Abstract of thesis entitled

“A Study of Channel Estimation for OFDM Systems and

System Capacity for MIMO-OFDM Systems”

Submitted by

Zhou Wen

For the degree of Doctor of Philosophy

at the university of Hong Kong in July 2010

This thesis concerns about two issues for the next generation of wireless

communications, namely, the channel estimation for orthogonal frequency-division

multiplexing (OFDM) systems and the multiple-input multiple-output orthogonal

frequency-division multiplexing (MIMO-OFDM) system capacity.

For channel estimation for OFDM systems over quasi-static fading channels having

resolvable mulitipath number

L

, a novel fast linear minimum mean square error (LMMSE)

channel estimation method is proposed and investigated. The proposed algorithm deploys

Fourier transform (FFT) and the computational complexity is therefore significantly

reduced to

O

(

N

p

log

2

(

N

p

)), as compared to that of

O

(

N

p

3

) for the conventional LMMSE

method, where the notation

O

(·) is the Bachmann–Landau function and

N

p

is the number

of pilots for an OFDM symbol. The normalized mean square errors (NMSE) are derived in

closed-form expressions. Numerical results show that the NMSE is marginally the same

with that of the conventional LMMSE for signal to noise ratio (SNR) ranges from 0 dB to

25 dB. For channel estimation for OFDM systems over fast fading and dispersive channels,

a novel channel estimation and data detection method is proposed to reduce the

inter-carrier interference (ICI). A new pilot pattern composed of the comb-type and the

grouped pilot pattern is proposed.

A closed-form expression for channel estimation mean

square error (MSE) has been derived. For SNR = 15 dB, normalized Doppler shift of 0.06,

and

L

= 6, both computer simulation and numerical results have consistently shown that

the ICI is reduced by 70.6% and 43.2%, respectively for channel estimation MSE and bit

error rate (BER). The pilot number per OFDM symbol is also reduced significantly by

92.3%, as compared to the comb-type pilot pattern.

A closed-form mathematic expression has been proposed for the capacity of the

closed-loop MIMO-OFDM systems with imperfect feedback channel. The lower threshold

of feedback SNR is derived. For

L

= 6, numerical results show that the lower threshold of

feedback SNR is proportional to antenna numbers

N′

and system SNR. The increasing rate

of the feedback SNR threshold increases from 0.82 to 1.01 when

N′

increases from 2 to 16.

The variance and mean of OFDM system capacity over Rayleigh channels and Ricean

channels have been respectively investigated that the closed-form expression for the

capacity variance has been proposed. The resultant system capacity variances over the two

channels are respectively evaluated by numerical method and also verified by computer

simulation. The joint probability density function (PDF) of two arbitrary correlated Ricean

random variables has also been derived in an integral form. Numerical results reveal that

the variance of OFDM system is proportional to SNR and inversely proportional to

L

for

the two channels respectively. For the same two respective channels, the variance

marginally increases with a linear rate of 0.166 bit

2

/dB and 0.125 bit

2

/dB, when

L

= 2 and

SNR ranges from 0 dB to 15 dB. The variance is reduced from 1.75 bit

2

to 1.30 bit

2

and

from 1.48 bit

2

to 1.26 bit

2

, when SNR = 10 dB and

L

ranges from 2 to 4.

(Total words: 495)

A Study of Channel Estimation for OFDM Systems and

System Capacity for MIMO-OFDM Systems

by

Zhou Wen

B. Eng., M. Eng., USTC, P. R. China

A thesis submitted in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy at the university of Hong Kong in July 2010.

i

Declaration

I declare that this thesis represents my own work, except where due

acknowledgement is made, and that it has not been previously included in a

thesis, dissertation or report submitted t to this University or any other

institution for a degree, diploma, or other qualifications.

Signature: ___________

Zhou Wen

ii

Acknowledgements

I would like to take this opportunity to express my gratitude to all the people who have

ever helped me in the thesis writing and the course of the research.

My sincere and hearty thanks and appreciations go firstly to my supervisor, Dr. W.H. Lam,

whose suggestions and encouragement have given me much insight into the research work.

It has been a great privilege and joy to study under his guidance and supervision. His

insightful observation and effective feedback inspired me during the research. Furthermore,

it is my honor to benefit from his personality and diligence, which I will treasure my whole

life.

I also gratefully acknowledge Prof. V.O.K. Li, Prof. G.L. Li, Prof. Y.C. Wu, Prof. S.C.

Chan, Prof. T.S. Ng and Prof. Agnes S.L. Lam for their interesting courses and helpful

discussions. I would like to thank the office staff and technical staff from the EEE

department for their helpful administrative and facility supports. Especially, Ms. Julie

Hung’s readiness to help students is very impressive. I also appreciate the HKSAR

government for the studentship support to the study in the University of Hong Kong.

I am extremely grateful to all my friends and classmates who have kindly provided me

assistance and companionship in the process of preparing this thesis: Dr. Zhi Zhang, Dr.

Zhiqiang Chen, Dr. Mingxiang Xiao, Dr. Fei Mai, Mr. Xueyong Liu, Mr. Xiaoguang Dai,

Ms. Ziyun Shao, Mr. Ka-Chung Leung, Mr. Peng Zhang, Dr. Yanhui Geng, Ms. Qiong Sun,

Mr. Haoling Xiahou, Mr. Zhibo Ni, Mr. Jun Zhang, Mr. Xiaolei Sun, Mr. Chengwen Xing.

They have made the life during the past four years an enjoyable and memorable experience.

Finally, I wish to express my hearty gratitude to my parents, for their encouragements and

love in all my endeavors.

iii

Contents

Declarations......................................................................................................................... i

Acknowledgements............................................................................................................. ii

Contents.............................................................................................................................. iii

List of Figures.....................................................................................................................vii

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

1.1 Research motivation................................................................................................ 4

1.2 Organization and contributions of the thesis........................................................... 5

Chapter 2: OFDM systems and MIMO systems .............................................................. 9

2.1 Wireless Channel................................................................................................... 10

2.1.1 Large scale propagation ............................................................................. 11

2.1.2 Small scale propagation ............................................................................. 13

2.1.3 Typical wireless channel models................................................................ 17

2.2 OFDM systems ..................................................................................................... 20

2.2.1 Basic principles and characteristics for OFDM systems ........................... 21

2.2.2 Peak-to-Average (PAR) of OFDM systems ............................................... 30

2.2.3 Channel estimation for OFDM systems..................................................... 33

2.2.4 Synchronization of OFDM systems........................................................... 38

2.2.5 Advantages and disadvantages of OFDM systems .................................... 39

2.3 MIMO systems...................................................................................................... 40

2.3.1 Basic MIMO system model ....................................................................... 40

2.3.2 Functions of MIMO systems...................................................................... 42

2.3.3 Overview of Space Time codes.................................................................. 45

2.3.4 Capacity of MIMO systems ....................................................................... 52

iv

2.4 MIMO-OFDM systems......................................................................................... 54

2.5 Summary ............................................................................................................... 56

Chapter 3: Channel estimation for OFDM systems over quasi-static fading channels

............................................................................................................................................. 57

3.1 Introduction........................................................................................................... 58

3.2 System Model ....................................................................................................... 61

3.3 The Proposed Fast LMMSE Algorithm ................................................................ 63

3.3.1 Properties of the channel correlation matrix in frequency domain ............ 63

3.3.2 The proposed fast LMMSE channel estimation algorithm ........................ 65

3.3.3 Computational complexity comparison between the proposed method and

the conventional LMMSE method...................................................................... 69

3.4 Analysis of the Mean Square Error (MSE) of the Proposed Fast LMMSE

Algorithm .................................................................................................................... 70

3.4.1 MSE analysis of the conventional LMMSE algorithm.............................. 71

3.4.2 MSE analysis for the proposed fast LMMSE algorithm............................ 72

3.5 Numerical and Simulation Results........................................................................ 75

3.6 Conclusion ............................................................................................................ 81

Chapter 4: Channel estimation and data detection for OFDM systems over fast

fading channels.................................................................................................................. 87

