dissertation wonchae kim

ADAPTIVE TRANSCEIVER DESIGN AND PERFORMANCE

ANALYSIS FOR OFDM SYSTEMS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Wonchae Kim

June 2009

c© Copyright by Wonchae Kim 2009

All Rights Reserved

ii

I certify that I have read this dissertation and that, in my opinion, it is fully

adequate in scope and quality as a dissertation for the degree of Doctor of

Philosophy.

(Donald C. Cox) Principal Adviser



Philosophy.

(John M. Cioffi)



Philosophy.

(Ravi Narasimhan)

Approved for the University Committee on Graduate Studies.

iii

Abstract

With the enormous demand for wireless access to the Internet for packet data and voice

applications, Wireless Local Area Networks (WLANs) and Wireless Metropolitan Area

Networks (WMANs) are becoming ubiquitous. As is the case in all wireless systems, appli-

cations carried over these networks are subject to impairments such as path-loss, shadowing

and fading in the wireless channel. These impairments lead to transmission errors and con-

sequently, packet loss, which degrades the Quality of Service (QoS) perceived by a user. In

this study, we focus on coded orthogonal frequency division multiplexing (OFDM)-based

WLANs and WMANs. Adaptive transceivers can provide considerable improvements in

the performance of OFDM systems ; however, the design of adaptive OFDM transceivers

can be very complex and challenging due to estimation errors and limited knowledge of

channel information.

The fading characteristics of the indoor wireless channel are very different from the

ones we know from mobile environment. In indoor wireless systems, the transmitter and

receiver are stationary and people are moving around, while in mobile systems the user

is often moving through an environment. As a result, we propose a new model for time

varying indoor channel in order to fit the Doppler spectrum measurements

In the second part of the dissertation, time and frequency synchronization problems

in an OFDM inner receiver will be presented. In the burst packet mode OFDM systems,

synchronization needs to be done very fast to avoid the reduction of the system capacity

and also must be very accurate to minimize interferences. We analyzed effect of estimation

iv

error on the system performance and proposed adaptive synchronization methods based on

windowing and Kalman filtering to mitigate estimation errors with reasonable complexity.

For several different channel environments, numerical results show that the proposed meth-

ods can significantly decrease synchronization errors without the need for prior knowledge

of channel conditions.

In the third part of the dissertation, we propose an enhanced DFT-based minimum mean

square error (MMSE) channel estimator using the Kalman smoother. In practical OFDM

systems with virtual carriers (VCs), conventional DFT-based approaches are not directly

applicable as they induce a spectral leakage owing to VCs, which results in an error floor

for the mean square error (MSE) performance. We applied Kalman smoothing to minimize

the leakage effect and time domain MMSE weighting is also used to suppress the channel

noise.

Finally, using Request to Send (RTS) and Clear to Send (CTS) mechanism, we in-

troduce a method to improve throughput performance by adaptively changing constellation

size and power distribution across the sub-carriers without sacrificing throughput due to ex-

plicit feedback. Based on theoretical analysis, part of this complex maximization problem

approximately reduced to a Lagrange equation and the objective function can be solved

by a simple iterative algorithm. Simulation results, using the proposed channel model,

show that this algorithm combined with the proposed estimation methods is a promising

approach to solving throughput optimization problems within practical impairments.

v

Acknowledgements

I would like to first thank my adviser, Professor Donald C. Cox. He has been a great mentor,

and I was very fortunate to have him as my principal adviser. His expertise in wireless

communication has been truly valuable in this research, and I have learned everything

from introductory communication theory through standard communication systems and

estimation theory from him. This dissertation would have not been possible without him.

My other members of the reading committee, Professor John M. Cioffi and Professor

Ravi Narasimhan, were very helpful and I would like to thank them for their time. Pro-

fessor Cioffi really introduced me into the field of multi-carrier modulation and I learned a

great deal on mathematical analysis from him, which I used extensively throughout this dis-

sertation. Professor Narasimhan gave me a lot of insights about wireless channel through

his papers, which helped me in finding a good topic for my research. I would like thank

Professor Cioffi for his valuable input as an expert in multi-carrier systems and Professor

Ravi for his comments from his background in wireless LAN system design.

Taking lectures from world famous scholars in Stanford was certainly a privilege for

me. I have taken invaluable classes from a number of professors in Stanford, and these lec-

tures not only prepared me in doing my research, but also increased my general knowledge

in this field.

I thank the members of the wireless communications research group for their helpful

discussions: Mehdi Soltan, Hichan Moon, Ali Faghfuri, Vahideh HosseiniKhah, Hyunok

Lee and Tom McGiffen. I also thank colleagues in different research groups including

vi

Eunchul Yoon, Jiwoong Choi and Seongho Moon.

I was really fortunate to have great friends at Stanford. They include, but are not lim-

ited to, Youngjae Kim, Changhwan Sung, Kwangmoo Koh, Wooyul Lee, Woongjun Jang,

Jeunghun Noh and Hochul Shin. They have been great friends, who gave me the courage

to move forward and finish my study. I am also grateful for what I have received from

Samsung Lee Kun Hee Scholarship Foundation, who took part in funding my study at

Stanford.

And finally, I would like to thank my family, my wife Juyoung Ha, my brother Wony-

oung Kim, and my parents Hongryul Kim and Jungsub Lee, for their unconditional love

and encouragement, which led to my Ph.D. degree at Stanford. This doctoral dissertation

is dedicated to my parents.

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Contents

Abstract iv

Acknowledgements vi

1 Introduction 1

1.1 Why OFDM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Research Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Indoor Wireless Channel 8

2.1 Types of small scale fading . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 ETSI Channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Modeling the Time Varying Channel . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Mobile Radio Channel . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.2 Indoor Wireless Channel . . . . . . . . . . . . . . . . . . . . . . . 16

3 Adaptive Timing Synchronization for OFDM Systems 21

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 Frequency and Timing Synchronization . . . . . . . . . . . . . . . . . . . 28

3.3.1 Coarse Frequency Offset Estimation . . . . . . . . . . . . . . . . . 28

viii

3.3.2 Adaptive Timing Synchronization method . . . . . . . . . . . . . . 29

3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . 34

3.4.2 Random Channel Generation . . . . . . . . . . . . . . . . . . . . . 34

3.4.3 Performance Results . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4 Residual Frequency Offset and Phase Tracking 42

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 The Effect of Residual Frequency Offset . . . . . . . . . . . . . . . . . . . 45

4.3 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.1 State-Space Modeling . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.2 The Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.3 Complexity Consideration . . . . . . . . . . . . . . . . . . . . . . 54



4.4.2 Performance result . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5 Enhanced DFT-Based MMSE Channel Estimation 61

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Kalman Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3 MMSE Filtering in the time domain . . . . . . . . . . . . . . . . . . . . . 69

5.4 Complexity issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71



5.5.2 Performance result . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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6 Throughput Enhancement for IEEE 802.11a Wireless LANs 76

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Throughput Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.3.1 Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.3.2 The Minimum PER Problem . . . . . . . . . . . . . . . . . . . . . 84

6.3.3 Throughput Enhancement Method . . . . . . . . . . . . . . . . . . 86



6.4.2 Performance of the Proposed Inner Receiver . . . . . . . . . . . . 88

6.4.3 Performance of Throughput Optimization . . . . . . . . . . . . . . 89

6.4.4 Benefits of Throughput Optimization . . . . . . . . . . . . . . . . 92

6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7 Conclusion 97

7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Bibliography 102

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List of Tables

2.1 ETSI channel models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34



6.1 IEEE 802.11a PHY parameters . . . . . . . . . . . . . . . . . . . . . . . . 81


xi

List of Figures

1.1 Block diagram of an OFDM transceiver . . . . . . . . . . . . . . . . . . . 2

1.2 OFDM as a broadband communication system . . . . . . . . . . . . . . . . 4

2.1 Two types of small scale fading . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Power delay profile for channel A and B . . . . . . . . . . . . . . . . . . . 11

2.3 Power delay profile for channel C and E . . . . . . . . . . . . . . . . . . . 12

2.4 Illustration of Doppler shift . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Geometry of a single ray . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6 Doppler power spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.7 Autocorrelation function . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.8 Comparison between Doppler spectrum measurement and proposed Doppler

spectrum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 802.11a - Frame and slot structure . . . . . . . . . . . . . . . . . . . . . . 24

3.2 802.11a - Subcasrrier allocation . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Timing synchronization diagram . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Exemplary plot of D(n) at SNR=10dB . . . . . . . . . . . . . . . . . . . . 31

3.5 QW output when W = 16, 8, 4 and 3 . . . . . . . . . . . . . . . . . . . . . 32

3.6 A time variation technique for simulation . . . . . . . . . . . . . . . . . . 35

3.7 Average packet error rate for 4QAM in Channel B . . . . . . . . . . . . . . 36

3.8 Average packet error rate for 64QAM in Channel B . . . . . . . . . . . . . 37

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3.9 Average packet error rate for 4QAM in Channel C . . . . . . . . . . . . . . 37

3.10 Average packet error rate for 64QAM in Channel C . . . . . . . . . . . . . 38

3.11 Histogram of timing estimates for Channel B, SNR=10dB: Proposed . . . . 39

3.12 Histogram of timing estimates for Channel B, SNR=10dB: Conventional . . 40

3.13 Histogram of timing estimates for Channel C, SNR=10dB: Proposed . . . . 40

3.14 Histogram of timing estimates for Channel C, SNR=10dB: Conventional . . 41

4.1 SNR degradation due to RFO . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 64-QAM signal constellation without RFO . . . . . . . . . . . . . . . . . . 48

4.3 64-QAM signal constellation with RFO . . . . . . . . . . . . . . . . . . . 48

4.4 Comparison of phase error for ε = 0.01: ML . . . . . . . . . . . . . . . . . 50

4.5 Comparison of phase error : Kalman . . . . . . . . . . . . . . . . . . . . . 55

4.6 Average packet error rate for 4-QAM without channel estimation error (ε =

0.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.7 Average packet error rate for 64-QAM without channel estimation error

(ε = 0.05) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.8 Average packet error rate for 4-QAM (ε = 0.1) . . . . . . . . . . . . . . . 59

4.9 Average packet error rate for 64-QAM (ε = 0.05) . . . . . . . . . . . . . . 59

4.10 Error variance of RFO estimation (ε = 0.1) . . . . . . . . . . . . . . . . . 60

5.1 Block diagram of DFT-based method . . . . . . . . . . . . . . . . . . . . . 64

5.2 Existence of virtual subcarriers . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Kalman filtering and smoothing output, SNR=10dB . . . . . . . . . . . . . 68

5.4 MSE comparison in Channel A . . . . . . . . . . . . . . . . . . . . . . . . 73

5.5 SER comparison in Channel A . . . . . . . . . . . . . . . . . . . . . . . . 73

5.6 MSE comparison in Channel B . . . . . . . . . . . . . . . . . . . . . . . . 74

5.7 SER comparison in Channel B . . . . . . . . . . . . . . . . . . . . . . . . 75

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6.1 Block diagram of the simulated BIC-OFDM system . . . . . . . . . . . . . 80

6.2 Timing of successful frame transmission . . . . . . . . . . . . . . . . . . . 83

6.3 Timing of frame transmission failure . . . . . . . . . . . . . . . . . . . . . 83

6.4 Flow chart for iterative procedure for finding power distribution for mini-

mizing packet error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.5 An exemplary plot of constellation size variation with respect to time . . . . 88

6.6 Throughput comparison for improved inner receiver: Channel A & B . . . . 90

6.7 Throughput comparison for conventional system : Channel A & B . . . . . 91

6.8 Throughput comparison for adaptive transceiver in Channel A & B . . . . . 93

6.9 Throughput comparison for adaptive transceiver in Channel A & B . . . . . 94

6.10 Throughput comparison for only adaptive transceiver in Channel A & B . . 95

xiv

Chapter 1

Introduction

Wireless communication has gained a momentum in the last decade of the 20th century

with the success of 2nd Generations (2G) of digital cellular mobile services. Worldwide

successes of GSM, IS-95, PDC, and IS-54/137 are of the few examples demonstrating the

advancement of wireless communications and applications. These systems have initiated

an innovative way of life for the new information and communication technology era. The

total number of cellular subscribers was more than 3 billion in 2007 and now is expected

to exceed approximately 4 billion in 2009. In addition, many of these new subscribers

have started using a number of different forms of data services as well as voice services.

Increasing user demands have drawn the industry to search for better solutions to support

data rates in the range of tens of Mbps. This motivated researchers towards finding a better

solution for handling the nature of wireless channels and limited resources such as power

and bandwidth.

The idea of using multi-carrier transmission for high data rate communications has sur-

faced recently in order to overcome the hostile environments of wireless channels. OFDM

is a special form of multi-carrier transmission where all the subcarriers are orthogonal to

each other. OFDM promises a higher user data rate and greater resilience to severe signal

fading effects of the wireless channel at a reasonable level of implementation complexity.

1

CHAPTER 1. INTRODUCTION 2

Bit & PowerAllocation

OFDMModulator

ChannelInner

ReceiverOuter

ReceiverEncoder

Interleaver

Timing Synchronization Frequency Offset Estimation Channel Estimation

Figure 1.1: Block diagram of an OFDM transceiver

OFDM has developed into a popular scheme for wideband digital communication, whether

wireless or over copper wires, and has been used in applications such as digital television,

audio broadcasting, wireless networking, and broadband internet access. In addition, wire-

less communication has utilized OFDM as the primary physical layer technology in high

data rate Wireless LAN/MAN standards. For example, IEEE 802.11a has the capability to

operate in a range of a few tens of meters in typical office space environment whereas IEEE

802.16a uses Wideband OFDM (W-OFDM), a patented technology of Wi-LAN, to serve

up to 1 km radius of high data rate fixed wireless connectivity. Furthermore, OFDM may

become the prime technology for 4G. Pure OFDM or hybrid OFDM will be most likely the

choice for physical layer technology in future generations of telecommunications systems.

1.1 Why OFDM?

A simplified OFDM transceiver system is described in Fig. 1.1. In a digital domain, binary

input data are collected and FEC coded with schemes such as convolutional codes. The

coded bit stream is interleaved to obtain diversity. Afterwards, a group of channel coded

bits are gathered together (1 for BPSK, 2 for QPSK, 4 for QPSK, etc.) and mapped to

corresponding constellation points. At this point, the IFFT operation is performed on the

parallel complex data and a cyclic prefix is inserted in every block of data according to the


system specification. Now, the data is OFDM modulated and ready to be transmitted. After

the transmission of an OFDM signal through a wireless channel, an inner receiver performs

carrier frequency synchronization and symbol timing synchronization. After these steps,

an FFT operation is performed and a channel estimate is obtained. At this point, the com-

plex received data are demapped according to the transmission constellation diagram using

inner receiver estimates. Finally, FEC decoding and deinterleaving are used to recover

the originally transmitted bit stream in the outer receiver. In this thesis, we are going to

present solutions for questions about how to improve inner receiver performance and how

to efficiently allocate bit and power across subcarriers.

OFDM can offer several advantages over single carrier communication systems[1].

First of all, it can efficiently handle frequency selective channels. At high data rates, chan-

nel distortion to data transmission is very significant, and it is difficult to fully recover the

transmitted data with a simple receiver. A very complex receiver structure is needed which

makes use of computationally extensive equalization and channel estimation. OFDM can

drastically simplify the equalization problem by turning the frequency selective channel

into a flat channel. A simple one-tap equalizer is needed to estimate the channel and recover

the data. In addition, in a relatively slow time-varying channel, OFDM can significantly

improve capacity by adapting data rate across subcarriers. This is very useful for multi-

media communications. Furthermore, OFDM is robust against narrowband interference

because such interference affects only a small percentage of the subcarriers. Lastly, OFDM

makes single-frequency networks possible, which is especially attractive for broadcasting

applications.

