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MEHRDAD MIRSHAFIEI

UWB PULSE SHAPING USING FIBER BRAGG GRATINGS

Mémoire présenté à la Faculté des études supérieures de l'Université Laval

dans le cadre du programme de maîtrise en génie électrique pour l'obtention du grade de maître ès science (M.Sc.)

DÉPARTEMENT DE GÉNIE ÉLECTRIQUE ET DE GÉNIE INFORMATIQUE FACULTÉ DES SCIENCES ET DE GÉNIE

UNIVERSITÉ LA VAL QUÉBEC

2009

© Mehrdad Mirshafiei, 2009

Résumé

Dans ce mémoire, nous concevons et générons des impulsions ultra large bande (UWB)

qui exploitent efficacement le masque spectral de la "US Federal Communications

Commission" (FCC). Une impulsion efficace améliore le rapport signal à bruit au récepteur

en utilisant la majorité de la puissance disponible sous le masque spectral défini par la FCC,

ce qui réduit la probabilité d'erreur. Pour trouver les formes d'onde efficaces, nous

combinons plusieurs impulsions de type monocycle Gaussien séparées avec certains délais.

Chaque monocycle Gaussien a une amplitude inconnue. Les amplitudes sont trouvées par

un processus d'optimisation qui maximise la puissance de l'impulsion en respectant le

masque spectral de la FCC sur toute la largeur de bande allouée aux communications

UWB.

Les impulsions efficaces sont réalisées par des filtres à réseaux de Bragg (FBG) dans · le

domaine optique. L'impulsion temporelle est écrite dans le domaine fréquentiel , et une fibre

inonomode fait la conversion fréquence-à-temps. La forme d'onde est inscrite dans le

domaine fréquentiel par un FBG. Un photo détecteur balancé élimine l' impulsion

rectangulaire non-désirée qui est superposée à la forme d'onde désirée. Une excellente

concordance entre les designs et les mesures est accomplie.

Les formes d'ondes générées sont propagées entre des antennes à large bande. La réponse

impulsionnelle non-idéale des antennes dégrade l'impulsion désirée, ce qùi réduit

l'efficacité. Nous mesurons la réponse impulsionnelle de l'antenne et l'utilisons dans le

processus d'optimisation pour concevoir une· forme d'onde efficace adaptée à la réponse de

l'antenne. Comme avant, cette forme d'onde est générée avec un FBG. Les résultats

expérimentaux montrent une excellente concordance avec la théorie et une amélioration

significative de l'efficacité de puissance.

11

Resume

In this thesis, we design and generate ultra-wideband (UWB) pulses that efficiently

exploit the US Federal Communications Commission (FCC) spectral mask. An efficient

pulse results in higher signal to noise ratio at the receiver by utilizing most of the available

power under the FCC spectral mask, lowering the probability of error. To find efficient

UWB waveforms, we combine several Gaussian monocycle pulses separated by certain

time delays. Each Gaussian monocycle has an unknown amplitude weight. The weights are

found by an optimization process which maximizes the power of the pulse while respecting

the FCC spectral mask over the entire UWB bandwidth.

We implement the efficient pulses by fiber Bragg grating (FBG) filters in the optical

domaine The time domain pulse shape is written in the frequency domain, and a single

modefiber performs the frequency-to-time conversion. The waveform is inscribed in the

frequency domain by the pulse shaping FBG. A balanced photodetector removes an

unwanted rectangular pulse superimposed on the desired waveform, assuring compliance at

low frequency. Excellent match between the designed and measured pulses is achieved.

The generated waveforms are propagated from wideband antennas. The non-flat impulse

response of the antenna degrades the designed pulse, lowering its efficiency. We measure

the antenna impulse response and take it into account in the optimization process to design

an efficient pulse adapted to the antenna response. As before, this pulse is generated by its

proper pulse shaping FBG. Experimental results show great match with theory and

significant improvement in terms of power efficiency.

III

Acknowledgement

There are many people who have helped me throughout the course ofmy graduate study. l

would like to thank my advisor Professor Leslie A. Rusch, for her guidance, encouragement

and support throughout my graduate career. The opportunities for growth and the

excitement of working in our group are deeply appreciated; l am honored to have had the

chance to be part of it. l would also like to thank my co-advisor, Professor Sophie

LaRocheIle. l truly appreciate her invaluable discussions about the fiber Bragg grating

aspects of my project.

Many thanks to my colleagues: Dr. Mohammad Abtahi, Serge Doucet, Julien Magné, and

aIl the rest, who helped me in various forms to finalize my project. Greatest thanks to

Mohamm"ad without whom this project would have never started. He was always there with

motivating discussions; taught me experimental work, and shared with me his technical

experience. AlI those cumbersome experiments would have been far from completion

without his efforts. Thanks to Serge for teaching me how to write FBGs and to Julien for

the mode locked laser. l would like to thank the COPL technicians, particularly Patrick

LaRocheIle for his assistance in the labo

My deepest appreciation goes to my parents for their support, and kindness in aIl and

every stage of my life. They have always been there for me, provided me with the best

education and encouraged me to leam. FinaIly, many thanks to aIl my teachers over the

years, from the first grade of elementary school to the university.

IV

Table of Contents

Résumé . ........... ........................................................................................ i

Resume .. ................................................................................................... ii

Acknowledgement .................................................................................... . iii

List of Figures ........ ...................................................................... .... ........ vi

List of Tables . .......................................................................................... ix

List of Acronyms ........ .............................................................................. x

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

1.1 . UWB Basics ............... ....................... ....... .. .. ........ ..... ................ ... ............................................. .... .. ... 2

1.2. UWB Compared to Other Wireless Technologies ...... .. .................................................. .. .......... ........ 5

1.3. Applications ........ ....................... .... ................ ... .... .... ... ....................... ... ..... ............. ....... .......... .... ...... 7

1.4. Structure of the Thesis .................................................. ........ .. ................... .............. .. ..... ..... ... ... ... .... .. 8

Chapter 2 Optimal UWB Waveforms ................................. .... ........ .. .. ... .... ........... ... ..... ...... ....... 10

2.1. Pulse Shaping Techniques ............................................................ .......... ... .... ..... ... ...... ........ ..... ..... ... Il

2.1 .1. Pulse shaping in the Electrical Domain ........................ ..... .. .. ................................................ .. ......... 12

2.1 .2. Pulse shaping in the Optical Domain .......................................... .. ............... ... .. ... .. ... ...... ... .. ..... .. ... ... 13

2.2. Optimization Process Based on Sampling ......................................................................................... 14

2.3 . Optimized Sum of Weighted Gaussian Monocycles .......... ...... .. .... ............. ................. ...... .. .......... .. 21

2.3.1. Optimization Procedure ...................................................... ........................ ' ............ .. .................... .... 22

2.3.2. Multiband UWB Pulse Design .. .......... ..... ... ........ .. ... ...... .................................... ........... ............ ....... 26

2.4. COl1clusions ............................................................... .. ........... ................................................... .. ..... 28

Chapter 3 Optical UWB Pulse Shaping Using FBGs ................................................ .. ......... 29

3.1. Optical Pulse Shaping Methods ................................................................................... ......... ............ 30

3.2. UWB Pulse Shaping Using FBGs .................................................................... .. .............................. 34

3.2.1. A Balanced Receiver Approach ......................... ..... .. .. .. ...... .. .. .. .. ..................................................... 34

3.2.2. FBG Design and Fabrication ..................... ................................................................ ....................... 35

v

3.2.3. Simulation Results ............................ ............ ............................................... .. .................................. . 41

3.2.4. Experimental Results ............................................ ..... ................................................. ...................... 43

3.3. ' Waveform Tuning Using a Band-pass Filter .................................................................................... 48

3.4. Conclusion ........................................................................................................................................ 52

Chapter 4 UWB Pulse Propagation and EIRP Optimization ........................................... 53

4.1. EIRP ......................................................................... ...... .. ... ..... ....... ........ ........... .............................. 54

4.2. Antenna Frequency Response .......................................................................................................... 56

4.2.1. UWB Antenna Characteristics .......................................................................................................... 56

4.2.2. Experimental Measurements .............. .............................................................................................. 58

4.3. EIRP Measurements for Various Waveforms .................................................................................. 62

4.3.1. Link Transfer Function ..................................................................................................................... 62

4.3.2. EIRP and Output Measurements ............................................ ' .......................................................... 63

4.3.3. Conclusion on EIRP Measurements ................................................................................................. 67

4.4. EIRP Optimization Using the Channel Frequency Response ........................................................... 67

4.4.1. Optimization Process ........................................................................................................................ 68

4.4.2. EIRP-Optimized Pulse Generation ................................................................................................... 69

4.5. Conclusion ............................. ... ......................................................................................................... 73

Summary and Future Research Direction ................................................................................ 74

Appendix A MA TLAB Programs ................................................................................................ 77

References .............................................................................................................................................. 81

VI

List of Figures

Figure 1.1 FCC spectral masks for indoor and outdoor communication applications ........... 3

Figure 1.2 UWB spectrum coexisting with other narrowband communication

systems [5] ............................................................................................................ 4

Figure 1.3 WiMedia landscape of UWB compared to Wireless local area networks

(WLAN) [5] .......................................................................................................... 5

Figure 2.1 Autocorrelation coefficients which result in an optimal response for

R(e Jw) under the FCC spectral mask ................................................................. 17

Figure 2.2 Normalized Autocorrelation spectrum, R(e Jw ) ................................................... 18

Figure 2.3 Optimal pulse samples ........................................................................................ 18

Figure 2.4 Time response of the optimal pulse, L = 20 ........................................................ 19

Figure 2.5 Optimal spectral response, L = 20 ....................................................................... 19

Figure 2.6 Normalized spectral response for L = 100 (a) and the corresponding time

domain response (b) ............................................................................................ 20

Figure 2.7 The top row gives time domain waveforms and the bottom row power

spectral densities for (a,d) Gaussian pulse, (b,e) Gaussian monocycle, and

(c,f) Gaussian doublet ......................................................................................... 22

Figure 1.8 Optimal UWB pulse shapes for L=2, 3, 7, 14 and 30 (a), and the

corresponding spectra (b) ................................................................................... 26

Figure 2.9 Efficiency vs. L for the optimization method based on sampling (red) and

combining Gaussian monocycle pulses (dashed blue) ....................................... 26

Figure 2.10 Normalized spectra ofUWB sub-band pulses; (a) 3.5----5GHZ, (b)

6----7.5GHZ, and (c) 8.5----10GHZ ......................................................................... 28

Figure 3.1 Spatial shaping using the SLM [16] .................................................................... 30

Figure 3.2 Broadband RF waveform generator, (a) Experimental apparatus. (b)

Reflective geometry Fourier transform [21] ....................................................... 31

Figure 3.3 UWB pulse generation based on spectral shaping of a MLFL ........................... 32

Figure 3.4 AlI optical UWB pulse generation based on phase modulation and

frequency discrimination .................................................................................... 33

VIl

Figure 3.5 Concept of arbitrary pulse generation by spectral pulse shaping ........................ 33

Figure 3.6 Block diagram of the UWB waveform generator ............................................... 35

Figure 3.7 Interference pattern ofa phase mask ................................................................... 36

Figure 3.8 MLFL normalized power spectral density .......................................................... 37

Figure 3.9 Flattening filter (FBG1) design; (a) required normalized spectrum, (b)

apodization profile .............................................................................................. 38

Figure 3.1 0 (a) Flattening filter transmission response measured using an optical

vector analyzer (b) a detailed view of the filter response ................................... 39

Figure 3.11 Pulse shaping filter (FBG2) design; (a) time domain target pulse, (b)

filter transmission profile, (c) apodization profile .............................................. 40

Figure 3.12 (a) L = 14 pulse shaping filter transmission -response measured using an

optical vector analyzer (b) same measurement after averaging ......................... 41

Figure 3.13 Simulation results for L=14. (a) Transmittivity ofFBGs, (b) PSD at

upper and lower arms, and (c) simulated and designed output pulse ................. 42

Figure 3.14 Experimental results for L = 14. (a) PSD at upper and lower arms, (b)

measured UWB pulse, and (c) the spectrum ...................................................... 45

Figure 3.15 Experimental results for L = 7. (a) measured UWB pulse, and (b) the

spectrum. The enlarged part shows the sinusoidal variations due to

multiple reflections ............................................................................................. 46

Figure 3.16 Experimental results for L = 30. (a) measured UWB pulse, and (b) the

spectrum ................................................................. ! •••••••••••••••••••••••••••••••••••••••••••• 46

Figure 3.17 Schematic diagram of the tunable UWB waveform generator ......................... 48

Figure 3.18 (a) Transmitti~ity of the pulse shaping FBG , tunable Filterl and Filter2,

(b) designed UWB waveform and filters' shapes ............................................... 49

Figure 3.19 Tuning filters transmission responses (a) the low pass filter (b) the high

pass filter (c) a band pass filter ........................................................................... 49

Figure 3.20 Generated and target waveforms and their spectrum: (a, b) Gaussian, (c,

d) monocycle, '( e, f) doublet and (g, h) FCC-compliant, power efficient

pulses .................................................................................................................. 51

Figure 4.1 (a) SkyCross (SMT-3T010M) UWB antenna, (b) azimuth radiation

pattern at 4.9 GHz ............................................................................................... 57

VIn

Figure 4.2 Antenna measurements, (a) antenna frequency response, (b) antenna link

delay, (c) antenna phase response, (d) antenna reflection response ................... 60

Figure 4.3 (a) Smoothed antennas frequency response, (b) normalized time response ....... 61

Figure 4.4 The wireless link, (a) setup block diagram, (b) PA frequency response, (c)

antenna frequency response, (d) LNA frequency response, (e) PA,

antennas and LNA frequency response .............................................................. 62

Figure 4.5Transmit pulses (1), spectrums (2), EIRPs (3), for Gaussian monocycle,

doublet and FCC-optimized pulses ..................................................................... 64

Figure 4.6 Received pulses (1) and spectrums (2), for Gaussian monocycle, doublet

and FCC-optimized pulses ....... .. ... .......................................... ... ........ .. ....... ... ..... 65

Figure 4.7 The FCC and the effective spectral masks .......................................................... 68

Figure 4.8 EIRP optimized pulse shaping, (a) time domain pulse shape, (b)

transmission response of the pulse shaping FBG, (c) apodization profile

of the FBG, (d) experimental insertion loss of the pulse shaping FBG

written in 3 sweeps ............................................................................................. 70

Figure 4.9 (a) the designed (dashed line) and the measured (solid line) pulse shapes,

(b) Measured PSD and the FT of the measured time domain pulse shape,

( c) The PSD of the designed and generated p.ulse and the corresponding

EIRPs ............................................................................................................. : .... 71

Figure 4.10 Waveform comparison (a) time domain measurements (b) PSDs

compared to the effective mask, (c) PSDs compared to the FCC mask ............. 72

- - ----- --------------

IX

List of Tables

Table 1.1 FCC EIRP limits for indoor and outdoor UWB Applications ................................ 3

Table 1.2 Categories of applications approved by FCC ..................... .................................... 7

Table 3.1 Cutoff Wavelengths of the Filters for Different UWB Waveforms ..................... 49

Table 4.1 Peak to peak voltage (Vpp), Average total power and PE for the Gaussian

monocycle, doublet and the FCC-optimized waveforms ..................................... 66

List of Acronyms

UWB FCC UMTS

' EIRP SNR PE LNA PAM OOK PPM HDTV WPAN FBG FIR RF LO BJT CMOS BER BBCS SLM PSD DFT SMF FT OIE LCM BPD DL ATT UV 1FT EDFA MLFL OSA FWHM Tx Rx PCB MLA VNA PA

Ultra-wideband US Federal Communications Commission Univers al Mobile Telecommunication System Equivalent Isotropically Radiated Power Signal to Noise Ratio Power Efficiency Low Noise Amplifier Pulse Amplitude Modulation On-Off Keying Pulse Position Modulation High-Definition Television Wireless Personal Area Network Fiber Bragg Grating Finite Impulse Response Radio Frequency Localoscillator Bipolar Junction Transistor Complementary Metal Oxide Semiconductor Bit Error Rate Broadband Coherent Source Spatial Light Modulator Power Spectral Density Discrete Fourier Transform Single Mode Fiber Fourier Transform Optical Electrical Conversion Liquid Crystal Modulator Balanced Photodetector Delay Line Attenuator Ultra-violet Inverse Fourier Transform Erbium Doped Fiber Amplifier Mode Locked Fiber Laser Optical Spectrum Analyzer Full Width HalfMaximum Transmi tter Receiver Printed Circuit Board Meander Line Antenna Vector N etwork Anal yzer Power Amplifier

x

Xl

Vpp Peak-to-Peak Voltage BR Bit Rate

Chapter i: introduction ,

Chapter 1

Introduction

Connectivity for "everybody and everything at any place and any time" is the vision of

wireless systems beyond the third generation. Short-range wireless technology will play a

key role in scenarios of ubiquitous communications over different types of links [1]. Novel

devices based on ultra-wideband (UWB) radio technology have the potential to provide

solutions for many of today's problems in the area of spectrum management and radio

system engineering.

2 Chapter 1: introduction

1.1. UWB Basics

UWB technology has existed since the 1980s [2]; it mainly has been used for radar

applications because of the wideband nature of the signal that results in very accurate

timing information. In the early days UWB was referred to as impulse radio, where an

extremely short pulse with no carrier was used instead of modulating a sinusoid to transmit

information. These sub-nanosecond pulses occupy several GHz of bandwidth and are

tr&nsmitted with very low duty cycles. In April 2002, after extensive commentary from

industry, the US Federal Communications Commission (FCC) issued its first report on

UWB technology, thereby providing regulations to support deployment of UWB radio

systems [3]. These regulations allowed the UWB radios to coexist with already allocated

narrowband radio frequency (RF) emissions.

The band allocated to UWB communications lS 7.5 GHz wide, by far the largest

allocation of bandwidth to any commercial terrestrial system. The FCC UWB rulings

allocated 1500 times the spectrum allocation of a single UMTS (universal mobile

telecommunication system) license [4]. However, the available power levels are very low.

If the entire 7.5 GHz band is optimally utilized, the maximum power available to a

transmitter is approximately 0.5 m W. This effectively relegates UWB to indoor, short

range, communications for high data rates, or very low data rates for substantial link

distances. In principle, trading data rate for link distance can be as simple as increasing the

number of pulses used to carry 1 bit. The more pulses per bit, the lower the data rate, and

the greater the achievable transmission distance.

