channel-state dependent scheduling of delay …akk4212/channel-aware-scheduling.pdf ·...

CHANNEL-STATE DEPENDENT SCHEDULING OF DELAY-BOUNDED TRAFFIC IN BEYOND 3G WIRELESS

MULTIMEDIA NETWORKS

By

Ahmed Khattab Fathi Khattab B.Sc. in Electronics and Communications Engineering – Cairo University

A Thesis Submitted to the

Faculty of Engineering at Cairo University in Partial Fulfillment of the

Requirements for the Degree of

Master of Science in

Electronics and Electrical Communications Engineering

Supervised by Dr. Khaled Mohamed Fouad Elsayed

Professor, Faculty of Engineering, Cairo University

Faculty of Engineering, Cairo University

Giza, Egypt 2004

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TABLE OF CONTENTS

TABLE OF CONTENTS ...…………………………………………………..... II

LIST OF TABLES …………………………………………………………... IV

LIST OF FIGURES …………………………………………………………... V

LIST OF SYMBOLS ……………………………………………………….... VIII

LIST OF ABBREVIATIONS ………………………………………………….. IX

ACKNOWLEDGEMENTS …………………………………………………..... X

ABSTRACT ………………………………………………………………..... XII

Chapter 1: Introduction ……………………………………………….... 1

1.1. Thesis Organization …………………………………………. 5

Chapter 2: Scheduling in Wireless Networks ………………………….. 7

2.1. Wireless Network Challenges ……………………………….. 8

2.1.1. Wireless Link Variability …………………………..... 8

2.1.2. Fairness …………………………………………….... 9

2.1.3. Scarcity of Resources ………………………………... 10

2.2. Multiuser Diversity in Wireless Systems …………………..... 10

2.3. Cross Layer Designs ……………………………………….... 13

2.4. Thesis Motivation ………………………………………….... 17

Chapter 3: Channel-Aware Scheduling Disciplines for Delay

Bounded Traffic in TDM-Based Wireless Networks ……..

19

3.1. Network Model ……………………………………………… 20

3.2. Previous Work ……………………………………………….. 23

3.3. The Proposed Scheduling Schemes …………………………. 27

3.3.1. Channel Dependent Earliest Due Date (CD-EDD)

Scheduling Discipline ………………………………..

29

3.3.2. A Set of Violation Fair Rules ……………………….. 31

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Chapter 4: Simulation Results and Discussions of the TDM-Based

Scheduling Disciplines ……………………………………...

35

4.1. Simulation Setup …………………………………………….. 35

4.2. Performance Metrics ………………………………………… 37

4.3. Results and Discussions ……………………………………... 39

Chapter 5: Channel-Aware Scheduling for Delay-Bounded Traffic in

OFDMA-Based Wireless Networks ………………………..

63

5.1. Network Model ……………………………………………… 65

5.2. Scheduling in OFDMA Networks …………………………… 68

5.2.1. Static Subcarrier Management ……………………..... 68

5.2.2. Dynamic Subcarrier Management …………………... 69

5.3. Problem Formulation ………………………………………... 72

5.4. Subcarrier Allocation Algorithm ……………………………. 75

5.5. Subcarrier Assignment Algorithm …………………………... 80

Chapter 6: Simulation Results and Discussions of the OFDMA-Based

Scheduling …………………………………………………...

83

6.1. Simulation Setup …………………………………………….. 83

6.2. Results and Discussions ……………………………………... 87

Chapter 7: Conclusions and Future Research ………………………… 101

7.1. Conclusions ………………………………………………….. 101

7.2. Future Research Directions ………………………………….. 103

REFERENCES ……………………………………………………………..... 105

APPENDIX A: CODE SAMPLES …………………………………………….. 111

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LIST OF TABLES

Table 4.1 The system capacity of HDR cell achieved by different

disciplines

Table 4.2 Fading levels and its corresponding capacities used in

simulations

Table 4.3 Simulation results summary

Table 6.1 Summary of simulation parameters

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LIST OF FIGURES

Figure 2.1 Throughput region for a simple channel model

Figure 3.1 Channel state dependent downlink scheduling architecture for

multiple users sharing a wireless TDMA channel

Figure 4.1 The average throughput per user for 20 m sec delay bound






Figure 4.7 Delay distributions of user 1 and user 14 for 20 m sec delay bound






Figure 4.13 The maximum and the minimum 95-percentile delays

Figure 4.14 The maximum and the minimum percentage of lost packets

Figure 4.15 Delay distributions of user 1 and user 14 for 20 m sec delay bound (VF rules)


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Figure 4.21 The maximum and the minimum 95-percentile delays (VF rules)

Figure 4.22 The maximum and the minimum percentage of lost packets (VF rules)

Figure 4.23 The throughput behavior at 20 m sec delay bound






Figure 5.1 Orthogonal Frequency Division Multiple Access (OFDMA) transceiver

Figure 5.2 An example of channel gain variations taken from [26]

Figure 5.3 Subcarrier Allocation Algorithm

Figure 5.4 Subcarrier Assignment Algorithm

Figure 6.1 The power-delay profile of the B Model pedestrian environment.

Figure 6.2 Throughput performance for a 20 msec delay bound.


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Figure 6.5 Throughput fairness indices of both the dynamic algorithm and the static algorithm for different delay bounds.

Figure 6.6 Deadline violation fairness for different delay bounds.

Figure 6.7 Delay tails of the best and worst channel users (N = 42 users).

Figure 6.8 Delay tails of the best and worst channel users (1.5% and 2.3% of the best and the worst users packets were lost) (N = 120 users, T = 20 msec).



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LIST OF SYMBOLS

ai Delay weighted constant

B Channel of bandwidth

C(t) The instantaneous Shannon channel capacity

di(t) Time to expire of user i HoL packet at time t

δi Deadline violation probability

δij(t) Indicator that subcarrier j is to be assigned to user i at time t

|h(t)| The normalized gain (or fading level) of the wireless channel at

the time t

μi(t) The actual rate that could be used for transmission by the ith

user at time t in TDM-based networks

iµ The mean rate supported or previously offered to the ith user in

TDM-based networks

μji(t) The actual rate that could be used for transmission by the ith

user over the jth subcarrier at time t in OFDMA-based networks

( )i tµ The average subcarrier capacity of the ith user

N Number of users in the system

Nt Number of active users at time t in the system

NVi(t) The number of deadline due date violations encountered in the

flow of the ith user up to time t.

( )NV t The average of the number of violations in all N queues

ni(t) The number of subcarriers to be assigned to the ith user at the

slot starting at time t

RT(t) The total instantaneous system throughput

ri The average rate of user i video stream

S Total number of subcarriers

S' Number of remaining subcarriers

t Time index

Ti Delay Bound of user i

Wi(t) Waiting time of user i HoL packet at time t

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LIST OF ABBREVIATIONS

CD-EDD Channel Dependent – Earliest Deadline Due

CDMA Code Division Multiple Access

EDD Earliest Deadline Due

EDGE Enhanced Data rates for GSM Evolution

FDMA Frequency Division Multiple Access

GPRS General Packet Radio Services

HDR High Data Rate

HoL Head of Line

LWDF Largest Weighted Delay First

MBWA Mobile Broadband Wireless Access

M-LWDF Modified – Largest Weighted Delay First

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

PDA Personal Digital Assistant

QoS Quality of Service

RTT Radio Transmission Technology

SISO Single Input Single Output

SNR Signal to Noise Ratio

TCP Transmission Control Protocol

TDMA Time Division Multiple Access

UMTS Universal Mobile Telecommunications System

UTRA UMTS Terrestrial Radio Access

VF Violation Fair

WWW World Wide Web

x

ACKNOWLEDGEMENTS

I have the pleasure and honor to express heart-felt gratitude to my thesis

supervisor Dr. Khaled M. Fouad Elsayed for encouragement and unfailing

guidance which enabled achieving the research goals.

Grateful thanks are also due to Dr. Mohammed Khairy for providing valuable

advice and needed information.

The role of engineer Islam Sherif is also gratefully acknowledged.

Last, but not least, a special expression of gratitude and appreciation goes to

my family for their patience and generous support.

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ABSTRACT

Providing delay guarantees to time-sensitive traffic in beyond 3G

wireless multimedia networks is a challenging issue. This is due to the time-

varying link capacities and the variety of real-time applications expected to be

handled by such networks. Multiuser diversity schemes exploiting variation in

users' channel conditions have been shown to offer orders of magnitude increase

in the performance of wireless systems. In this thesis, we address the problem of

channel-aware scheduling of delay bounded traffic for two different wireless

network models.

First, we consider this problem in a Time Division Multiple Access

(TDMA) based wireless networks. We propose two channel-aware scheduling

disciplines that are capable of providing such delay guarantees in wireless

networks. Namely, the Channel Dependent Earliest-Due-Date (CD-EDD)

discipline, which attempts to guarantee the targeted delay bounds, and the

Violation Fair (VF) scheduling, which attempts to provide fairness in both

bandwidth sharing as well as the targeted delay bounds delivered to the different

users.

The second system considered is multiuser scheduling in Orthogonal

Frequency Division Multiple Access (OFDMA) based broadband wireless

networks. In ODFMA, the scheduling problem is further complicated by the

existence of multiple subcarriers. We propose heuristic algorithms for both

subcarrier allocation and assignment in such a network. These dynamic

algorithms utilize multiuser diversity to increase the system efficiency by

attempting to guarantee the required delay bounds while providing fairness in

throughput sharing among different users.

A unique feature of our work is the possibility of explicit provisioning of

statistical QoS as well as enhancing fairness in data rate, delay bound, and delay

bound violation. We provide extensive simulation results to show the different

performance aspects of the proposed schemes.

1

Chapter 1 Introduction

Future wireless networks are designed to support wideband data

communications as well as voice communications. Such networks will be the

basis for a wireless information society where access to information and

information services is available anytime, anywhere, and to anybody. This

objective has been encouraged by the tremendous growth of the wireless industry

over the few past decades. Internet is another branch of the telecommunication

industry which has enjoyed similar dramatic growth which has resulted in the

ever growing range of services available through the World Wide Web (WWW).

Thus, the introduction of mobile Internet brought about by the convergence of

these two technologies is the future objective of the telecommunication industry.

Multiple enhancements have being implemented in both the currently

deployed cellular mobile systems and the Internet networking. The progressive

introduction of the General Packet Radio Services (GPRS), Enhanced Data rates

for GSM Evolution (EDGE), the High Data Rate (HDR/CDMA) and the third

generation Universal Mobile Telecommunications System (UMTS) clearly

illustrates this evolution. At the same time, several wireless technologies have

been designed in order to include arrangements for accessing Internet services

such as IEEE 802.11, 802.16 and HIPERLAN2. Each of these technologies has

been optimized for operation over a particular range of service bit rate versus

user speed of mobility. Moreover, several technologies have been upgraded to

enable ad-hoc networking. In this hybrid environment, the need to provide

ubiquitous connectivity for slow and fast moving users with different rate

requirements arises. Beyond 3G and 4G networks are being developed towards

achieving this objective. Such networks could be implemented based on a

common Internet Protocol (IP) core network internetworking with multiple

2

access networks for broadcast, wide area cellular and short range

communications. Thus, beyond 3G and 4G wireless networks should enable the

"person to machine" and "machine to machine" networking parallel to the

"person to person" communication concept of cellular wireless for ubiquitous

connectivity to the Internet services.

Because wireless frequency is a scarce resource, efficient frequency

utilization is becoming increasingly important. Resource allocation schemes and

scheduling policies are critical to achieving these goals. In wireline networks,

resource allocation schemes and scheduling policies play important roles in

providing service performance guarantees, such as throughput, delay, delay-jitter,

fairness, and loss rate [1]. However, resource allocation and scheduling schemes

from the wireline domain do not carry over to wireless systems because wireless

channels have unique characteristics not found in wireline channels, such as

limited bandwidth, time-varying and location-dependent channel conditions, and

channel-condition-dependent throughput.

In wireless networks, the channel conditions of mobile users are time-

varying. Radio propagation can be roughly characterized by three nearly

independent phenomena: path-loss variation with distance, slow log-normal

shadowing, and fast multipath-fading. Path losses vary with the movement of

mobile stations. Slow log-normal shadowing and fast multipath-fading are time-

varying with different time scales. Thus, users perceive time-varying service

quality and/or quantity because channel conditions are time-varying. For voice

users, better channel conditions may result in better voice quality. For packet

data service, better channel conditions (or larger signal to interference plus noise

ratio (SINR)) can be used to provide higher data rates by reducing coding or

spreading and/or increasing the constellation density. Previous research showed

that cellular spectral efficiency (in terms of b/s/Hz/sector) can be increased by a

factor of two or more if users with better links are served at higher data rates.

Procedures to exploit this are already in place for all the major cellular standards:

adaptive modulation and coding schemes are implemented in the 3G TDMA

3

standards, and variable spreading and coding are implemented in the 3G CDMA

standards. In general, a user is served with better quality and/or at a higher bit

rate when the channel condition is better.

On one hand, good scheduling schemes should be able to exploit the

time-varying channel conditions of users to achieve higher utilization of wireless

resources. On the other hand, the potential to exploit higher data throughputs in

an opportunistic way, when channel conditions permit, introduces the tradeoff

problem between wireless resource efficiency and fairness among users. Because

wireless spectrum is a scarce resource, improving the efficiency of spectrum

utilization is important, especially to provide high-rate-data services. Hence, we

cannot expect the same throughput for all users because the users in general can

have very different channel conditions. However, a scheme designed only to

maximize the overall throughput could be very unfair among users, especially

users with widely disparate distances from the base station. For example,

allowing only users close to the base station to transmit with high transmission

power may result in very high throughput, but is unfair to other users. This basic

dilemma motivates our work: to improve wireless resource efficiency by

exploiting time-varying channel conditions, and at the same time satisfy the

delay quality of service (QoS) for multiple multimedia users sharing a fading

channel, and enhancing the level of fairness among users.

In this thesis, we address this problem in two wireless network models

based on different multiple access methods. We develop simple and efficient

scheduling schemes, which can yield substantial capacity gain. The efficiency is

achieved by virtue of multiuser diversity. Multiuser diversity refers to a type of

diversity present across different users in a fading environment. This diversity

can be exploited by scheduling transmissions so that users transmit when their

channel conditions are favorable. Using such an approach leads to a system

capacity that increases with the number of users. In order to realize this

mechanism, the scheduler should be equipped with a scheme to estimate the

channel state of every user in the system, with this information, the scheduler can

4

exploit multiuser diversity. However, making the scheduling decision only

dependent on the users' channel conditions will cause severe degradation of the

service offered to the users with long period of bad channel states. The proposed

solutions employ mechanisms to compensate such users in order to serve their

packets before expiry. A unique feature of our work is explicit provisioning of

statistical QoS, which is the capability characterized by a data rate, delay bound,

and delay-bound violation probability triplet.

First, we consider a time-slotted system in which time is the resource to

be shared among the users. Such a network is called Time Division Multiple

Access (TDMA) networks. The scheduler function is to select only one user for

transmission in each time slot. We propose two scheduling disciplines applicable

in such a network.

In the second part of the thesis, we address scheduling in OFDMA-based

broadband wireless networks. Orthogonal Frequency Division Multiple Access

(OFDMA) is a multiple access scheme used in such networks to support high

speed communication over fading channels. The channel is subdivided into a set

of subcarriers as in Orthogonal Frequency Division Multiplexing (OFDM). This

set of subcarriers is the common system resource to be shared among users. The

scheduling problem is how to distribute this set of subcarriers among users

present in the system. Such a kind of problem is computationally complex. So,

our methodology is to subdivide it into a couple of lower complexity problems,

namely, subcarrier allocation problem and subcarrier assignment problem. We

propose novel practical opportunistic algorithms for these two problems in this

thesis. The objective of these algorithms is also to fairly provide the requested

quality of service to real-time traffic users, and in the meantime, increase the

system efficiency by utilizing multiuser diversity.

5

1.1 Thesis Organization

The remainder of this thesis is organized as follows. In chapter 2, we

highlight the basic characteristics of wireless systems which make scheduling

multiple users a challenging issue. Then we discuss multiuser diversity and the

recently introduced concept of cross-layer optimization in wireless systems.

Multiuser diversity is our key technique to increase the system efficiency in

resource utilization. The motivation of the thesis is then identified.

In chapter 3, we consider the channel-aware scheduling problem in TDM-

based wireless networks for multiple delay-sensitive users. First, we describe the

network model. Then, we present a comprehensive study of the literature in this

area. From this study, we identify the main characteristic of the solution of such a

problem. We propose two channel-aware scheduling schemes that are capable of

providing delay guarantees for time-sensitive traffic in wireless networks. The

first proposed scheme, the Channel-Dependent Earliest-Due-Date (CD-EDD)

discipline, attempts to guarantee the targeted delay bounds in addition to

exploiting multiuser diversity to make best utilization of the variable capacity of

the channel. In the second scheme, the Violation Fair (VF) scheduling, we

attempt to ensure that the number of packets dropped due to deadline violation is

fairly disturbed among users. This provides fairness in both bandwidth sharing as

well as the quality of service delivered to different users.

