AN ABSTRACT OF A THESIS

PERFORMANCE ANALYSIS OF ULTRA-WIDEBANDTRANSMITTED REFERENCE SYSTEM AND

ENHANCEMENT TECHNIQUES

Satish Kaza

Master of Science in Electrical Engineering

The transmitted reference (TR) receivers have been known of for many decades,but there is a renewed interest for application of TR receivers as a suboptimal solu-tion for ultra-wideband (UWB) communications because of the difficulty being facedin estimating the channel accurately for an optimal solution. In this research, theperformance of UWB-TR receivers in an indoor UWB channel was evaluated .

In this work, performance of UWB-TR receivers was first evaluated in non-intersymbol interference (ISI) case. Few techniques, e.g., differential TR and referenceenhanced differential TR, were tried to improve the performance in this case. Impactof variation in integration length on the performance of the system was also studiedin case of no ISI. At higher data rates, performance of TR receivers are not promisingbecause of the presence of ISI. Performance of TR receivers when used along witha temporal focusing technique known as time reversal (TiR) in the presence of ISIwas also evaluated. Performance of a digital approach to TiR was also studied viasimulations.

The performance of reference enhanced TR receiver’s showed significant im-provement over simple TR receivers. Simulations suggested that integration intervalis an important design parameter, which in turn improves the effective SNR of thedecision variable thus improving receiver performance. TiR based TR receivers (TiR-TR) showed significant performance improvement at higher data rates. The digitalapproach to TiR-TR showed almost identical performance as the original (TiR-TR)approach at optimum thresholding.

PERFORMANCE ANALYSIS OF ULTRA-WIDEBAND

TRANSMITTED REFERENCE SYSTEM AND

ENHANCEMENT TECHNIQUES

A Thesis

Presented to

the Faculty of the Graduate School

Tennessee Technological University

by

Satish Kaza

In Partial Fulfillment

of the Requirements for the Degree

MASTER OF SCIENCE

Electrical Engineering

December 2004

CERTIFICATE OF APPROVAL OF THESIS

PERFORMANCE ANALYSIS OF ULTRA-WIDEBAND

TRANSMITTED REFERENCE SYSTEM AND

ENHANCEMENT TECHNIQUES

by

Satish Kaza

Graduate Advisory Committee:

R. C. Qiu, Chairperson date

P. K. Rajan date

J. R. Austen date

Approved for the Faculty:

Francis OtuonyeAssociate Vice President forResearch and Graduate Studies

Date

ii

STATEMENT OF PERMISSION TO USE

In presenting this thesis in partial fulfillment of the requirements for a Master

of Science degree at Tennessee Technological University, I agree that the University

Library shall make it available to borrowers under rules of the Library. Brief quota-

tions from this thesis are allowable without special permission, provided that accurate

acknowledgment of the source is made.

Permission for extensive quotation from or reproduction of this thesis may be

granted by my major professor when the proposed use of the material is for scholarly

purposes. Any copying or use of the material in this thesis for financial gain shall not

be allowed without my written permission.

Signature

Date

iii

DEDICATION

This thesis is dedicated to my parents.

iv

ACKNOWLEDGMENTS

I would like to express my sincere appreciation to my advisor, the chairperson

of my committee, Dr. R. C. Qiu, for his excellent guidance and immense patience

throughout this work. I would like to thank Dr. Rajan and Dr. Austen for serving

as my committee members, reviewing my thesis work, and for patiently answering

all the questions that I asked. I need to thank Dr. N. Guo for all the long technical

conversations which he had with me, which had a significant impact on the research

conducted in this work. I would also like to thank all my friends and colleagues who

were really helpful to me throughout the year.

Last but most important I would like to thank my family who have always been

a source of encouragement throughout my life. Finally, I would also like to thank the

Department of Electrical and Computer Engineering, and Center for Manufacturing

Research for the financial support provided during my study.

v

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Chapter

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Motivation and Scope of Research . . . . . . . . . . . . . . . 1

1.2 Literature Survey of Transmitted Reference Systems . . . . . 2

1.3 Research Approach . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Organization of the Thesis . . . . . . . . . . . . . . . . . . . 4

2. ULTRA WIDEBAND COMMUNICATION (UWB) . . . . . . . . . . . 6

2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Definition and Frequency of Operation . . . . . . . . . . . . 7

2.3 Shape and Spectrum of UWB Signals . . . . . . . . . . . . . 8

2.4 UWB Modulation Techniques . . . . . . . . . . . . . . . . . 12

2.4.1 On-Off Keying (OOK) . . . . . . . . . . . . . . . . . . . 12

2.4.2 Pulse Position Modulation (PPM) . . . . . . . . . . . . . 14

2.4.3 Bi-phase Modulation . . . . . . . . . . . . . . . . . . . . 15

2.5 Multiple Access Techniques . . . . . . . . . . . . . . . . . . . 17

2.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

vi

vii

Chapter Page

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3. TRANSMITTED REFERENCE SYSTEM . . . . . . . . . . . . . . . 22

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

3.2 Transmitted Reference (TR) . . . . . . . . . . . . . . . . . . 22

3.2.1 System Structure . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Performance Analysis of TR Receiver . . . . . . . . . . . 25

3.3 Differential Transmitted Reference (DTR) . . . . . . . . . . 30

3.3.1 System Structure . . . . . . . . . . . . . . . . . . . . . . 30

3.3.2 Performance Analysis of DTR Receiver . . . . . . . . . . 33

3.4 Modified Differential Transmitted Reference (MDTR) . . . . 34

3.4.1 Performance Analysis of MDTR Receiver . . . . . . . . . 35

3.5 Time Reversal and Transmitted Reference (TiR-TR) . . . . 37

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4. SIMULATIONS AND RESULTS . . . . . . . . . . . . . . . . . . . . . 43

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

4.2 Simulation Approach . . . . . . . . . . . . . . . . . . . . . . 43

4.2.1 Pulse Generator . . . . . . . . . . . . . . . . . . . . . . . 43

4.2.2 Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.3 Channel Model . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.4 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . 46

4.2.5 Bit Error Rate (BER) Calculation . . . . . . . . . . . . 47

viii

Chapter Page

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3.1 Performance in the Absence of Intersymbol Interference(ISI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3.1.1 Integration interval optimization . . . . . . . . . . . 48

4.3.2 Performance in the Presence of ISI . . . . . . . . . . . . 54

4.3.3 Time Reversal and TR (TiR-TR) . . . . . . . . . . . . . 57

4.3.4 Performance with Monobit TiR-TR . . . . . . . . . . . . 60

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5. CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . . . 61

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Recommendations for Future Work . . . . . . . . . . . . . . 62

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

APPENDICES

A: PERFORMANCE ANALYSIS OF SUBOPTIMAL RECEIVERS . . . . . 71

A.1 Transmitted Reference . . . . . . . . . . . . . . . . . . . . . 72

A.2 Differential Transmitted Reference . . . . . . . . . . . . . . 76

A.3 Modified Differential Transmitted Reference . . . . . . . . . 78

B: IEEE CHANNEL MODEL IEEE P802.15.3A . . . . . . . . . . . . . . . . 81

B.1 Multipath Channel Model . . . . . . . . . . . . . . . . . . . 82

B.2 Channel characteristics desired to model . . . . . . . . . . . 84

C: MATLAB CODE LIST . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

C.1 List of System simulation M-files . . . . . . . . . . . . . . . 89

ix

Chapter Page

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

LIST OF TABLES

Table Page

4.1 Multipath delay spread time for the channels . . . . . . . . . . . . . . . 45

B.1 Channel model components and parameters . . . . . . . . . . . . . . . 83

B.2 Example channel characteristics and model parameters. . . . . . . . . . 84

x

LIST OF FIGURES

Figure Page

2.1 Spectral Mask for Indoor Applications . . . . . . . . . . . . . . . . . . 8

2.2 Spectral Mask for Outdoor Applications . . . . . . . . . . . . . . . . . 9

2.3 Shape of a UWB Pulses in Time Domain . . . . . . . . . . . . . . . . . 10

2.4 Spectrum of the UWB Pulses . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 UWB Modulation Schmes, (a) On-Off Keying (OOK), (b) Pulse PositionModualtion (PPM), (c) Biphase Modulation . . . . . . . . . . . . . . 16

2.6 Probability of Bit Error for Different Modulation Schemes with MatchedFilter Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1 TR Frame Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Block Diagram of TR Transmitter . . . . . . . . . . . . . . . . . . . . . 24

3.3 Block Diagram of TR Receiver . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 TR Frame Example given by Equation (3.1) . . . . . . . . . . . . . . . 26

3.5 TR frame at the Receiver Without AWGN noise . . . . . . . . . . . . . 27

3.6 DTR Frame Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.7 (a) Block Diagram of DTR Transmitter, (b) Block Diagram of DTRReceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.8 DTR Frames Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.9 DTR frames at the Receiver without AWGN noise . . . . . . . . . . . . 33

3.10 Modified DTR receiver with M=2 . . . . . . . . . . . . . . . . . . . . . 35

xi

xii

Figure Page

3.11 Closed Form curves of BEP of the three receiver structures in densemultipath environment without any ISI . . . . . . . . . . . . . . . . . 37

3.12 ISI when Tf < Tmds, when information bits (1 0 0 0) are sent using TR 38

3.13 Autocorrelation of Channel Impulse Response . . . . . . . . . . . . . . 39

3.14 Received Signal with TiR Prefilter at the Transmitter. Infomation bitssent were (1 0 0 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 CM 1: LOS (0-4 m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Comparing Closed form and Simulation Model results . . . . . . . . . . 48

4.3 Energy Capture versus Time for Channel CM 4 . . . . . . . . . . . . . 49

4.4 BER Performance of TR system at Different Integration Lengths forChannel CM 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.5 BER Performance of TR system versus Integration Interval length forChannel CM 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.6 BER Performance of TR system at Different Integration Lengths forChannel CM 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.7 Performance of DTR Receivers at Different Integration Length forChannel CM 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.8 Performance of TR in Channel CM 1 at High Data Rates . . . . . . . . 55

4.9 Performance of TR in Channel CM 4 at High Data Rates . . . . . . . . 56

4.10 Time Reversal and TR at different Integration Lengths . . . . . . . . . 57

4.11 Performance Improvement after Using Time Reversal with TR (CM 4) 58

4.12 Performance with diffferent thresholds (CM 4) . . . . . . . . . . . . . . 59

B.1 CM 1: LOS (0-4 m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

xiii

Figure Page

B.2 CM 2: NLOS (0-4 m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

B.3 CM 3: NLOS (4-10 m) . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

B.4 CM 4: Extreme NLOS . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

CHAPTER 1

INTRODUCTION

1.1 Motivation and Scope of Research

In 2002, the United States Federal Communication Commission (FCC) al-

located 7.5 GHz spectrum from 3.1 GHz to 10.6 GHz for ultra-wideband (UWB)

devices. After this, the following years have seen significant increase in research ac-

tivity in both industry and academic circles [1] in the field of UWB systems for short

range indoor communications [2]. UWB communication involves transmitting data

using very short pulses thus occupying very large bandwidth. The energy of the UWB

signals is spread over a large spectrum thus having the inherent property of being

overlaid over existing systems in that frequency range. The advantage of using short

pulses is fine timing resolution thus more channel multipaths can be resolved [3]. But

the channel distorts these short pulses so that per-path distortion is encountered in

UWB systems. As discussed in [4] and [5], the design of a reception scheme is a key

issue for UWB communication.

The rake receiver [6] which is a popular choice in case of multipath channels

might require tens or even hundreds of fingers in some cases to capture the available

energy [7]. This kind of receiver combined with maximal ratio combining (MRC)

would be an optimal approach in the case of no per-path distortion, but in the case

of UWB, traditional rake may not work and even if it works with some modification,

for example, the one suggested by Altes [8], the solution would not be inexpensive.

The Altes structure originally proposed in underwater acoustics was introduced into

UWB in [4], [5]. An alternate approach is based on orthogonal frequency division

1

2

multiplexing (OFDM) techniques [9, 10, 11] where a large number of sub bands are

used. The signal used to transmit data over these subbands is a narrowband signal

so that frequency dispersion should not be a problem. This might be a good solution

but is not an inexpensive solution either.