UWB devices are intentional radiators under FCC Part 15 Rules. The FCC report

introduced four different categories for allowed UWB applications, and set radiation masks

for them. For a radiator to be considered UWB the fractional bandwidth defined as

must be at least 0.2. In the formula above, fH and JL are the higher and lower -10 dB

bandwidths, respectively.

Chapter i: introduction

Table 1.1 Fee EIRP limits for indoor and outdoor UWB Applications

Freq uency (GHz)

0.96-1.61

1.61-1.99

1.99-3.1

3.1-10.6

Above 10.6

.96 : 1.99 3.1 1.61

-63.3 1

-75,.1 1

Indoor EIRP (dBm)

-75.3

-53.3

-51.3

-41.3

-51.3

-41.3

..... lndoor ••• Outdoor

frequency (GI'Iz)

Outdoor El RP (dBm)

-75.3

-63.3

-61.3

-41.3

-61.3

• '. • • •

-51.3

• ,·61 ~ ....... _-

10.6

Figure 1.1 Fee spectral masks for indoor and outdoor communication applications

3

Also, according to the Fee UWB rulings the signal is recognized as UWB if the signal

bandwidth, i.e. , IH - I L' is 500MHz or more. The radiation limits set by the Fee are

presented in Table 1.1 for indoor and outdoor data communication applications. These

limitations are expressed in terms of equivalent isotropically radiated power (EIRP). EIRP

is the product of the transmit power from the antenna and the antenna gain in a given

direction relative to an isotropic antenna. Further discussion about EIRP will follow in

section 4.1. Figure 1.1 shows the EIRP limits imposed by the Fee spectral masks for the

indoor and outdoor communication systems. Other applications such as vehicular radar, are


restricted by different masks. Allowed UWB emission levels are less than or equal to the

level allowed for unintentional radiators such as computers and other electronic devices

(-41.3 dBm/MHz). Thus the UWB transmitter can be treated like noise by other

communication systems.

The strict power limitations imposed by the FCC spectral mask necessitate spectral pulse

shaping: designing spectrally efficient pulses that eke out most of the power available under

the FCC mask. UWB system performance highly depends on the signal to noise (SNR)

ratio. Therefore choosing efficient pulses for UWB. communication systems is of critical

importance. In this thesis, we design and generate sorne efficient UWB waveforms which

show significant improvements in terms of transmit power over the widely adopted

Gaussian UWB waveform ~amily.

The power efficiency (PE) is the average power of a pulse normalized by the total

admissible power under the FCC spectral mask (----0.5 m W). The goal of this work is to

maximize the PE for the indoor UW·B communication systems by generating efficient

pulses that exploit the FCC mask in the best way.

Emitted Signal Power

Bluetooth, Zigbee WLAN 802.11 b WPAN 802.15.4

3G Cellular

WiMax Indoor

4G Cellular Indoor

(Future)

UW8 Spectrum FCC "Part 15 limits"

2.4 2.7 3.1 3.4 3.8 4.2 4.8 5.5 Frequency (GHz)

10.6

Figure 1.2 UWB spectrum coexisting with other narrowband communication systems 15]

Chapter i : introduction

1.2. UWB Compared to Other Wireless Technologies

1000

UWB 480Mbps @ 2m Short 200Mbps @ 4m

Distance . Fast

Download... UWB 110Mbps @ 10m _------_ _ ""Room-range

High-definition Quality of service,

streaming

Bluetooth

ZigBee

802.11 a/b/g/n Data Networking

.11n promises 100Mbps @ 100m

UWB, low data-rates, location & tracking

10 Range (m) 100

Figure 1.3 WiMedia landscape of UWB compared to Wireless local area networks (WLAN) [5]

5

Figure 1.2 highlights the low power but wideband nature of the UWB compared to other

wireless networks. UWB coexists with other narrowband networks; the interference caused

by a UWB transmitter can be viewed as a wideband interferer, and it has the effect of

raising the noise floor of the narrowband receiver. A major benefit to UWB of low power

constraint is preserving battery life. Another benefit of low PSD is low probability of

detection which is a concem for both military and consumer applications. The weak UWB

pulses are inherently short range which makes the operation of multiple independent links

possible within the same house. The broadband property of the UWB signal makes it

resistant to interference because any interfering signal is likely to affect a small portion of

the desired signal spectrum.

UWB can provide very high speed but short distance communication links. Figure 1.3

. shows the WiMedia landscape ofUWB services compared to IEEE 802.11 networks [5]. It

can be seen that UWB is the fastest in close range while the IEEE 802.11 is more suitable

for distances more than 10 m. The spatial capacity, an indicator of data intensity in a

transmission medium, is over 106 bit/s/m2 for UWB, whereas just 1000 bit/s/m2 for IEEE

802.11 b [2]. No system is capable of reaching a spatial capacity as high as that of a UWB

6 Chapter 1: Introduction

system. A reason is the Shannon channel capacity theorem [6]. The upper ' bound on the

capacity of a channel grows linearly with the available bandwidth. Thus, the UWB systems

,occupying several GHz of bandwidth show great potential for the future high capacity

wireless networks.

Sorne important issues attributable to UWB are discussed here.

a) Antennas: Antennas have a filtering effect on the UWB pulse. Good impedance

matching over the entire UWB bandwidth is desired to reduce reflection losses from

the antennas. The impulse response of the antenna changes with angles in azimuth and

elevation. Therefore, the transmitted pulse is differently distorted at every angle.

b) Low noise amplifiers (LNAs): Design of amplifiers ~s another challenge for UWB

applications. Due to the low power and wideband nature of the UWB signal, very low

noise and wideband amplifiers are essential at the receiver side.

c) Modulation: For pulsed UWB systems, the widely used modulation schemes are pulse

amplitude modulation (P AM), on-off keying (OOK), and pulse position modulation

(PPM). The OOK scheme results in energy detection receivers of lower complexity,

whereas the PPM shows better error performance but lower bit rates.

d) Multipath: In the indoor environment the signal bounces off objects located between

the transmitter and receiver creating multipath reflections. If the delay spread of the

echoes is smaller than the pulse width, the echoes can combine destructively leading

to multipath fadi,ng. However, for an indoor UWB system with a range of 10 m, the

delay spread is typically several nanoseconds [7]; significantly more than a typical

UWB signal pulse width. This makes UWB resistant to multipath interference. To

maximize the received energy, one can use a RAKE receiver to combine the signaIs

coming over resolvable propagation paths. However, combining many multipath

components increases the complexity of the receiver.

e) Multiband: Multiband UWB provides a method where the FFC approved 7.5 GHz

UWB bandwidth is split into several smaller frequency bands, each having a

minimum of 500 MHZ bandwidth. The signaIs do not interfere with each other

7 Chapter 1: Introduction

Table 1.2 Categories of applications approved by FCC 18]

Class/ Application Frequency band of operation

Communications and measurement systems 3.1-10.6 GHz

Imaging: ground penetrating radar, wall , <960 MHz or 3.1-10.6 GHz medical imaging

1 maging: through wall <960 MHz or 1.99-10.6 GHz

Imaging: surveillance 1.99-10.6 GHz

Vehicular ·24-29 GHz

because they operate . at different frequencies. Multiband systems provide another

dimension for multiple access via frequency division. The sm aller bandwidth of each

pulse reduces the overall design complexity, at the cost of losing sorne multipath

immunity.

1.3. Applications

The FCC regulations classify UWB application into several categories with different

emission regulations in each case. Table 1.2 shows these categories and their corresponding

frequency bands of operation. Among recent applications of UWB are the following.

a) Cable replacement: Today, most computer and consumer electronic devices

(everything from a digital camcorder and DVD player to a mobile PC and a high

definition TV (HD.TV)) require wires to record, play or exchange data. UWB will

eliminate these wires, allowing people to "unwire" their lives in new and unexpected

ways [9]. A mobile computer user could wirelessly connect to a digital projector in a

conference room. Digital pictures could be transferred to a photo print kiosk for

instant printing without the need of a cable. An office worker could put a mobile PC

on a desk andinstantly be connected to a printer or a scanner.


b) Wireless Personal Area Networking (WP AN): A high speed wireless UWB link can

connect cell phones, laptops, cameras, Mp3 players. This technology provides mu ch

higher data rates than Bluetooth or 802.11. UWB a portable MP3 player could stream

audio to high-quality surround-sound speakers anywhere in the room.

c) Vehicle collision avoidance: UWB can provide enough resolution to distinguish cars,

people, and poles on or near the road. This information can be used to alert the driver

and prevent collisions. UWB radar has the resolution to sense road conditions (i.e. ,

potholes, bumps, and gravel vs. pavement) and provide information to dynamically

adjust suspension, braking, and other drive systems.

d) Radar: UWB can provide centimeter accuracy in ranging because of its high time

resolution. Improved object identification (greater resolution) is achieved because the

received signal carries the information not only about the target as a whole, but also

about its separate elements. The low power of the UWB signaIs reduces the

probability of detection by hostile interceptors [10].

e) Other applications of UWB are public safety systems including motion detection

applications, RF tag for personal and asset tracking, medical monitoring and so forth.

Our proposed optical UWB pulse generation technique targets the applications a) and b)

rnentioned above. These applications require high speed, high range wireless

communications and our approach in efficient pulse generation can help fulfill these needs.

1.4. Structure of the Thesis

The basic concepts of the emerging UWB communications were outlined in this chapter.

The power restrictions imposed by the FCC spectral mask emphasizes the importance of

using efficient pulses as the building blocks of a UWB communication link. In Chapter 2,

'we develop a linear optimization program -to find optimal, pulses to exploit the power

available under the FCC spectral mask. In Chapter 3, we propose a method to implement

the efficient UWB waveforms using Fiber Bragg gratings (FBGs). We demonstrate

experimental results that accurately respect the FCC mask while maximizing the permitted

-- ---- - ---------- - - ------,


power. Later, we generate several UWB pulses with the same setup by introducing a band

pass tunable filter. In Chapter 4, we discuss the effect of antennas on the transmission of

UWB pulses. The impulse response of the antenna is measured using a network analyzer.

This non-ideal response affects the received signal, degrading the power efficiency at the

receiver. Subsequently, the antenna impulse response is taken into account in the

optimization process to design a new pulse which maximizes the EIRP. The

implementation of this newly designed pulse shows exceptiorÙ11 power efficiency and great

match to theoretical calculations.

This work has been truly coIlaborative in aIl the steps. My individual contributions are

detailed in Chapters 2 (development and generation of optimal UWB waveforms) and

Chapter 4 (characterization ofUWB pulse through transmit and receive antennas, and EIRP

optimization). Chapter 3 reports experiments run with Dr. Abtahi. While Dr. Abtahi was

responsible for supervising FBG development, deterrnining the experimental layout and

overaIl measurement strategies, l was an active participant in the measurements. The FBGs

used in Chapter 3 were fabricated by J. Magné, however l also participated in fabrication

and ,am now trained in writing FBGs. l wrote aIl FBGs presented in Chapter 4.

10 Chapter 2: Optimal UWB Waveforms

Chapter 2

Optimal UWB Waveforms

In UWB systems the conventional analog waveform, representing a message symbol, is a

simple pulse that in general is directly radiated. These short pulses have typical widths in

the pico second range, and thus bandwidths of over 1 GHz. In the literature, the most

common of these pulses are Gaussian monocycle and doublet pulse shapes [11]. Although

traditionally employed for UWB systems, these shapes poorly exploit the permissible

power under the FCC mask. Performance of a UWB system is mainly decideq by the

received SNR. To achieve the highest possible SNR, we have to eke out aIl the permissible

power under the FCC spectral mask. Therefore choosing the most efficient pulse for UWB

communication systems is of critical importance.

Il Chapter 2: Optimal UWB Waveforms

Recently, Giannakis et al. [12] suggested a digital finite impulse response (FIR) filter

approach to synthesizing UWB pulses and proposed filter design techniques by which

optimal waveforms that closely match the spectral rna~k can be obtained efficiently. For

single pulse design, a convex formulation is developed for the design of the FIR filter

coefficients that maximizes the spectrum utilization in terms of both the bandwidth and the

power allowed by thè spectral mask. Although we do not intend to irnplement optimal

pulses with an FIR filter approach, still we use this method to find optimal pulse

waveforms. The resuIting waveforms will be implernented not via FIR fiItering but by a

cornpletely different method in Chapter 3 using optics.

In 2.1.1 , we address sorne of the common RF rnethods to generate UWB pulses. We

discuss optical . pulse shaping methods in section 2.1.2. The shortcomings of these

techniques in the generation of highly efficient UWB pulses lead us to design new

waveforms in sections 2.2 and 2.3.

2.1. Pulse Shaping Techniques

Transrnitter architectures for pulse-based UWB signaIs in the FCC UWB band (3.1-10.6

GHz) can be grouped into two categories depending on how the pulse is generated. The

first category of transmitters generate a pulse at baseband and up-convert it to a center

frequency in the UWB band by mixing with a local oscillator (Lü). The second category

generates a pulse directly in the UWB band without frequency translation. A base band

impulse may excite a filter that shapes the pulse, or the pulse may be directly synthesized at

RF without requiring additional filtering. The up-conversion architecture generally offers

more diversity and control over the frequency spectrum, but at the cost of higher power,

since an Lü must operate at the pulse center frequency.

Electrical pulse shapers can be designed based on either of the two approaches, but optical

pulse shaping methods directly generate the desired baseband waveform. Sorne examples of

electrical and optical approaches of pulse shaping are discussed in this section.


2.1.1. Pulse shaping in the Electrical Domain

We take a brief look at the electrical pulse shaping methods, although we will focus on

optical methods in this work. As mentioned before, the pulses are either directly shaped in

the UWB bandwidth or are up-converted from baseband. As an example of up-conversion

of a wideband pulse, we consider generation of a multiband UWB pulse [13]. A near

Gaussian pulse is shaped from a triangular input signal by exploiting the exponential

properties 0 a bipolar junction transistor (BJT). The pulse is up-converted to one of the

fourteen 528 MHz-wide channels in the 3.1-10.6 GHz UWB band. Pulse shaping is

integrated into the mixer performing up-conversion, fabricated in a 0.18 ",m SiGe

BiCMOS process. We will see that the Gaussian s4ape poorly exploits the FCC spectral

mask.

ln [14] , an overall design of pulse generator and transmit antenna is proposed. They

design a chip . to generate Gaussian monocycle pulses for use with pulse position

modulation (PPM). The impulse generatoris preceded by a programmable pulse-position

modulator. The impulse generator consists of a triangular pulse generator and a cascade of

complex first -ord~r systems made up of differential pairs each approximating a Gaussian

monocycle waveform. The complete pulse generator is fabricated in IBM 0.18-,um Bi-

CMOS IC technology. The minimum attaina~le pulse width is about 375 ps, with 330 ps

offset for pulse-position modulation.

ln another technique, a single-chip CMOS pulse generator with pulse shaping is proposed

that combines various delayed pulses to form a short pulse that is filtered to obtain the

UWB pulse [15]. A separate band-pass filter (3.1 to 5 GHz) is ,used to obtain an FCC

compliant pulse with duratîon of about 1.5 ns; the generated pulse is, however, not power

efficient.

The major advantages of electrical generation of UWB pulses are low-cost and possibility

of integration on a single chip. The major drawback is the imprecision of the generated

pulses leading to violation of the FCC mask. As a result, the pulse power should be

lowered, reducing the SNR and worsening the bit error rate (BER). Another disadvantage is


that the electrical methods normally do not cover aIl of the available bandwidth, which

degrades the spectral utilization.

2.1.2. Pulse shaping in the Optical Domain

Optical pulse generation techniques for UWB have been proposed based on optical

spectral shaping and frequency-to-time conversion. The general concept is to shape the

spectrum of a broadband coherent source (BBCS) to match the desired time-domain

waveform. The spectral shape is converted to a time domain shape (a pulse shape) by

passing through a dispersive medium such as dispersive fiber or a crnrped fiber Bragg

grating. In this section, we present a concise review of previous UWB optical pulse shaping

techniques. These methods, along with our proposed method ofUWB pulse generation will

be thoroughly covered in Chapter 3.

Consider first a free space optical implementation. The pulse shaping device in [16] is a

4-f grating and lens apparatus consisting of two free space bulky gratings, two large focal

length lenses to angularly disperse the frequency components, and a spatial light modulator

(SLM) to modulate the, amplitude of frequency components. Although this setup is tunable

and can generate various pulses, it suffers from high free-space losses and bulky packaging.

A more realistic method of implementation is using optical fibers. An all-fiber pulse

shaper was proposed in [17] in which two optical filters with complementary spectra are

placed in two arms of an interferometer to shape the power spectrum to a Gaussian

monocycle or doublet pulse. In general, optical pulse shaping methods are of higher

precision compared to their electrical counterparts. However, research has usually focused

on generation of Gaussian pulses which have a po or coverage of the FCC mask. In the next

section, we will discuss the design of more sophisticated but efficient pulses which can be

generated using low-cost FBGs.

]4 Chapter 2: Optimal UWB Waveforms

·2.2. Optimization Process Based on Sampling

To best exploit the UWB bandwidth, the subject of stringent FFC emission regulations,

we seek an optimized time domain pulse shape which maximizes the transmit power

subject to the FCC spectral mask. The normalized spectral mask for indoor

communications is plotted in Figure 1.1

Let pet) be a UWB pulse that we sample at Fs = 28 GHz. As the FCC spectral mask is

nonflat up to 10.1 GHz, this sampling rate is sufficient up to 14 GHZ per the N yquist

sampling criterion [18]. The sampling theorem states that the UWB pulse can be related to

the samples,p[k] , by

00

p(t) = 2:p[k ]sinc [Ct - kTo)~. ] (2.1) k =o

where Ta is the sample spacing and Fs = liTa is the sampling rate. We can approximate pet)

as a truncated sum of L terms; the UWB pulses have very short time do main responses,

justifying keeping only L terms, as samples quickly approach zero. Of course, the larger

that Lis, the better the approximation.

Our optimization criteria is the maximization of the transmit power, which is calculated as

the integral of the power spectral density (PSD) of the signal. The PSD of p(t) is Ip ( ej@ )1 2

,

where (j) is the angular frequency and P ( e}fj» ) is the Fourier transform of pet). In other

words, the problem is to

(2.2)

subject to Ip (e }{ù )1 fal.ling under the FCe mask over the entire frequency range. The

parameters a and fJ set the bandwidth of interest. Meeting this condition for aIl

frequencies would require an infinite number of constraint equations. The infinite number

of inequalities can be reduced to a finite number by sampling the frequency range. The


number of frequency samples should be high enough to assure good precision and at the

same time offer reasonable computation time.