1.2 Research Challenges

The radio channel has a crucial impact on the transmission of information through it. Multi-

path propagation will occur during a significant part of the time and this causes a frequency


Sub-carrier

magnitude

Carrier

Channel

Figure 1.2: OFDM as a broadband communication system

and time selective behavior of the channel response. As the phenomena are random, chan-

nel models for the linear time-variant radio channels are required to estimate the perfor-

mance of radio links and radio networks.

Also, if there are some estimation errors in carrier frequency or symbol timing, it will

induce significant errors in communication. The success of wireless OFDM system de-

pends strongly on synchronization. The higher the data rates are, the stricter the synchro-

nization requirements become. In order to build systems to support higher and higher data

rates, there is a need for algorithms and system designs that can facilitate robust estimation

of the synchronization parameters with minimum computational complexity.

Channel estimation is another primary requirement of an OFDM transceiver that per-

forms coherent reception. The capacity of a system is largely dependent on the channel

estimation scheme used in the system. The more accurate the channel estimate is, the bet-

ter the quality of service. OFDM offers a built-in very simple frequency domain channel

estimation scheme. Despite the fact that the scheme is simple enough, it does not perform

accurately under very low SNR conditions.

In 802.11a, the link adaptation algorithm is intentionally left open. Although many

previous studies have been focused on this particular topic, many of them are not directly

applicable to real systems. In addition, the actual optimization benefit that can be realized


after taking into account complexity always remains a question.

This dissertation explores the applicability of statistical estimation and optimization

techniques to the above mentioned problems in OFDM systems. Using 802.11a as an ex-

ample, we analyze the effect of various estimation errors and propose novel methods to mit-

igate synchronization and channel estimation error with reasonable complexity. Moreover,

we introduce a simple method to improve throughput performance by adaptively chang-

ing constellation size and power distribution across the sub-carriers without sacrificing

throughput due to explicit feedback. By employing the proposed scheme, we examine

the value of optimization with practical impairments.

1.3 Outline of the Thesis

Chapter 1 is a brief introduction and motivation. Chapter 2 considers an indoor wireless

channel model. An indoor wireless channel is always very unpredictable with harsh and

challenging propagation conditions. Measurement results show that an indoor wireless

channel is very different from a mobile channel in many ways. We particularly focused on

a delay spread model in this study and propose a new model for Doppler power spectrum

for an indoor channel. These models in Chapter 2 will be the basis for our discussion on

how we can improve the current systems in later chapters.

Adaptive timing synchronization for frequency selective channels is studied in Chapter

3. In burst packet mode OFDM systems, timing synchronization need to be done within a

single training symbol time to avoid reduction of the system capacity. Due to this stringent

requirement on synchronization time, standards incorporate preambles suitable for corre-

lation to estimate symbol timing. However, in time-dispersive multi-path channels, the

conventional timing synchronization methods might synchronize to a path in the middle

of the overall channel impulse response (CIR). Consequently, the receiver may not capture

some of the multi-path components. This results in an inter-symbol interference (ISI) and


an inter-carrier interference (ICI). In this chapter, we present a novel timing synchroniza-

tion method for OFDM systems to detect the most significant channel taps by adaptively

changing observation window length. The method does not require any extra channel infor-

mation such as signal to noise ratio (SNR) or average power delay profile, while allowing

detection of the first arrived path position. Additionally estimating maximum delay spread

and total channel power can be used to increase system capacity in other applications.

Chapter 4 moves on to a residual frequency offset and phase tracking problem. In

OFDM systems, carrier frequency offset (CFO) due to mismatch of the local oscillators

causes ICI, which may result in significant performance degradation. Although, several

frequency synchronization schemes were reported in the past, there can remain frequency

offset and that can still generate ICI and induce phase distortion of the OFDM symbols.

In this chapter, we propose a method to compensate both residual frequency offset (RFO)

and RFO induced phase error (PE) for OFDM systems by using the Kalman filter. In our

proposed method, the linear state-space model for RFO and PE is derived using estimated

SNR. After building a state-space model, the Kalman filter is applied to track and estimate

RFO and PE simultaneously. The proposed method allows unknown parameters to evolve

in time due to frequency drift of the local oscillator. The method is an optimal linear

estimator assuming signal and noise are jointly Gaussian. Furthermore, the computation

cost of the proposed method is much lower than that of the LS phase fitting method due to

the small dimension of the state-space model.

Chapter 5 also considers another estimation problem in an OFDM inner receiver. In

practical OFDM systems with virtual carriers (VCs), conventional DFT-based approaches

are not directly applicable for channel estimation as they induce a spectral leakage owing

to the VCs. This results in an error floor for the mean square error (MSE) performance. To

circumvent this problem, we propose an enhanced DFT-based minimum mean square error

(MMSE) channel estimator using the Kalman smoother. Our approach is based on building

a robust state-space model for a channel frequency response (CFR). Kalman filtering and


smoothing is then applied to minimize the leakage effect. Time domain MMSE weighting

is also used to suppress the channel noise. This proposed method does not require extra

knowledge about the channel statistics and can be implemented with small complexity

while achieving similar performance to the optimal MMSE estimation.

As we mentioned above, OFDM in combination with bit-interleaved coded modula-

tion is an efficient and robust high-speed transmission technique used in the IEEE 802.11a

standard. In Chapter 6, using the request to send (RTS)/ clear to send (CTS) mechanism,

we present a throughput enhancement method by deriving a simplified expression for the

throughput in the 802.11a system. The IEEE 802.11 MAC specifies for the contention-

based distributed coordination function (DCF) access method to exchange short control

frames - RTS/CTS prior to data transmission. RTS/CTS handshaking is essentially a

medium reservation scheme, and this mechanism is one of the effective ways to alleviate the

hidden node problem under DCF. Assuming channel reciprocity, we incorporate this mech-

anism for getting channel information at the transmitter without sacrificing throughput due

to explicit feedback. After acquiring channel knowledge, a simple iterative algorithm is

used to select constellation sizes and power distribution across the sub-carriers to enhance

the throughput.

As a conclusion, we review the results we have obtained and present some ideas for

future research in Chapter 7 and conclude this thesis.

Chapter 2

Indoor Wireless Channel

Due to the nature of wireless communications, wireless channels have very different char-

acteristics from wire-line channels. The mechanisms which govern radio propagation are

complex and diverse, and they can generally be attributed to three basic propagation mech-

anism as follows: reflection, diffraction and scattering. One of the most important charac-

teristics of a multi-path channel is the time varying nature of the channel which is called

small-scale variation. This time variation occurs because of the movement of the transmit-

ter or the receiver or the location of the obstacles.

In this chapter, we describe small scale fading characteristics of wireless channels

which are suitable for describing indoor wireless communication. We then give a brief

overview of European Telecommunications Standards Institute (ETSI) channel models and

propose a new autocorrelation model for temporal variation of an indoor wireless channel.

It is important to understand the different characteristics and properties of indoor wire-

less channels because the measurements of indoor channels show distinct differences from

mobile channel measurements.

8

CHAPTER 2. INDOOR WIRELESS CHANNEL 9

2.1 Types of small scale fading

The types of fading experienced by a signal propagating through a mobile radio channel

depends on the relation between the signal parameters, such as bandwidth and symbol

period [2][3]. Fig. 2.1 summarizes the types of fading experienced by a signal passing

through mobile radio channels with different characteristics. Based on delay spread, wire-

less channels can be divided into two categories: flat fading and frequency selective fading.

Furthermore, based on Doppler spread, channels can be divided into two other categories:

fast fading and slow fading. Therefore, the time dispersion and frequency dispersion in

a mobile channel lead to four possible distinct effects, which depend on the nature of the

transmitted signals, the channels, and velocities. While multipath delay spread leads to time

dispersion or frequency selective fading, Doppler spread leads to frequency dispersion or

time selective fading. Multipath dispersion can be described using similar mathematical

models for mobile channels with different parameters. However, there are some differ-

ences between the indoor and the mobile channel. First of all, while spatial variation of a

user is more important for a mobile channel, an indoor channel is neither stationary in time

nor in space. This temporal variation comes from motion of people and equipment around

low height portable antennas.

2.2 ETSI Channel models

In this study, power delay profiles for office environment are generated by ETSI models.

The ETSI channel models define five power delay profiles for the small-scale variations of

wireless channels in an office environment and open space[4]. The channel models describe

the delay spread of the channels. The Doppler and angular spreads, large-scale fading and

path-loss are not addressed in the ETSI channel models. In Table.2.1, we outline the five

channels and types of environment represented by these channels.


Figure 2.1: Two types of small scale fading

Table 2.1: ETSI channel modelsChannel RMS delay spread Environment LOS/NLOS

A 50ns Typical office NLOSB 100ns large open space and office NLOSC 150ns large open space NLOSD 140ns large open space LOSE 250ns large open space NLOS


0 0.1 0.2 0.3 0.40

5

10

15

20

25

30

Delay spread (µ s)

Pow

er (

−dB

)

(a) ETSI Channel A

0 0.2 0.4 0.6 0.80

5

10

15

20

25

Delay spread (µ s)

Pow

er (

−dB

)

(b) ETSI Channel B

Figure 2.2: Power delay profile for channel A and B


0 0.5 1 1.50

5

10

15

20

25

Delay spread (µ s)

Pow

er (

−dB

)

(a) ETSI Channel C

0 0.5 1 1.5 20

5

10

15

20

25

Delay spread (µ s)

Pow

er (

−dB

)

(b) ETSI Channel E

Figure 2.3: Power delay profile for channel C and E


Since Channel C and D have the same power delay profile, the power delay profile for

only Channel A, B, C and E are shown Fig.2.2 and Fig.2.3. From the power delay profile

of channel A in Fig.2.2, we can observe that the maximum delay spread is about 0.4 µ

secs and the power delay profile consists of two clusters of exponentially decaying paths.

Another point worth noticing is the first arrived path for the profile is not the strongest one

except in Channel A. This effect on timing synchronization will be discussed in the next

chapter. We also observe that the maximum delay spread increases from Channels B to

C to E. This increase in frequency selectivity not only increases diversity gains but also

implies an increase in intersymbol interference (ISI). ISI occurs when delayed copies of a

transmitted symbol overlap the next transmitted symbol and usually degrades the perfor-

mance of wireless systems. In addition, while the power delay profiles for Channels C and

D are the same, there is a line of path (LOS) with power of about 10dB higher than the

sum of average power of all paths in the power delay profile for Channel D. Consequently,

the frequency selectivity of the two channels are the same but Channel D is more stable

due to the non-faded path. Therefore, a system in Channel D would perform better than in

Channel C and, hence, Channel D will not be used in this study.

2.3 Modeling the Time Varying Channel

The fading characteristics of indoor wireless channels are very different from the previously

reported mobile cases. However, in indoor wireless systems, the transmitter and receiver

are stationary and people are moving in between, whereas in outdoor mobile systems, the

user is moving through an environment. Although, this sort of time variation has been

observed in the literatures, for example [5] and [6], it is not thoroughly analyzed yet. A

stochastic time variation model was proposed for fixed wireless communication [7]. How-

ever, numerical methods are needed to implement this model and an inclusion of numerical

components will cause additional delay in practical simulations. In this section, we extend


the method of [7] and derive a closed form stochastic channel model for an indoor wireless

communication simulation.

2.3.1 Mobile Radio Channel

The complex baseband representation of a wireless channel impulse response can be de-

scribed as,

h(t, τ) =∑

n

αn(t)e−jφn(t)δ(τ − τn(t)) (2.1)

where τn(t) is the delay of the nth path and αn(t) is its real amplitude. Due to the motion

of the user, αn(t)e−jφn(t) represents a wide-sense stationary narrowband complex Gaussian

process, which is independent for different path. If the user moves at speed v in the direc-

tion of θ as shown in Fig. 2.4, The phase change of a ray due to the moving receiver can be

easily obtained as

φ(t + ∆t)− φ(t) = 2πfcv

c∆t cos θ (2.2)

Therefore, assuming the power of each incident wave is uniformly distributed, the corre-

sponding autocorrelation function and Doppler power spectrum for nth tap are [3],

R(∆t) = E[exp(φ(t + ∆t)− φ(t))]

=1

2π

∫ 2π

0

exp(j2πfcv

c∆t cos θ)dθ

= J0

(2π

fcv

c∆t

)(2.3)

where fc is the carrier frequency. Fourier transforming above equation, we can derive

power spectrum as,


Receiver

Incident Plane Wave

Figure 2.4: Illustration of Doppler shift

S(f) =1

π√

f 2d − f 2

(2.4)

where fd denotes Doppler frequency and c is the speed of light. This model is called the

Jake’s model [45] and widely accepted for cellular environments where spatial variation

is more important than temporal variation. However, it deviates from measured Doppler

spectra in indoor wireless channel environments.


Transmitter Receiver

Reflector

Figure 2.5: Geometry of a single ray

2.3.2 Indoor Wireless Channel

Fig. 2.5 shows the case when the transmitter and receiver are stationary and reflectors are

moving in the direction of θ at speed v. The phase change of a ray due to a moving reflector

can be easily obtained as [7],

φ(t + ∆t)− φ(t) = 4πfcv

c∆t cos θ cos ψ (2.5)

Assuming all reflectors are moving in a similar manner and the power of each incident

wave is uniformly distributed, the autocorrelation function and Doppler power spectrum


can be computed as

R(∆t) = E[exp(φ(t + ∆t)− φ(t))]

=1

(2π)2

∫ 2π

0

∫ 2π

0

exp(j4πfcv

c∆t cos θ cos ψ)dθdψ

= J20

(2π

fcv

c∆t

)(2.6)

Fourier transforming the above equation, the power spectral density is

S(f) =

∫ fd

−fd

1

πfd

√1− x2

f2d

· 1

πfd

√1− (f−x)2

f2d

=1

π2fd

K

(√1− (

f

2fd

)2

)(2.7)

However, in reality, some of the received power is from static objects and also reflectors

usually do not move at the same speed. Therefore, we assume that the factor p of the

received power is static and comes from fixed reflectors while the factor (1 − p) of the

received power is time varying and comes from moving reflectors. Based on the above

reasoning, the autocorrelation function of this channel can be represented as sum of the

power from static reflectors and the power from moving reflectors.

R(∆t) = p + (1− p)E

[J2

0

(2π

fcv

c∆t

)](2.8)

Moreover, if we assume velocities of moving reflectors are exponentially distributed with

a parameter a, we can derive a closed form expression for the autocorrelation function as,

R(∆t) = p + (1− p)

∫ ∞

0

1

aexp

(− 1

av

)J2

0

(2π

fcv

c∆t

)dv (2.9)

= p + (1− p)2

aπγK

(4πfc∆t

cγ

)(2.10)


where a is mean velocity of the moving reflectors, K is the complete elliptic integral and

γ =√

1a2 + 4(2π fc

c∆t)2. Once we have an autocorrelation function, we can generate a ran-

dom process of the channel by spectrum filtering or spectrum sampling [3] and implement

a multipath fading simulator.

The Doppler power spectra and the autocorrelation functions for different environments

are shown in Fig.2.6 and Fig.2.7. The dotted line corresponds to the Jake’s model when a

receiver is moving at 4km/h and the dashed line, referred to as the worst case, represents the

case when p is zero and all reflectors are moving at 4km/h. Finally, the solid line represents

the proposed model when p is zero and a is 4km/h. Note that the proposed model gives

rise to more peaky Doppler spectrum and has wider spread of the power spectrum than the

Jake’s model in the frequency domain. Also, the autocorrelation function of the proposed

model shows less oscillatory behavior than that of the Jake’s model in the time domain.

