MMSE/LSE ESTIMATION AND EQUALIZATION FOR ......Ultra-Wide Band (UWB) radio is a fast-emerging...

MMSE/LSE ESTIMATION AND EQUALIZATION

FOR BETTER SIGNAL QUALITY AND PACKET DETECTION

IN ULTRA-WIDE BAND SYSTEMS

by

JEBIN JACOB

DALE W. CALLAHAN, COMMITTEE CHAIR

GREGORY A. FRANKLIN

THOMAS C. JANNETT

A THESIS

Submitted to the graduate faculty of The University of Alabama at Birmingham

in partial fulfillment of the requirements for the degree of

Master of Science

BIRMINGHAM, ALABAMA

2010

ii

MMSE/LSE ESTIMATION AND EQUALIZATION

FOR BETTER SIGNAL QUALITY AND PACKET DETECTION

IN ULTRA-WIDE BAND SYSTEMS

JEBIN JACOB

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

ABSTRACT

Ultra-Wide Band (UWB) radio is a fast-emerging technology that operates at a

huge bandwidth using low-power and ultra-short information-bearing pulses. Coupled

with Orthogonal Frequency Division Multiplexing (OFDM) which is highly efficient in

terms of bandwidth utilization and a robust multi-carrier modulation scheme, UWB can

be an effective solution to the demand for low-cost, high-speed, wireless links for short-

range communication.

Packet detection is defined as the process of detecting the presence of data packet

symbols in the received signal. The Federal Communications Commission (FCC) has

limited the maximum emission strength of all UWB signals to be very close to the noise

floor, which is defined as the strength of the sum of all noise sources, such as thermal

noise and other interfering signals present in a communication channel. This limitation on

emission strength increases the chances of a receiver missing a packet symbol, and

ultimately the whole system can go out of synchronization. This situation demands a very

high signal quality at the UWB receiver so that the probability of packet detection is high

and the system remains synchronized.

This thesis explores Minimum Mean-Square Error (MMSE) and Least-Squares

Error (LSE) methods for estimating the impulse response of the UWB channel. Digital

signal processing is performed on the received signal using the estimated impulse

iii

response to carry out a process called equalization. Equalization helps increase the signal

quality by improving the signal peaks and lowering the noises during correlation. The

processed output is called the equalized output.

Extensive simulations were carried out to establish the effectiveness of schemes

for improving the received signal quality in an UWB communication system. Based on

the distance between the transmitter and receiver and their line-of-sight as defined by the

IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs), four

different channel scenarios were considered for the simulation. Results show that the

MMSE and LSE equalizers improve the overall signal quality and make the equalized

outputs more accurate and similar to the transmitted signal.

iv

DEDICATION

This thesis is dedicated to my family and friends, for the never-ending love,

support, and encouragement they have given me.

v

ACKNOWLEDGMENT

It is a pleasure to thank the many people who made this thesis possible.

First, I thank my advisor, Dr. Dale W. Callahan, for his invaluable advice, kind

assistance, and contribution towards the thesis; without him, this thesis would have been

impossible.

My sincere gratitude is extended to my committee members, Dr. Gregory A.

Franklin and Dr. Thomas C. Jannett, from the Department of Electrical and Computer

Engineering.

I especially thank Dr. Jeffrey R. Foerster, for his kind help and technical

assistance during my thesis.

From the formative stages of this thesis to the final draft, I owe an immense debt

of gratitude to my mentor, Dr. George P. Koomullil. I also thank Dr. Roy P. Koomullil

for his guidance, love, and support, which were invaluable in the completion of this

thesis.

I am grateful to Ms. Sandra Muhammad for assisting me with all of the

administrative formalities required to bring my thesis to completion.

Last and most important I wish to thank my parents, Jacob P. Koomullil and Saly

Jacob. They raised me, supported me, taught me, and loved me. Their support and

confidence in me helped make the completion of my graduate work possible.

vi

TABLE OF CONTENTS

Page

ABSTRACT........................................................................................................................ ii

DEDICATION ................................................................................................................... iv

ACKNOWLEDGMENTS................................................................................................... v

LIST OF TABLES ............................................................................................................. ix

LIST OF FIGURES............................................................................................................. x

LIST OF ABBREVIATIONS ..........................................................................................xiii

CHAPTER

I. INTRODUCTION .................................................................................................. 1

A. Ultra-Wide Band Communication and its Importance.............................. 1

B. Problem Definition .................................................................................... 3

C. Approach and Contribution ....................................................................... 4

D. Thesis Outline............................................................................................ 6

II. MULTIBAND OFDM UWB SYSTEM ................................................................ 8

A. History of UWB ........................................................................................ 8

B. Definition of UWB ................................................................................ 10

C. Types of UWB......................................................................................... 11

D. Regulatory Issues .................................................................................... 14

E. Introduction of Multiband OFDM System .............................................. 15

F. OFDM System Model.............................................................................. 18

1) Transmitter............................................................................... 18

2) Receiver ................................................................................... 19

G. Mathematical Analysis of OFDM ........................................................... 19

H. Overview of an UWB Model .................................................................. 21

1) Bernoulli Binary....................................................................... 22

2) Rate Encoder............................................................................ 22

3) Interleaver ................................................................................ 22

vii

TABLE OF CONTENTS (CONTINUED)

Page

4) QPSK Modulator ................................................................... 22

5) OFDM Transmitter ................................................................ 22

6) Frequency Hopping and Filtering .......................................... 23

7) UWB Channel........................................................................ 24

8) Frequency Dehopping and Filtering ...................................... 24

9) OFDM Receiver..................................................................... 24

10) QPSK Demodulator ............................................................... 24

11) Synchronization ..................................................................... 24

12) Deinterleaver.......................................................................... 25

13) Viterbi Decoder...................................................................... 25

III. UWB TIMING SYNCHRONIZATION............................................................... 26

A. Synchronization....................................................................................... 26

1) Frequency Synchronization .................................................... 26

2) Timing Synchronization.......................................................... 27

B. Packet Detection ...................................................................................... 27

C. Packet Detection Algorithms................................................................... 30

1) Received Signal Energy Detection ......................................... 30

2) Double Sliding Window Packet Detection ............................. 30

3) Correlation Detection.............................................................. 32

4) Delayed Correlation or Autocorrelation Detection................. 33

IV. RESEARCH METHODOLOGY......................................................................... 36

A. Introduction ............................................................................................. 36

B. System Model .......................................................................................... 37

C. Standard Test Data................................................................................... 38

D. UWB Channel Model.............................................................................. 39

E. Cross-Correlation..................................................................................... 46

F. Autocorrelation ..................................................................................... 46

G. MMSE and LSE Estimators .................................................................... 48

H. Data Analysis .......................................................................................... 49

I. UWB Operating SNRs............................................................................. 50

J. MMSE/LSE Channel Estimation and Signal Equalization

Block Diagram ........................................................................................ 52

V. RESULTS.............................................................................................................. 56

VI. DISCUSSION ....................................................................................................... 66

viii

TABLE OF CONTENTS (CONTINUED)

Page

VII. CONCLUSION AND FUTURE WORK ............................................................ 71

A. Conclusion............................................................................................... 71

B. Future Work............................................................................................. 73

LIST OF REFERENCES .................................................................................................. 74

ix

LIST OF TABLES

Table Page

1 Summary of FCC Restrictions on UWB Operation .............................................. 17

2 Summary of the Four Channel Model Properties.................................................. 40

3 Channel Characteristics and Corresponding Model Parameters .......................... 42

x

LIST OF FIGURES

Figure Page

1 Spatial capacity comparison between IEEE 802.11, Bluetooth, and UWB............ 2

2 Comparison of the fractional bandwidth of a narrow band and UWB

communication system ......................................................................................... 10

3 Spectrum of an Impulse Ultra-Wide Band signal ................................................ 13

4 Spectrum of an OFDM-based MB-UWB signal ................................................... 13

5 FCC spectral mask for UWB systems .................................................................. 16

6 FCC spectral mask for UWB systems .................................................................. 16

7 An ideal model of an OFDM transmitter ............................................................. 19

8 An ideal model of an OFDM receiver................................................................... 20

9 Top level model of a typical UWB system ........................................................... 23

10 Application of the packet detection in the timing synchronization....................... 29

11 Packet detection using received signal energy detection method ......................... 31

12 Packet detection using double sliding window packet detection method ............. 32

13 Packet detection using cross-correlation detection method .................................. 34

14 Packet detection using delayed correlation detection method .............................. 35

15 Base-band OFDM system ..................................................................................... 37

16 Block diagram of test data constructed using PLCP preamble ............................. 39

17 Impulse response realization for channel model 1 ................................................ 43


xi

LIST OF FIGURES (CONTINUED)

Figure Page


20 Impulse response realization for channel model 4 ............................................... 45

21 Cross-correlation between test series f(t) and PLCP preamble g(t) ...................... 47

22 Autocorrelation plot of the test series f(t) using a single PLCP period g(t) .......... 48

23 Available SNR at the receiver as a function of distance between

the UWB transmitter and the receiver................................................................... 53

24 Steps involved in the estimation and equalization process using the

MMSE/LSE estimation and equalization method................................................. 55

25 PLCP preamble cross-correlated with ideal channel output (a),

non-equalized output (b), MMSE equalized output (c), and

LSE equalized output (d). ..................................................................................... 57

26 PLCP preamble cross-correlated with ideal channel output (a),

non-equalized output (b), MMSE equalized output (c), and

LSE equalized output (d) ..................................................................................... 57

27 Expanded version of Fig. 26 ............................................................................... 58

28 Autocorrelation using ideal channel output (a), non-equalized

output (b), MMSE equalized output (c), and LSE equalized

output (d). ............................................................................................................. 59

29 Autocorrelation using ideal channel output (a), non-equalized

output (b), MMSE equalized output (c), and LSE equalized

output (d) ............................................................................................................. 59

30 Average autocorrelation power for ideal channel output, non-

equalized output, MMSE equalized output, and LSE equalized

output ................................................................................................................... 60



output ................................................................................................................... 61

xii

LIST OF FIGURES (CONTINUED)

Figure Page



output ................................................................................................................... 61



output ................................................................................................................... 62



output ................................................................................................................... 62

35 Cross-correlation PAPR for ideal channel output, non-equalized

output, MMSE equalized output, and LSE equalized output................................ 63








output, MMSE equalized output, and LSE equalized output................................. 65

xiii

LIST OF ABBREVIATIONS

ADC Analog to Digital Converter

AWGN Additive White Gaussian Noise

DAC Digital to Analog Converter

DARPA Defense Advanced Research Projects Agency

dB Decibel

dBm Decibel-milliWatt

DSSS Direct-Sequence Spread Spectrum

DS-UWB Direct Sequence Ultra-Wide Band

ECMA European Computer Manufacturers Association

EIRP Effective isotropic radiated power

ESD Energy Spectral Density

FAA Federal Aviation Administration

FCC Federal Communications Commission

FEC Forward Error Correction

FFT Fast Fourier Transform

GPS Global Positioning System

HDTV High Definition Television

IEEE Institute of Electrical and Electronics Engineers

IFFT Inverse Fast Fourier Transform

xiv

LIST OF ABBREVIATIONS (CONTINUED)

I-UWB Impulse Ultra-Wide Band

LANL Los Alamos National Laboratory

LLNL Lawrence Livermore National Laboratory

LSE Least-Squared Error

MB Multi-Band

MC Multi-Carrier

MIR Micro power Impulse Radar

MMSE Minimum Mean-Squared Error

NTIA National Telecommunications and Information Administration

OFDM Orthogonal Frequency Division Multiplexing

PAM Pulse Amplitude Modulation

PAPR Peak-to-Average Power Ratio

PLCP Physical Layer Convergence Protocol

PN Pseudo Noise

PPM Pulse Position Modulation

PSK Phase-Shift Keying

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase-Shift Keying

RF Radio Frequency

SNR Signal to Noise Ratio

TH-UWB Time-Hopping Ultra-Wide Band

USAF United States Air Force

xv

LIST OF ABBREVIATIONS (CONTINUED)

USB Universal Serial Bus

UWB Ultra-Wide Band

WiFi Wireless Fidelity

WPAN Wireless Personal Area Network

1

I. INTRODUCTION

A. Ultra-Wide Band Communication and its Importance

One of the main features of any Ultra-Wide Band (UWB) communication system

is its huge bandwidth. Usually, the instantaneous available bandwidth is much higher

than what the communication system actually needs to deliver the data [1]. Shannon’s

channel capacity equation gives the maximum data rate that can be achieved for a given

bandwidth and signal-to-noise ratio (SNR) in a data channel [2].