In chapter 4, we provide extensive simulation results to show the different

performance aspects of the proposed schemes. In particular, we show that it can

simultaneously guarantee a delay upper bound while providing fairness in these

guarantees among all users, as well as providing fairness in the throughput

sharing among different users in fading wireless channel networks.

6

In chapter 5, we tackle the problem of channel-aware scheduling of

multimedia users in OFDMA-based wireless networks. After describing such

wireless networks, we discuss the scheduling problem and briefly describe the

different scheduling schemes proposed so far in the literature. We present a

mathematical formulation of the scheduling problem. Then we propose efficient

opportunistic subcarrier allocation and assignment algorithms that utilize

multiuser diversity to achieve a performance gain while yet satisfying the QoS

constraints of multimedia traffic.

In chapter 6, we explore the various characteristics of the subcarrier

allocation and assignment algorithms proposed in chapter 5 through a set a

simulation tests. In order to qualify the achievements of our dynamic algorithms,

we compare them with the best known static algorithm.

Finally, in chapter 7, we summarize the thesis and conclude the main

findings of this research. Then we point out some future research directions

advised from this study.

7

Chapter 2 Scheduling in Wireless Networks

The rapid growth of wireless technology, when coupled with the

explosive growth of the Internet, has increased the demand for wireless data

services. Traffic on beyond 3G wireless networks is expected to be a mix of real-

time traffic such as voice, multimedia teleconferencing, games; and data-traffic

such as WWW browsing, messaging and file transfers. These applications will

require diverse quality of service (QoS) guarantees. Various scheduling

disciplines have been developed in order to guarantee certain required QoS over

wireline networks. However, these service disciplines, such as Weighted Fair

Queuing (WFQ), virtual clock, and Earliest-Due-Date First (EDD) [1], are not

directly applicable in wireless networks because they do not consider the

characteristics of wireless channel. These characteristics include high error rate,

bursty errors, location-dependent and time-varying wireless link capacity, scarce

bandwidth, user mobility, and power limitation of the mobile hosts. All of the

above characteristics cause the development of efficient and effective scheduling

algorithms for wireless networks to be very challenging.

In this chapter, we first highlight the wireless network peculiarities that

made the design of efficient scheduling disciplines a very challenging issue. We

then briefly introduce a new kind of diversity inherently present in a wireless

network with a multiple of users. This type of diversity is called multiuser

diversity which exploits variation in channel states of the users in a wireless

system. This issue has been recently considered as cross-layer optimization

technique in wireless networks; and have been shown to offer orders of

magnitude increase in the capacity and the performance of wireless systems.

8

2.1 Wireless Networks Challenges

2.1.1 Wireless Link Variability

The biggest difference between a wireless network and a wireline

network is the transmission link variability. Due to the high quality of the wired

transmission media such as fiber and copper, packet transmissions on wireline

networks enjoy very low error rate. However, wireless channels are more error-

prone and suffer from interference, fading, and shadowing. As a result, the

capacity of a wireless link has very high variability. Specifically, there are two

types of wireless link variations [2]:

(i) Small-scale channel variations

This is the rapid fluctuations of the signal's strength over a small

travel distance or small time interval. Such fast changes may be caused

by either the multipath propagation of radio signals or the mobility of

the user terminals as well as the surrounding environment. Thus, this

phenomenon is usually called multipath fading or shadowing. Fast

channel variations due to fading are such that thee states of different

channels can asynchronously switch from “good” to “bad” within a few

milliseconds and vice-versa. This causes bursts of errors to occur during

which packets cannot be efficiently transmitted on the link.

(ii) Large-scale channel variations

Unlike the fast channel variations caused by fading, there is

another type of variations occurring on a much greater space – time

scale. Large-scale channel variations means that the average channel

state conditions (signal strength) changes according to the relative

distance between the transmitter and the receiver. For example, in a

cellular wireless system, the same wireless link capacity may be seen

having different value depending on relative location to the base station.

9

Thus, due to small-scale and large-scale changes in the channel, some

users may inherently demand more resources (e.g. channel access time or

bandwidth) than others based on their location or mobility pattern, even if their

data rate requirement is the same as or even less than other users. Such link

variations require the scheduling algorithms to be equipped with certain dynamic

mechanisms that can deal with these time-dependent and location-dependent

changes.

2.1.2 Fairness

Since wireline media may be considered error-free, the service rate

allocated is indeed the amount of service share that is received by a particular

flow. Providing fairness in resource sharing in wireline networks is usually

guaranteed by dedicating a certain service rate to a flow, and the scheduling

algorithm prevents different flows from interfering with each other. However, the

fairness issue in wireless networks is more complicated because of the wireless

link peculiarities discussed above. It may happen that a packet is scheduled for

transmission on a wireless link according to a certain service discipline or

fairness guideline, which is independent of link state, and the link is actually in a

high-error state. If the packet is transmitted, it will be corrupted and the

transmission will waste transmission resources. In this case, deferring

transmission of this packet till the link recovers from the high-error state is

clearly a reasonable choice. The affected flow, hence, temporarily loses its share

of the transmission bandwidth. To ensure fairness, the flow should be

compensated for this loss later when the link recovers. But determining how to

compensate for it is not an easy task. An alternative view of fairness arises in

wireless networks. In particular, the system should provide fair temporal access

to the transmission medium rather than fair throughput, i.e. ensure that each user

is able to access the medium for a (weighted) fair share of time. Also, fairness

guarantees may be required on a long-term basis or short-term basis.

10

2.1.3 Scarcity of Resources

The most precious resource in wireless networks is the bandwidth. A very

challenging issue in wireless networks designs is the efficient utilization of the

wireless channels. This can be achieved by maximizing the effective service

delivered, and at the same time, minimizing the unproductive transmissions on

low quality links.

Usually, mobile terminal in wireless networks are operated with limited

amount of power. This imposes another constraint in wireless designs. For

example, a scheduling algorithm that needs to use every uplink packet’s arrival

time to compute scheduling order is not a good choice. This is because it

demands a large amount of power from mobile hosts for transmitting the

information of arrival times to the base station.

Another important issue that characterizes wireless networks is that real-

time services such as voice and multimedia applications should be provided

efficiently. Thus, the complexity of different algorithms deployed in wireless

networks, such as admission control and scheduling algorithms, should not be

too high. So that it can be executed at high speed to serve real-time multimedia

traffic with stringent timing requirements.

2.2 Multiuser Diversity in Wireless Systems

An effective way to increase the capacity of a time-varying channel is the

use of diversity. The idea of diversity is to create multiple independent signal

paths between the transmitter and the receiver so that higher channel capacity can

be achieved. Diversity can be implemented over time, space, and frequency.

These traditional diversity methods are essentially applicable to a single-user

11

link. The basic idea is to improve performance by having several independent

signal paths between the transmitter and the receiver.

Recently, however, Knopp and Humblet [3] introduced another kind of

diversity, which is inherent in a wireless network with multiple users sharing a

time-varying channel. This diversity, termed multiuser diversity [4,5], comes

from the fact that different users usually have independent channel gains for the

same shared medium. With multiuser diversity, the strategy of maximizing the

total Shannon (ergodic) capacity is to allow at any time slot only the user with

the best channel to transmit. This strategy is called Knopp and Humblet’s

scheduling.

This multiuser diversity is best motivated by an information theoretic

result of Knopp and Humblet [3]. They focused on the power control uplink in

the single cell, with multiple users communicating to the base station via time-

varying channels. To maximize the total information theoretic capacity, they

showed that the optimal strategy is to schedule at any one time only the user with

the best channel to transmit to the base station. This means that the only user who

is allowed to transmit is the one with the largest instantaneous power (received at

the base station), and the others must remain quite until one of them becomes the

strongest. Diversity gain arises from the fact that in a system with many users,

there is likely to be a user with a very good channel at any time instant. Overall

system throughput is maximized by allocating at any time the common channel

resource to the user that can best exploit it.

This is completely in opposite sense to conventional power control.

Conventional power control is used to equalize the powers received from

different users at the base station. In wireless networks, the average received

power of a given user is related to his distance from the base station, and

correspondingly there is a certain loss in signal strength or path loss. The

instantaneous power, on the other hand, is usually time-varying due to multipath

fading. Power control is usually done in two ways, namely, open-loop or closed-

12

loop manners. The former refers to the case where the uplink and downlink

channels are assumed to be strongly correlated and estimation of the received

power at the base station is based on the signal received by the user. In the later,

estimation is performed in the base station which then instructs the users, via the

downlink channel, to transmit at a certain power. Provided that the received

powers don't vary too quickly, the power controller simply attempts to keep all

the received powers at some nominal level by inverting both the path loss and

fading effects of the channel.

Results in [3] have shown that Knopp and Humblet scheduling can

increase the total (ergodic) capacity dramatically, in the absence of delay

constraints, as compared to the traditionally used (weighted) round robin (RR)

scheduling where each user is a priori allocated fixed time slots. However, under

this scheme, a user in a fade of an arbitrarily long period will not be allowed to

transmit during this period (for example when a user is far from the base station

and its mobility is low may never have the opportunity to transmit it data),

resulting in an arbitrarily long delay; therefore, this scheme provides no delay

guarantees and thus is not suitable for delay-sensitive applications, such as voice

or video.

Another problem of such greedy scheduling is the unfairness in resource

sharing. This is due the absence of a way to compensate users in fade for

relatively long periods. In [6] and [7], the authors present a scheduling scheme

for the Qualcomm/HDR system which satisfies the following fairness property: if

another scheduling algorithm is used to increase the throughput of a specific user

by x% over what that user receives under the HDR scheduling algorithm, the

sum of all the percentage decreases suffered by the throughputs of all the other

users under the new algorithm will be more than x% [7]. The scheduler at the

base station determines the next terminal to be served based not only on the

instantaneous channel gain of the users but also on the amount of data that has

already been transmitted to each terminal. Therefore, when a user is prevented

from transmission for relatively long period its data transmission rate decreases

13

significantly. This make the scheduler give this user the advantage to transmit

over all other users even though there channel qualities may be much better that

this one's. This property is known as proportional fairness.

The authors of [8 – 14] have studied opportunistic wireless scheduling.

Opportunistic transmission scheduling polices are those who exploits the time

varying channel conditions and maximizes the system performance stochastically

under a certain resource allocation fairness constraint. They extend scheduling

policies for wireline networks to wireless networks which provide various

degrees of performance guarantees, including short-term and long-term fairness,

as well as short-term and long-term throughput bounds. For example, the authors

in [8] presented a wireless credit-based fair queuing, a scheduler for wireless

packet networks with provable short- and long-term transmission rate fairness

guarantees. A framework for opportunistic scheduling over multiple wireless

channels was developed in [9]. In [10, 11, 14], the authors summarize various

opportunistic scheduling schemes and discuss the advantages and costs

associated with opportunistic scheduling. The authors of [12] generalized the

opportunistic scheduling problem to include multiple interface systems in which

several users can be served simultaneously. An efficiency-based scheduling

scheme that gives flexibility in adjusting the way resources are allocated among

multiple interactive best-effort data users was proposed in [13].

2.3 Cross Layer Designs

Recently there has been increased interest in protocols for wireless

networks which rely on intelligent interactions between various layers of the

network protocol stack. Generically termed cross layer design, many of these

proposals are aimed at achieving performance improvements [15]. In this section,

we provide an overview of the cross-layer paradigm shift that is beginning to

14

take place as wireless communications evolves from a circuit-switched

infrastructure to a packet-based infrastructure.

Cross-layer networking can be easily demonstrated when the knowledge

of the physical and MAC layers is shared with higher layers in order to provide

efficient methods for allocating network resources to different users and

applications. In essence, future networks will need to provide "impedance

matching" of the instantaneous radio channel conditions of layer 1 and layer2

with the traffic and congestion conditions for layers 3 and above. Further, such

matching will need to be coordinated with a wide range of particular

applications, making the topic of cross-layer networking an increasingly

important one for the evolving wireless build-out. The advantages of cross-layer

networking appear to be real, and will be increasingly important as capacities

offered through the wireless LAN interface approach the level of capacity that

can be handled over the Internet backbone. For example, network layer

throughput performance can be significantly improved if the physical layer

information (channel conditions) is used at the network layer and transport layer

for controlling TCP traffic over wireless links. Energy-based routing algorithms

[16-18], currently developed for ad-hoc wireless networks, are another example

of how different layer information can be shared to improve wireless networks

performance. Also, channel state dependent scheduling (a cross-layer method) of

multiple users sharing a wireless link, can be used to increase the overall system

throughput. This last example of cross-layer designs will be the main focus of

this thesis.

In order to get insight of how significant gains can be achieved by cross-

layer networking, let us consider the following simple example [15], in which the

idea of the throughput region of a multi-user wireless network is illustrated.

Consider a wireless network with two users. Suppose that packets arriving from

the wireline network to the base-station are temporarily buffered, before they are

forwarded to the mobile users. Let us denote the rate at which data arrives for

mobile users 1 and 2 (from the wireline network) by λ1 and λ2 packets/slot,

15

respectively. A natural question one should ask is “what are the pairs of (λ1, λ2)

that the wireless system can support without the queues at the base-station

overflowing?” Assuming a very simple wireless channel model as follows: In the

first channel state, if user 1 is scheduled, the data rate achieved by User 1 is ’a’

packets/slot, while if user 2 is scheduled, the data rate achieved by User 2 is ’b’

packets/slot. Similarly, in the second channel state, if user 1 is scheduled, the

achieved rate (for User 1) is ’c’ packets/slot, while if user 2 is scheduled, the

achieved rate (for User 2) is ’d’ packets/slot.

In Figure 2.1, we have illustrated the rates described above. The left-most

panel illustrates the first channel state. The x-axis indicates the rate allocated to

user 1 in channel state 1, and the y-axis indicates the rate allocated to user 2.

Suppose that whenever the wireless channel is in state 1, the base-station

scheduler decides to transmit to user 1 half the time, and for the other half of the

time, user 2 is scheduled. Then, the average rate allocated to user 1 in state 1

would be a/2 packets/slot, and the average rate allocated to user 2 would be b/2

packets/slot. Similarly, we can choose various splitting rules for channel state 1

(for example, 1/5 of the time send to user 1, 3/5 of the time send to user 2, and do

nothing for 1/5 of the time). The shaded region in the left-most panel in Figure

2.1 is the collection of average rates to users 1 and 2 over all such splitting rules.

Similarly, the middle panel illustrates the corresponding achievable region in

channel state 2.

Figure 2.1 Throughput region for a simple channel model taken from [15].

Channel state 2

π2 = 0.5

R2

c

µ2

d

µ1

Channel state 1

π1 = 0.5

R1

a

µ2

b

µ1

Stability region

achievable rates

µ2

µ1 a+c 2

b+d 2

µ1: User 1 rate µ2: User 2 rate

16

Now, choose any vectors νi Є Ri, i = 1, 2 where R1, R2 are the achievable

regions in states 1 and 2, respectively. Then, the throughput region is defined as

V = { ν : ν = π1ν1 + π2ν2 }, where π1, π2 are the steady-state probabilities of being

in channel-states 1 and 2, respectively. Observe that V is merely the convex

combination of the achievable regions in each state. This is illustrated in the right

panel in Figure 2.1. Thus, if the packet arrival rates (λ1, λ2) lie within the

throughput region, we can be guaranteed that the queue lengths will not become

unbounded.

It can be shown that if the channel state was not used for packet

scheduling, the throughput region would be that to the left of the dotted line in

the right panel of Figure 2.1 (sub-optimal use of network resources). The

significant gains due to channel state dependent scheduling algorithms can be

illustrated by means of a simple example. Consider a wireless system consisting

of three users in a TDM-based network. The access time is slotted, and the

channels to be constant over a time-slot. We assume that the channels are either

ON or OFF, equally likely, and the channels being independent of each user.

Thus, in this system, there are eight possible (instantaneous) channel states for

the three independent users, ranging from (ON,ON,ON) to (OFF,OFF,OFF).

When a user’s channel is ON, one packet can be transmitted successfully to the

mobile user during the time-slot. The associated scheduling problem is to decide

which user is allowed access to the channel during each particular time-slot.

A naive scheduling rule would be to employ the round-robin mechanism.

In such a scheme, the users periodically are given access to the channel, with

each user getting 1/3 of the slots over time. As the channel of each user is equally

likely to be ON or OFF in each time-slot, it follows that over time, on average,

each user will get a data rate of 1/6 packets/slot.