Fig.2.8 shows a comparison between an indoor channel measurement result in [8] and

the proposed model. p and a are set to be 0.97 and 8km/h respectively and the power

spectral density of the proposed model is normalized to have the same received power

as the measurement. We can see that the proposed model matches the indoor channel

measurement well. In addition, it can be seen that the Jake’s model can not be fitted to this

measurement regardless of fd. Consequently, the proposed model can be used for more

accurate simulations of indoor wireless channels than the Jake’s model. In addition, since

the proposed model has a closed form expression, it has a lower computational complexity

than the model in [7]. This time variation model will be used throughout this dissertation.


−2 −1 0 1 2−30

−25

−20

−15

−10

−5

Normalized frequency

Mag

nitu

de (

dB)

Jakes modelWorst caseExponentional model with p=0

Figure 2.6: Doppler power spectrum

0 0.05 0.1 0.15 0.2−0.5

0

0.5

1Jakes modelWorst caseExponentional model with p=0

Figure 2.7: Autocorrelation function


−10 −5 0 5 10−100

−90

−80

−70

−60

−50

−40

−30

Frequency (Hz)

Doppler Power Spectrum

Figure 2.8: Comparison between Doppler spectrum measurement and proposed Dopplerspectrum model

Chapter 3

Adaptive Timing Synchronization for

OFDM Systems

In burst packet mode OFDM systems, timing synchronization needs to be done within a

single training symbol time to avoid reduction of the data throughput. Due to this stringent

requirement on synchronization time, standards incorporate preambles suitable for using

correlation to estimate symbol timing. However, in time-dispersive multi-path channels,

conventional timing synchronization methods may synchronizes to a path in the middle of

the overall channel impulse response (CIR). Consequently, the receiver may not capture

some of the multi-path components. This results in an inter-symbol interference (ISI) and

an inter-carrier interference (ICI). In this chapter, we propose a simple adaptive timing

synchronization method to locate the first arriving path based on the use of one training

symbol in the preamble. Our computer simulation results show that the proposed method

can significantly improve error rate performance. The performance gain becomes higher as

delay spread increases.

21

CHAPTER 3. ADAPTIVE TIMING SYNCHRONIZATION FOR OFDM SYSTEMS 22

3.1 Introduction

In OFDM, the modem can invert dispersive broadband channels into parallel narrow band

sub-channels, thus significantly simplifying equalization at the receiver. However, this

inherent immunity of OFDM to time-dispersive multi-path channels comes at the price of

increased sensitivity to synchronization error. Imperfect synchronization causes ISI and

ICI which can result in significant performance degradation [1] [11].

Several approaches have been proposed on the basis of using training symbols or using

the repetition property of cyclic prefixes [12] [13]. In burst packet mode OFDM systems,

the method using a preamble is preferred for fast time and frequency synchronization due

to the stringent requirement to minimize synchronization time. In [12] and [13], an auto-

correlation based timing metric is calculated. This calculation correlates the received sam-

ples and their delayed copies. These algorithms, based on the auto-correlation, inevitably

result in an ambiguity in timing due to a plateau region and to enhanced sensitivity to burst

noise. This ambiguity must be resolved after the auto-correlation process. One solution

to this problem is to use a cross-correlation method, which correlates the received samples

with known training samples. The cross-correlation peak of the received samples is used

for symbol timing. This method has very good performance in an AWGN environment

but has significant drawbacks since it is sensitive to frequency offset and the power delay

profile of the channel. In [23], short training symbols (STS) are used for timing estimation

via a combination of an auto-correlation and a cross-correlation. However, as mentioned

above, frequency offset in the local oscillator can disturb the cross correlation peaks sig-

nificantly, which will significantly affect the accuracy of the timing estimate. Furthermore,

a few sample errors in the coarse timing estimate may cause significant timing errors in

the resulting fine timing estimate. Therefore, in order to use a cross-correlation method to

estimate timing, frequency offset must be kept small, such as within 50Khz for 802.11a

and HiperLAN/2 environments [18].


In [19], after coarse frequency offset is compensated, fine timing estimation is done

using the periodic property of long training symbols (LTS). This algorithm, however, makes

no effort to estimate the position of the first arriving multi-path component, leading to an

inefficient utilization of the guard interval in multi-path channels. This also causes ISI

and ICI in the demodulation process. One intuitive solution to this problem is to shift

a few samples in the appropriate direction from the acquired correlation peak position.

However, since neither average nor instantaneous power delay profiles (PDP) of the channel

are available, it is not obvious how many samples should be shifted. In [16], they used a

double auto-correlation method to estimate the timing and the energy of the CIR to find the

first arriving path of the signal which may not be the strongest. However, this method has

a weakness that the timing estimate can be compensated only after channel estimation and

it is also not straightforward to decide the optimal window size, which is dependent on the

delay spread of the channel.

In this chapter, we present an adaptive timing synchronization method for OFDM sys-

tems using burst packet mode. In our proposed method, before symbol timing estimation,

frequency offset is corrected by a typical maximum likelihood (ML) method. Hence, the

cross-correlation based timing estimation accuracy is not affected by frequency offset, and

the cross-correlation output is used to detect the most significant channel taps by adaptively

changing an observation window. The proposed method in this chapter does not require

any extra channel information such as signal to noise ratio (SNR) or PDP, while allowing

detection of the first arriving path position and additionally estimating the maximum de-

lay spread and total channel power which can be used to increase system throughput in

other applications. We evaluate the performance of our method with the 802.11a standard

[9] in four different indoor PDP scenarios [4]. Simulation results show that our proposed

method significantly outperforms conventional peak selection methods and is robust to var-

ious channel environments with practical impairments.


10 2 3 4 65 7 8 9 GI2 T1 T2

P1 P2 Header Data Data ……. Data

Details of the preamble field

10 short symbols (0.8*10 = 8 s) 2 long symbols (1.6+2*3.2 = 8 s)

Signal detection, AGC, Coarse timing

recovery, Freq. acquisition

Fine timing recovery, Freq. offset

estimation, Channel estimation

8 s 8 s 4 s

4 Pilot sub-carriers for phase tracking

Figure 3.1: 802.11a - Frame and slot structure

3.2 System Model

Fig.3.1 shows an example of OFDM frame and slot structure In the WLAN standard

adopted by the IEEE 802.11a. Each data packet consists of preamble and a payload. The

preamble consist of 10 short training symbols (STS) of length of 16 samples (8µs) and long

training symbols (LTS) of length of 64 samples (8µs) which are all utilized for synchro-

nization and channel estimation. The data carrying part consists of a variable number of

symbols and the length of each data symbol is 64 samples. Note that a short symbol serves

as a cyclic prefix for a subsequent short symbol. For LTS, GI2 is the cyclic prefix for T1

and it contains 32 of the last samples (1.6µs) of T1. In the frequency domain, a data symbol

contains data subcarriers and some known pilot subcarriers that are usually used for phase

tracking. Fig.3.2 shows an example of the subcarrier allocation for the IEEE 802.11a sys-

tem. Out of the 64 possible subcarriers, only 52 subcarriers are used. Of the 52 subcarriers

used, 48 subcarriers are dedicated to data transmission and 4 are pilot subcarriers.

More generally, let’s consider an OFDM system with FFT length N where a total of


−40 −30 −20 −10 0 10 20 30 40frequency index

Data subcarriersGuard bandPilot subcarriers

Figure 3.2: 802.11a - Subcasrrier allocation

Nu subcarriers are used for transmission. The transmitted signal s(n) is generated by an

IFFT of data symbols Ak and a guard interval of length Tg = Ng · Ts is placed in front of

the useful portion Tu = N · Ts of the signal to prevent ISI. Ts denotes the sampling time

period. Then

s(n) =1

N

Nu/2+1∑

k=−Nu/2

Ak · expj2πnk

N(3.1)

for −Ng ≤ n ≤ N − 1

The baseband impulse response of the channel is assumed to be in the form of

h(n) =L−1∑

l=0

h(l)δ(n− l) (3.2)

where L is the maximum delay spread of the channel and h(l) represents the complex gain

of the lth multi-path component. Assume time invariance over one OFDM symbol. After


transmission over this multi-path channel, the samples at the receiver are

r(n) =L−1∑

l=0

s(n− l − nt) · h(l) · exp (j2πεn

N+ θ) + N(n) (3.3)

where N(n) is complex white Gaussian noise at time n, nt = δt/Ts is the timing offset, θ is

an unknown phase and ε = NTs ·δf is the normalized carrier frequency offset. If the guard

interval is correctly removed, the signal is then demodulated by FFT resulting in output at

the subcarrier k of

Yk = Hk · Ak + Nk (3.4)

for −Nu/2 ≤ k ≤ Nu/2 + 1 (3.5)

As long as the start position of the FFT window is in the ”Region A” in Fig.3.3, no

ISI or ICI occurs. Changing the start position will only induce phase rotation across the

subcarriers and this rotation can not be distinguished from actual channel phase response

so performance degradation does not occur. However, if the FFT start position is in the

”Region B”, it will cause ISI and ICI [15]. This effect is minimized when the energy of the

channel inside the guard interval of Ng in Fig.3.3 is the maximum.

In the presence of timing estimation error, the post FFT signal can be derived as

Yk = Hk · Ak · α(nt) + Nk + Nnt,k (3.6)

for −Nu/2 ≤ k ≤ Nu/2 + 1

Attenuation, α(nt), can usually be neglected for large N , so the main disturbance comes

from additional noise, Nnt,k. It was shown that this noise can be approximated by Gaussian


N Ng

B A B

FFT Window

L

FFT Start Position

Channel Response

Figure 3.3: Timing synchronization diagram

noise with power [14],

σ2nt

=∑

i

|hi|2(2 · g(nt)− g(nt)2) (3.7)

where g is a linear function depending on relative timing offset. Furthermore, a timing

offset will have another effect on the performance. Since some portion of the effective

channel is shifted, this portion can not contribute to the channel estimate. The resulting

channel estimation error is given by [24],

σ2c = E[|Hk −H∆,k|2] =

Nsu

N

∑i∗|hi∗ |2 (3.8)

SNR′ ≈ f 2

N(ε) · SNR(1− f 2

N(ε)) · SNR · (N/Nsu) + 1(3.9)

fN(ε) =sin(πε)

N sin(πε/N)


3.3 Frequency and Timing Synchronization

The proposed method can be broken into two steps. In order to use a cross-correlation

based timing synchronization method, frequency offset is compensated first using STS.

After successful frequency offset compensation, the FFT start position is found by our

proposed timing synchronization method.

3.3.1 Coarse Frequency Offset Estimation

STS are periodic after Ns samples. Then ML estimate of frequency offset can be obtained

by auto-correlation of the received signal.

A(n) =Wa−1∑m=0

r(n + m)r∗(n + m + Ns) (3.10)

ε =−N

2πNs

· tan−1(A(n)) (3.11)

where Ns = 16 for 802.11a [9], Ns = 64 for 802.16a [10] and Wa is the averaging length

which is dependent on the automatic gain control (AGC). During the AGC stabilization

time, the received signal will be corrupted by large gain fluctuations that cause the auto-

correlation output to be unstable. For most AGC systems, this process will last for the

first 48-80 samples of the STS [20]. Therefore, Wa is set to be less than 4 STS periods

for 802.11a systems. Using the method in [21], acquisition range and Cramer-Rao lower

bounds (CRLB) can be obtained as,

|ε| ≤ N

2Ns

(3.12)

var(ε) ≥ (N

2π · ks ·Ns

)2 · 1

Ns · SNR(3.13)


where ks is the number of STS such that Wa = ks · Ns and SNR is defined as E[|r(n) −n(n)|2]/E[|n(n)|2]. After symbol timing is acquired as described in the next section, the

LTS are used to further reduce the frequency offset estimation error. For this case, Ns is set

to be the length of the LTS, NL, and ks is set to be 1.

3.3.2 Adaptive Timing Synchronization method

After the packet detection algorithm signals the start of the packet, the symbol timing

algorithm refines the timing estimation to a sample period precision. This is conventionally

done by using the cross-correlation between the received signal r(n) and a known reference

tn with length NL. The reference, tn, can be made by concatenating last NL/2 samples of a

LTS with the first NL/2 samples of a LTS. The value of n that corresponds to the maximum

absolute value of the cross-correlation in (3.14) is the symbol timing estimate.

Tf = arg maxn

(|NL−1∑m=0

r(n + m)t∗m|2) (3.14)

tn = [LNL/2:NLL0:NL/2−1] (3.15)

where NL = 64 for 802.11a, NL = 128 for 802.16a. If the first arriving path is the strongest

path, this conventional method can detect the boundary between the last STS and the first

LTS, which is n = 161. Since the guard interval for the LTS is 32 samples, the exact FFT

start position, n = 193, can be found. But the conventional method that is mentioned above

fails to find true FFT start position if the first arriving path is not the strongest path. In such

cases , cross-correlation may take the highest correlation value associated with the path that

arrives later than the first path and this may result in severe ISI and ICI.

In order to avoid this problem, we utilize the fact that the cross-correlation output ap-

proximately coincides with scaled instantaneous channel power. Suppose C(n) is defined

as a cross-correlation output. The conditional expectation of C(n), given h(n), is obtained


as the following equation when a multi-path component exists at index n:

E[C(n)|h(n)] = E[|NL−1∑m=0

r(n + m)t∗m|2|h(n)] (3.16)

= |h(n)|2(Nu

N)2 + σ2

n

Nu

N+ σ2

I (3.17)

However, if a multi-path component does not exist at index n, the above equation be-

comes

E[C(n)|h(n)] = σ2n

Nu

N+ σ2

I (3.18)

where the number of used subcarriers, Nsu, is 52 for 802.11a and σI is additional

noise due to the imperfect cross-correlation property of the pseudo random sequence in

the preamble.

Let us define D(n) and QW (n) as

D(n) = C(n)− σ2n

Nu

N− σ2

I (3.19)

QW (n) =W−1∑m=0

D(n + m) (3.20)

where W is a summation window length. The QW (n) represents a normalized summation

of W consecutive samples of C(n). Also, the conditional expectation of QW (n) is zero

if a multi-path component does not exist within summation interval, W . Fig.3.4 shows an

exemple plot of D(n) when the maximum channel length is five sample periods.

As long as the window length, W , is greater than the maximum delay spread of the

channel, the maximum of QW (n) does not change except for some fluctuation due to noise.

Meanwhile, if the window length becomes less than the maximum delay spread of the


W

Figure 3.4: Exemplary plot of D(n) at SNR=10dB


Max delay spread = 4

Figure 3.5: QW output when W = 16, 8, 4 and 3


channel, the maximum of QW (n) will be significantly decreased. Therefore, the position of

the first arriving path can be estimated by detecting a significant decrease of the maximum

of QW (n). However, since the noise fluctuation of the maximum of QW (n) could lead to

an incorrect timing estimate, QW , which is defined as the average of the samples whose

magnitudes are greater than 90% of the maximum of QW (n), is used for timing estimation

instead of the maximum of QW (n). Suppose the window size W ∗ and the 90% maximum

start decreasing more than ξ%. Then it can be seen that arg maxn(QW ∗+1(n)) corresponds

to the first arriving path position since it indicates the starting time of the window which

contains the maximum power of the CIR. For example, Fig.3.5 represents QW (n) output

when {W = 16, 8, 4, 3} according to the D(n) in Fig.3.4. Since QW (n) starts decreasing

when W ∗ = 3, the resulting timing estimate can be obtained from arg maxn(QW ∗+1(n)) =

193. If we used the conventional peak-detection method, the resulting timing estimate

would be n = 196. The above method can be executed by a binary search algorithm with

high efficiency. It also can provide an estimate of the instantaneous maximum delay spread,

W ∗ + 1 and an estimate of the instantaneous total channel power.

