Accurate and Efficient Electromagnetic Modeling

Transcription

Accurate and Efficient Electromagnetic Modeling of
Antenna-Body Interactions: Application to
Speech Sensing and BAN
By
Ahmed Mohamed Ali Moussa Eid
A thesis submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
in Electrical Engineering
Approved, Thesis Committee:
Prof. Dr. Jon Wallace
Jacobs University Bremen, Germany
Prof. Dr. Mathias Bode
Prof. Dr. Buon Kiong Lau
Lund University, Sweden
Date of Defense: November 12, 2010
School of Engineering and Science
Jacobs University, Bremen, Germany
Abstract
Accurate and efficient simulation of body-antenna interactions is identified as a vital
requirement for the design and optimization of wireless systems that operate near the
human body. Examples of such systems include cellular phones and wireless body area
network (WBAN) sensors.
To this end, efficient simulation methods with high accuracy are developed for two
important and diverse applications. First, speech sensing is considered, whose aim is to
sense and track the process of human speech, requiring information about the position and
movement of lips, tongue, glottis, etc., potentially improving synthetic speech production,
speech pathology and therapy, and speech recognition. For this purpose, a simplified
FDTD model of the head-vocal tract is used which is efficient enough to be simulated on a
desktop PC. In the FDTD head-vocal tract model, the important propagation mechanism
is identified as waveguiding of the mouth/throat which suggests that a hollow waveguide
model can be developed for the speech channel.
To improve efficiency of the speech-sensing application, a mode-matching waveguide model
is developed. Comparing simulation times, the proposed method is orders of magnitude
more efficient than direct simulation with the FDTD solver. The work is also appropriate
to support future work in inverse scattering of waveguides, such as what is needed for
speech sensing.
Next, the FDTD model is used to design and optimize an antenna that enhances coupling
of propagating waves to mouth and throat. To test the accuracy of the modeling procedures and explore the feasibility of speech sensing, a prototype speech sensing system
is built and deployed. Comparisons indicate that the model and measurement agree for
large movement of different parts of the speech system. A speech recognition experiment
is also performed as a proof-of-concept to motivate the idea of speech sensing.
As a second target application, modeling for body area networking is presented. This
application focuses on the shadowing aspect of the body which is most challenging impediment to the communications. An efficient two-dimensional lossy dielectric cylinder
model for the body is adopted and extended to arbitrary polarization and arbitrary cross
section using a surface-based method of moments solution. Additionally, measurements
with short dipoles are performed in a compact anechoic chamber and compared with
simulations to illustrates utility and accuracy of the models. The result demonstrates
that the simple models are appropriate for rapid simulation of BANs, also indicating
their utility for developing optimized antennas for BAN channels.
I certify that I have written this PhD thesis by my own without any impermissible
assistance.
Ahmed Mohamed Ali moussa Eid
Matriculation Number: 20327741
School of Engineering and Science
November 2010
To my parents
Acknowledgements
Until writing this page, I have spent almost three years for the PhD study. During the
course of my study, I have received support from individuals and organizations. This
thesis would not have been possible without their support.
I would like to thank my advisor Prof. Dr. Jon Wallace for giving me an opportunity to
study and work at Jacobs University. I would especially like to thank him his support
and encouragement during this study. Also, for giving me constructive criticisms, which
motivated and trained me to improve the quality of my research. Furthermore, his insights
and experiences were so valuable for me to enhance my research and presentation skills.
I would like to thank Prof. Dr. Mathias Bode for his kind acceptance to be in the
committee member as the reviewer of my PhD research. I would like to thank Prof. Dr.
Buon Kiong Lau from Lund University, Sweden, for his kind acceptance to serve as an
external member of the committee.
I would like to thank my parents for their continuing support in every aspect of my life.
I cannot reward them with these few words but I wrote these words to partially honour
them in such occasion where their role is not visible but valuable.
Finally, I would like to thanks my wife Walla and my kids, Rana, Karim and Merna for
allowing me to conduct my research and not giving them enough time for their childhood.
Without their encouragement and understanding it would have been impossible for me to
finish this work. My special gratitude is due to my brother Tamer, my sisters Rasha and
their families for their loving support.
I
CONTENTS
Contents
List of Figures
VII
List of Tables
IX
1 Introduction
1.1 Antenna Design for Wireless Devices . . .
1.2 Sensing and Imaging of the Body . . . . .
1.2.1 State-of-the-Art Techniques . . . .
1.2.2 Ultra-wideband Microwave Imaging
1.3 Body Area Networking . . . . . . . . . . .
1.4 Motivation of Research . . . . . . . . . . .
1.5 Contributions of this Thesis . . . . . . . .
1.6 Organization of the Thesis . . . . . . . . .
2 Speech Sensing and UWB
2.1 Existing Speech Sensing Techniques .
2.2 Ultra-Wideband Technology . . . . .
2.3 UWB Sensing . . . . . . . . . . . . .
2.3.1 Heart Rate Sensing . . . . . .
2.3.2 Tumor Detection . . . . . . .
2.3.3 UWB Through Wall Imaging
2.4 UWB Speech Sensing . . . . . . . . .
2.5 Summary . . . . . . . . . . . . . . .
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3 UWB Antenna Design for Speech Sensing
3.1 UWB Antenna Requirements . . . . . . . .
3.2 Types of UWB Antennas . . . . . . . . . . .
3.3 Broadband Monopole Antenna . . . . . . . .
3.3.1 Optimization of Antenna Parameters
3.4 Modified Broadband monopole . . . . . . . .
3.4.1 Slotted Disk Monopole Antenna . . .
3.4.2 Circular Ring Monopole . . . . . . .
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II
CONTENTS
3.5
3.6
3.7
3.4.3 Circular Patch with Reflector
Vivaldi Antenna . . . . . . . . . . . .
UWB Antenna Measurement . . . . .
Summary . . . . . . . . . . . . . . .
4 Speech Sensing: Full-wave Modeling
4.1 Detailed Head, Vocal Tract Model . .
4.1.1 Electrical Properties of Tissue
4.1.2 Head/Neck Surface Modeling
4.1.3 Internal Vocal Tract Model .
4.1.4 FDTD Simulation of Model .
4.2 3D Flat-Face Stacked Layer Model .
4.3 One Dimensional Model . . . . . . .
4.4 Summary . . . . . . . . . . . . . . .
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5 Speech Sensing: Simulation and Experimental Validation
5.1 Optimization of Antenna Placement . . . . . . . . . . . . . .
5.1.1 Vertical/Horizontal Offset gx , gy . . . . . . . . . . . .
5.1.2 Antenna-Head Gap gz . . . . . . . . . . . . . . . . .
5.2 Sensing of Large Vocal Tract Changes . . . . . . . . . . . . .
5.2.1 Lips Movement . . . . . . . . . . . . . . . . . . . . .
5.2.2 Tongue Movement . . . . . . . . . . . . . . . . . . .
5.3 Frequency-Dependent Tissue Properties . . . . . . . . . . . .
5.4 Vocal Tract Measurements for Large Movement . . . . . . .
5.5 UWB Speech-Recognition Experiment . . . . . . . . . . . .
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Speech Sensing: Multimode Waveguide Modeling
6.1 Principles of the Mode Matching Technique . . . .
6.1.1 Transverse Field Expressions . . . . . . . . .
6.1.2 The Scattering Matrix . . . . . . . . . . . .
6.2 Cascading S-Parameters . . . . . . . . . . . . . . .
6.3 Scattering Matrix of a Uniform Section . . . . . . .
6.4 Mode Matching Validation . . . . . . . . . . . . . .
6.5 Vocal Tract S-Parameter . . . . . . . . . . . . . . .
6.6 Vocal Tract Shape Estimation . . . . . . . . . . . .
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . .
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7 Body Area Network: Numerical Methods
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7.1 Circular Cylinder BAN Model (Closed-Form Solution) . . . . . . . . . . . 85
7.1.1 Incident Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
III
CONTENTS
7.2
7.3
7.4
7.5
7.1.2 Scattered Fields . . . . . . . . . . . . . . . . . .
7.1.3 Determination of Unknown Coefficients . . . . .
7.1.4 Non-singular Expression for Incident Field . . .
Surface-based Numerical Solution for BAN Propagation
7.2.1 Governing Equations . . . . . . . . . . . . . . .
7.2.2 Incident Fields . . . . . . . . . . . . . . . . . .
7.2.3 Boundary Conditions . . . . . . . . . . . . . . .
7.2.4 Discretization . . . . . . . . . . . . . . . . . . .
Point Source . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Methods Validation . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Body Area Network: Modeling and Experimental Validation
8.1 Human Torso Models . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Field Around the Torso Model . . . . . . . . . . . . . . .
8.1.2 Field Inside and Outside Torso Model . . . . . . . . . . .
8.2 BAN Measurement Setup . . . . . . . . . . . . . . . . . . . . .
8.2.1 Network Analyzer-Based System . . . . . . . . . . . . .
8.2.2 BAN Antenna . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3 Anechoic Chamber and Outdoor Measurement . . . . . .
8.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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9 Conclusion and Future Work
123
9.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A Publications
127
V
LIST OF FIGURES
List of Figures
2.1
2.2
2.3
2.4
UWB monocycle pulse both in the time and frequency domains . . . .
FCC spectral mask for UWB indoor communication systems . . . . . .
ECC spectral mask for UWB indoor communication systems in Europe
Block diagram of the network-analyzer based measurement system . . .
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
Low cost UWB antenna designed . . . . . . . . . . . . . . . . . . . . . .
Double sided printed bow tie antenna . . . . . . . . . . . . . . . . . . .
Truncated rectangular patch . . . . . . . . . . . . . . . . . . . . . . . . .
Ice cream cone antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Microstrip circular antenna . . . . . . . . . . . . . . . . . . . . . . . . . .
Reflection coefficient of disk monopole antenna . . . . . . . . . . . . . . .
Simulated current distributions of the circular disc antenna . . . . . . . .
3D radiation patterns of the circular disc monopole antenna . . . . . . .
Back radiation antenna canceling . . . . . . . . . . . . . . . . . . . . . .
Disk monopole antenna return loss with reflector . . . . . . . . . . . . . .
3D radiation patterns of disk monopole antenna with reflector . . . . . .
Return loss for different feed gaps . . . . . . . . . . . . . . . . . . . . . .
Return loss for different widths of the ground plane . . . . . . . . . . . .
Return loss for different radius . . . . . . . . . . . . . . . . . . . . . . . .
Slotted disk monopole antenna . . . . . . . . . . . . . . . . . . . . . . .
Slotted disk monopole antenna return loss . . . . . . . . . . . . . . . . .
Microstrip circular ring antenna . . . . . . . . . . . . . . . . . . . . . . .
Microstrip circular ring antenna return loss . . . . . . . . . . . . . . . . .
The designed directional UWB antenna . . . . . . . . . . . . . . . . . . .
Return loss of the guided circular disc monopole antenna . . . . . . . . .
3D radiation patterns of the guided circular disc monopole antenna . . .
Vivaldi antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vivaldi antenna return loss . . . . . . . . . . . . . . . . . . . . . . . . . .