On the other hand, suppose that the base-station uses knowledge of the

instantaneous channel state. Then, a simple policy would be to schedule and

transmit to a user whose channel is in the ON state. If more than one user’s

17

channel is in the ON state, then the scheduler could pick a user randomly

(equally likely) among those users whose channel are ON, and send data to the

selected user. This simple example assumes that all the users have identical

traffic demands. For the case where some users have greater needs than others,

such users would be assigned channel access with greater likelihood. We observe

that this policy ensures that no data is sent by the base-station if and only if all

users’ channels are OFF (which occurs on average, only 1/8 of the time). Thus,

the total data rate achieved by this state dependent rule is 1 – 1/8 = 7/8

packets/slot. As this rule is symmetric across users, it follows that on average, the

data rate per user is 7/24 packets/slot, which is almost twice the throughput as the

round-robin scheme which provided 1/6 packets/slot. In addition, the base station

does not radiate power during bad channel conditions, thereby decreasing

interference levels in the wireless network. Moreover, it is obvious that the larger

the variation in the channel, the larger will be the gain due to state-dependent

scheduling. This gain achieved due to channel-state dependent scheduling is the

multi-user diversity gain discussed in section 2.2.

The above example illustrates the significance of multi-user diversity

gain in network scheduling. However, a central question is how to design on-line

algorithms which achieve this gain, while also supporting diverse quality of

service requirements for various users.

2.4 Thesis Motivation

The previous sections illustrate the challenges imposed on the scheduling

problem by the wireless nature. The gains that can be accrued based on cross-

layer methods, such as multiuser diversity schemes, were clarified. However,

these schemes provide no delay guarantees and thus are not suitable for delay-

sensitive applications. Besides, greedy schemes such as Knopp and Humblet

scheduling don't provide farness in system resource management. Now, we

18

formulate the objective of our research. In this thesis, we are trying to find

answers to the following questions:

(i) How can multiple real-time data users be supported simultaneously

with good quality of service (QoS), namely, with packet delays not

exceeding given thresholds with high probability?

(ii) How can system resources be fairly allocated among various users

(keeping in mind that some users may demand more system resources

than others, even if their QoS requirements are the same or even less,

due to the difference in their wireless channel quality)?

Though these questions have not been answered fully, there has been

extensive research on various aspects of the above problems. In the rest of this

thesis, we are attempting to find practical answers in different wireless networks.

Specifically, we are considering two different popular multiplexing schemes that

are candidates for systems beyond 3G, namely TDMA and OFDMA.

19

Chapter 3 Channel-Aware Scheduling Disciplines for Delay-

Bounded Traffic in TDM-Based Wireless Networks

Providing delay guarantees to time-sensitive traffic in future wireless

multimedia networks is a challenging issue. This is due to the time-varying link

capacities and the variety of real-time applications expected to be handled by

such networks. Multiuser diversity schemes exploiting variation in channel states

of users in a wireless system have been shown to offer orders of magnitude

increase in the performance of wireless systems. In this chapter we propose and

evaluate the performance of two channel-aware scheduling schemes that are

capable of providing such delay guarantees in wireless networks. In the first

proposed scheme, the Channel-Dependent Earliest-Due-Date (CD-EDD)

discipline, the expiration time of the head of line packets of users' queues is taken

into consideration in conjunction with the current channel states of users in the

scheduling decision. This policy attempts to guarantee the targeted delay bounds

in addition to exploiting multiuser diversity to make best utilization of the

variable capacity of the channel. In the second scheme we attempt to ensure that

the number of packets dropped due to deadline violation are fairly disturbed

among users. This provides fairness in both bandwidth sharing as well as the

quality of service delivered to different users. A unique feature of our work is

explicit provisioning of statistical QoS as well as ensuring fairness in data rate,

delay bound, and delay bound violation.

In the next chapter, we provide extensive simulation results to show the

different performance aspects of the proposed schemes. In particular, we show

that it can simultaneously guarantee a delay upper bound while providing

fairness among all users with different channels, as well as providing fairness of

throughput sharing among different users in fading wireless channel networks.

20

3.1 Network Model

We first describe the cellular wireless network model used, and more

specifically the downlink of such a network, where a base station transmits data

to N mobile terminal users, each of which requires certain QoS guarantees. In

cell-structured wireless networks, the service area is divided into cells, and each

is served via a base station. A single cell is considered in which a centralized

scheduler at the base station controls the downlink scheduling, and uplink

scheduling uses an additional mechanism such as polling to collect transmission

requests from mobile terminals [8], [9]. We assume that downlink and uplink

transmission don't interfere with each other. We consider a time slotted system,

where time is the resource to be shared among users. A time-slotted cellular

system can have more than one channel (frequency band), but at any given time,

only one user can occupy a given channel within a cell. Here, we focus on the

scheduling problem for a single channel over which a number of users could be

time-division multiplexed. Time division multiple access (TDMA) systems

divides the time into time slots of length Ts, during which data transmission of a

single user, the scheduled user, is carried out using all resources available to the

base station at that time instant. For downlink scheduling, packets destined to

different users are put in separate queues, one corresponding to a user's data

flow.

As described in the previous chapter, The time varying channel

conditions of wireless links are related to three basic phenomena: fast fading on

the order of milliseconds, shadow fading on the order of tens to hundreds of

milliseconds, and finally, longtime-scale variations due to user mobility. The

channel fading processes of the users are assumed to be stationary, ergodic and

independent of each other, and we also assume that the channel gains are

constants over one time slot's duration. Since our algorithm will exploit the

users’ channel conditions in making the scheduling decision, we consider

wireless systems with mechanisms to make predicted channel conditions

available to the base station as is commonly the case with technologies such as

21

HDR [6], UMTS-HS-DPA [19], (E)GPRS [20], etc. The particular mechanism

employed by a system depends on the communication standard. For example, in

HDR and UMTS-HS-DPA, the underlying physical channel uses explicit channel

notification so that the scheduler has the best possible knowledge about the

channel conditions. In UMTS-DCH, there is a logical control channel assigned

with every user that allows a coarse estimation of the channel condition. The

packet extensions (E)GPRS to GSM-TDMA systems offer various coding

schemes to support data transmission over a wide range of channel conditions.

These are typically switched on a slower timescale, e.g., based on experienced

frame error rates. Regardless, the recently selected coding scheme that

determines the ‘throughput per RLC-block’ can serve as a coarse indicator of the

channel condition for the scheduler. In general, the faster and more precisely the

channel quality can be predicted, the better the scheduler can incorporate this

information into its decision as to which user to schedule next [8]. Thus, we will

assume that base station has the current (or delayed) channel state information of

each user.

Figure 3.1 shows the architecture for channel state aware scheduling of

multiuser traffic over a fading time slotted wireless channel. The scheduler

makes a decision to serve a particular queue at the beginning of every time slot.

This decision could depend on HoL packet delay information, such as its waiting

time and its time to expire, as well as channel states. Once a decision has been

made, the chosen queue is serviced in that slot at the maximum possible rate

corresponding to the state of its channel.

A very important and challenging problem in the design of high speed

communications networks is that of providing Quality of Service (QoS)

guarantees, usually specified in terms of rate guarantees, loss probabilities or

delays of packets in the network. The control of delays is often of crucial

importance, especially for real time applications like audio and video streaming.

Real-time traffic class have been modeled as a stream of packets, with each

packet having an expiry time beyond which the packet is of no use to the end

22

user. The objective of the scheduler is to transmit each packet before its expiry,

and if this is not possible, to minimize the number of lost packets due to deadline

expiry. Expiry occurs when a packet have been waiting in the base station queue

time greater than its deadline and have not been served. Such a packet is dropped

by the system.

Such QoS requirements can be specified in terms of deadline Ti

(deterministic QoS requirements) or accompanied with allowed violation

probability δi (opportunistic QoS) for each user traffic flow. In this thesis, we

will use the following model in defining QoS: for every user out of the N users in

the system, let Wi to be the delay encountered by user i packets, then the

scheduling rule should also satisfy the QoS constraints given in the form

( )P i i iW T δ> ≤ (3.1)

for i = 1, 2, …. , N. The problem is to minimize the violation occurrences.

Figure 3.1. Channel state dependent downlink scheduling architecture for multiple users sharing a

wireless TDMA channel.

1

2

User 1

User 2

User N N Scheduler

Wireless channel

Mobile Terminals

Link Status Monitoring

Base Station

23

In what follows in this chapter, all scheduling disciplines, either the

proposed ones or the existing ones, are introduced and discussed in systems

functioning according to the model presented in this section, unless other models

are stated.

3.2 Previous Work

In this section, we present a survey of existing scheduling disciplines

applicable in wireless networks with delay-sensitive users' traffic. In [21], the

authors proposed to apply the wireline EDD discipline scheduling in wireless

networks. They called it Feasible Earliest Due Date (FEDD) scheduling. They

assumed a simple channel state model in which the channel can be either "good"

or "bad". Thus, FEDD scheduling chooses to schedule the packet which has the

earliest time to expiry from the set of queues whose channels are marked good

only. So that, such a scheduler is similar to the wireline one. Wireline EDD was

proved to be optimal for i.i.d. Bernoulli arrival processes. This algorithm showed

unfairness in throughput sharing, since the user suffering from long periods of

bad state will not be compensated by any mechanism, thus the authors suggested

to use a rate-proportional scheduler which provides guaranteed minimum

bandwidth to each connection and distributes the residual bandwidth using the

FEDD criterion.

The authors in [22] proposed a modification to the Largest Weighted

Delay First (LWDF) scheduling discipline that take the time varying

characteristics of wireless channels. The LWDF [23] discipline is a

parameterized version of the first-input first-output (FIFO) that works as follows:

at the beginning of the time slot starting at time t, serve at the maximal possible

rate the queue of user j, where

arg max{ ( )}i iij aW t= (3.2)

24

where Wi(t) is the waiting time of the ith user head of line (HoL) packet (i.e. the

maximum waiting time of any packet of the ith queue) at the time slot starting at

time t, and ai > 0, i = 1,2, …., N, are a fixed set of constants. If the delay QoS

requirements for all users is in the form of the deadline due violation probability

as in equation (3.1). It was proved in [23] that the choice of weights ai that makes

LWDF discipline nearly throughput optimal (note however that this choice of the

weights is valid only for large values of the delay bound Ti and very small values

of δi) is :

log ii

i

aTδ

= − (3.3)

The proposed modification of [22] was to use multiuser diversity in order

to increase the efficiency of channel utilization (and hence the system

throughput) and also compensate delayed users. The proposed Modified Largest

Weighted Delay First (M-LWDF) discipline schedules the jth user, where

arg max{ ( ) ( )}i i iij t W tγ µ= (3.4)

where μi(t) is the state of the channel of user i at time t, i.e. the actual rate

supported by the channel. This rate is assumed to be constant over one slot. It

had been proven in [22] that choosing ii

i

aγ

µ= , where ai is chosen as in (3.3)

and iµ is the mean rate supported over the ith channel that corresponds to the

average fading level of the channel, makes the M-LWDF discipline throughput

optimal. In practice, the mean rate can be measured over a certain, but relatively

long, time window [7] by averaging the rate actually given to that user in that

window. The M-LWDF scheduling rule could be rewritten as schedule the jth

user, where

25

( )arg max{ ( )}i

i iii

tj a W tµµ

= (3.5)

The scheme provides good QoS for delay sensitive users only with properly

chosen parameters and can be easily implemented. It was shown in [22] that M-

LWDF rule is optimal in the sense that it can handle all the offered traffic and

renders the stability of all queues if this is feasible to any other rule, such a rule is

called a throughput optimal one. The authors in [22] also showed how M-LWDF

can be used to achieve alternative QoS defined in terms of a predefined

minimum long-term throughput for each user. Unfortunately, M-LWDF

scheduling was found to be highly dependent on the value of the parameters ai,

and its performance change significantly with the QoS requirements of users'

flows.

In order to reduce the dependency of the M-LWDF rule on the settings of the

parameters ai, the authors in [22] also proposed a new scheduling discipline,

which was further investigated and implemented in [24] for CDMA/HDR system

and modified in [25]. The proposed scheme was called the exponential rule

scheduling discipline. This scheme schedules the jth user at the time slot starting

at time t for transmission, where

( )

arg max{ ( ) }i ia W t aW

b aWi ii

j t eγ µ−

+= (3.6)

and

1

1 ( )N

i ii

aW a W tN =

= ∑ (3.7)

and b > 0 is an arbitrary constant, and γi > 0, i = 1,2, … ,N, were set as in the M-

LWDF in the form ii

i

aγ

µ= to represent the tradeoff between the QoS

requirements and being proportionally fair discipline. For b =1, the exponential

rule will be in the form [22]

26

( )

1( )arg max{ }

i ia W t aW

i aWii

i

tj a eµµ

−

+= (3.8)

This policy attempts to equalize the weighted delays aiWi(t) of all the

queues when their differences are large. If one of the queues would have larger

(weighted) delay than the others by more than order aW , then the exponent

term becomes very large and overrides the channel considerations (as long as its

channel can support a non-zero rate), hence leading to that queue getting priority.

(It can be easily noticed that the aW term in the exponent can be dropped

without changing the rule as it is common for all queues. This term is present

only to emphasis the motivation of the rule). On the other hand, for small

weighted delay differences (i.e. less than order aW ), the exponential term is

close to unity, and the policy behaves as the proportionally fair rule. Hence, the

exponential rule policy gracefully adapts from a proportionally fair one to one

which balances delays [22], [24]. The choice of b = 1 in [24] is simply to prevent

the exponent from blowing up when the weighted delays are small.

It was proven in [26] that the exponential rule is a throughput optimal

policy for a quit general assumptions on the channel and arrival processes.

Moreover, simulation results in [24] showed that the exponential rule scheduling

exhibits better delay tails compared to any other scheduling policy in the sense

that the delays of all users are about the same and are all reasonably small but for

large values of Ti and very small values of δi, which is not desired practically.

Besides, like the M-LWDF discipline, the exponential rule scheduling was found

to be highly dependent on parameter settings. Therefore, It was advised that for

future research identifying good scheduling rules which are less dependent on the

"proper" parameter setting would be desirable [22].

27

3.3 The Proposed Scheduling Schemes

The goal of this thesis is to find good performing disciplines for delay

sensitive traffic, that could be used to schedule users with time-varying link

conditions. From the above study of such a problem, we mean by the word "good

performing" that such a discipline should have attempt to achieve the following

objectives:

§ Maximize the overall system throughput

This could be easily achieved if the scheduling discipline utilizes the

multiuser diversity, inherently existing in systems under consideration.

Multiuser diversity efficiently utilize the channel capacity by giving

higher priority to the user with the best channel conditions at a certain

time instant, which means that this user can transmit with the highest

possible rate, and thus increase the system throughput.

§ Graceful compensation of large delays

For real-time traffic packet, it is necessary that the delivery of such a

packet be done within a certain time period, usually defined by a

deadline, otherwise, the information contained in this packet will be

irrelevant for the receiver. So that the system drops such a packet and

may ask the transmitter to resend it, which reduce the system efficiency.

Thus, a good scheduling discipline should have a mechanism to

compensate queues whose packets are experiencing long delays in the

system. This case may be encountered by users far from the base station,

which yields that their channels are suffering from long periods of bad

conditions. Such a mechanism will :

i. Guarantee the QoS requirements if defined as delay bound or

packet loss ratio.

28

ii. Minimize the number of packets dropped due to deadline

violation, which in turn increase the system throughput.

§ Fairness in resource sharing

Fairness is an intuitively desirable property of scheduling disciplines. A

fair scheduling discipline should distribute the resources available to the

system, such as capacity and time, fairly among different users. Fairness

may be accomplished in

i. Delay distributions

A scheduling algorithm that keeps all the delays close to each

other at a relatively small value is much better one that keeps one

user's (or some users') delay very small while other users

experience much larger delays

ii. Service rate

On the long term, the difference between any two users in the rate

by which their queue are served should be as small as possible.

This could be achieved by means of proportionally fair rate

assignment.

iii. Number of packets lost

This also will increase the fairness in throughput sharing.

§ Weak dependency on the parameters setting

As advised for future research in [22], it is desirable to identify good

scheduling disciplines which are less dependent on the proper parameter

setting, i.e. their performance does not change significantly for wide

29

range of QoS requirements, and thus could be employed in different

systems serving wide range of applications.

3.3.1 Channel Dependent Earliest Due Date (CD-EDD)

Scheduling Discipline

In classical wireline earliest due date scheduling, each packet is assigned

a deadline, and the scheduler serves packets in order of their deadlines. The

queue with the smallest deadline will be served first by the maximum available

rate. If the scheduler is overcommitted, then some packets miss their deadlines.

Thus with EDD, scheduled packets are experiencing delays lower than the

assigned deadlines, so it can be used to provide QoS requirement of delay

sensitive applications. This policy was shown to be optimal in the wireline case

(for independent identically distributed Bernoulli arrival and channel processes).

EDD can not be employed in wireless networks since it does not consider the

time varying characteristics of wireless links. It was not reported in the literature

the existence of a scheduling discipline that combines the EDD scheduling

concept with a mechanism to adapt with the characteristics of wireless networks.

(with the exception of the attempt in [21] which dos not actually adapt with the

time varying nature of wireless channel, since it assumed the very ideal channel

model of good or bad).