4.1 Introduction........................................................................................................... 88

4.2 System Model ....................................................................................................... 91

4.3 The Proposed Channel Estimation and Data Detection ........................................ 92

4.3.1. The proposed pilot pattern ........................................................................ 92

v

4.3.2. Channel Estimation and data detection for the first M

1

OFDM symbols of

each block ........................................................................................................... 94

4.3.3. Channel estimation and data detection for the last

M

2

OFDM symbols of

each block ........................................................................................................... 95

4.3.4. Summary of the proposed channel estimation and data detection............ 98

4.4. Analysis of MSE of the proposed channel estimation method ............................ 99

4.4.1. MSE analysis of channel estimation for the first M

1

OFDM symbols ... 100

4.4.2. MSE analysis of channel estimation for the last M

2

OFDM symbols .... 103

4.4.3 MSE analysis of channel estimation for one OFDM block ..................... 105

4.5 Numerical and Simulation Results...................................................................... 106

4.6. Conclusion ......................................................................................................... 112

Chapter 5: MIMO-OFDM system capacity with imperfect feedback channel ......... 118

5.1 The open-loop and closed-loop capacity for MIMO Systems ............................ 119

5.1.1 MIMO system model ............................................................................... 119

5.1.2 MIMO system capacity............................................................................ 120

5.1.3 Numerical Results and discussion............................................................ 124

5.2 The closed-loop capacity with imperfect feedback channel for MIMO-OFDM

systems ...................................................................................................................... 127

5.2.1 System Model .......................................................................................... 128

5.2.2 Closed-Loop Capacity and Feedback SNR for MIMO-OFDM Systems 130

5.2.3 Numerical Results.................................................................................... 136

5.3 Summary ............................................................................................................. 142

Chapter 6: Capacity of OFDM systems over time and frequency selective fading

vi

channels............................................................................................................................ 144

6.1 Introduction......................................................................................................... 145

6.2 OFDM System Model......................................................................................... 147

6.3 OFDM System Capacity ..................................................................................... 148

6.3.1 OFDM system capacity over Rayleigh fading channels.......................... 148

6.3.2 OFDM system capacity over Ricean fading channels ............................. 153

6.4 Numerical and Simulation Results...................................................................... 157

6.5 Conclusion .......................................................................................................... 161

Chapter 7: Conclusions and future works .................................................................... 167

7.1 Conclusions......................................................................................................... 167

7.2 Future works ....................................................................................................... 169

APPENDIX A: The derivation of the rank of channel frequency autocorrelation matrix

R

HH

in Chapter 3............................................................................................................... 170

APPENDIX B: The derivation of equation (3-20) in Chapter 3....................................... 171

APPENDIX C: The derivation of the joint PDF of two arbitrary correlated Ricean random

variables ............................................................................................................................ 173

Appendix D: List of Abbreviations ................................................................................... 176

REFERENCES.................................................................................................................. 179

Publications....................................................................................................................... 191

vii

List of Figures

Fig 1.1: Organization of the thesis. ....................................................................................... 6

Fig 2.1: Path Loss, shadowing and multipath versus distance............................................ 11

Fig 2.2: The Doppler power spectrum function expressed by (2-4). .................................. 14

Fig 2.3: The multi-path effect between the transmitter and the receiver in wireless

communication........................................................................................................ 14

Fig 2.4: Time varying impulse response of a wireless channel, for the path number

N

= 3, 4,

and 5........................................................................................................................ 15

Fig 2.5: Four kinds of small scale propagations. ................................................................ 16

Fig 2.6: PDFs for Rayleigh fading with the variance σ

2

= 0.5, 2, and 5, respectively........ 17

Fig 2.7: PDFs for Ricean fading with Ricean factor

K

r

= 0 dB, 10 dB, and 20 dB,

respectively.............................................................................................................. 18

Fig 2.8: PDFs for Nagakami-m fading with

m

= 0.5, 1, and 10.......................................... 19

Fig 2.9: The continuous OFDM system model................................................................... 22

Fig 2.10: The waveform of ( )

k

Gw

....................................................................................... 24

Fig 2.11: Equivalent transmitter for OFDM systems.......................................................... 25

Fig 2.12: Equivalent receiver for OFDM systems. ............................................................. 25

Fig 2.13: CP for an OFDM symbol..................................................................................... 26

Fig 2.14: SNRloss versus CP length. .................................................................................. 27

Fig 2.15: The inter-symbol interference of OFDM systems without CP. ........................... 28

Fig 2.16: Extraction of the data in frequency domain......................................................... 28

Fig 2.17: The discrete baseband OFDM system model. ..................................................... 29

Fig 2.18: The output power versus the input power for a power amplifier......................... 31

Fig 2.19: The power spectrum comparison between the input signal and the output signal

passing through an amplifier. .................................................................................. 32

Fig 2.20: Two kinds of pilot patterns (black dot: pilot, white dot: user data)..................... 34

Fig 2.21: Pilot-aided channel estimation for OFDM systems............................................. 35

Fig 2.22: The basic MIMO system model. ......................................................................... 40

Fig 2.23: Received signal after diversity operation. ........................................................... 43

viii

Fig 2.24: Diversity-multiplexing tradeoff, d*(r) versus r. .................................................. 44

Fig 2.25: The Alamouti STBC diagram for 2×2 MIMO systems. ...................................... 46

Fig 2.26: V-BLAST system diagram................................................................................... 49

Fig 2.27: The baseband MIMO-OFDM system model....................................................... 55

Fig 3.1: Baseband OFDM system. ...................................................................................... 61

Fig 3.2: Channel estimation based on comb-type pilots. .................................................... 62

Fig 3.3: The first row of the channel autocorrelation matrix

pp

HH

R

,

A

. ............................. 82

Fig 3.4: The first row of the LMMSE matrix

1

SNR

β

−

⎛⎞

+

⎜⎟

⎝⎠

pp pp

HH HH

RR I

with different SNRs.

................................................................................................................................. 83

Fig 3.5: Normalized Mean square error (NMSE) of channel estimation of LMMSE

algorithm versus that of the proposed fast LMMSE algorithm by computer

simulation and numerical method. .......................................................................... 83

Fig 3.6: NMSE of LMMSE algorithm with matched SNR and mismatched SNRs versus

SNR, by simulation and numerical method, respectively. ...................................... 84

Fig 3.7: NMSE of the proposed fast LMMSE algorithm with matched SNR and

mismatched SNRs versus SNR, by simulation and numerical method, respectively.

................................................................................................................................. 84

Fig 3.8: Bit error rate (BER) of the LS, LMMSE, the proposed fast LMMSE and perfect

channel estimation versus SNR............................................................................... 85

Fig 3.9: BER comparison between LMMSE channel estimation with matched SNR and

LMMSE channel estimation with designed SNRs.................................................. 85

Fig 3.10: BER comparison between the proposed fast LMMSE channel estimation with

estimated SNR and the proposed fast LMMSE channel estimation with designed

SNRs. ...................................................................................................................... 86

Fig 4.1: Pilot pattern (gray circle: user data, black circle: pilot). ..................................... 114

Fig 4.2: The normalized mean square error (NMSE) of channel estimation for the first M

1

OFDM symbols, for

d

f T

= 0.01, 0.06 and 0.1, respectively. ................................. 114

Fig 4.3: The NMSE of channel estimation based on equi-spaced and grouped pilot pattern,

ix

for the polynomial order

Q

=1, 2, 3 and the normalized Doppler shift

d

f T

= 0.01 and

0.1, respectively..................................................................................................... 115

Fig 4.4: The NMSE of channel estimation based on grouped pilot pattern, for

c

=1, 2, 3 and

the normalized Doppler shift

d

f T

= 0.01 and 0.1, respectively.............................. 115

Fig 4.5: The NMSE of channel estimation based on grouped pilot pattern, for the number

of pilot groups

group

N

=18, 36, 72 and the normalized Doppler shift

d

f T

= 0.01 and

0.1, respectively..................................................................................................... 116