The FCC mask amplitude constraints are not convex in the optimization variables p[k] and

hence algorithms for solving it must deal with local optima. As proposed in [19] , we

examine autocorrelation coefficients instead of the pulse itself; this converts the problem to

a linear optimization problem. Autocorrelation of p[ k] is defined as:

L- k

r[k]= LP[i)P[i+k] k=-L, ... ,O, ... ,L (2.3) ;=0

Note that r [k] = r [-k]. Taking the discrete Fourier transform (DFT) ofr [k] , we find

R ( el'" ) = f r [ k ] e - i",k k=-oo

L

= r [0] + 2 L r [k] cos (km) (2.4) k=1

From (2.2) and (2.4), the optimization goal becomes:

(2.5)

subject to R ( ejOJ) falling under the FCC spectral mask. We also require that R ( ejOJ

) be

strictly non-negative. This is a necessary and sufficient condition for existence of p[ k]

satisfying (2.3) by the Fejer-Riesz theorem [19]:

Suppose C denotes the complex numbers field. If a complex function Wez):

C ~ C satisfies

m

W(z)= L w(n)z-n and W(z)~O Vlzl=l, n=-m

then there exists fez): C -) C and y(O), ... , y(m) E C such that

Chapter 2: Optimal UWB Waveforms

m

y (z) = l y( n) z-n and w (z) =/ y (z) /2 'v' / z /= 1 . n=-m

Y(z) is unique if we further impose the condition that aU its roots be in the

unit circle 1 z I~ 1 .

16

Now we have a linear objective in terms of r[k] and the constraints are also sets of infinite

inequalities in r[k]. This type of optimization problems can be solved using a convex

optimization solver. We choose SeDuMi, a MA TLAB optimization toolbox developed at

McMaster University [20]. This toolbox can solve the following problem:

maxBTy (2.6)

such that c. - A. Y > 0 for i = 1, 2, ... , n. • 1 1

Therefore, we just need to convert our optimization goal and its constraints to this format.

The A, Band C matrices are found to be:

2cosaJ1 2cos 2aJ1 2cosLaJ\

2cos0J2 2 cos 2OJ2 2cosL0J2

1 2 cos aJn 2cos20Jn 2 cos aJn A=

-1 -2 cos OJ1 -2cos20J\ -2cosL0J1

-1 -2 cos OJ2 -2cos 2OJ2 -2cosL0J2

1 -2cosOJn -2 cos2aJn -2cosLOJn (2.7)

B=[,B-a 2(sin,B-sina) ... L(sin,B-sina)]T


0.5

0.4

~ 0.3 '"1::'

cJÎ ë al 0.2 ()

~ u 0.1 c 0

~ ~ 0

<::) 0 g :5 -0.1 <{

-0.2

-0.3 0 10 15 20 25

Figure 2.1 Autocorrelation coefficients which result in an optimal response for R ( e)m) under

the Fee spectral mask.

17

where L is the number of taps, lUI ' lU2 ' ••• , lU n are the n samples of the angular frequency

(i -1) range, {ùi == --1[ , and Ui are the samples of the FCC spectral mask taken at the

n

. corresponding angular frequency, wi •

SeDuMi solves the equations to find:

y == {r[O],r[I], ... ,r[L]}T

We use a sampling frequency of Fs = 28 GHz and L = 20. TheMATLAB pro gram in

Appendix A solves the set of equations for these values and gives the autocorrelation

coefficients plotted in Figure 2.1. The Fourier transform of the autocorrelation function and

the FCC spectral mask are plotted in Figure 2.2. As we ean see, R ( e)m) effieiently eovers

the mask over the whole frequency range without violating it.

The next step is to find p[ k] from its autocorrelation. We use the spectral factorization

method explained in [19]. This method is based on Fejkr-Riesz theorem.


The optimal pulse samples, p[k] , are obtained by the spectral factorization method from

the autocorrelation function using the program explained in Appendix A; the pulse samples

are plotted in Figure 2.3.

0

-10 ,-- -

\ ~ -20

1

E \: :1 2 ~ 1 i -30

Il , CI)

c 0 ~ -40 ~ cs g :5 -50 ct

-60

-70 0 2 4 6 8 10 12 14

Frequency (GHz)

Figure 2.2 Normalized Autocorrelation spectrum, R (ejw)

0.4

0.3

0.2

~ cr 0.1 ctÎ Q)

a. 0 E

cu CI)

Q) CIl -0.1 "3 a..

-0 .2

-0.3

-0.4 0 5 10 15 20 25

Figure 2.3 Optimal pulse samples


0.8

0.6

0.4

CL 0.2

"0 Q.l

.~ 0 ëij E Cs -0.2 z

-0.4

-0.6

-0.8

-1 -1 -0.5 o 0.5 1.5

t (ns)

Figure 2.5 Time response of the optimal pulse, L = 20.

Having the samples, p[k], it is straightforward to find the continuous time response pet)

using (2.1 ). Figure 2.5 shows pet) obtained from the p[k] coefficients in Figure 2.3. We can

see sorne slowly decaying variations on either side of the pulse, attributed to the tails of the

sinc function in (2.1). The power spectrum of the optimal pulse is illustrated in Figure 2.4.

The power efficiency

o .. _ .. ·---r-~V:.: " -~'--'-----"-~\" : : 1

-10 1"

-20 CI en :\ a.. "0

.~ -30

\1\ ni E 0 z

-40

-50 1

\i

-60 0 2 4 6 8 10 12 14

f(GHz)

Figure 2.4 Optimal spectral response, L = 20.


(2.8)

is the average power of the pulse normalized by the total admissible power under SFCC( (J)) ,

the Fee mask. BW is the UWB bandwidth over which we integrate to find the power.

We note from Figure 2.4 that the optimized pulse completely satisfies the Fee spectral

mask and has 75% efficiency. By increasing the pulse length (or equivalently, L), the

spectrum of the pulse better fits the mask, and the spectral utilization factor or power

efficiency increases. The larger the number of taps, the higher the power efficiency but also

the greater the complexity. Because of this trade-off between efficiency and pulse length, a

reasonable value for the number of taps should be chosen.

To examine an extreme case, L is set to 100. Figure 2.6a shows the spectrum in this case:

an extremely tight fit to the mask and efficiency of 94%. The resulting time domain pulse is

plotted in Figure 2.6b. The pulse has become very lengthy with many small variations at

the tail that are impractical to implement. We must strive for a simple, spectrally-efficient

pulse that is easy to implement as discussed in the next chapter.

o (/)

CL

-10

-20

~ -30

1 z -40

-50

\

-60 L--.w...J......J_--'_--'-_----'-_--'-_ ----'-_---'

o 6 8 10 12 1 (GHz)

(a)

0.8

0.6

0.4

f 0.2

~ .~ 0 ëii E ~ -0.2

-0.4

-0.6

-0.8

-1 L-----'----'--'------'----'-_-'------'-_-'-----'--_'-----'

-1 -0.5 0.5 1.5 t (ns)

(b)

2.5 3.5

Figure 2.6 Normalized spectral response for L = 100 (a) and the corresponding time domain response (b).


FinaIly, we conclude from our results that although many samples provide more power

efficient pulses, a high number of samples is not easily implemented. This is mainly caused

by the slowly decaying tail of the sinc function. The techniques used in this section can be

applied to a more realistic implementation, i.e., with smaller L. In section 2.3, we take the

concept of optimizing a sum of weighted sinc functions, and instead apply the optimization

to a sum ofweighted Gaussian monocycles [12].

2.3. Optim,ized Sum of Weighted Gaussian Monocycles.

Gaussian waveforms, ploned in Figure 2.7, are a family of functions deriving from a

Gaussian pulse defined as,

(2.9)

where A is an amplitude scaling factor and Tg is a time scaling factor. The Gaussian

monocycle (2.10) is the first derivative of the Gaussian pulse, and the second derivate

results in the Gaussian doublet (2.11).

(2.10)

(2.11 )

At each derivative, one zero-crossing is added. The Gaussian has no zero-crossing, a

monocycle has one, and so on. Furthermore, at each additional derivative the fractional

bandwidth decreases, while the center frequency increases (Figure 2.7).

An important aspect of these Gaussian waveforms is their wideband spectrum. By

combining many multi-GHz pulses, we can carve the desired spectral shape. In the time

domain, Gaussian waveforms are smooth and weIl behaved functions, making them easier

to implement, as discussed in Chapter 4. In addition, a Gaussian pulse is easy to directly

Chapter 2: Optimal UWB W. avef orms

V "'0

.~ ë 0.. := E !: ~

~ ~ O. 5 Co . ~ ~ ~

E o

Gaussian

200 t eps)

(a)

Z (~--~--~~----

o 5 10 15 20

f(GHz) (d)

v 1 "'0

.~ 0.. E ~

"'0 0 V .~ ~ E

~-I -200

v "'0

.~ 0.. E ~

~ O. ~ . ~ ~ E 0 Z 0

0

Monocycle

( 100 200 t (p)

(b)

J 10 15 _0

f(GHz) (e)

v "'0

.~ 0.. E ~

"'0 V .~ ~-

E 0 Z

v "'0

.~ 0.. E ~

-0 0. :-v

. ~ ~ E 0 z

Doublet

te ps)

(c)

22

200

;) JO j 5 20

f(GHz) (f)

Figure 2.7 The top row gives time domain waveforms and the bottom row power spectral densities for (a,d) Gaussian pulse, (b,e) Gaussian monocycle, and (c,f) Gaussian doublet.

generate ln electronics. For these reasons we choose the Gaussian monocycle as the

building block of the optimization process for this chapter as suggested in [12].

2.3.1~ Optimization Procedure

The optimization procedure to find the weights of combined Gaussian monocycles is quite

similar to the method discussed in section 2.2 for the sinc. The desired pulse shape, pet), is

written as a summation ofweighted Gaussian monocycles,·

L -I

pet) = Lw[k]gm(t -kTa) (2.12) k=o

where gm is the Gaussian monocycle, Ta is the pulse spaclng, {w [k] } ~ :~- I are real

coefficients to be determined by the optimization process. By increasing the number of

coefficients, L, we can obtain a better power efficiency, but the pulse duration will be

greater.


Pif) , the F ouriér transform of pet), can be expressed as

1 P (f) 1 = Iw (ej2 ~.fTo ) IIGm (f) 1· (2.13)

where G m cr) is the Fourier transform of the Gaussian monocycle and W is the discrete

Fouriertransform ofvector w defined by w = [w [O] ,w [l] , ··. ,w [L -1] J.

The UWB pulse pet) should be designed with an optimization process to maximize" the

permitted power within the UWB frequency range,

2

max Ir IpU)1 dl. p(t) l' p

(2.14)

where Fp is the desired UWB bandwidth. Tbis maximization problem is subject to the PSD

restrictions imposed by the FCC spectral mask. The power spectrum, Ip (/)1 2 , should be

under the FCC spectral mask over the desired frequency range. This optimization problem

is non-convex, requiring rigorous numerical methods. To transform this to a convex

optimization problem we again turn to the autocorrelation of w, defined as

r[k]==LiW[i]w[i+k] (2.15)

with vector representation by r == [r [0], r [1], ... , r [L -.-: 1 ]]T We define two auxiliary

vectors, v Cf, L) and ü Cf, L) by

- (1 L) == [1 j27rj To j27rf2To ••• j27rf (L-I)To JT v, ,e ,e "e (2.16)

(2.17)

The following equalities are useful in simplifying the problem.

(2.18)

24 Chapter 2: Optimal UWB .Waveforms

(2.19)

(2.20)

. where H indicates Hermitian transpose of a matrix and we have used the property

r[ k] = r[ -k] in (2.19). From (2.19) and (2.20), we can find

(2.21)

From (2.13), (2.14), and (2.21) the optimization goal can be simplified as

(2.22)

= fÛT (f,L )rpm (f)1 2d! = B T .r

Fp

where B = fû(f,L)P(f)12

d!, 1:;P

The FCC-imposed limit can be expressed as f' (eJ27rj7o )12 p (f)I~ s S FCC (f), Therefore the

optimization problem is simplified to

maxB T .r (2.23)

subject to üT (f,L)f s S FCC (1)/ Pm (1)12 f E Fp

To ensure a valid autocorrelation vector we also require ü T (f, L ) r ~ 0 f E Fp •

These constraints, forming a convex semi-infinite linear optimization problem, can be

made discrete to form a finite linear program. While this gives an approximate solution,

enough samples ensure acceptable precision of the solution. The problem can be solved


using a convex cone optimization toolbox such as SeDuMi optimization tool, as in section

2.2.

Transforming our optimization problem (2.23) to the SeDuMi format (2.6) results in the

following matrixes

i = 1

Bi = 2 fPm (f)1

2 COS (27rf(i -l)To)df i = 2, ... ,L

Fp

rp

{C , } 2n = 0 1 i=n+1 (2.24)

j = 1

j = 2, ... ,L'

A =- A , ' { }i=2n)=L {}i=n)=L

Ij i =n + 1) = 1 IJ i = 1 J' = 1

, where n is the number of equally spaced frequency samples over the UWB bandwidth F p •

After obtaining the optimal autocorrelation vector r using SeDuMi, we find the optimal

filter tap coefficients m by spectral factorization [19]. Once we know the optimal tap

coefficients, finding the UWB pulse which optimally exploits and respects the Fee mask is

trivial via (2.12).

Figure 2.8 shows the power efficient UWB pulses generated by combining different

number of Gaussian monocycles with parameters Ta = 35.7 ps and Tg = 46.5 ps. We see

clearly that increasing L results in longer and more complicated waveforms which have

better power efficiency. For L = 2 the result is a Gaussian monocycle and L = 3 yields a

Gaussian doublet. Any pulse, can become compliant by reducing their power to respect the

Fee mask especially at the 1.6 GHz edge. This leads to a very poor power efficiency, as

for the Gaussian monocycle withjust 0.12% of efficiency.


o --

-10

co ~ -20

ID ~ o

a.. -30 "0 ID .~ ro E -40 o Z

-50

-60

_ï-- :,;\\

: 1- L=30 L=~~ .. o ........ . . o .. L=3 1 1

1 1 1 1 .--0- - ' 0_. L=2 1 1

L=2 SE=0.12 % L=3 SE=1 .38 % L=7 SE=47.5 % L=14 SE=67.0 % L=30 SE=75.1 % Norm~lized FCC Mask

- -- ------- ---- -

26

_70~o----~----~----~----~----~----~ ____ ~ o 0.2 0.4 0.6 0.8 1.2

Time (ns) (a)

o 2 4 6 8

Frequency (GHz) (b)

10 12 14

Figure 2.8 Optimal UWB pulse shapes for L = 2, 3~ 7, 14 and 30 (a), and the correspo.nding spectra (b).

Figure 2.9 shows the spectral efficiency versus L for both optimization methods used, i.e.

the optimization based on sampling and optimization by combining Gaussian monocycle

pulses. Interpolating curves have been fitted to the calculated points. We can see that using

pulse samples will result in a better efficiency, especially for large values of L. However,

larg~ values of L lead to very complex pulses. In the reasonable range of L ~ 30 , the two

methods have similar efficiencies. In this region, the Gaussian pulse combination method is

preferable because it offers smoother and shorter pulses. This graph helps us to choose an

appropriate value of L for good efficiency.

2.3.2. Multiband UWB Pulse Design

AlI the waveforms we studied up to now correspond to traditional UWB technology based

on single-band systems that directly modulate data into a sequence of pulses which occupy

the available bandwidth from 3.1 to 10.6 GHz. In multiband UWB schemes, as proposed in

[21] , the UWB frequency band is divided into several sub-bands, each with a bandwidth of

at least 500 MHz in compliance with the FCC regulation~ [21]. By interleaving the


transmitted symbols across sub-bands, multiband UWB systems can still maintain the

average transmit power as if the large GHz bandwidth is used. The advantage is that the

information can be processed over much smaller bandwidth, thereby reducing overall

design complexity, as weIl as improving spectral flexibility and worldwide compliance.

Multiband UWB facilitates coexistence with legacy systems and worldwide deployment by

enabling sorne sub-bands to be tumed off in order to avoid interference and comply with

different regulatory requirements. In addition, multiband systems provide another

dimension for multiple access via frequency division. Different users can use different

pulses for multiple access, and frequency hopping can also be easily implemented by

switching among those [12].

We can easily generate sub-band UWB pulses by our MATLAB code by changing the

bandwidth Fp • We choose L = 70, To = 32.5 ps, rg == 62 ps and divide the UWB bandwidth

in 3 regions of (3.5~5GHZ), (6~7.5GHZ), and (8.5-10GHZ). We have put 1GHz of guard

band between the sub-bands. The resulting spectra of UWB sub-band pulses are plotted in

Figure 2.10. The high suppression of the out of band frequencies is to avoid interference.

9 ~ ........ ~ ......... ~ ......... ~ ....... . . ~ ......... ~ ........ . ~ ......... : .......... ~ ..... ~

· . . . . . . • • • • o' • • · . . .. .:+: .

8 . . . . . ._.+.~.+-.. ~~~.~ . . . . . .

. . . . --; - Sa~pling ~ 7 ............... . . ..... ':' ....... ':' ....... ':' ....... ':' ... .-...., .. ~ . . Ga~ssian· . ~

5 j ..... /j ........ . j ....... . . j ..... .... j .... ..... j ......... j ......... j ........ . j .... .... ~ : /: : : : : : : : : : 1. ~ : ~ ~ ~ ~ ~ ~

4 .. ..... ~ ........ : ........ ~ ......... : ......... : ..... .. .. ~ .' ....... : ........ ~ . ..... . . ~ · . . . . . . . . · . . . . . . . . · . . . . . . . . · . . . . . . . . · . . . . . . . . · . . . . . . . . .

3 : ........ : ......... ~ .. .. . . ... : ......... : . .. ... ... : . ..... . .. : ......... ~ ........ ~ . ....... ~ · . . . . . . .

i 5 10 15 20 25 30 35 40 45 50

L

Figure 2.9 Efficiency vs. L for the optimization method based on sampling (red) and combining Gaussian monocycle pulses (dashed blue)


1

" ~ (\ .1(

. 2(

.3( ~ .3(

- -

-41.1\ 1\ Il ft Il 1\ n f1 11 11 f1 fi J -4{ll\lIl1ft fl l\ f1 Il

.5( ·sc

-6C

1

.2(

. 3(

. 5(

-6C

28

\

6 8 10 12 14 .7o-----J....I-~U---.I.--L...L.-6 ----=-"--'-8 ~~10 -L--J.