We propose a new scheduling discipline, which we call the channel

dependent earliest due date first (CD-EDD) policy. This is basically a channel

state-dependent EDD policy where the scheduler chooses to schedule the queue

whose HoL packet has the earliest time to expire and the best channel conditions,

and consequently the highest transmission rate, among all queues. The proposed

CD-EDD scheduling policy is as follows:

30

At the time slot starting at time t, schedule with the maximum possible

rate the queue of the jth user, where

( ) ( )arg max{ }( )

i iii

ii

t W tj ad t

µµ

= (3.9)

where

ai is the weighting parameter reflecting the statistical QoS requirements

of the ith user.

μi(t) is the actual rate that could be used for transmission by the ith user at

time t, which reflects the current channel state of the user's channel.

iµ is the mean rate supported or previously offered to the ith user. Wi(t) is the delay experienced by the HoL packet since its entrance to the

ith user queue in the base station.

di(t) is the time to expire of the ith user HoL packet, which is the

difference between the deadline, Ti, and the delay experienced till time t,

Wi(t), i.e.

( ) ( )i i id t T W t= − (3.10)

The behavior of the CD-EDD policy can be described as follows: when

certain queue have its HoL packet waiting in the system for a relatively long

period (but have not expired yet), its time to expire will decrease significantly.

So that, the term ( )( )

i

i

W td t

will grow significantly due to the contribution of 1( )id t

until it overcomes other terms in the policy which represent the cause of such a

large delay, namely the bad channel conditions of that user. This also reduces the

number of packets that could be lost due to deadline due violation. On the other

hand, if the delay characteristics of all users are about the same, i.e. their time to

31

expire and waiting times are close, the term ( )( )

i

i

W td t

will be common to all users,

and the policy then reduces to a proportionally fair one that exploit multiuser

diversity to efficiently utilize the channel bandwidth of multiuser systems in a

quite fair manner. It is worth mentioning that weights ai doesn't contribute

significantly in the decision. A rule of thumb for choosing ai which works in

practice is the one given in (3.1) since this rule is suggested by large deviations

of optimality results.

In other words, the CD-EDD is a scheduling discipline that can be used to

provide QoS guarantees, defined in terms of delay bounds, for real-time traffic in

wireless networks. This is achieved by increasing the priority of delayed users to

get access to the medium over time. An important feature of the CD-EDD policy

is its weak dependency on the value of QoS required, and thus can be used for a

wide variety of QoS requirements.

3.3.2 A Set of Violation Fair Rules

Another new idea than can be applied in conjunction with any scheduling

discipline in order to enhance the fairness characteristics of these policies is

proposed here, which is based on the number of deadline violations occurring to

packets of different queues. This requires that each queue in the base station to

be accompanied with a counter that counts the number of packets lost in this

queue's flow. This may be implemented practically be means of sliding windows

basis. Let us define

NVi(t) to be the number of deadline due date violations encountered in the

flow of the ith user up to time t.

( )NV t to be the average of the number of violations in all N queues, i.e.

32

1

1( ) ( )N

ii

NV t NV tN =

= ∑ (3.11)

The scheduler may use these numbers of deadline violations and find a

way to compensate users suffering from unfairness in the number of packets

recently lost. For example the scheduler could give more credit or increase the

priority level so that such a user could access the system resources. This could be

achieved be a scheduling discipline that includes a term like ( )( )

iNV tNV t

, such a

scheduling discipline we will call a violation fair (VF) discipline.

Initially, we considered this idea directly to the proportionally fair [7]

scheduling discipline, yielding the violation fair-proportionally fair policy. So, in

each time slot the scheduler chooses the jth user, where

( ) ( )arg max{ }( )

i i

ii

t NV tjNV t

µµ

= (3.12)

This will reduce the number of packets lost for users of bad channel

conditions which enhances the fairness characteristics of the proportionally fair

policy. On the other hand, it still lacks a mechanism for provisioning QoS

guarantees for delay sensitive traffic.

Applying the proposed idea to both the M-LWDF and the exponential

rule policy, resulting in the violation fair modified largest weighted delay first

(VF-M-LWDF) discipline

( ) ( )arg max{ ( )}

( )i i

i iii

t NV tj a W tNV t

µµ

= (3.13)

and the violation fair exponential (VF-EXP) discipline

33

( )

1( ) ( )arg max{ }( )

i ia W t aW

i i aWii

i

t NV tj a eNV t

µµ

−

+= (3.14)

enhances their performance in the sense that the addition of the violation fair

term will ensure fairness in both the delay times and throughput. This could be

explained since both the M-LWDF and the exponential minimize the packet

delay and when the number of lost packets is fairly distributed among users, the

long term service rate will be equal for all users. Another very important gain of

these two disciplines, which appeared in simulation results, is that their

performance is not much dependent on the parameter setting as was the case in

the original rules.

Finally, if the proposed violation fairness technique is applied with the

previously proposed CD-EDD, we can get a scheduling discipline applicable in

wireless network that explicitly provide QoS to delay sensitive traffic, with a

unique fairness characteristic in data rate, delay bound, and delay bound

violation triplet. The violation fair-channel dependent-earliest deadline due date

(VF-CD-EDD) scheduler chooses, at the time slot starting at time t, the jth user

for transmission, where

( ) ( ) ( )arg max{ }

( ) ( )i i i

iiii

t W t NV tj ad t NV t

µµ

= (3.15)

In chapter 4, we provide an extensive set of simulation that explore the

characteristics our proposed CD-EDD discipline compared with the M-LWDF

and the exponential rule disciplines as a reference. We also show the advantages

achieved by their violation fair versions, namely the VF-CD-EDD, the VF-M-

LWDF, and the VF-exponential scheduling discipline.

35

Chapter 4 Simulation Results and Discussions of the TDM-Based

Scheduling Disciplines

4.1 Simulation Setup

First, we describe the system model used in simulating the wireless cell-

structured channel-aware scheduler described in section 3.1. We chose the High

Data Rate (HDR) CDMA system model. HDR technology has recently been

proposed as a TDM-based overlay to CDMA as a means of providing packet data

services to mobile users. HDR is a downlink packet data service which occupies

a single data carrier of a CDMA system, where users share the channel in a time

division multiple access, i.e. at each time slot Ts only one user can transmit its

data at the full power available to the base station. A very attractive feature of

HDR enabling the use of efficient scheduling algorithms since it provides a

mechanism for link status monitoring as in chapter 3.

The cell serves N mobile users each receiving a data flow. The base

station contains N queues, one corresponding to a different data flow and an

associated scheduler. The scheduler makes a decision every 1.667 millisecond

based on the current information available at the start of the time slot. As we are

mainly interested in scheduling users with time sensitive traffic, we model the

packet arrival processes to each of the N user's queues as a Bernoulli processes

with a mean rate of 28.8 Kbps. This rate corresponds to the typical rate required

for streaming audio over the Internet. Real time users, like streaming audio, will

indeed generate a smooth traffic, and hence, a Bernoulli model seems reasonable

for such traffic. Like the original EDD, the CD-EDD is expected to be

throughput optimal for such traffic model. The HDR packet size is 128 bytes.

36

The QoS requirements of each user are expressed in the form of the probability

that the waiting time encountered by a typical packet of the ith user stream

exceeds the deadline Ti is less than or equal to δi . We assume for simplicity that

all users require the same service quality, i.e. they all have the same Ti and δi.

Even thought all users share a common channel, the channel capacity, of

that channel seen by different users is different. This is due to the wireless link

characteristics described above. The instantaneous capacity of a wireless can be

given by

2

2( ) log (1 ( ) )C t B h t SNR= + (4.1)

where C(t) is the channel capacity or the data rate (in bits per second) that can be

transmitted on a channel of bandwidth B (Hertz). The bandwidth of

HDR/CDMA channel is 1.25 MHz. While |h(t)| is the normalized gain (or fading

level) of the wireless channel at the time t, and SNR is the required signal to

noise ratio at the receiver antenna (13 dB for HDR/CDMA system). For

simulation purpose, we use the typical HDR and cell parameters given in [6].

The average fade level distribution of a typical mobile in HDR cell can be easily

found. The fading process of each user's channel can be represented by a

Rayliegh process. So, in order to simulate N channels, we pick N fading levels

according to the above distribution, and generate N Rayleigh processes with

means equal to these fading levels after being normalized. A sample of such a

process represents the normalized channel gain of a certain channel at time t with

a probability

2

222( )

r

Rrp r e σ

σ

−= , r ≥ 0 (4.2)

where σ is related to the mean normalized fading level h according to

37

2h π

σ= (4.3)

Accordingly, the mean data rate iµ that can be supported on the a channel of

mean fading level ih is

2

2log (1 )i iB h SNRµ = + (4.4)

It is worth mentioning that HDR doesn't not support arbitrary

transmission rates, i.e. the scheduled user can not transmit with the rate

computed above rather than the maximum possible rate from a set of discrete

rates. HDR user can transmit data at a rate of 9.6 * 2i Kbps, i = 0, 1,…, with a

maximum rate of 2 Mbps. Thus the state of channel ( )i tµ at the start of the time

slot at time t will be the actual rate that the channel can support, rather than the

channel capacity at that time instant. We have assumed that the channel

conditions do not change significantly within a time slot duration. Finally, all

simulations will be carried out for a duration of 10 minutes.

4.2 Performance Metrics

Here, we discuss the performance metrics we used to evaluate the

performance of various scheduling algorithms. These are the delay, throughput,

and loss criteria. We briefly outline them in turn.

§ Delay performance measures:

For real-time traffic, a good measure of performance is the delays packets

incur at the base station. A good scheduling algorithm should keep all delays

below the delay bound Ti with high probability. So that, the delay distribution

38

curves can be used to illustrate the delay behavior of the scheduling

disciplines under consideration. As remarked earlier, scheduling algorithms

which keep the delays of all the users about the same and keep them all

reasonably small are superior to those which may have better delay tails for

one of the users but have very bad delays for other users. (We remind that we

have assumed for simplicity that all users needs the same QoS).

Some parameters of the delay distribution, such as the worst-case delay, the

mea delay, or the 95-percentile delay, could be used to evaluate the QoS

received by a user. We will consider the 95-percetile delay as our measure of

the delay guarantees offered by a scheduling discipline. The 95-percentile

delay is defined as the delay which ninety-five of the packets of a user's

queue have suffered delays smaller than it.

§ Throughput measure:

Unlike non-real-time users, which may have their QoS requirements in the

form of a guaranteed minimum rate, real-time users do not need the scheduler

to preserve certain bandwidth for their packets' transmission. So that, we will

only take the total throughput achieved be the system as a measure of the

throughput performance of the scheduling disciplines at hand. The fairness of

bandwidth sharing between users is also a good indication of the efficiency

of any scheduling discipline.

§ Loss measure:

The fraction of packets lost, due to deadline violation, for a user can be used

to evaluate the loss performance of a scheduling discipline. This fraction is

required to be as small as possible in order to say that the scheduler is

suitable for scheduling real-time traffic. From fairness point of view, it is

better to equalize the fraction of packets lost in different queues.

39

4.3 Results and Discussions

First, we estimate the number of users, with traffic like the one described

above, that can be supported by a single HDR cell under each of the previously

mentioned scheduling policies. In this experiment, we simulate N users,

uniformly distributed throughout the cell, and monitor the average service rate

received by a single user for different values of N. Starting with only two users in

the system, as we increase N, and as long as the channel capacity can support

such a number of users, it is expected that the service rate received by each user

will be similar to its arrival rate. Any further increase of the number of user,

while keeping the channel capacity unchanged, will make the scheduler unable to

serve such users in the appropriate time so more packets will be discarded and

thus the average throughput share of each user will decrease. So, we will take the

number of users beyond which the average service rate received by any user in

the system start to decrease as the maximum number of user that can be

supported our network, or the system capacity.

Figures 4.1 through 4.6 show the average service rate per user versus the

number of users in the cell for different delay bounds, more specifically, 20, 60,

100, 200, 300, 400 milliseconds, respectively, and for a violation probability

(δi)of 95%. These delay-bounds are encountered practically in multimedia

streams. It is clear that the higher the delay bound, the higher the number of users

supported by the system because, for higher bounds, it takes relatively long time

before a packet expires so the scheduler can serve more users in that times. Table

4.1 summarizes the results of this experiment.

Delay bound (m sec) 20 60 100 200 300 400

CD-EDD 4 12 16 16 16 16

M-LWDF 4 10 12 16 16 16

EXP 4 8 12 16 16 16

Table 4.1. The system capacity of HDR cell achieved by different disciplines.

40

Figure 4.1. The average throughput per user for 20 m sec delay bound.


41



42



Note that the decreasing tendency of the previous figures is clear even though some unexpected increases appear due to the random nature of generating different simulation runs.

43

In our second experiment, we investigate the delay performance of

various scheduling disciplines. We begin with a comparison of the proposed CD-

EDD scheduling disciplines versus to both the M-LWDF and the exponential

rule scheduling disciplines reported as the most suitable policies for scheduling

delay sensitive traffic in the literature. In order to be able to evaluate the

performance of the scheduling techniques, the system should be loaded with its

maximum capacity. Based on the results of the first experiment in Table 4.1, we

will assume that the cell is serving 14 mobile terminals, i.e. N =14, and generate

14 i.i.d. Bernoulli processes each with a men rate of 28.8 Kbps to represent their

packet arrival processes. Using the procedure described before, we also generate

14 Rayleigh-faded channels with mean channel gains and the corresponding

channel capacities listed in Table 4.2.

User Number Mean Normalized

Channel Gain Mean Rate (Kbps)

1 0.1102083 400.72

2 0.1096598 397.14

3 0.1087368 391.14

4 0.1077732 384.91

5 0.1040045 360.88

6 0.1009808 342.00

7 0.0898876 276.01

8 0.0836667 241.43

9 0.0819434 232.18

10 0.0798461 220.60

11 0.0739499 191.24

12 0.0660818 154.27

13 0.0652852 150.72

14 0.0623138 137.80

Table 4.2. Fading levels and its corresponding capacities used in simulations.

44

In Figures 4.7 through 4.12, we plot the delay distribution tails for both

user 1 (with the best channel conditions) and user 14 (with the worst channel

conditions) for the M-LWDF, exponential rule, and the proposed CD-EDD

scheduling disciplines for the values of the delay bound given above. It is

obvious that all policies will have the same performance for very small bounds,

e.g. 20 milliseconds, with such a scare resources the networks can not serve such

a number of users with this high QoS. We observe that for moderate delay

bounds, e.g. 60 and 100 milliseconds, the performance of the exponential rule

scheduling slightly outperforms both the M-LWDF and CD-EDD disciplines. In

this case, all delays are kept at small value and about the same for all users.

While for higher bounds, e.g. 200, 300,and 400 milliseconds, we find that the

delay performance of the CD-EDD scheduler don't change significantly, while

the performance of both the M-LWDF and the exponential rule schedulers

degrades severely as the gab between the tails of the best user and the worst user

gets wider. This severe degrading in performance is caused by the dependency of

both rules on the quality of service required, which affects the value of the

weights {ai} that controls the performance of these rules. (Keep in mind that the

goal of the M-LWDF is to minimize the weighted delays while the exponential

rule scheduling tries to keep all the delays around the average of these weighted

delays ( aW ),they both do not target a certain bound to serve as much packet as

possible before this bound is violated.) On the other hand, the CD-EDD policy

does not suffer from such a dependency on the QoS, and consequently the weight

values, since the philosophy of this rule is mainly to serve more packets before

their deadlines expire. This may cause the packets of the best channel users to

experience relatively higher delays than in the case of other rules, but still lower

than the worst user. This occurs on the expense of preventing more packets from

being dropped due to deadline violation.

This can be further demonstrated when we plot the maximum and the

minimum 95 percentile delay and percentage of packets lost due to deadline

violations versus the delay bounds as shown in Figure 4.13 and 4.14,

45

respectively. It is clear that it is not desirable to keep one or some users' delays

below a value much smaller than the required bound while leaving one or some

users suffering from dropping a large percentage of their packets as the case with

both the M-LWDF and exponential rule schedulers. While in CD-EDD

discipline, the maximum and the minimum 95 percentile delay are about the

same and so close to the delay bound, besides the packet loss ratios are very

small and very close to each other. So, the base stations can guarantee strong

delay bounds for all delay sensitive users in a fair manner by using the CD-

EDD scheduling discipline, regardless of the value of those bounds.

When the same experiment was carried out for the violation fair versions

of the above disciplines, it was found that the performance of all the violation

fair policies is not much dependent on the QoS required (including the

disciplines which was originally suffering from that dependency). Figures 4.15

through 4.20 show their delay distribution tails of the best user and the worst user

for different delay bounds. It is observed that the tails became much more closer

for the violation fair CD-EDD, but a little bit higher delays, than those of either

the violation fair M-LWDF or violation fair exponential policies.

As shown in Figures 4.21 and 4.22, where the maximum and the

minimum 95 percentile delay and percentage of packets lost due to deadline

violations are plotted versus the delay bounds of the violation fair policies, the

service offered to different user, in terms of 95% delay, is about the same.