Fig 4.6: The NMSE of channel estimation for the proposed algorithm and LS algorithm by

numerical method and simulation at

d

f T

= 0.01 and 0.06, respectively. ............... 116

Fig 4.7: Bit error ratio (BER) of LS, the proposed algorithm and the algorithm in [29], for

normalized Doppler shift

d

f T

= 0.01 and 0.06, respectively. ................................ 117

Fig 5.1: The eigenmode transmission of MIMO systems. ................................................ 123

Fig 5.2: The MIMO system open-loop capacity versus the number of transmitter

antennas

T

N

, for the number of receiver antennas

1

R

N =

...................................... 124

Fig 5.3: The MIMO system open-loop capacity versus the number of receiver antennas

R

N

,

for the number of transmitter antennas

1

T

N =

....................................................... 124

Fig 5.4: The capacities of the N by 1 MISO system, the 1 by N SIMO system, and the N by

N MIMO system as a function of N, for SNR = 5 dB........................................... 125

Fig 5.5: The open-loop and closed-loop capacity for MIMO systems, versus SNR. ....... 126

Fig 5.6: The closed-loop MIMO-OFDM system model. .................................................. 128

Fig 5.7: The open-loop and closed-loop system capacity for MIMO-OFDM systems

having different transmitter antenna and receiver antenna numbers. ................... 138

Fig 5.8: The capacity gain of the closed-loop capacity with imperfect feedback over that of

the open-loop capacity versus feedback channel SNR, for

4

TR

NN= =

. .............. 140

Fig 5.9: The capacity gain of closed-loop capacity with imperfect feedback over that of the

open-loop capacity versus feedback channel SNR, for system SNR = 10 dB...... 140

Fig 5.10: The lower threshold of the feedback SNR versus the MIMO-OFDM system SNR,

x

for different antenna pairs. .................................................................................... 142

Fig 6.1: The PDF of the capacity at a certain subcarrier,

,

()

ik

C

f x

in (6-36), for SNR = 0 dB,

5 dB, 10 dB, and 20 dB, respectively.................................................................... 162

Fig 6.2: The joint PDF of of

2

1

|(,)|Hik

and

2

2

|(,)|Hik

,

22

12

|(,)|,|(,)|

(, )

Hik Hik

f xy,for the coefficient

of equation (6-23), γ = 0.61................................................................................... 162

Fig 6.3: The coefficient of equation (6-24), γ, versus different subcarrier gap between

1

k

and

2

k

. ................................................................................................................ 163

Fig 6.4: The variance of OFDM system capacity for the number of channel paths L = 2, 4,

and 8, over the Rayleigh fading channel............................................................... 163

Fig 6.5 The variance of OFDM system capacity versus the CP of an OFDM symbol in unit

of sample point, over the Rayleigh fading channel............................................... 164

Fig 6.6: The variance of OFDM system capacity versus the number of subcarriers of one

OFDM symbol, for Rayleigh fading channels. ..................................................... 164

Fig 6.7: The variance of OFDM system capacity over Ricean fading channels for L = 2, 4,

8, respectively........................................................................................................ 165

Fig 6.8: The mean value of OFDM system capacity for Rayleigh fading channel and

Ricean fading channel, by numerical method....................................................... 165

Fig 6.9: The variance of OFDM system capacity for Rayleigh fading channel and Ricean

fading channel, by computer simulation and numerical method. ......................... 166

1

Chapter 1: Introduction

The research on wireless communication systems with high data rate, high spectrum

efficiency and reliable performance is a hot spot. There are several advanced

communication technologies or protocols proposed recently, including Orthogonal

frequency division multiplexing (OFDM) [1], multiple input multiple output (MIMO) [2],

Ultra-Wideband (UWB) technology [3], cognitive radio [4], World Interoperability for

Microwave Access (WiMAX) [92], and 3GPP Long Term Evolution (LTE) [92], [93].

OFDM is an efficient high data rate transmission technique for wireless communication.

OFDM presents advantages of high spectrum efficiency, simple and efficient

implementation by using the fast Fourier Transform (FFT) and the inverse Fast Fourier

Transform (IFFT), mitigration of inter-symbol interference (ISI) by inserting cyclic prefix

(CP) and robustness to frequency selective fading channel. MIMO is the use of multiple

antennas at both the transmitter and receiver to improve communication performance. It is

one of several forms of smart antenna technology. MIMO technology has attracted

attention in wireless communications, because it increases in data throughput without

additional bandwidth or transmit power. It achieves this by higher spectral efficiency and

link reliability or diversity. The combination of MIMO with OFDM technique is a

promising technique for the next generation wireless communication. A new protocol draft

employing the MIMO-OFDM as the physical layer technology, IEEE 802.11n, as an

amendment to IEEE 802.11 standards has been proposed [53]. Wireless LAN technology

2

has seen rapid advancements and MIMO-OFDM has gradually been adopted in its

standards. The following table shows the existing IEEE 802.11 WLAN protocols.

Table 1.1 Existing 802.11 WLAN Standards

IEEE Protocol Name 802.11b

802.11a

802.11g

802.11n

Standard Approved

Sept. 1999 Sept. 1999

June

2003

Released in

2009

Available Bandwidth

83.5 MHz 580 MHz 83.5 MHz

83.5/580

MHz

Frequency Band of

Operation

2.4 GHz

5 GHz

2.4 GHz

2.4/5 GHz

Non-Overlapping

Channels (US)

3

24

3

3/24

Data Rate per Channel

1–11 Mbps 6–54 Mbps 1–54 Mbps

1–600

Mbps

Modulation Type

DSSS,

CCK

OFDM

DSSS,

CCK,

OFDM

DSSS,

CCK,

OFDM,

MIMO

UWB is a technology for transmitting data spread over a large bandwidth (usually larger

than 500 MHz) that shares among users. UWB was traditionally applied in

non-cooperative radar imaging. Most recent applications include sensor data collection,

precision locating, and tracking applications. The concept of cognitive radio was first

proposed by Dr. J. Mitola and Prof. G. Q. Maguire [4] in 1999 and was an extension to the

concept of software radio. Cognitive radio is an intelligent communication system that

could detect and track the communication environments. It would adjust the transmitter

and the receiver

’

s parameters adaptively according to the changes of environment

parameters such as the mobile velocity of the user, so that the system stability could be

3

ensured, the system performance could remain a good condition, and the spectrum

efficiency could be improved. WiMAX is a telecommunications protocol that provides

fully mobile Internet access. The name "WiMAX" was created by the WiMAX Forum,

which was founded in 2001. The forum refers to WiMAX as a standards-based technology

enabling the delivery of last mile wireless broadband access as an alternative to cable and

digital subscriber line (DSL). The basis of WiMAX is IEEE 802.16 standard which is

sometimes referred to as

“

WiMAX

”

equivalently. The current WiMAX revision is based

on IEEE 802.16e, which was approved in December 2005. The physical layer of WiMAX

adopts a lot of advanced technologies such as scalable orthogonal frequency division

multiplexing access (OFDMA), MIMO, adaptive antenna array and so on. Current

WiMAX that is based on the IEEE 802.16e protocol belongs to 3G family. Future WiMAX

is based on IEEE 802.16m, which has been submitted to the International

Telecommunication Union (ITU) for International Mobile Telecommunication Advanced

(IMT-Advanced) standardization. Future WiMAX, or the proposed WiMAX release 2, is

considered as a candidate of 4G family. LTE is the latest standard in the mobile

communication systems. The current generation of mobile communication system is

collectively known as 3G. Although LTE is often referred to as 4G, the first released LTE is

actually a 3.9G technology as it does not completely meet the 4G requirements. The main

advantages of LTE include high throughput, low latency, plug and play, a simple

architecture resulting in low power consumption, supporting seamless passing by base

stations with former wireless networks such as Global System for Mobile Communications

4

(GSM), Universal Mobile Telecommunications System (UMTS), and CDMA2000. LTE

also adopts OFDM and MIMO technologies in the physical layer. It uses a 2 by 2 MIMO

system as the basic configuration, that is, both the base station and the mobile end equip 2

antennas. The next step for LTE evolution is LTE Advanced and is currently being

standardized by 3rd Generation Partnership Project (3GPP) organization.