+×=N

SBC 1log 2 (1)

In (1), C is the maximum channel capacity in bits/sec, B is the channel bandwidth in Hz,

S is the signal power in watts, and N is the noise power in watts. The traditional narrow

band technologies focus on improving the SNR to increase the data rate. However, the

UWB uses a larger bandwidth to increase the total throughput through the channel. From

(1), it is evident that the data capacity increases faster with an increase in bandwidth

rather than an increase in the SNR. As a result, the UWB system can achieve higher data

throughput than a traditional narrowband system.

The spatial capacities of some of the wireless standards that are being developed

by the Bluetooth special interest group and the Institute of Electrical and Electronics

Engineers (IEEE) 802 working group are shown in Fig. 1. Spatial capacity is defined as

the total data throughput of all the systems that can coexist in a non-interfering basis in an

available spectrum and area and is calculated as the ratio of total throughput to the area

2

for a given wireless standard [3]. The spatial capacities of other narrowband wireless

standards are nowhere comparable to that of UWB (Fig. 1). The limited capacities of

other standards can be traced back to the restricted available bandwidth for these systems,

since all of the systems are bound by the channel capacity theorem. UWB systems have a

very high data throughput, since they usually have more than 2 GHz of available

spectrum [3].

0

200

400

600

800

1000

1200

Wireless Standards

Projected Spatial Capacity (kbps)

802.11b

1 kbps/sq.m

Bluetooth 1

30 kbps/sq.m

802.11a

83 kbps/sq.m

Ultra Wideband

1000 kbps/sq.m

Fig. 1. Spatial capacity comparison between IEEE 802.11, Bluetooth, and UWB.

Even though UWB can provide a very high channel capacity, this very high data

throughput is available only at a limited range. The Federal Communications

Commission (FCC) mandated the Effective Isotropic Radiated Power (EIRP) emission of

all UWB signals to be very close to the noise floor. Noise floor is defined as the strength

of the sum of all noise sources, such as thermal noise and other interfering signals present

in a communication channel [4], [5]. This limitation in EIRP made UWB technology the

3

most effective in short-range (less than 10 meters) applications. The throughput decreases

exponentially after this range [4].

B. Problem Definition

One of the important steps to be performed at the receiver in a complex system,

such as UWB, is data synchronization. FCC has mandated that EIRP emission of all

UWB signals to be below -40 dBm [4], [5]. This limitation in the UWB signal power

increases the chances of a receiver missing a data packet and, ultimately, the data

received at the receiver become worthless. In addition, a UWB system functions at a very

high data rate, and missing a synchronization packet can result in the loss of a huge

amount of data. Therefore, the receiver must continuously scan for incoming data and

perform rapid data synchronization.

The most important step in data synchronization is the detection of the data packet

at the receiver, which is the process of detecting the presence of the data packet in the

received signal. Normally, the packet detection is performed by monitoring the energy of

the received signal. A sudden change in the energy indicates the presence of the data

packet. The packet detection is successful if the power of the signal goes above a preset

threshold. This concept of modeling packet detection as a binary hypothesis is further

discussed in Chapter 3. This scheme for packet detection is critical for UWB

communication, since the maximum allowed EIRP is close to the noise floor. A sudden

change in noise power can result in high energy in the received signal. This peak in noise

energy can lead to a false detection of a packet and, sometimes, missing the packet

detection completely.

4

The probability of successful packet detection depends on the quality of the

received signal. If the quality of the received signal is sufficiently high, the receiver can

successfully distinguish the energy peak at the instant of packet arrival and discard the

noise between the peaks. This situation demands a scheme that can increase the quality of

the received signal, leading to a high probability of detecting a data packet. This thesis

focuses on increasing the received signal quality through the use of equalization to

eliminate the channel-induced signal distortions by estimating the channel impulse

response and performing digital signal processing on the received signal.

C. Approach and Contribution

As mentioned in the previous section, the central purpose of this thesis is to

investigate methods to improve received signal quality. The improvement in signal

quality is achieved by equalization, which is the process of convolving the inverse of the

estimated impulse response of the channel with the received signal. The estimation and

equalization process is performed in three stages: estimating the channel impulse

response from the channel model, computing the inverse of the impulse response, and

convolving the inverse impulse response with the output of the channel. Ideally, the

equalized signal is completely devoid of channel-induced distortions and is similar to the

transmitted signal.

Two estimators based on well-known Minimum Mean-Squared Error (MMSE)

and Least-Squared Error (LSE) methods are presented for the estimation of the channel

impulse response. These two methods have been proven to be effective in Gaussian

channels and other scenarios, such as in probability theory and linear prediction models

5

[6], [7]. However, MMSE and LSE methods have not been used in UWB systems for

estimation of channel impulse responses and equalization.

Extensive simulations were carried out using a UWB channel model defined by

the IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs). Four

different channel scenarios based on the distance between the receiver and transmitter

and their line-of-sight were considered for establishing the effectiveness of the scheme

for estimation and equalization. The output signals from the four channel models are

without any signal processing and are called non-equalized outputs. These non-equalized

outputs are equalized using the MMSE and LSE estimated channel impulse responses.

The autocorrelation and cross-correlation results of MMSE/LSE estimated and

equalized signals are compared to that of an ideal channel without any multipaths, having

only Additive White Gaussian Noise (AWGN). Ideally, the equalized output should be

similar to the ideal channel output, since the equalization process is trying to remove the

effect of channel multipaths from the non-equalized output. The simulation results are

also compared with the autocorrelation and cross-correlation results of a non-equalized

signal. Cross-correlation graphs show that the MMSE and LSE estimators and

equalization perform better in the presence of high SNRs. As the complexity of the

channel impulse response grows, a gap develops between the ideal performance and the

performance of MMSE/LSE equalization and estimation.

The Peak Average Power Ratio (PAPR) of the cross-correlation is also used to

analyze the results of the channel estimation and signal equalization schemes. The PAPR

of a signal is defined as the ratio of the peak power of the signal to the total noise

between the two peaks in the cross-correlation. Equalization improves the PAPR of the

6

signal, since the peak of the signal is higher and the noise level between two peaks is

lower. Improved PAPR indicates a higher quality received signal and, thus, PAPR gives a

measure of the quality of the signal.

D. Thesis Outline

This thesis is divided into two parts. The first part (Chapters 1 to 3) deals with the

problem statement and covers UWB radio fundamentals, OFDM modulation, and spectral

characteristics of UWB channels. The second part (Chapters 4 to 7) is dedicated to the

discussion of the research methodology and the idea of using MMSE/LSE estimation and

equalization for improving signal quality, followed by results and detailed discussion.

The chapters are organized as follows:

Chapter 2 introduces the core concepts of UWB radio communications, OFDM

systems, and definitions used for the UWB radio signal. This chapter also includes a top-

level UWB model and various modules in the system.

Chapter 3 introduces the concept of timing synchronization, packet detection,

channel estimation, and signal equalization. This chapter also explains various problems

associated with achieving a good synchronization.

Chapter 4 explains the research methodology and approach used to improve the

received signal quality by the use of better equalization methods. A new approach for

channel estimation and equalization using MMSE and LSE methods is presented in this

Chapter.

Chapter 5 includes the results from the simulations using MMSE and LSE

methods for equalization.

7

Chapter 6 is dedicated to a detailed discussion of the results and figures presented

in Chapter 5.

Chapter 7 includes a conclusion and a discussion of the results. Some thoughts on

future work are also included.

8

II. MULTIBAND OFDM UWB SYSTEM

A. History of UWB

The progress made in the field of microwave networks led to the origin of UWB.

These pioneering studies during the early 1960s were lead by Ross and Robins at Sperry

Rand Corporation, Harmurth at the Catholic University of America, and Van Ettan at the

United States Air Force (USAF) Rome Air Development Centre, as well as engineers at

Lawrence Livermore and Los Alamos National Laboratories (LLNL and LANL) [1].

These studies tried to explain the transient behavior of microwave networks using their

impulse response. The arrival of sampling oscilloscopes and the development of

techniques for the generation of sub-nanosecond pulses helped researchers directly

observe and measure the impulse response [8].

Later in the 1960s, it became obvious to the researchers at Sperry Rand

Corporation that short-pulse radar and communications systems could be developed using

the latest technologies. They later started using these radars widely in applications as

radar and communications. The first patented design of a UWB communications system

in 1972 was made possible at the Sperry Rand Corporation by the invention of a sensitive

baseband pulse receiver as a replacement for the sampling oscilloscope [1].

By the early 1970s, the commercial applications of UWB began to gain

popularity. Morey at the Geophysical Survey Systems Corporations made the first

ground-penetrating radar using UWB technology, and this radar was commercially

9

available in 1974 [1]. By 1975, researchers could build UWB systems from commercially

available Tektronix parts [1].

After the 1970s, the researchers started experimenting with UWB technology as a

medium for RF communication and sensing using transient pulses in a way that did not

interfere with other existing systems. Robert Scholtz at the University of Southern

California, in 1993, described a multiple access technique for UWB communications in

which each user/system is given a unique spreading code that determines specific

intervals when the user allows the data transmission [9]. This publication was a landmark

paper since Scholtz’s technique can be used not only for UWB radar and point-to-point

communications but also for UWB wireless networks. In 1994, McEwan at LLNL was

the first one in history to develop a compact, inexpensive, low-power UWB system called

Micro-Power Impulse Radar (MIR) [10].

Recently, many companies have entered the UWB market. This large-scale

interest in UWB was mainly due to the FCC’s decision to allocate a huge bandwidth for

the operation of unlicensed UWB devices [11]. Some of the big players in the UWB

technology are the FCC, the National Telecommunications and Information

Administration (NTIA), the Federal Aviation Administration (FAA), and the Defense

Advanced Research Projects Agency (DARPA). They spent many years investigating

UWB technology and its effect on existing wireless systems. The results from their

investigation helped in guiding the FCC on setting the UWB standards and mode of

operations.