Furthermore, the amount of packets dropped in the system due to deadline

violations becomes very small. Moreover, this amount is distributed among all

users in a fair manner. Like the CD-EDD, the VF-CD-EDD have the superiority

since t achieves the smallest number of packets lost due to deadline violations.

46

Figure 4.7. Delay distributions of user 1 and user 14 for 20 m sec delay bound.


47



48



49

Figure 4.13. The maximum and the minimum 95-percentile delays.

Figure 4.14. The maximum and the minimum percentage of lost packets.

50

Figure 4.15. Delay distributions of user 1 and user 14 for 20 m sec delay bound (VF rules).


51



52



53

Figure 4.21. The maximum and the minimum 95-percentile delays (VF rules).

Figure 4.22. The maximum and the minimum percentage of lost packets (VF rules).

54

Finally, we study the throughput characteristics of the aforementioned

scheduling disciplines. Here we are interested in studying the overall throughput

of the system as well as how the throughput is divided among users with

different channel conditions, i.e. fairness in throughput sharing. The results of

this experiment is illustrated in Figures 4.23 through 4.28. In part (a) of these

figures plot the overall throughput of the system versus the number of users

using the simulation setup of the first experiment. When the system is operating

with number of users less than the system capacity, the total throughput of the

system equal the sum of the arrival rate. When the system is serving more users

than the system capacity, we observe that, regardless of the delay bound:

§ The total throughput achieved using the CD-EDD is higher than any other

rule because this policy causes the smallest number of packet to be lost

due to deadline expiry.

§ The total throughput achieved using any violation fair discipline is less

than the throughput achieved with the non-violation fair counterpart. This

is because in order to achieve fairness in the ratio of packets lost among

different user, the violation fair polices may prevent users with good

channel conditions from transmitting their data for the sake of users with

bad channel conditions (such channels support low transmission rates

only). So the overall throughput achieved by the system will be lower

than the case where the scheduling policy do not intend to make users

with good channel condition drop some packet for the purpose of

fairness.

In part (b) of Figures 4.23 through 4.28, we compare the average

throughput share of a single user against the actual throughput shares of both the

best channel user and the worst channel user for different delay bounds for both

the original disciplines and their violation fair counterparts. In this experiment,

we use the same simulation model used in the previous experiment where the

base station serves the 14 user listed in Table 4.2. As seen in these figures, the

55

CD-EDD discipline achieves the greatest average throughput per user, besides, it

keeps the actual throughput share as close as possible to that average. Note that

the throughput shares of the best channel user and worst channel user are always

close to each other for various delay bounds for CD-EDD scheduling. This

means that the CD-EDD discipline is the most throughput fair policy that can

guarantee delay bounds for real-time users. On the other hand, even though the

violation fair disciplines leads to a slightly lower throughput per user as

previously discussed, they ensure fairness in throughput sharing among all users

regardless the delay bound. This is because in such disciplines, the number of

packets dropped due to deadline expiry is almost equal for all users. We

summarize the main results of our simulation experiments in Table 4.3.

CD-

EDD

M-

LWDF EXP

VF-CD-

EDD

VF-M-

LWDF VF-EXP

Delay bound

guarantee √ X X √ √ √

Independency

of QoS

requirement

√ X X √ √ √

Total system

throughput Highest Moderate Lowest Less than original counterparts

Delay

fairness √ Depend on QoS √ √ √

Throughput

fairness Best Good Worst √ √ √

Delay bound

violation

fairness

√ Bad Worst √ √ √

Table 4.3. Simulation results summary.

56

a) The total throughput achieved.

b) Throughput fairness.

Figure 4.23. The throughput behavior at 20 m sec delay bound.

57




58




59




60




61




63

Chapter 5 Channel-Aware Scheduling for Delay-Bounded Traffic in

OFDMA-Based Wireless Networks

The proliferation of cheap, small and powerful notebook computers,

Personal Digital Assistants (PDAs) and other high speed mobile data terminals

has fueled the persisting demand for a mobile alternative to the wireline access

techniques, such as DSL and cable modems. Mobile Broadband Wireless Access

(MBWA) is an appealing system for providing flexible and easy deployment

solution to high speed mobile communications. The IEEE 802.20 (MBWA)

working group was formed to develop a standard which sets the specification of

physical and medium access control layers of an air interface for interoperable

mobile broadband wireless access systems, operating in licensed bands below 3.5

GHz, optimized for IP-data transport, with peak data rates per user in excess of 1

Mbps. It supports various vehicular mobility classes up to 250 Km/h in a MAN

environment and targets spectral efficiencies, sustained user data rates and

numbers of active users that are all significantly higher than achieved by existing

mobile systems [27].

Operating in the Giga-Hertz bands, channel impairments, multipath fading

and path loss become more significant with the increase in the number of

subscribers. Improved and flexible multiple access methods are needed to cope

with these impairments. Orthogonal Frequency Division Multiple Access

(OFDMA) is a promising multiple access scheme that has attracted interest.

OFDMA is based on Orthogonal Frequency Division Multiplexing (OFDM) and

inherits OFDM immunity to inter-symbol interference and frequency selective

fading. OFDM is a special case of multicarrier transmission, where a single high

speed data stream is transmitted over a number of lower rate subcarriers [28]. In

a single carrier system a single fade can cause the entire link to fail, but in

multcarrier systems, only a small percentage of the subcarriers will be affected.

64

So, multiuser OFDM is identified as a promising interface solution for broadband

wireless networks.

The scheduling problem in OFDMA-based networks is completely

different from the scheduling problem in other systems, and a much more

complicated one. Here, the scheduler is responsible for deciding how the

available subcarriers will be distributed among different users. Static subcarrier

assignment is an inefficient utilization of scarce radio resource. This is due to the

time-varying channel conditions, and the diverse quality of service requirements

of multimedia users. Recently, multiuser diversity [3] was introduced as a key

approach to enhance the resource utilization efficiency of wireless networks.

Dynamic resource management of OFDMA-based networks has attracted

enormous research interest. In this chapter, we consider the subcarrier

management problem in the downlink of OFDMA wireless multimedia networks.

This complex problem is subdivided into a couple of simpler ones: the subcarrier

allocation problem and subcarrier assignment problem. We propose an

opportunistic subcarrier allocation algorithm that uses the channel state

information and the delay information of different users to calculate the number

of subcarriers to be assigned to each active user in the system, while attempting

to guarantee the QoS required by these users. We also propose another

opportunistic algorithm for subcarrier assignment problem. The proposed

algorithm monitors the deadline violations in all queues, then progresses to

ensure fairness among different users in their service rates. This is achieved by

distributing the violation occurrences among all users evenly.

In this chapter, we first provide an overview of OFDMA-based networks

and the characteristics of the wireless channels in such networks. Then, we

describe the multiuser scheduling problem in such networks. A briefing survey of

the solution of this problem in the literature is included. Finally, the proposed

subcarrier allocation and subcarrier assignment algorithm are introduced. In the

next chapter, we provide an extensive set of simulation results that illustrates the

performance gains achieved by our opportunistic algorithms.

65

5.1 OFDMA Network Model

We consider a cell-structured OFDMA system model that consists of a

base station communicating simultaneously with N mobile user terminals using S

OFDM subcarriers. Although the presented study is applicable both to the uplink

and the downlink, for the sake of simplicity we concentrate here on the downlink

only, which is shown in Figure 5.1. As mentioned before, an OFDMA system is

a special case of OFDM systems. The only difference between them is that

OFDM is a transmission scheme that splits a single high data-rate stream into a

lower rate streams that are transmitted over a number of subcarriers. However,

OFDMA is a multiple access scheme that is used to coordinate the transmission

of multiple data streams (which belong to different users) over a number of

subcarriers. Thus, OFDMA transmitter employs a subcarrier allocation and

assignment function instead of the serial to parallel conversion used in OFDM

systems as a first step. Different modulation schemes could be used to transmit

data efficiently over subcarriers with different gains. The rest of OFDMA system

is the same as an OFDM system as seen in Figure 5.1. Inverse Fourier Transform

(or any practical implantation) can be used to generate the orthogonal carriers

required for OFDM signal. The OFDMA symbol is then converted to the serial

form. Intersymbol interference is eliminated almost completely by introducing a

guard time in every OFDMA symbol. Like OFDM, the OFDMA symbol is

cyclically extended to avoid intercarrier interference.

At the receiver of a certain user, the guard interval is firstly removed from

the received OFDMA symbol. The OFDMA symbol is fed to a serial to parallel

converter. Then Fourier Transform is used to retrieve the data from the

subcarriers. The base station is responsible for informing each user terminal

which subcarriers are assigned to it via the control subcarriers. Therefore, the

data sent to this user could be easily received by demodulating only those

subcarriers with the appropriate demodulation technique.

66

Figure 5.1. Orthogonal Frequency Division Multiple Access (OFDMA)

transceiver.

An OFDMA symbol is generally made of two types of subcarrier: data

subcarriers for data transmission, and pilot (control) subcarriers for other control

and various estimation purposes.

Wireless channels operating at high frequencies, like those used in

OFDMA-base networks, are characterized by their time-varying, frequency-

selective fading nature. Channel gains vary from subcarrier to subcarrier for a

single wireless terminal due to multipath propagation. Besides, channel gains of

each subcarrier vary over time, for the same user terminal, due to the movement

of the terminal and other objects within the surrounding area. So that, at a given

time, some frequency intervals (subcarriers) suffers severe fading, while others

User 1

User i

User N

Subcarrier Extraction for User i

Adaptive Demodulation



FFT

Guard

Removal

S/P

Subcarrier Allocation

and Assignment

with Different

Modulation

Adaptive Modulation Adaptive Modulation Adaptive Modulation Adaptive Modulation

IFFT

Guard

Insertion

P/S :

Channel Information from user i

i = 1, 2, ….N

Wireless Channel

User i Receiver

67

have a good response. In this case, if the channel information is available, sub-

carriers that have a good response could be selected for transmission. Thus,

higher transmission rate could be used to transmit data on that subcarrier.

Furthermore, Channel gains of a specific subcarrier vary from wireless terminal

to wireless terminal due to statistical independence. This implies that certain sub-

carriers that are in deep fade for some users are not necessarily bad for others

since the user channel fading characteristics are not the same for different users.

Hence, selection of good sub-carriers for one user may not necessarily block

other users from accessing their good sub-carriers. Figure 5.2 illustrates an

example of such channel gain variations [29]. This gives the general motivation

to develop the resource allocation algorithm that exploits multiuser diversity to

assigns an active user its best subcarriers, and hence increase the efficiency of

channel utilization. Another important question that arises here is how to select

the number of sub-carriers to be allocated for each user.

Figure 5.2. An example of channel gain variations taken from [29].

68

5.2 Scheduling in OFDMA Networks

In OFDMA networks, where a single channel (divided into a set of

subcarriers) is shared by multiple users, the scheduling problem becomes a

resource management one. The scheduler will be responsible for dividing the set

of subcarrier available to the base station into a number of mutually disjoint

subsets of subcarriers. Each subset is assigned to a certain user for a certain

period of time (scheduling interval). Recently, there has been some research on

subcarrier and bit allocation in multiuser OFDM systems. Those algorithms can

be categorized as static and dynamic allocation algorithms.

5.2.1 Static Subcarrier Management

Static subcarrier management schemes result from the use of the traditional

multiple access schemes, such as Time Division Multiple Access (TDMA) and

Frequency Division Multiple Access (FDMA), as a mechanism for distributing

the subcarriers in multiuser OFDM networks. In OFDM-TDMA, one of the users

(the scheduled one) is assigned all the subcarriers for a certain time interval (the

scheduling time slot). Due to the variation of the subcarrier channel gains for this

terminal, channel gains for some subcarriers might be quite low, while they are

quite high for other subcarriers. Due to the channel gain variations regarding one

subcarrier for different terminals, the subcarriers with a low channel gain for the

one terminal might experience a high channel gain for some other terminal.

TDMA, however, does not provide the flexibility to adapt fully to these channel

gain variations. Alternatively, in OFDM-FDMA, each user is assigned one or

several predetermined subcarriers. This scheme ignores the channel gain

variations of a certain subcarrier for the same user caused by the mobility of the

user. Thus, statically assigning certain subcarriers to terminals without adapting

to the channel gain variations would not exploit the performance enhancement

provided by multiuser diversity. As a consequence, any fixed assignment of

subcarriers to terminals will waste either power or bit rate [30, 31].

69

5.2.2 Dynamic Subcarrier Management

Recently, dynamic (real-time) radio resource management that considers

the users' instantaneous channel conditions has attracted enormous research

interest. This is due to the significant overall system efficiency increase obtained

when variations in channel gains among users (multiuser diversity) is exploited.

Many schemes known as bit loading algorithms [29 – 32] have been suggested

which adapt transmission power or bit rates optimally to the channel gains of

different subcarriers, where either a feasible overall bit rate or a maximum

available transmit power is given. They are based on a result from information

theory describing how to distribute transmission power over a set of subcarriers

with different channel gains in order to maximize the channel’s capacity. This is

known as the water filling principle first discussed by Shannon.

Wong et al [31] addressed the problem of minimizing the transmitted

power at a given bit rate per terminal. Subcarrier and bit allocation was done

dynamically through the use of nonlinear optimization with integer variables. An

extremely computationally complex iteration is required to find the two

Lagrangian multipliers used in the nonlinear optimization. A simple modification

to Wong's algorithm was proposed in [29]. The proposed extension allows each

user to specify its individual QoS requirements, defined in terms of bit rate and

bit error rate, and thus distributes subcarriers and transmit power among multiple

users according to their QoS traffic requirements.

An alternative problem of maximizing the overall bit rate of multiple

wireless terminals while the transmit power is upper bounded have been

considered in [32] by Yin and Liu. Such a problem can be decomposed into two

tasks: first determining the number of subcarriers each terminal is assigned and

then choosing the concrete subcarriers to be assigned. Yin and Liu suggested a

scheme where first the number of subcarriers assigned to each terminal is

determined by considering each terminal’s average channel gains and its required

bit rate. Then, the assignment of subcarriers to terminals is done. However,

70

assigning subcarriers to wireless terminals is not a trivial operation, even if the

number of subcarriers to be assigned to each terminal is already determined. Yin

and Liu suggested to solve this problem by using a graph algorithm solving the

maximum weight perfect matching problem. While this algorithm computes the

optimal assignment of subcarriers to terminals, it is still fairly computationally

expensive.

Due to the high complexity of the optimization techniques, the question of

heuristic approximations to such a kind of optimization problems became

relevant. Many suboptimal heuristic algorithms have been proposed recently [33

– 37]. The computational complexity of the heuristics is considerably smaller

than that of the optimum solution. On the other hand, their results are usually

close to the optimum solutions.

An iterative solution of the total transmit power minimization problem was

proposed in [33]. The problem is decomposed into two procedures: A subcarrier

allocation with fixed modulation, and then by using bit loading scheme, the

number of bits is incremented. The authors have also introduced a possible

resource allocation scheme when the objective is to maximize capacity, based on

proportional fair scheduling algorithm for point-to-point communication.

In [34], the authors presented two related heuristic algorithms for the

problem of assigning subcarriers to terminals, assuming that the number of

subcarriers allocated to each terminal is fixed. These algorithms assigned each

user the current best subcarriers in a prioritized manner.

Another dynamic subcarrier and bit allocation algorithm, which takes

advantage of the knowledge of instantaneous channel gain properly in subcarrier

and bit allocation, is presented in [35]. Initially, the greedy single user water-

filling approach is used to allocate subcarriers and bits as if all the subcarriers in

the system could be used exclusively by this user. In case that a subcarrier is

71

desired by more than one user, the algorithm will arbitrate the subcarrier to one

user appropriately so that total transmit power is minimized.

The authors in [36] introduced a different approach aiming to minimize the

number of subcarriers based on the rate requirements first, and then adjust the

minimum required transmitted power accordingly. In addition, interference

learning techniques were used in conjunction with the proposed scheme to

enhance the system performance for voice services.

When other types of QoS requirements, such as the delay requirements of

real-time traffic, are to be considered, the problem at hand becomes much more

complicated. This is pursued in [37, 38]. The authors in [37] presented a new

subcarrier allocation method that finds the number of subcarriers to be assigned

to each user in the start of every time slot. The method is based on allocating

subcarriers for terminals depending on the actual queue size of each terminal

relative to the overall data queued at the access point. In contrast to other

methods described above, channel gain information as well as any stream

specific knowledge is not included in the allocation of subcarriers. Although this

method is very simple, it responds intuitively to changes in the transmission

situation regarding wireless channel qualities or queue sizes. In the case of a

severe quality degradation of most channels for one terminal, its queue simply

increases, leading to a higher number of subcarriers allocated to this terminal for

the next downlink phases. Similarly, a burst of data arriving at the access point

for one terminal will lead to a higher number of subcarriers allocated to this

terminal for the next downlink phases. As a consequence the proposed variable

subcarrier allocation method can take advantage of the statistical variations in

data streams without explicitly provided information of the streams at the access

point.