The thesis studies two issues: channel estimation for OFDM systems and

MIMO-OFDM system capacity. The chapter is organized as follows. Section 1.1 describes

the research motivation. Section 1.2 provides the thesis contributions and the overall

organization of the thesis.

1.1 Research motivation

Earlier OFDM systems such as the digital audio broadcasting (DAB) system in Europe

does not require channel estimation module. It only uses DPSK demodulation for the sake

of reducing the complexity of the receiver. However, with increasing demands of high data

transmission rate and reliable communication quality, channel estimation has become a

necessary part in the OFDM system. For example, the digital video broadcasting (DVB)

system adopts the channel estimation module. In a broadband wireless environment, the

channel is often time varying and frequency selective, which distorts the transmitted signal

significantly, so that accurate and real time channel estimation is the challenging topic in

the OFDM system. Channel state information can be used for the detection of the received

signal, improving the capacity of the system throughput by adjusting the modulation at the

5

transmitter through the feedback. Therefore, one issue of the thesis studies channel

estimation for OFDM systems over time varying and frequency dispersive fading

channels.

With the increasing number of mobile phone users and higher demands for wireless

services, future communication systems should have higher system capacity. MIMO

technique is a breakthrough of improving system capacity. Telatar [46] and Foschini [47]

have firstly formulated the system capacity of the MIMO systems assuming independent

and identically distributed fading at different antennas. They have proved that the MIMO

system capacity for n transmitter antennas and n receiver antennas increases linearly with

n at a fixed transmitter power. That is, MIMO systems can improve the system capacity

significantly without increasing the system bandwidth. A number of MIMO techniques

known as layered space time architectures or Bell Laboratories layered space time

(BLAST) architectures [5]–[8] have been proposed. Many studies on MIMO system

capacity have been conducted. Since the combination of MIMO with OFDM is a trend, a

lot of research work has been done on the MIMO-OFDM system capacity. However, the

research on MIMO-OFDM system capacity with imperfect feedback channel is not mature

and corresponding work is not much. Therefore, the second issue of the thesis is to study

the MIMO-OFDM system capacity with imperfect feedback channels.

1.2 Organization and contributions of the thesis

Firstly, we briefly describe the organization of the thesis. Chapter 1 gives a general

6

introduction, research motivation, organization, and contributions of the thesis. Chapter 2

describes the basic OFDM system model and MIMO system model. The wireless channel

model, the principles of OFDM and MIMO systems, the combination of MIMO and

OFDM, that is, MIMO-OFDM system is also introduced in Chapter 2. Next, as depicted in

Fig 1.1, the thesis begins with the first issue, that is, channel estimation. The proposed

channel estimation method in Chapter 3 is based on quasi-static fading channels and that in

Chapter 4 is based on fast fading channels. Then, the thesis switches to next issue, that is

system capacity. In Chapter 5, the MIMO-OFDM system capacity with imperfect feedback

channel is investigated. In Chapter 6, the capacity variances for OFDM systems over

Rayleigh and Ricean fading channels are derived, respectively. Finally, Chapter 7

concludes the thesis and discusses future research works.

Fig 1.1: Organization of the thesis.

7

Secondly, the major contributions of this thesis are summarized as follows.

9

A fast linear minimum mean square error (LMMSE) channel estimation method for

OFDM systems over slow fading channels has been proposed. Unlike the

conventional method, the channel state information is not needed in advance.

Almost the same performance with the conventional LMMSE channel estimation in

terms of the normalized mean square error (NMSE) of channel estimation and bit

error rate (BER) could be achieved for the proposed method. The computational

complexity can be reduced significantly since the proposed method replaces the

inverse operation with FFT operation. (Chapter 3)

9

A new pilot pattern and corresponding channel estimation method and data

detection for OFDM systems over fast fading channels have been proposed. The

proposed channel estimation and data detection based on the proposed pilot pattern

can eliminate inter-carrier interference (ICI) effect effectively. And the number of

required pilots is also reduced significantly, compared with the conventional least

square (LS) method. MSE analysis for the channel estimation based on the grouped

pilot pattern is provided, too. (Chapter 4)

9

The closed-loop MIMO-OFDM system capacity with imperfect feedback channel

has been formulated. We use the feedback SNR to measure the closed-loop capacity.

Since low feedback SNR may not yield positive gain of closed-loop capacity over

8

open-loop capacity, there exists a lower threshold of feedback SNR. The lower

thresholds for different antenna pairs are further investigated by numerical method.

(Chapter 5)

9

The variances of OFDM system capacity over Rayleigh fading channels and Ricean

fading channels have been derived. The effects of SNR, the number of channel

paths, power profile of fading channel, the delay of the channel on the variance

have been thoroughly investigated, for both multipath Rayleigh channels and

multipath Ricean channels. The joint PDF of two arbitrary correlated Ricean

random variables has been provided in an integral form. (Chapter 6)

9

Chapter 2: OFDM systems and MIMO systems

Since the thesis studies the channel estimation for OFDM systems and system capacity for

MIMO-OFDM systems, this chapter briefly introduces the background of OFDM systems

and MIMO systems.

OFDM is an effective technology which provides high spectrum efficiency, high data

transmission rate and is robust to multi-path fading [1]. OFDM has already been widely

put into practice in DAB system, DVB system and WLAN. MIMO systems which employ

multi-element antenna arrays at the transmitter and receiver ends are capable of high data

rate transmission. A number of MIMO techniques known as layered space time

architectures or BLAST architectures have been proposed [5]-[7], [9].

As OFDM technique can mitigate the ISI and transform the frequency selective fading

channel into a set of flat fading channels, the combination of MMO with OFDM technique

is a trend for future wireless communication. A new protocol draft, IEEE 802.11n, as an

amendment to IEEE 802.11 standards has been proposed and investigated [53]. The draft

proposes MIMO-OFDM as the physical layer technique and is to be approved by IEEE.

The chapter is organized as follows. Section 2.1 provides an introduction to wireless

channel in communication systems. Section 2.2 describes the basic OFDM system model,

principles, and related key technologies in OFDM systems. Section 2.3 introduces the

basic MIMO system model and briefly overviews the existing MIMO systems. Section 2.4

presents the MIMO-OFDM system model. The last section 2.5 summarizes the chapter.

10

2.1 Wireless Channel

Since there exist reflections, scattering, and diffraction in the transmission of

electromagnetic wave, the spatial environments such as the landscape of a city,

obstructions and so on will make complicated impacts on the transmission of

electromagnetic wave. There are two kinds of propagation, including the large-scale

propagation and the small scale propagation. The signal variations due to path loss or

shadowing occur over relatively large distances, this variation is referred to as the large

scale propagation effects. Path loss is a major component in the analysis and design of the

link budget of a telecommunication system. The small scale propagation refers to the

phenomena that the amplitude of the received wireless signal varies very fast in a short

time period or a short distance. The sources of small scale propagation include the Doppler

shift effect and multi-path effect. We begin with the introduction of the large scale

propagation.

11

2.1.1 Large scale propagation

Fig 2.1: Path Loss, shadowing and multipath versus distance.

Fig 2.1 plots the ratio of the received-to-transmit power in dB versus the distance for

the combined effects of path loss, shadowing, and multipath. Observe that the free space

path loss is linearly proportional to the log-distance between the transmitter and receiver.

The shadowing loss has slower variations compared to that of the multipath effect. The

large scale path loss model has many successful types including the free space path loss

model, the Hata model, and the Okumura model and so on. Most of them are obtained by

a combination of the analytical and empirical methods. We next briefly introduce the free

space path loss model as an example of path loss effect.