Vivaldi 3D radiation patterns at (a) 3, (b) 5,(c) 6 and (d) 7 GHz . . . .
Simulated and measured reflection coefficient of the broadband monopole
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4.1
Head model for FDTD simulations of the human vocal tract . . . . . . . . 38
VI
LIST OF FIGURES
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Controlling the movement of the lower jaw muscles . . . . . . . . . . .
Blender weight painting process . . . . . . . . . . . . . . . . . . . . . .
MRI images showing vocal tract shape for open and closed mouth . . .
Vocal tract shape manually created in Blender to match an MRI image
Head model with three point polygons for FDTD simulation . . . . . .
Stacked layer model for FDTD simulations of the human vocal tract . .
One dimensional reflection and transmission model . . . . . . . . . . .
One dimensional attenuation model for speech sensing . . . . . . . . . .
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5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
Relative power level (dB) 2 cm into the mouth for different gx , gy offsets
Relative power level (dB) 2 cm into the mouth for different gz offsets . .
Time-domain delta response for lips . . . . . . . . . . . . . . . . . . . . .
Detailed head model exposed to UWB field with lips closed . . . . . . . .
Detailed head model exposed to UWB field with lips open . . . . . . . .
Time-domain delta response for tongue tip . . . . . . . . . . . . . . . . .
Flat head model exposed to UWB field with tongue up and down . . . .
Detailed head model exposed to UWB field with tongue tip down . . . .
Detailed head model exposed to UWB field with tongue tip up . . . . . .
Time-domain delta response for movement of the back of the tongue . . .
Head model exposed to UWB field with the back of the tongue up . . . .
Head model exposed to UWB field with the back of the tongue down . .
Delta responses for large movement at different frequencies . . . . . . . .
Time-domain delta response for lips . . . . . . . . . . . . . . . . . . . .
Time-domain delta response for tongue tip . . . . . . . . . . . . . . . .
Time-domain delta response for tongue back . . . . . . . . . . . . . . . .
Time-domain delta response with long time . . . . . . . . . . . . . . . .
Delta response of two repeated vocalization of the words five and seven .
Speech-recognition experiment . . . . . . . . . . . . . . . . . . . . . . . .
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50
51
52
53
54
54
55
56
56
57
57
58
59
61
61
62
62
64
65
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
Vocal tract segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mode matching at discontinuity . . . . . . . . . . . . . . . . . . . . . . .
Cascading two port scattering matrices . . . . . . . . . . . . . . . . . . .
Thick iris in a circular waveguide . . . . . . . . . . . . . . . . . . . . . .
Vocal tract as two port networks . . . . . . . . . . . . . . . . . . . . . .
Incident and reflection wave coefficient at plane inside the vocal tract . .
Scattering parameters of the vocal tract represented as two port network
Vocal tract reconstruction using a library lookup based method . . . . .
Vocal tract reconstruction using a library lookup based method . . . . .
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68
69
73
75
76
77
78
80
81
7.1
7.2
Two-step procedure for body area modeling . . . . . . . . . . . . . . . . . 84
Circular cylinder excited with a line current source . . . . . . . . . . . . . 85
VII
LIST OF FIGURES
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
Arbitrarily shaped biological body illuminated by electromagnetic wave
The nth segment for the method-of-moments discretization procedure .
Integration path for case of m = n . . . . . . . . . . . . . . . . . . . . .
Integration path for observing fields in Region 0 . . . . . . . . . . . . .
Integration path for observing fields in Region 1 . . . . . . . . . . . . .
A parabolic contour integral around singularity kz = k0 . . . . . . . . .
Channel comparison of Ez in response to a z-directed line source . . . .
Channel comparison of Eρ in response to a ρ-directed line source . . . .
Channel comparison of Eφ in response to a φ-directed line source . . .
Channel comparison of Eρ in response to a φ-directed line source . . . .
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93
97
98
99
100
103
104
104
105
105
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
Camera-based torso measurement . . . . . . . . . . . . . . . . . . . . . .
Measured torso of the subject . . . . . . . . . . . . . . . . . . . . . . . .
Human torso model for circular, elliptical and superquadtratic shape . .
Model comparison of Ez in response to a z-directed point source . . . . .
Model comparison of Eρ in response to a ρ-directed point source . . . . .
Model comparison of Eφ in response to a φ-directed point source . . . . .
Model comparison of Eρ in response to a φ-directed point source . . . . .
Model comparison of Eφ in response to a ρ-directed point source . . . . .
Electric field as a function of observation radius . . . . . . . . . . . . . .
Field around and into a lossy human model . . . . . . . . . . . . . . . .
BAN measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reflection coefficient of the short monopoles used in BAN measurements
Antennas for the BAN measurement . . . . . . . . . . . . . . . . . . . .
Anechoic chamber measurement with subject . . . . . . . . . . . . . . . .
Outdoor measurement with subject . . . . . . . . . . . . . . . . . . . . .
Measurement and model comparison of Eρ in response to a ρ . . . . . . .
Wall reflection with anechoic chamber measurements . . . . . . . . . . .
Measurement and model comparison of Ez . . . . . . . . . . . . . . . . .
Measurement and model comparison of Eφ . . . . . . . . . . . . . . . . .
Measurement and model comparison of Eφ . . . . . . . . . . . . . . . . .
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108
108
109
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111
111
112
112
113
113
114
115
115
116
117
118
118
119
120
120
LIST OF TABLES
IX
List of Tables
4.1
Electrical properties of tissues at different frequencies [66] . . . . . . . . . . 38
5.1
Example speech recognition experiment . . . . . . . . . . . . . . . . . . . . 65
6.1
6.2
Comparison of the reflection coefficient S11 as a function of L . . . . . . . 75
Percent error performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
XI
LIST OF TABLES
List of Abbreviations
BAN
Body Area Network
CAT
Computer Aided Tomography
EIRP
Equivalent Isotropically Radiated Power
FCC
Federal Communications Commission
FDTD
Finite Difference Time Domain
GEMS
Glottal Electromagnetic Sensors
HRV
Heart Rate Variability
MMW
Millimeter Wave
MOM
Method of Moments
MPE
Maximum Permissible Exposure
MRI
Magnetic Resonance Imaging
PEC
Perfect Electrical Conductor
PIFA
Planar Inverted F-Antenna
PML
Perfectly Matched Layer
SAR
Specific Absorption Rate
SAR
Synthetic Aperture Radar
SSI
Silent Speech Interfaces
STW
See Through Wall
UWB
Ultra Wide band
WBAN
Wireless Body Area Network
1. INTRODUCTION
1
Chapter 1
Introduction
Accurate modeling of electromagnetic fields distributed in or around biological objects
is of paramount importance for current and future applications of wireless technology.
For example, since the introduction of cellular telephones, there has been concern on the
health effects of wireless technology. Also, microwave imaging of the body is an emerging
application that can improve tumor detection. Both of these applications require accurate
characterization of the interaction of the radiated waves with the body.
This introductory chapter reviews these and other important applications where bodyantenna modeling is important, and highlights two diverse applications that are studied
in this thesis, namely speech sensing and body-area networking. The contribution of this
work is described and the structure of the thesis is given.
1.1
Antenna Design for Wireless Devices
Accurate electromagnetic modeling of the fields distributed in or around biological objects
requires the antenna to be close to the human body, which naturally affects the antenna
performance, typically reducing the radiation efficiency, altering the resonant frequency,
and increasing the antenna bandwidth [1–4]. In some cases, the human body also affects other parameters, such as antenna gain, return loss, radiation pattern, and input
impedance [3, 5–9]. However, the interaction of electromagnetic waves with the human
body is very complicated since there are scattering and absorption in various tissues of
the body that are close to the antenna. In addition, there are also diffractions or creeping
waves along the body surface.
Health risk assessment of cellular phones is an example application where antenna-body
interactions must be modeled, where the transmitting antenna is close to the user’s head,
and it must be determined whether people using the device are exposed to hazardous levels
2
1.2. SENSING AND IMAGING OF THE BODY
of electromagnetic radiation or not. In order to investigate this topic, it is necessary to
assess the electromagnetic field induced inside (and around) the head of the user and to
compare this field with a proper safety level related to the electromagnetic risk. The
maximum exposure of human tissue to electromagnetic fields has been defined in terms
of Specific Absorption Rate (SAR) exposure [10], indicating the power absorbed per kg
of tissue.
The IEEE safety standard [10] defines the maximum permissible exposure (MPE) limits in
controlled and uncontrolled environments. For controlled environments the MPE limits is
given by 0.4 W/kg as averaged over the whole-body and spatial peak SAR not exceeding
8 W/kg as averaged over any 1 gram of tissue (defined as a tissue volume in the shape of
a cube). Exceptions of these limits are the hands, wrists, feet and ankles, where here the
spatial peak SAR shall not exceed 20 W/kg, as averaged over 10 grams of tissue (defined
as a tissue volume in the shape of a cube). Relaxed requirements are also defined for
uncontrolled environments.
Antennas play a paramount role in wireless personal communication devices, and the
accurate analysis and a comprehensive understanding of electromagnetic interactions
between antennas and nearby human body are essential for optimally designing modern
personal communication systems. Modern wireless devices, such as cellular phones and
laptops, often use antennas that are close to the human body (which acts as a scatterer).
Much effort has been dedicated to reducing the antenna radiation towards human body
and hence reducing the SAR value. For example, reduced SAR can be achieved by
mounting the antenna on the back side of the mobile terminal or profiling the handset [11].
The use of the planar inverted F-antenna (PIFA) has attracted many researchers, due to
reduced SAR, a simple low-profile structure, reasonable antenna performance, and halfspace radiation characteristics [9] and [12].
Thus, for accurate and efficient determination of the distributed electromagnetic field in
the body, accurate modeling of the head and antenna is required [13].
1.2
Sensing and Imaging of the Body
Non-invasive medical imaging techniques of the body are highly desirable, allowing visualization of the detailed internal structure and functional behavior of the body. Also,
one of the desired requirements of such imaging methods is to have real-time capability,
allowing true functional information of the body to be obtained, not just static images.
Computer aided tomography, magnetic resonance imaging and ultrasound imaging are
state of the art methods which can reliably and safely image internal structure of the
body and detect anomalies of the tissues.
1. INTRODUCTION
3
Here, some of these existing imaging methods are reviewed and existing drawbacks are
highlighted. Related to this thesis, ultrawideband imaging and sensing is introduced,
which in some cases is advantageous compared to existing methods.
1.2.1
State-of-the-Art Techniques
Computer aided tomography (CAT) is similar to the classical X-ray system except that
it images the subject at multiple angles and uses electronic sensors to digitally store the
signals. Cross-sectional imaging of the body is then possible by digitally processing the
series of rotated images to compute the specific attenuation of the volumetric medium,
which is performed with a computer [14]. Although CAT can provide 3D imaging, the
method is slow and requires the use of ionizing radiation.
An MRI (magnetic resonance imaging) scan is a radiology technique that uses magnetism,
radio waves, and a computer to produce images of body structures. The MRI scanner
is a tube surrounded by a giant circular magnet. The patient is placed on a moveable
bed that is inserted into the magnet. The magnet creates a strong magnetic field that
aligns the protons of hydrogen atoms, which are then exposed to a beam of radio waves.