The proposed adaptive resource allocation algorithm in [38] is based not

only on the channel conditions and power limitation observed in the physical

layer, but also the queue status, packet arrival, QoS requirements, service

72

discipline, and user fairness observed at the data link layer. The objective of the

authors was to minimize the overall transmission power while maintaining the

channel errors at a sufficiently low level, so that the assumption of error-free

channel in the scheduling part is generally valid. With error-free links, the system

can fairly guarantee various QoS requirements to all the users from the physical-

layer’s point of view.

5.3 Problem Formulation

In this chapter, we introduce a new approach to subcarrier management in

OFDMA-based wireless multimedia networks. The idea behind this approach is

that the subcarrier allocation and assignment is not only dependent on the

instantaneous channel conditions of different users, but also on the QoS

requirements and fairness among users. The QoS requirement of real-time traffic

users are generally defined in terms of a delay bound. A packet should be

delivered to the receiver before that deadline, otherwise, the information

contained in this packet will be of no use to the receiver. Before we formulate

our problem let us define the following parameters:

N : The number of users in the system.

Nt : The number of active users (i.e. its queue have at least one valid

packet) at time t.

S : The total number of data subcarriers.

ni(t) : The number of subcarriers to be assigned to the ith user at the slot

starting at time t.

ri : The average rate of the traffic of ith user.

μij(t) : The channel capacity (the maximum possible data transmission

rate) of the subcarrier number j if allocated to the ith user.

( )i tµ : The average "potential" subcarrier capacity of the ith user (if it

was allocated all the subcarriers).

73

( ) ( )1

1 S

i ijj

t tS

µ µ=

= ∑ (4.5)

di(t) : The time to expire of the ith user HoL packet, which is the

difference between the deadline, Ti, and the delay experienced by its HoL

packet up till time t, Wi(t), i.e

( ) ( )i i id t T W t= − (4.6)

We assume that the channel information is known at both the transmitter

and the receiver. The channel is assumed to be reciprocal. Mobile terminals may

be equipped with mechanisms to measure the rate at which they have been

served. This data may be reported back to the base station, so that it can estimate

the channel of all mobile channels based on that data as long as the channel

variation is slow. As a result, the resource allocation should be done within the

coherence time of the channel.

With the channel information, our objective of the resource allocation

problem can be defined as maximizing the total system throughput subject to a

constraint regarding the user’s QoS requirements. As we clarify further, the QoS

required by real-time users is assumed to be in the from of guaranteeing a delay

bound before which packets must be serviced, otherwise the system drops it.

Let’s define δij(t) as the indicator of allocating the subcarrier j to the user i in the

time slot starting at time t. Thus

( )ij

1 if subcarrier j is assigned to user it

0 otherwiseδ

=

(4.7)

and the total instantaneous system throughput RT(t) is

( ) ( ) ( )1 1

N S

T ij iji j

R t t tδ µ= =

= ∑∑ (4.8)

74

So that we formulate our subcarrier allocation/assignment problem as

( )

( ) ( ) { }max 0,1ij

T ijtR t for t

δδ ∈ (4.9)

subject to

( )1 1

N S

iji j

t Sδ= =

=∑∑ (4.10)

and

( )i iW t T i = 1,2,..., N< (4.11)

Note that, even though the second constraint in (4.11) don't explicitly

reflect the subcarrier assignments in the current time slot, however, it represent

the history of the previous assignments. This can be explained as follows: when

the previous assignments of a certain user(s) do not satisfy its delay requirement,

its waiting time approaches its deadline. The role of this constraint comes into

play by forcing the current assignments to compensate such user(s) by either

allocating more subcarriers or assigning better quality subcarriers in order to

prevent its (their) packets from expiry. However, a mathematical expression that

formulate the relationship between the waiting time of the HoL packet of a

certain queue and the subcarriers assigned to it (either in the current assignments

or the previous assignments) can not be driven explicitly. Thus, the optimal

solution of the above problem can not be obtained mathematically.

If this relationship between subcarrier assignments and HoL packets delays

could be found, the above problem can be solved with Integer Programming. We

refer to this approach as the optimal solution to our resource allocation problem.

Although the optimal solution gives the exact results, from an implementation

75

point of view, it is not preferred since in a time varying channel. In order to

allocate the subcarriers within the coherence time, the allocation algorithm

should be fast and the Integer Programming complexity increases exponentially

with the number of constraints. This real-time implementation requirement leads

to the quest for suboptimal solutions that are fast and close to the optimal

solution.

In what follows we propose a heuristic suboptimal solution of the above

problem. We decouple this NP-hard problem into two steps [32]:

1) Subcarrier Allocation: This step decides how many subcarriers to

be assigned to each user (i.e. determines ni(t)).

2) Subcarrier Assignment: This step determines which subcarriers to

be assigned to each terminal (i.e. the vectors δij(t) are calculated).

5.4 Subcarrier Allocation Algorithm

In our attempt to solve the above problem, we first determine the number

of subcarriers ni(t) to be assigned to every user in the set of active users Nt at that

time instant. Our allocation is based on three factors: the instantaneous subcarrier

channel gains of active users, users' average rates, and the delay information of

the HoL packets of these users. We not only exploit the statistical variations of

the users' channels, but also we use the statistical variations of users' queues in

order to increase the efficiency of channel throughput utilization.

The first step of our proposed dynamic subcarrier allocation algorithm is

to initially allocate to every active user in the system a number of subcarriers

( )'in t given by:

76

( ) ( )( )

'

1 1

t t

iii

j jj N j Nt t

trnr t

N N

t µ

µ∈ ∈

=∑ ∑

(4.12)

First, lets us assume that the weighting factor 1/t

i jj Nt

r rN ∈

∑ is equal for all

users and have a unity value. Then, a user with a relatively good channel

conditions in a certain video class, i.e. its average subcarrier capacity ( )i tµ , at

the time instant t, is greater than the mean of the average subcarrier capacities of

all the active users at that time instant, will be assigned initially two subcarriers.

On the other hand, a user with a relatively bad channel conditions in the same

class, i.e. its average subcarrier capacity ( )j tµ is less than or equal to the mean

of the average subcarrier capacities of all the active users at any time instant t,

will be assigned initially only one subcarrier. In this step, we exploit multiuser

diversity in order to efficiently utilize the scarce bandwidth of wireless channels.

However, video streams could be classified according to their average traffic

rates {ri} (which reflects the video quality). The weighting factor

1/t

i jj Nt

r rN ∈

∑ reflects the class of the ith user stream. If the average rate of the of a

certain user is greater than the mean of the average rates of all active users, then

number of subcarriers initially assigned to this user is increase due to its weight,

and vice versa.

At the end of this step, if all the available data subcarriers are assigned to

the set of users currently seeking service from the system, the allocation

algorithm terminates. However, if some subcarriers remain unused after this step,

the unused subcarriers are allocated to some of the active users. Let us denote the

number of the remaining unused subcarriers by S', where

( )'

t

iN

S S n t′ = − ∑ (4.13)

77

The role of the second step is to distribute any remaining subcarriers not

allocated by the first step among the active users. In this step of the algorithm, as

well as in the next step, the main goal is to use the remaining subcarriers

efficiently to prevent as many packets from expiry, and thus being dropped by

the system. In order to achieve this goal, the subcarrier allocation algorithm

should allocate the biggest share of the remaining subcarriers S' to the user with

the smallest time to expire di(t), and vice versa. Since the value of ( )1

id t

increases significantly as the time to expire di(t) decreases, our proposed

algorithm will distribute the remaining set of subcarriers S' among the active

users according to the ratios of ( )1

id t. When deadline due violations start to

occur (when the system is heavily loaded with users), the allocation algorithm

adapts to this situation by considering the number of violations NVi(t) in

calculating the share of additional subcarriers. Using ( ) ( )i iNV t /d t as the

distributing ratio, users recently suffering from more violations (than the average

of all users) will be compensated by allocating them more subcarriers. The

number of violations reflects the history of the previous assignments. However,

due to practical implementation it is computed in a certain time window (not the

entire history). Note that, this enhances causes fairness in distributing the

violations occurrences among all users. At this point, the number of subcarriers

to be assigned to the ith active user is now

( ) ( )

{ }( )

{ }( )

'

max 1, ( )

max 1, ( )

t

i

ii i

j

j N j

NV td t

n t n t SNV t

d t∈

′= +

∑ (4.14)

It is clear that the second component of the equation (4.14) may lead to

( )t

jj N

n t S∈

≥∑ . If the total number of allocated subcarriers equals the available

78

number, the algorithm terminates, and then moves to the subcarrier assignment

algorithm. In the next step of our proposed resource allocation algorithm, we

ensure that the number of subcarriers allocated is exactly equal to those available

in the system.

The last step in our subcarrier allocation procedure is only used when the

subcarrier allocation done in the first two steps exceeds the total number of data

subcarriers available to the system. Its function is to decrease the number of

subcarriers allocated to some users, so that the total allocated subcarriers equals

S. Our criteria in choosing these users, whose number of allocated subcarriers are

to be decreased, is the time to expire of their HoL packets and their violation

occurrences similar to what was done in the previous step of the algorithm. First,

we arrange the set of active users in a descending order according to their time to

expire. Then, the scheduler iterates over users in that order. In every iteration, the

scheduler decreases the number of subcarriers allocated to the user in turn by

one. Then checks whether the total subcarrier allocated equal to S or not. If it was

not yet equal, the algorithm continues one more iteration.

It is easily noticed that in the final step of the algorithm, users whose

packets' time to expire is small are allowed to keep their number of allocated

subcarriers in the first two steps. On the other hand, users whose number of

allocated subcarriers is most probably decreased are those whose packets' time to

expire are relatively large. Such a procedure for selecting users to degrade their

allocated resources is suitable for scheduling the delay-sensitive packets of

multimedia traffic. Figure 5.3 summarizes the subcarrier allocation algorithm.

The computational complexity of this algorithm is given by O (Nt

log(Nt)): The algorithm sorts the active users in the system according to their

time to expire once in every scheduling interval. Sorting a set of x elements

requires an algorithmic complexity of O(x log(x)).

79

Figure 5.3. Subcarrier Allocation Algorithm

Initially allocate every active user

( ) ( )( )

'

1 1

t t

iii

j jj N j Nt t

trnr t

N N

t µ

µ∈ ∈

=∑ ∑

( )t

iN

n t S=∑

Go to Subcarrier Assignment Algorithm

( )t

iN

n t S<∑

Distribute the remaining subcarriers

( )'

t

iN

S S n t′ = − ∑

among users according to their time to expire

( ) ( )

{ }( )

{ }( )

'

max 1, ( )

max 1, ( )

t

i

ii i

j

j N j

NV td t

n t n t SNV t

d t∈

′= +

∑

Arrange the active users in descending order

according to their time to expire

Decrease the number of subcarriers allocated to the user with the largest time to expire (in turn)

Yes

No

Yes

No

80

5.5 Subcarrier Assignment Algorithm

Once we have determined the number of subcarriers ni(t) allocated to the

ith user, the remaining part of the scheduling problem is to find out the exact

subcarrier assignment that maximize the total rate. This objective can be

achieved if multiuser diversity is used to assign every active user its best ni(t)

subcarriers. Such an assignment problem is equivalent to the maximum weighted

perfect matching problem in bipartite graphs [34]. An optimal solution can be

generated by the Hungarian algorithm [39], which has the complexity of O(S3),

where S is the number of subcarriers.

With the objective of enhancing the fairness characteristics of the

scheduling algorithm while maximizing the total rate, we propose a new low

complexity dynamic subcarrier assignment algorithm. The proposed algorithm is

a priority based algorithm. At some time instant (the start of a time window), the

algorithm assigns initially a unity priority to all users. Whenever a deadline due

violation occurs in a packet in a certain user's queue, its priority is incremented

by one. In every scheduling interval, the subcarrier assignment algorithm sorts

the active users in the system in a descending order according to their priorities.

The user with the highest priority starts to pick the best allocated subcarriers

from the set of all subcarrier. After assigning those subcarriers to that user, the

algorithm removes them from the set of available subcarriers. Then the algorithm

allows the user with the next higher priority to choose from this set of remaining

subcarriers, and so on. Clearly such an algorithm assigns the wireless terminal

with the highest priority (maximum number of recent deadline violations)

subcarriers with a better quality than it assigns the wireless terminal with the

lowest priority. Thus enhances the fairness performance of the scheduler. If more

than one user shares the same priority level, ties are broken by giving priority to

the user with the best channel quality (averaged over all subcarriers) to pick up

81

its allocated subcarriers first. This helps in maximizing the overall rate of the

system.

This case of equal priorities eventually occurs when the system supports

relatively small number of users (less than the maximum system capacity). In

this case no violations occur owing to the efficiency of our proposed subcarrier

allocation algorithm (as will be demonstrated by the simulation results). Hence,

the proposed subcarrier assignment algorithm reduces to an algorithm that

utilizes multiuser diversity in assigning the available subcarriers to the active

user in the system (by letting the user with the best channel conditions at ant time

instant to pick up its allocated subcarriers before the next better channel user, and

so on). Figure 5.4 summarizes the proposed subcarrier assignment algoritm.

The algorithm assigns S subcarriers to Nt wireless terminals. Each user

picks up its allocated subcarriers from a sorted list, which has to be regenerated

for each user (due to removal of some subcarriers assigned to the previous user).

Thus, the worst-case computational complexity of this assignment procedure is

given by O (Nt S log(S)). Even when added to the complexity of sorting the

active users according to their priorities (O (Nt log(Nt))), the computational

complexity of complete subcarrier assignment algorithm is much lower than that

of the optimal (Hungarian) algorithm.

In the next chapter, we carry out an extensive set of simulation

experiments in order to gain insight of the different performance aspects of the

proposed subcarrier allocation and assignment algorithms. Specifically, we are

interested in evaluating the delay, throughput, and fairness characteristics of the

algorithms. Without loss of generality, we assume that all users belong to the

same video quality class.

82

Figure 5.4. Subcarrier Assignment Algorithm

At the beginning of a time window: Reset the priorities of all users to 1

For every user

If a packet is dropped due to deadline expiry

à Increase the priority of this user by 1

Arrange the active users in a descending order according to their

priorities

Note that: In case of equal priorities, priority is to the user with the better

channel conditions

Allow the user with the highest priority (in turn) to select the best nj(t) subcarriers from the set of the

available subcarriers.

Remove the selected nj(t) subcarriers from the set of the available

subcarriers

83

Chapter 6 Simulation Results and Discussions of the OFDMA-

Based Scheduling

6.1 Simulation Setup

We first describe the simulation environment used in evaluating the

performance of the proposed subcarrier allocation and assignment algorithms. As

mentioned in chapter 5, we will consider the IEEE 802.20 Mobile Broadband

Wireless Access (MBWA) system model. The Mobile Broadband Wireless

Access (MBWA) systems being discussed in IEEE 802.20 standards group are

designed to provide a broadband, IP-oriented connection to a wireless user that is

comparable to wired broadband connections that are in use today. It is expected

that there will be a mixture of user applications similar to that of such wired

systems [40]. MBWA system shall support peak per-user data rates in excess of 1

Mbps on the downlink and in excess of 300 kbps on the uplink. These peak data

rate targets are independent of channel conditions, traffic loading, and system

architecture. The peak per user data rate targets are less than the peak aggregate

per cell data rate to allow for design and operational choices. Average user data

rates in a loaded system shall be in excess of 512Kbps downlink and 128Kbps

uplink. This shall be true for 90% of the cell coverage or greater [41].

Mobile broadband radio channel is a challenging environment, in which

the high mobility causes rapid variations across the time-dimension, multi-path

delay spread causes severe frequency-selective fading, and angular spread causes

significant variations in the spatial channel responses. For best performance, the

receiver and the transmitter algorithms must accurately track all dimensions of

the channel responses [42]. The proposed algorithms utilize these variations in

increasing the system capacity.

84

Among the different channel bandwidths suggested in [41, 43], we use a

channel of 5 MHz bandwidth. We assume that the number of data subcarriers S is

equal to 128 subcarriers. Data is transmitted on each subcarrier with an adaptive

modulation scheme, where five modulation types are available (BPSK, QPSK,

16-QAM, 64-QAM and 256-QAM). The modulation types are chosen such that

the highest possible rate can be transmitted in every scheduling interval.

For simulation purpose, the IEEE 802.20 working group adopted the test

environments and associated Single Input Single Output (SISO) channel models

put forth for UMTS Terrestrial Radio Access (UTRA). This is because the

deployment and propagation scenarios for which the UTRA models were

developed are so similar to those currently envisioned for IEEE 802.20 MBWA.

The working group defines three broad deployment/propagation scenarios [42],

referred to therein as "Test Environments", in which the performance of

candidate UTRA radio transmission technologies (RTTs) are to be evaluated.

These test environments are labeled Indoor Office, Pedestrian, and Vehicular.

Each test environment broadly defines a particular wireless propagation scenario,

and each scenario in turn has an associated channel model.