9

Free

space path loss model: An example of path loss effect

Consider a signal transmitted through free space to a receiver located at distance d from

the transmitter. It is assumed that there does not exist any obstructions between the

“A Study of Channel Estimation for OFDM Systems and

System Capacity for MIMO-OFDM Systems”

Submitted by

Zhou Wen

For the degree of Doctor of Philosophy

at the university of Hong Kong in July 2010

This thesis concerns about two issues for the next generation of wireless

communications, namely, the channel estimation for orthogonal frequency-division

multiplexing (OFDM) systems and the multiple-input multiple-output orthogonal

frequency-division multiplexing (MIMO-OFDM) system capacity.

For channel estimation for OFDM systems over quasi-static fading channels having

resolvable mulitipath number

L

, a novel fast linear minimum mean square error (LMMSE)

channel estimation method is proposed and investigated. The proposed algorithm deploys

Fourier transform (FFT) and the computational complexity is therefore significantly

reduced to

O

(

N

p

log

2

(

N

p

)), as compared to that of

O

(

N

p

3

) for the conventional LMMSE

method, where the notation

O

(·) is the Bachmann–Landau function and

N

p

is the number

of pilots for an OFDM symbol. The normalized mean square errors (NMSE) are derived in

closed-form expressions. Numerical results show that the NMSE is marginally the same

with that of the conventional LMMSE for signal to noise ratio (SNR) ranges from 0 dB to

25 dB. For channel estimation for OFDM systems over fast fading and dispersive channels,

a novel channel estimation and data detection method is proposed to reduce the

inter-carrier interference (ICI). A new pilot pattern composed of the comb-type and the

grouped pilot pattern is proposed.

A closed-form expression for channel estimation mean

square error (MSE) has been derived. For SNR = 15 dB, normalized Doppler shift of 0.06,

and

L

= 6, both computer simulation and numerical results have consistently shown that

the ICI is reduced by 70.6% and 43.2%, respectively for channel estimation MSE and bit

error rate (BER). The pilot number per OFDM symbol is also reduced significantly by

92.3%, as compared to the comb-type pilot pattern.

A closed-form mathematic expression has been proposed for the capacity of the

closed-loop MIMO-OFDM systems with imperfect feedback channel. The lower threshold

of feedback SNR is derived. For

L

= 6, numerical results show that the lower threshold of

feedback SNR is proportional to antenna numbers

N′

and system SNR. The increasing rate

of the feedback SNR threshold increases from 0.82 to 1.01 when

N′

increases from 2 to 16.

The variance and mean of OFDM system capacity over Rayleigh channels and Ricean

channels have been respectively investigated that the closed-form expression for the

capacity variance has been proposed. The resultant system capacity variances over the two

channels are respectively evaluated by numerical method and also verified by computer

simulation. The joint probability density function (PDF) of two arbitrary correlated Ricean

random variables has also been derived in an integral form. Numerical results reveal that

the variance of OFDM system is proportional to SNR and inversely proportional to

L

for

the two channels respectively. For the same two respective channels, the variance

marginally increases with a linear rate of 0.166 bit

2

/dB and 0.125 bit

2

/dB, when

L

= 2 and

SNR ranges from 0 dB to 15 dB. The variance is reduced from 1.75 bit

2

to 1.30 bit

2

and

from 1.48 bit

2

to 1.26 bit

2

, when SNR = 10 dB and

L

ranges from 2 to 4.

(Total words: 495)

A Study of Channel Estimation for OFDM Systems and

System Capacity for MIMO-OFDM Systems

by

Zhou Wen

B. Eng., M. Eng., USTC, P. R. China

A thesis submitted in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy at the university of Hong Kong in July 2010.

i

Declaration

I declare that this thesis represents my own work, except where due

acknowledgement is made, and that it has not been previously included in a

thesis, dissertation or report submitted t to this University or any other

institution for a degree, diploma, or other qualifications.

Signature: ___________

Zhou Wen

ii

Acknowledgements

I would like to take this opportunity to express my gratitude to all the people who have

ever helped me in the thesis writing and the course of the research.

My sincere and hearty thanks and appreciations go firstly to my supervisor, Dr. W.H. Lam,

whose suggestions and encouragement have given me much insight into the research work.

It has been a great privilege and joy to study under his guidance and supervision. His

insightful observation and effective feedback inspired me during the research. Furthermore,

it is my honor to benefit from his personality and diligence, which I will treasure my whole

life.

I also gratefully acknowledge Prof. V.O.K. Li, Prof. G.L. Li, Prof. Y.C. Wu, Prof. S.C.

Chan, Prof. T.S. Ng and Prof. Agnes S.L. Lam for their interesting courses and helpful

discussions. I would like to thank the office staff and technical staff from the EEE

department for their helpful administrative and facility supports. Especially, Ms. Julie

Hung’s readiness to help students is very impressive. I also appreciate the HKSAR

government for the studentship support to the study in the University of Hong Kong.

I am extremely grateful to all my friends and classmates who have kindly provided me

assistance and companionship in the process of preparing this thesis: Dr. Zhi Zhang, Dr.

Zhiqiang Chen, Dr. Mingxiang Xiao, Dr. Fei Mai, Mr. Xueyong Liu, Mr. Xiaoguang Dai,

Ms. Ziyun Shao, Mr. Ka-Chung Leung, Mr. Peng Zhang, Dr. Yanhui Geng, Ms. Qiong Sun,

Mr. Haoling Xiahou, Mr. Zhibo Ni, Mr. Jun Zhang, Mr. Xiaolei Sun, Mr. Chengwen Xing.

They have made the life during the past four years an enjoyable and memorable experience.

Finally, I wish to express my hearty gratitude to my parents, for their encouragements and

love in all my endeavors.

iii

Contents

Declarations......................................................................................................................... i

Acknowledgements............................................................................................................. ii

Contents.............................................................................................................................. iii

List of Figures.....................................................................................................................vii

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

1.1 Research motivation................................................................................................ 4

1.2 Organization and contributions of the thesis........................................................... 5

Chapter 2: OFDM systems and MIMO systems .............................................................. 9

2.1 Wireless Channel................................................................................................... 10

2.1.1 Large scale propagation ............................................................................. 11

2.1.2 Small scale propagation ............................................................................. 13

2.1.3 Typical wireless channel models................................................................ 17

2.2 OFDM systems ..................................................................................................... 20

2.2.1 Basic principles and characteristics for OFDM systems ........................... 21

2.2.2 Peak-to-Average (PAR) of OFDM systems ............................................... 30

2.2.3 Channel estimation for OFDM systems..................................................... 33

2.2.4 Synchronization of OFDM systems........................................................... 38

2.2.5 Advantages and disadvantages of OFDM systems .................................... 39

2.3 MIMO systems...................................................................................................... 40

2.3.1 Basic MIMO system model ....................................................................... 40

2.3.2 Functions of MIMO systems...................................................................... 42

2.3.3 Overview of Space Time codes.................................................................. 45

2.3.4 Capacity of MIMO systems ....................................................................... 52

iv

2.4 MIMO-OFDM systems......................................................................................... 54

2.5 Summary ............................................................................................................... 56

Chapter 3: Channel estimation for OFDM systems over quasi-static fading channels

............................................................................................................................................. 57

3.1 Introduction........................................................................................................... 58

3.2 System Model ....................................................................................................... 61

3.3 The Proposed Fast LMMSE Algorithm ................................................................ 63

3.3.1 Properties of the channel correlation matrix in frequency domain ............ 63

3.3.2 The proposed fast LMMSE channel estimation algorithm ........................ 65

3.3.3 Computational complexity comparison between the proposed method and

the conventional LMMSE method...................................................................... 69

3.4 Analysis of the Mean Square Error (MSE) of the Proposed Fast LMMSE

Algorithm .................................................................................................................... 70

3.4.1 MSE analysis of the conventional LMMSE algorithm.............................. 71

3.4.2 MSE analysis for the proposed fast LMMSE algorithm............................ 72

3.5 Numerical and Simulation Results........................................................................ 75

3.6 Conclusion ............................................................................................................ 81

Chapter 4: Channel estimation and data detection for OFDM systems over fast

fading channels.................................................................................................................. 87