This aligns the spins of protons in body, tissues producing a faint signal that is detected
by the receiver portion of the MRI scanner. The receiver information is processed by a
computer, and an image is produced. The image and resolution produced by MRI is quite
detailed and can detect tiny changes of structures within the body. However, the size and
cost of MRI equipment can be prohibitive in many cases, and the subject’s movement is
very limited.
Ultrasound is an imaging method used for many clinical applications, possessing many
of the advantages of CAT and MRI, but at a significantly lower cost [15]. Images from
ultrasound equipment are obtained by transmitting high frequency sound waves with a
transducer that is in direct physical contact with the tissue being imaged. The system
generates and transmits pulsed ultrasound waves in the 1-10 MHz frequency range and
receives reflected echo signals, from which a real-time image can be produced.
Ultrasonic imaging has the advantages of being safe, non-invasive, externally applied, and
real-time. However, direct contact with the skin is required, which may be inconvenient
or inappropriate for certain applications.
1.2.2
Ultra-wideband Microwave Imaging
More closely related to the work of this thesis, ultra-wideband (UWB) microwave imaging
and sensing techniques are being developed for a variety of medical and biological applications, such as early-stage breast cancer detection [16–19]. In breast cancer detection,
4
1.3. BODY AREA NETWORKING
the antenna-body interactions are used to sense the significant contrast in the dielectric
properties of normal breast tissue and malignant tumors, which provides a strong motivation for breast cancer detection with this technique. Another existing application of UWB
imaging techniques is the heart rate variability (HRV) imaging as stated and reviewed
in [20].
Through wall radar sensing is another interesting UWB microwave imaging technique,
consisting of radars that have the capability of localizing and tracking people in critical
environments or in hindered conditions. For example, people can be tracked through
walls for security operations or people trapped in collapsed buildings from earthquakes
or explosions can be localized [21]. UWB sensing also has applications in biomedicine for
remote monitoring of patients. In all the previous applications, the signaling should be
robust, secure, high-performance, and efficient.
Since structure, function, and state of the body must be inferred from UWB signals,
accurate electromagnetic models for the antenna and the part of the body being sensed
are required. Also, inverse scattering methods based on these models benefit from models
that are computationally efficient.
1.3
Body Area Networking
In body area networks (BANs), communicating nodes are situated in the clothes, on
the body or under the skin of the users. Applications of BANs include biomedicine,
emergency rescue, law enforcement, military, sports, and consumer electronics [22, 23].
Since these BAN nodes use antennas that are very close to the user’s body, the antennabody interactions must be taken into consideration in the design and manufacture of
these devices. An important step in the development and design of BAN devices is
the characterization of the path loss between two nodes on the body, requiring a detailed
characterization of the electromagnetic wave propagation and antenna behaviour near the
human body. Optimal design of BAN communications for peak performance, efficiency,
and security is only possible by accurately taking these effects into account.
Modeling efficiency is also important for developing BAN systems. For example, for network simulations, the model must be used repeatedly which can be very time consuming,
and a simple model is desirable. Also, the synthesis of optimal BAN antennas requires the
performance of the antenna to be computed repeatedly, perhaps 100s or 1000s of times,
requiring a computationally efficient model.
1. INTRODUCTION
1.4
5
Motivation of Research
To obtain useful techniques for modeling antenna-body interactions, it is required to
identify and develop methods that not only are accurate enough to capture the important
propagation mechanisms, but also are efficient as possible. This will give useful strategies
and tools that will allow more optimal design of systems where antennas are in close
proximity to the body. In addition, accurate modeling allows optimal antennas to be
designed that provide higher performance, efficiency, safety, and security of body sensing
and communications applications.
The applications that were selected for this thesis were chosen to cover two very different
aspects of body-antenna interactions. In the first application, measuring and tracking a
specific body function is of primary interest, and these interactions are to be enhanced
by the antenna design. In the second application, communication is taking place in the
presence of the body, and the body represents impairment to performance. Thus the
body-antenna interactions should be mitigated in this case.
For the sensing and tracking application, it was identified that significant work and
progress had already been made in heart-rate, respiration, and tumor detection. Instead of
considering these more developed applications, this thesis considers the unique application
of speech sensing, potentially improving synthetic speech production, speech pathology
and therapy, and speech recognition. The method may allow for completely silent voice
recognition and silent two-way communications, of interest for law-enforcement or military
applications.
For the communication application, the development of efficient and accurate nodes for
BAN communications was a natural choice that still requires significant research attention.
Although simple path loss models provide a very efficient modeling strategy, these methods
may be too simple for many applications. For example, consider array and diversity
studies where detailed characterization of phase is also important. Closed-form solutions
for the body employing a lossy cylinder model represent another useful modeling solution,
but these may also be too simple for some applications. Since for some applications,
accurate and efficient characterization methods are still lacking, improved methods for
modeling BAN channels are considered in this thesis.
Although there are powerful commercial packages like Computer Simulation Technology
(CST) or High Frequency Structure Simulator (HFSS) that have very high simulation
accuracy assuming the model of body is correct, the key propagation mechanisms are often
not well understood by applying these brute force techniques. In addition, computational
resources for direct numerical simulation can be very large. For example, modeling the
complete body and details of antenna can require 10s of GB of RAM and possibly a cluster
of computers. Simulation time may also be too slow inhibiting rapid network simulation
6
1.5. CONTRIBUTIONS OF THIS THESIS
or optimization of antennas. Finally, the price of software and licenses for the software
packages can be prohibitive.
It should be mentioned that direct measurement is an alternative to modeling, giving an
exact assessment of the system. The drawbacks of direct measurement, however, are that
it is costly, time consuming, and not always repeatable, due to several random factors
of subject and environment. Also, direct measurement is not ideal for optimization of
antennas, since only a very limited number of measurements can be done.
1.5
Contributions of this Thesis
First, this thesis identifies the speech sensing concept as an interesting application where
accurate and efficient modeling of antenna-body interactions is needed. In this area, the
following specific contributions were made:
1. A simplified FDTD model of the head-vocal tract is developed, which is efficient
enough to be simulated on a desktop PC. Application of this model allows the
important propagation mechanism of waveguiding in the mouth and throat to be
identified, suggesting that a hollow waveguide model can be developed for the speech
channel.
2. Building on the previous point, a mode-matching waveguide model is developed
for application to the speech channel. Comparing simulation times, the proposed
method is orders of magnitude more efficient than simulation with the FDTD solver.
The developed model is also appropriate to support future work in inverse scattering
of waveguides, such as what is needed for speech sensing.
3. The simple FDTD model developed in the thesis is used to optimize the placement
of an antenna that enhances coupling of propagating waves into mouth and throat.
4. A prototype speech sensing system is built and deployed. Measurements show that
the model and measurement agree for large movement of different parts of the speech
system.
5. A proof-of-concept speech recognition experiment is performed to further motivate
the idea of speech sensing and illustrate that such applications may be useful.
The second application which the thesis considers is modeling of body area networks,
where the focus is on the shadowing aspect of the body where communication is most
challenging. Contributions of the thesis in this area are as follows:
1. INTRODUCTION
7
1. The work in [24] for the circular cylinder model is extended to the case of arbitrary
polarization.
2. The work is further extended to cylinders of arbitrary cross section by development
of a surface-based method of moments solution which is likely to be important for
some applications and antennas.
3. A compact anechoic chamber is constructed and measurements with short monopoles
are performed and compared with simulations to illustrate the utility and accuracy
of the models. The result demonstrates that the simple models are appropriate for
rapid simulation of BANs, and that they can be used to develop optimized antennas
for BAN channels.
1.6
Organization of the Thesis
The content of the thesis is divided into 9 chapters, where Chapters 2-6 deals with
the speech sensing application, while Chapters 7-8 focus on BAN modeling. Chapter
2 provides details on existing speech sensing methods. Chapter 3 provides details on
the designing UWB antennas for speech sensing. Chapter 4 focuses on models that are
appropriate for sensing via volumetric scattering. Chapter 5 gives the experimental and
simulation result of the speech sensing. Chapter 6 describes the mode matching technique
used for analysis the modes propagation inside the vocal tract. Chapter 7 presents the
numerical methods used for body area network modeling. Chapter 8 provides details on
models of the human torso, BAN simulations, and comparison of the simulations with the
direct measurement. Chapter 9 summarizes the thesis and provides directions for future
work.
2. SPEECH SENSING AND UWB
9
Chapter 2
Speech Sensing and UWB
Humans are capable of producing and understanding normal as well as whispered speech
in quiet environments at remarkably low signal levels. Most people can also understand a
few unspoken words by lip-reading. This chapter reviews conventional methods for speech
sensing, and introduces and motivates the idea of UWB speech sensing.
2.1
Existing Speech Sensing Techniques
Obtaining accurate and reliable speech signals is necessary for humans to communicate
and exchange information with each other. Automatic sensing and analysis of speech
using computers is useful in many applications, including speech recognition, speech
pathology, and language training. The vast majority of research has developed techniques
for passively detecting speech parameters from acoustic signals, as is done by human
hearing organs. Conventional speech and acoustic transducers, such as microphones,
detect speech signals by perceiving the motion of air particles when sound is spread via
an air medium [25, 26].
An alternative method for sensing speech parameters is by active radar techniques. A
millimeter wave (MMW) Doppler radar with grating structures for the application of
detecting speech signals was presented in [27, 28]. Similar to the work in this thesis, the
MMW Doppler radar uses the principle of detection of the change of various parts of the
face and neck to detect speech. Specifically, in [28], the transmitter generates a short
pulse train of four to six cycles, lasting a few nanoseconds, that radiates from monopole
antennas. A range gate is delayed, relative to the start of the transmitted pulse, by a fixed
time of a few nsec and drives a diode sample gate that detects the reflected EM waves
received by a nearby receiver antenna and the receiver signal is electronically filtered to
remove reflected signals from non moving or slowly moving interfaces.
10
2.1. EXISTING SPEECH SENSING TECHNIQUES
A silent speech interface (SSI) which detects the speech when an audible acoustic signal
is unavailable is introduced in [29]. These sensors may be used as an aid for the speechhandicapped, or as part of a communications system operating in silence-required or high
background noise environments.
A Doppler acoustic radar was presented in [30], consisting of a high-frequency ultrasound
emitter and a receiving acoustic transducer that is matched in frequency to the transmitter. The ultrasound tone emitted from the sensor is reflected from the speakers face
and undergoes a Doppler frequency shift that is proportional to normal velocity of the
portion of the face that it is reflected from. The Doppler spectrum of the reflected signal
thus contains information about the motion of the speakers cheeks and lips, and possibly
internal features like the tongue, teeth, etc.
A non-acoustic voiced speech sensor was presented in [31], which detects small perturbations in the dielectric properties of neck during the glottal cycle. Its operation
depends on measuring the relative permittivity of the glottis by employing an equivalent
capacitor model, in which case the relative permittivity is a direct function of the measured
capacitance.