The proposed method is summarized below:

1. Compensate frequency offset ε by (3.11).

2. Calculate C(n) and D(n).

3. Execute binary search algorithm to find W ∗ using initial W = Ng.

4. Declare timing estimate as arg maxn(QW ∗+1(n)).


Table 3.1: Simulation ParametersSampling time, Ts 50nsFFT length, N 64Useful subcarriers, Nu 52Number of data subcarriers 48Guard interval length, Ng 16Auto-correlation window, Wa 32Threshold, ξ 95Subcarrier spacing 312.5 KHzInitial frequency offset, δf 469 KHzModulation 4 QAM, 64QAMPacket length 540 BytesNumber of packets 10000Channel coding rate 1/2

3.4 Simulation Results

3.4.1 Simulation Environment

I simulated a transmitter and a receiver according to the parameters established by the

802.11a standard [9]. The simulation parameters are listed in Table 3.1.For the channel

model, only the small-scale fading is considered. Both the distance dependent path loss

and the shadowing are assumed to be constant over the simulation and incorporated into

the SNR. Two different PDPs, Channel B and C in Fig 2.2 and Fig 2.3 [4], are generated

and the time variation model in Chap 2 is employed. Details of random channel generations

are described in the next section. Two long training symbols in the preamble are used for

least-square channel estimation and four pilot subcarriers are used for residual frequency

offset compensation by the ML method [1].

3.4.2 Random Channel Generation

An average power of each tap in an channel impulse response is set according to a given

PDP. In order to generate time evolutions for each tap, an average velocity, a in (2.9), is


Time

Delay

Packetduration

Figure 3.6: A time variation technique for simulation

set to 4km/h. After obtaining a Doppler power spectrum, S(f), as described in Chap 2, a

spectrum sampling method [3] is used to independently generate time domain samples for

each tap. Consequently, the baseband representation of a channel impulse response at the

kth tap is,

hk(t) =∑N

n=1

√S(fn) · e−j(2πfnt+φn)

where S(·) is a Doppler power spectrum in Chap 2 and φn are random phases on [0, 2π].

Since the channel variation between adjacent two OFDM symbols are small, only two time

samples are generated for a tap inside a packet. The two time samples are chosen to be the

beginning and the ending time of a packet. A time variation inside these two time samples

is obtained by a linear interpolation as shown in Fig.3.6.


6 8 10 12 14 16 1810

−2

10−1

100

Average SNR (dB)

Ave

rage

pac

ket e

rror

rat

e

ProposedConvIdeal

Figure 3.7: Average packet error rate for 4QAM in Channel B

3.4.3 Performance Results

Fig.3.7 - Fig.3.10 show average packet error rate for the proposed method in two differ-

ent delay spread environments. The ordinate represents average packet error rate and the

abscissa represents average SNR. ”Ideal” is the case when ideal timing estimation is avail-

able and ”Conv” is the case when the peak location of the cross-correlation is declared

as the FFT start position. As you can see from the figures, the proposed method method

significantly outperforms the conventional method in all scenarios. This result is expected

from the PDP of the channel since the conventional method tends to be synchronized to a

path in the middle of the overall CIR. The probability that the first arriving path becomes

the strongest path is low for these channels. With incorrect timing estimate, the conven-

tional method experiences ISI and ICI and these interference become larger as the delay

spread increases finally leading to an error floor and this effect is more critical as modu-

lation complexity increases. The performance improvement in the proposed method over


18 20 22 24 26 28 3010

−2

10−1

100

Average SNR (dB)

Ave

rage

pac

ket e

rror

rat

e

ProposedConvIdeal

Figure 3.8: Average packet error rate for 64QAM in Channel B

6 8 10 12 14 16 1810

−2

10−1

100

Average SNR (dB)

Ave

rage

pac

ket e

rror

rat

e

ProposedConvIdeal

Figure 3.9: Average packet error rate for 4QAM in Channel C


18 20 22 24 26 28 3010

−2

10−1

100

Average SNR (dB)

Ave

rage

pac

ket e

rror

rat

e

ProposedConvIdeal

Figure 3.10: Average packet error rate for 64QAM in Channel C

conventional method is a result of capturing all components in the received signal while ISI

and ICI do not exist. Note that the gap between ”Ideal” and ”Proposed” is almost all from

channel estimation error and frequency offset estimation error, which means the proposed

method does not experience noticeable performance degradation from timing estimation

error.

To demonstrate the detailed performances of the proposed method as opposed to the

conventional method, histograms of timing estimate are shown in Fig.3.11 and Fig.3.12.

For these figures, average SNR is set to be 10dB and 10,000 packets are transmitted to

obtain the result for Channel B. Fig.3.11 shows the timing estimate of the proposed method

and Fig.3.12 shows the timing estimate of the conventional method for Channel B when

the true FFT start position is 193 sample. Note that the timing estimate distribution of the

conventional method tends to be shifted to the right side from sample 193. In contrast,

the timing estimate of the proposed method tends to be shifted to the left side from actual


185 190 195 2000

1000

2000

3000

4000

5000

Sample index

Proposed

Figure 3.11: Histogram of timing estimates for Channel B, SNR=10dB: Proposed

timing at sample 193. It can be seen that the proposed method achieves correct timing

more often than the conventional one. Also, even when the proposed method misses correct

timing, it makes an error in the direction of ”Region A” of Fig.3.3 where timing error may

not affect system performances as long as the channel delay spread is short enough. The

performance gain is larger in Channel C as shown in Fig.3.13 and Fig.3.14. Since the RMS

delay spread of the Channel C is lager than that of the Channel B as shown in the previous

chapter, the conventional synchronization method fails to find the true timing boundary

more often. The probability of finding the correct timing boundary for the proposed method

is around 48% and the probability for conventional method is only 6.4%.


185 190 195 2000

1000

2000

3000

4000

5000

Sample index

Conventional

Figure 3.12: Histogram of timing estimates for Channel B, SNR=10dB: Conventional

185 190 195 2000

1000

2000

3000

4000

5000

Sample index

Proposed

Figure 3.13: Histogram of timing estimates for Channel C, SNR=10dB: Proposed


185 190 195 2000

1000

2000

3000

4000

5000

Sample index

Proposed

Figure 3.14: Histogram of timing estimates for Channel C, SNR=10dB: Conventional

3.5 Conclusions

Here, we propose an adaptive timing estimation method for OFDM systems. By changing

an observation window length, the method can locate the first arriving path, which may not

be the strongest path. The correct timing can effectively avoid ISI and ICI. This method

does not require any prior knowledge, such as SNR or PDP, and our simulation results

show that it is robust to various channel environments. Furthermore, our proposed method

additionally provides an estimate of instantaneous total received power and maximum delay

spread which can be used in other applications to increase system throughput. Although

the simulation is done using parameters for the 802.11a standard, our method can be used

to perform timing synchronization for different burst packet mode OFDM systems.

Chapter 4

Residual Frequency Offset and Phase

Tracking

In orthogonal frequency division multiplexing (OFDM) systems, carrier frequency offset

(CFO) due to mismatch of the local oscillators can cause an inter-carrier interference (ICI),

which may result in significant performance degradation. Although several frequency syn-

chronization schemes were reported by previous studies, frequency offset still remains and

generates ICI as well as induces phase distortion of the OFDM symbols. In this chapter, we

propose a method to compensate both residual frequency offset (RFO) and RFO induced

phase error (PE) by using the Kalman filter. Our approach is based on building a simple

robust state-space model and the Kalman filter is then applied to estimate and track the

RFO and PE. Our simulation results show that the proposed method significantly reduces

the performance degradation due to RFO and almost achieves ideal packet error rate (PER)

performance with lower complexity.

42

CHAPTER 4. RESIDUAL FREQUENCY OFFSET AND PHASE TRACKING 43

4.1 Introduction

OFDM is a powerful modulation technique for high data rate transmission over frequency-

selective channels. However OFDM as a multi-carrier system has a different structure than

a single-carrier system. OFDM can tolerate relatively larger timing errors than a single-

carrier system due to a longer symbol period and a cyclic prefix. On the other hand, the

frequency synchronization requirement for OFDM is tighter than a single-carrier system

because the data are transmitted in parallel narrow sub-bands. If there exist a CFO, then

the number of cycles in the FFT interval is no longer an integer, with the result that ICI

occurs after the FFT [1]. Several approaches have been developed to estimate CFO [21]-

[23]. Unfortunately, it is difficult to completely compensate CFO, and CFO remains as a

residual frequency offset (RFO). This RFO can cause ICI and can induce phase error (PE)

in the OFDM symbols after the FFT. In order to decrease RFO effects, a tracking stage is

required in the OFDM receiver because even a very small RFO can cause a phase to rotate

continuously in every OFDM symbol.

In [25], a decision-feedback loop is used to compensate RFO by estimating the phase

differences between two consecutive OFDM symbols. Although this can actually remove

ICI from RFO, the performance is only guaranteed in relatively high signal to noise ra-

tio (SNR) regions due to the decision-feedback structure. Recently, a RFO compensation

scheme using an approximate SAGE algorithm is proposed [26]. It can compensate the per-

formance degradation due to RFO even in low SNR regions. In this scheme, an expectation

step is used to remove ICI and a maximization step is used to estimate RFO. However,

it is based on an iterative process and requires several maximization calculations, which

may not be possible in practical systems due to the inherent complexity and the processing

delay. In [27], assuming ICI from RFO is negligible, phase error (PE) is simply estimated

by averaging instantaneous phase estimates from pilot sub-carriers in each OFDM sym-

bol. Although the influence of AWGN in the instantaneous phase estimates can be reduced


by the averaging process, these estimates may be biased due to channel estimation errors

and, thus, averaging can lead to accumulation of PE. In contrast, an extended Kalman filter

was used to track only RFO in [28]. Although this method can track RFO by a recursive

procedure, this state-space modeling could require considerable computation because of

correlation matrix estimation. Furthermore, the solution for effects of PE was not clearly

addressed. Another solution for this problem is to use least-square (LS) phase fitting [29].

This method does not accumulate PE from channel estimation error and also can estimate

both RFO and PE. However, no claims about optimality can be made and the computation

cost increases as O(n3), where n is the number of samples used for the line fitting.

In this chapter, we propose a method to compensate both RFO and RFO induced PE

for OFDM systems using a Kalman filter. In our proposed method, the linear state-space

model for RFO and PE is derived using estimated signal to noise ratio (SNR). After building

a state-space model, a Kalman filter is applied to track and estimate RFO and PE simul-

taneously. The proposed method allows unknown parameters to evolve in time to track a

frequency drift of the local oscillator. The method is an optimal linear estimator assuming

signal and noise are jointly Gaussian. Also, the computation cost of the proposed method

is much lower than that of the LS phase fitting method [29] due to the small dimension of

the state-space model. We evaluate the performance of our method with parameters from

the 802.11a standard [9] in typical office environment. Our simulation results show that the

proposed method significantly compensates the performance degradation due to RFO and

almost achieves an ideal performance in terms of packet error rate in the range of signal to

noise ratios we have tested.


4.2 The Effect of Residual Frequency Offset

We consider an OFDM system having an FFT length N . Then the output of the mth OFDM

symbol is given by

sm(n) =1

N

N−1∑

k=0

Am(k) · expj2πnk

N(4.1)

for −Ng ≤ n ≤ N − 1

where Am(k) is a data symbol for the kth subcarrier, Ng = Tg/Ts is the guard interval

length in samples. Ts denotes the sampling time period and Tg denotes the guard interval

period. The baseband impulse response of the channel is assumed to be in the form of

h(n) =L−1∑

l=0

h(l)δ(n− l) (4.2)

where L is the maximum delay spread of the channel and h(l) represent the complex gain

of the lth multi-path component. Given a normalized RFO, ε = NTs · δf , and unknown

phase, θ, the received mth OFDM symbol with ideal timing estimation can be expressed by

[24]

rm(n) = (h(n) ∗ sm(n)) · cm(ε, n) + nm(n) (4.3)

cm(ε, n) , ej2πεn

N · e(j2πεm(1+α)+jθ) (4.4)

where ∗ is the convolution operator, α = Ng/N and n(n) is complex white Gaussian noise

at index n. After correctly removing the guard interval, the signal is demodulated by an


FFT and the resulting output at the subcarrier k is

Ym(k) = (H(k)Am(k))⊗ 1

NCm(ε, k) + Nm(k) (4.5)

=1

NCm(ε, 0)H(k)Am(k) + Im(k) + Nm(k)

Cm(ε, k) =

(sin(π(ε− k))

sin(π(ε− k)/N)ejπ(ε−k)(1−1/N)

)

·e(j2πεm(1+α)+jθ) (4.6)

Im(k) =1

N

N−1∑u=1

Cm(ε, u)H(k − u)Am(k − u) (4.7)

where ⊗ is the circular convolution operator. Cm(ε, k) is the FFT of cm(ε, n) and Im(k) is

the FFT of ICI.

Without loss of generality, we can assume that the total average channel power is nor-

malized to a constant,∑L−1

l=0 E[|h(l)|2] = 1. Then the approximate SNR in the time domain

can be derived using a method similar to [24]

SNR′ ≈ f 2

N(ε) · SNR(1− f 2

N(ε)) · SNR · (N/Nu) + 1(4.8)

fN(ε) =sin(πε)

N sin(πε/N)(4.9)

SNR , E[|r(n)− n(n)|2]E[|n(n)|2] (4.10)

where Nu is the number of subcarriers used. Fig.4.1 shows comparison between SNR

and SNR′

with respect to ε. We can see from Fig.4.1 that ε should be kept less than 0.01

to avoid SNR degradation due to RFO for SNR < 25dB. However, even a very small

RFO still can be a problem since it causes phase to rotate continuously for every OFDM

symbol in the packet. As the symbol index m increases, the e(j2πεm(1+α)+jθ) term in (4.6)

accumulates PE and finally results in a demodulation error. This effect is more serious


5 10 15 20 25 305

10

15

20

25

30

Ideal SNR(dB)

Act

ual S

NR

(dB

)

ε = 0

ε = 0.1

ε = 0.05

ε = 0.01

Figure 4.1: SNR degradation due to RFO

when the constellation becomes more complex. For example, if the FFT length, N , and

guard interval length, Ng, are 64 and 16 respectively, then a RFO (ε = 0.01) rotates the

constellation by 0.0785 radians per one OFDM symbol from (4.6). Therefore, even without

noise, it takes only two OFDM symbols to make a demodulation error for 64-QAM since

0.1342 radians is the minimum PE to cross a decision boundary for 64-QAM modulation.

Therefore, it takes 11 symbols for 4-QAM modulation for PE to make a demodulation

error. While Fig.4.2 shows an ideal 64-QAM signal constellation when ε = 0 at SNR =

30dB, Fig.4.3 demonstrates the resulting rotation of a 64-QAM signal constellation when

ε = 0.01 at SNR = 30dB.


−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

In−phase

Qua

drat

ure

Figure 4.2: 64-QAM signal constellation without RFO

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

In−phase

Qua

drat

ure

Figure 4.3: 64-QAM signal constellation with RFO


4.3 The Proposed Method

4.3.1 State-Space Modeling

After CFO estimation and channel estimation are completed using the preamble, the pilot

tones in the OFDM symbols can be used to track the RFO. Suppose there are Np pilot

tones in each OFDM symbol. The mth OFDM symbol output for the kn pilot tone, after

removing the pilot symbol, is

Pm(kn) = Cm(ε, 0)H(kn)/N + Im(kn) + Nm(kn) (4.11)

for kn ∈ A = {k1 . . . kNp}

Also the estimated channel frequency response from the preamble can be written as

H(k) = Cp(ε, 0)H(k)/N + Ip(k) + Wp(k) (4.12)

where p denotes the location where PE is zero and Wp(kn) is channel estimation noise.