10

B. Definition of UWB

As mentioned in the previous chapter, the main attribute of any UWB

communication system is its huge bandwidth. For any UWB transmission system, the

instantaneous spectral occupancy is more than 500 MHz, or the fractional bandwidth is

more than 20% [4]. The fractional bandwidth of a system is defined as the ratio of energy

bandwidth to the center frequency. The energy bandwidth concept is illustrated in Fig. 2.

In this figure, Lf is the lower limit and Hf is the higher limit of the Energy Spectral

Density (ESD). The energy bandwidth is identified by the frequencies Lf and Hf , which

delimit the interval where most of the instantaneous energy of the waveform falls. The

interval [ ]HL ff , is called the energy bandwidth, which is −10 dB bandwidth, and the

center frequency is defined as2

)( LHc

fff

+= .

Fig. 2. Comparison of the fractional bandwidth of a narrow band and UWB

communication system.

Frequency (Hz)

Narrowband

fL -10 dB fH

En

erg

y S

pec

tral

Den

sity

(d

B)

11

Often, the term “percent bandwidth” is used instead of fractional bandwidth.

Percent bandwidth is defined as the fractional bandwidth represented in percent units. For

example, a signal with an energy bandwidth of 1 MHz and a center frequency of 2 MHz

has a percent bandwidth of 50% and is a UWB signal, since its fractional bandwidth is

0.5, which is higher than the lower limit of 0.20. According to the FCC first report and

order [11], UWB systems with 5.2>cf GHz need to have a −10 dB bandwidth of at

least 500 MHz, while UWB systems with 5.2<cf GHz need to have a fractional

bandwidth at least 0.20.

Due to these properties of UWB signals, the UWB radios using these signals have

some unique advantages [4]:

1) UWB signals can penetrate through obstacles more efficiently.

2) UWB signals can be used for precision sensing and tracking even at the

centimeter level.

3) UWB can be used for very high data rates even if the number of users/systems

that coexist are huge.

4) UWB radios can be made smaller, with lower processing power requirements.

C. Types of UWB

There are two methods in which UWB signal transmissions are performed: the

first method is based on sending very short interval pulses to convey information, and the

second method is based on using several simultaneous carriers. The first method of UWB

transmission is known as Impulse Ultra-Wide Band, and the second type of UWB

12

transmission is called as Multi-Carrier Ultra-Wide Band. These two methods of UWB

transmissions are discussed in the following section.

UWB signals are traditionally radio frequency (RF) pulses that are of very short

duration. UWB transmissions that use these types of signals are called Impulse Ultra-

Wide Band (I-UWB) and are the most commonly used method of transmission. The

spectrum of an I-UWB signal is shown in Fig. 3. Typically, the information data symbols

are modulated using Pulse Position Modulation (PPM) and Pulse Amplitude Modulation

(PAM). The data symbols are encoded using pseudo-random or pseudo-noise (PN) codes

in order to shape the spectrum of the generated signal according to the FCC mandated

spectral mask for UWB communications. A time dither is introduced, usually to the data

symbols, and such a signal is called Time-Hopping UWB (TH-UWB). The encoded data

symbols are amplitude modulated by Direct Sequence Spread Spectrum (DSSS), and the

resultant UWB signal is called Direct Sequence Ultra-Wide Band (DS-UWB).

An alternative to DS-UWB is to divide the available bandwidth into sub-bands

and then split orthogonal sub-carriers into a train of short pulses, send the pulses over a

channel, and reassemble them at the receiver to recover each sub-carrier separately [1],

[12]. This mode of operation is called Multi-Band (MB) Orthogonal Frequency Division

Multiplexing (OFDM), and the UWB signal is called MB-OFDM UWB. Recent

proposals regarding UWB in the United States and in the IEEE 802.15.TG3a working

groups seems to favor MB-OFDM UWB. This fact is evident by the final channel

modeling sub-committee report released in April 2005. A detailed discussion about MB-

OFDM is presented later in this chapter. The spectrum of an OFDM-based MB-UWB

signal is shown in Fig. 4.

13

Fig. 3. Spectrum of an Impulse Ultra-Wide Band signal.

Fig. 4. Spectrum of an OFDM-based MB-UWB signal.

Frequency (GHz)

Rel

ativ

e P

ow

er (

dB

)

0 4 7 10

0

-25

-50

Frequency (GHz)

Rel

ativ

e P

ow

er (

dB

)

0 3 7 10

0

-15

-40

-50

14

The major difference in the spectral characteristics of I-UWB and MB-UWB

signals are shown in Figs. 3-4. For an I-UWB, the frequencies lie in the whole spectrum

for a single impulse. The power slowly increases, reaches a maximum at 3 GHz, and then

decreases slowly. For a MB-UWB signal, there are many sub-carriers operating in a band

of frequencies (Fig. 4). Since these carrier frequencies are orthogonal, they do not

interfere with each other.

D. Regulatory Issues

In the late 1990s, the FCC realized the importance of UWB technology and that it

could be used for some very important applications, such as radars for high precision

tracking, plotters for medical and through-wall imaging, sensors for remote sensing, and

transreceiver for secure voice and data communications. This realization about the

importance of UWB led the FCC to issue a Notice of Inquiry on September 1, 1998, for

revising Part 15 rules allowing the use of bandwidth for UWB devices without any

license.

Usually, the FCC divides unused spectrum into smaller bands and allocates the

bands to specific users or services. However, the FCC allowed UWB devices to function

in all frequencies from 960 MHz to 31 GHz. The maximum EIRP was limited so that the

UWB operation would not hurt the other wireless systems coexisting in the frequency

band, such as Global Positioning Systems (GPS) and Wireless Fidelity (WiFi). UWB was

allowed to interfere with the operation of these coexisting systems, but these systems

would not experience any performance degradation since UWB operates at very low

signal strength that is close to the noise floor. Other narrow band wireless systems

15

observe the UWB signals as a noise, and this noise is filtered out at the wireless system

receiver.

On February 14, 2002, the FCC issued its First Report and Order regarding the

unlicensed operation of UWB, based on more than 1000 documents from 150 different

organizations [11]. The report classified UWB operations into three separate categories:

1) Communication and measurement systems.

2) Vehicular radar systems.

3) Imaging systems, including ground penetrating radar, through-wall imaging

and surveillance systems, and medical imaging.

Each category was allocated a specific spectral mask (Figs. 5–6). The FCC limits

EIRP levels of radio transmissions in the frequency spectrum. These limitations are

known as the spectral mask, sometimes also referred to as the transmission mask. These

restrictions on the spectral mask reduce the interference in other systems by limiting

EIRP in specific bandwidths that are being shared by different wireless systems. For

example, the maximum allowed EIRP at 6 GHz is below -40 dBm/MHz for an indoor

commercial system. For a vehicular radar system, the maximum allowed EIRP at 6 GHz

is less than -60 dBm/MHz (Fig. 5). Table 1 summarizes some of the UWB applications

and their frequency band of operation, along with user restrictions that are imposed when

operating in that particular application mode [1], [4], [11].

E. Introduction of Multiband OFDM system

Orthogonal Frequency Division Multiplexing (OFDM) is a form of multi-carrier

transmission. In this form of transmission, the sub-carriers are made to overlap in

16

0 5 10 15 20 25 30 35-80

-75

-70

-65

-60

-55

-50

-45

-40

Frequency GHz

UWB EIRP Emission Level (dBm/M

Hz)

Mask 1

Mask 2

Mask 3

Fig. 5. FCC spectral mask for UWB systems. Mask 1 represents the mask for indoor

UWB communication systems. Mask 2 represents the mask for outdoor UWB

communication systems. Mask 3 represents the mask for UWB vehicular radar systems.

0 5 10 15-70

-65

-60

-55

-50

-45

-40

Frequency (GHz)

UWB EIRP Emission Level (dBm/M

Hz)

data1

data2

data3

Fig. 6. FCC spectral mask for UWB systems. Mask 1 represents the mask for UWB low

frequency imaging. Mask 2 represents the mask for UWB mid frequency imaging. Mask

3 represents the mask for UWB high frequency imaging.

17

TABLE 1

SUMMARY OF FCC RESTRICTIONS ON UWB OPERATION

Application Frequency Band for

Operation

User Restriction

Communication and

measurement systems

(Sensors)

3.1 – 10.6 GHz (different

emission limits for indoor

and outdoor systems)

None

Vehicular radar for

collision avoidance, and

suspension system control

24 – 29 GHz None

Ground-penetrating radar

to visualize or spot buried

objects

3.1 – 10.6 GHz and below

960 MHz

Law enforcement, fire

and rescue, research

institutions, mining and

constructions

Wall imaging systems to

visualize objects contained

in walls


960 MHz


and rescue, research

institutions, mining and

constructions

Through-wall imaging

systems to spot location or

movement of objects

placed on the other side of

a barrier


960 MHz


and rescue

Medical systems for

visualizing in the interior

of people and animals

3.1 – 10.6 GHz Medical personnel

Surveillance systems for

intrusion detection

1.99 – 10.6 GHz Law enforcement, fire

and rescue, public

utilities, and industry

18

frequency and avoid mutual interference, resulting in better spectral efficiency than any

other scheme. Multiple users can be supported in the same spectrum by allocating each

user a group of sub-carriers. OFDM-UWB is mainly intended for data transfer in the

physical layer for high bit-rate, short-range (10–20m) communications networks. The

OFDM-UWB transmitter splits orthogonal sub-carriers into a train of short pulses, sends

the pulses over a channel, and reassembles them at the receiver to recover each sub-

carrier separately [1], [12].

F. OFDM System Model

1) Transmitter: A number of orthogonal sub-carriers constitute an OFDM carrier

signal. Each sub-carrier carries a bit of baseband data, and these data are independently

modulated using a commonly used modulating method, such as Quadrature Amplitude

Modulation (QAM) or Phase-Shift Keying (PSK).

An ideal model of an OFDM transmitter is shown in Fig. 7. At the transmitter, x0,

x1…… xn are the symbols modulated by using a constellation map. A constellation map

gives the relationship between the discrete inputs and the real space to which these

discrete data will be converted during modulation. These input symbols are used to

compute an Inverse Fast Fourier Transform (IFFT) and results in a set of OFDM

symbols. The real and imaginary components are then separated. These separated

components are converted to the analog domain using digital-to-analog converters

(DACs). A different analog carrier signal having a frequency, fc, is used at the

modulation. This carrier wave’s cosine and sine waves are modulated by the analog

19

signal at the baseband from the DACs. The final transmission signal s(t) is obtained by

adding these two analog signals.

Fig. 7. An ideal model of an OFDM transmitter.

2) Receiver: An ideal model of an OFDM receiver is shown in Fig. 8. The receiver

picks up the transmitted signal r(t). The cosine and sine waves at the carrier frequency are

then quadrature mixed with the received signal, and the result is the baseband signal. A

low-pass filter is used to filter out the components above 2fc that are created during the

mixture. The resultant baseband analog signals are converted to a digital form by

sampling and digitizing using analog-to-digital converters (ADCs). The Fast Fourier

Transform (FFT) is computed to convert the OFDM symbols to data symbols. The result

symbols at the OFDM receiver are y0, y1…… yn (Fig. 8).

G. Mathematical Analysis of OFDM

In an OFDM system, a number of sub-carriers are used for symbol transmission.