Another interesting speech sensing technique is that one developed by the CALL research
at the Center for Speech Technology (CTT) [32]. This technique focuses on building a
Virtual Language Tutor, using an animated talking agent which serving as a conversational partner, teacher and an untiring model of pronunciation for language learning. The
aim of the system is to recognize the utterances of the user and to detect and recognize
deviations between the model pronunciation and the pronunciation of the user. In this
system, the speaker articulatory model must adapt to each new user to allow for correct
articulatory inversion and to provide the user with visual feedback that corresponds to
his or her anatomy. The adaptation can be done using medical imaging, such as Magnetic
Resonance Imaging (MRI), to exactly scale the articulatory model to a new user, but it
is of course unrealistic that every user be scanned with MRI before being able to use the
system.
These previously developed techniques have potential limitations. Traditional acoustic
sensing is passive, making it difficult to reconstruct the state of speech organs. In addition,
some sensors require that the transmit/receive transducer be placed in direct contact with
the talker’s skin in a suitable location [30, 31] which may be unpleasant to the user and
inhibit natural motion of speech organs.
In this work, UWB [33] speech sensing is investigated, whose aim is to sense and track the
process of human speech, obtaining information about the position and movement of lips,
tongue, glottis, etc., potentially improving synthetic speech production, speech pathology
and therapy, and speech recognition. The method may allow for completely silent voice
recognition and silent two-way communications, of interest for law-enforcement or military
11
Time domain
Frequency domain
−40
1
−50
−60
Amplitude, dBm
Amplitude
0.5
0
−0.5
−70
−80
−90
−100
−110
−1
−0.2
0
0.2
Time, nsec
−120
0
20
40
Frequency, GHz
Figure 2.1: UWB monocycle pulse both in the time and frequency domains
applications.
2.2
Ultra-Wideband Technology
This section briefly introduces UWB technology, which is used for the speech sensing
applications. UWB signals are based on the use of very narrow monocycle Gaussian pulses,
typically on the order of nanoseconds, as a basic signal structure. These pulses, being
short in the time domain, give rise to spectral content covering a very wide bandwidth
in the frequency domain, as shown in Figure 2.1. Because UWB signals consist of subnanosecond electromagnetic pulses, the pulses can penetrate body tissues and give good
spatial resolution.
The monocycle’s pulse width determines the center frequency and the bandwidth. The
Gaussian function in the time domain is given by
v(t) =
t −( t )2
e τ ,
τ
(2.1)
where τ is a time decay constant that determines the monocycle’s duration and t is time.
UWB signals are generally defined to be radio signals with a fractional bandwidth greater
than 0.2 or which occupy more than 500 MHz of spectrum. The fractional bandwidth ∆f
is defined as
12
2.2. ULTRA-WIDEBAND TECHNOLOGY
UWB EIRP Emission Level, dBm
−40
−45
−50
10.6 GHz
−55
−60
3.1 GHz
Indoor limit
Outdoor limit
Part 15 limit
−65
−70
−75
−80
0
1
10
10
Frequency, GHz
Figure 2.2: FCC spectral mask for UWB indoor communication systems
∆f =
2(fH − fL )
,
(fH + fL )
(2.2)
where fH and fH are the highest and lowest frequencies in the transmission respectively,
measured at −10 dB below the peak emission point.
Because UWB radios share the environment with other radio systems, causing interference
to each other as well as existing services, the Federal Communication Commission (FCC)
in the USA has set conditions that limit the interference from UWB radiators to other
radio systems, or specifically that EIRP in any 1 MHz band is limited to −41.3 dBm [34].
To allow government and industry to conduct UWB testing, frequency spectrum from
3.1 GHz to 10.6 GHz was allocated for communications use below this specified power
level, seen in Figure 2.2, and this represents about 7.5 GHz bandwidth operating at
−41 dBm/MHz for biomedical applications.
The organizations involved in the regulation of UWB in Europe are ETSI (European
Technical Standard Institute) and Electronic Communications Committee (ECC) of the
CEPT ( European Conference of Postal and Telecommunication Administration). These
institutions conduct UWB compatibility and spectrum sharing studies and advise regulatory mechanisms. The technical requirement for the devices using UWB technology in
bands below 10.6 GHz permitted under current ECC requirements is depicted in Figure
2.3 [35]. The depicted limits are for indoor UWB communications.
13
UWB EIRP Emission Level, dBm
−40
−50
−60
−70
−80
−90 0
10
1
10
Frequency, GHz
Figure 2.3: ECC spectral mask for UWB indoor communication systems in Europe
2.3
UWB Sensing
UWB signals are attractive for biomedical sensing applications, due to the high resolution
afforded by narrow pulse widths, making them suitable for remote sensing of vital signals
such as heart rate, as well as detecting anomolies in the body such as tumors. In addition
to UWB medical applications, UWB through wall radar can be used to detect the presence
of people with heart beat and breathing rate detection. Recently, work related to medical
imaging using the human phantom and also actual human body within the spectrum
mask approved by FCC has been demonstrated to illustrate the penetrative nature of
sub-nanosecond pulses [36]. This section describes some existing applications of UWB
that are related to the work in this thesis.
2.3.1
Heart Rate Sensing
Recently, research has appeared on wireless measurement of heart rate variability (HRV)
[20,37,38] using UWB. Such systems are potentially applicable for detecting irregularities
in heart rate, based on detecting the mechanical motion of the heart. HRV can give clues
on the medical condition of the patient which may be connected to a database indicating
the level of support that the patient requires. HRV is also useful for disaster rescue
scenarios, where people can be detected who are buried under building obstructions or
in an avalanche. If a person is motionless, the detection can be performed using person’s
heart and thorax beats and then suitable aid may be given [39].
14
2.3.2
2.4. UWB SPEECH SENSING
Tumor Detection
Bond [40] reported that it is possible to use microwave imaging signal processing techniques on a UWB radar system to detect early breast cancer. Prior published work [41]
tends to use lower microwave frequencies below 3 GHz which does not operate within the
FCC’s mask.
Recently, UWB microwave imaging has been extensively studied in the detection of early
breast cancer [16]. The significant contrast in the dielectric properties of normal breast
tissue and malignant tumors provides a strong rationale for breast cancer detection with
low power microwaves [19]. A UWB pulse is transmitted to illuminate the breast by
a transmitting antenna. The backscatter signals are received by each antenna in the
receiving array and the array signal is employed to locate the tumor [42].
2.3.3
UWB Through Wall Imaging
See-through-wall (STW) technology is another interesting application of UWB technology
[43, 44]. The STW is based on the transmission and reception of UWB pulses in the time
domain using synthetic aperture radar (SAR). This type of imaging can be utilized in
rapid detection of humans behind walls, and rescue operations in avalanche and collapsed
buildings, through acquiring relatively high-resolution images. STW radar has the ability
to detect targets through relatively high-density materials such as concrete blocks, brick,
wood, and fiberglass.
2.4
UWB Speech Sensing
In this thesis, it is proposed to use UWB signals for the tracking of speech production.
This type of sensing is accomplished by a single UWB antenna in the monostatic radar
configuration, where UWB signals are transmitted from the antenna, interact with the
face, mouth, and throat, and are reflected and measured by the UWB antenna. To do
this, a single UWB antenna will be designed and fabricated taking into consideration the
weight and the orientation of the antenna since it will be attached to helmet to be worn
by the subject doing the measurements. In addition, a head model that approximates the
true human head will be developed to study the interaction of the antenna with the head
for certain positions of the tongue and lips.
Not only is simulation of UWB speech sensing performed in this work, but also direct
measurement is also carried out. Measurements are accomplished by a single UWB
sensor in the monostatic radar configuration in Figure 2.4(a), where UWB signals are
15
Figure 2.4: Block diagram of the network-analyzer based measurement system: (a) block
diagram (b) photo of antenna fixture
transmitted from the antenna, interact with the face, mouth, and throat, and are reflected
and measured by the UWB sensor in the reflection coefficient Γ. The antenna is fixed to
be approximately 2 cm in front of the mouth using the headset in Figure 2.4(b), consisting
of a jaw rigidly connected to a hard hat. To avoid unwanted reflections, the jaw is made
of wood and the antenna is fastened to the jaw with nylon screws.
The reflection coefficient Γ is obtained by connecting the UWB sensor to Port 1 of a
Rohde&Schwarz VNB20 vector network analyzer, with a frequency sweep of 101 points
over the range of 500 MHz to 10 GHz, a resolution bandwidth of 100 kHz, and transmit
power 10 dBm. Note that in this work, only the points from 3 GHz to 10 GHz are
employed to be compatible with the mask for UWB.
Time variation of the UWB response is captured using an external trigger driven by a
digital pattern generator (sync unit) that generates a burst of pulses with a 20 ms period
spanning an arbitrary acquisition time. Calibration is performed to remove the effect of
the cable up to the UWB antenna. The response is stored on a PC, where Γkn refers to
the complex reflection coefficient at frequency index k and time point n.
2.5
Summary
This chapter has reviewed a number of candidate techniques used for speech sensing, and
attractive features of UWB sensing were identified, such as the high temporal resolution,
real-time tracking information, and no need for direct contact with the user. The hardware setup for speech sensing was also introduced, which will be modeled and used in
subsequent chapters.
3. UWB ANTENNA DESIGN FOR SPEECH SENSING
17
Chapter 3
UWB Antenna Design for Speech
Sensing
Tracking of speech production requires transmitted UWB signals to interact with the
mouth and throat and the resulting scattered waves to be measured. The primary
objective of this chapter is to design and investigate miniaturized and compact UWB
antennas. Planar monopole (UWB) antennas having a broadband operation range (3.110.6 GHz) with better than 10 dB return loss are also studied and simulated for the
purpose of speech sensing applications.
3.1
UWB Antenna Requirements
UWB technology has become a primary candidate for short-range high-speed wireless
communication systems, but there are many challenges in UWB antenna design. One
primary challenge is achieving the wide impedance bandwidth while still maintaining high
radiation efficiency, where UWB antennas are required to attain a fractional bandwidth
that is greater than 100%. Also, high radiation efficiency and stability are required for
UWB applications [45]. Other challenges of the UWB antenna design include the compact
size of the antenna size and low manufacturing cost. In addition, for the speech sensing
application, the UWB antenna is attached to a helmet which will be worn by a subject,
and therefore the antenna should be lightweight. The requirements suggest that a planar
structure is attractive for the speech sensing application.
18
3.2
3.2. TYPES OF UWB ANTENNAS
Types of UWB Antennas
Numerous antenna geometries have been proposed and developed for operation in the
UWB range from 3 to 10 GHz. Although frequency independent antennas, such as
biconical, spiral and log periodic antennas offer broadband and UWB behaviour, these are
often bulky, non-planar structures. Planar UWB antennas are often more convenient, due
to compact size, non-dispersive (radiate similar waveforms in all directions) [46] and ease
of integration with other electronics. Among these antenna configurations is the low-cost
knight’s helmet shape double-sided PCB antenna shown in Figure 3.1. This antenna was
fabricated using 1.6 mm FR4 substrate and has a return loss of better than 10 dB [46].
Another type of planar antenna is the double-sided printed bow-tie antenna [47] shown
in Figure 3.2. The thickness and relative permittivity of the used substrate are 1.27 mm
and 6.15. The proposed antenna satisfies the requirement of return loss better than 10
dB in the range of 3.1 − 10.6 GHz.