4.1 Introduction........................................................................................................... 88

4.2 System Model ....................................................................................................... 91

4.3 The Proposed Channel Estimation and Data Detection ........................................ 92

4.3.1. The proposed pilot pattern ........................................................................ 92

v

4.3.2. Channel Estimation and data detection for the first M

1

OFDM symbols of

each block ........................................................................................................... 94

4.3.3. Channel estimation and data detection for the last

M

2

OFDM symbols of

each block ........................................................................................................... 95

4.3.4. Summary of the proposed channel estimation and data detection............ 98

4.4. Analysis of MSE of the proposed channel estimation method ............................ 99

4.4.1. MSE analysis of channel estimation for the first M

1

OFDM symbols ... 100

4.4.2. MSE analysis of channel estimation for the last M

2

OFDM symbols .... 103

4.4.3 MSE analysis of channel estimation for one OFDM block ..................... 105

4.5 Numerical and Simulation Results...................................................................... 106

4.6. Conclusion ......................................................................................................... 112

Chapter 5: MIMO-OFDM system capacity with imperfect feedback channel ......... 118

5.1 The open-loop and closed-loop capacity for MIMO Systems ............................ 119

5.1.1 MIMO system model ............................................................................... 119

5.1.2 MIMO system capacity............................................................................ 120

5.1.3 Numerical Results and discussion............................................................ 124

5.2 The closed-loop capacity with imperfect feedback channel for MIMO-OFDM

systems ...................................................................................................................... 127

5.2.1 System Model .......................................................................................... 128

5.2.2 Closed-Loop Capacity and Feedback SNR for MIMO-OFDM Systems 130

5.2.3 Numerical Results.................................................................................... 136

5.3 Summary ............................................................................................................. 142

Chapter 6: Capacity of OFDM systems over time and frequency selective fading

vi

channels............................................................................................................................ 144

6.1 Introduction......................................................................................................... 145

6.2 OFDM System Model......................................................................................... 147

6.3 OFDM System Capacity ..................................................................................... 148

6.3.1 OFDM system capacity over Rayleigh fading channels.......................... 148

6.3.2 OFDM system capacity over Ricean fading channels ............................. 153

6.4 Numerical and Simulation Results...................................................................... 157

6.5 Conclusion .......................................................................................................... 161

Chapter 7: Conclusions and future works .................................................................... 167

7.1 Conclusions......................................................................................................... 167

7.2 Future works ....................................................................................................... 169

APPENDIX A: The derivation of the rank of channel frequency autocorrelation matrix

R

HH

in Chapter 3............................................................................................................... 170

APPENDIX B: The derivation of equation (3-20) in Chapter 3....................................... 171

APPENDIX C: The derivation of the joint PDF of two arbitrary correlated Ricean random

variables ............................................................................................................................ 173

Appendix D: List of Abbreviations ................................................................................... 176

REFERENCES.................................................................................................................. 179

Publications....................................................................................................................... 191

vii

List of Figures

Fig 1.1: Organization of the thesis. ....................................................................................... 6

Fig 2.1: Path Loss, shadowing and multipath versus distance............................................ 11

Fig 2.2: The Doppler power spectrum function expressed by (2-4). .................................. 14

Fig 2.3: The multi-path effect between the transmitter and the receiver in wireless

communication........................................................................................................ 14

Fig 2.4: Time varying impulse response of a wireless channel, for the path number

N

= 3, 4,

and 5........................................................................................................................ 15

Fig 2.5: Four kinds of small scale propagations. ................................................................ 16

Fig 2.6: PDFs for Rayleigh fading with the variance σ

2

= 0.5, 2, and 5, respectively........ 17

Fig 2.7: PDFs for Ricean fading with Ricean factor

K

r

= 0 dB, 10 dB, and 20 dB,

respectively.............................................................................................................. 18

Fig 2.8: PDFs for Nagakami-m fading with

m

= 0.5, 1, and 10.......................................... 19

Fig 2.9: The continuous OFDM system model................................................................... 22

Fig 2.10: The waveform of ( )

k

Gw

....................................................................................... 24

Fig 2.11: Equivalent transmitter for OFDM systems.......................................................... 25

Fig 2.12: Equivalent receiver for OFDM systems. ............................................................. 25

Fig 2.13: CP for an OFDM symbol..................................................................................... 26

Fig 2.14: SNRloss versus CP length. .................................................................................. 27

Fig 2.15: The inter-symbol interference of OFDM systems without CP. ........................... 28

Fig 2.16: Extraction of the data in frequency domain......................................................... 28

Fig 2.17: The discrete baseband OFDM system model. ..................................................... 29

Fig 2.18: The output power versus the input power for a power amplifier......................... 31

Fig 2.19: The power spectrum comparison between the input signal and the output signal

passing through an amplifier. .................................................................................. 32

Fig 2.20: Two kinds of pilot patterns (black dot: pilot, white dot: user data)..................... 34

Fig 2.21: Pilot-aided channel estimation for OFDM systems............................................. 35

Fig 2.22: The basic MIMO system model. ......................................................................... 40

Fig 2.23: Received signal after diversity operation. ........................................................... 43

viii

Fig 2.24: Diversity-multiplexing tradeoff, d*(r) versus r. .................................................. 44

Fig 2.25: The Alamouti STBC diagram for 2×2 MIMO systems. ...................................... 46

Fig 2.26: V-BLAST system diagram................................................................................... 49

Fig 2.27: The baseband MIMO-OFDM system model....................................................... 55

Fig 3.1: Baseband OFDM system. ...................................................................................... 61

Fig 3.2: Channel estimation based on comb-type pilots. .................................................... 62

Fig 3.3: The first row of the channel autocorrelation matrix

pp

HH

R

,

A

. ............................. 82

Fig 3.4: The first row of the LMMSE matrix

1

SNR

β

−

⎛⎞

+

⎜⎟

⎝⎠

pp pp

HH HH

RR I

with different SNRs.

................................................................................................................................. 83

Fig 3.5: Normalized Mean square error (NMSE) of channel estimation of LMMSE

algorithm versus that of the proposed fast LMMSE algorithm by computer

simulation and numerical method. .......................................................................... 83

Fig 3.6: NMSE of LMMSE algorithm with matched SNR and mismatched SNRs versus

SNR, by simulation and numerical method, respectively. ...................................... 84

Fig 3.7: NMSE of the proposed fast LMMSE algorithm with matched SNR and

mismatched SNRs versus SNR, by simulation and numerical method, respectively.

................................................................................................................................. 84

Fig 3.8: Bit error rate (BER) of the LS, LMMSE, the proposed fast LMMSE and perfect

channel estimation versus SNR............................................................................... 85

Fig 3.9: BER comparison between LMMSE channel estimation with matched SNR and

LMMSE channel estimation with designed SNRs.................................................. 85

Fig 3.10: BER comparison between the proposed fast LMMSE channel estimation with

estimated SNR and the proposed fast LMMSE channel estimation with designed

SNRs. ...................................................................................................................... 86

Fig 4.1: Pilot pattern (gray circle: user data, black circle: pilot). ..................................... 114

Fig 4.2: The normalized mean square error (NMSE) of channel estimation for the first M

1

OFDM symbols, for

d

f T

= 0.01, 0.06 and 0.1, respectively. ................................. 114

Fig 4.3: The NMSE of channel estimation based on equi-spaced and grouped pilot pattern,

ix

for the polynomial order

Q

=1, 2, 3 and the normalized Doppler shift

d

f T

= 0.01 and

0.1, respectively..................................................................................................... 115

Fig 4.4: The NMSE of channel estimation based on grouped pilot pattern, for

c

=1, 2, 3 and

the normalized Doppler shift

d

f T

= 0.01 and 0.1, respectively.............................. 115

Fig 4.5: The NMSE of channel estimation based on grouped pilot pattern, for the number

of pilot groups

group

N

=18, 36, 72 and the normalized Doppler shift

d

f T

= 0.01 and

0.1, respectively..................................................................................................... 116