Another approach, namely transmitted reference (TR), initially proposed for

spread spectrum communication has regained popularity. The TR scheme used along

with correlation-based receivers or more popularly known as suboptimal receivers

does not require channel estimation. Because of the cost issues and complexity issues

suboptimal reception schemes have become very popular. This was the motivation

for this thesis to evaluate the performance of suboptimal receiver techniques for UWB

TR systems.

The objective of this research was to better understand the performance of sub-

optimal receivers via simulations and try to improve the performance of the existing

receivers. Performance at higher data rates in case of multipath rich channels, where

intersymbol interference (ISI) is an important issue, was also investigated. Methods

to improve the performance at higher data rates were also investigated.

1.2 Literature Survey of Transmitted Reference Systems

Transmitted reference is not a new technique. Decades ago it was proposed as

a technique for communicating in random and unknown channels [12, 13, 14]. In year

2002 Hoctor and Tomlison proposed and experimented a simple UWB delay-hopper

TR (DHTR) system [15, 16, 17] that captures all the received signal energy without

requiring channel estimation and provides multi-user capability. In this scheme each

code divison multiple access (CDMA) code chip is represented by multiple pulse pairs

(data pulse and reference pulse). For each code chip the time interval between pulse

3

pairs is unique. The major drawback of this system is the use of noisy template for

demodulation. In [18], an autocorrelation receiver that averages previously received

reference pulses to suppress noise was presented. This TR system’s performance was

evaluated using pulse position modulation (PPM). But the implementation of the

averaging operation as described in this approach is a complicated process.

Chao and Scholtz in [19] described optimal and suboptimal receivers for UWB

TR systems. The suboptimal receiver based on differential coding was described

in this paper and the system was named differential transmitted reference (DTR).

This system is a modification of the TR system since in this, instead of transmitting

a separate pulse the data are differentially modulated using previously sent pulses.

A 3 dB gain in performance was obtained with the modification. A drawback in

this system is that its performance is not good because of noisy template problem.

Some enhancement techniques were defined in [20, 21] that improve the quality of

reference and thereby improving the performance of the receivers. In the same time

when this work was being finished Mitra [22] published the results for integration

interval optimization. This work was done independent to that work. The results

of this work are consistent with Mitra’s result and thus restate the importance of

integration interval optimization for improving the performance of these suboptimal

receivers.

Performance at higher data rates suffers from intersymbol interference (ISI)

because of the large multipath delay spread of the channels. To improve performance

an older transmission scheme called time reversal (TiR) [23, 24, 25] was used. Time

reversal [26, 27] is a technique in which spatial and temporal focusing is obtained in

multipath rich environment. This technique was used along with MMSE equalizer in

[28]. In order to improve TR systems performance in case of ISI with acceptable level

4

of complexity time reversal was used in conjunction with TR to evaluate performance

at higher data rates. Around 9 dB improvement compared to simple TR scheme was

obtained using this approach.

1.3 Research Approach

Different correlation based receivers are studied and implemented using Matlab

software package. Bit error rate (BER) performance will be used as the performance

parameter. Performance of the receiver would be evaluated in case of IEEE P802.15.3a

[29] indoor channel model. Performance of the receivers is evaluated using the sim-

ulation models and then the system parameters are varied so as to optimize the

performance for no ISI case. For ISI case first system performance is evaluated and

then a novel receiver technique is tested for the same ISI model at high data rates.

1.4 Organization of the Thesis

Chapter 2 presents basic theory behind UWB communication; spectral regu-

lations, pulse shapes, different modulation schemes, and applications are discussed.

A brief discussion about performance of these modulation schemes is also discussed.

Chapter 3 investigates different kinds of correlation receivers and also presents

their analytical performance. Some modifications done to some existing schemes to

improve BER performance are also discussed.

Chapter 4 focuses on evaluating the performance of different receiver schemes

via simulation based approach. This chapter also presents performance in ISI scenario

and performance evaluation for time reversal based systems.

5

Finally, Chapter 5 presents results and conclusions on the performance of dif-

ferent systems discussed earlier with emphasis on optimization in non-ISI case and

performance in ISI case. Recommendations for future work are also presented in this

chapter. Appendix A contains the analytical analysis of the modulation schemes dis-

cussed in Chapter 3. Appendix B briefly introduces the IEEE channel model IEEE

P802.15.3a. Listing of the Matlab code is given in Appendix C.

CHAPTER 2

ULTRA WIDEBAND COMMUNICATION (UWB)

In this chapter, basic theory behind Ultra Wideband (UWB) communication

is presented. Spectral regulation, shapes and spectrum of UWB pulses, modulation

techniques, and multiple access techniques are discussed. Additionally, applications

of UWB technology are also discussed in the end.

2.1 History

Genesis of UWB technology is from work in time-domain electromagnetic that

began in 1962 [30]. The concept was to characterize linear, time-invariant (LTI)

systems by their output response to an impulse excitation, instead of the more con-

ventional means of swept frequency response (i.e., amplitude and phase measurements

versus frequency). This output response is known as impulse response h(t). Output

response y(t) of a LTI system to any input response x(t) is determined by the convo-

lution integral [31]:

y(t) =

∞∫−∞

h(τ)x(t− τ)dτ . (2.1)

However, it was not possible to measure the impulse response directly until

the development of impulse excitation and measurement techniques. Once these

techniques were in place it was obvious that these could be used for short pulse radar

and communication systems. In 1978 Ross and Bennett [32] applied these techniques

for radar and communication applications.

6

7

This technology was referred to as baseband, carrier-free or impulse until late

80’s and was termed “ultra wideband” by the U. S. Department of Defense around

1989. By that time, UWB theory has experienced 30 years of development. Although

UWB technology is old, its application for communication is a relatively new trend.

2.2 Definition and Frequency of Operation

UWB technology in principle is the use of extremely short pulses for transmit-

ting information. Since the pulse is very short it produces a very wide instantaneous

bandwidth signal. A signal is classified as a UWB signal if its fractional bandwidth is

greater than 0.2 or it occupies more than 500 MHz of spectrum. Fractional bandwidth

(Bf ) is defined as

Bf = 2(fh − fl)

(fh + fl)(2.2)

where

fh=upper frequency measured -10 dB below peak emission point

fl=lower frequency measured -10 dB below peak emission point.

The Federal Communication Commission (FCC) alloted 7.5 GHz of usable

spectrum bandwidth from 3.1 GHz to 10.6 GHz for communications use to be operated

under a strict spectral mask. Spectral masks are in place to protect the existing users

operating within the spectrum. UWB signals may be transmitted at power spectral

density (PSD) levels up to -41.3 dBm per MHz, which complies with general Part 15

emission limits to control radio interference. Figure 2.1 and Figure 2.2 shows spectral

masks for indoor and outdoor operations. Outdoor operation has a higher degree of

8

100 101

−75

−70

−65

−60

−55

−50

−45

−40

Frequency in GHz

UW

B E

IRP

Em

issi

on L

evel

in d

Bm

/ MH

z

Indoor LimitPart 15 Limit

Figure 2.1. Spectral Mask for Indoor Applications

attenuation than the indoor operation at the out-of-band region to protect the GPS

receivers, centered at 1.6 GHz.

2.3 Shape and Spectrum of UWB Signals

It is evident from the definition of UWB technology that UWB systems spread

transmitted power over an extremely large frequency band and thus have a very small

PSD in case of limited amount of transmitted power. “Gaussian Waveforms” are

the most popular choice for UWB communication because of the ease of generation

9

100 101

−75

−70

−65

−60

−55

−50

−45

−40

Frequency,GHz

UW

B E

IRP

Em

issi

on L

evel

in d

Bm

/ MH

z

Outdoor LimitPart 15 Limit

Figure 2.2. Spectral Mask for Outdoor Applications

and simple mathematical formulation. These waveforms are termed as Gaussian

waveforms because of their similarity to the Gaussian function. A Gaussian waveform

as shown in Figure 2.3 can be described by

pg (t) = Ae−( tτ )

2

(2.3)

where

A is the pulse amplitude (volts)

10

−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time in ns

Nor

mal

ized

Am

plitu

deGaussian Pulse1st order Differential2nd order Differential

Figure 2.3. Shape of a UWB Pulses in Time Domain

t is the time (seconds)

τ is the parameter that determines the pulse width (seconds).

Another waveform shown in Figure 2.3 can be produced by differentiating the

Gaussian pulse once, this pulse is called a Rayleigh Monocycle [33]. This waveform

has one zero crossing point and is given by

p1 (t) = At

τe−( t

τ )2

(2.4)

11

0 2 4 6 8 10 12

10−30

10−25

10−20

10−15

10−10

10−5

100

105

Frequency in GHz

Nor

mal

ized

Am

plitu

de in

dB

Gaussian Pulse1st order Differential2nd order Differential

Figure 2.4. Spectrum of the UWB Pulses

and in frequency domain it is given by

P1 (f) = −jfτ 2e−f2τ2

. (2.5)

As shown in Figure 2.3 and Figure 2.4 as the order of differentiation increases,

number of zero crossing points increase, bandwidth decreases, and the center fre-

quency increases if τ is kept constant.

Since the PSD of the UWB pulses is very low this limits the amount of in-band

interference to the narrowband signals. The interference due to UWB systems at most

12

contributes in raising the noise floor slightly for the narrowband or any other receiver

working in that frequency band. Thus it can be concluded that a limited number of

UWB systems can co-exist with current communication signals in the same frequency

band.

2.4 UWB Modulation Techniques

For coherent detection numerous modulation techniques were used initially for

UWB communication but three techniques that are most popular and found place

in many papers and journals are On-Off Keying (OOK), Pulse Position Modulation

(PPM) and Bi-phase Modulation.

2.4.1 On-Off Keying (OOK)

OOK is a shape-based modulation technique where in the presence or absence

of a pulse is synonymous to binary information bit “1” or “0,” respectively. Following

equation represents a OOK modulated UWB transmitted signal and the waveform is

as shown in Figure 2.5:

s (t) =∞∑

n=−∞bnp (t− nTf ) (2.6)

where

s(t) is the UWB signal

bn ∈ 0, 1 data bits

p(t) is the UWB pulse

Tf is the frame time.

13

The main advantage of OOK scheme over other shape-based modulation tech-

niques is its ease of physical implementation. Only one pulse generator is required

for OOK modulated system so that this pulse generator is switched on or off using a

RF switch depending on whether a “1” or a “0” is transmitted.

The main drawback for OOK over other shape-based modulation systems like

Bi-phase modulation is its bit error rate (BER) performance [34] as shown in Figure

2.6. This is because for an equal symbol energy in both the cases OOK has smaller

symbol separation and thus has worse performance based on the fact that BER per-

formance is directly proportional to separation between symbols. BER performance

of an OOK system under the assumption of a matched filter reception is given by

Pe = Q

(√Eb

N0

)(2.7)

where

Pe is the probability of error

Q is the Q-function

Eb is the average energy per bit (Joules)

N0 is the noise energy spectral density at the detector (Joules/Hz).

The Q-function [35] is the tail integral of the standard Gaussian density func-

tion (mean µ = 0 and variance σ = 1) and is defined by

Q (x) =

∞∫x

1√2π

e−z2/2dz. (2.8)

14

2.4.2 Pulse Position Modulation (PPM)

PPM is a time-based modulation technique so that the important parameter

is the delay of the pulse. That is, the timing of pulses is varied to transmit data

instead of amplitude as was the case in earlier modulation techniques. For a binary

PPM method, when a data bit “1” is sent an additional time shift δ is added to the

pulse and for sending “0” no additional time shift is added so that a uniformly spaced

pulse train is sent as shown in Figure 2.5. Binary PPM technique is given by

s (t) =∞∑

n=1

p (t− nTf − δbn) (2.9)

where

bn ∈ 0, 1 data bits

δ is time shift.