Moreover, the PE due to RFO for the mth OFDM symbol can be modeled from (4.6) as

φm = φ0 + m · κ (4.13)

κ = 2πε(1 + α) (4.14)

for 1 ≤ m ≤ M


0 5 10 15 20 250

0.5

1

1.5

2

2.5

OFDM symbol index

Comparison of Phase Error

Pha

se e

rror

(ra

d)Without Noise

ML

Figure 4.4: Comparison of phase error for ε = 0.01: ML

where M is the total number of OFDM symbols in one packet. Then the maximum likeli-

hood (ML) estimate of the PE, φm, can be derived as

tan(φm) =Im[PmH∗]

Re[PmH∗](4.15)

Pm = [Pm(k1)Pm(k2) . . . Pm(kNp)]

H = [H(k1)H(k2) . . . H(kNp)]

Fig. 4.4 shows an example plot of actual PE without noise and the corresponding ML

estimates with respect to the OFDM symbol index when ε = 0.01. Assuming |φm−φm| ¿1, the tangent can be approximated by its argument and the ICI can also be approximated as

a zero mean Gaussian random variable for sufficiently large N by the central limit theorem


[21]. The estimation error can be written then as

φm − φm ≈ Dm/Em

where Dm and Em are defined as

Dm ,( ∑

kn∈AIm[(NfN

(ε)H∗(kn) + (Nm(kn) + Im(kn))e−jφm)

·(f ∗N(ε)H∗(kn) + (Wp(kn) + Ip(kn))∗)])

Em ,( ∑

kn∈ARe[(NfN

(ε)H∗(kn) + (Nm(kn) + Im(kn))e−jφm)

·(f ∗N(ε)H∗(kn) + (Wp(kn) + Ip(kn))∗)])

At high SNR, the above equation can be further approximated by,

φm − φm ≈ D′m/E

′m

where D′m and E

′m are defined as

D′m ,

( ∑

kn∈AIm[(Nm(kn) + Im(kn))f ∗N(ε)H∗(kn)e−jφm

+fN(ε)H(kn)(Wp(kn) + Ip(kn))∗])

E′m ,

( ∑

kn∈A|fN(ε)H(kn)|2)

from which we can deduce that the estimate is conditionally unbiased

E[φm − φm|ε,H(kn)] = 0 (4.16)


Moreover, the conditional variance of the estimate is

σ2ML = Var(φm − φm|ε)

≈ 2(1− f 2N(ε)) + σ2

N + σ2W

2Np · f 2N(ε)

(4.17)

where σ2N = E[|N(k)|2] and σ2

W = E[|Wp(k)|2]. Note that σ2ML is a function of ε. It

is not obvious how to determine σ2ML since the statistical distribution of ε is usually un-

known. Therefore, in order to design the robust estimator, σ2ML should be set according to

the expected worst case value of εmax in the acquisition range. In addition, the unknown

constants, σ2N and σ2

W , can be estimated in advance using the auto-correlation output of

the CFO estimation during the preamble. Suppose |J(n)| is the absolute magnitude of the

auto-correlation output,

|J(n)| = |Wa−1∑i=0

r(n + i)r∗(n + i + Ns)|

≈Wa−1∑i=0

|q(n + i)|2 (4.18)

where Ns is the repeating period, Wa is the averaging length and q(n) = h(n) ∗ s(n). Due

to the repeating property of the preamble, the noise variances can be estimated as follows:

E[|q(n)|2] ≈ |J(n)|/Wa

E[|r(n)|2] ≈ (Wa−1∑i=0

|r(n + i)|2)/Wa

σ2N = N · (E[|r(n)|2]− E[|q(n)|2]) (4.19)

σ2W = β · σ2

N (4.20)

where β is a known constant which depends on the channel estimation method. Therefore

combining (4.13), (4.17), (4.19) and (4.20), we obtain the following state-space model for


xm = [φm, κ]T .

xm = Fm−1xm−1 (4.21)

ym = Gmxm + qm (4.22)

where Fm−1 =

1 1

0 1

, Gm =

(1 0

)and

E[|q|2] = σ2ML =

2(1− f 2N(εmax)) + σ2

N(1 + β)

2Np · f 2N(εmax)

4.3.2 The Kalman Filter

From the above state-space model, the consecutive vector xm|m−1 and xm|m, with error

covariance matrix P , are recursively estimated given the measurement history and current

measurement ym through the Kalman filter. Based on this basic state-space representation

for RFO, the conventional Kalman equations are calculated as follows :

• Prediction step is

xm|m−1 = Fm−1xm−1|m−1

Pm|m−1 = Fm−1Pm−1|m−1FTm−1

• Update step is

Km = Pm|m−1GTm[GmPm|m−1G

Tm + σ2

ML]−1

xm|m = xm|m−1 + Km[ym −Gmxm|m−1]

Pm|m = Pm|m−1 −KmGmPm|m−1


Thus far, we have formulated the Kalman equations for recursively estimating the state vec-

tor xm. All that needs to be done to complete the recursion is to determine how the recursion

should be initialized. Since the CFO estimate is unbiased, E[κ] = 2π(1 + α)E[ε] = 0 and

E[φ0] = E[−pκ] = 0 from (4.13). Also E[κ2] can be approximately obtained from the

error variance of the CFO estimation [21]. Therefore, the initial estimate and initial value

for the error covariance matrix can be determined as

P0|0 = E[x0xT0 ] = σ2

κ

p2 −p

−p 1

(4.23)

x0|0 = E[x0] = E

[ −pκ

κ

]=

0

0

(4.24)

To demonstrate the features of the Kalman filtering as opposed to ML method, Fig.

4.5 shows an example plot of phase errors with the different RFO tracking methods when

ε = 0.01. Note that the proposed method can significantly reduce RFO induced phase error.

It has better performance because it utilizes not only instantaneous phase measurement but

also history of the phase estimation.

4.3.3 Complexity Consideration

In order to measure the computational complexity of different estimation methods, we use

the number of floating-point operations (flops). The LS phase fitting generally requires

O(M3) flops to obtain parameters where M is the number of samples used for the line

fitting. In contrast, the Kalman filter in the proposed method requires fewer than 100 flops

for each step and the complexity increases linearly with respect to M . Therefore, if more

than ten ML estimates are used for the LS phase fitting, the complexity of the proposed

method is lower than that of the LS phase fitting while achieving better performance. The

Kalman filter is usually of high complexity. But for our particular application, that uses


0 5 10 15 20 250

0.5

1

1.5

2

2.5

OFDM symbol index

Pha

se e

rror

(ra

d)

Comparison of Phase Error

Without Noise

Proposed

ML

Figure 4.5: Comparison of phase error : Kalman

a simple state-space model for PE, it can be verified that the Kalman implementation for

refining ML estimates obtained from pilot tones, does not significantly increase computa-

tional complexity. Indeed, due to basic formulation of the PE, the Kalman filter equations

can be largely simplified and complex matrix calculation is avoided. Another interesting

property to note about the Kalman filter is that Km and Pm|m do not depend on the data

xm. Therefore, it is possible for both of these terms to be computed off-line prior to any

filtering. This fact is not used for calculating complexity in this section.



We simulated a transmitter and receiver according to the parameters established by the

802.11a standard [9]. Details of simulation parameters are listed in Table 5.1. For the


Table 4.1: Simulation ParametersSampling time, Ts 50nsFFT length, N 64Number of used subcarriers, Nu 52Number of pilot subcarriers, Np 4Guard interval length, Ng 16Subcarrier spacing 312.5 KHzModulation 4-QAM, 64-QAMPacket length 100 symbolsNumber of packets 10000Channel coding rate 1/2

channel model, only small-scale fading is considered. Both the distance dependent path

loss and the shadowing are assumed to be constant over the simulation and incorporated

into the SNR. The power delay profile for typical office environment, based on the ETSI

model A in Fig.2.2 [4], is generated and time variation model in Chap 2 is employed.

Details of random channel generations are described in Sec 3.4. Moreover, one packet is

composed of 100 OFDM symbols. The proposed timing synchronization method in Chap

3 and LS channel estimation are used and SNR estimation is carried out as stated in (4.19).

In order to clearly demonstrate the performance of the proposed method, RFO, ε, is set at

constant 0.1(= 31.25KHz) for 4-QAM modulation and 0.05(= 15.62KHz) for 64-QAM

modulation before initial CFO estimation.

4.4.2 Performance result

In Fig.4.6 and Fig.4.7, we present average PER of the proposed method for the different

values of SNR with no channel estimation error. Cases are also shown for the ideal per-

formance when ε is zero, for the performance with ML method using Np(=4) pilots as

specified in the standard, for the performance without RFO compensation. We see that the

proposed method is superior to the conventional method. In particular, the performance for


64-QAM modulation with higher SNR is greatly improved. The difference in the perfor-

mance with respect to SNR is expected from Fig.4.1. While the performance gain in the

low SNR region is mainly due to decreased PE estimation error, the performance gain at

high SNR mostly comes from ICI reduction by RFO compensation.

Fig.4.8 and Fig.4.9 show average PER performance of the proposed method with chan-

nel estimation error. It can be seen that the gap between the proposed method and ”Ideal”

is slightly increased. This effect occurs because the channel estimation error may make the

ML estimate of PE biased and this can cause the PE output of the Kalman filter to converge

to an incorrect estimate. Also, since it takes a few OFDM symbols for the Kalman filter to

correctly estimate the RFO, ICI is not completely compensated during the initial tracking

period. However, These factors induce almost negligible PER performance degradation

and the performance gain over ML method is even increased since the proposed method is

able to update channel estimation result using the estimated RFO.

Fig.4.10 shows the RFO estimation error variance of the proposed method with channel

estimation error when ε = 0.1. The variance is calculated using the RFO estimates from

the 10th, 50th and the last OFDM symbol in each packet. It can be seen in Fig.4.10 that

the the estimation performance improves as the OFDM symbol index increases since more

measurement history is used for the estimation. For SNR greater than 15dB, the proposed

method can reduce the error variance below 10−8 for the last OFDM symbol in the packet.

The resulting standard deviation of the RFO estimation error is less than 31.25Hz.

4.5 Conclusions

In this chapter, we propose a residual frequency offset (RFO) compensator that compen-

sates both RFO and RFO induced phase error (PE) by using a Kalman filter. In our pro-

posed method, after the state-space model for RFO and PE is derived, a Kalman filter is

applied to track and estimate RFO and PE simultaneously. This method, when compared


4 6 8 10 12 14 1610

−2

10−1

100

Average SNR (dB)

Ave

rage

PE

R

ProposedIdealMLWithout Comp

Figure 4.6: Average packet error rate for 4-QAM without channel estimation error (ε = 0.1)

16 18 20 22 24 26 2810

−2

10−1

100

Average SNR (dB)

Ave

rage

PE

R


Figure 4.7: Average packet error rate for 64-QAM without channel estimation error (ε =0.05)


4 6 8 10 12 14 1610

−2

10−1

100

Average SNR (dB)

Ave

rage

PE

R


Figure 4.8: Average packet error rate for 4-QAM (ε = 0.1)

16 18 20 22 24 26 2810

−2

10−1

100

Average SNR (dB)

Ave

rage

PE

R


Figure 4.9: Average packet error rate for 64-QAM (ε = 0.05)


0 5 10 15 20 2510

−9

10−8

10−7

10−6

10−5

10−4

Average SNR (dB)

Err

or v

aria

nce

100th

symbol50

th symbol

10th

symbol

Figure 4.10: Error variance of RFO estimation (ε = 0.1)

with LS phase fitting, offers improved estimation and tracking behavior for RFO with less

complexity. Numerical results show that the proposed method significantly overcomes the

performance degradation due to RFO and almost achieves ideal PER performance.

Chapter 5

Enhanced DFT-Based MMSE Channel

Estimation

In practical OFDM systems, in order to limit the interference to adjacent channels, some

subcarriers are set to zero. These non-existent subcarriers are are often referred to as

virtual carriers (VCs). Due to these VCs, conventional DFT-based approaches are not

directly applicable because they induce spectral leakage, which results in an error floor

for the mean square error (MSE) performance. To circumvent this problem, we propose

an enhanced DFT-based minimum mean square error (MMSE) channel estimator using a

Kalman smoother. Our approach is based on building a robust state-space model for chan-

nel frequency response (CFR) followed by Kalman filtering and smoothing to minimize the

effects of leakage. Time domain MMSE weighting is also used to suppress channel noise.

Our simulation results show that the proposed method almost achieves the performance of

the optimal MMSE estimator while having a limited computational complexity.

61

CHAPTER 5. ENHANCED DFT-BASED MMSE CHANNEL ESTIMATION 62

5.1 Introduction

OFDM is an effective technique for overcoming multipath fading and achieving high-bit-

rate transmission over wireless channels. However, without channel estimation, OFDM

systems have to use differential phase shift keying (DPSK), which has 3dB SNR loss com-

pared to coherent demodulation. If coherent OFDM is adopted, channel estimation be-

comes a necessary requirement and pilot tones are usually used for channel estimation. In

general, the realization of pilot-aided channel estimation is based on least square (LS) [31]

or minimum mean square error (MMSE) [30]. The LS approach is simple but has poor per-

formance, whereas the MMSE approach has good performance but is complex and requires

a priori knowledge of channel statistics. As a compromise between LS and MMSE, a dis-

crete Fourier transform (DFT) based channel estimation that utilizes the channel impulse

response has been widely studied for OFDM systems [31] [32].

Fig. 5.1 shows a block diagram of DFT-based channel estimation. This method trans-

forms the channel from the frequency domain into the time domain by an inverse discrete

Fourier transform (IDFT). After that, a time domain windowing is applied to the channel

impulse response assuming the window length is longer than the maximum delay spread of

the channel. Finally, this method transforms the channel impulse response back to the fre-

quency domain by a DFT. Hence, the noise in the taps beyond the maximum delay spread

of the channel is filtered out in the time domain and this improves a performance. However,

this method assumes that all subcarriers of the OFDM signal are used for pilot transmis-

sion. Otherwise, after the IDFT operation, the power may spill over all the taps in the time

domain, and the noise filtering process becomes inapplicable. For example, in the WLAN

802.11a standard, in order to limit the interference to adjacent channels, subcarriers at the

band edge of the shaping filter are left unmodulated and set to zero. These unused subcar-

riers are called virtual carriers (VCs) and hence a direct application of DFT-based channel


estimation can not be used. Furthermore, the CFR at VCs can not be estimated by conven-

tional channel estimation approaches. Fig. 5.2 shows a CFR of the OFDM system where

11 subcarriers out of total 64 subcarriers are VCs. Although VCs are located at both edges

of the bandwidth, this figure shows the CFR from 0 to 64 instead of from -32 to 32 since

the DFT is periodic. It can be seen that direct application of a DFT to the CFR leads to

leakage in the time domain. In other words, windowing in the frequency domain can lead

to severe distortion in the time domain and hence the resulting channel estimate becomes

erroneous.

A windowed DFT-based channel estimation was proposed in [33] to reduce an aliasing

error and suppress the noise, but it requires searching for an optimal generalized Hanning

window shape to minimize MSE. Furthermore, implementation complexity is too high to

be used in practical systems for the non-interpolation case. In [34], robust Wiener filter-

ing is applied to eliminate the leakage effect due to absence of pilot symbols in the VCs.

This approach tried to improve BER performance by combining Wiener interpolation and

Wiener filtering for interpolation cases.

In this chapter, I present an enhanced DFT-based channel estimation method with sim-

ple Kalman filtering and smoothing. Moreover, a weighting function is applied to the

effective channel impulse response. The weighting function is chosen so that the MSE

between CFR and its estimate is minimized.

5.2 Kalman Smoothing

Autoregressive (AR) modeling is commonly used to model discrete time random processes.