Fig 4.6: The NMSE of channel estimation for the proposed algorithm and LS algorithm by

numerical method and simulation at

d

f T

= 0.01 and 0.06, respectively. ............... 116

Fig 4.7: Bit error ratio (BER) of LS, the proposed algorithm and the algorithm in [29], for

normalized Doppler shift

d

f T

= 0.01 and 0.06, respectively. ................................ 117

Fig 5.1: The eigenmode transmission of MIMO systems. ................................................ 123

Fig 5.2: The MIMO system open-loop capacity versus the number of transmitter

antennas

T

N

, for the number of receiver antennas

1

R

N =

...................................... 124

Fig 5.3: The MIMO system open-loop capacity versus the number of receiver antennas

R

N

,

for the number of transmitter antennas

1

T

N =

....................................................... 124

Fig 5.4: The capacities of the N by 1 MISO system, the 1 by N SIMO system, and the N by

N MIMO system as a function of N, for SNR = 5 dB........................................... 125

Fig 5.5: The open-loop and closed-loop capacity for MIMO systems, versus SNR. ....... 126

Fig 5.6: The closed-loop MIMO-OFDM system model. .................................................. 128

Fig 5.7: The open-loop and closed-loop system capacity for MIMO-OFDM systems

having different transmitter antenna and receiver antenna numbers. ................... 138

Fig 5.8: The capacity gain of the closed-loop capacity with imperfect feedback over that of

the open-loop capacity versus feedback channel SNR, for

4

TR

NN= =

. .............. 140

Fig 5.9: The capacity gain of closed-loop capacity with imperfect feedback over that of the

open-loop capacity versus feedback channel SNR, for system SNR = 10 dB...... 140

Fig 5.10: The lower threshold of the feedback SNR versus the MIMO-OFDM system SNR,

x

for different antenna pairs. .................................................................................... 142

Fig 6.1: The PDF of the capacity at a certain subcarrier,

,

()

ik

C

f x

in (6-36), for SNR = 0 dB,

5 dB, 10 dB, and 20 dB, respectively.................................................................... 162

Fig 6.2: The joint PDF of of

2

1

|(,)|Hik

and

2

2

|(,)|Hik

,

22

12

|(,)|,|(,)|

(, )

Hik Hik

f xy,for the coefficient

of equation (6-23), γ = 0.61................................................................................... 162

Fig 6.3: The coefficient of equation (6-24), γ, versus different subcarrier gap between

1

k

and

2

k

. ................................................................................................................ 163

Fig 6.4: The variance of OFDM system capacity for the number of channel paths L = 2, 4,

and 8, over the Rayleigh fading channel............................................................... 163

Fig 6.5 The variance of OFDM system capacity versus the CP of an OFDM symbol in unit

of sample point, over the Rayleigh fading channel............................................... 164

Fig 6.6: The variance of OFDM system capacity versus the number of subcarriers of one

OFDM symbol, for Rayleigh fading channels. ..................................................... 164

Fig 6.7: The variance of OFDM system capacity over Ricean fading channels for L = 2, 4,

8, respectively........................................................................................................ 165

Fig 6.8: The mean value of OFDM system capacity for Rayleigh fading channel and

Ricean fading channel, by numerical method....................................................... 165

Fig 6.9: The variance of OFDM system capacity for Rayleigh fading channel and Ricean

fading channel, by computer simulation and numerical method. ......................... 166

1

Chapter 1: Introduction

The research on wireless communication systems with high data rate, high spectrum

efficiency and reliable performance is a hot spot. There are several advanced

communication technologies or protocols proposed recently, including Orthogonal

frequency division multiplexing (OFDM) [1], multiple input multiple output (MIMO) [2],

Ultra-Wideband (UWB) technology [3], cognitive radio [4], World Interoperability for

Microwave Access (WiMAX) [92], and 3GPP Long Term Evolution (LTE) [92], [93].

OFDM is an efficient high data rate transmission technique for wireless communication.

OFDM presents advantages of high spectrum efficiency, simple and efficient

implementation by using the fast Fourier Transform (FFT) and the inverse Fast Fourier

Transform (IFFT), mitigration of inter-symbol interference (ISI) by inserting cyclic prefix

(CP) and robustness to frequency selective fading channel. MIMO is the use of multiple

antennas at both the transmitter and receiver to improve communication performance. It is

one of several forms of smart antenna technology. MIMO technology has attracted

attention in wireless communications, because it increases in data throughput without

additional bandwidth or transmit power. It achieves this by higher spectral efficiency and

link reliability or diversity. The combination of MIMO with OFDM technique is a

promising technique for the next generation wireless communication. A new protocol draft

employing the MIMO-OFDM as the physical layer technology, IEEE 802.11n, as an

amendment to IEEE 802.11 standards has been proposed [53]. Wireless LAN technology

2

has seen rapid advancements and MIMO-OFDM has gradually been adopted in its

standards. The following table shows the existing IEEE 802.11 WLAN protocols.

Table 1.1 Existing 802.11 WLAN Standards

IEEE Protocol Name 802.11b

802.11a

802.11g

802.11n

Standard Approved

Sept. 1999 Sept. 1999

June

2003

Released in

2009

Available Bandwidth

83.5 MHz 580 MHz 83.5 MHz

83.5/580

MHz

Frequency Band of

Operation

2.4 GHz

5 GHz

2.4 GHz

2.4/5 GHz

Non-Overlapping

Channels (US)

3

24

3

3/24

Data Rate per Channel

1–11 Mbps 6–54 Mbps 1–54 Mbps

1–600

Mbps

Modulation Type

DSSS,

CCK

OFDM

DSSS,

CCK,

OFDM

DSSS,

CCK,

OFDM,

MIMO

UWB is a technology for transmitting data spread over a large bandwidth (usually larger

than 500 MHz) that shares among users. UWB was traditionally applied in

non-cooperative radar imaging. Most recent applications include sensor data collection,

precision locating, and tracking applications. The concept of cognitive radio was first

proposed by Dr. J. Mitola and Prof. G. Q. Maguire [4] in 1999 and was an extension to the

concept of software radio. Cognitive radio is an intelligent communication system that

could detect and track the communication environments. It would adjust the transmitter

and the receiver

’

s parameters adaptively according to the changes of environment

parameters such as the mobile velocity of the user, so that the system stability could be

3

ensured, the system performance could remain a good condition, and the spectrum

efficiency could be improved. WiMAX is a telecommunications protocol that provides

fully mobile Internet access. The name "WiMAX" was created by the WiMAX Forum,

which was founded in 2001. The forum refers to WiMAX as a standards-based technology

enabling the delivery of last mile wireless broadband access as an alternative to cable and

digital subscriber line (DSL). The basis of WiMAX is IEEE 802.16 standard which is

sometimes referred to as

“

WiMAX

”

equivalently. The current WiMAX revision is based

on IEEE 802.16e, which was approved in December 2005. The physical layer of WiMAX

adopts a lot of advanced technologies such as scalable orthogonal frequency division

multiplexing access (OFDMA), MIMO, adaptive antenna array and so on. Current

WiMAX that is based on the IEEE 802.16e protocol belongs to 3G family. Future WiMAX

is based on IEEE 802.16m, which has been submitted to the International

Telecommunication Union (ITU) for International Mobile Telecommunication Advanced

(IMT-Advanced) standardization. Future WiMAX, or the proposed WiMAX release 2, is

considered as a candidate of 4G family. LTE is the latest standard in the mobile

communication systems. The current generation of mobile communication system is

collectively known as 3G. Although LTE is often referred to as 4G, the first released LTE is

actually a 3.9G technology as it does not completely meet the 4G requirements. The main

advantages of LTE include high throughput, low latency, plug and play, a simple

architecture resulting in low power consumption, supporting seamless passing by base

stations with former wireless networks such as Global System for Mobile Communications

4

(GSM), Universal Mobile Telecommunications System (UMTS), and CDMA2000. LTE

also adopts OFDM and MIMO technologies in the physical layer. It uses a 2 by 2 MIMO

system as the basic configuration, that is, both the base station and the mobile end equip 2

antennas. The next step for LTE evolution is LTE Advanced and is currently being

standardized by 3rd Generation Partnership Project (3GPP) organization.