The main disadvantage of PPM scheme is its BER performance [34] which is

the same as that of OOK scheme but worse than Bi-phase modulation for the same

average energy. Figure 2.6 shows the BER performance of PPM scheme and it can

be seen that its performance in case of matched filter reception is the same as that

of OOK and is given by

Pe = Q

(√Eb

N0

). (2.10)

The advantage of PPM is that it is an orthogonal signaling scheme such that

each pulse is independent of the other. Thus during each symbol period a pulse

15

is transmitted in its specified time slot. For M-ary modulation schemes PPM per-

forms better than Bi-phase modulation in terms of BER performance and efficiency

of transmission.

In M-ary case, PPM suffers from the problem of intersymbol interference (ISI)

at higher data rates since multiple positions are required for high data rate. Therefore

pulse data rate should be kept low to reduce the effect of ISI. And in case of dense

multipath environment even at low data rates the performance of PPM receivers is

not good because the pulses tend to overlap with next data pulses thus increasing bit

errors at the receivers.

2.4.3 Bi-phase Modulation

Bi-phase modulation or antipodal modulation is a technique which involves

modulating the polarity of the pulse. For example, a positive pulse is transmitted

for a “1” and a negative pulse is transmitted for a “0” as shown in Figure 2.5.

Mathematically Bi-phase is given by

s (t) =∞∑

n=−∞bnp (t− nTf ) (2.11)

where

bn ∈ 1,−1 data bits.

An advantage of Bi-phase modulation over OOK and PPM is the improvement

in BER performance, because Eb/N0 is 3 dB less for the same probability of error.

Assuming that a matched filter receiver was used the BER performance [34] as shown

16

0 5 10 150

0.5

1

Nor

mal

ized

Am

plitu

de

0 5 10 150

0.5

1

Nor

mal

ized

Am

plitu

de PPMUniform Pulse Train

0 5 10 15−1

−0.5

0

0.5

1

Time in ns

Nor

mal

ized

Am

plitu

de

(a)

(b)

(c)

Figure 2.5. UWB Modulation Schmes, (a) On-Off Keying (OOK), (b) PulsePosition Modualtion (PPM), (c) Biphase Modulation

in Figure 2.6 is given by

Pe = Q

(√2Eb

N0

). (2.12)

Although it has many advantages its main disadvantage is the physical im-

plementation part. A Bi-phase modulated system requires two pulse generators with

opposite polarities as compared to one in an OOK system. Although the imple-

mentation is a bit complex, still Bi-phase modulation is a very efficient and popular

technique for transmitting UWB pulses.

17

0 5 10 1510−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

Pro

babi

lity

of E

rror

BiPhase

OOK , Binary PPM

3 dB

Figure 2.6. Probability of Bit Error for Different Modulation Schemes withMatched Filter Reception

2.5 Multiple Access Techniques

There are two common multiple access techniques for impulse radio UWB

systems that are used along with the earlier discussed modulation techniques. A

technique proposed by Scholtz [36, 37] known as Time Hopping is one such tech-

nique. This technique can be used in conjunction with all the modulation techniques

described in Section 2.4. A typical time-hopped signal with PPM modulation defining

18

a transmitted for kth user is given by

sk (t) =∑n

p(t− nTf − ck

nTc − δbkbn/Nsc

)(2.13)

where

p(t) is the transmitted pulse

Tf is the frame repetition time (seconds)

ckn is the hopping code to avoid collision in multiple accessing

Tc is the time interval when a user is active (seconds)

bn is the nth binary symbol

δ is the time shift for PPM

Ns is the number of pulses transmitted per symbol.

In this modulation format a single symbol is transmitted for a time duration

Ts = NsTf . Thus the symbol rate Rs (per second) is defined as

Rs =1

Ts

=1

NsTf

. (2.14)

Direct Sequence (DS) is another multiple access technique that is popular in

UWB community. At the transmitter information symbol to be transmitted is first

spread with a pseudo random or PN sequence and then amplitude modulated with

a train of short pulses. At the receiver the received information is initially dispread

using the same PN sequence used for spreading. This system of communication is

called DS-UWB [38] and the transmitted signal for the kth user is given by

sk (t) =∑n

Nr−1∑i=0

bkna

ki p (t− nTr − iTc) (2.15)

19

where

Nr is the spread spectrum processing gain, Nr = Tr/Tc

aki is the kth user spreadng chips

Tr is the bit period

Tc is the chip period.

2.6 Applications

UWB technology is popular for its multipath immunity, high data throughput,

better wall penetration, low power consumption, and low probability of interception

and detection. Because of all these features UWB technology has become increas-

ingly accepted for numerous applications in civilian and military field. Some of the

applications that can be integrated with UWB are listed below

Through-wall Sensing System

To detect the motion of a person or objects that are placed on the other side of

a wall, high resolution is required. Precision time gating is required to track multiple

targets at longer ranges as in [39]. And an UWB system is a reliable solution in

providing this kind of resolution and through-wall penetration capabilities.

Precision Location

Modern day Global Positioning Satellite systems (GPS) suffer from numerous

sources of errors. But these can be improved and location can be precisely estimated

within 1-2 meters using differential GPS system for outdoor application. But using

UWB in addition to these technologies is a viable solution for extending the location

finding capabilities to the indoor. And even in the vicinity of buildings and large

20

topographic features GPS receivers have major problems due to multipaths. But a

UWB augmented GPS system can work really well in these kinds of situations [39].

UWB Radar

UWB pulses are short in time duration and thus millions of pulses could be

sent in a second so that a near perfect image of the target is obtained. Advantage

in using UWB in this application is that due to its inherent time resolution property

it reduces post detection signal processing as is required in narrowband radars to

improve the detected image [39, 40].

UWB underground penetrating radars can be used to find live things in a pile

of rubble [41]. And these kinds of radars could also be used to check if any under-

ground cables or pipes are present before digging. Thus these kinds of radars can

be used in numerous applications like target specific application, civil engineering

applications, geophysical application, and many more.

Sensor Networks (IEEE 802.15.4a)

Sensor networks are currently used for surveillance, automobiles, and medical

situations and for numerous other applications. If a wired network is used it is very

cumbersome, expensive, and uncomfortable in situations where wires are visible and

in the way of work. UWB is a viable solution as a wireless communication link in

these kinds of application so that although the work is being done, but the network

is still unnoticeable and invisible to others. And sometimes UWB signal itself can be

used as a sensor.

21

UWB technology applications are not limited. As there is more improvement

in source, receiver and antenna technologies UWB would find more and more appli-

cations so that there exists a wires free world

2.7 Summary

This chapter discussed communication fundamentals using UWB pulses. The

regulatory issues and different pulse shapes that are used along with different modu-

lation schemes that could be implemented in conjunction with UWB signals were also

discussed. A discussion on multiple access techniques was also presented and some

applications of UWB technology in communication area were also examined.

CHAPTER 3

TRANSMITTED REFERENCE SYSTEM

3.1 Introduction

In this chapter, correlation receivers are studied. Three receiver structures,

namely transmitted reference (TR), differential transmitted reference (DTR), and

modified differential transmitted reference (MDTR), are discussed. Analytical per-

formance of these receivers is evaluated. The concept of intersymbol interference for

a TR is explained and a solution is discussed to counter this problem.

3.2 Transmitted Reference (TR)

Channels encountered by UWB communication systems are highly dispersive

in nature and so the channel estimation is a very challenging task. Designing a

receiver that generates reference locally at the receiver, estimates the channel, and

captures enough energy for data detection is a difficult and costly process. But

instead of locally generating the reference signal, it can be transmitted along with

the information data. Such a system is known as transmitted reference (TR) system.

TR scheme is not a new technique but had been proposed more than 50 years back for

spread spectrum communication [12, 13, 14, 42]. TR has regained popularity with

UWB communication systems after Hoctor and Tomlinson [15, 16] proposed a UWB

TR system with a simple receiver structure which captures all of the energy available

in a UWB multipath channel for demodulation at the receiver. TR is a correlation

receiver system; thus a TR system does not require channel estimation and has weak

dependence on distortion.

22

23

3.2.1 System Structure

In its most basic form a TR communication system is one in which a pair of

pulses are transmitted in each frame. Of these two pulses first one is the unmodulated

reference pulse, which provides the multipath channel’s pulse response to the demod-

ulator at the receiver end. Second pulse is the data modulated pulse. The separation

between modulated and the reference pulse takes place in time was introduced in

[12, 13, 14]. Since the two pulses are transmitted within a very short time period, it

is assumed that the channel response is the same for both pulses in a TR frame [19].

Placement of the two pulses in a TR frame is as shown in Figure 3.1.

The block diagram of a TR transmitter system is shown in Figure 3.2. As

shown in the figure, transmitter of a TR system comprises of a pulse generator, a

delay line, and an antenna unit.

Pulse generator produces pulses after some fixed frame time and a replica of

this pulse is delayed with the help of a delay line. This delayed pulse is modulated

according to the information bit and added to the pulse generated earlier. This is

how a TR frame is produced having a structure as shown in Figure 3.1. The biggest

advantage of this system as shown in Figure 3.3 is its simple receiver structure. The

Figure 3.1. TR Frame Structure

24

Figure 3.2. Block Diagram of TR Transmitter

receiver comprises of a delay line and a correlator to demodulate the signal, and an

addition unit to add over Ns pulses so that enough energy is captured to estimate

the information bit.

Assuming a single-user UWB system with antipodal modulation (binary pulse

amplitude modulation), a typical transmitted reference frame is given by

str (t) =∑k

p (t− kTf ) + bbk/Nscp (t− kTf − Td) (3.1)

Figure 3.3. Block Diagram of TR Receiver

25

where

p(t) is the Gaussian pulse with pulse width Tw

k is the frame index

Tf is the frame time

Td is the delay between reference and modulated pulse

Ns is the number of successive times the frame is repeated to achieve

adequate bit energy required for detection

bl is the lth binary data bit ∈ 1,−1.

Figure 3.4 is an example TR frame. For a single user case when operating in

a multipath channel with multipath delay spread time Tmds, to avoid inter symbol

interference (ISI) problem a TR frame is designed such that Tf ≥ 2Td ≥ 2Tmds.

3.2.2 Performance Analysis of TR Receiver

The received signal is given by

r(t) = str(t)⊗ h(t) + n(t) (3.2)

where

⊗ represents convolution operation

h(t) is the channel impulse response

n(t) is the additive white gaussian noise (AWGN) with two sided power

spectral density N0/2 and zero-mean.

For a multipath channel h(t) spread over time Tmds the received signal r(t)

corresponding to a transmitted signal str is as shown in Figure 3.5. As it can be

26

0 20 40 60 80 100 120−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time(ns)

Norm

alize

d Am

plitu

de

Td (ns)

Td (ns)

Reference Pulse

Data Modulated Pulse Bit 0 sent in the frame.

Figure 3.4. TR Frame Example given by Equation (3.1)

seen in Figure 3.5 the two pulse responses corresponding to the reference pulse and

the modulated pulse are not overlapping on each other. This case is referred to as a

non-ISI case and is possible because of the careful placement of the two pulses in a

TR frame.

To evaluate the performance of the structure the received signal is passed

through an ideal LPF to limit the out-of-band noise. The bandwidth W of the LPF

is wide enough so that the signal spectrum is not distorted when the signal passes

27

0 20 40 60 80 100 120

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time (ns)

Norm

alize

d Am

plitu

de

Response of information carrying pulse to mutipath channel CM1 Response of reference pulse to multipath channel CM1

Figure 3.5. TR frame at the Receiver Without AWGN noise

through it. The filtered received signal is expressed as

∧r(t) = str (t)⊗

∧h (t) +

∧n (t) (3.3)

where

∧r(t),

∧h (t) and

∧n (t) represent the terms defined earlier at the output

of the filter.