This is due to the simplicity with which the parameters can be computed and due to their

correlation matching property. AR process of order p can be generated as


LS IFFT FFT

Freq domain Time domain Freq domain

H(1)

H(N)

H(2)

h(L)

H’(2)

H’(N)

H’(1)

0

h(1)

Figure 5.1: Block diagram of DFT-based method


0 20 40 600

0.5

1

1.5

2

index

mag

nitu

deIdealLS

Figure 5.2: Existence of virtual subcarriers

xn = −p∑

k=1

akxn−k + wn (5.1)

where w(n) is a complex white Gaussian noise process with uncorrelated real and imag-

inary components. Using Yule-Walker equations, the corresponding autocorrelation matrix

can be calculated using the autocorrelation function R as [35],

Rxa = −v (5.2)


where

Rx =

R(0) R(−1) · · · R(−p + 1)

R(1) R(0) · · · R(−p + 2)...

... . . . ...

R(p− 1) R(p− 2) · · · R(0)

a =(

a1 a2 · · · ap

)T

v =(

R(1) R(2) · · · R(p))T

For a non-interpolation channel estimation case, increasing the order of the AR model

not only increases computational complexity but also degrades the estimation performance

due to singularity of the channel correlation matrix, Rx, [36]. Suppose the LS estimate of

the channel frequency response is Hk and the channel dynamics follows an AR(1) model,

then a state space model for the CFR can be written as

Hk = A ·Hk−1 + qk−1

Hk = Hk + rk

where Hk is the CFR at index k, qk−1 ∼ N(0, Qk−1) and rk ∼ N(0, Rk). Using the

above equations, the prediction and update steps of the Kalman filter are :


Prediction steps :

mp = A ·mk−1

Pp = A · Pk−1 · AH + Qk−1

Update steps :

Kk = Pp · (Pp + Rk)−1

mk = mp + Kk(Hk −mp)

Pk = Pp −KkPp

A can be obtained simply as the ratio of correlations of Hk as A ≈ R(1)/R(0) from the

Yule-Walker method. Also, Qk−1 ≈ R(0) − |R(1)|2/R(0). The two unknown correlation

values, R(1) and R(0), can be estimated from an LS estimate of the channel frequency

response. In practice, the Kalman filter equations easily cope with missing values or VCs.

When missing values occur, the prediction steps are processed as usual, the update steps

are changed as mk = mp and Pk = Pp. After obtaining the Kalman filter output, then the

Kalman smoother is applied to the Kalman filtered output. The Kalman smoother calculates

recursively the state posterior distributions.

p(Hk|H0:N−1) = N(Hk|msk, P

sk ) (5.3)

The difference between filtering and smoothing is that the smoothed outputs are con-

ditioned to all of the measurement data, while the filtered outputs are conditioned only to

the measurement obtained before and at the time step k. So the smoothed output can be

calculated from the Kalman filter result by recursions as follows:


0 20 40 600

0.5

1

1.5

2

index

mag

nitu

deIdealFilterFilter+Smooth

Figure 5.3: Kalman filtering and smoothing output, SNR=10dB

P−k+1 = APkA

H + Qk

Ck = PkAH(P−

k+1)−1

msk = mk + Ck(m

sk+1 − Amk)

P sk = Pk + Ck(P

sk+1 − P−

k+1)CHk

starting from the last step N−1, with msN−1 = mN−1 and P s

N−1 = PN−1. Fig.5.3 shows

an example plot of output of Kalman filtering and smoothing at SNR=10dB when missing

values occur between k = 27 and k = 37. It can be seen that smoothing significantly

decreases the estimation error of filtering above.


5.3 MMSE Filtering in the time domain

By the IDFT operation, we transform the entire channel estimate obtained from the Kalman

prediction into a time domain channel impulse response

hkal(n) =1

N

N−1∑

k=0

msk exp(j2πkn/N) (5.4)

Since the prediction steps change white noise into colored Gaussian noise, the resulting

correlation vector of the colored noise in the time domain can be obtained by the scaled

IDFT of P sk

rnn(m) = E[nl+mn∗l ] =1

N2

N−1∑

k=0

P sk exp(j2πkm/N) (5.5)

The MMSE filtering matrix, M , in the time domain can be derived from the following

equations,

min|h−M · hkal(n)|2 (5.6)

By the orthogonality principle, M can be written as

M = Rhh · (Rhh + Rnn)−1 (5.7)

where

Rnn = t(rnn)

Rhh = E[hhH ]


where t denotes an operator that transforms a vector into a Toeplitz matrix. Since the

time domain correlation matrix of the channel impulse response is usually unavailable, Rhh

for a uniform channel power delay profile is used instead for robustness of the estimator.

Assuming a WSSUS (wide sense stationary uncorrelated scattering) channel [37], Rhh is

given by

Rhh =

1N

R(0) 0

0 0

(5.8)

R(0) = E[HkH∗k ] =

N−1∑n=0

|h(n)|2 (5.9)

where NGI denotes the length of the cyclic prefix and I represents a NGI by NGI iden-

tity matrix. Since the number of virtual carriers at the left and right side for the guard band

are the same, the resulting Rnn is a real matrix. Therefore, the resulting M matrix is a

real NGI by N matrix. Based on the above analysis, the overall estimation step can be

summarized as

msk = S(HLS) (5.10)

Htotal = F ·M ·G ·msk (5.11)

where S denotes a Kalman smoother, HLS is an initial LS estimate of the channel

frequency response, G is an N by N IDFT matrix and F is an N by NGI DFT matrix.


5.4 Complexity issues

In order to measure the computational complexity of different estimation methods, we use

the number of complex multiplications. The MMSE estimation generally requires O(N2)

and the window method [33] requires Nu + N + (2N/3)log2N + Nu. In contrast, for the

proposed method, a Kalman smoother requires O(N) and MMSE filtering requires NGI ·N .

So the total required complex multiplication is O(N)+N ·NGI +(2N/3)log2N . Although

the proposed method may appear to increases computational complexity over the window

method, the window method is very sensitive to window size which needs to be decided by

a complex optimization procedure. Therefore, implementation complexity of the window

method is much higher than that of the proposed method. To summarize, the proposed

method requires much less computational complexity than MMSE, while achieving almost

equivalent performance and it can be implemented simpler than the window method even if

it increases computational complexity a little in some sense. Note that although the Kalman

equations are usually of high complexity, for our particular application that uses a simple

state-space model for estimation, it can be verified that the Kalman implementation does

not significantly increase computational complexity and has better performance than the

window method. Furthermore, an interesting and useful property of the Kalman imple-

mentation is that, since the Kalman gain and error covariance matrix do not depend on the

data, it is possible for these terms to be calculated off-line prior to any filtering.



We simulated a transmitter and receiver according to the parameters established by the

802.11a standard [9]. The simulation parameters are listed in Table 5.1. For the channel

model, only small-scale fading is considered. Both the distance dependent path loss and


Table 5.1: Simulation ParametersSampling time, Ts 50nsFFT length, N 64Number of used subcarriers, Nu 52Number of pilot subcarriers, Np 4Guard interval length, Ng 16Subcarrier spacing 312.5 KHzModulation 64-QAMNumber of OFDM symbols 64Number of packets 10000Channel coding rate 1/2

the shadowing are assumed to be constant over the simulation and incorporated into the

SNR. The channel is assumed to be stationary and the power delay profiles for a typical

office environment, based on the ETSI model A and B in Fig.2.2 [4], are generated. The

maximum delay spreads for these channels are 50ns and 100ns respectively. Details of

random channel generations are described in Sec 3.4. Finally, the proposed synchronization

methods in Chap 3 and Chap 4 are employed.

5.5.2 Performance result

A packet error rate was used as a performance measure for Chap 3 and Chap 4. However,

we focus on a mean square error (MSE) and a symbol error rate (SER) here for better

comparison of the proposed method with the past results [33][34].

Fig. 5.4 shows MSE plot of various estimation methods. ”LS” denotes least-square

initial channel estimate and ”Direct FFT” denotes a conventional DFT-based method that

simply pads zeros at the end of the time domain LS estimate of the channel. ”Kalman”

denotes the proposed method and ”MMSE” denotes optimal MMSE channel estimation. It

can be seen that the proposed method achieves almost the same performance as the optimal

MMSE estimator. The performance gain comes from the prediction of the CFR in the guard

band and MMSE filtering in the time domain. On the other hand, it can be seen that the


0 10 20 30 4010

−5

10−4

10−3

10−2

10−1

100

Average SNR (dB)

MS

E

KalmanMMSELSDirect FFT

Figure 5.4: MSE comparison in Channel A

0 10 20 30 4010

−4

10−3

10−2

10−1

100

Average SNR (dB)

SE

R


Figure 5.5: SER comparison in Channel A


0 10 20 30 4010

−5

10−4

10−3

10−2

10−1

100

Average SNR (dB)

MS

E


Figure 5.6: MSE comparison in Channel B

conventional DFT-based method quickly reaches an error floor due to aliasing.

Average SER performance is presented in Fig.5.5. The proposed method experiences

negligible performance loss in terms of SER compared to optimal MMSE and achieves

more than 2dB gain over LS channel estimation. The performance gain becomes more

obvious in Channel B as shown in Fig. 5.6 and Fig. 5.7. It can be seen that the proposed

method actually achieves the same SER performance as optimal MMSE estimation. There

are two reasons for this. First, since we assumed a uniform PDP when we derive the

proposed estimator due to lack of channel statistics, Channel B looks more like a uniform

power distribution than Channel A. In other words, the model risk that comes from our

assumption can be decreased as the RMS delay spread increases. Moreover, larger RMS

delay spread leads to more frequency selectivity and hence leads to more variation in the

LS measurement data in the frequency domain. Therefore, AR modeling in the frequency

domain becomes more exact and better filtering and smoothing are possible.


0 10 20 30 4010

−4

10−3

10−2

10−1

100

Average SNR (dB)

SE

R


Figure 5.7: SER comparison in Channel B

5.6 Conclusions

In this chapter, I propose an enhanced DFT-based channel estimation using Kalman filter-

ing and smoothing for OFDM systems with VCs in a multipath fading channel. VCs are

used in OFDM systems to ease shaping filter implementation and to provide guard bands.

However, VCs cause dispersive distortion of a channel impulse response and prohibit the

use of conventional DFT-based channel estimation. The proposed method achieves almost

equivalent performance compared to optimal MMSE channel estimation. Furthermore, it

does not require a priori channel knowledge of statistics and the implementation complexity

is lower than complexity for optimal MMSE channel estimation.

Chapter 6

Throughput Enhancement for IEEE

802.11a Wireless LANs

Orthogonal frequency division multiplexing (OFDM) in combination with bit-interleaved

coded modulation (BICM) is an efficient and robust high-speed transmission technique

used in the IEEE 802.11a standard. In this chapter, using the request to send (RTS) /

clear to send (CTS) mechanism, we present a method to improve throughput performance

by adaptively changing constellation sizes and power distribution across the sub-carriers

without sacrificing throughput due to explicit feedback. Based on the theoretical analysis,

this complex maximization problem can be approximately solved by a simple iterative

algorithm. Simulation results show that the proposed method can significantly improve

throughput performance with low implementation complexity.

6.1 Introduction

Multi-carrier modulation (MCM) is a powerful and practical technique for high data rate

transmission over frequency-selective channels. Popular implementations of MCM include

orthogonal frequency division multiplexing (OFDM). IEEE 802.11a systems adopt OFDM

76

CHAPTER 6. THROUGHPUT ENHANCEMENT FOR IEEE 802.11A WIRELESS LANS77

in conjunction with coding and bit-interleaving, known as bit-interleaved coded modulation

(BICM). Conventional coded-OFDM systems, currently used in 802.11a systems, allocate

equal bits and power across the sub-channels. This uniform power distribution leads to

an inefficient use of power since the power loaded onto the sub-channels with deep fades

is most likely to be wasted. If channel information is available at the transmitter, then

the transmitter can allocate the bits and the power more efficiently. Indeed, over the past

decade, it has been shown that link adaptation can improve actual throughput performance

when knowledge of the channel is available at the transmitter.

Throughput is defined as the ratio of the average delivered data payload to the average

transmission time. It is the fundamental performance metric for reliable and efficient com-

munication accounting for all the overhead, inter-frame time and possible data retransmis-

sion time. There have been many link adaptation algorithms for throughput enhancement.

Automatic Rate Fallback (ARF) protocol [40] is used in the commercial WaveLAN- II net-

working devices. In this protocol, if two consecutive Acknowledgement frames (Ack) are

lost, the transmission rate is decreased and a timer is set. When either the timer expires or

the number of successfully received Ack reaches 10, the transmission rate is increased to

the higher rate and the timer is canceled. Although this scheme is easy to implement, this

scheme is purely heuristic and does not quickly react to channel variation.

A MAC Service Data Unit (MPDU)-based link adaptation scheme has been developed

in [41]. It is a table-driven approach and the basic idea is to pre-establish a best PHY

mode table by dynamic programming and the best PHY mode is indexed by the Signal to

Noise Ratio (SNR), MPDU size, and retransmission count. However, the suggested scheme

assumes the radio channel matches to a particular stochastic model and takes measured

SNR as the only input from the PHY layer. Therefore, it may not fully exploit the full

potential of PHY knowledge and can lead to sub-optimal results.

In [38] and [39], schemes which utilize full channel knowledge to minimize packet

error rate (PER) were presented. They can effectively increase throughput by adaptively


assigning optimal power distribution across sub-carriers. However, since the number of

used sub-carriers are changing according to channel conditions, these schemes may result

in unavoidable spectral efficiency degradation.

In this chapter, we extend the scheme in [38] and present a throughput enhancement

method by deriving a simplified expression for the throughput in the 802.11a system. The

IEEE 802.11 MAC specifies for the contention-based distributed coordination function

(DCF) access method to exchange short control frames - RTS/CTS prior to data trans-

mission [9]. RTS/CTS handshaking is essentially a medium reservation scheme, and this

mechanism is one of the effective ways to alleviate the hidden node problem under the

DCF. Assuming channel reciprocity, we incorporate this mechanism for getting channel in-

formation at the transmitter without sacrificing throughput due to explicit feedback. After

acquiring channel knowledge, a simple iterative algorithm is used to select constellation

size and power distribution across the sub-carriers to enhance the throughput. Simulation

results show that the proposed method can significantly improve throughput performance.

However, the performance gain is dependent on channel estimation and synchronization

error, and an improved inner receiver is required to achieve the desired performance gain.

6.2 System Model

We consider an OFDM system having a fast Fourier transform (FFT) length N where a total

of Nu subcarriers are used for transmission. The transmitted signal s(n) is generated by

inverse fast Fourier transform (IFFT) of data symbols Ak and a guard interval, sometimes

known as a cyclic prefix, of length Tg = Ng · Ts is placed in front of the useful portion

Tu = N ·Ts of the signal to prevent inter-symbol interference (ISI). Ts denotes the sampling


time period.

s(n) =1

N

Nu/2+1∑

k=−Nu/2

Ak · expj2πnk

N(6.1)

for −Ng ≤ n ≤ N − 1

The baseband impulse response of the channel is assumed to be in the form of

h(n) =L−1∑

l=0

h(l)δ(n− l) (6.2)

where L is the maximum delay spread of the channel and h(l) represent the complex gain

of the lth multi-path component assuming time invariance over one OFDM symbol. After

transmission over this multi-path channel, the samples at the receiver are

r(n) =L−1∑

l=0

s(n− l − nt) · h(l) · exp (j2πεn

N+ θ) + n(n) (6.3)

where n(n) is complex white Gaussian noise at time n, nt = δt/Ts is the timing offset, θ is

unknown phase and ε = NTs ·δf is the normalized carrier frequency offset. After correctly

removing the guard interval assuming perfect synchronization, the signal is demodulated

by FFT. The resulting output at the subcarrier k is

Yk = Hk · Ak + Nk (6.4)

for −Nu/2 ≤ k ≤ Nu/2 + 1


Channel

EncoderInterleaver

Bit Allocation

& Mapper

Power

AllocationOFDM Mod

Channel

OFDMDemod

ChannelEstimator

DemapperDeinterleaverChannelDecoder

Data

Out

Feedback

Figure 6.1: Block diagram of the simulated BIC-OFDM system

We define average SNR in the time domain as

SNR , E[|r(n)− n(n)|2]E[|n(n)|2] (6.5)

=E[|Xk|2] · E[|Hk|2]

E[|Nk|2]N

Nu

(6.6)

In our proposed method, assuming channel reciprocity, a clear to send (CTS) or an Ack

packet is used to estimate channel information on each sub-carrier at the transmitter. The

transmitter adjusts constellation size, which is the same for all sub-carriers, and power level

of each sub-carrier for near optimal throughput based on the estimated channel information.