1L-2 ~1 4 .7()---J-.....J....I-L-L-I--U-..I.-~6 ~U--8 -.1.-,;10 --l-.l..-'-U-

12 ---L-..I-J

14 Frequency (GHz) Frequency (GHz) Frequency (GHz)

(a) (b) (c)

Figure 2.10 Normalized spectra ofUWB sub-band pulses; (a) 3.S--SGHZ, (b) 6--7.SGHZ, and (c) 8.S-10GHZ.

2.4. Conclusions

In this chapter, we di scussed the importance of pulse design in the performance of UWB

systems. We developed a linear optimization pro gram to find pulses that maximize the PE

vis-a-vis the FCC spectral mask. A MATLAB pro gram finds the pulse samples that

maximize the PSD while respecting the FCC mask. ~ptimization based on combining

weighted Gaussian monocycles did a better job in producing power efficient and temporally

smooth waveforms. Although we do not intend to implement optimal pulses with an FIR

filter approach, we used this method to find the optimal waveforms. We next look at optical

implementation of sorne of the optimally designed waveforms in Chapter 3.

29 Chapter 3: Optical UWB Pulse Shaping Using FBGs

Chapter 3

Optical UWB Pulse Shaping

Using FBGs

Various electrical and optical pulse shaping architectures have been proposed to generate

UWB waveforms. In the past, most of the research had been focused on generating the

widely adopted Gaussian, monocycle and doublet pulses [11] and [13-17]. In this chapter,

after sorne literature review of optical pulse shaping methods in section 3.1, we propose a

new approach to generate UWB pulses that are FCC-compliant and maximize the transmit

power. This method is based on balanced photodetection of a spectrally shaped

30 Chapter 3: Optical UWB Pulse Shaping Using FEGs

femtosecond laser source. Balanced detection not only, to sorne extent, reduces different

noise components but also eliminates the undesired superimposed rectangular pulse

imprinted on the desired pulse during conversion to the time domaine A simple method to

tune the setup to generate various UWB waveforms will be discussed in section 3.3.

3.1. Optical Pulse Shaping Methods

As first stated in section 2.1.2, there are numerous optical pulse generator architectures;

most focus on the widely adopted Gaussian, monocycle and doublet pulses. The most

promising optical pulse generation techniques are based on optical spectral shaping and

frequency-to-time conversion using a dispersive medium.

As an example, in [16] , lalali et al. showed an RF-photonic arbitrary waveform generator.

As illustrated in Figure 3.1 , a wide band optical pulse is spectrally shaped by a spatial light

modulator (SLM) after being diffracted by a diffraction grating. The 128 pixel SLM is

controlled by a computer and has a maximum optical dynamic range of 30 dB in amplitude

modulation. The resulting shape in spectrum is mapped in time do main by frequency-to

time conversion using a certain length of single mode fiber (SMF). The total amount of

dispersion determines the pulse duration. The time domain pulse is generated by

sc

Desiree Waveform \'oltage

~F~ • ~ .... :",. : ... .. : .. ", : ••... i.· •. ::! ..•. " .... i.;.!',.i;.i.. t:IDri~c' r' ''c ---+, ~. :;%;~:, •.

~pmal lJgtit Mcdubtor (SLM)

Ue n er.a1l!d

Figure 3.1 Spatial shaping using the SLM [16].

T 0 Dis.-persWe Medi .. m


photodetection of the optical pulse. The maXImum bandwidth IS limited by the

photodetector and the repetition rate by the laser source.

A similar work is demonstrated in [22]. Broadband RF waveforms suitable for UWB

systems are photonically synthesized via open-Ioop reflection-mode dispersive Fourier

transform optical pulse shaping. This method relies on the ability to shape the optical power

spectrum in a Fourier transform (FT) pulse . shaper followed by frequency-to-time

conversion in a dispersive medium. A block diagram of the experimental apparatus is

illustrated in Figure 3.2a. Short pulses from a mode locked erbium doped fiber laser (100

fs , 30 nm bandwidth) are spectrally filtered in a reflective FT pulse shaper. ·This allows the

impression of an arbitrary filter function onto the optical spectrum. These shaped pulses are

then dispersed in 5.5 km of single mode fiber. After optical-to-electrical (OIE) conversion

of the time-domain optical waveform, the measured RF waveform exhibits the shape of the

filter function applied to the optical power spectrum. Figure 3.2b shows the reflective

geometry FT pulse shaper configuration. The dispersed frequency components are

amplitude modulated in parallel under voltage control by the combination of the 128-pixel

(a)

(b)

Fs pulse

~ drculator .--____ ---.

---+lC-:0 2 Reflective

Ta port3

1 'v FT Pu Ise Shaper

Incidentfrom port2 of ci rcutator

PBS ~~

Al=f LeM Len~~'l~""~ . ' / . , { \ ~ -----~ J7 mirror:~/ :.:. I l. 1. ---~ k

~~ . \ ' i -_. __ ._~~'" V Grating

!of . . .' ._ ............... • \ 'r r.' --. 1/. ., /1, \JU V Y'l .. Wave plate

\.. ................... ,( ................. .J \.. ................. y ................ ..l

f f

Figure 3.2 Broadband RF waveform generator, (a) Experimental apparatus. (b) Reflective geometry Fourier transform 1221.

Chapter 3: Optical UWB Pulse Shaping Using FBGs

'--w /fJ' .

Figure 3.3 UWB pulse generation based on spectral shaping of a MLFL.

32

liquid crystal modulator (LCM). After modulation, the frequency components are

recombined by the lens/ grating combination.

Although these arbitrary waveform generators offer tremendous flexibility, and can

generate the desired UWB pulse, they cannot be used in many applications due to their

large size and high opticalloss.

A research group in Ottawa has recently proposed sorne pulse shaping techniques based

on fiber optics. In [17], two optical filters with complementary spectra are placed in two

arms of an interferometer (Figure 3.3). They use a mode locked fiber laser as the source.

The spectrum of the ultra-short pulse from port 1 is shaped by a tunable optical filter; and

the spectrum of the pulse from port 2 is spectrally shaped by a fiber Bragg grating (FBG),

acting as a transmission filter with a center wavelength that can also be slightly tuned by

applying tension. By adjusting the spectral widths and the center wavelengths of the two

optical filters, Gaussian monocycle or doublet pulses can be generated. The generated

pulses, however, do not resemble the desired waveform, and the RF spectrums con~ain non

FCC-compliant baseband spectral content below 1 GHz. In addition, the interferometric

structure of this pulse shaper leads to sensitivity to environmental changes such as

temperature or vibration.

In another approach [23], a femtosecond pulse laser is spectrum sliced to the required

pulse width. The optical pulse train is then injected into a nonlinear fiber, together with a

CW probe laser, to create cross-phase modulation (Figure 3.4). An FBG is used as a

frequency discriminator. By locating the probe laser at the linear or the quadrature slopes of

Chapter 3: Optica/ UWB Pu/se Shaping Using FBGs

r----------------------------: r· ·~~~~·::;··;:~:·: · · l t P f\ I ! source i UL 1 L.. .. _ ... _ ... _ ... _ .............. _.l 1

1....-------, 1 l '------' 1

1

Rf T-\A ~

Circulator

- - - -- - - -- - - - - - -- - - --UWBPulse auiPùt-TLD: Tunable Laser Diode PC: Polarizatjon Controller

OA: Optical Amplifier PD: Photodetector

UFBG: Uniform Fiber Bragg Grating NLF: Nonlinear Fiber P: Optical Power R: Reflectivity

a: Amplitude of electrical pulse C 0

Figure 3.4 Ali optical UWB pulse generation based on phase modulation and frequeilcy discrimination.

33

the FBG reflection spectrum, UWB monocycle or doublet pulses are generated. The two

laser sources used in this technique makes it complex and costly. More importantly,

additional electrical filtering is required to remove the non-compliant spectral content

below 1.6 GHz.

From this brief literature review, we understand that one of· the principle methods of

generating UWB waveforms is to spectrally shape a broadband laser source. Frequency-to

time conversion maps the spectral shape to time domain and finally a photodetector

converts the pulse from optics to RF. This basic concept is shown in Figure 3.5.

One of the drawbacks of the discussed methods is that instead of generating FCC

compliant, efficient pulses, they are confined to generation of simple Gaussian waveforms.

Coherent BBS

Spectral Pulse Shaper

Dispersive Medium

Detector

Figure 3.5 Concept of arbitrary pulse generation by spectral pulse shaping.


In the next section, we propose a new approach to generate UWB pulses that is both FCC

compliant and maximizes the transmitted power. Our technique is also of the form shown

in Figure 3.5, with an FBG for spectral pulse shaping.

3.2. UWB Pulse Shaping Using FBGs

In this section, we propose and experimentally demonstrate the use of FBGs for spectral

pulse shaping. The setup is discussed in section 3.2.1. Basic concepts in FBG design and

fabrication are presented in section 3.2.2. We will also see th.e characteristics and the

measured transmission responses of our gratings. We will show promising experimental

. pulse shaping results in section 3.2.4, where the FBGs achieve high precision target

matching in both time and frequency domains.

3.2.1. A Balanced Receiver Approach

We use the general concept as in Figure 3.5 to generate the optimally designed pulses of

section 2.3 [24, 25]. A mode-Iocked fiber laser (MLFL) with large full width half

maximum (FWHM) bandwidth is used as a coherent broadband source. The spectral pulse

shaper in our design is a fiber Bragg grating in transmission with a transfer function

proportional to the desired pulse. We use an appropriate length of SMF as the dispersive

medium to generate the total required dispersion for the frequency-to-time conversion.

The particular form of our embodiment is heavily influenced by the requirement to

remove the undesired superimposed rectangular pulses imprinted on the desired pulse

during conversion to the time domain. Recall that aIl pulses generated by optical pulse

shaping techniques using frequency-to-time conversion contain an unwanted additive

rectangular pulse superimposed on the desired pulse shape, leading to strong, unwanted

spectral components in low frequencies «-----1 GHz) that cannot be removed by a dc-block.

We use a balanced photodetector (BPD) to completely remove unwanted low frequency

components, as seen in Figure 3.6.


FBG2

SMF ~ MLFL FBG1

t //--....",- )

Desire pulse plus

~ rectangular pulse

+

BPD

Rectangular pulse

35

Measuring Deviee

Figure 3.6 Block diagram of the UWB waveform generator.

The block diagram of our proposed technique is shown in Figure 3.6. FBG 1 is used to

flatten the mode-locked source spectrum over the desired bandwidth. The optical signal is

then divided into two arms. In the first arm, we use a second chirped grating, FBG2, with a

complex apodization profile optimized to imprint the desired pulse shape on the spectrum

of the source. In the second arm, the optical delay line (DL) and the variable attenuator

(A TT) are used to balance the amplitude and the delay of the two arms. We used an isolator

to prevent back and forth reflections between the two FBGs. The SMF may be placed

anywhere along the generator; placing it before spectral shaping avoids requiring SMF in

both arms of the BPD.

3.2.2. FBG Design and Fabrication

A fiber Bragg grating (FBG) is a longitudinal periodic perturbation of the glass refractive

index induced in the optical fiber core [26]. This index modulation forms a filter reflecting

certain wavelengths. To produce this perturbation, we expose an uncoated piece of

photo sensitive optical fiber to the interference pattern of an ultraviolet (UV) laser. The

refractive index increases in the regions where the light intensity is high, thus causing a

periodic modulation of the index of refraction in the core. The interference pattern is

normally obtained from a so-called phase mask.

Phase masks are surface relief gratings etched in fused silica. In most applications, a

phase mask essentially serves as a precision diffraction grating that divides an incident


Laser beam

+ 1 thorder

Figure 3.7 Interference pattern of a phase mask.

monochromatic beam into two outgoing beams (Figure 3.7). The incident radiation is

usually in the UV range. By generating two outgoing beams, a phase mask creates an

interference pattern in the region the beams overlap. Typically the, phase masks are

operated in the + 1/-1 configuration where the power is maximum in + 1 and -1 diffraction

orders. In this case, the laser beam is directed perpendicularly to the phase mask. The

period of the fringe pattern created by the interference of the + 1 and -1 beams is exactly

one half of the period of the phase mask, regardless of the wavelength of the incident

radiation. Exposing a photo sensitive optical fiber to the interference pattern results in an

FBG. The UV exposure increases the average refractive index, &Ide' and also introduces a

sinusoidal modulation, b.nae , with a period equal to the period of the fringe pattern. In

apodized gratings these index changes can vary along the length of the grating.

Perturbations in core refractive index ' can couple the incoming light in the fundamental

fiber mode to the reflected fundamental mode, or to the cladding depending on the grating

period. The Bragg wavelength, defined as the- wavelength of maximal reflection can be

obtained from [27]

(3.1)


where ÀB is the Bragg wavelength, nef!' is the effective refractive index, and A is the fringe

period. Chirped FBGs can be obtained using chirped phase masks. In a chirped mask, the

period of the groove changes along the mask according to A ( z ) = Ao + Cmz , where Ao is

the initial period, z is the length and Cm is the chirp expressed in nmlcm. A chirped grating

enlarges the reflection bandwidth because, from (3.1), a range of Bragg wavelengths are

produced along the grating as the etching period changes.

The grating apodization is the slowly varying envelope of the grating profile. A uniform

grating has no envelope variation. In general , finding the apodization profile of a grating

operating in transmission is a relatively easy task, as long as the target spectral profile does

not vary too rapidly. The chirped grating's spectral response, TCA) , and the apodization

profile is typically related by [28]

(3.2)

This equation links the index modulation amplitude, lYlac (À) to the desired transmission

profile T(À). In (3.2), Cm is the index modulation chirp, and r is the ratio of modal power

that overlaps with the grating (r is the confinement factor if the grating is confined in the

fiber core). Once the apodization profile is obtained, we simulate the grating spectral

0.8 E 2 t5 ~ 0.6

Cf)

"0 Q)

~ 04 ro . E L-

o Z

0.2

o ~~ ____ ~ ____ ~~ ____ ~ ____ ~~ 1536 1540 1544 1548 1552

Wavelength (nm)

Figure 3.8 MLFL normalized power spectral density.


response using a standard transfer matrix method performed by IFO Gratings software

available from Optiwave Corporation. This grating spectral response is then compared to

the target response; slight modifications are made to the apodization profile to tune it to the

target response. After several iterations the apodization profile leading to the best spectral

response is achieved.

After looking at the basic concepts of FBGs, we next start to design the gratings we need,

as shown in the setup (Figure 3.6). The PSD of the passive mode locked fiber laser (MLFL)

is measured using an optical spectrum analyzer (OSA), as shown in Figure 3.8. This

spectrum can be approximated by

(3.3)

where (j) and ())o are the angular and the centre frequencies, respectively, and a is a

constant. Referring again to Figure 3.6, FBG 1 is used to flatten the source spectrum,

therefore, its ideal transfer function is

0.9

E 0.8 :::J Z. 0.7 U

~ 0.6 CI)

"'0 0.5 Q)

~ 0.4 cu E 0.3 o Z 0.2

0.1 1

1570 o~--~ __ ~~J __ ~\~~ __ ~ __ ~. 1510 1520 1530 1540 1550

Wavelength (nm) (a)

1560

( !1()) !1()))

()) E OJ -- ()) +-c 2' c 2 (3.4)

otherwise

\ l 0.9

Q) 0 .8

~ 0 0 .7

cl: 0.6

C 0

~ 0.5

N :0 0.4

0 0.. 0.3 «

0.2

0.1 ~ 0 0 10 12 14

Length (cm)

(b)

Figure 3.9 Flattening filter (FBGl) design; (a) required normalized spectrum, (b) apodization profile.


0

-10 m ~ c -20 0 en o~ E -30 en c ~ r -40 (9 en LL -50

-6q530 1535 1540 1545 1550 Wavelength (nm)

(a)

1555

-2 x: 1539 Y : -20563

m 3 ~ -c o

0(i5 -4 en °E en ~ -5 r (9 -6 CD LL

-7

1539 1541 1543 1545 1547 Wavelength (nm)

(b)

39

Figure 3.10 (a) Flattening filter transmission response measured using an optical vector analyzer (b) a detailed view of the filter response.

where ~ OJ is the desired bandwidth around (j) c • From (3.3), (3.4), and by choosing

À E(1539, 1548) as the desired bandwidth for the flattening filter, we can obtain the FBG 1

transmission spectrum, H FBGI (À) , plotted in Figure 3.9a. The apodization profile, shown in

Figure 3.'9b, is obtained by a transformation of Figure 3.9a. The y axis which shows the

apodization profile is found from (3.2) by setting nef!' = 1.452, r = 0.84 and Cm = 2.5

nm/cm. The abscissa is obtained by mapping the wavelength range to the 14 cm available

mask length. We fabricate the FBG using a standard phase mask scanning technique with a

244 nm UV laser beam. For FBG1, we used a 14 cm mask with a chirp rate of2.5 nm/cm

and a H2-loaded photo sensitive specialty fiber (UVS-INT fiber from Corative). The grating

apodization was performed by phase-mask dithering during the UV scan. Next, the fiber is

annealed to stabilize the response for future use. The flattening filter (FBG 1) transmission

response is plotted in Figure 3.1 O.

The transfer function of FBG2 can be obtained by a time-to-frequency mapping of the

designed UWB pulse shape, p(t). In this case, the pulse duration, flT, is mapped to the LU

linewidth corresponding to !1OJ = 2nc!1Â / Â~ , the available bandwidth. The ratio ~T / ~À is

equal to the total required dispersion of the fiber (i.e., D x L f ) and determines the required

length of SMF for converting the pulse to the time domaine


0.9

0.8 ~ ~0. 8 t= t= 2 0.7 0

0.6 0- 0:0.6

i: c c 0

'V; .2

0.4 . ~ 0 . 5 ~

~ .t::0.4 "0

c 8. ~

0.2 ~ 0.3 <:0.2

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0'1.538 1.54 1.55 1.552 0 L-o ----':--..L------':6-....L-8 ---'-::-----'------l

Time (ns) Wavelength (um) Length (cm) (a) (b) (c)

Figure 3.11 Pulse shaping flUer (FBG2) design; (a) time domain target pulse, (b) flUer transmission profil~, (c) apodization profile.