The receiver exploits the diversity inherent to the multipath channel by using

the autocorrelation demodulation technique [18]. For any transmitted symbol the

receiver correlates the channel response of the corresponding reference pulse and the

28

channel response of the information carrying pulse. Assuming perfect synchroniza-

tion, sum total of all correlated values over Ns frames is used as the decision statistic

to detect the transmitted data symbol (bn), the decision statistic (y) is given by

y =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∧r (t− Td)

∧r (t) dt. (3.4)

From Equations (3.4) and (3.2), the correlator output (y) can be rewritten as:

y =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

[str (t− Td) ∗

∧h (t− Td) +

∧n (t− Td)

] [str (t) ∗

∧h (t) +

∧n (t)

]dt

=Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

[str (t− Td) ∗

∧h (t− Td)

] [str (t) ∗

∧h (t)

]dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

[str (t− Td) ∗

∧h (t− Td)

]∧n (t) dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

[str (t) ∗

∧h (t)

]∧n (t− Td) dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∧n (t− Td)

∧n (t) dt

(3.5)

= Y + N1 + N2 + N3. (3.6)

The decision at the decision unit is based on y. As shown in Equation (3.6)

Y is the desired correlator output. Y is the mean of the random variable y and the

three terms N1, N2, and N3 are the noise terms. N3 is the noise cross noise term

which mainly degrades the performance of the TR system where as N1 and N2 terms

are produced by the product of noise term in the reference part of frame and desired

signal in data part or vice versa. Thus the detection SNR [33, 43, 44] as defined at

29

the output of the correlator is given by

SNRtr∼=

Y 2

var (N1) + var (N2) + var (N3)(3.7)

where

var(Ni) is the variance of the noise terms.

By following the steps shown in Appendix A Equation 3.7 reduces to

SNRtr =

(

N0

Ep

)1

Ns

+

(N0

Ep

)2TmdsW

2Ns

−1

(3.8)

where

W is the one sided noise bandwidth of the receiver

Ep is the pulse energy and is evaluated as Ep =∞∫

−∞p2(t)dt.

Thus probability of bit error (Pe) of the TR system is given by

Pe = Q

(N0

Ep

)1

Ns

+

(N0

Ep

)2TmdsW

2Ns

− 12

. (3.9)

But here Eb defined as energy per bit transmitted is given as Eb = 2NsEp.

Then the Pe reduces to

Pe = Q

[(N0

Eb

)2 +

(N0

Eb

)2

2NsTmdsW

]− 12

. (3.10)

The bit error performance (BEP) of TR receiver in the presence of AWGN as

given by Equation (3.10) is shown in Figure 3.11.

30

3.3 Differential Transmitted Reference (DTR)

3.3.1 System Structure

Chao and Scholtz [19] defined a system based on the concept of autocorrelation

demodulation and differential encoding [44] and named it DTR system. A DTR

system is obtained by a simple modification to the TR system in which a reference is

not transmitted separately but instead the pulse previously sent is used as a reference

pulse. As shown in Figure 3.6 and Figure 3.8 the pulse for bit m also acts as the

reference for pulse for bit (m+1) which is produced after time Tf . By using the

previous pulse as reference a 3 dB improvement in performance and higher data rates

than TR system are expected of the new system. DTR system is a differentially

coherent technique. Like TR, DTR does not require channel estimation and very

weakly suffers from propagation distortion.

The transmitter and the receiver block diagrams for a DTR receiver are shown

in Figure 3.7. And comparing the TR and the DTR system it can be concluded that

between the two systems the difference is at the transmitter. At the transmitter of

DTR the pulse sent earlier is used as reference and is fed back and is modulated with

the following data bit bk. The receiver structures are similar in both the cases. The

Figure 3.6. DTR Frame Structure

31

Figure 3.7. (a) Block Diagram of DTR Transmitter, (b) Block Diagram ofDTR Receiver

transmitted signal as shown in Figure 3.8 for a DTR system can be described by

sdtr =∑k

b′kp (t− kTf ) (3.11)

32

0 20 40 60 80 100 120 140 160

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Time (ns)

Norm

alize

d Am

plitu

dePulse for bit (m−1)Pulse for bit (m)Pulse for bit (m+1)

Tf

1

0 0

Figure 3.8. DTR Frames Example

where

b′k is defined as b′k = b′k−1bdbk/Nsc

and bdl = blbl−1 is the differentially

encoded data.

Since the reference is not transmitted in each frame, for a single user case when

there is no ISI, Tf > Tmds with parameters being the same as defined for TR system.

33

0 20 40 60 80 100 120 140 160−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25Response for Pulse (m−1)Response for Pulse (m)Response for Pulse (m+1)1

0 0

Figure 3.9. DTR frames at the Receiver without AWGN noise

3.3.2 Performance Analysis of DTR Receiver

The received signal of a DTR system as shown in Figure 3.9 is given by

r (t) = h (t)⊗ sdtr (t) + n (t)

=∞∑

k=−∞b′kgdtr (t− kTf ) + n (t)

(3.12)

where

gdtr(t) is defined as gdtr (t) = h (t)⊗ p (t).

34

Under the assumption of perfect synchronization the decision statistic for data

detection on the signal after passing through an ideal LPF is defined as

y =Ns−1∑k=0

kTf+Tmds∫kTf

∧r (t− Tf )

∧r (t) dt

= Y + N1 + N2 + N3

(3.13)

where

Ni is as defined for TR system.

As shown in Appendix A the detection SNR at the output of the correlator is

SNRdtr =

(

N0

Ep

)(2Ns − 1)

N2s

+

(N0

Ep

)2TmdsW

2Ns

−1

. (3.14)

Thus the BEP performance of a DTR receiver is

Pe = Q

(N0

Ep

)(2Ns − 1)

N2s

+

(N0

Ep

)2TmdsW

2Ns

− 12

. (3.15)

Here Eb = NsEp, replacing this in Equation (3.15), then BEP of DTR system

as shown in Figure 3.11 is given by

Pe = Q

[(N0

Eb

)(2Ns − 1)

Ns

+(

N0

Eb

)2 NsTmdsW

2

]− 12

. (3.16)

3.4 Modified Differential Transmitted Reference (MDTR)

In moving from TR to DTR a 3 dB improvement in performance was at-

tained. But in both receivers the quality of reference limits the performance. Guo

35

and Qiu [20], and Liu, Tian, and Zhao [21] recommended a receiver configuration

which generates a reference by combining M consecutively generated symbol wave-

forms in a DTR receiver. This type of receiver is termed the MDTR receiver.

Shown in Figure 3.10 is a MDTR receiver with M=2. Thus by combining

two consecutive pulse waveforms a 3 dB improvement in SNR of reference pulse is

obtained. This improvement comes at the cost of some added complexity because a

MDTR (for M=2) requires an additional delay line and an addition unit.

3.4.1 Performance Analysis of MDTR Receiver

Transmitted signal for MDTR system is similar to that of a DTR system and

is given by

smdtr =∑k

b′kp (t− kTf )

Figure 3.10. Modified DTR receiver with M=2

36

The received signal is given by

r (t) = h (t)⊗ smdtr (t) + n (t) . (3.17)

If the signal at the output of the LPF is∧r (t), then without loss of generalization

the decision statistic y at output of the differential correlator for b′k = 1 is

y =

kTf+Tmds∫kTf

∧r (t)

1

M

[∧r (t− Tf ) +

M∑m=2

bestk−m

∧r (t−mTf )

]dt (3.18)

where

bestk−m is the (k −m)th estimated bit.

As shown in Appendix A, under the assumption of no ISI and no feedback

error the SNR at the output of the correlator is given by

SNRmdtr =

(

N0

Ep

)[1 + 1/M

2

]+

(N0

Ep

)2TmdsW

2M

−1

. (3.19)

The BEP of a MDTR is given by

Pe = Q

(N0

Ep

)[1 + 1/M

2

]+

(N0

Ep

)2TmdsW

2M

− 12

. (3.20)

Since in this receiver it was assumed that Ns = 1, thus Ep = Eb then Equation

(3.20) reduces to

Pe = Q

[(N0

Eb

) [1 + 1/M

2

]+(

N0

Eb

)2 TmdsW

2M

]− 12

. (3.21)

BEP performance of a MDTR system is as shown in Figure 3.11.

37

−5 0 5 10 15 20 2510−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

RTRDTRMDTR

Figure 3.11. Closed Form curves of BEP of the three receiver structures indense multipath environment without any ISI

3.5 Time Reversal and Transmitted Reference (TiR-TR)

At higher data rates when the multipath delay spread of the channel is larger

than the pulse repetition frequency, in this kind of scenario ISI would occur. To

illustrate ISI and its effect, Figure 3.12 shows the response of a TR frame in which

the reference and the modulation pulses are separated by 15 ns in a channel with a

multipath delay spread greater than 100 ns. In this scenario, getting a clean (free from

any interference) demodulation reference is not feasible. Therefore the performance

38

of the earlier discussed receivers would suffer in this case. To counter this drawback

in the case of rich multipath and scattering channels so that better performance at

higher data rates is achieved an older transmission scheme called time reversal (TiR)

[26, 27, 45, 46, 47, 48] has recently caught the attention of communication engineers

[23, 24, 25]. TiR was initially used for wideband transmission in under-water acoustics

and for ultra-sound. TiR was used to focus power of broadband signals in space

(spatial focusing) and time (temporal focusing) at the intended receiver. For UWB

communication both the properties are essential. By virtue of spatial focusing, peak

power is obtained at the receiver and the power profile decays rapidly away from

0 50 100 150−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Time (ns)

Nor

mal

ized

Am

plitu

de

Figure 3.12. ISI when Tf < Tmds, when information bits (1 0 0 0) are sentusing TR

39

−100 −80 −60 −40 −20 0 20 40 60 80 100−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (ns)

Nor

mal

ized

Am

plitu

de

Figure 3.13. Autocorrelation of Channel Impulse Response

receiver so that co-channel interference is minimal. And by temporal focusing the

effective length of the channel impulse response (CIR) is reduced drastically. Since the

effective channel length is reduced thus much higher data rates are possible without

any ISI problem.

The novel receiver scheme proposed in this work uses correlational receivers in

conjunction with TiR as discussed earlier. In doing so better performance is expected

at higher data rates. As proposed in [27] first the intended receiver sounds the UWB

channel by sending a pulse to the transmitter. The transmitter then estimates the

channel and this estimated CIR is used as a prefilter at the transmitter.

40

When transmitting, the transmitter sends the time reversed version of the

CIR back into the channel. This time reversed CIR backtracks the same channel

and focuses in space and time at the intended receiver. Spatial focusing is achieved

because the prefilter is sensitive to location of the receiver. This spatial focusing could

be used to provide a secured communication between a transmitter and receiver pair.

For a channel with CIR h(τ), the effective channel response as shown in Figure 3.13

at the receiver with prefilter in place at the transmitter is

hnew (t) = h∗ (−τ)⊗ h (τ) (3.22)

where

h∗(τ) is a complex conjugate of the channel impulse response.

When TR is used along with TiR the transmitted signal is given by Equation

3.1.

str (t) =∑k

p (t− kTf ) + bkp (t− kTf − Td)

Then the received signal at the receiver as shown in Figure 3.14 is given by

r (t) = str (t)⊗ hnew (t) + n (t) . (3.23)

Since the reference as well as the modulated pulses both encounter the same

kind of environment one can estimate the information bit as is done in the case of a

correlational receiver. Performance of this new scheme is evaluated via simulations.

41

0 50 100 150−1.5

−1

−0.5

0

0.5

1

1.5

Time (ns)

Nor

mal

ized

Am

plitu

de

Figure 3.14. Received Signal with TiR Prefilter at the Transmitter. Infoma-tion bits sent were (1 0 0 0)

The proposed prefilter is a real time adjustable filter. One-way of implementing

this prefilter as suggested by Guo [49] is to use a digital approach. For practical digital

implementation, monobit A/D conversion with states (±V ) is a promising solution.

However large quantization noise is introduced when signal is weak. To reduce the

effect of this noise use of a 3-level A/D conversion method with states (0,±V ) was

proposed and this was named monobit TiR-TR with thresholding. For an efficient

operation of this new method, optimal thresholding level is an important parameter.

The effect of thresholding on performance of the receiver, evaluated via simulations,

is presented in the next chapter.