The thesis studies two issues: channel estimation for OFDM systems and

MIMO-OFDM system capacity. The chapter is organized as follows. Section 1.1 describes

the research motivation. Section 1.2 provides the thesis contributions and the overall

organization of the thesis.

1.1 Research motivation

Earlier OFDM systems such as the digital audio broadcasting (DAB) system in Europe

does not require channel estimation module. It only uses DPSK demodulation for the sake

of reducing the complexity of the receiver. However, with increasing demands of high data

transmission rate and reliable communication quality, channel estimation has become a

necessary part in the OFDM system. For example, the digital video broadcasting (DVB)

system adopts the channel estimation module. In a broadband wireless environment, the

channel is often time varying and frequency selective, which distorts the transmitted signal

significantly, so that accurate and real time channel estimation is the challenging topic in

the OFDM system. Channel state information can be used for the detection of the received

signal, improving the capacity of the system throughput by adjusting the modulation at the

5

transmitter through the feedback. Therefore, one issue of the thesis studies channel

estimation for OFDM systems over time varying and frequency dispersive fading

channels.

With the increasing number of mobile phone users and higher demands for wireless

services, future communication systems should have higher system capacity. MIMO

technique is a breakthrough of improving system capacity. Telatar [46] and Foschini [47]

have firstly formulated the system capacity of the MIMO systems assuming independent

and identically distributed fading at different antennas. They have proved that the MIMO

system capacity for n transmitter antennas and n receiver antennas increases linearly with

n at a fixed transmitter power. That is, MIMO systems can improve the system capacity

significantly without increasing the system bandwidth. A number of MIMO techniques

known as layered space time architectures or Bell Laboratories layered space time

(BLAST) architectures [5]–[8] have been proposed. Many studies on MIMO system

capacity have been conducted. Since the combination of MIMO with OFDM is a trend, a

lot of research work has been done on the MIMO-OFDM system capacity. However, the

research on MIMO-OFDM system capacity with imperfect feedback channel is not mature

and corresponding work is not much. Therefore, the second issue of the thesis is to study

the MIMO-OFDM system capacity with imperfect feedback channels.

1.2 Organization and contributions of the thesis

Firstly, we briefly describe the organization of the thesis. Chapter 1 gives a general

6

introduction, research motivation, organization, and contributions of the thesis. Chapter 2

describes the basic OFDM system model and MIMO system model. The wireless channel

model, the principles of OFDM and MIMO systems, the combination of MIMO and

OFDM, that is, MIMO-OFDM system is also introduced in Chapter 2. Next, as depicted in

Fig 1.1, the thesis begins with the first issue, that is, channel estimation. The proposed

channel estimation method in Chapter 3 is based on quasi-static fading channels and that in

Chapter 4 is based on fast fading channels. Then, the thesis switches to next issue, that is

system capacity. In Chapter 5, the MIMO-OFDM system capacity with imperfect feedback

channel is investigated. In Chapter 6, the capacity variances for OFDM systems over

Rayleigh and Ricean fading channels are derived, respectively. Finally, Chapter 7

concludes the thesis and discusses future research works.

Fig 1.1: Organization of the thesis.

7

Secondly, the major contributions of this thesis are summarized as follows.

9

A fast linear minimum mean square error (LMMSE) channel estimation method for

OFDM systems over slow fading channels has been proposed. Unlike the

conventional method, the channel state information is not needed in advance.

Almost the same performance with the conventional LMMSE channel estimation in

terms of the normalized mean square error (NMSE) of channel estimation and bit

error rate (BER) could be achieved for the proposed method. The computational

complexity can be reduced significantly since the proposed method replaces the

inverse operation with FFT operation. (Chapter 3)

9

A new pilot pattern and corresponding channel estimation method and data

detection for OFDM systems over fast fading channels have been proposed. The

proposed channel estimation and data detection based on the proposed pilot pattern

can eliminate inter-carrier interference (ICI) effect effectively. And the number of

required pilots is also reduced significantly, compared with the conventional least

square (LS) method. MSE analysis for the channel estimation based on the grouped

pilot pattern is provided, too. (Chapter 4)

9

The closed-loop MIMO-OFDM system capacity with imperfect feedback channel

has been formulated. We use the feedback SNR to measure the closed-loop capacity.

Since low feedback SNR may not yield positive gain of closed-loop capacity over

8

open-loop capacity, there exists a lower threshold of feedback SNR. The lower

thresholds for different antenna pairs are further investigated by numerical method.

(Chapter 5)

9

The variances of OFDM system capacity over Rayleigh fading channels and Ricean

fading channels have been derived. The effects of SNR, the number of channel

paths, power profile of fading channel, the delay of the channel on the variance

have been thoroughly investigated, for both multipath Rayleigh channels and

multipath Ricean channels. The joint PDF of two arbitrary correlated Ricean

random variables has been provided in an integral form. (Chapter 6)

9

Chapter 2: OFDM systems and MIMO systems

Since the thesis studies the channel estimation for OFDM systems and system capacity for

MIMO-OFDM systems, this chapter briefly introduces the background of OFDM systems

and MIMO systems.

OFDM is an effective technology which provides high spectrum efficiency, high data

transmission rate and is robust to multi-path fading [1]. OFDM has already been widely

put into practice in DAB system, DVB system and WLAN. MIMO systems which employ

multi-element antenna arrays at the transmitter and receiver ends are capable of high data

rate transmission. A number of MIMO techniques known as layered space time

architectures or BLAST architectures have been proposed [5]-[7], [9].

As OFDM technique can mitigate the ISI and transform the frequency selective fading

channel into a set of flat fading channels, the combination of MMO with OFDM technique

is a trend for future wireless communication. A new protocol draft, IEEE 802.11n, as an

amendment to IEEE 802.11 standards has been proposed and investigated [53]. The draft

proposes MIMO-OFDM as the physical layer technique and is to be approved by IEEE.

The chapter is organized as follows. Section 2.1 provides an introduction to wireless

channel in communication systems. Section 2.2 describes the basic OFDM system model,

principles, and related key technologies in OFDM systems. Section 2.3 introduces the

basic MIMO system model and briefly overviews the existing MIMO systems. Section 2.4

presents the MIMO-OFDM system model. The last section 2.5 summarizes the chapter.

10

2.1 Wireless Channel

Since there exist reflections, scattering, and diffraction in the transmission of

electromagnetic wave, the spatial environments such as the landscape of a city,

obstructions and so on will make complicated impacts on the transmission of

electromagnetic wave. There are two kinds of propagation, including the large-scale

propagation and the small scale propagation. The signal variations due to path loss or

shadowing occur over relatively large distances, this variation is referred to as the large

scale propagation effects. Path loss is a major component in the analysis and design of the

link budget of a telecommunication system. The small scale propagation refers to the

phenomena that the amplitude of the received wireless signal varies very fast in a short

time period or a short distance. The sources of small scale propagation include the Doppler

shift effect and multi-path effect. We begin with the introduction of the large scale

propagation.

11

2.1.1 Large scale propagation

Fig 2.1: Path Loss, shadowing and multipath versus distance.

Fig 2.1 plots the ratio of the received-to-transmit power in dB versus the distance for

the combined effects of path loss, shadowing, and multipath. Observe that the free space

path loss is linearly proportional to the log-distance between the transmitter and receiver.

The shadowing loss has slower variations compared to that of the multipath effect. The

large scale path loss model has many successful types including the free space path loss

model, the Hata model, and the Okumura model and so on. Most of them are obtained by

a combination of the analytical and empirical methods. We next briefly introduce the free

space path loss model as an example of path loss effect.

9

Free

space path loss model: An example of path loss effect

Consider a signal transmitted through free space to a receiver located at distance d from

the transmitter. It is assumed that there does not exist any obstructions between the

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