transmission link from SU 1 to SU 2. Note that it is different from(2, 1) representing the link from SU 2 to SU 1.


Table 6.1: Evaluation of Generalized EM algorithm.

Algorithm Ave. Throughput Ave. running time

generalized EM 1.74 Mbps 1 ms

branch-and-bound 1.75 Mbps 6 ms

6.4.2 Complexity Analysis

The Generalized EM algorithm converges to a local maximum of the original optimiza-

tion problem [57]. We can carefully select the initial conditions, resulting in the global

maximum. One efficient approach to set the initial values is to solve the LP relaxation

of the original problem, and get the feasible solution by randomized rounding. Running

the algorithm several times with different initial conditions is also helpful.

We perform a set of simulations to evaluate the Generalized EM algorithm in our

problems by comparing with the traditional branch-and-bound algorithm, running over

Intel Core Duo machine at 1.83 GHz and a memory of 2 GB. The results are listed

in Table 6.1. With respect to the performance of average throughput over SUs, the

Generalized EM algorithm performs very close to the branch-and-bound algorithm, within

a 1% difference on average. Further, we observe that the Generalized EM algorithm is

able to converge within 1 ms on average which is much faster than the branch-and-bound

algorithm. Thus, it is suitable for practical WiMAX systems.


We are now ready to resort to extensive simulations to study the performance of cognitive

WiMAX with femto cells. To be realistic, the simulations are conducted over a long term,

where practical settings of WiMAX and CR configuration are adopted according to [23].

In our simulations, there are a total of 20 PUs located across 8 femto cells sharing 12

channels. Around the service region, a number of SUs are randomly moving with random


Table 6.2: Simulation parameters for evaluating cognitive WiMAX.

Channel Type Rayleigh fading and AWGN

Path loss Model COST-HATA-231

Transmitter Power (macro BS) 25 dBm

Transmitter Power (SU) 5 dBm

Noise Power -129.5 dBW

Adaptive Modulation used

initial locations. The channel availability state evolves according to a Markov chain with

symmetric transition probabilities between the ON and OFF states given by 0.5. The

simulation parameters are listed in Table 6.2.

We simulate our proposed protocol with different numbers of active SUs, denoted as

“Coop-X” (“X” represents the number of SUs). For comparison, we simulate the tradi-

tional resource management protocol in cognitive WiMAX with power control in a coarse

granularity, by simply using the maximum feasible power for macro transmission (follow

the constraint (6.3)) without cooperative communication and flow control, referred to as

“NOCoop.” Further, to specifically examine the advantages of the cognitive WiMAX

architecture, we simulate the resource management protocol in traditional WiMAX net-

works without the CR technique, referred to as “Trad,” where the transmission is only

performed when feasible channels exist across the entire macro area and is provisioned

under maximum power.

We first examine the throughput performance. Fig. 6.2 shows the results on average

throughput over SUs via a 15000-second simulation. We observe that “Trad” performs

worst, indicating the advantage of the new architecture by applying CR technique. Even

“NOCoop” outperforms “Trad” with a substantial gain (21%) by exploiting spectrum

reuse in a higher degree. Further, “Coop-30,” “Coop-40,” and “Coop-50” defeat “NO-

Coop” by 36%, 50%, and 63% respectively, and of course outperform “Trad” with much


0 100 200 300 400 5000.8

1

1.2

1.4

1.6

1.8

Time (rounds)

Aver

age

Thro

ughp

ut (M

bps)

Coop!30Coop!40

Coop!50NOCoop Trad

Figure 6.2: Average throughput perfor-

mance of all protocols.

0.1 0.2 0.3 0.40

0.2

0.4

0.6

0.8

1

Throughput Variance

F(x)

Coop!30Coop!40Coop!50NOCoop

Figure 6.3: CDF of throughput variance,

which indicates fairness performance.

higher margins. It coincides with our intuition that resource management with coopera-

tive communication, power control, flow routing, and other important cross-layer designs

naturally fits in the design of cognitive WiMAX with femto cells, and is able to achieve

significant throughput improvement due to its effective use of the wireless spectrum. An-

other trend to notice is that the margin that “Coop” outperforms “NOCoop” and “Trad”

becomes more substantial with an increasing number of SUs. This observation indicates

that a larger number of SUs create a higher degree of cooperation, which is beneficial for

throughput performance.

Regarding the fairness performance, we capture the variance on the average through-

put over SUs. At each time slot t, we calculate, for each SU, the average throughput over

time horizon [1, t], and then compute the throughput variance as the ratio between the

standard deviation of the average throughput over time and the time average throughput

itself. Fig. 6.3 plots the CDF of this throughput variance for all protocols. Not surpris-

ingly, “Coop”s outperform “NOCoop,” which shows the improvement of our protocol on

fairness performance.

To obtain a deeper understanding of the advantages of our proposed protocol, we in-

vestigate the channel utilization performance, which is calculated as the sum throughput


0 100 200 300 400 50015

20

25

30

Time (rounds)

Utiliz

ation

Impr

ovem

ent (

%)

Coop!40Coop!60Coop!80

Figure 6.4: Performance on the channel

utilization improvement.

0 100 200 300 400 5000.05

0.1

0.15

0.2

0.25

0.3

Time (rounds)

Norm

alize

d Bu

ffer B

acklo

g

datacollision

Figure 6.5: Performance on the buffer

backlog.

of all SUs over the aggregate throughput in the network including both SUs and PUs.