Moreover, each test environment is combined with a pair of

representative tapped delay line impulse response specifications, labeled A and

B, which characterize delay spread. The A model represents a frequently

occurring low delay spread situation, and the B model a frequently occurring

high delay spread situation within that test environment. In this work, we only

consider the B Model Pedestrian test environment. This model is valid for non-

line-of-sight case only. The tapped-delay line impulse response parameters for

the B Model Pedestrian test environment is shown in Figure 6.1. This model has

6 rays, an RMS delay spread of 750 ns. The Doppler velocity distribution model

is specified Jakes’. The user mobility rates of this environment range from 3

Km/hr up to 120 Km/hr [44]. According to these velocities, the maximum

Doppler frequency shift equals to 211 Hz for a carrier frequency of 1.9 GHz.

Thus, the coherence time of such a channel is about 4.7 milliseconds.

85

Figure 6.1. The power-delay profile of the B Model pedestrian environment.

Our approach in generating streams of packets that need to be transmitted

over the system is based on an actual video trace file. The file basically has

output from a 30 frames/sec MPEG-4 encoder targeted for an average rate of 256

Kbps and a peak rate of 2.3 Mpbs [45]. Each user receives the same video

stream, however they are randomly time-shifted at the beginning so that different

parts of the video stream arrive at different times at the access point for different

users. Each frame is decomposed into 50 bytes packets to be transmitted. A

packet is assigned a deadline before which it should be delivered to its

destination. We consider three values of this deadline, specifically, 20, 50, and

100 milliseconds. Such values are much less than the end-to-end delay allowed

for transmitting video streams (about 400 milliseconds). (In essence, we relax the

delay requirements of the core network). Video quality degradation is caused

receiving outdated packets or when not receiving these packets at all (if such a

packet is dropped by the scheduler).

86

At the base station, a centralized scheduler is responsible for multiplexing

multiple users sharing the previously described common channel. As discussed

above, this channel varies from one user to another due to the location-dependent

path loss, as well as the channel of a certain user varies over time due to the user

mobility. However, the channel gains do not change significantly within the

channel coherence time (which is 4.7 milliseconds in our case). Thus, setting the

scheduling interval (over which subcarrier allocation and assignment is

performed) to 1.667 milliseconds is a good choice. This is because in such a case

the scheduling decision can be based on a one-slot delayed version of the channel

information. This gives the scheduler/base station enough time to collect the

subcarrier channel gain information for all active users.

In the next section, we will provide an extensive set of simulation

experiments of the proposed scheduling scheme in the MBWA system. These

experiments will explore the various characteristics of the proposed opportunistic

subcarrier allocation and assignment algorithms including the overall system

capacity, fairness in both rate and delay requirements, and the control of

violation occurrences. The simulation period is three minutes.

Carrier frequency 1.9 GHz

Channel bandwidth 5 MHz

Number of data subcarriers (S) 128

User mobility speeds 3 – 120 Km/hr

Doppler frequency 211 Hz

Doppler spectrum Jakes' (6 rays)

Scheduling interval 1.667 msec

Traffic model Real trace file of MPEG-4 encoder

Frame rate: 30 frames/sec

Traffic average rate / peak rate 256 Kbps / 2.3 Mbps

Packet size 50 bytes

Table 6.1. Summary of simulation parameters.

87

6.2 Results and Discussions

In this section we present numerical results of the introduced

opportunistic subcarrier allocation and assignment algorithms. For comparison

reasons we always include also the results of the static OFDM-FDMA subcarrier

assignment. As discussed in chapter 5, OFDM-FDMA has been identified as the

best static subcarrier assignment. Thus we use it as a bench mark for illustrating

the performance gains achieved by our opportunistic subcarrier allocation and

assignment.

In the first experiment, we study the throughput performance of our

proposed scheduling algorithm via admitting users to the network while

monitoring the average throughput per user as well as the maximum and the

minimum throughput achieved. Figures 6.2-a, 6.3-a 6.4-a show the average user

throughput versus the number of admitted users for a 20, 50, and 100

milliseconds delay bounds, respectively. The aim of this experiment is to

determine the system capacity (the number of supportable terminals) for the

proposed opportunistic algorithm. The maximum number of users to be admitted

to the network if OFDM-FDMA assignment is used is 42 users only. This is

because for our model of user's traffic, 3 subcarriers per user are fairly enough to

support this traffic. Thus, a new user is admitted in this case only if there exist at

least 3 unused subcarriers. Defining the system capacity as the number of users

beyond which the average throughput per user falls to 99% of the average arrival

rate; we find that when the opportunistic allocation/assignment is used the

system can support 120, 165, and 165 users for a 20, 50, and 100 milliseconds

delay bound, respectively. While using static assignment, even though the system

can admit up to 42 users, the system can only support 15 users for 50

milliseconds delay bound and less than 10 users for 20 milliseconds delay bound

without degrading their service rates significantly. This is because with such

strong delay requirements, three low-quality subcarriers can not support the

required service rate.

88

It worth mentioning here that: the MBWA systems are required to

support more than 100 simultaneous active users per carrier [41]. An active user

is a terminal that that is registered with a cell and is using or seeking to use air

link resources to receive and/or transmit data within a short time interval. Thus,

the proposed subcarrier allocation and assignment algorithm is suitable for

application in future MBWA systems.

The explanation of the significant difference in system capacity of our

opportunistic algorithms is as follows: a user is not allocated/assigned any

subcarriers unless its queue contains at least one packet ready for transmission.

In addition to the capacity gain obtained from utilizing multiuser diversity in the

allocation/assignment processes. Thus our algorithms don't only take advantage

of the statistical variation of users' channels but also the statistical variation in

their queue states.

In order to qualify the fairness characteristics of the proposed

opportunistic subcarrier allocation and assignment algorithms, we plot the

maximum and the minimum achieved throughput for the above experiments in

Figures 6.2-b, 6.3-b 6.4-b. As show in these figures, when using the opportunistic

algorithm, the difference between the maximum and the minimum achieved

throughput is insignificant when the system is serving a number of users less

than or equal to the system capacity. Even when serving more than the system

capacity the difference is still acceptable. However, for the static OFDM-FDMA

assignment, that difference is highly noticed, especially for 20 and 50

milliseconds delay bounds. This is because even though 3 high-quality

subcarriers are enough to handle user's traffic, 3 low-quality channels can not

handle that traffic. As a consequence, the throughput share of users with low-

quality channels is much lower than their traffic arrival rates. Thus, low-quality

users play the major role in degrading the performance (the system capacity) of

the static algorithm. We define the throughput fairness index as the ratio of the

difference between the maximum and the minimum achieved throughput (λmax

and λmin, respectively) to the average throughput per user (λavg), i.e.

89

a) The average throughput per user.

b) The maximum and the minimum achieved throughput.

Figure 6.2. Throughput performance for a 20 msec delay bound.

90


c) The maximum and the minimum achieved throughput.


91


d) The maximum and the minimum achieved throughput.


92

max min

avg

Throughput Fairness Indexλ λ

λ−

= (6.1)

Using this index as a formal indicator of the fairness performance of the

scheduling algorithm, we gain more insight of the performance advantage of the

proposed opportunistic algorithms. The throughput fairness indices of both the

opportunistic algorithm and the static algorithm for different delay bounds are

plotted in Figure 6.5. The perfect fairness of the opportunistic algorithm when

the system is operating with a number of users less than its capacity (fairness

index approaches 0) can be easily noticed. The favor of this super fairness

performance is owed to the main objective of the proposed algorithm of

preventing all users from losing any of their packets (by being dropped due to

deadline expiry) by allocating them more subcarriers. Even when the system is

operated with users more than its capacity (users starts to lose their packets), the

fairness of distributing these lost packets among all users is achieved via the

subcarrier assignment algorithm. This is demonstrated by the next experiments.

Figure 6.5. Throughput fairness indices of both the opportunistic algorithm and

the static algorithm for different delay bounds.

93

Now, we study the deadline due violations behavior of the proposed

opportunistic algorithms. Figure 6.6 shows the maximum and the minimum

number of violation occurrences experienced by users in the same simulation

setup of the previous experiment. Again, it is clear that the subcarrier allocation

algorithm succeeded in saving users' packets from being dropped due to deadline

expiry regardless the channel-quality of different users. (Since no deadline

violations occurs for all users packets until the system is operating near its

capacity). Moreover, when the number of users in the system exceeds the system

capacity, the subcarrier assignment algorithm cooperates with the allocation

algorithm to ensure that the number of dropped packets in the system is fairly

distributed among all users in the network. This can be seen in Figure 6.6 where

the maximum percentage of packets lost (most probably in the queue of a low-

quality channel user) is close to the minimum percentage of packets lost (most

probably in the queue of a high-quality channel user). A remarkable result is that

this fairness behavior is independent of the value of the value of the delay bound.

On the other hand, the static subcarrier assignment lacks such characteristics.

a) Delay bound = 20 msec.

94

b) Delay bound = 50 msec.

c) Delay bound = 100 msec.

Figure 6.6. Deadline violation fairness for different delay bounds.

95

In our last experiment, we consider the delay performance of the

proposed subcarrier allocation and assignment algorithms. This can be achieved

through studying the distribution of the delays that users' packets incur at the

base station. A good scheduling algorithm should keep all delays below the delay

bound with high probability, which is achieved roughly when the delays are kept

close for all users. Due the large number of users the system can support, we

focus only on the delay distribution of the user with the best channel quality and

the user with the worst channel quality. The delay distributions of these

particular couple of users are sufficient to evaluate the delay performance of the

scheduling algorithm since they represent the opposite extremes of the channel

qualities.

First, we consider the system is serving only 42 users (the maximum

supportable number of users using the OFDM-FDMA static assignment). The

delay tail of both the static and the opportunistic scheduling algorithms for

different delay bounds are shown in Figure 6.7. A couple of observations can be

easily noticed: The first observation is that the delay performance of the

opportunistic algorithm (the delay distributions and the maximum delays of the

best and the worst channel users) is similar regardless the value of the delay

bound. The other observation is that the opportunistic algorithm keeps the delay

of all users far below the deadline and also close to each other. On the other

hand, the delay performance of the static algorithm is dependent on the value of

the delay bound and has a very poor performance compared to the opportunistic

algorithm. For example, when the delay bound is 100 msec (Figure 6.7-c), there

is a big gap between the delays incurred by the best channel user and those of the

worst channel user. While when the delay bound is 20 msec (Figure 6.7-a) the

gap is smaller but with packet delays close to the delay bound. Actually, some

packets incurred delays greater than the delay bound and thus dropped by the

system (the best channel user has lost 5% of its packets while the worst channel

user has lost 50% of its packets). Thus the small performance difference in

Figure 6.7-a is somehow misleading.

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The good delay performance of the opportunistic algorithm comes from

the mechanism of compensation of low-quality users employed in the algorithm.

When a certain user (or group of users) is suffering from a long period of bad

channel conditions, the delay of its (their) HoL packet increases (increase), so

that the allocation algorithm allocates more subcarriers to this (these) user (even

on the expense of taking a part or all of the subcarrier initially assigned to other

higher-quality users). Preventing high-quality users from their subcarrier shares

increases their HoL packets delay. Thus in the next scheduling interval the

algorithm allocates them more subcarriers, and so on. Thus the delays of all users

are always kept small and below the deadline. It is worth mentioning that this

mechanism is not affected by the value of the delay bound since it is only

concerned by the difference in HoL delays of different users.

In order to have a fair comparison with the static assignment, we also

studied the delay performance of our opportunistic algorithm the system is

supporting its full capacity. The delay distributions of the best and the worst

channel users for a 20 milliseconds (and 120 users), a 50 milliseconds (and 165

users), and a 100 milliseconds (and 170 users) is shown in Figures 6.8, 6.9, and

6.10, respectively. As shown in these figures, even with such high user

population, our opportunistic subcarrier assignment and allocation algorithms

managed to keep the delays of users with different channel conditions very close.

These results emphasizes the efficiency of our algorithms to control the delay

performance independently of other factor such as the value of the delay bound

and user population.

Finally, the results presented in this chapter can be concluded as follows:

though rather a computationally inexpensive algorithm, the proposed

opportunistic scheduling algorithm can be used to provide statistical delay

guarantees for time-sensitive traffic in OFDMA-based wireless networks. The

algorithm exhibits a unique fairness behavior in the services (packet delays and

throughput) delivered to different users. Moreover, multiuser diversity used in

the algorithm offers orders of magnitude increase in the system capacity.

97

a) Delay bound = 20 msec (5.3% and 48.5% of the best and the worst users packets were lost).

b) Delay bound = 50 msec (18.3% of the worst user packets was lost).

98

c) Delay bound = 100 msec (2.9% of the worst user packets was lost).

Figure 6.7. Delay tails of the best and worst channel users (N = 42 users).

Figure 6.8. Delay tails of the best and worst channel users (1.5% and 2.3% of the best and the

worst users packets were lost) (N = 120 users, T = 20 msec).

99

Figure 6.9. Delay tails of the best and worst channel users (0.07% and 1.4% of the best and

the worst users packets were lost) (N = 165 users, T = 50 msec).

Figure 6.10. Delay tails of the best and worst channel users (6.7% and 16.9% of the best and

the worst users packets were lost) (N = 170 users, T = 100 msec).

101

Chapter 7 Conclusions and Future Research

7.1 Conclusions

This thesis addresses the problem of opportunistic scheduling of multiple

time-sensitive users sharing a common resource in wireless multimedia

networks. Opportunistic scheduling means that the scheduling decision is based

on the instantaneous user information, e.g. in our case, the channel state

information of different users and their delay information. We considered this

problem in two different models of wireless networks that are candidates of

beyond 3G networks. First, we studied TDM-based networks (in which time is

the resource to be shared among users). Then we tackled on OFDMA-based

mobile broadband wireless networks (in which the scheduler function is to

distribute the available subcarriers "the common resource" over different users).

Our approach was to exploit multiuser diversity inherently existing in

wireless systems. Multiuser diversity scheduling offers orders of magnitude

increase in the overall system performance. However, multiuser diversity

scheduling is unfair in resource sharing among different users cause it always

gives higher priority to high channel-quality users. As a consequence, low

channel-quality users will be prevented from accessing the wireless link, and thus

not obtain their required QoS (delay-bound guarantees in this case). In order to

remedy this situation, we introduced mechanisms to compensate such users and

that statistically guarantee their QoS requirements as well as achieving fairness

in resource sharing among all users in the system.

Regarding the problem of scheduling real-time users over TDM-based

wireless multimedia networks, we introduced the Channel Dependent Earliest-

Due-Date first (CD-EDD) scheduling discipline, a discipline that provides

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statistical delay bound guarantees for time-sensitive traffic in networks with

time-varying channels. Gains in throughput and realized delay are achieved by

exploiting multi-user diversity techniques in which the scheduling decision takes

into account the current channel state for each user in the system. By considering

the packet loss due to deadline violation, we also presented a set of scheduling

policies that achieve fairness in delays, throughput, and packet loss ratios among

different users regardless of the value of the delay bound. The proposed

disciplines outperforms other existing polices in the sense that the services

received by different real-time users, namely, delays, rates, and loss ratios, are

fairly achieved for a wide of applications. The proposed policies have low

computational complexity and are suitable for application in future broadband

fixed or mobile wireless systems such as 802.16a and 802.20.

Also, we presented new opportunistic subcarrier allocation and

assignment mechanisms for parallel transmission of data streams to different

terminals in OFDMA-based broadband wireless systems. The subcarrier

allocation algorithm instantaneously determines the number of subcarriers each

terminal should receive by a dynamic assignment algorithm for the next

downlink scheduling interval. Our subcarrier allocation method is based on

allocating subcarriers for terminals depending on the knowledge of the channel

gain information of different users as well as other stream specific delay

information (the time to expire of the HoL packet) and the number of recent

deadline violations. Initially, we utilize multiuser diversity in allocation

subcarriers to active users. In the case of a severe channel-quality degradation of

one (or some) user channel, its (their) HoL packet time to expire approaches

zero, leading to a higher number of subcarriers allocated to this terminal for the

next downlink intervals. Similarly, any increase in the number of violations

experienced by a certain user over the average number of violations will lead to a

higher number of subcarriers allocated to this terminal for the next downlink

intervals. The allocated numbers of subcarriers are assigned to terminals

dynamically in a manner that ensure fairness in the deadline violation

occurrences among different users. The proposed algorithms have low

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computational complexity and are suitable for application in 4G mobile

broadband wireless access systems such as the IEEE 802.20 standard.

7.2 Future Research Directions

During conducting this research, some interesting related ideas that may

be addressed relaying on the findings of this thesis came into picture. Among

these research ideas:

• How to further modify the proposed scheduling schemes in order to

be able to simultaneously provide different kinds of QoS (e.g. rate

guarantees for non-real-time users and delay guarantees for real-time

users). Supporting real-time flows with delay requirements and non-

real-time flows with throughput constraints simultaneously is an

important challenge for future wireless networks. Indeed, providing

differentiated quality-of-service levels increases a system’s total

utility when applications have diverse performance requirements, e.g.,

some preferring low delay, others high throughput, and others merely

best effort service. Consequently, both medium access control and

network-layer scheduling algorithms must select and transmit packets

in accordance with their QoS requirements.