If k represents the number of sub-carriers used, and M represents alternative symbols

Inv

erse

FF

T

DAC

DAC

90 deg.

fc

Real

Imag.

x0

x1

.

.

.

xn

s(t)

20

used for modulation of each sub-carrier, then the total OFDM word consists of KM

symbols. The OFDM signal for these symbols can be expressed as

Fig. 8. An ideal model of an OFDM receiver.

TteItVN

k

Tkti

k ≤≤=∑−

=0 ,)(

1

0

/2π. (2)

In (2), { }kI are the data symbols, N is the number of sub-carriers, and T is the OFDM

symbol time. The sub-carrier spacing of T

1Hz maintains the orthogonality. This property

is expressed as

( ) ( ) ( )

≠

=== ∫∫ −

21

21

0

/)(2

0

/2*/2

,0

,1

1

11221

kk

kkdte

Tdtee

T

T

Ttkki

T

TtkiTtki πππ . (3)

In (3), * denotes the complex conjugate operator.

To avoid inter-symbol interference, a guard interval, 0≤≤− tTg , is introduced in

multi-path fading channels. The guard period is inserted before the transmission of the

OFDM symbols, and a cyclic prefix is transmitted during this guard period interval. The

FF

T

ADC

ADC

90 deg.

fc

Real

Imag

y0

y1

.

.

.

yn

r(t)

21

cyclic prefix transmitted is the last portion of the OFDM symbol having a length equal to

the guard period. The OFDM signal with cyclic prefix can be represented as

TtTeItV g

N

k

Tkti

k ≤≤−=∑−

= ,)(

1

0

/2π. (4)

This OFDM signal can be either real or complex-valued. Usually, the baseband

data is transmitted in real-valued equivalent signals; however, for wireless applications,

the signal is transmitted typically in complex-valued. A carrier frequency, fc, is used to

up-convert the baseband signal and is represented as [1], [12]

{ }tfi cetVtsπ2

)(2

1)( ℜ= . (5)

For wireless applications, V(t) becomes

( ) ( )[ ]kc

N

k k ItTkfItV arg /2cos )(1

0++=∑

−

=π . (6)

H. Overview of an UWB Model

The purpose of this section is to illustrate the details of a multi-band orthogonal

frequency division multiplexing (MB-OFDM) UWB system based on a draft proposed to

the IEEE 802.15.3a standards group in September 2003. This system also is the basis for

wireless USB, which is the UWB common platform of the WiMedia Alliance. The

essential technology has not changed in the later proposals. The proposal supports seven

data rates in the range of 55−480 Mbps. The highest mandatory rate is 200 Mbps, using a

frequency hopping (multi-band) scheme for OFDM signals transmission. The functioning

of a UWB system is explained as follows with the help of the top-level simulation model

in Fig. 9.

22

1) Bernoulli Binary: The Bernoulli Binary Generator block generates random binary

numbers using Bernoulli distribution function. The Bernoulli distribution generates zero

with probability p and one with probability 1-p. The mean value of the Bernoulli

distribution is 1-p and variance is p(1-p) [13].

2) Rate Encoder: The rate encoder changes the rate of the bit stream using a

convolutional encoder. Rate encoding is an important process in many digital

communication systems involving Forward Error Correction (FEC) coding. Time

diversity is provided by the encoded symbols to prevent localized alteration or burst

errors in the symbols [13].

3) Interleaver: The interleaver adds redundant bits to the rate encoded data to

protect the data transmission from burst errors. Interleaving enables the receiver to

successfully retrieve data from the received transmission if burst errors corrupt a large

number of bits in a row [12].

4) QPSK Modulator: The Quadrature Phase-Shift Keying (QPSK) Modulator

modulates the input signal from the interleaver using the quaternary phase-shift keying

method. The QPSK modulator accepts binary data and converts the binary to a complex

form according to the QPSK constellation map [13].

5) OFDM Transmitter: The OFDM transmitter converts a set of QPSK symbols from

the QPSK modulator into OFDM symbols (165 samples each). These OFDM symbols are

23

then sent to the transmitter’s front-end for transmission. Various additional bits are added

in this section for timing synchronization and to prevent inter-frame interference [12].

Fig. 9. Top-level model of a typical UWB system.

6) Frequency Hopping and Filtering: Frequency hopping is a modulation technique

used for the output from the transmitter in spread spectrum signal transmission. During a

transmission, the signal is repeatedly switched between frequencies. This frequency

switching is implemented to minimize the unauthorized interception or jamming of the

transmitted signal and to prevent data loss due to frequency selective fading [14]. In this

UWB scheme, the signal is hopped between three frequencies.

Binary

Data

Rate

Encoder Interleaver

QPSK

Modulator

UWB

Channel

Frequency

Dehopping and

Filtering

OFDM

Receiver

QPSK

Demodulator

Deinterleaver Synchronization Viterbi

Decoder Data

Frequency

Hopping and

Filtering

OFDM

Transmitter

24

7) UWB Channel: The UWB channel model simulates an indoor UWB channel

programmed by Intel and used by the IEEE 802.15.3a group. The channel model

simulates the channel response as the time increases. The current proposal defines four

possible UWB channel models [15], which are discussed further in Chapter 4.

8) Frequency Dehopping and Filtering: Frequency dehopping takes inputs, which

are being switched between three different frequency spectrums of the UWB channel,

and retrieves the OFDM signal. During this process, the offset frequency due to the UWB

channel is also calculated and synchronized [14].

9) OFDM Receiver: The OFDM receiver decodes the OFDM signal and retrieves the

data from the received signal. All of the redundant bits are removed and necessary

compensations applied to recover the original signal.

10) QPSK Demodulator: The QPSK demodulator demodulates the signal using the

quaternary phase shift keying method. QPSK demodulator accepts the complex-valued

QPSK symbols and converts these symbols into binary data according to the QPSK

constellation map [12].

11) Synchronization: The synchronization block deals with the timing

synchronization of the signal. This block ensures the correct identification of the data

packets. The synchronization block makes sure that the start of the data packets is

correctly identified by making use of the Physical Layer Convergence Protocol (PLCP)

25

preambles. PLCP preambles are redundant data bits that are added in front of actual data

bits and are defined in the UWB standard [16].

12) De-interleaver: The de-interleaver removes the redundant bits added during

interleaving. Interleaving enables the receiver to successfully retrieve data from the

received transmission if burst errors corrupt a large number of bits in a row [12].

13) Viterbi decoder: The Viterbi decoder uses the Viterbi algorithm for decoding a bit

stream that has been rate encoded using forward error correction based on a convolution

code.

This thesis focuses on improving the signal quality of UWB signals using

equalization to improve cross-correlation PAPR. The improvement in cross-correlation

PAPR will enable better signal quality, which can lead to better packet detection due to

better signal peaks and less noise levels.

26

III. UWB TIMING SYNCHRONIZATION

A. Synchronization

In any wireless system, one of the important steps to ensure that the received

signal is properly synchronized so that the output data is meaningful. Since the UWB

systems usually deal with very high data throughput, a rapid and accurate

synchronization of the incoming data at the UWB receiver is very critical. A missed

synchronization can result in losing several packets of data and, ultimately, in system

failure. There are two main types of synchronizations in an OFDM UWB system that are

necessary for a successful communication between transmitter and receiver: frequency

and timing synchronizations [12]. Discussions of these two kinds of synchronizations are

included in the following section.

1) Frequency Synchronization: Frequency synchronization is defined as the process

of correcting the differences between the carrier frequencies in the receiver and the

transmitter. This frequency offset can occur for many reasons, such as instability in the

receiver or transmitter oscillators. There is also a Doppler effect if the systems are in

motion, and the frequencies can change when the transmitted signal reaches the receiver

[12].

Due to errors in frequency synchronization, two phenomena can occur. First, there

will be a reduction in signal amplitude, since the signal will not be sampled at peak

points. Instead, the signals will be sampled elsewhere, resulting in a degradation of signal

27

strength. Second, an offset in frequency results in the sampling of two adjacent carriers,

which can lead to inter-carrier interference (ICI) [12].

For very small frequency errors, the degradation in SNR of the signal is given by

( ) dBN

ETfSNR

o

s

loss

2

10ln3

10∆= π . (7)

In (7), ∆f is the frequency error, T is the sampling period, sE is the symbol power,

and oN is the noise power [17]. There are many algorithms to correct the frequency error.

A detailed discussion of those algorithms is beyond the scope of this thesis, and an

interested reader can refer to [12] for more details.

2) Timing Synchronization: Timing synchronization is defined as the process of

detecting the data packet in a received signal so that receiver can sample the signal

properly to retrieve a meaningful data. The timing synchronization can be considered a

two-step process. The first step is to successfully detect the presence of data packets

when they arrive at the receiver. The second step is to align the receiver to start reading at

the instant when the presence of data packet is detected. These two processes are termed

as data packet detection and symbol synchronization [12]. This thesis deals with ways to

improve received signal quality, which results in better packet detection in OFDM UWB

systems.

B. Packet Detection

Packet detection is an important step to be performed during the timing

synchronization, since the rest of the synchronization process is dependent on good

28

packet detection. The UWB uses the IEEE 802.11 Medium Access Control (MAC)

protocol, and the UWB receiver does not have a prior knowledge about the time of arrival

of a packet. Any algorithm to be used in UWB receivers needs to conduct the packet

detection without any prior knowledge, and that makes the synchronization of UWB

packets very difficult. The application of the packet detection in the timing

synchronization is illustrated in Fig. 10. There are two types of UWB communications:

high data rate and low data rate. In high data rate UWB communication, two of the major

task groups are IEEE 802.15.3a and wireless Universal Serial Bus (USB). In any type of

UWB communication, synchronization between transmitter and receiver is important. As

mentioned in the previous section, there are two types of synchronizations: frequency

synchronization and timing synchronization. Packet detection is one of the most

important steps in timing synchronization. Improving the received signal quality, which

can result in better packet detection, is the focus of this thesis.

The packet detection can be modeled as a binary hypothesis test, and the two

outcomes of the test are “packet is present” and “packet is absent.” Assuming B is the

parameter of interest, v is the decision variable, and Th is the predefined threshold, then

the actual test can be represented as follows.

• B0: ⇒< Thv Packet not present

• B1: ⇒≥ Thv Packet present

29

Fig. 10. Application of the packet detection in the timing synchronization.

Two probabilities are used to evaluate the performance of any packet detection

algorithm: probability of detection, PD, and probability of false alarm, PFA. The

probability of detection is defined as the probability that the packet detection algorithm

will correctly identify the presence of a data packet, while the probability of false alarm is

defined as the probability that the algorithm will misinterpret the decision variable and

falsely identify the presence of a data packet when there are no packets present [12].

UWB

Low Data Rate

IEEE 802.15.4a

High Data Rate

IEEE 802.15.3a

Wireless USB IEEE 802.15.3a

Transmitter / Receiver Synchronization / Acquisition

Timing Synchronization

Symbol Synchronization Packet Detection

Signal Quality

(MMSE/LSE Estimation

and Equalization)

Frequency Synchronization

30

Ideally, the probability of detection should be high, and the probability of false alarm

should be low.

C. Packet Detection Algorithms

The commonly used packet detection algorithms are described as follows.