We normalize pet) to be centered around 0.5 and adjust its peak-to-peak roughly from 0.1

to 0.9 as shown in Figure 3.11a, to have margin in generation of the apodization profile. We

use 5.46 km of optical fiber with a total dispersion of 89 ps/mn for time-to-frequency

conversion. Figure 3.11b shows the filter transmission profile, H FBG2 (m) , after the time-to-

frequency mapping. The ideal transfer function of pulse shaping FBG2 can be expressed

by,

H FBG2 (m)l . == 1 + a p(271c / (j)) Ideal

(3.5)

where a is a constant. As with FBG 1, we use (3.2) to obtain the apodization profile from

the transmission profile of FBG2 as shown in Figure 3.11 c. Two smoothly decaying

functions have been fit at the two sides of the apodization profile in Figure 3.11 c to avoid

abrupt changes to zero. An abrupt change to zero will produce ringing in the FBG response.

FBG2 was fabricated with a phase mask with a chirp rate of 0.498 mn/cm. The spectral

response of the FBG in transmission mode can be measured by a Luna Technologies optical

vector analyzer. Figure 3 .12a shows the filter response which contains sorne high frequency

noise. We can get rid of this noise by taking a moving average as shown in Figure 3.12b.

We focused on the gen~ration of the UWB pulse with L = 14, however, as we will explain

later, we repeated the experiment for L = 7 and L = 30 with minor modification to our

setup. The measured spectral response of the grating differs from the. predicted response via

simulation because of fabrication errors. Errors are due to phase mask imperfections and


non-uniforrnities in fiber photosensitivity. Sorne errors occur during the FBG writing setup

alignment and include the UV laser bearn quality, the laser emission angle on the fiber, the

parallelisrn of the fiber and the phase rnask.

3.2.3. Simulation Results

In this section, we sirnulate the output response of the UWB pulse shaping setup shown in

Figure 3.6. The functionality of each component in the setup can be rnodeled by a transfer

function in order to simulate the generated pulse shape at the BPD output. Neglecting the

propagation delay of the pulse envelope, the transfer function of a lossless dispersive SMF

can be rnodeled with very good precision [30] by

(3.6)

where L f is the fiber length. Also, /32 = a2 /3(~)

aOJ IS known as the second order

dispersion parameter and J3 (OJ) is the mode propagation constant. D (ps/km.nm) is related

to the dispersion parameter through /32 = -Â~ D / 271C • The center wavelength is

Âo = 21CC / OJo and C is the light speed. For typical SMF, the third order dispersion parameter

-3

-4 iD "0

~ -5 o "iii .~ -6 ri)

c ~ -7 ..... N

as -8 u..

-9

-10

1535 1540 1545 1550 1555

iD ~-3 c o "iii .~ -4 E ri) c ~ -5 N C> fe -6 "0 CIl

g-7 Ci> >

<{

-8

1538 1540 1542 1544 1546 1548 1550

Wavelength (nm) Wavelength (nm)

(a) (b)

Figure 3.12 (a) L = 14 pulse shaping filter transmission response measured using an optical vector analyzer (b) same measurement after applying a moving average

-- -- - --~ - -- --------- - ---.,


~0.8 e ·E ~ 0.6 ro .= ~ 0.4 u..

0.2

i\

- F8G2 ---- F8G1

O~~~-~~--'--~~

1538 1542 1546

Wavelength (nm) (a)

1550

0.5

o 0.4 CI) Cl..

~ 0.3 . ~ ro E 0.2 o Z

0.1

rf""A-~~HV'l

1 1

Cl> "0 .2 ~ 0.4 E « "0

.§ Ot--~-' ro E

~ -0.4

- Simulation - --- Design

o "-"""----"_-"------'-_....&....-_____ -0.8 ~--'-_ _'______''---__"'_ _ _'____J

1538 1542 1546 1550 0 0.2 0.4 0.6 0.8

Wavelength (nm) Time (ns) (b) (c)

Figure 3.13 Simulation results for L=14. (a) Transmittivity of FBGs, (b) PSD at upper and lower arms, and (c) simulated and designed output pulse.

is very small and thus third order chromatic dispersion is negligible over short distances

and for narrow bandwidths. In the present case, we assume that the fiber group delay is

linear over the frequency band of interest.

The Fourier transform of the optical signaIs at the inputs to the balanced photodetector

can be expressed by

El (m) == al As (m) H SMl - (m) H FBG l (m) H FBG 2 (m) (3.7)

(3.8)

where al represents the total loss in the first arm, and a 2 can be adjusted by variable

attenuator to balance the power in the two arms. A variable delay r in the second arm

compensates for any delay between these two lines.

Finally, the detected signal at the output of the balanced photodetector is

(3.9)

where ei(t) == 1FT {~({ù)}, i == 1,2 ; 1FT stands for inverse Fourier transform. We supposed

that the BPD has a fiat transfer function over the signal bandwidth. In practice the BPD

transfer function is not fiat and decays near the cut-off frequency.


We now examine our pulse shaping strategy via simulation. The measured spectrum of

the broadband source is used to design the apodization profile of FBG 1, as explained in

section 3.2.2. The role of this filter is to carve out the desired wavelength band, and

compensate for the non-flat spectrum of the broadband source. The simulated transmittivity

of FBG 1 is given by the dotted line in Figure 3.13a. Kinks in this curve are the result of a

finite duration apodization profile. FBG2 was designed to realize the optimized pulse shape

when L = 14 taps are used in (2.12). The simulated transmittivity ofFBG2 is given by the

solid line in Figure 3.13a. The simulated spectra of the output of FBG 1 using the fitted

curve for the broadband source spectra as input, is given by the dashed line in Figure 3.13b.

We see ringing at the cutoff wavelengths. Subsequent filtering by FBG2 yields the spectra

given by the solid line in Figure 3.13b. We see the ringing of FBG 1 now imprinted on the

output of FBG2. We now add 5.46 km of SMF with 16.3 ns/kmInm dispersion to our

simulator, and examine the electrical output from each of the photodetectors in the balanced

photodetector. Figure 3.13c gives time traces for the output of the photodetectors in the

upper and lower arms. In the upper arm we have the desired pulse shape plus the undesired

rectangular pedestal; note the ringing near the pulse edges. In the lower arm we have the

rectangular pedestal alone; note again the ringing. The output of the balanced photodetector

is also shown in Figure 3.13c. By subtracting the lower arm from the upper arm, the vast

majority of the ringing has been eliminated. In this plot, we have superimposed the final

result of our simulation (solid line) with the target optimized pulse in a dashed line . .

3.2.4. Experimental Results

The block diagram of the setup is very similar to Figure 3.6. We used an MLFL fabricated

in our lab by J. Magné [29] based on the general concept in [31]. The MLFL generates 270

fs sech2 pulses with a repetition rate of 31.25 MHz. As in the simulation, we used 5.46 km

of SMF with a measured dispersion of 16.3 ns/km/nm. We used an erbium doped fiber

amplifier (EDF A) after the SMF to provide more optical power at the BPD inputs and thus

increase the detected signal power over the noise floor of the detector and measuring

devices. As the EDFA has non-flat gain, we measured the optical PSD after the EDFA and

fabricated FBG 1 with an apodization profile to flatten the amplified mode-Iocked source

spectrum over ,....,7.5 nm bandwidth.


The power spectral density (PSD) incident on each photodetector in the BPD is shown in

Figure 3.14a; the solid line represents the PSD after FBG2 in the upper arm and the dashed

line represents the PSD after DL in the lower arme The optical spectra are measured by an

optical spectrum analyzer (OSA) with a resolution of 0.1 nm (ANDO AQ6317B). The

power spectral density at the output of FBG 1 is equal to the PSD of the lower arm (dashed

line in Figure 3.14a) except for a constant attenuation factor. As we expected, FBG 1 cuts

the source spectrum and compensates (flattens) source spectrum. The small variation from

a flat spectrum is due to imperfections in the FBG writing process.

The two optical signaIs (upper and lower arms) are input to a 10 GHz DSC-710 BPD. The

output UWB pulse shape (Figure 3.14b) is then viewed by a 40 GHz sampling scope

(Agilent 86100A) and its electrical power spectrum (Figure 3.14) is measured by a high

speed RF spectrum analyzer (HP 8565E). Comparing the designed pulse (dashed line) with

the measured pulse (solid line) in Figure 3.14b, we see a good match, despite sorne

modifications in the peaks attributable to imperfections in the FBG writing process and to

the imperfect, band-limited frequency response of the BPD. The measured peak-to-peak

voltage is about 200 mv. The electrical PSD of the pulse in Figure 3.14c scrupulously

respects the FCC spectral mask (dashed line) and follows our design (solid line). The

reduced power in frequencies above 10 GHz is mainly due to the frequency response of the

BPD that inflicts more than 5 dB loss at 14 GHz compared to the OC level. The gray area

in this figure represents the noise floor of the BPDand the RF spectrum analyzer. We note

that the pulse has an almost flat spectrum in the 4 to 9 GHz range.

The experiment was repeated for the optimized UWB pulses with L = 7 and L = 30 taps as

weIl, with sorne modifications. The pulse duration, t1T , for L = 7 is almost half of the pulse

duration for L = 14. Thus, we can either use half of the available source bandwidth, or

decrease the mapping ratio, I1T / I1A by' a factor of 2. We chose to use half the available

bandwidth by adding an optical filter to , cut the upper half of the already flattened spectrum.

We calculated the apodization profile for the L = 7 pulse shape and wrote another FBG-2.

The measured and target pulse are shown in Figure 3.15a; an excellent match can be

observed. The spectrum of the pulse in Figure 3.15b perfectly follows the designed

spectrum (solid line) and respects the FCC mask. Waveforms with even simpler shape (e.g.,

Chapter 3: Optical UWB Pulse Shaping Vsing FBGs

-10 r---...-----..-----,

Ê-20 c E OJ ~ -30

~ 'ë ~ -40 -0

ID ~ -50

Cl..

~ . . . . . . . . . . . . . . . . . .t . . . . .

. .

:---- Lower:arm

1540 1545 1550

Wavelength (nm) (a)

Q) "0 :€ 0.5

0.. E

<1:: "0 Q)

.~ ro E 0-0.5 Z

-1

- Measured pulse

---- Designed pulse

L=14

o 0.2 0.4 0.6 0.8

Time (ns) (b)

o

â) -10

~

~ -20 o

Cl.. "0 -30 Q)

. ~

ro -40 E o z -50

45

2 4 6 8 10 12 1·

Frequency (GHz) (c)

Figure 3.14 Experimental results for L = 14. (a) PSD at upper and lower arms, (b) measured UWB pulse, and (c) the RF spectrum.

Gaussian monocycle and doublet) could also be generated with high precision using this

method.

A small part of the spectrum in Figure 3 .15b is enlarged in the inset to show the sinusoidal

variation in the envelope of the measured spectrum. We attribute this variation to

teflections of the pulse between the BPD and the RF spectrum analyzer due to impedance

mismatch, and verified this hypothesis as follows. Let a be the reflection coefficient and

r r the delay for each reflection. The ' measured spectrum can be modeled by

~ef (co) = P( co )(1 + ae - jwrr + a 2 e - jw2rr +. "), where P ((jJ) . is Fourier transform of the

designed pulse. We assume only two reflections, and fit a and r r to our measurements.

The femtosecond laser used at the experimental setup has a repetition rate of 31 ~25 MHz.

Therefore, the generated pulse at the output of the photodetector can be written as a

repeated impulse,

(3.10)

where T is the laser repetition rate. The function rePr (.) represents the periodic repetition

of a pulse with period T. This signal and its reflection arrive at the spectrum analyzer

resulting in the signal


Q) 0.8 "'0

:ê a. 0.4 E

<t: "0 0 Q)

.~

~ -0.4 o z -0.8

o 0.2

L=7

-- Measured pulse

---- Designed pulse

0.4 0.6 lime (ns)

(a)

0.8

_ 0 -CD "0 ~ -10 Q)

~ ~ -20 "0

.~ -30 ro E -40 o z

-50

o 2 4 6 8 10 12 14 Frequency (GHz)

(b)

46

Figure.3.15 Experimental results for L = 7. (a) measured UWB pulse, and (b) the RF spectrum. The enlarged part shows the sinusoidal variations due to multiple reflections.

~ 0.8 :ê ~ 0.4 <t: ~ 0 .~ ro E -0.4 o z

-0.8

-- Measured pulse

---- Designed pulse

~~---~~---~-----~~~~

o 0.4 0.8 lime (ns)

(a)

1.2 1.6

en 0 "0 ~-10 Q)

~ ~ -20 "0

.~ -30 ro E -40 0 z

-50

0 2 4 6 8 10

Frequency (GHz) (b)

12 14

Figure 3.16 Experimental results for L = 30. (a) measured UWB pulse, and (b) the spectrum.

x(t) = repT[p(t) + rp(t - Tr )] (3.11 )

00

Consider the Dirac comb function combT{t) = l 8{t-kT), where J(t) lS the Dirac k=-oo

delta function. The spectrum of x(t) can be obtained by taking the Fourier transform:

1 . X(f) = --.combllTFT {p(t) + rp(t - Tr )}

T (3.12)


x(J) = ~ combIl AP(J)( 1 + re-j27rj T, )l (3.13)

The l/T coefficiel!t is tri vial since the power will be normalized. The sampling rate of the

comb function is equal to 1/ T = 31.25 MHz. This is the frequency gap in the measured

amplitude points of Figure 3.15b. By producing this signal in MATLAB and changing the

two parameters, 'r = 7 ns and r.=O.23 , we achieve the best possible fit to the experimental

result shown in Figure 3.15b. The spectrum predicted using two refiections is given by the

dashed line in the inset, verifying the source of the variation as an impedance mismatch.

Our experiment for L = 30 showed that generation of more complex pulses requires higher

precision in the FBG fabrication process. For L = 30, the pulse duration is doubled

compared to the first design for L = 14. As the total available bandwidth is limited, we

chose to increase the mapping ratio and use the same bandwidth as before. Therefore, the

SMF length was increased for an appropriate frequency-to-time conversion, i.e. , 10.56 km

of SMF with total dispersion of 173.9 ps/nm.

We fabricated another FBG2 for the pulse with L = 30, and present results in Figure 3.16.

By comparing the measured pulse with the designed pulse in Figure 3.16a, we observe an

acceptable match in the first half of the pulse, but deviations in the second half are severe.

During the FBG writing process, we observed significant FBG fabrication noise when pulse

amplitude went below 10 percent of the peak amplitude. At the same time, since our

mapping ratio was doubled, the apodization profile includes a much greater number of

swings for the same fixed phase mask length (and beamwidth), also leading to greater

deviation from the designed pulse in the fQrm of overshoots. The measured electrical

spectrum of the pulse (Figure 3 .16b) is not fiat in the 3 to 9 GHz frequency range and

contains large spectral content at low frequencies « 2GHz), violating the FCC spectral

mask. This experiment demonstratès the practical limits (not theoretical) of the proposed

method. A more precise fabrication device could reduce these limitations.


3.3. Waveform Tuning Using a Band-pass Filter

In section 3.2, we generated efficient UWB pulses using FBG; but we had to design an

FBG for each pulse shape. In this section, we will see how we can generate . various

waveforms using one pulse shaping FBG and two tunable FBGs (one high pass, one low

pass). The setup block diagram is shown in Figure 3.17 [32]. The optical pulse travels 5.46

km of SMF with total dispersion of 88.9 ps/nm in order to map the 4.5 nm source

bandwîdth to 0.4 ns. Filters 1 and 2 are chirped gratings (phase mask chirp = 2.5 nm/cm)

used to eut-off the lower and upper band of the spectrum. The FBGs are mounted on

stretchers for tuning. In this section, we choose L = 7 as the target to generate a simple

waveform that respects the FCC mask at aIl frequencies. This waveform, shown in

Figure 2.8a, contains two large positive and negative peaks confined between two smaller

peaks with a total duration of ---0.4 ns. By appropriate windowing of this FCC-compliant

pulse, a very good approximation of Gaussian (L = 1), Gaussian monocycle (L = 2) and

doublet (L = 3) pulses can be obtained. Figure 3.18a shows the transmittivity of the pulse

shaping FBG (solid line), as well as those of two filters (dashed and dotted lines). The

cutoff wavelengths of Filter1 , ~, and Filter2, ~, are varied between al to a2 and b l to b3,

respectively. By stretching the FBGs, the cutoff wavelengths are located at the appropriate

positions (based on the) to generate' the Gaussian, monocycle, doublet and the FCC

compliant waveforms.

SMF MLFL+

Flatten i ng 1-----------1

Filter EDFA

Tuning Filters

tQ--- .. 1 1 1 1

f1 f2

Pulse Shaping t-----.

FBG t------. UWB

Pulse

Figure 3.17 Schematic diagram of the tuna~le UWB waveform generator.


~ ~ 0.8 .S; :.t:J ~

E (f)

0.6 c CO 0.4 ~

~

<.? en 0.2 u.

0 1538

:1 Filter 11

1

:lx;r

i .

1 i 1 1: Filter 2

j~~r \ ! i i •

1542 1546 Wavelength (nm)

(a)

1550

~ 0.8 Q)

""C ::J ~ 0.4 0-

Filter 1

~ 0.----+-' ""C Q)

.~ -0.4 CO E 0-0.8 z

o 0.2 0.4 0.6 Time (ns)

(b)

Filter 2

Designed waveform

0'.8

Figure 3.18 (a) Transmittivity of the pulse shaping FBG ,tunable Filter1 and Filter2, (b) designed UWB waveform and filters' shapes.

Table 3.1 Cutoff Wavelengths of the Filters for DifferentUWB Waveforms.

CD ~ -10 c o "in en

"~ -20

c CIl

~ -30 LL ~ ....J

-40

Waveform

Guassian pulse

Monocycle pulse

Doublet pulse

FCC-compliant pulse (L = 7)

CD ~ c -10 o ën en "ë en c ~ -20 LL ~ I

A, ~

a2 b3

a2 b2

al b2

al bl

1530 1535 1540 1545 1550 1555

Wavelength (nm)

-30L---'----->--->----'-------' 1530 1535 1540 1545 1550 1555

(a) Wavelength (nm)

(b)

CD "0 ~ -20 o "in (J)

"ë ~ -40 ~ l-LL ~ co -60

1530 1535 1540 1545 1550 1555 151

Wavelength (nm)

(c)

Figure 3.19 Tuning filters transmission responses (a) the low pass filter (b) the high pass filter (c) a band passfilter.

50 Chapter 3: Optical UWE Pulse Shaping Using FEGs

The generated waveforms depend on the transition shape of the filters taking into account

the effects of the limited bandwidth of the BPD. Figure 3.18b shows the optimized FCC

compliant pulse and the measured shape of the filters around · the cutoff wavelengths. The

optical filtering of the pulse shaping FBG' s spectrum is equivalent to the time windowing

of the designed pulse. The two filters are fabricated by the phase mask fabrication method

explained in section 3.2.2. Figure 3.19a and Figure 3.19b show the low-pass and the high

pass filters , respectively. Figure 3.19c is a band-pass filter which can be used separately or

along with the low-pass and the high-pass filters for more control over the cut-off and the

band pass regions.