This value accurately reflects the improvement on the spectrum utilization. Evident

from the results shown in Fig. 6.4, the increase of the channel utilization reaches 30%

in the best case (“Coop-60”). It demonstrates that the spectrum can be more efficiently

utilized with our protocol. Another observation from the results is that the performance

will degrade when the number of SUs is overly large (“Coop-80”), since the interference

effect begins to dominate. A sweet spot may exist with respect to the number of SUs in

cognitive WiMAX. We will further study it in our future work.

We further track the buffer backlogs of both data and collision queues. The results

are shown in Fig. 6.5, and the curves capture the normalized buffer backlog, calculated

by the ratio between the backlogs and the bounds (obtained in (6.27) and (6.28)). The

results show that the buffer remains bounded over the long term, which is desirable in

the system design.

Regarding protocol overhead, all the protocol control messages are transmitted over

wired lines and shared by all BSs (including Macro and Femto BSs). These messages can

be exchanged periodically and each message is within the size of a few hundred bytes.

The, this message overhead is substantially small.


6.6 Summary

In this chapter, we propose cognitive WiMAX with femto cells and study the resource

management problem in the network. Tightly integrated with the novel cognitive WiMAX

architecture, our cross-layer resource management protocol is designed to apply power

control, multi-hop cooperative communication and flow management techniques, achiev-

ing near-optimal performance. It is based on a sound theoretical foundation using

stochastic Lyapunov optimization, but not without careful considerations of the prac-

ticality, feasibility, and efficiency of implementing these solutions. With this chapter, we

are convinced that it is a win-win approach by applying the CR technique to WiMAX

with the employment of our resource management protocol by fully exploiting spectrum

reuse and incorporating user, channel, and cooperative diversities.

Chapter 7

Concluding Remarks

Readers do not need to be reminded about the importance of studying WiMAX like

multi-channel wireless networks: they represent the future generation of high-bandwidth

wireless access technologies and it is challenging and important to effectively utilize the

scarce wireless spectrum in order to provide high quality of services. The objective

of this thesis is to have research on multi-channel wireless networks with WiMAX as

the representative, and optimize the performance, which are not fully studied in both

academia and industry.

This thesis presents our research findings in two main arms including four parts

towards this objective, step by step further and deeper on the exploration. First, we

investigate the use of network coding when applied in the MAC-layer of WiMAX. We have

observation that random network coding indeed provides salient improvement in terms

of throughput and transmission resilience in WiMAX. With this finding, we proposed

a MAC-layer random network coding protocol, MRNC in short, which is designed to

take full advantage of the favorable properties of random network coding and tightly

integrate with the multi-channel communication structure in WiMAX. Especially, we

have two adaptive algorithms embedded in MRNC with well-tuned designs which are

able to facilitate MRNC to achieve even larger benefits.

132

Chapter 7. Concluding Remarks 133

Admittedly, MRNC provides quite satisfactory performance in the regular cases.

However, in the conditions of low channel qualities, transient unpredictable bit errors

would corrupt the entire packet which would waste scarce wireless spectrum. In the sec-

ond step, built on top of MAC-layer random network coding scheme, we seek to further

improve the performance through effective error control in the physical layer especially

under the poor channel conditions. We introduced, designed, and evaluated a cooper-

ative symbol-level random network coding protocol in WiMAX, named Drizzle, which

further exploit the power of random network coding. Tightly integrated with WiMAX

physical layer, Drizzle provides error control in fine granularity and minimizes the waste

of bandwidth in various multi-channel communication scenarios in WiMAX. Through

our extensive simulation evaluation, we show both MAC-layer and symbol-level network

coding protocols, with our fine-tuned designs, are able to provide significant improvement

on system performance.

Clearly, the ultimate goal of the protocol optimization and standardization in WiMAX

with IEEE 802.16 is to provide high quality of services/applications and attract users to

evolve in the networks. After solving the challenges in the fundamental communication

in WiMAX with the research in the first two steps, we study the important services in

WiMAX and seek to provide specific designs regarding these services which are crucial

for practical WiMAX systems. First, we focus on multicast broadcast services (MBS)

in WiMAX. We propose a novel multicast scheduling with multi-hop multi-path trans-

missions over multiple OFDMA channels to fully exploit the advantages provided by

cooperative communication and random network coding. This design provides a solution

to solve the problems in traditional multicast scheduling, and this study creates a new

paradigm of multi-hop cooperative communication in WiMAX.

Within such paradigm, in the last step, we focus on femto cell architecture which

is a cost-effective means of providing ubiquitous connectivity in WiMAX. Recently, a

number of large ISPs start to deploy femto cells in the real systems. We propose a cog-

Chapter 7. Concluding Remarks 134

nitive WiMAX architecture with femto cells, by exploring the benefits of collaboration

of popular cognitive radio technique, multi-hop paradigm, as well as femto cell struc-

ture. Such design provides flexibility for resource management, and an efficient resource

management framework is generated and provided accordingly in our study. We provide

both rigorous theoretical analysis and realistic simulation evaluation for both multicast

scheduling protocol and cognitive resource management in WiMAX, which show near-

optimal performance.

With our complete cycle of study on WiMAX protocols and the research findings

across, we believe our proposals have great potentials to be implemented in the practical

WiMAX systems, and smoothly applied to other next generation wireless communication

networks. In the future work, we will extend our understanding and study on other

emerging attractive applications by applying advanced technologies.

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