42

TiR is a front-end technique. So it can be combined with any receiver structure

to form new schemes. For example, it can be combined with TR, DTR, and MDTR to

form new schemes TiR-TR, TiR-DTR, and TiR-MDTR. TiR can also be used jointly

with the matched filter plus MSEE to form optimum detection scheme [23, 24, 25].

The performance of these TiR based schemes is easy to obtain. Comparing

Equation 3.23, Equation 3.2, Equation 3.12, and Equation 3.17, then after replacing

h(t) in these equations by hnew(t), all the equations following Equations 3.2, 3.12,

and 3.17 are still valid.

It should be noted that the TiR technique is different than channel equaliza-

tion. Although TiR greatly increases the amount of energy captured, it will not result

in the capture of all the signal energy.

3.6 Summary

Correlational receivers were discussed in this chapter. Their analytical per-

formance evaluation was done. In the later part of the chapter a new receiver was

discussed that is expected to rectify the drawbacks in the earlier discussed receiver

models.

CHAPTER 4

SIMULATIONS AND RESULTS

4.1 Introduction

Earlier chapters introduced different UWB system models and provided the

analytical performance for each receiver under the assumption of no ISI case. In

this chapter system is analyzed to optimize the performance of the system using the

Monte Carlo simulations. Performance of the earlier defined systems is studied under

different conditions to get a better view of the systems proposed. MATLAB software

package was used for simulating the transmitter and receiver of the system discussed

earlier. Conditions used during the simulation of the system are presented in this

chapter. BER curves for systems under non-ISI assumption and for ISI cases are

generated.

4.2 Simulation Approach

To verify the receiver designs discussed in Chapter 3, an end-to-end com-

munication system was simulated. Necessary simulation software was developed in

MATLAB.

4.2.1 Pulse Generator

Simulations were done with the assumption that only a single user is operating

at a time so that the system is free from multiple access interference. The pulse

43

44

generated by the pulse generator is a gaussian waveform and is modeled as

p (t) =e−

(t−µ)2

2σ2

√2πσ

(4.1)

where

t is time (seconds)

µ is the mean value of the gaussian pulse

σ is the standard deviation of the gaussian pulse and determines the

pulse width Tp = 2π × σ.

In this work a normalized gaussian waveform with pulse width of 2 ns was

used. This pulse was sampled with a sampling period of 0.13333 ns.

4.2.2 Transmitter

The signals transmitted for different systems are modeled as follows.

For TR the transmitted signal is modeled as

str (t) =∑k

p (t− kTf ) + bbk/Nscp (t− kTf − Td) (4.2)

where bl are the channel symbols with values ±1, generated randomly having equal

probability of occurrence.

For a DTR and MDTR, transmitted signal is modeled as

s (t) =∑k

b′kp (t− kTf ). (4.3)

45

where b′k contains the differentially encoded data as defined in Equation 3.11. For the

simulation purpose the number of frames per symbol is set, Ns = 1.

4.2.3 Channel Model

The channel model is the one recommended by IEEE P802.15.3a [29] channel

modeling subcommittee. This channel was used to evaluate the performance of UWB

systems in indoor case. The channel impulse response is represented by

h (t) = XL∑

l=0

K∑k=0

αk,lδ (t− Tl − τk,l) (4.4)

where

αk,l are the multipath gain coefficients

Tl is the delay of the lth cluster

τk,l is the delay of the kth multipath component relative to the lth

cluster arrival time Tl

X represents the log-normal shadowing.

In simulations, channels were sampled with a sampling period of 0.13333 ns

and for no ISI case frame time (Tf ) is greater than multipath delay spread time (Tmds).

(Tmds) for different channel models are listed in Table 4.1.

For simulation purpose channel model 1 (CM 1) and 4 (CM 4) were used. CM1

and CM 4 correspond to channels with antenna separation being 0- 4 m with line of

Table 4.1. Multipath delay spread time for the channelsChannel CM 1 CM 2 CM 3 CM 4Tmds (ns) 40 60 122 200

46

0 20 40 60 80 100 120−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4Channel Impulse response

Time (nS)

Figure 4.1. CM 1: LOS (0-4 m)

sight (LOS) and an extreme non-LOS propagation respectively. IEEE channel model

is discussed in detail in Appendix B. CM 1 has a response as shown in Figure 4.1.

4.2.4 Monte Carlo Simulation

Monte Carlo simulation technique [50, 51] is the most widely used simulation

technique for evaluating the performance of the communication systems and is based

on games of chance. In this approach a random experiment is repeated N times until

the occurrence of an event or set of events so that one can estimate the required

parameter of the system accurately. This technique was used to estimate the system

BER by estimating the conditional probability that an error happened, so that a

binary 0 was received when 1 was transmitted or vice-versa.

47

4.2.5 Bit Error Rate (BER) Calculation

To evaluate the performance of the UWB correlational receivers BER calcula-

tion was done. Since the transmitted data bit was known in advance, using the UWB

receiver the information bit was detected. The detected and the transmitted bits

were compared. This experiment was repeated N number of times until NA number

of errors were counted. Then probability of error was estimated as

Pe =NA

N. (4.5)

In this simulation model, to evaluate the performance of a receiver, Monte

Carlo simulations were performed until NA = 100 errors were counted. In this model

BER is plotted in terms of Eb/N0, defined as the bit energy at the output of the filter

at the receiver front end. In simulation, the receiver filter has a bandwidth 7.5 GHz

with a rectangular transfer function.

4.3 Results

Performance of the systems as discussed earlier is evaluated via simulations

in this section. Initially analytical performance of the three systems, namely, TR,

DTR, and MDTR, represented by Equation (3.10), Equation (3.16), and Equation

(3.21) respectively, is compared to that obtained via the simulation model to verify

the simulations.

48

4.3.1 Performance in the Absence of Intersymbol Interference (ISI)

Performance of the three systems in case when ISI is avoided is shown in

Figure 4.2. From the figure it can be seen that the performance of a TR system

is about 3 dB worse than the DTR as was expected. For the MDTR system with

M = 2, a performance gain of around 1.4 dB is obtained when compared to DTR

system. For an energy limited system, like a UWB system, these gains are significant.

4.3.1.1 Integration interval optimization. For non-ISI case, at the

integrator block, integration was done for the entire length of the channel delay spread

4 6 8 10 12 14 16 18 20 22 2410−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

TR (Theoretical)DTR (Theoretical)MDTR (Theoretical)TR (Simulation)DTR (Simulation)MDTR (Simulation)

Figure 4.2. Comparing Closed form and Simulation Model results

49

Tmds as was suggested by the previous work. But, since indoor wireless channels

change with location and distance between transmitter and receiver, it was realized

that channel delay spread and thus integration time should be jointly taken into

account to optimize the performance of systems. For a TR or any of the other

two systems working in an environment for example channel 1 of CM 4 having a

channel delay spread of Tmds, length of integration determines the amount of pulse

energy as well as the noise captured, thus affecting the effective SNR of the decision

variable. Figure 4.3 shows the energy captured versus the channel length profile for

an example CM 4 channel. It can seen that around 95% of the channel multipath

0 20 40 60 80 100 120 140 160 1800

10

20

30

40

50

60

70

80

90

100

Delay Spread Length (ns)

Per

cent

age

Ene

rgy

Cap

ture

d

Figure 4.3. Energy Capture versus Time for Channel CM 4

50

energy is captured in less than 100 ns in a channel with a channel delay spread of

200 ns and the rest 5% of the energy is captured in the interval 100 − 200 ns. In

this interval more noise energy is accumulated and thus the BER performance should

be worse when the integration interval length is too long. And similarly when the

integration interval is too short very little amount of channel multipath energy is

captured. Thus an optimal integration interval should be determined to optimize the

performance of the structures defined earlier.

4 6 8 10 12 14 16 18 20 2210−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Ti=4 ns

Ti=10 ns

Ti=20 ns

Ti=30 ns

Ti=40 ns

Figure 4.4. BER Performance of TR system at Different Integration Lengthsfor Channel CM 1

51

Based on the earlier observation on integration interval two channel models

CM 1 and CM 4 were studied. CM 1 as defined earlier is LOS of sight channel

with a multipath delay spread of 40 ns and CM 4 is a non-LOS channel with a

multipath delay spread of 200 ns. Figure 4.4 shows the BER performance of a TR

receiver for different integration lengths. For a BER of 10−3 a gain of more than

1.6 dB is obtained when an integration interval Ti = 10 ns (96% energy captured)

instead of Ti = Tmds = 40 ns. A loss of around 1 dB occurs when Ti = 4 ns (83%

energy captured). Figure 4.5 plots BER versus integration interval at different Eb/N0

5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

Integration Time Ti (ns)

BE

R

Eb/N

0=14.7

Eb/N

0=15.7

Eb/N

0=16.7

Eb/N

0=17.7

Figure 4.5. BER Performance of TR system versus Integration Intervallength for Channel CM 1

52

values for a channel in CM 1. From this it can be concluded that optimal integration

time lies in the range 10 − 12 ns and this is also verified in the earlier figure where

for Ti = 10 ns system has the best performance. These results are in agreement

to the one published by Franz and Mitra [22] in the same time as this work was

being finished independently. As suggested by Mitra the accuracy of determining the

optimal integration length increases with high Eb/N0.

Figure 4.6 shows the result for BER versus integration interval (Ti) at different

Eb/N0 values for the example CM 4 channel. Along the lines of this observation it

40 60 80 100 120 140 16010−4

10−3

10−2

10−1

100

Integration Time Ti (ns)

BE

R

Eb/N

0=28

Eb/N

0=29

Eb/N

0=30

Figure 4.6. BER Performance of TR system at Different Integration Lengthsfor Channel CM 4

53

can be seen that system gives optimum performance for integration interval in the

range 90− 120 ns.

Performance of other receiver structures discussed is also affected by the inte-

gration interval. To confirm this performance of DTR receiver structure at different

integration interval is given by Figure 4.7. It can be seen that in this case around

2 dB gain in performance is obtained when integration interval is changed from 40 ns

to 20 ns. Performance suffers when enough energy is not captured.

2 4 6 8 10 12 14 16 1810−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Ti=10 ns

Ti=20 ns

Ti=30 ns

Ti=40 ns

Figure 4.7. Performance of DTR Receivers at Different Integration Lengthfor Channel CM 1

54

4.3.2 Performance in the Presence of ISI

Seen in the earlier section is a scenario when data rate is low. But in the ever

changing wireless world one demand that never dies off is of higher and higher data

rate. Higher data rate for wireless is mainly restricted by ISI caused by the multipath

effect of the channel. Data rate for a TR system is calculated as

R =1

NsTf

(4.6)

where

Tf = 2Td + 2Tp

and Td =Delay between two pulses in a frame.

In ISI scenario analytical analysis is difficult to obtain so via simulations the

performance of receiver structures is evaluated. Figure 4.8 shows the performance

of a TR receiver for CM 1 when Tf < 2(Tmds + Tp) so that ISI occurs. Data rate

calculations are done for Ns = 1. When data rate R = 63 Mb/s and in this model

where Tp = 2 ns, then one can calculate that Td = 6 ns. In this case each pulse will

overlap and interfere with 6 other pulses. As is known, a main drawback of a TR

system is the noisy template used for detection. In the presence of ISI, the template

that was already noisy suffers from the overlapping of the earlier transmitted pulses

via multipath, thereby limiting the performance of the system. For an information

rate of 63 Mb/s compared with ISI-free case, it can be seen that for a BER of

2× 10−3 a 6 dB loss in performance is observed. An error floor is encountered when

even higher data rates are tried. But when the data rate is 42 Mb/s corresponding

55

4 6 8 10 12 14 16 18 20 22 2410−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Bit Rate=84 Mb/sBit Rate=63 Mb/sBit Rate=42 Mb/sBit Rate=12 Mb/sClosed Form

Figure 4.8. Performance of TR in Channel CM 1 at High Data Rates

to Td = 10 ns which lies in the range of optimal integration interval, performance

close to the situation (Td = Tmds = 40 ns) of no ISI is obtained. But when compared

to non ISI case with integration interval being 10 ns the system suffers a 2 dB loss.