Note that there exists a time delay between the channel estimation and the actual data

transmission. However, the time delay is much smaller than the transmission duration for a

data frame and the resulting channel estimation error is negligible. Fig. 6.1 shows a block

diagram of the simulated BIC-OFDM system. Also we evaluate our method’s performance

through simulation for both an ideal case and a more realistic case with channel estimation

error and synchronization error.


Table 6.1: IEEE 802.11a PHY parametersParameters Value CommentstSlotTime 9 µs slot timetSIFS 16 µs SIFS timeaCWmin 15 min contention window sizeaCWmax 1023 max contention window sizetPLCPPreamble 16 µs PLCP preamble durationtPLCPHeader 4 µs PLCP signal field durationtSymbol 4 µs OFDM symbol time

6.3 Throughput Enhancement

6.3.1 Throughput Analysis

The IEEE 802.11a standard specifies an optional four way hand-shaking procedure, known

as request to send (RTS) / clear to send (CTS) mechanism. Before transmitting a packet,

a station reserves the channel by sending a RTS short frame. The destination station ac-

knowledges the RTS frame by sending the CTS frame, and the normal packet transmission

and Ack response occurs afterwards. The RTS and CTS frames carry the information of

the length of the packet to be transmitted. This information can be read by any listening

stations. Therefore, by detecting either the RTS or CTS frames, the neighboring stations

can delay transmissions and thus avoid collisions. [42].

In this study, we assume no collision of a RTS frame. Timing diagrams of fragment

bursts in the RTS/CTS mechanism are shown in Fig. 6.2 and 6.3. We also assume all con-

trol frames and a Physical Layer Convergence Procedure (PLCP) header are successfully

transmitted since the probability of error in a data frame is much larger than that of other

frames. Table 6.1 lists the related characteristics for the IEEE 802.11a PHY [9].

From the Fig. 6.2 and 6.3, we notice that transmission cycle can be represented by two

time duration as follows: one time duration when a packet is successfully transmitted and

the other time duration when a packet is lost. These two time durations can be represented


as Ts and Tf , which are defined in the following equations,

Ts = tData + tSIFS + tAck + SIFS

Tf = tData + AckTimeout + backoffi

+ tRTS + tSIFS + tCTS + tSIFS (6.7)

where Ts denotes the time duration when a packet is successfully transmitted, Tf denotes

the time duration when a packet is lost and AckTimeout is equal to a tSIFS plus tAck plus

tSlotTime.

The transmission duration for data frame (tData), RTS frame (tRTS), Ack frame (tAck)

and CTS frame (tCTS) are defined as follows,

tData = tPLCPPreamble + tPLCPHeader

+ d28 · 8 + (16 + 6) + L · 8c

e · tSymbol

tRTS = tPLCPPreamble + tPLCPHeader

+ d20 · 8 + 22

ce · tSymbol

tAck = tPLCPPreamble + tPLCPHeader

+ d14 · 8 + 22

ce · tSymbol

tCTS = tAck (6.8)

where L denotes a packet length in bytes and c denotes total data bits in one OFDM symbol.

The random backoff interval is in the unit of tSlotTime and this random integer is uni-

formly distributed over the interval [0,CW]. CW means a contention window size and

its initial value is aCWmin. In the case of unsuccessful transmission, CW is updated to

[2× (CW +1)− 1]. Once CW reaches aCWmax, it remains at that value until it is reset. In

the case of successful transmission, CW is reset to aCWmin. The average backoff interval


RTS

CTS

Frame1

ACK ACK

Frame2

SIFS SIFS

SIFS SIFS

Figure 6.2: Timing of successful frame transmission

RTS

CTS

Frame1

ACK Timeout

CTS

RTS

SIFS

SIFS

Backoff

Figure 6.3: Timing of frame transmission failure

before the ıth transmission attempt can be represented by [41]

backoffi =min[2i−1 · (aCWmin + 1)− 1, aCWmax]

2 / tSlotTime(6.9)

For a simple analysis, we assume only two stations are communicating with each other

with no interference. Under this assumption, the channel is always acquired after random

backoff.

From the above transmission cycle analysis, we can derive a throughput equation. Let

packet error rate (PER) be pe, then the throughput maximization problem can be written as

max8L∑∞

k=0(1− pe) · pke · (kTf + Ts)

(6.10)

where k denotes retransmission attempts. Since Ts and Tf are not dependent on power

distribution and they are constants for given c, optimal power distribution for (6.10) can be

approximately obtained by solving the minimum PER problem.


6.3.2 The Minimum PER Problem

Symbol error probability for square QAM modulation is given by [46]

ps ≤ 4 ·Q(√

3 · E[|Xi|2] · Pi · |Hi|2E[|Ni|2] · (2m − 1)

)(6.11)

where m is a constellation size in bits. Using the Chernoff bound, the average un-coded bit

error probability over the sub-carriers is

pave ≤ 2

m ·Nd

·Nd∑i=1

exp

(−1.5 · E[|Xi|2] · Pi · |Hi|2

E[|Ni|2] · (2m − 1)

)(6.12)

where Nd is the number of data sub-carriers. It was proved in [38] that minimizing PER is

equivalent to minimizing (6.12). Therefore, the minimum PER problem can be simplified

as

min log

[N∑

i=1

e−γi·Pi

]

s.t.∑

Pi = P, Pi ≥ 0 (6.13)

where γi = 1.5·E[|Xi|2]·|Hi|2E[|Ni|2]·(2m−1)

and P represent a total power constraint. Note that the objective

function is convex and has a unique minimum. It can be solved by a simple iterative algo-

rithm using the Lagrange theorem. By the KKT condition, the optimal power distribution

for the minimum PER satisfies following equations.

−γi · e−γi·Pi = KN∑

i=1

1

−γi

ln(−K

γi

) = P (6.14)


i = N

Sort sub-channelsγ

1 > γ

2 > ... > γ

N

Compute power

PER approximation

i = i -1

Pi = 0

yes

no

γ

γ

γ

γ

γ γ( )

++

++

+

−=

i

i

i

P

K

��

��

��

1...

1

ln1

...)ln(1

exp

1

1

1

−

j = 1,2, ... iγ γ

=

jj

j

KP

��ln

1 −−

Check P < 0j −

Figure 6.4: Flow chart for iterative procedure for finding power distribution for minimizingpacket error rate

where K is a constant. If one or more of Pi < 0, then Pj of the sub-carrier that has the

smallest channel gain is set to zero and (6.14) is solved again with N → N − 1 until all

the constraints are met. This iterative procedure can be implemented by the flow chart of

Fig. 6.4. Since the above method uses the upper bound as a cost function, we can not say

this procedure is optimal in a strict sense. However the upper bound approach can result in

a robust PER performance when a closed form formula is not available and is very close to

the actual performance for most SNR ranges of interest.


6.3.3 Throughput Enhancement Method

After acquiring the optimal power distribution for minimum PER, (6.12) can be calculated

again as

p∗ave ≤2

m ·N∗ ·N∗∑i=1

exp

(−1.5 · E[|Xi|2] · P ∗

i · |Hi|2E[|Ni|2] · (2m − 1)

)(6.15)

where N∗ is the number of sub-carriers used after the optimization procedure. It can be

shown that the probability of decoding the all-zero codeword as the ıth codeword with

distance d is upper bounded by [43].

pd ≤ [4 · p∗ave(1− p∗ave)]d/2 (6.16)

Using the above quantity, the union bound on the first-event error probability, p∗u, is bounded

by

pu ≤∞∑

d=dfree

ad · pd (6.17)

where ad is the total number of error events of distance d. From this union bound, the

resulting PER, p∗e, can be predicted heuristically using the method in [38] and [44].

pe ≈Lβ· pu

1 + Lβ· pu

(6.18)

where β is a constant which can be obtained by empirical fitting. Therefore, the constella-

tion size m for maximizing (6.10) can be obtained using the predicted PER. Fig. 6.5 shows

an example plot of constellation size selection during a 50ms interval. Diamond shapes in

the x-axis represent the times of erroneous packet receptions and the bottom plot represents

an average channel gain across sub-carriers at that time. It can be seen that the proposed


method finds the best constellation size for maximum throughput even if it results in more

packet errors. In other words, the proposed method compensates the decreased spectral

efficiency due to the power optimization by assigning an optimal constellation size to max-

imize the throughput. Based on the results from our analysis, the throughput enhancement

method can be summarized by following steps:

1. Set the constellation size m for modulation.

2. Calculate Ts and Tf based on the constellation size and the number of retransmission

attempts at that time.

3. Find a power distribution for minimum PER.

4. Calculate throughput using PER, Ts and Tf obtained from step (3) and (2). (6.3.1)

5. Change constellation size and go back to step (2) until all throughput values for all

possible constellation sizes are obtained.

6. Find the maximum among the obtained throughput values and set constellation size

and power distribution according to the maximum.



To evaluate the performance of the proposed method in frequency selective channels, a

simulator has been developed according to the parameters specified in the 802.11a standard

[9]. We assume an infinite resolution for an analog to digital converter and a perfectly

linear amplifier at the transceiver. The simulation parameters are listed in Table 6.2. For

the channel model, only small-scale fading is considered. Both the distance dependent path


0 0.01 0.02 0.03 0.04 0.050

2

4

6

m

Time (seconds)

0 0.01 0.02 0.03 0.04 0.050

1

2

3

Time (seconds)

E[|H

k|2

Packet error

Figure 6.5: An exemplary plot of constellation size variation with respect to time

loss and the shadowing are assumed to be constant over the simulation and incorporated

into the SNR. Two different power delay profiles (PDPs), Channel A and B in Fig 2.2[4],

are generated and the time variation model in Chap 2 is employed. Details of random

channel generations are described in Sec 3.4. Moreover, packet length, L, is set to be

540 bytes and the proposed synchronization methods in Chapter 3 and 4 and the proposed

channel estimation method in Chapter 5 are used for simulation.

6.4.2 Performance of the Proposed Inner Receiver

Fig. 6.6 and Fig. 6.7 show the comparison of performance between a conventional 802.11a

system and the system with the proposed synchronization and channel estimation methods

at the receiver in Channel A and Channel B. The ordinate represents throughput in Mbps

and the abscissa represents an average SNR defined in (6.5). It can be seen that the system

with the proposed methods significantly improves throughput over a conventional 802.11a


Table 6.2: Simulation ParametersSampling time, Ts 50nsFFT length, N 64Number of used sub-carriers, Nu 52Number of data sub-carriers, Nd 48Number of pilot sub-carriers, Np 4Guard interval length, Ng 16Subcarrier spacing 312.5 KHzModulation 4-QAM, 16-QAM, 64-QAMNumber of packets 10000Channel coding rate 1/2Packet length 540 Bytes

system in all SNR region we have tested. The performance gain for Channel B is much

larger than that for Channel A. Furthermore, the performance gain increases as the mod-

ulation becomes more complex. As shown in Chapter 3, this result is expected since a

conventional timing estimator often does not find a good timing boundary for the power

delay profile of Channel B. Hence, significant ISI and inter-carrier interference (ICI) are

induced. Moreover, as the constellation size increases, the system becomes more sensitive

not only to the synchronization error but also to the channel estimation error and an error

floor results.

6.4.3 Performance of Throughput Optimization

Fig. 6.8 shows the performance improvement by the throughput optimization. The solid

lines represent the performance of the system with the proposed inner receiver and without

an optimization. The line with circle represents the performance of the system with the

proposed optimization method and the proposed inner receiver. The ordinate represents

throughput in Mbps and the abscissa represents an average SNR defined in (6.5). We can

see that the proposed method improves throughput particulary for transition region between

two different modulations. The performance gain is maximized around the SNR boundary


10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

4−QAM16−QAM64−QAM

(a) Inner Rcv in Channel A

10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)


(b) Inner Rcv in Channel B

Figure 6.6: Throughput comparison for improved inner receiver: Channel A & B


10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)


(a) Conventional system in Channel A

10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)


(b) Conventional system in Channel B

Figure 6.7: Throughput comparison for conventional system : Channel A & B


of two different modulations, such as 16dB and 24dB, since the proposed method has more

degrees of freedom to select power allocation and constellation size. If SNR is larger than

30dB, the performance gain becomes negligible since the average SNR is large enough

to use 64-QAM modulation for all sub-carriers in this region. Note that the performance

improvement generally becomes larger as the frequency diversity increases. For example,

the performance improvement for Channel B is greater than that for Channel A as shown

in Fig. 6.8 and Fig. 6.9. This happens since less power is allocated to the sub-carriers with

low channel gains to increase the minimum distance of the channel code. Fig. 6.9 shows

the same throughput results with a conventional 802.11a system for comparison. We can

see that the system with the proposed methods significantly outperforms a conventional

system.

6.4.4 Benefits of Throughput Optimization

Fig. 6.10 shows the performance result of the throughput optimization with a conventional

receiver. Unlike the previous result, the improvement from the optimization is limited to

a small range of SNR for Channel A. Moreover, the optimization can degrade the system

performance in Channel B. The rationale behind this is that the channel estimation and

the synchronization error not only result in erroneous optimization at the transmitter but

also they degrade the system performance at the receiver. Therefore, the proposed opti-

mization method is more sensitive to the channel estimation and the synchronization error

than a conventional 802.11a system. The optimization consistently shows somewhat better

performance in Channel A where the channel estimation and the synchronization error are

smaller than Channel B.


10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt+Inner

(a) adaptive transceiver with Inner Rcv in Channel A

10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt+Inner

(b) adaptive transceiver with Inner Rcv in Channel B

Figure 6.8: Throughput comparison for adaptive transceiver in Channel A & B


10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt+Inner

(a) adaptive transceiver with Conventional in Channel A

10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt+Inner

(b) adaptive transceiver with Conventional in Channel B

Figure 6.9: Throughput comparison for adaptive transceiver in Channel A & B


10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt only

(a) adaptive transceiver with Conventional in Channel A

10 15 20 25 300

5

10

15

20

Average SNR (dB)

Thr

ough

put (

Mbp

s)

Opt only

(b) adaptive transceiver with Conventional in Channel B

Figure 6.10: Throughput comparison for only adaptive transceiver in Channel A & B


6.5 Conclusions

We propose a simple throughput enhancement method by deriving a throughput equation

for the 802.11a system. The key ideas are 1) RTS/CTS frame exchange is used to circum-

vent a hidden node problem and to acquire channel information at the transmitter before

the data transmission begins. an Ack frame is used to acquire channel information af-

ter successful data transmission and 2) the transmitter uses this information to optimize

throughput performance without reducing throughput due to explicit feedback. The com-

plexity of the optimum solution can be reduced by a simple iterative algorithm. A typical

office environment is simulated with system parameters specified in the 802.11a standard.