Figure 3.20a shows the measured pulse when ~ and ~ are adjusted to a 2 and b3

according to the notation of Tabl~ 3.1. The Gaussian pulse is approximated by extracting

the large peak of the optimized pulse (see Figure 3.18a). This puJse weIl approximates a

negative Gaussian pulse with r = 54.9 ps, and FWHM of 68.3 ps. The measured spectrum

of the pulse is normalized and shown in Figure 3.20b. Clearly the Gaussian pulse is not a

good choice for UWB applications due to the large dc component.

F or the monocycle pulse, shown in Figure 3.20c, the filters ' cutoff wavelengths are

located at a2 and b2. In this case, the generated pulse can be approximated by the first

derivative of the Gaussian waveform with r = 62.4 ps. The spectrum, given in

Figure 3.20d, violates the mask in the frequencies less than 1.6 GHz. The transmitted power

should be reduced by at least 25 dB to respect the mask, or additional filtering must be

used.

The doublet waveform, Figure 3.20e, is generated by locating the filter cutoff wavelengths

at al and b2; it approximates the second derivative of a Gaussian waveform with r = 66.3

ps. A good fit is achieved at the two side peaks, but the central peak is shallow. However,

from Figure 3.20f, the spectrum of the generated doublet pulse represents a good match to

the spectrum of the targeted curve (solid line). In this case, the transmitted power should be

reduced by about 15 dB to be completely below the FCC mask.


~ 0 Q) :ê -0 .2

a. E -0.4 cu

~ -0 .6 .~ ro E -0.8 0 z -1

0

~ Q) 0 .5 -0

:ê a. E 0 cu "0 w N ro -0 .5 E 0 Z

-1

0

_ 0.5 G Q) -0

:ê 0 a. E cu -0

.§ -0.5 ro E 0 Z -1

0

~ 0.8 Q) -0

:ê 0.4 a. ~ 0 -0 Q)

~ -0.4 E ~ -0 .8

---- Gaussian T= 54.9 ps

0 .1 0 .2 0 .3 0.4 0 .5 0 .6 Time (ns)

(a)

-- Measured pulse

- - - - Monocycle r=62.4ps

0 .1 0 .2 0.3 0.4 0 .5 0 .6 Time (ns)

(c)

-- Measured pulse - - - - Doublet

r= 66.3 ps

0 .1 0.2 0 .3 0.4 0 .5 0 .6 Time (ns)

(e)

-- Measured pulse

- - - - FCC-compliant

o 0.2 0.4 0.6 0.8 Time (ns)

(9)

~ -.~ ro E 0 z

0

ID ~ -20

Cl...

~ -30 .~ ro E -4 0 z

-5

_ 0 co ~ -10 ID ~ &. -20 -0

.§ -30 ro § -40 o z

-50

0 2

0 2

0 2

4 6 8 10 12 14 Frequency (GHz)

(b)


(d)


(f)

o 2 4 6 8 10 12 14 Frequency (GHz)

(h)

51

Figure 3.20 Generated and target waveforms and their spectrum: (a, b) Gaussian, (c, d) monocycle, (e, f) doublet and (g, h) FCC-compliant, power efficient pulses. .

Finally, when the cutoff wavelengths of the filters are located at al and hl, we can obtain

the optimized pulse completely as shown in Figure 3.20g, where . an . excellent match

-between the designed and the generated pulses is observed. The measured spectrum of the

pulse in Figure 3.20h optimally exploits and scrupulously respects the FCC spectral mask


(dashed line) and follows our design (solid line). There is no need for reduction in the

transmi tted power.

As we can see, the proposed UWB waveform generator is able to generate not only the

Gaussian, monocycle and doublet pulses, but also an FCC-compliant power optimized

pulse by simply stretching two FBG filters. If only the FCC-compliant, power efficient

pulse is of interest, the two filters can be fabricated by one FBG to reduce system

complexity Figure 3.19 (c).

3.4. Conclusion

In this chapter, we designed, simulated and experimentally demonstrated optical

generation of the power-efficient, FCC-compliant UWB pulses using fiber Bragg gratings.

Our approach is robust against environmental changes such as temperature or vibration.

Three FCC-compliant pulses with duration of 0.3, 0.6 and 1.2 ns and theoretical power

efficiency of 47.5, 67 and 75.10/0, respectively, are designed and demonstrated. An

excellent match between the designed and measured pulses is observed for the first two

waveforms, with spectrums scrupulously respecting the FCC spectral mask. The generation

of the more . complex waveforms is limited by ~abrication noise due to phase mask

imperfections, non-uniformities in fiber photosensitivity and cladding mode coupling. Note

that imperfections in the tlattening FBG are compensated by balanced detection that

removes the small unwanted variations in the signal spectrum.

We also showed a method ofwaveform tuning without changing the pulse shaping FBG.

The Gaussian, monocycle and doublet pulses can be easily generated by stretching two

FBGs responsible for the filtering of the lower and upper sides of the tlattened source .

spectrum. Although the Gaussian monocycles and doublet are poorly adapted to the

spectral mask imposed by the FCC, they can be used in sorne applications when less

transmitted power is required.

53 Chapter 4: UWB Pulse Propagation and EJRP Optimization

Chapter 4

UWB Pulse Propagation and

EIRP Optimization

The ultimate goal of an indoor UWB communication system is to transmit and receive

high speed data via a wireless link. This makes the study of antennas an inevitable part of

the system design. Though the pulses generated by the pulse shaping method of Chapter 3

are of exceptional precision, it should be noted that optimized pulses are at the transmitter

side before the antenna. However, the FeC spectral mask constrains the effective

isotropically radiated power (EIRP) of the antenna rather than PSD of pulses before

transmission. This requires sorne further study of the antenna effects on UWB pulses.


In section 4.1 , we define EIRP and also the Friis free-space transmission formula. We find

a formula to express EIRP as a function of the transmit power spectrum, what we measured

in Chapter 3, and the channel frequency response. Subsequently, in section 4.2, after a brief

introduction to wideband antennas, we measure experimentally the UWB wireless channel

frequency response using a vector network analyzer for two commercially available

identical wideband omni-directional antennas.

In section 4.3 , the optically generated Gaussian monocycle, doublet and FCC-optimized

UWB pulses of Chapter 3 are propagated between two wideband antennas and the received

signaIs are measured both in time and frequency domains. EIRP is calculated using the

antenna impulse response and it is compared to the FCC spectral mask to verify

compliance. We use power efficiency to gauge the performance of each pulse.

Investigating these results, we understand that the antenna frequency response has a

significant effect on the EIRP measurements. Therefore generation of optimal pulses will

not be possible without taking the antenna into account. In section 4.4, the antenna

frequency response is used to modify the optimization process developed in Chapter 2 to

compensate for the antenna frequency response. The optimal FCC-compliant pulse

designed by this method is then generated by the method presented in Chapter 3, using

proper FBGs. A good efficiency improvement is achieved through this design process.

4.1. EIRP

F or an isotropic antenna the gain is identical in all directions, so that

where Gr is the transmit antenna gain, rjJ is the zenith angle and B is the azimuth angle in

the spherical coordinate system. The radiation power density is

( ) _ Py. (/)GT (/)

P 1 - 47rd2 -


over a sphere of radius d. Fr (/) is the transmitted power density.

The radiated power of an isotropic antenna at a reference distance d rel IS

IRP(J) = d;ef r rPT(J)G;(J) sinBdBdt/J 41rdref

= P T (/)GT (/).

For an arbitrary antenna, not necessarily isotropic, the FCC requires that on any point of

the sphere at d rel ' the radiated power should not exceed that of an isotropic antenna, hence

the term EIRP.

EIRP(/) = maxPr (/)GT (/,r/J,B) rp ,e

= Pr (f) GT (l, r/Jo' 80 )

(4.1)

where (fJo' Bo) represents the direction of maximal gain.

For simplicity we will write GT (/) for the maximal gain of frequency Ifor any direction,

hence

EIRP(/) = Fr (/) GT (/)·

A general procedure for determining the EIRP per unit bandwidth is the use of the Friis

power transmission formula in its simple form where antennas are assumed to be both

impedance and polarization matched [33]

PR (f) - G (f)G (f)(_C_J2 ~, (/) - T R 41rdf

(4.2)

where PR (/) is the received power density, GR (/) is the receive antenna gain, c is the

speed of light, dis the far field radial distance between the transmitter and the receiver and.!

is the frequency of operation. Equation (4.2) is valid for r.1arger than 2Dmax 2 / A, where

56 Chapter 4: UWB Pulse Propagation and EIRP Optimization

Dmax is the maximum dimension of the transmit antenna and Â IS the free space

wavelength. When Dmax is much greater than the wavelength, the far field criterion

becomes very large and the field strength that must be measured at the far field location is

less than the receiver noise floor. In such cases, the near field measurement techniques

should be used for EIRP determination [34]. The dimensions of antenna and the maximum

frequency of interest (10 GHz) in our case result in a reasonable far field distance where

(4.2) is still valid.

To obtain the EIRP, we use similar transmit (Tx) and receive (Rx) antennas and measure,

using a network analyzer, the total frequency response of system, HCH (/) = ~ (/) / Fr (/)

[~5]. This channel response, H CH , includes free space propagation and transmit and receive

antennas responses. The orientations of antennas are carefully adjusted so that they see each

other with the same angle. Thus, for similar transmit and receive antennas (identical

models), G(/) = Gr (1) = GR (/) and from (4.1) and (4.2) wehave

(4.3)

vyT e assume no II?-ultipath reflections in the Friis formula. We recreate this condition

experimentally by attenuating the major reflections by placing RF absorbers around the ·

antennas during H CH ·measurement; aIl remaining multipath reflections are easily removed

by truncating the channel impulse response. The truncated impulse response is then Fourier

transformed and used in (4.3) for the EIRP calculation.

4.2. Antenna Frequency Response

4.2.1. UWB Antenna Characteristics

As is the case in conventional wireless communication systems, an antenna also plays a

crucial role in UWB systems. However, there are more challenges in designing a UWB

antenna than a narrowband one [36, 37]. What distinguishes a UWB antenna from other


antennas is its ultra wide frequency bandwidth. According to the FCC definition, a suitable

UWB antenna should be able to yield an-absolute bandwidth no less than 500 MHz or a

fractional bandwidth of at least 0.2 [1]. The performance of a UWB antenna is required to

be consistent over the entire operational band. Ideally, antenna radiation patterns, gains and

impedance matching should be stable across the entire band. For indoor communication

purposes the antenna is required to be omni-directional.

A suitable antenna needs to be small enough to be compatible to the UWB unit especially

in mobile and portable devices. It is also highly desirable that the antenna be compatible

with printed circuit board (PCB).

Lastly, a UWB antenna is required to achieve good time domain characteristics. UWB

systems often employ extremely short pulses for data transmission occupying enormous

bandwidth. Thus the antenna acts like a band-pass filter and has significant impact on the

input signal. As a result, a good time domain performance, i.e. minimum pulse distortion in

the received waveform, is a primary concern of a suitable UWB antenna. If waveform

distortion occurs in a predictable fashion it may be possible to compensate for it. In [38] ,

the y present a technique based on photonic arbitrary electromagnetic waveform generation

for UWB signal synthesis that allows the transmit waveform to be pre-compensated for

antenna dispersion. Through time-domain impulse response measurements, they extract the

RF spectral phase contributed by broadband ridged TEM horn antennas to signaIs

transmitted over a wireless link and apply the conjugate spectral phase to the transmit

(a) (b)

Figure 4.1 (a) SkyCross (SMT-3TOIOM) UWB antenna, (b) azimuth radiation pattern at 4.9 GHz.

Chapter 4: UWB Pulse Propagation and EfRP Optimization

waveform to achieve signal compression at the receiver.

58

For our purpose, we choose commetcially available 3.1-10 GHz omni-directional

antennas (SkyCross SMT-3T010M-A). This antenna, seen in Figure 4.1a, has a small size

and is azimuth omni-directional (Figure 4.1 b) [39]. This antenna belongs to a new .

generation of antennas developed by SkyCross based on the meander line antenna (MLA)

technology. MLA technology allows designing physically small, electrically large antennas.

4.2.2. Experimental Measurements

Two similar SkyCross antennas are used for line-of-sight (LOS) transmission in lab

environment over a distance of 65 cm and a height of 120 cm off the ground. In our

experiment we chose 65 cm to facilitate making measurements in our somewhat confined

laboratory environment. Measurements for different antenna distances and orientations are

a subject of interest for future work. Please note that the distance between antennas plays

no role in calculating EIRP from (4.3), since HCH (/) is inversely proportional to d 2 •

Therefore, while any distance between antennas is possible, a closer range is preferable to

reduce multipath reflections. The LOS response with no reflections is the channel response

we need to calculate EIRP from (4.3). The 65 cm separation of the antennas was chosen so

as we could attenuate multipath reflections by placing RF isolators around the antennas

within the confines of our laboratory.

The antennas are placed in their peak radiation direction in the azimuth plane. Note FCC

regulations require peak EIRP measurements over aIl directions, not only azimuth, however

rotational antenna mounts were not available for our experiment. Our EIRP measurement

method holds for either case.

The channel response is measured by a 20 GHz vector network analyzer (VNA-N5230A)

as shown in Figure 4.2a [35, 40]. The VNA captured 6401 points across a span of 0.2 to 14

GHz and averaged 16 times to improve the dynamic range. Figure 4.2b is the amplitude of

S21 which represents the antenna frequency response. We can see that the response is not

completely flat in the radiation bandwidth of the antenna and this will obviously ' introduce

differences between the transmitted and the received pulse shapes. The antenna phase

59 Chapter 4: UWB Pulse Propagation and EfRP Optimization

response is plotted in Figure 4.2d, where the red lines are ± 1800

• From the inset we can see

that the phase response is quite linear in the antenna bandwidth. This is not true about out

of band frequencies, say around 1 GHz, but it does not matter as the antenna is not radiating

in the se frequency bands according to Figure 4.2b. The delay is fairly constant over the

bandwidth of interest (Figure 4.2c), a fact resulting from the linear phase response. Note the

average delay value which cornes from the distance between the antennas and the

measuring equipment path delay. Therefore, aIl the frequency components of the

transmitted pulse from the antenna undergo a certain delay while propagating in the

channel, reducing temporal distortion of the pulse. Figure 4.2e shows the reflected power

from the antenna. This low SIl is an indication of the wide bandwidth of the antenna.

Observation of the channel over longer periods of time shows no differences in the

response and we conclude that the channel is non-varying.

The smoothed antenna frequency response is plotted in Figure 4.3a. Figure 4.3b plots the

time response of the antenna obtained from the inverse Fourier transform of the frequency

response. The inset figure shows the presence of several weak multi-path reflections from

the indoor environment, in addition to main LOS response. These are mainly due to

reflections from wal~s , ceiling, floor and lab equipments. Use of an RF absorber placed on

the ground between the two antennas reduces the multipath reflection by 75%, obviating

the use of an anechoic chamber. We eliminate the remaining multipath reflections by

truncating the measured impulse response.


Tx Rx

65cm

= RF Absorber

(a)

100~--~--~--~----------~ -40 . .... ... ...... . ... ....................... ra....

fi -50 ~ .....-.-.

N ~ -60 ID

..0

~ -70 . .

-80 o 5

Frequency (GHz) (b)

10

200~----------------------~

fi 100 ~ .....-.-. T"""

N

~ ID ID cu

o

-&. -100

-200 ""'"-________ ....Io-________ --'--__ ~

o 5 Frequency (GHz)

(d)

10

Ci) ,s :::>. cu

0 Qi 0 ~ c :.J

-1 00 ""'"-__ '""--_______ .......... __ ---'-__ ----A. __ ---'

o 2 4 6 8 Frequency (GHz)

(c)

10

5 ~----------------------~

o fi ~ -5 -;: -10 ~ ~ -15 ~

-20

-25""'"-------~~--------~--~

o 5 10 Frequency (GHz)

(e)

Figure 4.2 Antenna measurements, (a) antenna frequency response, (b) antenna link delay, (c) antenna phase response, (d) antenna reflection response.

From the' measured channel response, HCH ' and the input pulse spectrum, we can find the

EIRP VIa (4.3). Notice that Fr (/) IS the transmit power after the PA,

Chapter 4: UWB Pulse Propagation and EIRP Optimization

-40

co -45

~ -50 l u

I -55 <li Cf)

c -60 0 0.. Cf)

-65 a.> et:: >- -70 u c a.> ::J -75 0-a.> U: -80

0.811•

~ 0.6 C

& 0.4 Cf)

~ 0.2

a.> JE 0 ::J 0..

2

É -0.2 ~ ·········· - .. · ...... t

"0 a.> -0.4 r ...... ·c ... . ... . . ,

. ~ ~ -0.6 ~ ...... .. .. c ..... ...... ,

: ) UWB Band 10 ~ 6 GHz

4 6 8 10 12

Frequency (GHz) (a)

.... ..... ~ .. 800 .. ps ... : ... .. ·"T .. ·lt .. ·; . ~ ... -....... ~ .... ........ ~ .......... -i ........... : . --.. -................ , .... -... ..

~ -0.8 ~ .. .. .. .. ....... .. ..... .. , , .... · .. · .. ·· .... · ...... 1·\· Î Î Multipath Reflections

-1 r ...... ·· .. ;·· .. ····· .. ·:·· .... .... ·: ...... ····· ~ .. l~----~------~~--~ o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

lime (ns) (b)

14

Figure 4.3 (a) Smoothed antennas frequency response, (b) normalized time response.

61

~, (/) = PBP/) (/)GpA (/), where PBPD (/) is the RF power measured after the balanced

photodetector (BPD) and GpA (/) is the power amplifier gain.

The generated RF pulses are measured in both the time domain and in the frequency

domaine The experimental results will follow in the next section.