A truncated rectangular patch and a trident shaped feeding strip for bandwidth enhancement is shown in Figure 3.3 [48]. The bandwidth enhancement is due to much more
vertical electric current achieved in the patch through the branches resulting in much
more regular distribution of magnetic current in the slot. Also, the cross polarization is
reduced by eliminating the horizontal electric current in the patch. This antenna was
etched on a substrate of height h = 0.813 mm and r = 3.38. The antenna radiates
using a rectangular slot of width W1 and resonant length L1 . The obtained results show
an omnidirectional radiation pattern and a bandwidth covering the whole FCC defined
UWB frequency band.
An ice cream cone antenna shown in Figure 3.4 was fabricated on Rogers RT Duroid
5880 substrate [49]. The best antenna performance was obtained with board dimensions
34 mm × 17.65 mm with FR4 substrate with a dielectric constant of 4.4. This antenna
Figure 3.1: Low cost UWB antenna designed
Figure 3.2: Double sided printed bow tie antenna
Figure 3.3: Truncated rectangular patch
19
20
3.3. BROADBAND MONOPOLE ANTENNA
Figure 3.4: Ice cream cone antenna
shows a VSWR between 1 to 2 for frequencies 3.1 GHz to 5.8 GHz in the band of 6.5 GHz
to 9 GHz.
In previous work, significant effort has been invested to find the planar shape providing
the widest operational bandwidth. Consequently, a number of planar monopoles with
different geometries have been experimentally characterized [50–52] and automatic design
methods have been developed in an attempt to achieve the optimum planar shape [53].
Moreover, other strategies to improve the impedance bandwidth which do not involve a
modification of the geometry of the planar antenna have been investigated, including the
use of feed gap optimization [54] and multiple feeds [55].
Initially, selection of the optimal UWB antenna for speech sensing is a difficult task, since
for near-field operation, the optimal “pattern”is not well defined. It is expected that
the ideal antenna has a near-field distribution that excites fundamental electromagnetic
modes affected by the features to be sensed. However, since the structure of these fields
is not well understood at the outset, a simple antenna design should be chosen that is
easily fabricated. Additionally, it is expected that the antenna should possess a symmetric
shape relative to the features being excited, which in this case is the mouth and throat.
Therefore, the broadband circular monopole was chosen for the investigation of bodyantenna modeling for the speech sensing application.
3.3
Broadband Monopole Antenna
Figure 3.5 depicts the design dimensions of the circular monopole used in this work, which
is to be fed with a 50 Ω microstrip feed line and fabricated using Rogers 4003C substrate
21
Figure 3.5: Microstrip circular antenna
having a thickness of h = 1.524 mm and a relative permittivity of r = 3.5. The design
was manually optimized using Agilent Advanced Design System (ADS) to obtain a target
reflection below -10 dB in the 3 to 10 GHz range. The width of the microstrip feed line
is fixed at W1 = 3.6 mm to achieve 50 Ω impedance. On the other side of the substrate,
the conducting ground plane with a length of L1 = 20 mm only covers the section of the
microstrip feed line. Optimization with Agilent ADS to minimize return loss in the range
of 3 to 10 GHz yielded r = 12.5 mm, g1 = 0.6 mm, g2 = 2 mm and l1 = 20 mm.
The simulated reflection coefficient of the designed disk monopole antenna is plotted in
Figure 3.6, which shows return loss better than 10 dB in the frequency range of 3 − 10
GHz, which is suitable for the sensing application.
There is an important phenomenon in Figure 3.6, which is that the first resonance occurs
near 3 GHz. At this frequency one quarter wavelength (25 mm) just equals the diameter
of the disc. Thus, this resonant frequency is mostly determined by the circular disc
dimension and is only slightly changed by the size of the ground plane. Figure 3.6 also
shows that the circular disc is capable of supporting multiple resonance modes, where the
higher order modes (f2 , f3 ...fn ) are the harmonics of the fundamental mode of the disc.
At higher order modes, the wavelengths satisfy the relation
2r =
nλn
,
4
(3.1)
where n is the mode number. These higher order modes are closely spaced and overlapping
and they lead to the UWB response [56].
The electromagnetic behavior of the antenna can be further understood by observing the
22
−5
−10
−20
S
11
(dB)
−15
−25
−30
−35
2
4
6
8
Freq (GHz)
10
12
Figure 3.6: Reflection coefficient of disk monopole antenna
current distributions and the radiation patterns. The typical current distributions on
the antenna close to the resonance frequencies are plotted in Figure 3.7. Figure 3.7(a)
shows the current distribution at the first resonance at 3 GHz, while 3.7(b) shows that
the second resonance of 5 GHz. Figures 3.7(c) and (d) illustrate two more complicated
current patterns at 8.5 GHz and 11.5 GHz, corresponding to the third and fourth order
harmonics, respectively.
In Figure 3.8, the 3D radiation patterns of the circular patch antenna are plotted. As
we can see, the pattern is similar to the radiation pattern of the fundamental mode of
a dipole antenna at the low UWB frequency range. As the frequency increases toward
the second, third and the fourth harmonics, the pattern changes its shape with increasing
gain. On one hand, the variation of the pattern with frequency may be undesirable since
it distorts the signal transmitted from the element. On the other hand, highlighting
different features at different frequencies may be provide a useful diversity effect.
One of the undesired characteristics of the broadband monopoles is that there are two main
beams, normal to the substrate on the front and back sides of the antenna. For biomedical
sensing applications, we should ideally only have a single beam, since reflections from
equipment or furniture in the back direction may corrupt the results. A single main beam
can be accomplished by placing a reflecting plane at a distance of λ/4 behind the antenna
as shown in Figure 3.9 (a), allowing the back radiation beam to be significantly reduced.
Since such a wide band must be covered, the distance will not be optimal and possibly
multiple reflectors must be used.
If a 3 dB loss in power can be tolerated, absorber could also be placed behind the antenna
to absorb the back radiation beam, as shown in Figure 3.9 (b), which would provide a
Figure 3.7: Simulated current distributions of the circular disc antenna
Figure 3.8: 3D radiation patterns of the circular disc monopole antenna
23
24
Figure 3.9: Back radiation antenna canceling
very broadband solution for removing the back lobe. A modified circular patch antenna
with a reflecting ground plane was investigated by placing an infinite plane at distance
18.75 mm behind the antenna in the simulation. Figure 3.10 depicts the resulting input
reflection coefficient and Figure 3.11 shows the simulated radiation pattern at 6 GHz.
Although the back lobe has been removed, a potential problem is that the variability of
the pattern with frequency is significantly increased, which may be undesirable. Although
more work can be done in this area, the simple two-beam antenna is used in this work,
and hence we do not consider the back radiation problem any further in this chapter.
0
Patch−reflector
Patch
−5
S
11
(dB)
−10
−15
−20
−25
−30
−35
2
4
6
8
Freq (GHz)
10
12
Figure 3.10: Disk monopole antenna return loss with reflector
25
Figure 3.11: 3D radiation patterns of disk monopole antenna with reflector
3.3.1
Optimization of Antenna Parameters
The important parameters which affect the antenna performance have been analyzed to
derive some design rules and achieve optimal performance. These parameters are feed
gap g1 , ground plane width W and ground plane length L1 .
Feed Gap g1
The first parameter is the feed gap g1 . As shown in Figure 3.12, when r is fixed at 12.5
mm, L1 at 10 mm and W at 47 mm, the performance of the disc monopole is quite
sensitive to g1 . It can be seen that the return loss curves have similar shape for the four
different feed gaps, but the 10 dB bandwidth of the antenna varies significantly with the
change of g1 . The optimal feed gap for maximum 10 dB bandwidth is found to be at
g1 =0.3 mm.
Ground Plane Width W
Another design parameter influencing the antenna operation is the width of the ground
plane W . The simulated return loss curves with r = 12.5 mm, L1 = 10 mm and optimal
feed gap g1 of 0.3 mm for different widths W are presented in Figure 3.13. The effect
of different dimensions of the finite ground plane is a change in the exact position of
resonances and the efficiency of the antenna. A sufficiently compact design with good
performance is achieved for W = 36.5 mm.
26
0
−5
−10
S
11
(dB)
−15
−20
g = 0 mm
−25
1
g = 0.3 mm
1
−30
g = 0.6 mm
1
g = 0.8 mm
−35
1
g = 1.1 mm
−40
1
4
6
8
Freq (GHz)
10
12
Figure 3.12: Return loss for different feed gaps
0
W = 35 mm
W = 36.5 mm
W = 38 mm
W = 40 mm
−5
S
11
(dB)
−10
−15
−20
−25
−30
−35
2
4
6
8
Freq (GHz)
10
12
Figure 3.13: Return loss for different widths of the ground plane
27
5
r = 11 mm
r = 12.5 mm
r = 13 mm
r = 25 mm
0
−5
S
11
(dB)
−10
−15
−20
−25
−30
−35
−40
2
4
6
8
Freq (GHz)
10
12
Figure 3.14: Return loss for different radius
Ground Plane Length L1
It is found that the performance of the antenna is almost independent of the length L1
of the substrate. This is understandable by inspecting current distributions in Figure
3.7, or that the current is mostly distributed on the top edge of ground plane. For this
application, L1 = 20 mm is chosen to maintain a compact size.
Circular Disk Radius r
It was explained previously that the circular patch is a resonant structure with multiple
modes, where the lowest resonance occurs when the disk diameter is approximately one
quarter wavelength, similar to a monopole over a small ground plane. Figure 3.14 shows
the simulated return loss for different dimensions of the disc. It can be seen that the
ultra wide impedance bandwidth can be obtained by all of these designs, and that r just
controls the minimum frequency of the element.
3.4
Modified Broadband monopole
Figure 3.7 shows that the current/field is mainly distributed along the edge of the patch.
This is an important phenomenon that the performance of the circular patch antenna
is independent of the central part of the radiating part, and hence cutting this part to
form a ring monopole or cutting a strip to form a slot circular monopole can still result
in an ultra wide bandwidth. Cutting out parts of the original broadband monopole has
28
3.4. MODIFIED BROADBAND MONOPOLE
Figure 3.15: Slotted disk monopole antenna
two advantages: there will be less metal which means less multiple scattering near the
face and opening the patch allows more possibility of fields coupling to the mouth (more
radiating edges).
3.4.1
Slotted Disk Monopole Antenna
Figure 3.15 shows a schematic of the slotted disk monopole antenna, which consists of
a printed disc with a rectangular slot. The disc radiator has the same dimension as
the orginal design, but now a slot is placed 5.4 mm away from the disc center, whose
dimensions are 11.58 × 2.35 mm2 . The width of the microstrip feed line is fixed at
W1 = 3.6 mm to achieve 50 Ω impedance. On the other side of the substrate, the
conducting ground plane with a length of L1 = 20 mm only covers the section of the
microstrip feed line.
The simulated return loss is illustrated in Figure 3.16. As a result, the 10 dB bandwidth
is remarkably extended from 3 to 12 GHz.