Our simulation results show that the proposed method can significantly improve through-

put performance. However, the performance gain depends on the channel estimation error

and the synchronization error. Therefore, an improved inner receiver is required to achieve

significantly improved performance. Finally, our method can be used to perform similar

analysis for other practical systems with different codings and other implementation con-

straints.

Chapter 7

Conclusion

7.1 Summary

In this section, each chapter of the thesis is briefly summarized. Chapter 2 describes charac-

teristics of small scale fading in wireless channels which are suitable for describing indoor

wireless communications. After a brief overview of the ETSI channel models, we propose a

closed form autocorrelation model for temporal variation of indoor wireless channels. It is

important to understand different characteristics and properties of indoor wireless channels

compared to those of the mobile wireless channels because the measurements for indoor

channels show distinct differences from the mobile channel measurements. The proposed

model gives rise to more peaky Doppler spectrum and has a wider spread of power spec-

trum than the Jakes’s model. Consequently, our proposed model can be used for more

accurate simulations of indoor wireless systems and we have shown that our model closely

matches indoor channel measurements.

In Chapter 3, we propose an adaptive timing estimation method for OFDM systems. By

changing an observation window length, the first arriving path can be located even though

it may not be the strongest path. By doing so, ISI and ICI can be effectively removed. Our

method does not require any prior knowledge, such as signal to noise ratio (SNR) or power

97

CHAPTER 7. CONCLUSION 98

delay profile, and is robust to various channel environments. In addition, it also provides an

estimate of instantaneous total received power and the maximum delay spread which can

then be used in other applications to increase system throughput. Our computer simulation

results show that the proposed method can significantly improve error rate performance.

The performance gain becomes higher as delay spread increases.

Chapter 4 describes a residual frequency offset (RFO) compensator that compensates

both RFO and RFO induced PE by using the Kalman filter. In our proposed method, after

the state-space model for RFO and PE is derived, a Kalman filter is applied to track and

to estimate RFO and PE simultaneously. This method, compared to least square (LS)

phase fitting, offers an improved estimation and tracking behavior for RFO and has less

complexity. Numerical results show that the proposed method significantly compensates

the performance degradation due to RFO and achieves an almost ideal PER performance.

In Chapter 5, we proposed an enhanced DFT-based channel estimation using Kalman

filtering and smoothing for OFDM systems with virtual subcarriers (VCs) in a multipath

fading channel. VCs are used to ease a shaping filter implementation and to provide a

guard band. However, it also causes dispersive distortion in a channel impulse response

and prohibits the use of conventional DFT-based channel estimation. Our proposed method

achieves almost equivalent performance compared to the optimal minimum mean square

error (MMSE) channel estimation. Furthermore, it does not require knowledge of channel

statistics, and the implementation complexity is lower than the optimal MMSE channel

estimation.

In Chapter 6, we propose a simple throughput enhancement method by deriving a

throughput equation for 802.11a systems. The key ideas are 1) ready to send (RTS)/clear

to send (CTS) frame exchange is used to circumvent a hidden node problem and to acquire


channel information at the transmitter before the data transmission begins. An acknowl-

edgement (Ack) frame is used to acquire channel information after successful data trans-

mission begins and 2) the transmitter uses this information to optimize throughput perfor-

mance without reducing throughput due to explicit feedback. The complexity of the opti-

mum solution can be avoided by a simple iterative algorithm. A typical office environment

is simulated with system parameters specified in the 802.11a standard. Simulation results

show that the proposed method can significantly improve throughput performance. How-

ever, the performance gain is dependent on the channel estimation and the synchronization

error and hence an improved inner receiver is required to achieve improved performance.

7.2 Future Work

This thesis discusses a few interesting problems related to designing adaptive OFDM sys-

tems and provides some solutions to them. Still, many interesting theoretic questions are

open and many practical constraints should be considered for a practical implementation.

First, synchronization is one of the most critical issues in OFDM systems and other

communication systems. It has great impact on ther issues, such as channel estimation,

equalization and decoding, to be implemented in communication systems. In Chapter 3 and

Chapter 4, details of the proposed synchronization methods based on adaptive techniques

have been discussed. In wireless LAN (WLAN) systems, carrier frequency synchroniza-

tion and symbol synchronization are done using a preamble transmitted as the header of

the packet. Although our work did not assume that a user has access to statistical knowl-

edge of the channel, it is still based on an additive Gaussian noise assumption. Therefore,

the sensitivity of system performance under different assumptions should be studied to see

the robustness of our methods. In addition, this work is done at the expense of a reduced

bandwidth efficiency. Blind and/or semi-blind algorithms can improve the estimation ac-

curacy without pilots or training symbols. In this dissertation, we did not consider blind


algorithms since they require significant statistical knowledge of both signals and channels

and can lead to a high computational complexity. Therefore, low computational complex-

ity blind algorithms should be studied to see if the performance of OFDM systems can be

further improved.

Second, only single-antenna wireless channel models are considered in this thesis.

However, new wireless networks have started to employ multiple antennas, which would

require more complex channel models. In addition, the distribution of channels for different

users may not be the same in these systems. Significant interference from inside or outside

of a single network can also exist. With more practical channel models, the mathematical

analysis of adaptive communications can become a daunting task. However, in principle,

the methods proposed in this thesis can be modified to be used in such practical channels

and could be verified by numerical simulations.

Third, the channel estimation method presented in Chapter 5 only considers a case for

indoor communication systems (WLAN). However, in a mobile channel, channel variation

within a OFDM packet can be significant and pilot subcarriers for channel estimation are

distributed across the time and the frequency. Consequently, interpolation techniques are

used to track the channel variation within a packet. Therefore, it would be interesting to

extend the result of this study to an mobile case such as a mobile worldwide interoperabil-

ity for microwave access (WiMAX). Further, a more sophisticated time series model can

be employed to represent a state-space model for a channel frequency response since an

autocorrelation matrix is no longer singular for an interpolation case. To derive a suitable

time series model, the Akaike’s information criterion or the Bayesian information criterion

can be used to determine the order of the time series model.

Finally, in Chapter 6, channel reciprocity is assumed to derive an optimal power alloca-

tion and a constellation size. In reality, however, the channel reciprocity is not perfect due

to the difference in hardware between a transmitter and a receiver. Therefore, the robust-

ness of the method to non-reciprocity should be investigated before applying it to practical


communication systems. Furthermore, the only constraints we considered for the power

allocation is that it is greater than zero. However, there is a maximum allowed power

transmission for each subcarrier in real communication systems and hence the maximum

power constraint should be added in the objective function. For this case, there is no simple

iterative algorithm for optimization. This kind of problem can consequently increase imple-

mentation complexity significantly. Therefore, the benefits of the optimization should be

studied to see how much improvement can be achieved given the implementation complex-

ity. These analysis will lead to a better understanding of the adaptive OFDM transceiver

and to a more robust improvement of conventional OFDM systems without adaptation.

Bibliography

[1] R. V. Nee and R. Prasad, ”OFDM For Wireless Multimedia Communications”,

Artech House Publishers, 2000

[2] T. S. Rappaport, ”Wireless Communications: Principles and Practice”, Prentice

Hall, 2002.

[3] Donald C. Cox, ”Introduction to Wireless Communication”, EE276 Course

Reader, Stanford University, 2008

[4] J. Medbo and P. Schramm, Channel Models For HIPERLAN/2 in Different In-

door Scenarios, ETSI/BRAN document no. 3ERI085B

[5] S.J.Howard and K.Pahlavan, ”Doppler spread measurements of the indooor radio

channels”, Electron. letter., vol. 26, no. 2, pp. 107-109, Jan. 1990

[6] A. Domazetovic, L.J. Greenstein, N.B. Mandayam and I. Seskar, ”Estimating the

Doppler spectrum of a short-range fixed wireless channel”, IEEE Transactions

on Communications, vol. 53, No. 7, pp. 1123-1126, Jul. 2005

[7] S. Thoen, L. Van der Perre and M. Engels, ”Modeling the Channel Time-

Variance for Fixed Wireless Communications”, IEEE Communications Letters,

Vol. 6, No. 8, pp. 331-333, Aug. 2002.

102

BIBLIOGRAPHY 103

[8] Vinko Erceg. Zyray Wireless et al., ”TGn Channel Models”, IEEE 802.11-

03/940r4, May 2004.

[9] IEEE 802.11a-1999: Wireless LAN Medium Access Control (MAC) and Physical

Layer (PHY) Specifications: High Speed Physical Layer in the 5 GHz Band,

1999

[10] IEEE 802.16a-1999: IEEE Standard for Local and Metropolitan Area Networks

Part 16: Air Interface for fixed Broadband Wireless Access Systems, Amendment

2: Medium Access Control Modifications and additional Physical Layer Specifi-

cations for 2-11GHz, 2003

[11] Y. Mostofi and D. Cox, ”Mathematical Analysis of the Impact of Timing Syn-

chronization Errors on the Performance of an OFDM System”, IEEE Trans. on

Comm., vol. 54, no. 2, 2006

[12] J.Beek, M. Sandell and P. Borjesson, ”ML Estimation of Time and Frequency

Offset in OFDM Systems”, IEEE Trans. Signal Proc., vol.45, pp.1800-1805,

1997

[13] T. Schmidl and D. C. Cox, ”Robust frequency and timing synchronization for

OFDM”, IEEE Trans. Commun, vol.45, pp.1613-1621, 1997

[14] F. Classen, ”Systemkomponenten fur eine terrestrische digitale mobile Breitban-

dubertragung”, Ph.D Dissertation,the RWTH-Aschen Germany: Shaker Verlag,

1996

[15] M. Speth, F. Classen and H. Meyer, ”Frame synchronization of OFDM systems

in frequency selective fading channels”, Proc. Vehicular Tech. Conf., 1997

[16] K. Wang, M. Faulkner and I. Tolochko, ”Timing Synchronization for 802.11a

WLANs under Multipath Channels”, Proc. ATNAC 2003

BIBLIOGRAPHY 104

[17] S. Chang and B Kelly, ”Time synchronization for OFDM-based WLAN sys-

tems”, IEE Electronics Letters, vol.39, pp.1024-1026, 2003

[18] A. Fort, J. Weijers, V. Derudder, W Eberle and A. Bourdoux, ”A performance

and complexity comparison of auto-correlation and cross-correlation for OFDM

burst synchronization”, ICASSP Proceedings, Hong Kong, 2003

[19] S. Manusani, R. Kshetrimayum and R. Bhattacharjee, ”Robust Time and Fre-

quency Synchronization in OFDM based 802.11a WLAN systems”, Anual India

Conf., 2006

[20] A. Fort and W. Eberle, ”Synchronization and AGC proposal for IEEE 802.11 a

burst OFDM systems”, em IEEE Globe Comm., 2003

[21] P. Moose, ”A technique for orthogonal frequency division multiplexing fre-

quency offset correction”, IEEE Trans. Comm., vol. 42, pp.2908-2914, 1994

[22] J. Li, G. Liu and G. Giannakis, ”Carrier Frequency Offset Estimation for OFDM

based WLAN”, IEEE Signal Processing Letters, vol.8, pp.80-82, 2001

[23] S. Chang and E. Powers, ”Efficient frequency-offset estimation in OFDM-based

WLAN systems”, IEE Electronics Letters, vol.39, pp.1554-1555, 2003

[24] J. Lee, H. Lou and J. Cioffi, ”SNR Analysis of OFDM Systems in the Presence

of Carrier Frequency Offset for Fading Channels”, IEEE Trans. Wireless Comm.

vol.5, pp.3360-3364, 2006

[25] J. Jo, H. Kim and D. Han, ”Residual frequency offset compensation for IEEE

802.11a”, Vehicular Technology Conference, 2004

[26] J. Lee and S. Kim, ”Residual frequency offset compensation using the approxi-

mate SAGE algorithm for OFDM system”, IEEE Trans. Comm., vol.54, pp.765-

769, 2006

BIBLIOGRAPHY 105

[27] P. Chia-Sheng, W. Kuei-Ann, ”Synchronization for Carrier frequency Offset in

Wireless LAN 802.11a System”, Proc. Wireless Personal Multimedia Comms.

Conf., 2002

[28] B. Chen and C Tsai, ”Frequency offset estimation in an OFDM system”, IEEE

IEEE Third Workshop on Signal Processing Advances in, pp.150-153, 2001

[29] J. Liu and J. Li, ”Parameter estimation and error reduction for OFDM-based

WLANs”, IEEE Trans. Mobile Computing, vol.3, pp.152-163, 2004

[30] O. Edfors, M. Sandel, J.-J. van de Beek, S. K. Wilson and P. O. Borjesson,

”OFDM channel estimation by singular value decomposition”, IEEE Trans.

Commun., vol. 46, no. 7, pp. 931-939, Jul. 1998.

[31] J.-J. van de Beek, O. Edfors, M. Sandel, S. K. Wilson and P. O. Borjesson, ”On

channel estimation in OFDM systems”, Proc. IEEE VTC95, pp. 815-919, Jul.

1995.

[32] H.Minn and V.K. Bhargava, ”An Investigation into time-domain approach for

OFDM channel estimation”, IEEE Trans. Broadcasting, vol. 46, no. 4, pp. 240-

248, Dec. 2000

[33] B. Yang, Z. Cao and K. B. Letaief, ”Analysis of low-complexity windowed DFT-

based MMSE channel estimator for OFDM systems”, IEEE Tran. Commun., vol.

49, no. 11, pp. 1977-1987, Nov. 2001.

[34] Dong Li, Feng Guo, Guosong Li, Liyu Cai, ”Enhanced DFT Interpolation-based

Channel Estimation for OFDM Systems with Virtual Subcarriers”, Vehicular

Technology Conference, 1580-1584, Spring 2006/

[35] Marple SL Jr., ”Digital spectral analysis with applications”, Prentice Hall, New

Jersey, 1987/

BIBLIOGRAPHY 106

[36] Kareem E. Baddour and Norman C. Beaulieu, ”Autoregressive modeling for fad-

ing channel simulation”, IEEE Transactions on Wireless Communications 4(4):

1650-1662, 2005

[37] P. A. Bello. ”Characterization of randomly time-variant linear channels” IEEE

Trans., vol. CS-11, no. 4, pp 360-393, 1963

[38] O. Awoniyi, O. Oteri and F. Tobagi, ”Adaptive Power Loading in OFDM-based

WLANs and Resulting Performance Improvement in Voice and Data Applica-

tions”, Vehicular Technology Conference, vol.2, pp. 789-794, Fall 2005

[39] H. Moon, ”Efficient Power Allocation for coded OFDM Systems”, Ph. D. Dis-

sertation, Stanford University, 2004

[40] A. Kamerman and L. Monteban, ”WaveLAN-: A High-Performance wireless

LAN for the Unlicensed Band”, Bell Labs Technical J., pp.118-133, summer

1997

[41] D. Qiao, S. Choi and K. Shin, ”Goodput analysis and link adaptation for IEEE

802.11a wireless LANs”, IEEE Trans. Mobile Computing, vol.1, pp.278-292,

Oct 2002

[42] G. Bianchi, ”Performance analysis of the IEEE 802.11 distributed coordination

function”, IEEE Journal on Selected Areas in Communication, vol.18, no.3,

March 2000

[43] D. G. Wilson, ”Digital Modulation and Coding”, Prentice Hall 1996

[44] K. Rege and S. Nanda, ”Irreducible FER for Convolutional Codes with Random

Bit Puncturing: Application to CDMA Forward Channel”, Vehicular Technology

Conference, vol.2, pp.1336-1340, Spring 1996

BIBLIOGRAPHY 107

[45] W. C. Jakes, ”Microwave Mobile Communication”, Wiley Publishers, 1974

[46] A. Goldsmith, ”Wireless Communications”, Cambridge University Press, 2005

dissertation wonchae kim

Documents

indoor wireless channel

indoor wireless systems

performance of ofdm

wireless access

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mobile systems

estimation errors