• The application of the channel-aware scheduling with QoS guarantees

in other future wireless networks such as multi-hop and ad-hoc

networks. However, due to the distributed nature of these networks,

nodes may not be able to determine the next packet that would be

transmitted in a (hypothetical) centralized and ideal dynamic priority

scheduler. But this difficult problem becomes easier in hybrid

networks (where the network combines a centralized core

interoperating with distributed nodes).

104

• Performing Mathematical analysis of the proposed CD-EDD

scheduling discipline in order to proof its throughput optimality.

105

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Appendix A Code Samples

Throughout the thesis, all simulation scenarios have been implemented

using C++ programs with the aid of IT++ library. IT++ is a C++ library of

mathematical, signal processing, speech processing, and communications classes

and functions. It has been developed by researchers in these areas. The itbase

library is the core of IT++ and it contains classes and functions for mathematics

with scalars, vectors, and matrices. This library is mainly built using a flexible

template of vector and matrix classes and lots of functions for vectors and

matrices. These functions are similar to the Matlab functions. Moreover, the

IT++ file format ".it" can be read using Matlab. This enabled us to use Matlab to

plot all figures in the thesis. The IT++ library originates from the former

department of Information Theory at Chalmers University of Technology,

Gothenburg, Sweden. Since the library is coded in C++ thus comes the name of

the library IT++.

Our simulation setup for different scenarios was carried out in two

separated steps. The first step was to simulate the channels of all users (according

to the intended channel model). These channels are then stored on disk. The

second step was to apply the scheduling algorithm over these users. This step

included the generation of users' traffic. The output of this step is the final output

to be passed to Matlab to be plotted.

As a sample of the channel simulation program, the code for simulating

the Jakes model of the 6-ray Rayliegh faded channel of the IEEE 802.20

Pedestrian-B environment used in testing the OFDMA algorithms is listed in

section A.1. Then in section A.2, we include the code of the proposed heuristic

subcarrier allocation and assignment as a sample of the scheduling programs.

112

A.1 Sample Program 1: Channel Simulation // This program simulates the 6-ray Rayliegh faded channels using Jakes Model. #include "itbase.h" #include "itcomm.h" using std::cout; using std::endl; void jakes (int K, double Jmax, int points, double p, cvec &h); int main() { int np = 6; // The number of paths per channel int N = 46; // Number of users int S = 128; // The number of subchannels double sim_period = 180.0; // The simulation period (in sec) double Ts = 5.0 * 0.001 / 3.0; // Ts is seconds double B = 5.0 * 1024.0 * 1024.0; // The channel BW = 5 MHz double EbNo = 2.0; // The signal to noise ratio in absolute units (3dB = 2) double Fd = (120000.0/(60.0*60.0)) * 1.9e9 / 3e8; // Doppler freq = Vmax*fc/C; double J = 1.0 / (2.0 * Ts * Fd); // The Jmax variable passed to jakes function int ns = ceil_i(sim_period / Ts); // Simperiod / Ts char file_name[128]; vec a(N); // Holds the gains of different users vec p(np); // The relative power of the different paths cvec h1(ns),h2(ns),h3(ns),h4(ns),h5(ns),h6(ns); // The 6 paths cvec currentchan(np); // Holds the states of the 6 paths at time t cvec currentsubchan(S); // Holds the states of subcarriers of a user at time t imat user(ns,S); Uniform_RNG A; // Initialization of some parameters p = "0 -0.9 -4.9 -8 -7.8 -23.9"; p = pow(10.0, p/10.0); // Generation of different users' gains RNG_randomize(); A.setup(1.0,2.0); a = A(N); sort(a); // Simulation of users' channels for (int u = N-1; u >= 0; u--) { jakes(0,J,ns,p(0),h1); jakes(0,J,ns,p(1),h2); jakes(0,J,ns,p(2),h3); jakes(0,J,ns,p(3),h4); jakes(0,J,ns,p(4),h5); jakes(0,J,ns,p(5),h6); for (int t = 0; t < ns; t++) { currentchan(0) = h1(t); currentchan(1) = h2(t); currentchan(2) = h3(t);

113

currentchan(3) = h4(t); currentchan(4) = h5(t); currentchan(5) = h6(t); currentsubchan = fft(currentchan, S); for (int sc = 0; sc < S; sc++) { user(t,sc) = floor_i(logb(2.0, ((B * logb(2.0,(1+sqr(abs(currentsubchan(sc)))*a(u)*EbNo/sum(p))) / S)/(9.6*1024)))); if (user(t,sc) < 0) user(t,sc) = 0; } } sprintf(file_name, "user%d%s", N-1-u, ".it" ); ofstream pf(file_name); if(!pf.is_open()) cout << " File is not open "; for (int nsi = 0; nsi < ns; nsi++) for (int Si = 0; Si < S; Si++) pf << user(nsi,Si) << " "; pf.close(); } return 0; } void jakes (int K, double Jmax, int points, double p, cvec &h) { // K = 0 (Rayleigh Channels) anf K = 1 (Rician Channel) // Jmax = 1/(Bd*T) where Bd is the Doppler frequency and T is the sampling rate // points = Number of instants you want to sample the channel // P = The Relative power of the channel (PATH) int N = 34; int No = 8; double alpha = 0.0; double beta = pi / (No + 1.0); double fac = randu() * 100000.0; double temp; vec xc(points), xs(points), X(points), Y(points); xc.zeros(); xs.zeros(); X.zeros(); Y.zeros(); for (int jj = 1; jj <= points; jj++) { xc(jj-1) = sqrt(2.0) * cos(pi*(jj+fac)/Jmax) * cos (alpha); temp = 0.0; for (int ii = 1; ii <= 8; ii++) temp = temp + 2.0 * cos(pi * cos(2.0*pi*ii/N) * (jj + fac) / Jmax) * cos(ii*beta); xc(jj-1) = xc(jj-1) + temp; } for (int jj = 1; jj <= points; jj++) { xs(jj-1) = sqrt(2.0) * cos(pi*(jj+fac)/Jmax) * sin (alpha); temp = 0.0; for (int ii = 1; ii <= 8; ii++) temp = temp + 2.0 * cos(pi * cos(2.0*pi*ii/N) * (jj + fac) / Jmax) * sin(ii*beta); xs(jj-1) = xs(jj-1) + temp; }

114

X = sqrt(2.0*K / (K+1.0)) + sqrt(1.0/(K+1.0)) * xc / sqrt(8.0); Y = sqrt(1.0/(K+1.0)) * xs / sqrt(9.0); h = to_cvec(X,Y); h = h * sqrt(p/2.0); }

A.2 Sample Program 2: The Scheduler #include "itbase.h" #include "itcomm.h" using std::cout; using std::endl; struct Queue { int len ; int HOL ; int violation_count; int HOL_pkt_len; vec elem_len_arriv; vec elem_HOL_wait; }; int sum(const ivec &V); void my_sort(vec array); int main() { // Variable Declaration double D = 20.0; // dead line of a packet double Ts = 5.0/3.0; // The time slot length (in msec) double sim_period = 180000.0; // The simulation period (in msecs) double current_time; // Time Slot Counter int Ts_counter = ceil_i(sim_period / Ts); int pktsize = 400; int S = 128; // The number of subcarriers int N = 46; // Number of users in the system int Nt; // number of active users at time t int St; double w_mean, m_mean; // hold the average of channels and delays at t double total_rate; vec subchan(S), w(N), m(N); ivec scheduled_users(N); // Holds the Indeces of the active users ivec z(N); // Hods the No. of subcarriers to be assigned to the users at t. ivec w_sorting(N); Queue user[N]; ivec vc(N); ivec p(N),q(N); bvec s(S); ivec throughput(N); // Some Initiations vc.ones(); throughput.zeros();

115

char file_name[128]; imat chan_state(N,S); ifstream ff[N]; RNG_randomize(); for (int f = 0; f < N; f++) { sprintf(file_name, "user%d%s", f, ".it" ); cout << file_name << endl; ff[f].open(file_name); if(!ff[f].is_open()) cout << " File is not open "; } // Initialize the queues for (int j = 0; j < N; j++) { user[j].len = 0; user[j].HOL = 0; user[j].violation_count = 0; user[j].HOL_pkt_len = pktsize; user[j].elem_len_arriv.set_size(2*Ts_counter); user[j].elem_HOL_wait.set_size(2*Ts_counter); user[j].elem_HOL_wait.ones(); user[j].elem_HOL_wait = -10 * user[j].elem_HOL_wait; } // Simulating Users Traffic int ii, l; float we; int start; for (int y = 0; y < N; y++) { ifstream in("terse.data"); if(!in.is_open()) cout << " File is not open "; l = 0; start = 11 * randi(0, 9327); // Find a random starting frame for this user while(!in.eof() && l < start) { in >> ii; l++; in >> we; } // Then reads the required number of frames from this starting frame for (int u = 0 ; u < 5400; u++) { in >> ii; l++; ii = ceil_i(1.0*ii/pktsize); // Calculate the number of packets in that frame for (int r = 0; r < ii; r++) //Add these packets to queue & Calculate their arrival times { user[y].elem_len_arriv(user[y].len) = u * 1000.0 / 30.0 ; user[y].len++; } in >> we;

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} user[y].elem_len_arriv.set_size(user[y].len, true); in.close(); } // Here starts the scheduling functions (runs once every scheduling interval) for (int i = 0; i < Ts_counter; i++) { current_time = i * Ts; Nt = 0; m_mean = 0; w_mean = 0; w.ones(); w = w * -1; m.ones(); m = m * -1; z.zeros(); scheduled_users.set_size(N,false); scheduled_users.ones(); scheduled_users = scheduled_users * -1; s = ones_b(S); for (int nii = 0; nii < N; nii++) for (int Sii = 0; Sii < S; Sii++) ff[nii] >> chan_state(nii,Sii); if (!(i%1000)) vc.ones(); // sliding window of the violation counting for (int j = 0; j < N; j++) { bool x = true; while (x) { // if there is a packet in the jth user queue if ( current_time >= user[j].elem_len_arriv(user[j].HOL) && user[j].HOL < user[j].len) { // if this packet hasn't expired yet if (current_time - user[j].elem_len_arriv(user[j].HOL) <= D) { scheduled_users(Nt++) = j; // increase the number of active users if (current_time - user[j].elem_len_arriv(user[j].HOL) == D) w(j) = 1000; // As infinity else

w(j) = 1.0 / ( D - (current_time - user[j].elem_len_arriv(user[j].HOL))); w_mean = w_mean + w(j); m(j) = 0; for (int ss = 0; ss < S; ss++) m(j) = m(j) + (pow2(chan_state(j,ss)) * 9.6 * 1024 / S ); m_mean = m_mean + m(j); x = false; } else // if this packet has expired increase the no. of violations and then

check if there is a new packet { user[j].HOL ++; user[j].violation_count ++; if (user[j].violation_count >=1) vc(j)++; // = ceil_i((0.2 * user[j].violation_count) + (0.8 * vc(j))); } } else // No new packets in the jth user queue so go to the next user {

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x = false; } } } // Subcarrer Allocation Algorithm if (Nt > 0) { w_mean = w_mean / Nt; m_mean = m_mean / Nt; scheduled_users.set_size(Nt,true); for (int y = 0; y < Nt; y++) z(scheduled_users(y)) = ceil_i(m(scheduled_users(y)) / m_mean); while (sum(z) != S) { if (sum(z) < S) { St = S - sum(z); if (!w_mean) for (int f = 0; f < Nt; f++) z(scheduled_users(f)) = z(scheduled_users(f)) + ceil_i( (double) St / Nt ); else for (int h = 0; h < Nt; h++) z(scheduled_users(h)) = z(scheduled_users(h)) + ceil_i(St * w(scheduled_users(h)) / (w_mean*Nt)); } else { w_sorting = sort_index(w); int r = 0; do { if (w(w_sorting(r)) >= 0) z(w_sorting(r))--; r++; if (r == N) r = 0; } while (S < sum(z)); } } } // Subcarrier Assignment Algorithm p.set_size(Nt,false); q.set_size(Nt,false); for (int t = 0; t < Nt; t++) p(t) = vc(scheduled_users(t)); for (int qq = 0; qq < Nt; qq++) { q(qq) = scheduled_users(max_index(p)); p(max_index(p)) = -1; } for (int e = 0; e < Nt; e++) { total_rate = 0; for (int sss = 0; sss < S; sss++)

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subchan(sss) = 9.6 * 1024 * pow2(chan_state(q(e),sss)); int z_count = 0; while (z_count < z(q(e))) { if (s(max_index(subchan))) { if (max(subchan) >= 0) { s(max_index(subchan)) = 0; z_count++; total_rate = total_rate + max(subchan); subchan(max_index(subchan)) = -1; } } else subchan(max_index(subchan)) = -1; } do { if (user[q(e)].HOL_pkt_len <= 0) user[q(e)].HOL_pkt_len = pktsize + user[q(e)].HOL_pkt_len; user[q(e)].HOL_pkt_len = user[q(e)].HOL_pkt_len - ceil_i(total_rate*Ts*0.001); if(user[q(e)].HOL_pkt_len <= 0) { if(user[q(e)].elem_len_arriv(user[q(e)].HOL + 1) <= current_time

&& user[q(e)].HOL < user[q(e)].len) { user[q(e)].elem_HOL_wait(user[q(e)].HOL) = current_time –

user[q(e)].elem_len_arriv(user[q(e)].HOL); user[q(e)].HOL++; throughput(q(e))++; } else { user[q(e)].elem_HOL_wait(user[q(e)].HOL) = current_time –

user[q(e)].elem_len_arriv(user[q(e)].HOL); user[q(e)].HOL++; throughput(q(e))++; user[q(e)].HOL_pkt_len = pktsize; } } }while(user[q(e)].HOL_pkt_len <= 0); } } for (int r = 0; r < N; r++) ff[r].close(); cout << "The total throughput = " << sum(throughput)*pktsize/180.0 << endl; cout << "The average throughput = " << sum(throughput)*pktsize/(N*180.0) << endl; cout << "The maximum throughput = " << max(throughput)*pktsize/180.0 << " of user " << max_index(throughput)<< endl; cout << "The minimum throughput = " << min(throughput)*pktsize/180.0 << " of user " << min_index(throughput)<< endl; cout << "The best user throughput = " << throughput(0)*pktsize/180.0 << endl; cout << "The worst user throughput = " << throughput(N-1)*pktsize/180.0 << endl; int zz;

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for (int i = 0; i < N; i++) { user[i].elem_HOL_wait.set_size(user[i].HOL, true); zz = 0; for (int l=0 ; l < user[i].elem_HOL_wait.length() ; l++) if (user[i].elem_HOL_wait(l) != -10) { user[i].elem_HOL_wait(zz) = user[i].elem_HOL_wait(l); zz++; } user[i].elem_HOL_wait.set_size(zz, true); } it_file u("dyn4620.it"); u << Name("y1") << user[0].elem_HOL_wait; u << Name("yN") << user[N-1].elem_HOL_wait; vec o(N), f(N); for(int u = 0; u < N; u++) { o(u) = user[u].violation_count; f(u) = (double) user[u].violation_count / (double) user[u].len; cout << user[u].violation_count << " " ; } cout << endl; for(int u = 0; u < N; u++) cout << user[u].elem_HOL_wait.length() << " " ; cout << endl; for(int u = 0; u < N; u++) cout << f(u) << " " ; cout << endl; cout << "The minimum number of violations is : " << min(o) << " for the user number : " << min_index (o) << endl; cout << "The maximum number of violations is : " << max(o) << " for the user number : " << max_index (o) << endl; cout << "The minimum drop ratio is : " << min(f) << " for the user number : " << min_index (f) << endl; cout << "The maximum drop ratio is : " << max(f) << " for the user number : " << max_index (f) << endl; my_sort(user[0].elem_HOL_wait); my_sort(user[N-1].elem_HOL_wait); return 0; } void my_sort(vec array) { int i, j; double temp; // holding variable int arrayLength = array.length( ); for (i=0; i< (arrayLength -1); i++) // to represent element to be compared { for(j = (i+1); j < arrayLength; j++) // to represent the rest of the elements { if (array(i) < array(j))

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{ temp= array(i); array(i) = array(j); array(j) = temp; } } } int x = 0; while(((double)(x+1)/(double)arrayLength) <= 0.05) x++; while (array(x-1) == array(x)) x--; cout << endl; cout << (double)(x+1)/ (double)arrayLength << " percent of the waiting times are above : "; cout << array(x) << endl; return; } int sum(const ivec &V) { int X = 0; for (int i = 0; i < V.size(); i++) X = X + V(i); return X; }

channel-state dependent scheduling of delay …akk4212/channel-aware-scheduling.pdf ·...

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