This loss is expected since the reference template in ISI case is not only noisy but

suffers from ISI interference caused by 3 other pulses. Although this interference is

small it is large enough to cause this performance degradation.

Shown in Figure 4.9 is the response of a TR receiver in the presence of ISI in

a CM 4 channel. As is known, the delay spread for a CM 4 channel is 200 ns. When

higher data rates were tried in this channel, performance started to degrade, as is

56

0 5 10 15 20 25 30 3510−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

Simulated TRClosed form TRData Rate= 5 Mb/sData Rate= 29 Mb/sData Rate= 18 Mb/sData Rate= 16 Mb/sData Rate= 11 Mb/s

Figure 4.9. Performance of TR in Channel CM 4 at High Data Rates

expected. But when the delay time Td is in the range of optimal integration interval

as determined in Section 4.3.1.1 then performance close to non ISI case is obtained.

From Figures 4.8 and 4.9, an observation can be made that maximum allowable data

rates with an acceptable error correspond to the case when delay time Td is equal

to the optimal integration interval. Similar kinds of characteristics were observed

for other receiver structures as well. When even higher data rates are required the

performance of TR, DTR, and MDTR receiver structures may be unsatisfactory.

57

4.3.3 Time Reversal and TR (TiR-TR)

Performance of TR is not good at high data rates because of the large delay

spread of the channels encountered. Performance analysis of a TR receiver with some

improvements, operating in a CM 4 channel at high data rates is done in this section.

Figure 4.10 shows the performance of receiver in which time reversal transmission

scheme is used for temporal focusing, along with transmitted reference scheme. When

the delay time Td = 10 ns, then the performance suffers because of large intersymbol

interference and the receiver did not work, as shown in the figure. But when a

10 12 14 16 18 20 22 24 26 28

10−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R TiR−TR, Ti = 2 nsTiR−TR, Ti = 10 nsTR, Ti = 10 ns

Figure 4.10. Time Reversal and TR at different Integration Lengths

58

prefilter (time reversal) is used and the decision variable is evaluated by integrating

over the entire delay length, then large performance gains are obtained in comparison

to ISI situation without prefiltering. But since temporal focusing is obtained with

prefiltering thus integration window size was intuitively reduced to pulse width and

about 4 dB gain in performance was achieved when compared to performance with

window size of 10 ns. This is because more than 50% of the energy is present in the

first peak and the rest of the 50% is distributed with in the rest of the delay length.

0 5 10 15 20 25 30 3510−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

TR at 19 Mb/sTR at 16 Mb/sTiR−TR at 19 Mb/sTiR−TR at 16 Mb/s

3 dB

9 dB

Figure 4.11. Performance Improvement after Using Time Reversal with TR(CM 4)

59

Figure 4.11 shows the performance gains after using TiR-TR operating under

ISI condition. It was found that the performance of the system at both the data rates

(when time reversal is used), is almost identical because now performance mainly

depends on the length of the integration window, the same in both the cases. It can

be seen that gains of the order of 3.5 dB and 9 dB are obtained when compared to

a simple TR system operating at data rates of 16 Mb/s and 19 Mb/s, respectively.

10 12 14 16 18 20 22 24 26 28 3010−4

10−3

10−2

10−1

100

Eb/N

0 (dB)

BE

R

TiR−TRMonobit TiR−TRMonobit TiR−TR with Thresholding (10 dB)Monobit TiR−TR with Thresholding (20 dB)Monobit TiR−TR with Thresholding (25 dB)Monobit TiR−TR with Thresholding (35 dB)

Figure 4.12. Performance with diffferent thresholds (CM 4)

60

4.3.4 Performance with Monobit TiR-TR

Figure 4.12 shows the performance of the monobit TiR-TR at different levels

of thresholding. In the figure it can be seen that as the level of thresholding increased

until 25 dB in this figure, the performance initially improves and later starts degrad-

ing as the level of thresholding is increased to 35 dB. This suggests that optimal

thresholding should be done to improve the performance.

4.4 Summary

In this chapter analytical performance analysis of different suboptimal receivers

obtained in Chapter 3 was verified via simulations. Performance improvement was

achieved by optimizing the integration interval which is an important system design

parameter. Performance in the presence of ISI was investigated and analysis of the

performance improvement technique was also carried out. TiR-TR is a promising

scheme. Pre-filter needs special attention for implementation.

CHAPTER 5

CONCLUSIONS AND FUTURE WORK

The objective of this thesis was to investigate the performance of the sub-

optimal receivers via simulations. Various suboptimal receivers were studied and

implemented. Performance was evaluated when ISI is absent as well as in its pres-

ence. Performance of TR when combined with time reversal was also investigated.

5.1 Conclusions

Performance results showed that reference enhancement is an important issue

as MDTR receiver showed a 1.4 dB gain when compared to DTR which in turn

showed a 3 dB performance gain in absence of ISI. Performance evaluation of TR

receivers in the absence of ISI showed that integration interval is an important design

parameter which affects the performance significantly. For a highly dispersive indoor

channel, optimum integration time was found to be less than total delay spread of the

channel. Better performance was attained at these integration times in comparison

to integrating over total multipath channel delay spread. Also at higher SNR values

accuracy of finding optimal integration time increased.

In the presence of ISI, reference is corrupted by ISI. In this case, performance

of the correlation based receivers degrades severely and in some cases the receiver

even stops detecting the information in severe ISI situations. Maximum achievable

data rates for these receivers in the presence of ISI with acceptable BER performance

correspond to data rates evaluated at optimal integration intervals. Analysis suggests

that TiR which provides temporal focusing, is one possible solution to deal with ISI

problem. For TiR based systems the integration should be chosen in such a way that

61

62

effective SNR of the decision variable is high. Proposed transceivers with digital back

end, in addition to optimal thresholding, should be used to improve the performance

of suboptimal receivers in the presence of ISI.

5.2 Recommendations for Future Work

This thesis work has opened numerous areas for future work which could be

done to better understand the performance of the UWB TR systems. Some of the

areas are as follows:

1. Single user case was addressed in this work, but performance of these re-

ceivers in multiuser scenario should be studied, when reference is not only

corrupted by ISI but also by multiple access interference (MUI).

2. Performance of the suboptimal receivers should be evaluated in an outdoor

channel model (IEEE channel model IEEE P802.15.4a) and for physics

based channel models [23, 24, 25].

3. Hardware Implementation issues related to suboptimal receivers should be

investigated.

4. Implementation issues related to prefilter technique in a TiR-TR scheme

should be addressed in future work.

REFERENCES

63

64

[1] M. Z. Win and R. A. Scholtz, “Impulse radio: How it works,”IEEE Communi-cations Letters, Vol. 2, pp. 36-38, Feb. 1998.

[2] J. R. Foerster, S. Roy, S. Somayazulu, and D. Leeper, “Ultrawideband radiodesign:The promise of High-Speed, Short-Range Wireless Connectivity,” Pro-ceedings of The IEEE, Vol. 92, No. 2, pp. 295-311, Feb. 2004.

[3] M. Z. Win and R. A. Scholtz, “On the robustness of ultra-wide bandwidth sig-nals in dense multipath environments,”IEEE Communications Letters, Vol. 2,pp. 51-53, Feb. 1998.

[4] R. C. Qiu, “A Generalized Time Domain Multipath Channel and Its Appli-cation in Ultra-Wideband (UWB) Wireless Optimal Receiver Design: SystemPerformance Analysis,”IEEE Trans. Wireless Communications, to appear.

[5] R. C. Qiu, “A Theoretical Study of the Ultra-Wideband Wireless PropagationChannel and Optimum UWB Receiver Design,”IEEE Journal on Selected Areasin Communications, special issue on UWB multiple access communications,Vol. 20, No. 12, Dec. 2002.

[6] R. Price and P. E. Green, Jr., “A communication technique for multipath chan-nels,” Proc. IRE, Vol. 46, pp. 555-570, Mar. 1958.

[7] M. Z. Win and R. A. Scholtz, “On the energy capture of ultrawide banwidth sig-nals in dense multipath environments,”IEEE Communications Letters, Vol. 2,pp. 245-247, Sep. 1998.

[8] R. A. Altes, “Sonar for generalized target description and its similarity toanimal echolocation systems,” Journal of the Acoustical Society of America,Vol. 59, pp. 97-105, Jan. 1976.

[9] R. Mosier and R. Clabaugh, “Kineplex: A bandwidth-efficient binary transmis-sion system,” AIEE Trans., Vol. 76, pp. 723-728, Jan. 1958.

[10] J. Balakrishnan, et al., “A Multi-band OFDM System for UWB Communica-tion,” Proc. IEEE Conf. on Ultra Wideband Systems and Technologies, Reston,VA, Nov. 2003.

[11] MultiBand OFDM Alliance (MBOA), Date accessed Aug. 16, 2004.

http://www.multibandofdm.org

65

[12] C. K. Rushforth, “Transmitted-reference techniques for random or unknownchannels,” IEEE Trans. Information Theory, Vol. 10, No. 1, pp. 39-42, Jan.1964.

[13] R. Gagliardi, “A geometrical study of transmitted reference communicationsystem,”IEEE Trans. Comm. Tech., Vol. 12, pp. 118-123, Dec. 1964.

[14] G. D. Hingorani, “A transmitted reference system for communication in randomor unknown channels,” IEEE Trans. Comm. Tech., Vol. 13, No. 3, pp. 293-301,Sep. 1965.

[15] R. Hoctor and H. Tomlinson, “An overview of delay-hopped, transmitted-reference RF communications,”Tech. Rep. 2001crd198, GE Research and De-velopment Center, 2002.

[16] R. Hoctor and H. Tomlinson, “Delay-hopped, transmitted-reference RF commu-nications,” IEEE Ultra Wideband Systems and Technologies, Baltimore, MD,pp. 265-269, May 2002.

[17] N. V. Stralen, A. Dentinger, K. Welles, R. Gans, R. Hoctor, and H. Tomlin-son, “Delay hopped transmitted reference experimental results,” IEEE UltraWideband Systems and Technologies, Baltimore, MD, pp. 93-98, May 2002.

[18] J. D. Choi and W. E. Stark, “Performance of ultra-wideband communicationswith suboptimal receivers in multipath channels,” IEEE Journal on SelectedAreas in Communications, Vol. 20, pp. 1754-1766, Dec. 2002.

[19] Y. L. Chao and R. Scholtz, “Optimal and suboptimal receivers forultra-wideband transmitted reference systems,” Proceedings GLOBECOM’03,pp.759-763, San Francisco, CA, 1-5 Dec. 2003.

[20] N. Guo and R. C. Qiu, “Low-complexity correlation receivers for UWB com-munications over ISI channels,” submitted to IEEE Trans. Veh. Tech..

[21] S. Zhao, H. Liu and Z. Tian, “A decision feedback autocorrelation receiverfor pulsed ultra-wideband systems,” Proc. IEEE Rawcon’04, Atlanta, GA, Sep.2004.

[22] S. Franz and U. Mitra, “Integration interval optimization and performanceanalysis for UWB transmitted reference systems,” Proc. 2004 IEEE Conf. on

66

Ultra Wideband Systems and Technologies, Tyoko, Japan, pp. 26-30, May 19-21,2004.

[23] R. C. Qiu, “Optimum and sub-optimum detection of physics-based ultra-wideband signals- A tutorial review,” Dynamics of Continuous, Discrete, andImpulse Systems, Series B: Application and Algorithms, Vol. 12b, No. 1-2, 2005.

[24] R. C. Qiu, “Optimum and sub-optimum detection of physics-based ultra-wideband signals in presence of inter-symbol interference,” IEEE WirelessCommunications and Networking Conference, Mar. 2005, to appear.

[25] R. C. Qiu, H. Liu, S. Shen and M. Guizani, “Ultra-wideband for multiple-access communication,” IEEE Comm. Mag., Special issue on, Multiple accesstechnologies for B3G wireless communications, Vol. 43, No.2, Feb. 2005.