3.4.2
Circular Ring Monopole
The ring microstrip antenna is a useful shape to be considered as a modified shape of
UWB monopole antenna because of its high radiation efficiency. The presence of edges
at the inner and outer radii causes more fringing than in the case of a circular microstrip
antenna, where the fringing occurs only at the outer edge, and this implies more radiation
from these edges. Also, the bandwidth achieved by ring antenna for certain value of the
29
−5
Slot patch
Patch
−10
−20
S
11
(dB)
−15
−25
−30
−35
2
4
6
8
Freq (GHz)
10
12
Figure 3.16: Slotted disk monopole antenna return loss
radii is often higher than that of a circular patch [57]. Further, the size of an annular ring
for a given mode of operation and a given frequency is smaller than that of the rectangular
or circular counterpart [57].
Circular ring monopoles use the fact that the current is mainly distributed along the edge
of the disc monopoles as shown in Figure 3.7. This implies that the performance of the
antenna is independent of the central part of the disc, and hence cutting this part to
form a ring monopole can still result in an ultra wide bandwidth [58]. A circular ring
monopole shown in Figure 3.17 has the same dimension as the orginal design but now with
inner radius of r2 = 5.8 mm and the same other parameters as the circular disc antenna
described in Section 3.3. Figure 3.18 shows the simulated return loss of the designed
circular ring monopole shown in Figure 3.17 with Rogers substrate of thickness 1.524 mm
and a relative permittivity 3.5. The result shows that the 10 dB impedance bandwidth is
very similar to the original design.
3.4.3
Circular Patch with Reflector
Figure 3.19 depicts the schematic views of the proposed UWB antenna structures in
planar technology including the top and bottom metal layers. The radiator is made up
of a circular patch element with radius r1 = 12.5 mm. A 50 Ω microstrip line with
W1 = 3.6 mm width and l1 = 17.6 mm length is used as the input line to excite the
circular patch element. On the bottom side of the substrate, the finite ground plane is
modified to include a ring that surrounds the circular patch, forming a crescent-shaped
gap between the metal in the top and bottom layers. This design was investigated with
r1 = 12.5 mm, r2 = 22.3 mm with its center 8 mm away from the radiator center and
30
3.4. MODIFIED BROADBAND MONOPOLE
Figure 3.17: Microstrip circular ring antenna
−5
Ring patch
Patch
−10
−20
S
11
(dB)
−15
−25
−30
−35
2
4
6
8
Freq (GHz)
10
12
Figure 3.18: Microstrip circular ring antenna return loss
31
Figure 3.19: The designed directional UWB antenna
r3 = 27.2 mm with its center at the top of the radiator center.
Figure 3.20 shows the input reflection coefficient of the directional UWB antenna as
obtained from ADS. The return loss in some frequency ranges are better than 15 dB
between 3 GHz and 10 GHz, which is about 5 dB better than the normal circular disc.
The radiation patterns of the modified circular disc UWB monopole antenna at different
frequencies are shown in Figure 3.21. These figures show that the radiation pattern is
more directive especially at higher frequencies.
−5
Guided patch
Patch
−10
S
11
(dB)
−15
−20
−25
−30
−35
−40
2
4
6
8
Freq (GHz)
10
12
Figure 3.20: Return loss of the guided circular disc monopole antenna
32
3.5. VIVALDI ANTENNA
Figure 3.21: 3D radiation patterns of the guided circular disc monopole antenna
3.5
Vivaldi Antenna
The Vivaldi antenna [59] is a planar traveling wave antenna with endfire radiation widely
used in wireless and radar applications due to broad bandwidth, low cross polarization,
and highly directive patterns [60–62].
The basic shape of the Vivaldi antenna is shown in Figure 3.22 which consists of a
microstrip feed line, transition from the feed line to the slotline and the radiating structure.
The radiating slot is usually exponentially tapered according to the following relation in
the x − y plane:
y = uepx − uep + s/2,
where
u=
W/2 − s/2
.
epL − ep
(3.2)
(3.3)
The coefficient p is the curvature parameter, s is the slotline width, W stands for aperture
width at the end of the taper, and L is the taper length.
The Vivaldi antenna requires a transformation from the microstrip line to slot line which
feeds the antenna. The slot line starts to radiate when the width is equal to s = λ2o .
33
Figure 3.22: Vivaldi antenna
Therefore, the wide end of the exponential taper approximately defines the lowest possible
frequency, while the width of slotline at the taper throat defines the high frequency
cutoff [63]. In order to achieve endfire radiation, the phase velocity vph of the traveling
wave has to satisfy vph ≤ c.
If the phase velocity exceeds c, the main beam in the radiation pattern is split and the
radiation is no longer endfire. The maximum directivity occurs in the case of a total phase
increase of 180◦ along the antenna structure, caused by the dielectric slowing down the
traveling wave. If the phase shift is higher than 180◦ , main beam will move away from
the endfire direction [64].
In the antenna design in this work, the antenna feed begins with an SMA connector with
a nominal impedance of 50Ω, which is connected to a 50Ω microstrip line near the edge
of the antenna board. Before the signal reaches the microstrip to slot line transition,
impedance of the microstrip line must be transformed to 100Ω to match the 100Ω slot
line, ensuring minimum mismatch over the UWB range. A linear taper is used in this work
for the impedance transition. The antenna parameters were optimized for fabrication on
Rogers R4003C substrate, resulting in the response shown in Figure 3.23.
The far-field radiation patterns of the antenna were also calculated using ADS, which are
shown in Figure 3.24 for the frequencies 3, 5, 6, and 7 GHz. The antenna shows directive
properties with an average front-to-back ratio which is greater than 13 dB across the
whole band, making it a good candidate for microwave imaging applications. Due to the
infinite substrate assumed in the ADS simulator, the main beam looks like it splits at the
edge, which is just an artifact of the simulator.
34
3.5. VIVALDI ANTENNA
0
−5
S
11
(dB)
−10
−15
−20
−25
−30
−35
−40
2
4
6
8
Freq (GHz)
10
12
Figure 3.23: Vivaldi antenna return loss
Figure 3.24: Vivaldi 3D radiation patterns at (a) 3, (b) 5,(c) 6 and (d) 7 GHz
35
0
−5
ADS simulation
−10
FDTD Simulation
S11 (dB)
−15
−20
−25
−30
−35
Measurement
(headset worn)
Measurement (antenna only)
−40
−45
2
Measurement
(in headset)
3
4
5
6
7
Frequency (GHz)
8
9
10
Figure 3.25: Simulated and measured reflection coefficient of the broadband monopole
3.6
UWB Antenna Measurement
All of the UWB antennas considered in this section are suitable candidates for the speech
sensing application. For simplicity, the UWB monopole antenna described in Section 3.3
will be used. Figure 3.25 plots the simulated input reflection coefficient S11 of the antenna,
performed with Agilent ADS (infinite substrate) and FDTD (finite substrate), indicating
that the target reflection below -10 dB is met.
Figure 3.25 also shows S11 of the fabricated antenna measured with a network analyzer in
an indoor laboratory environment. It is expected that reflections from walls and furniture
can cause deviations in the measured S11 values from simulation. Error due to multipath
was partially removed by averaging over 150 snapshots of S11 taken over a 30 s acquisition
time (20 ms per sweep), where the antenna was slowly rotated in both azimuth and
elevation during this time. This rotation of the antenna causes the multipath to come
from different angles, and it is expected that this random component should average
out leaving S11 that is due to static reflections from the antenna only. It is observed
that the exact shapes of the S11 curves is somewhat different between measurement and
simulations, but that the approximate positions of nulls and peaks are quite similar.
The other two curves in Figure 3.25 show the reflection when the antenna is mounted in
the prototype headset described in Section 2.4, with or without a human subject wearing
it, where again a measurement with slow rotation of 30 s was performed. The result
indicates that the headset and subject change the response of the antenna, but this does
not significantly reduce the matching efficiency of the antenna.
36
3.7
3.7. SUMMARY
Summary
This chapter has investigated a number of candidate UWB antennas and their suitability
for the speech sensing application. Although traditional multi-octave antennas, such as
log-periodic structures and horns have the desired radiation characteristics, these are
too bulky for the present application. Planar microstrip antenna, including broadband
monopole antenna and Vivaldi antenna were designed, optimized, and simulated. Although the Vivaldi antenna has perhaps the most suitable pattern, exhibiting a single
main beam and small back lobe, mounting of the antenna is somewhat problematic for the
speech sensing application. From the standpoint of matching efficiency, all investigated
antennas are sufficient for the goals of this work, and the simple circular monopole is
chosen due to its compact size and ease of fabrication and mounting.
37
4. SPEECH SENSING: FULL-WAVE MODELING
Chapter 4
Speech Sensing: Full-wave Modeling
In this chapter, a detailed FDTD model of the vocal tract is first developed for the purpose
of simulating and optimizing the speech sensing application. To do this, the MakeHuman
project [65] is used to generate a 3D model of the head surface and neck. The vocal tract,
which is the main part of speech production, is created in the model using MRI images.
In addition, a simplified flat-face model and one-dimensional (1D) dielectric layer model
are introduced. The interaction of the UWB antenna with the head and vocal tract using
the detailed FDTD model will be considered in the next chapter.
4.1
Detailed Head, Vocal Tract Model
First, the most detailed model for the human head and the vocal tract is presented. This
model is used as the reference model for the simplified models and is also employed to
optimize placement of the UWB antenna for speech sensing.
4.1.1
Electrical Properties of Tissue
The electrical properties of lossy tissues can be described by the complex permittivity,
which is related to conductivity [66], [67]. Complex permittivity is given as
0
00
ˆ = − j ,
0
(4.1)
00
where is the real permittivity of the material, and is associated with material losses,
given by
00
= σ/(0 ω),
(4.2)
where σ is the conductivity (S/m), 0 = 8.854 × 10−12 F/m is the permittivity of free
space, and ω the angular frequency of the field.
38
4.1. DETAILED HEAD, VOCAL TRACT MODEL
Table 4.1: Electrical properties of tissues at different frequencies [66]
3 GHZ
6 GHZ
10 GHZ
εr
σ(s/m) εr
σ(s/m) εr
σ(s/m)
Skin
Fat
Muscles
Tongue
37.45
5.2239
52.058
51.859
1.7406
0.13004
2.1421
2.2377
34.946
4.9367
48.217
47.506
3.8912
0.30623
5.2019
5.4875
31.29
4.6023
42.764
41.484
8.0138
0.58521
10.626
11.077
The dielectric properties of tissue are highly dispersive (frequency dependent) [68]. The
electrical properties of skin, fat and muscles at 3, 6 and 10 GHz are shown in Table 4.1,
which will be used in the subsequent models.
4.1.2
Head/Neck Surface Modeling
Figure 4.1 depicts a detailed model, where a human head was generated using a threedimensional (3D) mesh taken from the MakeHuman project [65] and subsequently edited
with Blender 3D computer animation software.
An armature (which is a non-rendered device, also called a bone) is used to deform the 3D
mesh for an open and closed mouth. Here, the armature is used to control the movement
of the lower jaw muscles as shown in Figure 4.2.