1) Received Signal Energy Detection: The simplest algorithm used for packet

detection is the received signal energy detection approach. The received energy of the

signal is continuously monitored for changes in energy. Until the arrival of the packet,

only the noise is present and the energy is low and remains constant. When the packet

arrives, there is a sudden change in energy of the signal that is taken as the criteria for

detecting the data packet [18]. In order to avoid false detection due to high magnitude

noises, a window filter known as a sliding window is introduced. The energy that falls

inside this window is summed. The summation increases gradually, reaches a peak, and

then decreases. A packet detection is confirmed when the decision variable goes over a

predefined threshold. In this case, the decision variable is the energy summation of the

signal. Assuming the length of the window is L, and the received signal is nr , the

accumulated energy in the window is given by [12]

∑−

=−=

1

0

2L

k

knn rE . (8)

The concept of received signal energy detection is illustrated in Fig. 11. A packet

having 100 bits is detected using a window with a length of 100 bits. The peak energy is

reached at 50, so that the threshold can be set at 25.

2) Double Sliding Window Packet Detection: The double sliding window packet

detection algorithm is similar to the received signal energy detection algorithm discussed

31

earlier. Instead of one window, there are two sliding windows. In this case, the decision

variable is the ratio of the total energy accumulated in the two windows.

Fig. 11. Packet detection using received signal energy detection method. A packet

having 100 bits is detected using a window having a 100 bit-length. Threshold is 25. Peak

energy is 50.

The concept of received signal energy detection is illustrated in Fig. 12. Initially,

when only the noise is present, the decision variable is flat. When the packet arrives, the

window ‘A’ starts accumulating energy. The decision variable slowly starts rising until

the packet reaches the window ‘B’. This is the peak of the decision variable. When

window ‘B’ starts accumulating energy, the decision variable slowly starts falling. A

packet detection is confirmed when the decision variable goes over a predefined

threshold. Assuming the length of the window ‘A’ is M, the length of the window ‘B’ is

L, and the receiving signal is nr , the decision variable is given by [12]

n

n

nb

aE = . (9)

Packet

Th

En

erg

y

Sample Number

En

0 100 200

50

25

32

In (9),

∑−

=−=

1

0

2M

m

mnn ra (10)

and

∑−

=+=

1

0

2L

l

lnn rb . (11)

A packet having 100 bits is detected in Fig. 12 using two sliding windows, each

with a length of 50 bits. The peak energy is reached at 50 so that the threshold can be set

at 25.

Fig. 12. Packet detection using double sliding window packet detection method. A

packet having 100 bits is detected using two windows, each with a length of 50 bits.

Threshold is 25. Peak energy is 50.

3) Correlation Detection: Another approach for packet detection is to add a preamble

before sending the actual data packets. The arrival of data packets is detected by the

presence of this preamble. One way to detect the presence of the preamble is to do a

cross-correlation of the expected pulse sequence with the received signal. The result will

Packet

Th

En

erg

y

Sample Number

En

0 100 200

50

25

A B

33

be a peak at the instant when the preamble arrives at the receiver. A detailed discussion

about the cross-correlation process is included in Chapter 4. In this packet detection

method, the decision variable is cross-correlation strength. The correlation strength at

instant n is given by

( ) ∑−

=−=×

1

0

M

m

mmnn prgf . (12)

In (12), p is the preamble, and r is the received signal. If the variables are complex, the

complex conjugate has to be taken for one of the variables.

( ) ( )∑−

=−=×

1

0

*M

m

mmnn prgf (13)

In (13), * represents the complex conjugate.

The concept of cross-correlation detection is illustrated in Fig. 13. Initially, when

only the noise is present, the decision variable or the correlation strength is flat. The

correlation strength reaches a peak when the preamble packet has arrived. A packet

detection is confirmed when the decision variable goes over a predefined threshold. A

preamble packet having 100 bits is used in Fig. 13 for packet detection. The peak

correlation strength is reached at 50, so the threshold can be set at 25.

4) Delayed Correlation or Autocorrelation Detection: Another approach for packet

detection is delayed correlation detection. The delayed correlation method is similar to

the correlation detection method. In the delayed correlation method, multiple numbers of

preambles are sent before the actual data transfer. Instead of correlating the received

signal with the preamble in the correlation detection, the received signal is correlated

with the delayed version of itself [19]. The correlation strength is normalized by the

34

received signal energy during the cross-correlation. In this case, the decision variable is

the normalized correlation strength.

Fig. 13. Packet detection using cross-correlation detection method. A preamble packet

having 100 bits is used for packet detection. Threshold is 25. Peak energy is 50.

The concept of delayed correlation detection is illustrated in Fig. 14. The

correlation strength reaches a peak when the delayed version of the signal exactly

matches the second copy of the preamble packet. Packet detection is confirmed when the

decision variable exceeds a predefined threshold. A preamble packet having 100 bits is

used in Fig. 14 for packet detection. The normalized peak correlation strength is 1, so the

threshold can be set at 0.5.

There are many more algorithms for packet detection. A detailed discussion of

those algorithms is beyond the scope of this thesis. Interested readers can refer to [20]

for more details.

Data

Th

Cro

ss-C

orr

elat

ion

Str

eng

th

Sample Number

En

0 100 200

50

25

Cross-Correlation

Preamble

Preamble

35

Most of the packet detection algorithms mentioned earlier, such as received signal

energy detection and double sliding window packet detection, do not address the issue of

Fig. 14. Packet detection using delayed correlation detection method. A preamble packet

having 100 bits is used for packet detection. Threshold is 0.5. Peak energy is 1.0.

data being altered during the transmission through the channel. This thesis focuses on

improving the quality of the received signal by first estimating the channel impulse

response and performing digital signal processing using the estimate. This digital signal

processing will remove the entire channel-induced signal distortions, and the processed

signal will have a better quality than the received signal. This greater signal quality will

ensure better packet detection.

Th

Co

rrel

atio

n S

tren

gth

Sample Number

En

0 100 200 300 400

1

0.5

Correlation

Preamble Preamble Preamble

Preamble Preamble Preamble

36

IV. RESEARCH METHODOLOGY

A. Introduction

The central purpose of this thesis is to investigate methods to improve received

signal quality. The improvement in signal quality is achieved by equalization, which is

the process of convolving the inverse of the estimated impulse response of the channel

with the received signal.

The first step in the simulation is to generate the UWB channel impulse response,

which is performed by using the channel model from the IEEE 802.15 Task Group 3a.

This impulse response is convolved with test data to model the transmission of data

through the UWB channel, and noise is added to the convolution output to simulate the

received signal. This received signal is termed as non-equalized output.

Two estimators based on well-known MMSE and LSE methods are used for the

estimation of UWB channel impulse response. The inverse of the estimated channel

impulse response is computed and is convolved with the non-equalized signal to remove

the channel-induced distortions in the received signal. This process is called equalization,

and the processed signal is called the equalized signal.

For data analysis, the equalization is performed on the non-equalized signal at

different SNRs. Cross-correlation between the signals and the PLCP preamble and the

autocorrelation of the signals are computed at each SNR. PAPRs are computed for the

correlation signals and are compared to evaluate the improvement in signal quality.

37

B. System Model

The first and foremost task for any system simulation is the formulation of the

system model. Consider the UWB system shown in Fig. 15, where xk are the transmitted

symbols, g(t) is the UWB channel impulse response, n(t) is the AWGN, and yk are the

received symbols.

Fig. 15. Base-band OFDM system. UWB channel is represented by g(t). Noise added to

the channel is n(t). The input and output are xk and ykI, respectively.

Consider the channel impulse response g(t) as a finite time function of the form

∑ −=m

smm Tttg )()( τδα . (14)

In (14), mα is the complex-valued amplitude, Gsm TT ≤≤ τ0 , sT is the sampling interval,

GT is the guard interval to prevent the inter-symbol interference, and mT is the delay. The

N-Point discrete-time Fourier transform (DFTN ) is used to model the system and can be

represented as [6]

+⊗= n

N

gxIDFTDFTy NN

~)( . (15)

In (15), ⊗ is cyclic convolution. If g(t) is the channel impulse response after sampling,

the observed channel impulse response is the vector N

g[6], i.e.

xk yk

IDF

T

DF

T

g(t)

n(t)

38

∑

−=

−+−

m

m

mNK

Nj

mk

kN

eN

gm

)(sin

)sin(1 ))1((

τπ

πτα

τπ

. (16)

The above system can be written as a set of N independent Gaussian channels,

1.......,1,0 , −=+= Nknxhy kkkk . (17)

In matrix notation, the output can be written as

ngFXy += ** . (18)

In (18), X is a matrix with the elements of x on its diagonal and

=

−−−

−

)1)(1(0)1(

)1(000

...............

........................................

........................................

.....................

NN

N

N

N

N

NN

WW

WW

F (19)

is the DFT-matrix with

N

nkj

nk

N eN

Wπ21 −

= . (20)

The output, y, can also be computed using convolution [21].

∫ −=t

dtgxy0

)()( τττ (21)

C. Standard Test Data

The second step for the simulation is the preparation of test data. In this

simulation, the test data is taken from the European Computer Manufacturers Association

(ECMA) standards for UWB systems. Each test dataset consists of 24 PLCP symbols.

Each PLCP symbol consists of 165 bits of data. A PLCP header is usually used to help

the receiver perform the timing synchronization and channel estimation [16]. A PLCP

39

header was chosen as the test data because of its excellent correlation properties. Using

the PLCP preamble reduces the probability of giving a false positive during correlation.

The test data is constructed as shown in Fig. 16.

Fig. 16. Block diagram of test data constructed using PLCP preamble.

As shown in Fig. 16, the test data consists of 24 PLCP preambles. Each preamble

is multiplied by a cover sequence consisting of either +1 or -1. A cover sequence is used

to increase the correlation properties of the sequence. In the simulation test data, the first

21 preambles are multiplied by +1, and the remaining 3 preambles in the sequence are

multiplied by -1. Finally, 5000 bits of zeros are added in front of the PLCP sequences to

prevent noise from creating false positives before the arrival of the test data (Fig. 16).

These 8960 bits of test data are transmitted as a burst during a single run of the

simulation.

D. UWB Channel Model

The third step for the simulation of the system model is the preparation of the

channel model. The IEEE P802.15 working group for WPANs submitted its channel

modeling sub-committee final report on November 18, 2002 [15]. This particular channel

P1 P2 P3 P22 P24 …… P21

Preamble * 1 Preamble * (-1)

……

24 PLCP Symbols, 3960 Bits

Zeros

5000 Bits

8960 Bits Test Data

40

model was used for the simulation of the system model. According to the IEEE P802.15

Working Group, four channel models are possible for simulating different channel

scenarios. The four channel scenarios are summarized in Table 2.

TABLE 2

SUMMARY OF THE FOUR CHANNEL MODEL PROPERTIES

Channel Model Properties

1 Line of sight channel, distance 0 – 4m

2 Non line of sight channel, distance 0 – 4m

3 Non line of sight channel, distance 4 – 10m

4 Extreme non line of sight channel

The UWB channel model is based on the well-known Saleh-Valenzuela (S-V)

indoor channel model that was established in 1987. In the S-V model, the UWB receiver

receives multi-path components in groups known as clusters. Cluster arrivals are Poisson

distributed with rate Λ. Subsequent arrivals within each cluster are also Poisson

distributed with rate λ > Λ. With this knowledge, the UWB channel impulse can be

expressed as

∑∑∞

=

∞

=

−−=0 0

,, )()( ,

m n

nmm

j

nm Tteth nm τδα θ. (22)

In (22), nm ,α denotes the gain, nm,θ denotes the phase, and nmmT ,τ+ denotes the arrival

time of the nth

multipath component of the mth

cluster [4].