4.3. EIRP Measurements for Various Waveforms

4.3.1. Link Transfer Function

Before transmission through the antennas, the pulses are amplified uSlng a power

amplifier (PA) with an average gain of 25.7 dB over the bandwidth of interest. A low noise

amplifier (LNA, Mini-Circuits ZV A-183-S) at the receiver side ensures receiving signaIs

weIl above the measurement equipment noise floor (Figure 4.4a). As seen in Figure 4.4b

PA UWB Pulse

t-----t

Generator

28

al ~ 24 --.. T'""

N 22 ~ en .0 20 «

18 0 5 10

frequency (GHz) (b)

28

--.. 26 cc "'0

:::: 24 T'""

N

~ 22 en .0 « 20

18 0 5 10

frequency (GHz)

(d)

(a)

-40

al . ~-50

~ -60 Ci) .0 « -70

o al ~ ~-20 N en Ci) .0 -40 «

LNA Measuring .>----.

5 10 frequency (GHz)

(c)

Deviee

-60~----~------~----~ o 5 10

frequency (GHz) (e)

Figure 4.4 The wireless link, (a) setup block diagram, (b) PA frequency response, (c) antenna freq uency response, (d) LN A frequency response, (e) PA, antennas and LNA freq uency response.

~~-------o


and Figure 4.4d, the PA and LNA frequency responses vary about 2 dB in the UWB

bandwidth. This non-ideality of response affects the link frequency response. Comparing

Figure 4.4c with Figure 4.4e, we can see that the amplifiers have increased the signallevel

by about 48 dB and have also changed the response shape.

4.3.2. EIRP and Output Measurements

The generated RF pulses are measured in the time domain by a 40 GHz sampling

oscilloscope (Agilent 86100A) and in the frequency domain by a high speed RF spectrum

analyzer (HP 8565E). The resolution bandwidth of RF spectrum analyzer is set to 1 MHz in

order to respect the regulations of FCC 15.51 7 spectral measurements [1].

Experimental results are shown in Figure 4.5 and Figure 4.6. The first column in

Figure 4.5 gives the targeted time domain pulse (dashed) and the measured pulse (solid) at

transmitter. The second column plots the measured RF spectrum and the Fourier transform

of the targeted pulse (solid). The third column gives the calculated EIRP from the measured

waveform (solid), as well as the EIRP calculated from the target waveforms (dotted),

superimposed on the FCC spectral mask (dashed). The first column in Figure 4.6 represents

the time domain received pulse, whereas the second column shows the measured RF

spectrum of the received pulse and the Fourier transform of the received pulse (solid). The

gray areas of the transmitted and received spectrums in Figure 4.5 and Figure 4.6 show

noise floors when no signal is being transmitted. The transmitter noise floor cornes from

BPD noise and RF spectrum analyzer internaI noise. The receiver noise floor is due to the

BPD noise amplified by transmitter PA, propagated by the antennas, amplified by the

receiver LNA; it also includes the interference signaIs present at the lab environment su ch

as the university WiFi internet signaIs at 2.4 GHz. AlI the spectral curves are normalized

for the sake of comparison. We are able to adjust the absolute power levels by controlling

the EDF A gain and systematically produce pulses that respect the absolute spectral mask.

Gaussian monocycle (Figure 4.5al), doublet (Figure 4.5b 1) and FCC-compliant pulse

(Figure 4.5cl) with respective durations of 186, 207 and 355 ps are generated by fine

tuning of the FBG filters. To ensure the quality of measured pulses, they are compared with

target pulses. The measured monocycle best fits the first derivative of a Gaussian with r =


Transmitted pulse Transmitted spectrum EIRP

__ 0 r------ I ~ -Measuered co 1 1 U >10 - - -Monocycle ~ N -50 1 1 ~

É- T = 55ps 0-10 I ~ Cf) ~ 0 ID a.. ~ -60 c "'0 0 ~-20 0 :ê ë c. ~ ~ SE=12%

C ~-10 m a.. - Measuered

= E-30 ~ -70 .;j 0 W · ··· ··Monocycle

~ Z = -20 -40 -80 = 0 0 0.2 0.4 0 5 10 0 5 10

l ime (ns) Frequency (GHz) Frequency (GHz)

(a1) (a2) (a3)

ê!l 0 r-- - -- -, N 1 1

10 ~ 1 1 S- I -50 Cl -10 ~ .s Cf)

E 0.. ~ ID 0

~ -20 co -60 SE=22%

~ "'0 ~ :c :ê .~ c. ro a.. = ~ -70

0 E -10 E -30 Q « <5 W

Z -20 -40 -80

0 0.2 0.4 0 5 10 0 5 10

lime (ns) Frequency (GHz) Frequency (GHz) (b1) (b2) (b3)

0 ~ ê!l 1---

~ 10 "'0 N 1

0' -10 -50 1 = > I

Q. ~ _1

É-Cf) J

~ a.. -20 E 1 C 0 - "'0 -60 1

.::g ID ID co 1 SE=51 % "'0 ~

ë. .a ~ -30 1

~-10 m a.. 1

ë E -40 ~ -70 1

0 E W 1 « 0 ~ Z ... 1 1

U -20 -80 U 0 0.2 0.4 5 10 0 5 10 ~ lime (ns) Frequency (GHz) Frequency (GHz)

(c1) (c2) (c3)

Figure 4.5Transmit pulses (1), spectrums (2), EIRPs (3), for Gaussian monocycle, doublet and FCCoptimized pulses.

64

55 ps and the measured doublet approximates the second derivative of a Gaussian with the

same r . An excellent match is observed between the generated impulses and the targets both

in time and frequency domains.

To compare compliance of different waveforms, we use the power efficiency (PE) as the

total EIRP normalized by the. total admissible power under the FCC mask,

Chapter 4: UWB Pulse Propagation and EfRP Optimization

Received pulse Received spectrum

ID âl 0 "0

~ .2 ~ () ~ 0.5 o -10 ~ () E Cf)

0 « a.. c "0 0 ~ -20 0 ID E .~ .~

c ~ -O.S-cu

.~ E -30 (/') 0 0 (/') z Z ::::3 -1 -40 ~

0 0 0.5 1 1.5 0 5 10 Time (ns) Frequency (GHz)

(a1 ) (a2)

ID co 0 -0

~ .~ c.. 0.5 0 -10 E

Cf) a.. « "0 ..... "0 0 -20 a;) ID

:0 ID .~ .~ cu ::::3 cu

0 E -0.5 E -30 0 0 0

z Z -1

0 0.5 1 1.5 5 10

Time (ns) Frequency (GHz)

(b1) (b2)

ID âl 0 a;) "0

~ :ê ~ ::::3 0.. 0.5 55 -10 0.. E ..... « a.. c .~ "0 0 ~ -20

ID 0.. .~ .~

E cu cu E-0.5 E -30

0 0 0 ()

1 Z Z U -1 -40 U 0 0.5 1 1.5 0 5 10 u... Time (ns) Frequency (GHz)

(c1) (c2)

Figure 4.6 Received pulses (1) and spectrums (2), for Gaussian monocycle, doublet and FCCoptimized pulses.

f EIRP(f)df

65

P E == ~B--::W:---___ _

f S"cc(f)df ' (4.4)

BW

where S FCC (f) is the PSD of the FCC mask and B W is the band of interest. For 3.1-10.6

GHz bandwidth, we obtain PE values of 12, 22 and 51 % for Gaussian monocycle, doublet


and the FCC-optimized pulses, respectively. Monocycle and doublet pulses are made lower

in amplitude to respect the spectral mask, resulting in lower efficiencies.

Normalized EIRP are compared to the FCC spectral mask to verify compliance. We can

see that the Gaussian monocycle has very low coverage of the UWB band since it easily

violates the mask in 1.61 and 10.6 GHz edges (Figure 4.5a3). The doublet, (Figure 4.5b3),

has more UWB band coverage but still does not exploit it optimally. The FCC-optimized

pulse fully respects the mask al transmitter side before the Tx antenna with an efficiency of

670/0 ' [32]; efficiency is reduced to 51 % after transmission from antennas (Figure 4.5c3).

This degradation is due to an optimization of the pulse shape without taking into account

the antenna channel response.

Numerical values corresponding to Figure 4.5 are represented in Table 4.1. A great match

is observed between the target and the measured waveforms. The pulse peak-to-peak

voltage (V pp) is chosen to make the EIRP respect the spectral mask. It should be noticed

that Vpp depends on the bit-rate. Table 4.1 values are for 31.25 MHz bit-rate. An increase

in the bit-rate will require less Vpp not to violate the mask and vice versa. The total average

power can be computed either from the time domain waveform or from the EIRP. The

FCC-optimized pulse has 5.5 dB more average power than the Gaussian monocycle which

can be interpreted as 5.5 dB gain at the receiver.

Table 4.1 Peak-to-peak voltage (Vpp), Average total power and PE for the Gaussian monocycle, doublet and the FÇC-optimized waveforms.

Vpp (mV) Total average

PE (0/0) Waveform power (dBm)

Goal Meas. Goal Meas. Goal Meas.

Monocycle 20 20.6 -36.8 -36.5 Il.3 12.2

Doublet 23.6 23.7 -35.2 -34.9 19.7 21.8

FCC-33.8 35.4 -31.1 -31.0 49.8 51.4

compliant


In Figure 4.6, the received pulses have a duration of about 1300 ps. It can be observed that

the antenna impulse response has a duration of ,.....,800 ps (Figure 4.3). Suppose that the pulse

shown in Figure 4.5c3, with a duration of 500 ps, is being transmitted; the received pulse

will be the conyolution of the transmit pulse and the channel impulse response, and willlast

about 1300ps, confirming Figure 4.6 results. The received pulse has a different shape from

the transmit pulse. This is a kind of pulse broadening caused by the channel impulse

response.

4.3.3. Conclusion on EIRP Measurements

We experimentally investigated transmission of optically generated ultra-wideband pulses

via wideband antennas. Experiments confirmed the important role of antenna spectral

variations in the received spectrums of the pulses. The non-flat response of the PA and the

antennas . completely changes the transmitted waveforms, which in tum results in an EIRP

that does not completely exploit the spectral mask and degrades the power efficiency. In

order to overcome this problem and fully exploit the use of FCC-compliant pulses, new

designs should take into account the frequency response of the PA and antennas while

finding the optimal pulse shape with the numerical optimization method.

4.4. EIRP Optimization Using the Channel Frequency

Response

In this section, we design a UWB pulse shape that achieves the maximum permissible

power, subject to EIRP being below the FCe mask. The pulse design strongly depends on

the transmit antenna gain, Gr(f). In 4.4.1 we explain our pulse design technique,an

optimization procedure to maximize the total average power under a newly defined mask.

The new mask is dependent on the antenna frequency response. Later we generate this

pulse by writing the proper pulse shaping FBG and show the experimental results in 4.4.2.


4.4.1. Optimization Process

The condition EIRP ~ SJ.cc ' where Sj.cc (f) lS the FCC mask, leads us to define an

effective spectral mask for a given antenna by

M(f) = cS/.cc(f)/ 4:rrf ~HCH (f) (4.5)

Now, the power spectral density of the UWB pulse should .respect M(f) instead of the

FCC mask

(4.6)

M (f) has singularities at very low frequency (due to 1 If dependence) and around the

cutoff frequency of HCH • Thus, we confine our de'sign to frequency band where M(f) is

weIl defined. In the case of the wideband antennas used, the limit frequencies cover the

main UWB band between 3.1 to 10.6 GHz. The optimization method is very similar to what

we did in section 2.3.1. The UWB pulse x(t) should be designed in order to maximize the

power within the UWB frequency range Fp,

-40

~ -50 ~

Ê 1

~ ~60 ···1 ·· ~ 1 1 : ~ ! 1 : ~ 1 . ~. : - -70 ····· f ··· -t· 't ······ .. .. . ~ 1 1 " , '

i ~ - 1 • ""; Cf) -80 . . . . . '; ... : . . '.' .;..;... .. . :..:...;. .. ..:....;.;. ~~...:....:....:....;....;....;...:....;.;:..:...:....;.;:..:...;..:....;.:...;..;..;...;....;..;..;...;...;..;..;:..;..;.:..:....:...:..~

" ' \.:: ~. FCC Spectral Mask -- Spectral Mask at the input of Tx Antenna

-90 .. ..... .'{ . . : .. " ......... .v. Effective Spectral Mask at the input of PA ..

o 2 4 6 8 10 12

Frequency (GHz)

Figure 4.7 The FCC and the effective spectral masks.

(4.7)


subject to IX (f)12

::s;; M (f). xe!) is written as a sum of weighted Gaussian monocycles and

the rest of the process is as before using MATLAB SeDuMi optimization toolbox [20].

We approximate the measured channel response, HCH in Figure 4.3a, as the product of

two identical antenna responses. Thus we can find the new spectral mask at the input of

transmit antenna via (4.5); this is shown by a solid line in Figure 4.7. It can be claimed that

if the PSD of the UWB signal at the input of transmit antenna respects the new mask, the

transmitted EIRP will respect the FCC spectral mask (dashed line).

Furthermore, in a case in which a power amplifier (PA) with an average gain of G PA is

used before the antenna, the modified spectral mask in (4.5) should be divided by G PA • As

before, we used a wideband PA with a 25.7 dB gain over the bandwidth ofinterest (Mini

Circuits ZV A-183-S). In this case, the effective spectral mask, M(f) , is shown by the

dotted line in Figure 4.7. We used this curve in our program to generate the optimized

UWB waveform. It is evident that an antenna with a different frequency response, would

require a different spectral mask M (f) , and as a result, a different optimized UWB pulse.

4.4.2. EIRP-Optimized Pulse Generation

When using the dotted line in Figure 4.7 as the spectral mask, the optimized UWB

waveform generated by our optimization program is shown in Figure 4.8a. We used eight

coefficients in optimization, and Ta and rare 38.5 and 58.5 ps, respectively. The pulse

duration is about 0.4 ns. The pulse shaping FBG design starts from this EIRP-optimized

waveform. First the FBG transmission response is found from the time-to-frequency

mapping using 5.46 km of SMF Figure 4.8b. The apodization profile results from the

transmission response using equation (3.2). Figure 4.8c plots the apodization profile. The

FBG is written in multiple sweeps of the UV laser over the photo sensitive fiber. The laser

power level and the sweeping speed are adjusted to make weaker insertion loss at each step

(Figure 4.8d). The average insertion loss level reaches -3.8 dB after three sweeps. After

annealing, the written profile loses about 15% of its strength, reaching the desired -3 dB

insertion loss value.


0.8

~ 0.6

:ê ~ 0.4 <{

-g 0.2 N

=ru 0 E

~ -0.2

-0.4

-0.6

0.9

0.8

0] o

~ 0 6 a. c .g fL5 .§ "5 0A a. <:

0.3

02

0.1

o 100

r 1 f

200 300 400

Time (ps)

(a)

1\ I~ 1 \

V \ \

80 . Length (mm)

(c)

500

0,9

0.8

~ 0.7 e ~ 0.6 o ~~ 0 5 E </}

~ 0.4 t=

Ci) ~

0.3

0.2

-2

~ -3 o -l

§ -4 € Q) II> .E -5

-6

70

( 1 544 1.546 1.548 1.55 1.552

Wavelength (um) x lO

(b)

1540 1542 1544 1546 1548 1550

wavelength (nm)

(d)

Figure 4.8 EIRP optimized pulse shaping, (a) time domain pulse shape, (b) transmission response of the pulse shaping FBG, (c) apodization profile of the FBG, (d) experimental insertion loss of the pulse

shaping FBG written in 3 sweeps.

The generated pulse is shown in Figure 4.9a, which is in good 'agreement with the target

waveform; sorne deviations in the lower peak are attributable to imperfections in the FBG

writing process. The spectrum of the signal is measured by a spectrum analyzer as plotted

in Figure 4.9b. This measurement is in good agreement with the Fourier transform of the

measured time domain waveform. The PSD of the generated and target waveforms, as weIl

as the corresponding calculated EIRPs, are shown in Figure 4.9c. With the appropriate

choice of pulse amplitude, the PSD of the pulse is below the effective spectral mask and as