Figure 4.1: Head model for FDTD simulations of the human vocal tract
39
Figure 4.2: Controlling the movement of the lower jaw muscles
To assign a portion of a mesh to a bone, the Blender weight painting process is used
which determines the level of influence that the bone has on the mesh. The way this is
done is by parenting the mesh to the armature as shown in Figure 4.3. In this figure, the
red parts represent a high influence while the blue parts represent less influence that the
bone has on the mesh.
Figure 4.3: Blender weight painting process
40
4.1. DETAILED HEAD, VOCAL TRACT MODEL
Mouth Opened
Mouth Closed
Figure 4.4: MRI images showing vocal tract shape for open and closed mouth
4.1.3
Internal Vocal Tract Model
Although the MakeHuman head already has a posable jaw and tongue, it was required to
create a model of the internal vocal tract in Blender and connect it to the mesh. The vocal
tract was modeled using MRI movies [69] for an open and closed mouth. A Matlab code
was written to extract the images for the vocal as shown in Figure 4.4. These images were
loaded in Blender as a background image. A cascaded series of cylinders with variable
cross section which match the shape of the vocal tract in the background image were
produced as shown in Figure 4.5.
Connecting the created vocal tract mesh to the human head mesh created with Blender
Figure 4.5: Vocal tract shape manually created in Blender to match an MRI image
41
11
10.5
10
9.5
9
8.5
8
7.5
9
7
−1.5
8
−1
−0.5
0
7
0.5
1
1.5
6
Figure 4.6: Head model with three point polygons for FDTD simulation
presented a challenge since all the surfaces of the head model must be regular and
continous in order to be used with the FDTD simulator. Faces were drawn to connect each
node of the created vocal tract with the closed node(s) of the human head mesh near the
lips. Also, any irregularities or unconnected points were removed to avoid irregularities
in the surface.
The model is exported with Stanford ply format which exports the current deformed
(posed) mesh correctly and is in ASCII, which is easily readible by Matlab. To have
a uniform grid of dielectric cells suitable for FDTD simulation, the 4-point polygons
obtained from Blender need to be converted to triangles to avoid non-planar (misformed)
polygons, as shown in Figure 4.6.
Finally, a Matlab code was written to adjust and resize the model, assign the electrical
parameters, and export the mesh into a format suitable for FDTD simulation. As will
be shown in Chapter 5, the frequency-selective nature of the medium has only a small
impact on the UWB response for the speech sensing application and therefore the tissue
was usually modeled using only the values given in Table 4.1 at the center frequency of
6 GHz only.
4.1.4
FDTD Simulation of Model
An FDTD simulation domain size of 7 cm × 12 cm ×10 cm is used, discretized into
80×80×100 cells in the x, y, and z directions, respectively, as depicted in Figure 4.1.
42
4.2. 3D FLAT-FACE STACKED LAYER MODEL
The PML is 10 cells thick on all sides with a quadratic conductivity gradient and normal
reflection coefficient of 10−5. The time step is set at 1.6 ps, sufficient for numerical
stability. The excitation is a modulated Gaussian pulse with a pulse width (standard
deviation) of 80 ps centered at a frequency of 6 GHz, providing adequate coverage of the
3 to 10 GHz range. In this model, the antenna is placed at a gap of gz in front of the
mouth at horizontal and vertical offsets gx and gy , respectively, relative to the axis of
the mouth. Note that the parts of the head in Figure 4.1 extending beyond the FDTD
simulation domain are truncated.
4.2
3D Flat-Face Stacked Layer Model
Although the detailed model in Section 4.1 models the face, head, and vocal tract as
faithfully as possible, the level of complexity in generating the model is quite high, which
may be unnecessary for the features to be modeled. Therefore, a simplified model of
the head is considered, where the vocal tract is modeled as a straight hollow circular
waveguide, the face as a flat surface with a circular aperture for the mouth, and flat
layers for the skin, fat, and muscle, as depicted in Figure 4.7. The skin and fat layers
have thicknesses of 1 mm and 7 mm, respectively. The tongue is modeled as a cube with
relative permittivity and conductivity given in Table 4.1 assuming a frequency of 6 GHz,
while the glottis has the same properties as muscle. The mouth and throat are modeled
as a hollow circular waveguide, having the same stratified layers and extending from the
face into the PML. The antenna is placed at a gap of gz in front of the mouth at horizontal
and vertical offsets gx and gy , respectively, relative to the axis of the mouth. Note that
the FDTD simulation parameters are identical to those for the detailed model in Section
4.1.
4.3
One Dimensional Model
Perhaps the simplest model for the face and vocal tract is the one-dimensional layered
media model proposed in [41] for heart motion sensing. This model was used in this
work initially to estimate the expected loss of the signals interacting with the vocal tract
organs. Since the model does not capture the wave-guiding effect of the vocal tract, it
is not suitable for speech sensing predictions. However, the model is included here for
completeness. Figure 4.8 shows the simplified model used to compute the transmission
and reflection coefficients.
In this model, it is assumed that the human body can be represented as a stack of
layers that are infinite in the direction transverse to propagation, and therefore the wave
43
Figure 4.7: Stacked layer model for FDTD simulations of the human vocal tract
propagates normal to the boundaries between layers.
The signal from the antenna can be modeled as a plane wave polarized in x̂ direction
and propagating in the ẑ direction. The field in any homogeneous region must satisfy the
wave equation
∇2 Ex (x, y, z) + β 2 Ex (x, y, z) = 0
Figure 4.8: One dimensional reflection and transmission model
(4.3)
44
4.3. ONE DIMENSIONAL MODEL
∂Ex ∂Ex ∂Ex
+
+
+ β 2 Ex = 0,
∂x2
∂y 2
∂z 2
(4.4)
Ex (x, y, z) = f (x)g(y)h(z).
(4.5)
whose solution is given by
Because the uniform plane wave travels in z direction, its solution is not a function of x
and y. Therefore Equation (4.5) reduces to
Ex (z) = h(z)
(4.6)
= Eo+ e−jβz + Eo− e+jβz
(4.7)
= Ex+ + Ex− ,
(4.8)
where Ex+ and Ex− are the transmitted and reflected signals, respectively. When the
incident wave encounters the interface between the two media, a portion of the wave
will be reflected into medium 1 and part will be transmitted into medium 2. In this
case, we can write the expressions for its incident, reflected, and transmitted electric field
components as
E i = Eo e−jβ0z x̂
(4.9)
E r = ΓEo e+jβ0z x̂
(4.10)
E t = T Eo e−jβ1 z x̂,
(4.11)
where Γ and T represent, respectively, the reflection and transmission coefficients at the
interface, and β is the wave number. Since the electric field is known, the magnetic field
can be determined by using Maxwell’s equation as
∇ × E = −jωµH
1
∇ × (Ex x̂)
jωµ
1 ∂Ex
ŷ.
= −
jωµ ∂z
(4.12)
H = −
(4.13)
Substituting Equation (4.8) into Equation (4.13)
1 ∂(Eo+ e−jβz + Eo− e+jβz )
ŷ
H = −
jωµ
∂z
β
=
(E + e−jβz − Eo− e+jβz )ŷ.
ωµ o
(4.14)
45
Since β 2 = ω 2 µε,
1
(Eo+ e−jβz − Eo− e+jβz )ŷ
µ/ε
1
(Ex+ − Ex− )ây
= p
µ/ε
= (Hy+ + Hy− )ŷ.
H = p
(4.15)
The ratio between the electric and the magnetic fields is defined by the propagation
p
impedance η = µ/ε , µo = 4π × 10−7 H/m is the permeability of vacuum and εo =
8.85410−12 F/m is the permittivity of vacuum. Thus, the magnetic field components can
be written as
H
H
i
r
H
t
Eo −jβ0 z
e
ŷ
η0
ΓEo
Eo e+jβ0 z ŷ
= −
η0
T Eo −jβ1 z
e
ŷ.
=
η1
=
(4.16)
(4.17)
(4.18)
The reflection and transmission coefficients are determined by enforcing continuity of the
tangential components of the electric and magnetic fields across the interface (at z = 0),
which leads to
1=Γ+T
(4.19)
Γ
T
1
=
+ .
η0
η0 η1
(4.20)
Solving Equations (4.19) and (4.20) for Γ and T , we can write
Γ=
η1 − ηo
η1 + ηo
2η1
.
η1 + ηo
Attenuation in each layer is governed by the attenuation constant
T =
σ
α=
2
r
µ
.
ε
(4.21)
(4.22)
(4.23)
Thus, the transmitted and received power density through a single layer of depth z can
be written in terms of the incident power density as
η1
2
i
t
|T | e−2α2 z Sav
Sav =
ηo
r
i
Sav
= |Γ|2 e+2α2 z Sav
,
(4.24)
46
4.4. SUMMARY
0
Air
Skin
Fat
Tongue
−5
−10
Attenuation (dB)
−15
−20
−25
−30
−35
−40
−45
−50
0
5
10
15
Depth ( mm )
20
25
Figure 4.9: One dimensional attenuation model for speech sensing
i
where Sav
is the incident power [70].
Typical wavelengths in the different body tissues are between 1 and 4 cm, and thus,
the radiated electromagnetic pulse coming from the transmitting antenna of the UWB
radar will be reflected partly at every tissue interface. The attenuation that a hypothetical
electromagnetic pulse will suffer on its way into the neck and back out is plotted in Figure
4.9.
This model shows a 45 dB round trip loss for the signal to reach the tongue and return
back to the receiver. This loss will increase significantly in the case of detecting deeper
features such as the glottis, indicating that for volumetric sensing, the receiver sensitivity
requirement may be too high for practical implementation, especially if low power levels
conforming to the UWB mask are required.
4.4
Summary
This chapter has presented a number of candidate human head models for the speech
sensing application. A detailed head and neck model were designed using MakeHuman
and Blender. An internal vocal tract model was developed by loading MRI images for the
open and closed mouth into the background of Blender and drawing a cascading series
of cylinders with different cross sections. Although the detailed model captures the face,
head, and vocal tract as faithfully as possible, the level of complexity in generating the
model is quite high, which may be unnecessary for the features to be modeled. Therefore
47
a simplified model of the head which considers the face as a flat surface with a circular
aperture for the mouth was developed. Although the one-dimensional (1D) model given
in this chapter is a very simplified representation of the human body, it indicates the
maximum receive power that one can expect the UWB sensor to receive. In Chapter 5,
the detailed model will be used to optimize the placement of the antenna. Also, it will be
shown that the simplified model is accurate enough to predict speech sensing responses
in many cases.
5. SPEECH SENSING: SIMULATION AND EXPERIMENTAL VALIDATION
49
Chapter 5
Speech Sensing: Simulation and
Experimental Validation
Building on the models developed in Chapter 4, this chapter explores the feasibility of
the speech sensing application introduced in Chapter 2 through both simulation and
measurement. First, full-wave FDTD simulations employing the detailed vocal tract
model of Section 4.1 are performed to optimize placement of the UWB sensor that was
introduced in Chapter 3. Second, the ability to sense pronounced changes in the vocal
tract is studied, indicating that the same behaviors are seen in both simulation and
measurement and that often simplified vocal tract model may be sufficient. Finally,
a proof-of-concept silent speech recognition system is developed, indicating that UWB
speech sensing is possible in practice.