41

The nine key parameters that define the UWB model are: cluster arrival rate, Λ;

ray arrival rate, i.e., the arrival rate of path within each cluster, λ; cluster decay factor, Γ;

ray decay factor, γ; standard deviation of cluster lognormal fading term (dB), 1σ ;

standard deviation of ray lognormal fading term (dB), 2σ ; standard deviation of

lognormal shadowing term for total multipath realization (dB), xσ ; number of multipath

arrivals that are within 10 dB of the peak multipath arrival, NP10dB; and the number of

multipath arrivals that are within 85% power of the peak multipath arrival, NP85. The

values of these parameters for each of the channel models are tabulated in Table 3 [15].

The impulse response realizations for channel models 1 to 4 are shown in Figs.

17-20. The impulse response, h(t), of any system is defined as the response of the system

when a unit impulse in applied at the input of the system [13]. A unit impulse is defined

as a signal having infinite amplitude, zero width, and unit area [13]. An impulse response

is important since the impulse response can be used in convolution to determine the

response of the system to any given input signal. The channel output is given by

)(*)()( thtxty = . (23)

In (23), )(tx is the input signal and * is the convolution operation defined in (21).

It can be noticed that the channel model 1 has the lowest multipaths and the highest

impulse response (Figs. 17-20). The number of multipaths increased and the impulse

response got lower as the channel got worse. The number of multipaths is highest for

channel number 4, since this is the worst-case scenario and has the least magnitude of

impulse response.

42

TABLE 3

CHANNEL CHARACTERISTICS AND CORRESPONDING MODEL PARAMETERS

Model Parameters

CM 1

CM 2 CM 3 CM 4

RMS delay (nsec) ( rmsτ ) 5.28 8.03 14.28 25

Λ (1/nsec) 0.0233 0.4 0.0667 0.0667

λ (1/nsec) 2.5 0.5 2.1 2.1

Γ 7.1 5.5 14.00 24.00

γ 4.3 6.7 7.9 12

1σ (dB) 3.3941 3.3941 3.3941 3.3941

2σ (dB) 3.3941 3.3941 3.3941 3.3941

xσ (dB) 3 3 3 3

NP10dB 12.5 15.3 24.9 41.2

NP85 20.8 33.9 64.7 123.3

A test exponential channel is used instead of the UWB channel to check the

integrity of the algorithm and the MATLAB program. This exponential channel is free

from multipaths. The ideal channel output, non-equalized output, and MMSE/LSE

estimated output should be similar in the ideal case, since the impulse response of the

exponential channel decreases uniformly in the absence of multipaths. In the subsequent

simulations, the UWB channels are used instead of the exponential channel.

The quality of channel degrades from channel model 1 to 4. In channel model 1

(Fig. 17), the impulse response is sharp and the number of taps is minimum. The delay is

43

approximately 50 ns. Almost the whole response of the channel is contained in this

period. In channel model 2 (Fig. 18), the impulse response is less sharp than channel

model 1 and the number of taps is higher. The delay increased to approximately 70 ns. In

0 50 100 150 200 250

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (nS)

Impulse Response

Fig. 17. Impulse response realization for channel model 1.

44

0 50 100 150 200 250

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (nS)

Impulse Response


0 50 100 150 200 250

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Impulse Response


45

0 50 100 150 200 250

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (nS)

Impulse Respose


channel model 3 (Fig. 19), the impulse response is more distributed than in channel

models 1 and 2. The number of taps is also higher. The delay is approximately 125 ns. In

channel model 4 (Fig. 20), the impulse response is almost flat and the number of taps is

very high. The delay is approximately 200 ns. These characteristics in the impulse

response indicate many multipaths, and the channel quality is very poor, as expected.

For simulating an ideal channel, the data is convolved with a unit impulse

response. Since the response is a unit impulse, the input data is not altered during

convolution. The output after the convolution will be similar to the input. However, the

output will have a time delay, thus simulating an ideal channel without any multipaths.

46

E. Cross-Correlation

Cross-correlation is one of the most important mathematical tools to analyze the

correlation between two signals. The cross-correlation of two complex functions f(t) and

g(t) of a real variable t, is defined in (12) and (13). Consider two test series, ,[)( 1gtg =

],.........2 ngg and ],........,,,........,[)( 2121 nn ggggggtf = . The cross-correlation plot

between f(t) and g(t) is shown in Fig. 21. In this case, the g(t) is taken as one period of

PLCP preamble having length n = 165. The peaks occur at bit periods n and 2n. At those

points, g(t) is correlated with an image of itself, and hence, the correlation is at a

maximum at those two points. This maximum correlation indicates the presence of the

data packet g(t) at that instant, and thus the cross-correlation can be used for packet

detection during timing synchronizations. The cross-correlation power is given by

)(*)( tgtf , where * is the convolution process defined in (21), and )(tf is the complex

conjugate of )(tf . In this example, there are only two symbols in the test sequence. If the

test sequence has a greater number of symbols, the peaks occur at bit periods n, 2n, 3n,

and so on.

F. Autocorrelation

Autocorrelation is another important mathematical tool used to measure the

correlation of a signal with a time-shifted version of itself. Autocorrelation is expressed

as a function of the amount of time shift. Let 1

0}{ −=

N

iiα be a periodic sequence. The

autocorrelation of the sequence is given by

∑−

=−−−=

1

0

M

m

Mmnmnn rrE . (24)

47

0 100 200 300 400 500 600 700-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Bit Numbers

Norm

alized Cross Correlation Power

Fig. 21. Cross-correlation between test series f(t) and PLCP preamble g(t).

In (24), r is the received signal, and M is the symbol length. If the variables are complex,

the complex conjugate has to be taken for one of the variables.

( )*1

0

∑−

=−−−=

M

m

Mmnmnn rrE (25)

In (25), * represents the complex conjugate. Consider two test series, ,..,[)( 21 ggtg =

]....... ng and )](),()......(),(),(),(),(),(),(),(),(),([)( tntgtntgtntgtntgtntgtntgtf = , where

n (t) is a random function. The autocorrelation plot of f(t) is shown in Fig. 22. The

autocorrelation is performed using one period of g(t). The peak occurs at the start of

symbol g(t) in the signal f(t), and then the correlation power gradually decreases until the

correlation finds the beginning of the next g(t). Thus, this method gives an indication of

presence of data packet g(t) and, therefore, the autocorrelation can be used for packet

detection during timing synchronization. In this case, the length of the g(t) used is 128,

48

and the length of the n(t) used is 37. Therefore, the first peak is at n =1, and the next peak

will be at n = 166 (Fig. 22).

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bit Numbers

Norm

alized Auto Correlation Power

Fig. 22. Autocorrelation plot of the test series f(t) using a single PLCP period g(t).

In cross-correlation, the signal is correlated with a known vector. In the previous

example, f(t) is the signal that is correlated with a known vector g(t). In autocorrelation,

the signal f(t) is correlated with a vector that is a time-delayed version of itself having a

period n. In the given example, n is taken as the period of g(t). This vector is unknown,

since the vector came from the time-delayed version of the received signal.

G. MMSE and LSE Estimators

The next step in the simulation is to formulate the MMSE and LSE estimators that

estimate the impulse response of the channel. If the channel vector g is Gaussian and

uncorrelated with the channel noise n, the MMSE estimate of g in frequency domain is

given by [6], [7]

49

yRRg yyggMMSE

1−=)

. (26)

In (26), gyR is the cross-covariance matrix between g and y, given by

{ } HH

gg

H

gy XFRgyR =Ε= (27)

and yyR is the auto-covariance matrix of y expressed as

{ } Nn

HH

gg

H

yy IXFXFRyyR2σ+=Ε= . (28)

In (28), ggR is the auto-covariance matrix of g, 2

nσ denotes the noise variance, y is the

UWB channel output, X is a matrix with the elements of x on its diagonal, and F is given

by (19) and (20).

The LSE estimate in frequency domain for the cyclic impulse response g is given

as [6]

yXhLS

1−=)

. (29)

After the impulse response calculation using either the MMSE or LSE method,

the inverse of the estimate is computed. The inverse and the output from the channel are

then convolved to get the error-compensated output of the signal. This final signal is free

from multipath errors and affected only by the noise in the UWB channel.

H. Data Analysis

After estimating the channel impulse response and equalizing the signal, the last

step in the simulation is to analyze the data for the improvement in received signal

quality. The simulation is performed for a SNR range of -20 dB to 80 dB. The equalized

signal is cross-correlated and autocorrelated to find the peaks indicating the start of the

data packets at each SNR value (Figs. 21-22). Once the cross-correlation and

50

autocorrelation are calculated, the signal quality is evaluated by calculating the PAPR at

each SNR value and plotting the PAPR. The PAPR value is calculated for four different

scenarios. The first scenario is the non-equalized output taken directly from the channel

output. The second scenario is the equalized output estimated using the MMSE estimator.

The third scenario is the equalized output estimated using the LSE estimator. The fourth

scenario is the ideal channel scenario where only noise is present. In the fourth scenario,

channel multipaths and attenuation do not affect the data, since the data is propagated

through an ideal channel. In this scenario, the signal is convolved with a unit impulse to

simulate the ideal channel.

Ideally, the equalized output should be similar to the ideal output, since

equalization process tries to remove the effect of the channel from the non-equalized

output. The estimator whose output is similar to that of the ideal channel output is

considered the optimum. A noise source is added to the ideal channel output for two

reasons. The first reason is to adjust the SNR of the signal. The second is that the

equalization process removes only the impairments caused by the channel, such as

multipaths and channel attenuation. The equalization process does not remove the effect

of noise on the signal. Therefore, to compare the equalized output and the ideal channel

output, a noise has to be added to the ideal channel output, since the effect of noise

remains even after equalization.

I. UWB Operating SNRs

For calculating the operating SNRs for UWB, two important parameters used in

any transmission system must be defined. The first parameter is decibel (dB). Decibel is

51

used when two greatly differing power levels, such as signal power and noise power, are

to be compared. The decibel is used to express these two signals as a ratio and is given by

[14]

=

o

sdB

N

PP 10)( log10 . (30)

In (30), Ps is the signal power in watts, and No is the noise power in watts.

The second important parameter is decibel-milliWatt (dBm). Decibel-milliWatt is

used to denote the absolute power of a signal in decibels. Decibel-milliWatt uses 1

milliwatt (mW) as the reference given by [14]

=

mW

PP s

dBm1

log10 10)( . (31)

In (31), Ps is the signal power in watts. For example, the signal power of an UWB signal

or the noise power at ambient temperature, is expressed in dBm.

According to FCC guidelines, the maximum allowed signal strength of an UWB

signal is -41 dBm/MHz, and the minimum signal strength is -76dBm/MHz. Using (31),

these upper and lower limits in signal strength can be expressed as 8109.7 −× W/MHz

and 11105.2 −× W/MHz. The noise power expressed in W/Hz is given by [14]

kTN o = . (32)

In (32), k is Boltzmann’s constant 23103803.1 −×= J/K, and T is the temperature in

Kelvin. Using (32) at a temperature of 290 K, the noise power is 21104 −× W/Hz or

15104 −× W/MHz; therefore using (30), the SNR range at which UWB devices function is

from 73-38 dB.