[26] D. Rouseff, et al. “Underwater acoustic communication by passive-phase conju-gation: Theory and experimental results,” IEEE Journal of Oceanic Engineer-ing, Vol. 26, pp. 821-831, 2001.

[27] S. M. Emami, J. Hansen, A. D. Kim, G. Papanicolaou, A. J. Paulraj, D. Che-ung, and C. Prettie, “Predicted time reversal performance in wireless commu-nications using channel measurements, ”IEEE Communications Letters, 2004,accepted for publication.

[28] T. Strohmer, S. M. Emami, J. Hansen, G. Papanicolaou, A. J. Paulraj, “Ap-plication of time reversal with MMSE equalizer to UWB communications,”GLOBECOM’04, Dallas, TX, 29 Nov.-3 Dec. 2004.

[29] IEEE 802.15.3a, “Channel modelling sub-committee final report,” IEEEP802.15-02/490r1-SG3a, Feb. 2003, Date accessed Nov. 2003 .

http://grouper.ieee.org/groups/802/15/

[30] R. J. Fontana, “A Brief History of UWB Communications”, Multispectral So-lutions, Inc. (MSSI), Germantown, MD, Date accessed Aug. 16, 2004.

http://www.multispectral.com/history.html

[31] J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Al-gorithms, and Applications, Prentice-Hall, Inc., 3rd edition, 1996.

67

[32] C. L. Bennett and G. F. Ross, “Time-domain electromagnetics and its applica-tions,” Proceedings of the IEEE, Vol. 66, No. 3, pp. 229-318, 1978.

[33] H. Stark and J. W. Woods, Probability and Random Process with Applicationto Signal Processing, Upper Saddle River, New Jersey: Prentice-Hall, Inc., 3rd

edition, 2002.

[34] L. W. Couch II, Digital and Analog Comminication Systems, 3rd edition, NewYork, Machmillan Publishing Company, 1987.

[35] S. G. Wilson, Digital Modulation and Coding, Upper Saddle River, New Jersey:Prentice-Hall, Inc., 1996.

[36] R. A. Scholtz, “Multiple access with time-hopping impulse modula-tions,”Conference record Military: Communications Conference, Communica-tions on the Move, MILCOM ’93, Vol. 2, 1993, pp. 447 -450.

[37] M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple access communications,”IEEETransactions on Communications, Vol. 48, pp. 679-691, Apr. 2000.

[38] J. Foerster, “The Performance of a Direct-Sequence Spread Ultra-WidebandSystem in the Presence of Multipath, Narrowband Interference and MultiuserInterference,”IEEE Conference on Ultra Wideband Systems and Technologies,Digest of Papers, pp. 87-92, May 2002.

[39] Time Domain Corporation, “PulsON Time Modulated Ultra-Wideband ForWireless Applications,” May 2000 Rev 2, Date accessed Aug. 16, 2004.

http://www.timedomain.com/Files/downloads/techpapers/

PulsONoverview.html

[40] “Bandwidth from thin air, Two new ways of transmitting data by wirelessexploit unconventional approaches to create valuable additional capacity,” TheEconomist, Nov. 6, 1999, p. 85, Date accessed Aug. 16, 2004.

http://www.timedomain.com/Files/HTML/news/TheEconomist.html

[41] Amara D. Angelica, “Powered by Pulse, More than a Pipe Dream,” Tech Week,May 3, 1999, Date accessed Aug. 16, 2004.

68

http://www.timedomain.com/Files/PDF/news/TechWeek.pdf

[42] R. A. Scholtz, “The origins of spread-spectrum communications,” IEEE Trans.Commun, Vol. 30, No. 5, pp. 822-854, May 1982.

[43] S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory, UpperSaddle River, New Jersey: Prentice-Hall, Inc., 1998.

[44] M. K. Simon, S. M. Hinedi and W. C. Lindsey, Digital Communication Tech-niques - Signal Design and Detection, Englewood Cliffs, New Jersey: PrenticeHall, 1994.

[45] M. G. Heinemann, A. Larazza, and K. B. Smith, “Acoustic communications inan enclosure using single-channel time-reversal acoustics,” Appl. Phys. Lett.,Vol. 80, pp. 694-696, 2002.

[46] G. F. Edelmann, et al., “An initial demonstration of underwater acoustic com-munications using time reversal,” IEEE Journal of Oceanic Engineering, Vol.27, pp. 602-609, 2002.

[47] A. Derode, et al., “Taking advantage of multiple scattering to communicatewith time-reversal antennas,” Phys. Rev. Letters, Vol. 90, 2003.

[48] A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Letters, vol. 75, pp. 4206-4209, 1995.

[49] N. Guo, Private Conversations, Tennessee Tech. Univ., 11 Oct. 2004.

[50] R. Y. Rubinstein, Simulation and the Monte Carlo Method, John Wiley & Sons,Inc., 1981.

[51] W. H. Tranter, K. S. Shanmugan, T. S. Rappaport and K. L. Kosbar, Princi-ples of Communication Systems Simulation with Wireless Applications, UpperSaddle River, New Jersey: Prentice-Hall, Inc., 2004.

[52] A. A. Saleh and R. A Valenzuela, “A statistical model for indoor multipathpropagation, ”IEEE Journal on Selected Areas in Communications, Vol. 5,pp. 128-137, 1987.

[53] J. R. Foerster, “The Effects of Multipath Interference on the Performance ofUWB Systems in an Indoor Wireless Channel,”IEEE VTS 53rd, Vol. 2, pp.

69

1176-1180, 2001.

[54] H. Hashemi,“Impulse Response Modeling of Indoor Radio Propagation Chan-nels,” IEEE Journal on Selected Areas in Communications, Vol. 11, No. 7, pp.967-978, Sept. 1993.

APPENDICES

70

APPENDIX A: PERFORMANCE ANALYSIS OF SUBOPTIMALRECEIVERS

71

72

A.1 Transmitted Reference

Transmitted signal for a TR system is given by

str (t) =∑k

p (t− kTf ) + bbk/Nscp (t− kTf − Td) (A.1)

where p(t) represents the transmitted pulse, k represents the kth frame, Ns is thenumber of times the pulse is transmitted to capture adequate energy for detection,Tf is the frame time, and Td is the delay between two pulses in a frame which fora non ISI case is greater than the multipath delay spread time Tmds. The receivedsignal is modeled as

r(t) = str(t)⊗ h(t) + n(t)= g (t) + n (t)

(A.2)

where n(t) is assumed to be AWGN noise with zero mean and h(t) is defined asthe generalized channel impulse response, one in which we take care of the channeldistortion also and is given by

h (t) =∑

i

αihi (t)⊗ δ (t− τi) (A.3)

where hi(t) is per pulse distortion, τi is the delay and the channel impulse response

is normalized such that,∞∫

−∞h2 (t)dt = 1.

Assuming that the frames are isolated in time so that Tf ≥ 2Td ≥ 2Tmds, thereis no ISI and each frame can be analysed independently. Let τi = its, where ts is thesampling time. Then from Equation A.2 and Equation A.3, the kth received frame isgiven by

rk (t) =∑

i

αigi (t− its − kTf ) + n (t)

where gi (t− kTf ) = str (t)⊗ hi (t).After low pass filtering (LPF) the kth frame is represented by

∧rk(t) =

∑i

αigi (t− its − kTf ) +∧n (t) . (A.4)

73

The decision variable y, conditioned on bk = 1, is defined as

y =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∧rk (t− Td)

∧rk (t) dt. (A.5)

Substituting Equation A.4 in Equation A.5, we get

y =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

∑j

[αigi (t− its − kTf ) +

∧n (t)

][αjgj (t− jts − kTf ) +

∧n (t− Tf )

]dt

=Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

∑j

[αigi (t− its − kTf )] [αjgj (t− jts − kTf )] dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

αigi (t− its − kTf )∧n (t− Tf ) dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑j

αjgj (t− jts − kTf )∧n (tf ) dt

+Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∧n (t− Tf )

∧n (tf ) dt

= Y + N1 + N2 + N3

where

Y =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

∑j

[αigi (t− its − kTf )] [αjgj (t− jts − kTf )] dt (A.6)

N1 =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

αigi (t− its − kTf )∧n (t− Tf ) dt

N2 =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑j

αjgj (t− jts − kTf )∧n (tf ) dt

74

N3 =Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∧n (t− Tf )

∧n (tf ) dt

Noise n(t) as defined earlier is a zero mean white gaussian noise and the threenoise terms N1, N2 and N3 are three uncorrelated zero mean random variables. Sothat the total noise variance σ2

n is given by

σ2n = var (N1) + var (N2) + var (N3) . (A.7)

Defining the detection SNR as

SNRtr =Y 2

σ2n

. (A.8)

To simplify the SNR evaluation to get a closed form equation lets us modelhi(t), for all possible values of i as

hi (t) = δ (t)

then

h (t) =∑

i

αiδ (t− τi) (A.9)

so that now∑i

α2i = 1. As a result of the assumption Equation A.6 reduces to

Y =Ns−1∑k=0

[|αi|2 Ep +

∑ ∑i6=j

αiαjRp [(i− j) ts]

]

where

Ep =∞∫

−∞p2 (t)dt

Rp (τ) =∞∫

−∞p (t− τ) p (t) dt

75

and in the absence of interpulse interference (IPI) Rp [i (ts)] = 0 for i 6= 0, thus

Y = NsEp. (A.10)

and the variance of the noise terms is calculated as

var (N1) = E

[Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

αig (t− its − kTf )∧n (t− Tf ) dt

Ns−1∑k=0

kTf+Td+Tmds∫kTf+Td

∑i

αjg(∧t−its − kTf

)∧n(∧t−Tf

)d∧t

]

= NsN0

2

[|αi|2 Ep +

∑ ∑i6=j

αiαjRp [(i− j) ts]

]

and in response to the earlier aaumption of no IPI we get

var (N1) =NsN0Ep

2(A.11)

also

var (N2) = var (N1) . (A.12)

Using central limit theorem, under the assumption of large number of multi-paths, the N3 noise term can be modeled as a gaussian random variable with variancegiven by

var (N3) =NsN

20 TmdsW

2. (A.13)

Then substituting Equation A.11, Equation A.12, and Equation A.13 in Equa-tion A.7

σ2n = NsN0Ep +

NsN20 TmdsW

2. (A.14)

76

Substituting Equation A.10 and Equation A.14 in Equation A.8 gives

SNR−1tr =

NsN0Ep +NsN2

0 TmdsW

2

N2s E2

p

this reduces to

SNRtr =

(

N0

Ep

)1

Ns

+

(N0

Ep

)2TmdsW

2Ns

−1

.

For a TR system Eb = 2NsEp. Then the probability of error (Pe) for a TR system isgiven by

Pe = Q

[(N0

Eb

)2 +

(N0

Eb

)2

2NsTmdsW

]− 12

. (A.15)

A.2 Differential Transmitted Reference

Transmitted signal for a DTR system is given by

sdtr =∑k

b′kp (t− kTf ) (A.16)

where b′k = b′k−1bdbk/Nsc

, where bdl = blbl−1 is the differentially encoded data.

The received signal can be modeled as

r (t) = h (t)⊗ sdtr (t) + n (t) (A.17)

where the channel h(t) is given by Equation A.9.When the frames are assumed to be isolated, so that there is no ISI then

Tf > Tmds. Substituting Equation A.16 in Equation A.17, the kth received frame ismodeled as

rk (t) =∑

i

αib′kp (t− its − kTf ) + n (t)

77

The signal at the output of the LPF is given by

∧rk (t) =

∑i

αib′kp (t− its − kTf ) +

∧n (t) (A.18)

Then the decision variable conditioned on b′k = 1 for a DTR system is evaluatedas

y =Ns−1∑k=0

kTf+Tmds∫kTf

∑i

∑j

[αip (t− its − kTf ) +

∧n (t)

][b′k−1αjp (t− jts − kTf ) +

∧n (t− Tf )

]dt

=Ns−1∑k=0

kTf+Tmds∫kTf

∑i

∑j

αiαjb′k−1p (t− its − kTf ) p (t− jts − kTf ) dt

+Ns−1∑k=0

kTf+Tmds∫kTf

∑i

αip (t− its − kTf ) n (t− Tf ) dt

+Ns−1∑k=0

kTf+Tmds∫kTf

∑j

αjb′k−1p (t− jts − kTf ) n (t) dt

+Ns−1∑k=0

kTf+Tmds∫kTf

n (t) n (t− Tf )dt

= Y + N1 + N2 + N3

Conditions for DTR receivers are assumed similar to that of TR receivers,as discussed earlier. And thus following the similar approach as before, total noisevariance is given by

σ2n = var (N1) + var (N2) + var (N3)

= (2Ns − 1) N0Ep +NsN2

0 TmdsW

2.