a result, the EIRP respects the FCC spectral mask.


~~~~----~-----r----~----~--~

>E

~ 2~" " " " " " " ' :"""" " ~ ë.. E « 0_-.. ········ ·· ···,

CI)

1/)

"3 a..

0.1 0 .2 0 .3

Time (ns )

(a)

~o

-50

~o

-100

Measured pulse

Designed pulse

0.4

Measured p SD

- Fr of the measVred time

o.

:.:t"'4-~---~~_._~-------. " . " . " : ~ :

6

Frequency (GHz)

(b)

EIRP for the Designed Pu se SE = 70 . 3% ~-------

EIRP for the Generated Pulse SE = 63 . 6 %

'<. , . '--'-'-"101:-:: ~~~~q~"l " , -,;

PSD of the Designed PUise ; ' :-.--

PSD of the Generated Pulse

domain pÎJ lse .;

10

-110 ~1----___ ....L.-__ --'-__ ----I ___ ..1-__ --'--__ ---J

10 12

Frequency (GHz)

(c)

Figure 4.9 (a) the designed (dashed line) and the measured (solid line) pulse shapes, (b) Measured PSD and the FT of the measured time domain pulse shape, (c) The PSD of the designed and

generated pulse and the corresponding EIRPs.

12

The maximum permissible power for the input pulse is determined by the bit time T =

11BR and the modulation scheme, where BR is the bit rate. For T = 2ns (BR = 500 Mb/s)

and PPM modulation where a pulse is sent in each bit, the maximum peak-to-peak (p-p)

voltage of the pulse is 6.8 mv, corresponding to a total power of -32.7 dBm. In the case of

OOK modulation, the UWB pulse is transmitted in half of the bits (assuming equal

probable input data) and the maximum p-p voltage is 9.6 mv. For any p-p voltage of the

. pulse less than the maximum value, the PSD of the signal is completely below the effective

spectral mask M(f) and the EIRP respects the FCC mask.


The efficiency is 70.30/0 for the EIRP-compliant pulse. By increasing the number of tap

coefficients, greater power efficiencies and longer pulses can be obtained. The total average

power of the generated pulse as measured is -32.8 dBm and the PE of the corresponding

EIRP is 63.6%.

Note that the non-optimized pulses traditionally employed in UWB applications are not

able to exploit high power efficiency: For instance, at the same bit-rate and using the same

PA and transmit antenna, the maximum p-p voltage of the Gaussian monocycle and doublet

pulses is 2.9 and 5.3 mv, with a pulse average power of -44.4 and -38.7 dBm, respectively

[35]. The average power of the generated pulse here represents more than Il.6 and 5.9 dB

improvement over Gaussian monocycle and doublet pulses, respectively. Figure 4.10 shows

various experimental waveforms. p-p amplitudes have been adjusted for each waveform to

respect the FCC mask at 500 Mb/s and with PPM modulation format. Figure 4.10b shows

the waveforms compared to the effective mask, whereas they are compared to the FCC

6 8 10 12

Fr Cl ne>, (GH )

(b)

0 .1 0.15 0.2 0 .25 0 .3 035 0.4 0 45 Time(ns)

(a)

: . .. ~ .. ..... ... : .. ... ..... .. : .... .. ... . .. . : .. .. .. - .. . . .

6 8 10 12 Fr-qu ncy GHz)

(c)

Figure 4.10 Waveform comparison (a) time domain measurements (b) PSDs compared to the . effective mask, (c) PSDs compared to the FCC mask.


mask in Figure 4.10c. AlI of these figures clearly indicate that the better the pulse IS

designed, the higher the absolute power.

4.5. Conclusion

The limited bandwidth and the non-uniform gaIn of wideband antennas over UWB

frequency band has a great impact on the maximum permissible transmit power and as a

results on the performance of overall UWB system. In this chapter, we started by measuring

the frequency response of the antennas, PA and the LNA. EIRPs and received waveforms

were measured for the Gaussian monocycle, doublet and the FCC-compliant pulse. Next,

we designed a UWB waveform taking into account the effects of the power amplifier and

antenna to maximize the permissible transmitted power, su ch that EIRP respects the FCC

spectral mask. The optimization process was very similar to the one in Chapter 2. A pulse

shaping FBG was written to generate the EIRP-optimized pulse. The measured results

showed our EIRP-optimized pulse has more than Il.6 and 5.9 dB improvement over

Gaussian monocycle and doublet waveforms, respectively. The EIRP-optimized pulse was

designed for a certain antenna frequency response. If the antenna orientation changes, the

pulse will no longer be optimum.

74 Summary and Future Research Direction

Summary and

Future Research Direction

The FCC regulations permit UWB radios to coexist with already allocated narrowband RF

emissions. The huge bandwidth and extremely low power of the UWB pulses relegates

UWB to indoor, short-range, communications for high data rates. However, efficient

generation of such impulses is very challenging and has inspired much research in recent

years.

We have demonstrated a novel technique in UWB pulse shaping using FBGs. Efficiently

designed waveforms are generated in the optical domain by shaping the spectrum of a laser

with an FBG. Frequency~to-time conversion and balanced detection of the pulse ensure


high quality output waveforms. An accurate match is attained between the experimental

works and the theoretical designs. The generated pulses rigorously respect the FCC spe~tral

mask, while exploiting most of the available power in the UWB bandwidth. We showed

results for the Gaussian, Gaussian monocycle, doublet and our optimized pulse. The

generation of the more complex waveforms is limited by fabrication noise in FBG writing

process.

Propagation of the UWB pulses using antennas affects the pulse shape due to the non-flat

impulse response of the antennas. In order to generate EIRP-optimized pulses, we measured

the antenna impulse response and took it into account in designing the efficient pulse by the

optimization program. Experimental results with the newly designed FBG showed the total

average power of the generated pulse is -32.8 dBm and the power efficiency of the

corresponding EIRP is 63.6%. This is a 12% advantage over the case where the antenna

response was not considered and a 50% advantage of PE over the widely employed

Gaussian monocycle pulse.

The obtainedresults are very promising, but using photonic technology for UWB pulse

generation is more costly than the CMOS UWB transmitters. Costs for our system are

dominated by the laser source. Optical integration would be the ideal solution to both cost

and size of the optical UWB transmitter.

Future work

In our experiments, the bit rate of the impulses was 31.25 Mb/s because of the repetition

rate lil1'l:itations of the passively mode-Iocked fiber laser (MLFL, 31.25 MHz). The pulse

rate can be increased by introducing duplicates of the pulse by Mach-Zehnder like

structures. This method has the disadvantages of deteriorating the polarization and

amplitude stability of the generated laser impulses. This instability directly affects the

UWB pulses generated and reduces the performance .of the receiver. A better option is

using an actively mode locked laser which will increase significantly the bit rate and add

more tunability to the setup. Writing appropriate FBGs for the active mode locked laser is a

future goal. Another approach is to write the UWB pulse on a smaller FBG bandwidth, say

1 nm. The reduced bandwidth enables the use of less expensive, low linewidth lasers


possible (e.g., a gain-switched distributed feedback (DFB) laser). In addition, avoiding the

MLFL significantly reduces the optical UWB transmitter costs.

Having generated efficient UWB pulses, the next step is naturally designing a receiver.

An energy detection receiver is a good choice in the case of OOK modulation. Extensive

study of the receiver is required to find less expensive sub-optimal structures which

maximize the received SNR by detecting the majority of the received signal energy. The

sensitivity and efficiency of the receiver play a very important role in further extending the

communication link range. Nevertheless, accurate synchronization is crucial for the

receiver and requires extensive research. In future , bit error rate measurements for different

. antenna orientations and distances would be of interest. With pulse duration of 0.5 ns, high

speed data transmis,sion on the order of l Gbps is feasible.

Appendix A: MATALAB Programs

clear .::3.11 clc close all L=9; n=lOO*L; Fs=28; ~~ in GHz, alphaO=2*pi*O.96/Fs; alpha=2*pi*1.61/Fs; beta=2*pi*3.1/Fs; gamma=2*pi*lO.6/Fs; b=b(L,O,pi); c=c(n,alphaO,alpha,beta,gamma); A=A (L, n) ; [x,r]=sedumi(A,b,c) n=size(r,l)-l; w=linspace(O,pi,400);

77

Appendix A

MATLAB Programs

Appendix A: MA TALAB Programs

R=zeros( 1 ,4 0 0 ) ; for k=l: n

R=R+ 2* r(k+1) *c o s(w* k ) ; end R=R+r ( l); % R jw) stern (r) ; yl abe l (' Autoc o rrelation coef f i c ien ts, r[ k ] ' ) ; x labe l ( , k ' ) ; figure p lot( w* F? / (2* p i) ,1 0*10g10( R) ) h o l d f= l insp a c e (0 , Fs/ 2 ,1 000) ; y=UWB_rnas k(f) ; plo t ( f , 10*10g1 0 (y) , ' r : ' ) '(s findinq the coefficient.s p [J<:.] [hh ] = spect ra l fac t ori z a tion( r ) ; p=real (hh ); fi g u re s t ern(p ) y label( 'Pul se Sarnples, p [k ] ' ) ; x labe l ( , k ' ) ; 'ès f the ~~pectrurll P f)

fftlen g th=2 A 13; P=fft (p,f f tlen gth); figure plot (f, 1 0 *10g10 (y), ' .:c : 1 )

hold w2= l i nspa c e(0,pi,fftlength /2) ; pl o t(w2* Fs/( 2*pi), 2 0 * log1 0 (abs(P(1:fftlength/2)) )) a x i s ( [0, 1 4, - 60, 0] ) ylabel (' Normalized P80 ' ); x label ( ! f GE z) ! );

% Time domaine se TO=l / Fs; %i n ns delta t=T O/10 %in ns k= O; for tt=-l:delta t:4 k=k+ 1; t(k)=tt; end pt=DAconversion(p,t,Fs) figure plot (t,pt/rnax (abs(pt) )) a x i s ( [-1, 4, -1, 1] ) y label('Norrnalized P(t) '); x label ('t (ns)');

f u nction A=A(L,n) A= z eros(2*n,L+1) ; fo r i=l:n

A(i,l)=l; end f or i=1:n+ 1

ornega(i)=(i-1)*pi/n; end

J\.. ~

Ü 1-1 "- t - () li % ~~ 1) % \~ ::;.

78

~ ~~ :.;:., 't ;:..; ~ t~ ~~ % ~5 ~ :'0 (t

Appendix A: MA TALAB Programs

for i=l:n

e n d

for j=l:L oA(i,j+1)=2*cos(j*omega(i) );

e n d

f or i=n+1:2*n A(i,l)=-l;

e nd for i=n+-1: 2 *n

e n d

fo r j=l:L A(i,j+1)=-2*cos(j*omega(i-n) );

end

f uncti o n c=b(L,alpha,beta) c=zeros(1,L+1); c(l)=(beta-alpha); fo r k= l :L

c( k+1)=2/k*(sin(k*beta)-sin(k*alpha) ); end

79

%%% ~ %% %%%%%%%% %% %% %%%% c f u n c tion %%~%%% %% %%%~%%%~ %%~%%%~%%%

f unction c=c(n,alphaO,alpha,beta,gamma) c=zeros C2*n, 1) ; f or i=1:n+1

omega(i)=(i-1)*pi/n; e nd UO=l; U1=10 A (-3.4); U2=10 A (-1) U3=1; U4=0.1; i=l; whi l e omega(i)<alphaO

c(i)=UO; i=i+1;

end whi le omega(i)<alpha

c(i)=U1; i=i+1;

end whi le omega(i)<beta

c(i)=U2; i=i+1;

end \'vhi le omega (i) <gamma

c(i)=U3; i=i+1;

end whi l e omega(i)<pi

c(i)=U2; i=i+1;

end f or i=n+1:2*n

c(i)=O;

80 Appendix A: MA TALAB Programs

end

factoriza t ion %~ %%%%%%%%%%%%%%%~%%%%%

function [hh] = spectralfactorization( r ) L=2 A ceil(log2(15*(2*length(r)-1) )); psd=exp ( i*(length(r)-1)*linspace(O,2*pi*(L-1)/L,L)' ) .*fft([fl ipud (r);r(2:1ength(r))],L); a=ifft(log(psd)); hh=if f t( e xp( fft( [a(1)/2;a(2:L/2)],L ) ) ) ; hh=hh (1 :1ength(r) );

function p=DAconversion (h ,t,Fs) L=max(size(h) )-1; p=zeros ( l,max(size(t))) ; f o r k=O :L

p=p+h(k+1)*sinc(Fs*(t-k/Fs) ); end

% % %%%~%%%%%%% %%% %%% %% FCC spectra rnask %~%%%%%%%~%%%~%%% S%~%%%~%

function y=UWB_mask(f) f : GHz y : dB

k=max(size(f) ); y=zeros(l,k); for m=l: k

if f(m)<=O.96 y(m)=l;

e nd if f (m»O.96 & f(m)<=1.61

y(m)=10 A (-3.4); ~2

end if f(m»1.61 & f(m)<3.1

y(m)=10 A (-1); end if f(m»=3.1&f(m)<10.6

y (m) = 1 ; (~; TJ 2 ,". 2

end if f(m»=10.6

end end

y(m)=O.l; ~> U3h2

References

References

D. Porcino, W. Hirt, "Ultra-wideband radio technology: potential and

challenges ahead," IEEE Comm. Magazine , vol. 41 ,no 7, July 2003

2 1. Foerster, E. Green, S. Somayazulu, and D. Leeper, "Ultra-wideband

technology for short- or medium-range wireless communications," Intel

Technology Journal, pp. 1-11 , 2nd Quarter, 2001.

3 First report and order, (Revision of part 15 of the commission' s rules

regarding ultra-wideband transmission systems), US. Fed. Comm.

Commission, adopted Feb. 14, 2002, released Apr. 22, 2002.

4 M. Ghavami, L. B. Michael, R. Kohno, "Ultra wideband signaIs and

systems in communication engineering," John Wiley & Sons, 2nd Ed, 2007.

5 WiMedia, "The Worldwide Ultra-Wideband Platform for Wireless

Multimedia," Wireless Symposium, London, June 19th 2007

6 T. M. Cover, J. A. Thomas, "Elements ofinformation theory," JohnWiley &

Sons, New York, 1991.

7 S. Stroh," Ultra-wideband multimedia unplugged," IEEE Spectrum, vol. 40,

no 9, pp. 23-27, Sep. 2003

8 R. A. Scholtz, D. M. Pozar, and W. Namgoong, "Ultra-wideband radio,"

EURASIP Journal on Applied Signal Processing, vol. 3, pp. 252-272, 2005.

9 "Ultra-wideband (UWB) technology," http://www.intel.com/technology/

comms/uwb/

10 1. 1. Immoreev, D.V. Fedotov, "Ultra wideband radar systems: advantages

and disadvantages,". Proc. 0.1 the IEEE Conf. on Ultra Wideband Systems

and Technology, Baltimore, MD, pp. 201-205, May 2002.

81

References

Il C. F. Liang, S. T. Liu, S. 1. Liu, "A calibrated pulse generator for impulse

radio UWB applications," IEEE J .Solid-State Circuits, vol. 41 , no. Il , Nov.

2006.

12 X. Wu, Z. Tian, T.N. Davidson, G.B. Giannakis, "Optimal waveform design

for UWB radios," IEEE Trans. Signal Processing, vol. 45 , no. 6, June 2006.

13 D. D. Wentzloff, A. P. Chandrakasan, "Gaussian pulse generators for

subbanded ultra-wideband transmitters," IEEE Trans. Microwave Theory

and Techniques , vol. 54, no. 4, April 2006.

14 S. Bagga, A. V. Vorobyov, S. A. Haddad, A. G. Yarovoy, W. A. Serdijn, 1.

R. Long, "Co-design of an impulse ge~erator and miniaturized antennas for

IR-UWB," IEEE Trans. Microwave Theory and Techniques , vol. 54, no. 4,

April 2006.

15 L. Smaini, C. Tinella, D. HelaI, C. Stoecklin, L. Chabert, C. Devaucelle, R.

Cattenoz, N. Rinaldi, D. Belot,. "Single-chip CMOS pulse generator for

UWB systems," IEEE J Solid-State Circuits, vol. 41, no. 7, July 2006.

16 J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform

generator," Photonics Technology Letters, vol. 15, no.4, pp. 581-83, April

2003.

17 C. Wang, F. Zeng, J. Yao, "All-fiber UWB pulse generation based on

spectral shaping and dispersion-induced frequency-to-time conversion,"

IEEE Photonics Tech. Lett., vol.19, no.3, Feb. 2007.

18 B. Sklar, " Digital Communications, " Pearson Education, 2nd Ed, 2001

19 S. Wu, S. Boyd and L. Vandenberghe, '·'FIR filter design via semidefinite

programming and spectral factorization," Proc. of the 35th Conference on

Decision and Control, Kobe, Japan, Dec. 1996.

82

References

20 1. F. Strum (1991) "Using SeDuMi 1.02, a MATLAB toolbox for

optimization over symmetric cones," [Online]. Available:

http://sedumi.mcmaster . ca

21 J. R. Foerster, V. Somayazulu, S. Roy, E. Green, K. Tinsley, C. Brabenac,

D. Leeper, M. Ho, "Intel CFP Presentation for a UWB PHY," IEEE

P802.15-03/109rl , Mar. 3, 2003.

22 1. S. Lin, J. D. McKinney, and A. M. Weiner, "Photonic synthesis of

broadband microwave arbitrary waveforms applicable to ultra-wideband

communication," IEEE Microwave Wireless Campan. Letter, vol. 15, no. 4,

pp. 226-228, Apr. 2005.

23 F. Zeng, Q. Wang, J. Yao, "All-optical UWB impulse generation based on

cross-phase modulation and frequency discrimination," Elec. Lett. , vol.43 ,

no.2, Jan. 2007.

24 M. Abtahi , J. Magné, M. Mirshafiei, L. A. Rusch, S. LaRochelle,

"Experimental generation of FCC-compliant UWB pulse using FBGs,"

European Conf. Optical Comm. (ECOC) , Berlin, Germany, Sept. 16-20,

2007.

25 M. Abtahi, J. Magné, M. Mirshafiei, L. A. Rusch, S. LaRochelle,

"Generation of Power-Efficient FCC-Compliant UWB Waveforms using

FBGs: Analysis and Experiment," IEEE J Lightwave Tech., vol. 26, no.5 ,

pp. 628-635, March 1, 2008.

26 S. Doucet, "Modélisation et Fabrication de Réseaux de Bragg à

Caractéristiques Spectrales Périodiques pour la Réalisation de Filtres

Optiques Multicanaux," thesis, Université Laval, Québec, Canada, 2006.

27 G. Keiser, "Optical fiber communications," McGraw-Hill, 3rd Ed, 2000.

83

References

28 S. Pereira, and S. LaRochelle, "Field profiles and spectral properties of

chirped Bragg grating Fabry-Perot interferometers," Optics Express, vol. 13,

pp. 1906-1915, March 2005.

29 J. Magné, "Traitement optique du signal émis par un laser à fibre

mode-Iocked pàssif : application à la multiplication et à la sculpture

d'impulsions, " thesis, Université Laval, Québec, Canada, 2007.

30 G. P. Agrawal, "Lightwave technology: telecommunication systems," John

Wiley & Sons, New Jersey, 2005.

31 H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse

additive pulse mode-Iocking in fiber ring lasers: theory and experiment,"

IEEE J Quantum Electronics, vol. 31, no. 3, March 1995.

32 M. Abtahi, M. Mirshafiei, J. Magne, L. A. Rusch, S. LaRochelle, "Ultra

wideband waveform generator based on optical pulse shaping," IEEE

Photonics Technology Letters, vol. 20, no. 2, pp. 135-137, Jan. 2008

33 D. Pozar, "Microwave engineering," John Wiley & Sons, 3rd Ed, 2005.

34 J. D. Brunett, R. M. Ringler, V. V. Liepa, "On measurements for EIRP

compliance of UWB devices," IEEE Electromagnetic Compatibility, vol. 2,

pp. 473- 476, Aug. 2005.

35 M. Mirshafiei, M. Abtahi, L. A. Rusch, S. LaRochelle, "Wideband Antenna

EIRP Measurements for Various UWB Waveforms," IEEE International

Conference on Ultra-Wideband (ICUWB), Hannover, Germany, Sept. 10-12,

2008.

36 Jianxin Liang, "Antenna Study and Design for Ultra-wideband

Communication. Applications," thesis, University of London, United

Kingdom, 2006.

84

R,eferences

37 K. Y. Yazdandoost and R. Kohno, "Ultra wideband antenna," IEEE

Communication Magazine , vol. 42, no. 6, 2004, pp. S29-S32.

38 J. D. McKinney and A. M. Weiner, "Compensation of the effects ofantenna

dispersion on UWB waveforms via optical pulse-shaping techniques," IEEE

Transactions on Microwave Theory Tech. , vol. 54, no. 4, pp. 1681-1686,

Jun.2006.

39 SkyCross antenna product, "3.1-10 GHz Ultra-wideband antenna for

commercial UWB applications," SMT-3T010M antenna element,

12/10/2003.

40 Y. W. Yeap, O. M. Chai and C. L. Law, "Evaluation of ultra wideband

signal transmission, propagation and reception with low cost UWB RF front

end," IEEE RF and Microwave Con[., pp. 72-75, Oct. 2006.

85