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
4 Chapter 1: introduction
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.
8 Chapter 1: introduction
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
-- ---- - ---------- - - ------,
9 Chapter 1: introduction
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.
12 Chapter 2: Optimal UWB Waveforms
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
13 Chapter 2: Optimal UWB Waveforms
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
15 Chapter 2: Optimal UWB Waveforms
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
Chapter 2: Optimal UWB Waveforms
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.
18 Chapter 2: Optimal UWB Waveforms
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
19 Chapter 2: Optimal UWB Waveforms
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.
20 Chapter 2: Optimal UWB Waveforms
(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).
21 Chapter 2: Optimal UWB Waveforms
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.
23 Chapter 2: Optimal UWB Waveforms
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
25 Chapter 2: Optimal UWB Waveforms
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.
Chapter 2: Optimal UWB Waveforms
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
27 Chapter 2: Optimal UWB Waveforms
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)
Chapter 2: Optimal UWB Waveforms
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
31 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
34 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
Chapter 3: Optical UWB Pulse Shaping Using FBGs
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
36 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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)
37 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
38 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
Chapter 3: Optical UWB Pulse Shaping Using FBGs
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
40 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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
41 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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
-- -- - --~ - -- --------- - ---.,
42 Chapter 3: Optical UWB Pulse Shaping Using FBGs
~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.
43 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
44 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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
Chapter 3: Optical UWB Pulse Shaping Using FBGs
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)
47 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
48 Chapter 3: Optical UWB Pulse Shaping Using FBGs
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.
Chapter 3: Optical UWB Pulse Shaping Using FBGs
~ ~ 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.
Chapter 3: Optical UWB Pulse Shaping Using FBGs
~ 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)
4 6 8 10 12 14 Frequency (GHz)
(d)
4 6 8 10 12 14 Frequency (GHz)
(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
52 Chapter 3: Optical UWB Pulse Shaping Using FBGs
(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.
54 Chapter 4: UWB Pulse Propagation and EJRP Optimization
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 -
55 Chapter 4: UWB Pulse Propagation and EJRP Optimization
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  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
57 Chapter 4: UWB Pulse Propagation and EJRP Optimization
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.
60 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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.
62 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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
63 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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 =
Chapter 4: UWB Pulse Propagation and EIRP Optimization
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
66 Chapter 4: UWB Pulse Propagation and EJRP Optimization
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
67 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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.
68 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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)
69 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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.
Chapter 4: UWB Pulse Propagation and EIRP Optimization
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.
71 Chapter 4: UWB Pulse Propagation and EIRP Optimization
~~~~----~-----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.
72 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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.
73 Chapter 4: UWB Pulse Propagation and EIRP Optimization
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
75 Summary and Future Research Direction
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
76 Summary and Future Research Direction
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
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