Thus the detection SNR is defined as

SNRdtr =Y 2

σ2n

.

78

Substituting the expressions gives

SNR−1dtr =

(2Ns − 1) N0Ep +NsN2

0 TmdsW

2

N2s E2

p

this expression reduces to

SNRdtr =

(

N0

Ep

)(2Ns − 1)

N2s

+

(N0

Ep

)2TmdsW

2Ns

−1

.

For a DTR system Eb = NsEp. Then Pe for a DTR system is given by

Pe = Q

[(N0

Eb

)(2Ns − 1)

Ns

+(

N0

Eb

)2 NsTmdsW

2

]− 12

. (A.19)

A.3 Modified Differential Transmitted Reference

Transmitted signal of a MDTR system is given by

smdtr =∑k

b′kp (t− kTf )

where b′k is as defined for DTR scheme in Section A.2.The received signal can be modeled as

r (t) = h (t)⊗ smdtr (t) + n (t)

where the channel h(t) is given by Equation A.9.When the frames are assumed to be isolated, so that there is no ISI then

Tf > Tmds. The signal at the output of the LPF is given by

∧rk (t) =

∑i

αib′kp (t− its − kTf ) +

∧n (t) . (A.20)

79

The decision variable for the kth information bit is given by

y =

kTf+Tmds∫kTf

∧r (t)

1

M

[∧r (t− Tf ) +

M∑m=2

bestk−m

∧r (t−mTf )

]dt. (A.21)

To ease the analysis we are evalauting closed form expression for the casewhere each information bit is transmitted only once. From Equation A.20 and Equa-tion A.21, the decision variable y conditioned on bk = 1 is given by

y =kTf+Tmds∫

kTf

∑i

∑j

[αip (t− its − kTf ) +

∧n (t)

]1M

[M∑

m=1

[αjb

estk−mp (t− jts − kTf ) +

∧n (t−mTf )

]]dt.

Assuming that there is no error in previous bit estimations, then it follows that

y =kTf+Tmds∫

kTf

∑i

∑j

αiαjbestk−mp (t− its − kTf ) p (t− jts − kTf ) dt

+kTf+Tmds∫

kTf

∑i

αip (t− its − kTf )1M

[M∑

m=1n (t−mTf )

]dt

+kTf+Tmds∫

kTf

∑j

αjbestk−mp (t− jts − kTf ) n (t) dt

+kTf+Tmds∫

kTf

M∑m=1

n (t) 1M

[M∑

m=1n (t−mTf )

]dt

= Y + N1 + N2 + N3

But as discussed earlier, in absence of IPI

Y = Ep. (A.22)

80

And the total noise variance, evaluated in the same as discussed in earliercases, is given by

σ2n = var (N1) + var (N2) + var (N3)

= N0Ep

2M+ N0Ep

2+

N20 TmdsW

2M.

(A.23)

Detection SNR is defined as

SNRmdtr =Y 2

σ2n

. (A.24)

Substituting Equation A.22 and Equation A.23 in Equation A.24, we get

SNR−1mdtr =

N0Ep

2M+ N0Ep

2+

N20 TmdsW

2M

E2p

this expression reduces to

SNRmdtr =

(

N0

Ep

)[1 + 1/M

2

]+

(N0

Ep

)2TmdsW

2M

−1

.

For MDTR Eb = Ep in this case, so that Pe for MDTR system is given by

Pe = Q

[(N0

Eb

) [1 + 1/M

2

]+(

N0

Eb

)2 TmdsW

2M

]− 12

. (A.25)

APPENDIX B: IEEE CHANNEL MODEL IEEE P802.15.3A

81

82

B.1 Multipath Channel Model

The channel is the environment that a signal passes through on its way froma transmitter to receiver. Clustering phenomenon was observed in several channelmeasurements and based on this clustering, IEEE proposed a UWB multipath channelmodel called IEEE P802.15.3a [29] derived from the Saleh-Valenzuela model [52] withsome slight modifications. Instead of a Rayleigh distribution for the multipath gainmagnitude a log-normal distribution is employed as the later better fits the modelas is supported by the measurement data. By log-normal what we mean is thatthe logarithm of the random variable has a normal distribution. Additionally, foreach cluster as well as each ray within the cluster independent fading is assumed.Taking these modification into considerations, the multipath channel model can berepresented by the following discrete time channel response:

hi (t) = Xi

L∑l=0

K∑k=0

αik,lδ

(t− T i

l − τ ik,l

)(B.26)

where:αi

k,l are the multipath gain coefficientsT i

l is the delay of the lth clusterτ ik,l is the delay of the kth multipath component relative to the lth

cluster arrival time Tl

Xi represents the log-normal shadowingi refers to the ith realization.

The proposed IEEE model uses the some definitions and parameters as pre-sented in Table B.1:

By definition, we have τ0,l = 0. The distribution of cluster arrival time andthe ray arrival time are given by

p (Tl |Tl−1 ) = Λ exp [−Λ (Tl − Tl−1)] , l > 0

p(τk, l

∣∣∣τ(k−1), l

)= λ exp

[−λ

(τk, l − τ(k−1) ,l

)], k > 0

(B.27)

The channel coefficients are defined as follows:

αk,l = pk,lξlβk,l, 20 log10 (ξlβk,l) ∝ Normal (µk,l, σ21 + σ2

2) ,

or |ξlβk,l| = 10(µk,l+n1+n2)/20

83

Table B.1. Channel model components and parametersComponent/Parameter

Meaning

Tl Arrival time of the first path of the lth clusterτk,l Delay of the kth path within the lth cluster relative to the

first path arrival time, Tl

Λ Cluster arrival rateλ Ray arrival rate, i.e., the arrival rate of path within each

clusterΓ Cluster decay factorγ Ray decay factorσ1 Standard deviation of cluster log-normal fading term (dB)σ2 Standard deviation of ray log-normal fading term (dB)σx Standard deviation of log-normal shadowing term for total

multipath realization (dB)

where n1 ∝ Normal(0, σ21) and n2 ∝ Normal(0, σ2

2) are independent and correspondto the fading on each cluster and ray, respectively

E[|ξlβk,l|2

]= Ω0e

−Tl/Γeτk,l/γ (B.28)

where Tl is the excess delay of bin l and Ω0 is the mean energy of the first path ofthe first cluster, and pk,l is equiprobable +/-1 to account for signal inversion due toreflections. The µk,l is given by

µk,l =10 ln (Ω0)− 10Tl/Γ− 10τk,l/γ

ln (10)− (σ2

1 + σ22) ln (10)

20(B.29)

In the above equations, ξl reflects the fading associated with the lth cluster,and βk,l corresponds to the fading associated with the kth ray of the lth cluster.

Finally, since the log-normal shadowing of the total multipath energy is cap-tured by the term, Xi, the total energy contained in the terms αi

k,l is normalizedto unity for each realization. This shadowing term is characterized by the following:

20 log10 (Xi) ∝ Normal(0, σ2

x

)(B.30)

84

B.2 Channel characteristics desired to model

Forester [53] and Hashemi[54] proposed some parameters i.e. number of mul-tipath, delay spread, multipath intensity profile, amplitude fading and mean arrivaltime.The parameters discussed in Table B.1 are calculated by matching importantcharacteristics of the channel. Channel characteristics that were used to derive themodel parameters were chosen to be the following:

• Mean excess delay• RMS delay spread• Number of multipath components (defined as the number of multipath

arrivals that are within 10 dB of the peak multipath arrival)• Power decay profile

And of these characteristics first three were used to match the parameters as itswas found that it was difficult to match to power decay profile. Channel parameterswere found using measurement data based on couple of channel characteristics fordifferent channel models and are shown in Table B.2:

Table B.2. Example channel characteristics and model parameters.Target Channel Characteristics5 CM 11 CM 22 CM 33 CM 44

Mean excess delay (ns) (τm) 5.05 10.38 14.18RMS delay (ns) (τrms) 5.28 8.03 14.28 25NP10dB 35NP (85%) 24 36.1 61.54Model ParametersΛ 0.0233 0.4 0.0667 0.0667λ 2.5 0.5 2.1 2.1Γ 7.1 5.5 14.00 24.00γ 4.3 6.7 7.9 12σ1 (dB) 3.3941 3.3941 3.3941 3.3941σ2 (dB) 3.3941 3.3941 3.3941 3.3941σx (dB) 3 3 3 3Model Characteristics5

Mean excess delay (ns) (τm) 4.9 9.4 13.8 26.8RMS delay (ns) (τrms) 5 8 14 26NP10dB 13.3 18.2 25.3 41.4NP (85%) 21.4 37.2 62.7 122.8Channel energy mean (dB) -0.5 0.1 0.2 0.1Channel energy std (dB) 2.9 3.3 3.4 3.2

85

• 1 Based on LOS (0-4 m) channel measurements reported by Pandegrass.• 2 Based on NLOS (0-4 m) channel measurements reported by Pandegrass.• 3 Based on NLOS (4-10 m) channel measurements reported by Pandegrass

and Forester.• 4 Represents an extreme NLOS multipath channel to fit a 25 ns RMS delay

spread.• 5 Sampling time for these characterics is 167 ps.

One hundred actual realizations for each channel model were derived from themodel above and the channel that was obtained is as shown in Figure 4.1-B.4.

Channel shown in Figure B.1 is one realization of channel CM 1. This channelmodel is of a line of sight (LOS) case with the transmitter and the receiver antennabeing separated by a distance in the range (0-4 m).

Figure B.2 shows single realization of the channel model CM 2. This channelis a model for a non line of sight (NLOS) case with antenna separation being in therange (0-4 m). Figure B.3 and B.4 represent channel models CM 3 and CM 4 forNLOS case with antenna separation being in the range (4-10 m) and an extreme caserespectively.

0 20 40 60 80 100 120−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4Channel Impulse response

Time (nS)

Figure B.1. CM 1: LOS (0-4 m)

86

0 20 40 60 80 100 120 140−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4Channel Impulse response

Time (nS)

Figure B.2. CM 2: NLOS (0-4 m)

0 20 40 60 80 100 120 140 160 180 200−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3Channel Impulse response

Time (nS)

Figure B.3. CM 3: NLOS (4-10 m)

87

0 50 100 150 200 250 300 350−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3Channel Impulse response

Time (nS)

Figure B.4. CM 4: Extreme NLOS

APPENDIX C: MATLAB CODE LIST

88

89

C.1 List of System simulation M-files

The following is a list of m-files required to run the system simulation inMATLAB. These were written by the author and can be found on the CD attachedto this thesis.

uwb_sv_cnvrt_ct.m

uwb_sv_eval_ct.m

uwb_sv_model_ct.m

uwb_sv_params.m

channel.m

bertr.m

berdtr.m

bermdtr.m

berinttime.m

bertrntr.m

bermonobit.m

pulse.m

sigpower.m

Q.m

VITA

Satish Kaza, son of Bapuji and Seeta Kaza, was born on January 28, 1980,

at Nizamabad in Andhra Pradesh, India. In 1998, he joined the four-year Bachelor

of Engineering degree program in Electronics and Communication Engineering at

Mahrishi Dayanand University and graduated in May 2002. In Fall 2002, he joined

Tennessee Technological University for his masters in Electrical Engineering. His area

of interest is in the field of communications and signal processing which led him to

this work in Ultra-wideband communication.

90