52

This SNR range is the power at which the UWB signals are sent from the

transmitter. The signal is attenuated as it travels through the communication channel.

Therefore, the SNR range available at the receiver is less than the value at which the

signal is being transmitted. The free space loss in a communication channel expressed in

dB is given by [14]

56.147)log(20)log(20)( −+= dfL dB . (33)

In (33), f is the carrier frequency, and d is the distance between the transmitter and

receiver. If it is assumed that the highest possible SNR value is used for packet detection

and the carrier frequency is 5 GHz, the SNR available at the receiver after the free space

loss is calculated using a free space loss equation for a transmitter-receiver range of 0-20

m and is plotted in Fig. 23. When the receiver is close to the transmitter, the SNR at

which the receiver has to perform the packet detection is 73 dB. The receiver has to

perform the packet detection at less than 0 dB, when the receiver is at a distance of 20 m

from the transmitter.

J. MMSE/LSE Channel Estimation and Signal Equalization Block Diagram

The block diagram showing the steps involved in the estimation and equalization

process using the MMSE/LSE equalization is shown in Fig. 24. The first block shows the

UWB channel generation. The impulse response on the channel is generated using the

MATLAB code obtained from IEEE task group. The transmission modeling block is the

53

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

70

80

Distance (m)

SNR (dB)

Fig. 23. Available SNR at the receiver as a function of distance between the UWB

transmitter and the receiver.

simulation of the UWB transmitter-receiver model. The test data is convolved with the

impulse response of the channel to get an output. The noise is added to this output to get

the non-equalized output. LSE channel estimation and MMSE channel estimation blocks

estimate the channel impulse response using LSE and MMSE estimation methods,

respectively. The LSE equalization block accepts the LSE estimated impulse response,

computes the inverse of the estimated impulse response, and convolves the inverse with

the non-equalized output to get the LSE equalized output. Similarly, the MMSE

equalization block accepts the MMSE estimated impulse response, computes the inverse

of the estimated impulse response, and convolves the inverse with the non-equalized

output to get the MMSE equalized output. The test data is convolved with a unit impulse

response, and noise is added to simulate an ideal channel. The ideal channel output, non-

equalized output, and LSE/MMSE equalized outputs are compared in the data analysis

54

block. The average autocorrelation power and cross-correlation PAPR are computed for

the outputs and are analyzed for an improvement in signal quality in the data analysis

block. The sources and references from which the design is taken and implemented are

also indicated in parenthesis.

55

Fig. 24. Steps involved in the estimation and equalization process using the MMSE/LSE

estimation and equalization method.

UWB Channel Generation

(Ref: IEEE 802.15 Task

Group 3a Proposal [15])

Transmission Modeling:

Convolve PLCP preamble with

channel impulse response to get

non-equalized output

PLCP preamble

(Ref: ECMA UWB

PHY & MAC

Standard [16])

Noise

LSE Channel Estimation

(Ref: Statistical Signal

Processing [6], [7])

LSE Equalization: Convolve

inverse of the estimated

impulse with non-equalized

output to get LSE equalized

output

MMSE Equalization: Convolve

inverse of the estimated impulse

response with non-equalized

output to get MMSE equalized

output

Data Analysis:

Compute the average auto-

correlation power & cross-

correlation PAPR

Noise

MMSE Channel Estimation

(Ref: Statistical Signal

Processing [6], [7])

PLCP preamble

(Ref: ECMA UWB

PHY & MAC

Standard [16])

Channel Impulse Response (IR)

Non-Equalized Output

LSE Equalized

Output

MMSE Estimated Channel IR

MMSE Equalized

Output

Ideal Channel

Output Non-Equalized Output

LSE Estimated Channel IR

56

V. RESULTS

The performance of the proposed MMSE/LSE estimation methods and signal

equalization for improving signal quality was evaluated using autocorrelation and cross-

correlation performances as the criteria. The correlation performance of the equalized

signals was compared to that of a non-equalized signal as well as to that of a signal from

an ideal AWGN channel. The cross-correlation PAPR of the signals was also compared

later for evaluating the improvement in the received signal quality.

The cross-correlation plot for a SNR of 25 dB is shown in Fig. 25. The channel

used for the simulation is an exponential channel for validating the MMSE/LSE

estimation and equalization process. The output of the estimators, f(t), was correlated

with a single period of PLCP preamble, g(t), using (13) and the power of the correlation

output is plotted. The cross-correlation for an ideal channel output, the non-equalized

output, and the MMSE/LSE equalized outputs are shown in the same figure.

The cross-correlation plot for a SNR at 25 dB is shown in Fig. 26. The channel

used for the simulation is the UWB channel model 1. The cross-correlation for an ideal

channel output, the non-equalized output, and the MMSE/LSE equalized outputs are also

shown in the same figure.

An expanded view of the cross-correlation plot using UWB channel 1 (Fig. 26) is

shown in Fig. 27. The y-axis is expanded to distinguish the peaks in the simulation result

for the UWB channel.

57

0 0.5 1 1.5 2

x 104

0

0.5

1

1.5

2

2.5x 10

8 Ideal Channel Output

Bit Number(a)

Cross Correlation power

0 0.5 1 1.5 2

x 104

0

0.5

1

1.5

2

2.5x 10

8 Non Equalized Output

Bit Number(b)

Cross Correlation Power

0 0.5 1 1.5 2

x 104

0

0.5

1

1.5

2

2.5x 10

8MMSE Equalized Output

Bit Number(c)


0 0.5 1 1.5 2

x 104

0

0.5

1

1.5

2

2.5x 10

8LSE Equalized Output

Bit Number(d)


Fig. 25. PLCP preamble cross-correlated with ideal channel output (a), non-equalized

output (b), MMSE equalized output (c), and LSE equalized output (d). SNR = 25 dB.

Exponential channel.

0 0.5 1 1.5 2

x 104

0

0.5

1

1.5

2

2.5x 10

8Ideal Channel Output

Bit Number(a)


0 0.5 1 1.5 2

x 104

0

1

2

3

4

5x 10


Bit Number(b)


0 0.5 1 1.5 2

x 104

0

2

4

6x 10


Bit Number(c)


0 0.5 1 1.5 2

x 104

0

2

4

6x 10


Bit Number(d)


Fig. 26. PLCP preamble cross-correlated with ideal channel output (a), non-equalized

output (b), MMSE equalized output (c), and LSE equalized output (d). SNR = 25 dB.

UWB channel model 1.

58

1.4 1.5 1.6 1.7 1.8

x 104

0

0.5

1

1.5

2

x 108 Ideal Channel Output

Bit Number(a)


1.4 1.5 1.6 1.7 1.8

x 104

0

1

2

3

4

x 107 Non Equalized Output

Bit Number(b)


1.4 1.5 1.6 1.7 1.8

x 104

0

1

2

3

4

5

x 107 MMSE Equalized Output

Bit Number(c)


1.4 1.5 1.6 1.7 1.8

x 104

0

1

2

3

4

5x 10

7 LSE Equalized Output

Bit Number(d)


Fig. 27. Expanded version of Fig. 26. Y-axis is expanded to show the peaks. PLCP

preamble cross-correlated with ideal channel output (a), non-equalized output (b), MMSE

equalized output (c), and LSE equalized output (d). SNR = 25 dB. UWB channel model

1.

The autocorrelation plot for a SNR of 25 dB is shown in Fig. 28. The channel

used for the simulation is an exponential channel for validating the MMSE/LSE

estimation and equalization process. The output of the estimators was autocorrelated

using a single period of PLCP preamble using (25). The power of the correlation output is

plotted as the y-axis for the figures. The cross-correlation for an ideal channel output, the

non-equalized output, and the MMSE/LSE equalized outputs are also shown in the same

figure.

The autocorrelation plot for a SNR of 25 dB is shown in Fig. 29. The channel

used for the simulation is the UWB channel model 1. The cross-correlation for an ideal

channel output, the non-equalized output, and the MMSE/LSE equalized outputs are also

shown in the same figure.

59

0 2000 4000 6000 8000 100000

0.5

1

1.5

2

2.5x 10

8 Ideal Channel Output

Bit Number(a)

Auto Correlation Power

0 2000 4000 6000 8000 100000

0.5

1

1.5

2

2.5x 10


Bit Number(b)


0 2000 4000 6000 8000 100000

0.5

1

1.5

2x 10


Bit Number(c)


0 2000 4000 6000 8000 100000

0.5

1

1.5

2

2.5x 10


Bit Number(d)


Fig. 28. Autocorrelation using ideal channel output (a), non-equalized output (b), MMSE

equalized output (c), and LSE equalized output (d). SNR = 25 dB. Exponential channel.

0 2000 4000 6000 8000 100000

0.5

1

1.5

2

2.5x 10

8Ideal Channel Output

Bit Number(a)


0 2000 4000 6000 8000 100000

2

4

6x 10

8Non Equalized Output

Bit Number(b)


0 2000 4000 6000 8000 100000

1

2

3x 10


Bit Number(c)


0 2000 4000 6000 8000 100000

0.5

1

1.5

2

2.5x 10


Bit Number(d)


Fig. 29. Autocorrelation using ideal channel output (a), non-equalized output (b), MMSE

equalized output (c), and LSE equalized output (d). SNR = 25 dB. UWB channel model

1.

60

The output of the estimators is autocorrelated using a single period of the PLCP

preamble using (25), and the average autocorrelation power was calculated as the ratio of

the average signal power to the average noise power. The average autocorrelation power

for an ideal channel output, non-equalized output, and the MMSE/LSE equalized outputs

are shown in Fig. 30. The channel used for the simulation is an exponential channel for

validating the MMSE/LSE estimation and equalization process. The simulation was

repeated for all four UWB channels. The channel used for the simulation in Fig. 31 was

the UWB channel model 1. UWB channel model 2 was used for the simulation in Fig. 32.

UWB channel model 3 was used for the simulation in Fig. 33. The channel used for the

simulation in Fig. 34 was the UWB channel model 4.

-20 -10 0 10 20 30 40 50 60 70 80-20

0

20

40

60

80

100

SNR (dB)

Average Autocorrelation Power (dB)


Ideal Channel Output

MMSE Equalized Output

LSE Equalized Output

Fig. 30. Average autocorrelation power for ideal channel output, non-equalized output,

MMSE equalized output, and LSE equalized output. SNR range from -20dB to 80dB.


61

-20 -10 0 10 20 30 40 50 60 70 80-20

0

20

40

60

80

100

SNR (dB)









-20 -10 0 10 20 30 40 50 60 70 80-20

0

20

40

60

80

100

SNR (dB)









62

-20 -10 0 10 20 30 40 50 60 70 80-20

0

20

40

60

80

100

SNR (dB)









-20 -10 0 10 20 30 40 50 60 70 80-20

0

20

40

60

80

100

SNR (dB)









63

The output of the estimators was cross-correlated with a single period of the

PLCP preamble, g(t), using (13). The PAPR was calculated as the ratio of the peak

correlation power to the average correlation power excluding the correlation peak. The

cross-correlation PAPR average autocorrelation power for an ideal channel output, the

non-equalized output, and the MMSE/LSE equalized outputs are shown in Fig. 35. The

channel used for the simulation was an exponential channel for validating the

MMSE/LSE estimation and equalization process. The simulation was repeated for all

four UWB channels. The channel used for the simulation in Fig. 36 was the UWB

channel model 1. UWB channel model 2 was used for the simulation in Fig. 37. UWB

channel model 3 was used for the simulation in Fig. 38. The channel used for the

simulation in Fig. 39 was the UWB channel model 4.

-20 -10 0 10 20 30 40 50 60 70 80-5

0

5

10

15

20

SNR (dB)

Cross-Correlation PAPR (dB)





Fig. 35. Cross-correlation PAPR for ideal channel output, non-equalized output, MMSE

equalized output, and LSE equalized output. SNR range from -20dB to 80dB.


64

-20 -10 0 10 20 30 40 50 60 70 80-5

0

5

10

15

20

SNR (dB)







equalized output, and LSE equalized output. SNR range from -20dB to 80dB. UWB

channel model 1.

-20 -10 0 10 20 30 40 50 60 70 80-5

0

5

10

15

20

SNR (dB)








channel model 2.

65

-20 -10 0 10 20 30 40 50 60 70 80-10

-5

0

5

10

15

20

SNR (dB)


Non-Equalized

Ideal Channel

MMSE Eq.

LSE Equalized



channel model 3.

-20 -10 0 10 20 30 40 50 60 70 80-5

0

5

10

15

20

SNR (dB)








channel model 4.

66

VI. DISCUSSION

The performance of the MMSE/LSE methods used to estimate the UWB channel

and equalization of the received signal to improve signal quality was evaluated by

running simulations using the system model described in Chapter 4. The exponential

channel in the simulations was used to check the integrity of the channel estimation and

signal equalization program. The exponential channel was used since the channel impulse

response decreases uniformly and is less complex in the absence of multipaths in the

channel. Therefore, the correlation properties of ideal output, non-equalized output, and

MMSE/LSE outputs are easier to compute when the exponential channel is used in the

simulations.

The cross-correlation figure (Fig. 25) shows that the MMSE/LSE estimation and

equalization gave an excellent performance using the exponential channel in the

simulation. The cross-correlation PAPR figure (Fig. 35) shows that the MMSE

equalization curve followed the ideal channel output curve very closely. The LSE

equalization curve shows that the LSE equalized output was better than the non-equalized

output in high SNRs, the signal quality degraded when the SNRs were lowered. The

results obtained from using the exponential channel confirms that the MATLAB

programs performed as expected. The exponential test channel was replaced with UWB

channels in later simulations.

The cross-correlation plot for the UWB channel model 1 (Fig. 26) shows that the

MMSE-equalized output had a higher peak and lower noise than the non-equalized

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output. The lowering of the noise and the increase in the peaks during the cross-

correlation improved the PAPR of the signal. In case of the LSE equalized output, noise

was lower when compared to the non-equalized output, even though the peaks were

comparable. This lowering of the noise in the cross-correlation improved the PAPR of the

signal.

The packet detection is successful if the power of the signal goes above a preset

threshold of the decision variable. The threshold has to be kept high for a non-equalized

output, in order to avoid false detection. The probability of failing to detect a packet is

also high if the threshold is kept high. This shortcoming can be eliminated using

equalized output. For an equalized output, the peaks in cross-correlation are high and the

noises between the peak are low, which enables the threshold to be kept low. There is a

higher probability of successful packet detection when keeping the threshold low, and the

probability of false packet detection is low since the noises are low. This higher

probability of successful packet detection is illustrated in Fig. 27, in which the y-axis of

Fig. 26 is expanded to distinguish between the peaks in the cross-correlation plot. The

decision variable was set at 7105.3 × , and the receiver successfully detected all 24 peaks

corresponding to 24 symbols present in the test sequence using both MMSE and LSE

equalized outputs. In the case of the MMSE-equalized output, the receiver detected four

false peaks, and in the case of the LSE-equalized output, the receiver detected the false

peak only once. However using the non-equalized output for packet detection, the

receiver detected 22 false positives along with the right peaks. When the decision

variable was set at7104× , the receiver successfully detected all 24 peaks using the

MMSE-equalized output with no false peaks. While using LSE-equalized output, the

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receiver detected 22 peaks with no false peaks. However, using the non-equalized output

for packet detection, the receiver detected only 21 peaks. These thresholds are true only

for this scenario and can change with different test cases. These results suggest that the

estimators improve signal quality and increase the probability of successful packet

detection.

The autocorrelation plots of various outputs are shown in Figs. 28-29. Both

figures show almost the same level of peaks for all of the outputs, and there was no

significant decrease in noise between the peaks. The average autocorrelation figures

(Figs. 30-34) show that there was little or no improvement in the average autocorrelation

power when using an MMSE or LSE equalizer. This degradation in average

autocorrelation power was expected for multi-path channels having delays less than or

equal to the autocorrelation length, since the multi-path channel distorts consecutive

signals equally, and thus each symbol and its distortion correlate well with the next

symbol and its own distortion. The output of the equalizers, f(t), was autocorrelated using

a single period of PLCP preamble, g(t), in the same signal using (25). The effect of

channel distortion on each symbol was the same as any other symbols. The adjacent

symbols correlate well during autocorrelation, since autocorrelation was done using the

adjacent symbols in the same signal.

However, the cross-correlation PAPR graphs (Figs. 35-39) show that there was a

marked difference between the MMSE/LSE equalized signals and the non-equalized

signals. The output of the equalizers f(t) was cross-correlated with a single period of

PLCP preamble g(t) using (13), and the PAPR of the signal was calculated. The PAPR is

calculated as the ratio of the peak correlation power to the average noise between the

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peaks. The preamble used here was the original symbol with a 165-bit symbol period,

hence the signal improvement achieved by the estimators is directly reflected in the

cross-correlation plots. The cross-correlation PAPR figure (Fig. 35) shows that the

estimators gave an exceptional result when used with a 165-tap exponential channel.

Both the estimators improve the signal overall, but MMSE performs better and followed

the ideal channel output curve very closely. The cross-correlation PAPR for UWB

channel model 1 (Fig. 36) shows that the equalized output was better than the non-

equalized output for the same SNR. The equalized signal degraded at lower values of

SNR. The cross-correlation PAPR for UWB channel model 2 (Fig. 37) shows that the

LSE equalized output was better than the non-equalized output for the same SNR. The

MMSE-equalized output was better than the non-equalized output at very high SNRs.

The cross-correlation PAPR for UWB channel model 3 (Fig. 38) shows that the

equalization failed to improve the non-equalized signal for all SNR values. The cross-

correlation PAPR for UWB channel model 4 (Fig. 39) shows that the LSE equalized

output was better than the non-equalized output for the same SNR. The MMSE

equalization failed to improve the quality of the signal.

In theory, the MMSE estimation and equalization is considered to be optimal as

illustrated in the cross-correlation PAPR figure for the exponential channel (Fig. 35). The

MMSE curve followed the ideal channel output curve very closely. However, the

estimators performed poorly for channel models 3 and 4. This can be due to many

reasons. The last two channels have many multi-paths and have a very complex impulse

response. One of the main reasons for the failure of the estimators in these conditions was

that the estimators were unable to calculate the error when it comes to such a complex

70

environment and thus failed to give a good estimation. Another factor was the number of

taps of the impulse response used for the error estimation. The preamble used for channel

estimation had a symbol period of 165 bits. Therefore, the number of taps of the impulse

response used was also constrained to 165 taps, which might be a reason that the

estimators fail in a complex UWB channel. A better preamble with a longer symbol

period or an estimator with a greater number of taps can track more complex channel

environments.

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VII. CONCLUSION AND FUTURE WORK

A. Conclusion

The demand for low-cost, high-speed, wireless links for short-range

communication has increased dramatically over the last decade. One way to transmit this

high-data rate information is to employ well-known conventional single-carrier systems.

However, with the advent of newer entertainment components and computer peripherals,

the data required to be sent wirelessly over a short distance has increased tremendously.

For example, a typical entertainment component such as a High-Definition Television

(HDTV) demands a data rate of several hundred megabits per second. UWB is the only

solution if the HDTV is to be connected wirelessly, since most conventional wireless

systems cannot handle the high-data rate required. Another application of UWB is in

wireless USB used to connect computer peripherals. Wireless USB works typically at

480 mbps, which is beyond the data rate capacity of other wireless communication

systems. When the FCC in the United States released a huge new bandwidth at very low

power for Ultra-Wide Band communication, UWB became the new standard for

delivering a high-data rate over a short distance.

The central purpose of this thesis was to investigate methods to improve received

signal quality. The improvement in signal quality was achieved by equalization, which is

the process of convolving the inverse of the estimated impulse response of the channel

with the received signal. Two estimators adopting MMSE and LSE methods performed

the channel estimation. Extensive simulations were carried out for establishing the

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effectiveness of the scheme to improve the received signal quality. The system model

was tested in a multi-path and noise environment using a UWB channel model defined by

the IEEE P802.15 Working Group for WPANs. Four simulation scenarios were

considered based on the distance between the UWB transmitter and receiver and their

line-of-sight.

The autocorrelation and cross-correlation results of MMSE/LSE estimated and

equalized signals were compared with that of an ideal channel having only AWGN. The

simulation results were also compared with the autocorrelation and cross-correlation

results of a non-equalized signal. Cross-correlation graphs show that the MMSE and LSE

estimators perform better in the presence of high SNR. The cross-correlation PAPR

figures show that equalization was successful in improving the received signal quality.

Both estimators improved the signal overall quality.

Enhancing received signal quality can lead to better packet detection. Better

cross-correlation PAPR can result in higher peaks and lower noise, which can lead to a

high probability of successful packet detection by lowering the rate of false detection and

of missing packets all together. Increasing the probability of packet detection can result in

better timing synchronization, since packet detection is the most important step in timing

synchronization, and the rest of the symbol synchronization by the receiver depends on

successful packet detection.

The results establish that using MMSE or LSE channel estimation and signal

equalization is an innovative approach to improve received signal quality. To use the

advantages that UWB offers, research and development has to concentrate on improving

UWB performance, capacity, and throughput in noisy channels. Maintaining a proper

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synchronization is the foremost criteria for the efficient working of an UWB OFDM

system. Proper implementation of channel estimation and signal equalization can lead to

this much-needed improvement in signal synchronization.

B. Future Work

The MMSE and LSE estimators assume an a priori knowledge of channel impulse

and noise variance. The knowledge is used for the calculation of channel estimates. In a

real scenario, this information is not readily available, and hence, the current scheme

cannot be applied directly in an UWB receiver. This thesis is a demonstration of the

importance of MMSE and LSE estimators and shows that the estimators can improve the

quality of the received signal. Improvement in signal quality can lead to a better packet

detection and, ultimately, good timing synchronization. Future work could include the

practical aspects of implementing MMSE and LSE estimators in UWB receivers.

The complexity of implementing the MMSE/LSE estimator and signal

equalization is large. The computation load on UWB receivers can be very high if the

current scheme for channel estimation and signal equalization is used. Future work could

address this drawback in computational complexity, and efforts can be made to decrease

computational load while increasing the accuracy.

74

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