5.1
Optimization of Antenna Placement
To provide maximum sensitivity of the measurement system to changes in the vocal tract,
it is desirable to optimize placement of the UWB sensor developed in Chapter 3 to provide
maximum coupling to the vocal tract. In this section, the detailed 3D vocal tract model is
employed to optimize for peak coupling with the vocal tract. Since it is likely that a UWB
sensor will be strongly affected by the lips and face regardless of the specific position or
orientation, the optimization here focuses on maximizing the fields that penetrate into the
mouth and throat. Therefore, the goal chosen was to maximize the squared magnitude
of the electric field intensity integrated over frequency and spatially over a cross section
of mouth aperture at a distance of 2 cm into the mouth, thus allowing information on
the teeth and tongue to be potentially sensed. The orientation of the circular monopole
is depicted in Figure 4.1, positioned so that the direction of the maximum radiation is
directed at the mouth. The following subsections consider optimal offset of the antenna
50
5.1. OPTIMIZATION OF ANTENNA PLACEMENT
4.5
4
−1
3
−2
−2
0
2.5
y
g (cm)
3.5
2
−1
−4
−2
1.5
1
−6
0.5
−8
−2
−6
−4
−4
−6
−6
−1
−4
−2
0
g (cm)
−8
1
−8
2
x
Figure 5.1: Relative power level (dB) 2 cm into the mouth for different gx , gy offsets
with respect to the mouth.
5.1.1
Vertical/Horizontal Offset gx, gy
A total of 81 FDTD simulations were carried out for gy ∈ {0.1, 0.7, 1.3, . . . , 4.9} cm and
gx ∈ {−2.4, −1.8, −1.2, . . . , 2.4} cm with gz =2 cm, and contours relative to integrated
power at 2 cm into the mouth are plotted in Figure 5.1. The results indicate that the
best location of the antenna relative to the mouth is gy = 2.5 cm = 2r and gx = 0 cm,
meaning that the tip of the disc is nearly aligned with the horizontal axis of the mouth.
5.1.2
Antenna-Head Gap gz
The distance between the antenna and the human face, commonly referred to as the
liftoff or standoff distance [71] is next investigated. Figure 5.2 shows the effect of distance
between the antenna and the human face for gz ∈ {1, 1.2, 1.4, . . . , 3} cm with gx =0
and gy =2r, which was the optimal offset found from the last subsection. It is noted
that approximately 2-3 dB of power coupling is lost per additional cm of separation.
Although having the antenna as close as possible is optimal, having the antenna too close
is inconvenient for the user and can inhibit speech production. Reasonable coupling and
freedom of movement can be achieved by using 2 cm separation, which will be used in
the rest of this work.
51
−8
Power (dB)
−9
−10
−11
−12
−13
−14
1
1.5
2
gZ (cm)
2.5
3
Figure 5.2: Relative power level (dB) 2 cm into the mouth for different gz offsets
5.2
Sensing of Large Vocal Tract Changes
During speech, the lips as well as the tongue will exhibit a particular motion. Some
sounds require just the movement of mouth like ’B’ and other sounds like ’L’ require
the movement of tongue. In this section, the ability to sense large changes in the lips
and tongue is investigated with simulation and checked with direct measurement. One
problem with speech sensing using the monostatic radar configuration is that a large
static reflection will be seen from the face, body, and nearby objects that is not correlated
with speech production. Assuming that these effects change much slower in time than
effects caused by speech, the static part can be approximately removed by considering
only the derivative of the UWB signals. To this end, the rest of this chapter focuses on the
derivative of the response only, which is refered to as the delta response, and is computed
as
Dkn = Γk,n+1 − Γkn
(5.1)
where Γkn , refers to the complex reflection coefficient at frequency index k and time point
n. Note that the delta response also removes the effect of static reflections due to antenna
mismatch.
To allow the range (i.e. delay) of features that significantly impact the delta response
to be identified, each frequency-domain delta response is transformed to a complex baseband time-domain response h(τ ). For a hypothetical continuous-frequency delta response
d(f ), the inverse Fourier transform of the equivalent complex baseband signal is h(τ ) =
R∞
w(f )d(f ) exp[j2π(f − f0 )τ ] df , where f is frequency, f0 = 6.5 GHz is the center
−∞
frequency, and the window function w(f ) is a Hamming window spanning 3 to 10 GHz.
52
5.2. SENSING OF LARGE VOCAL TRACT CHANGES
For the discrete frequency samples obtained from our measurements, the inverse Fourier
transform is approximated in a conventional manner by applying a discrete Hamming
window, zero padding, and an inverse FFT. The time axis is transformed to one-way
distance by assuming free-space propagation.
5.2.1
Lips Movement
First, lip movement, or opening and closing of the mouth, is considered. Here, the delta
response is defined as the change between the two extreme states: mouth open to 3
cm diameter (n=0) and mouth closed (n=1), where in both cases the tongue rests on
the bottom of the mouth. Figure 5.3 depicts the resulting delta response from FDTD
simulations employing the detailed and flat-face models from Chapter 4. As can be seen,
the responses for the two models are very similar. The small difference between the two
models is likely due to the curvature of the face in the detailed model as shown in Figures
5.4 and 5.5, which depicts the total electric field distributed in and around the head model
for closed and open mouth, respectively. Note also that the cross section of the vocal tract
in the flat model is always circular, whereas it is semi-elliptical in the detailed model.
It is observed that the fields propagating in the mouth and throat decay rapidly, which can
be explained by considering simple waveguide propagation. The physical dimensions of
the mouth determine the cutoff frequency for each of the propagating modes. for example
consider the TE waves propagating inside the mouth, the fields may be written as [72]
Hz = Jm (kρ ρ ) sin(mφ)e−jkz z
(5.2)
0.35
Detailed model
Stacked layer model
0.3
|h(τ)|
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
Distance (cm)
8
10
Figure 5.3: Time-domain delta response for lips
53
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Lips closed
(b) Lips closed
Figure 5.4: Detailed head model exposed to UWB field with lips closed
with the dispersion relation
kz2 + kρ2 = ω 2 µε
p
kz = ω 2 µε − (x0mn /a)2
(5.4)
kc,mn = x0mn /a.
(5.5)
(5.3)
where a is the mouth radius and x0mn is the nth root of the mth order derivative Bessel
function, thus the cutoff wavenumber for the TEmn mode is given by
For a given radius, if k < kc,mn then kz will be imaginary (−jα) and consequently e−jkz z
= e−αz . Thus, the electromagnetic energy will be attenuated to a low value in a relatively
short distance. For the frequencies of the impressed signal above the cutoff frequency for
a given mode, the electromagnetic energy can be transmitted through the mouth for that
particular mode with minimal attenuation.
5.2.2
Tongue Movement
The human tongue plays a significant part in speech production. Sounds are differentiated,
among other factors, by the position of the tongue relative to the palate, and by the
curvature and contraction of the tongue. Figure 5.6 shows the delta response for an open
mouth (3 cm), where the two states are the tip of the tongue resting on the bottom of the
mouth (n=0) as shown in Figures 5.7(a) and 5.8 versus touching the roof of the mouth
(n=1) as shown in Figures 5.7(b) and 5.9. Both models show a small shift of the peak
54
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
−50
8
Z (cm)
(a) Lips open
(b) Lips open
Figure 5.5: Detailed head model exposed to UWB field with lips open
response to the right relative to case of lip in Figure 5.3. Note also that the magnitude of
the peak delta response is much smaller for tongue movement compared to the previous
case of lip movement.
Again, small differences are seen in the flat-face and detailed models, but the results are
remarkably similar, indicating that a simple waveguide model should suffice for the speech
sensing application.
The tongue is a highly flexible organ which can be bent, twisted and tensed [73]. It is of
0.08
Detailed model
Stacked layer model
0.07
0.06
|h(τ)|
0.05
0.04
0.03
0.02
0.01
0
0
2
4
6
Distance (cm)
8
10
Figure 5.6: Time-domain delta response for tongue tip
55
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Tongue down
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(b) Tongue up
Figure 5.7: Flat head model exposed to UWB field with tongue up and down
56
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Tongue down
(b) Tongue down
Figure 5.8: Detailed head model exposed to UWB field with tongue tip down
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Tongue up
(b) Tongue up
Figure 5.9: Detailed head model exposed to UWB field with tongue tip up
57
0.014
Detailed model
Stacked layer model
0.012
|h(τ)|
0.01
0.008
0.006
0.004
0.002
0
0
2
4
6
Distance (cm)
8
10
Figure 5.10: Time-domain delta response for movement of the back of the tongue
interest to see whether changes in the tongue for deeper penetration into the mouth can
be sensed. Figure 5.10 depicts the delta response for the back of the tongue, where the
two states are the back of the tongue up as in Figure 5.11 (n=0) or down as in Figure
5.12 (n=1) for the detailed and simple models with a mouth opening of 3 cm diameter.
Both models show significant energy coming from between 3-6 cm, roughly corresponding
to the distance to the back of the tongue. Although the region of support and reflected
field magnitude are similar for the detailed and simple models, model differences are more
evident for this case which is expected due to the deeper penetration of fields.
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Tongue back up
(b) Tongue back up
Figure 5.11: Detailed head model exposed to UWB field with the back of the tongue up
58
5.3. FREQUENCY-DEPENDENT TISSUE PROPERTIES
6
−10
4
−15
−20
y (cm)
2
−25
0
−30
−35
−2
−40
−4
−45
−6
−2
0
2
4
6
8
−50
Z (cm)
(a) Tongue back down
(b) Tongue back down
Figure 5.12: Detailed head model exposed to UWB field with the back of the tongue down
5.3
Frequency-Dependent Tissue Properties
As discussed in Section 4.1.1, the dielectric properties of human tissues are highly dispersive as indicated in Table 4.1. Thus, a more general approach is to simulate the vocal
tract separately at different frequencies, allowing the effects of the dispersion to be exactly
modeled.
Figure 5.13 plots the delta response for lip and tongue movement for 3 different cases
involving the detailed model, where electrical parameters defined at 3, 6, 10 GHz are
used. The results show that the exact material parameters play a minor role in determinig the UWB response. This result is reasonable, since the propagation of the hollow
waveguide will be more sensitive to the diameter and shape of the waveguide than the
exact parameters of the walls. The result also justifies the simplified simulation strategy
of using constant material parameters taken at 6 GHz that is used throughout the work.
5.4
Vocal Tract Measurements for Large Movement
In this section, direct measurement of the response of the vocal tract to pronounced
changes is performed and compared with the simulation results. The goal is to determine
whether the developed models faithfully represent the vocal tract, and to indicate whether
or not measured delta responses actually correspond to movement of the vocal features
studied so far, rather than other environmental effects.
As with the simulations in Section 5.2, the delta response is considered where dk =
59
0.35
3 GHz
6 GHz
10 GHz
0.3
|h(τ)|
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
Distance (cm)
8
10
(a) Lips
0.07
3 GHz
6 GHz
10 GHz
0.06
|h(τ)|
0.05
0.04
0.03
0.02
0.01
0
0
2
4
6
Distance (cm)
8
10
(b) Tongue(tip)
0.014
3 GHz
6 GHz
10 GHz
0.012
|h(τ)|
0.01
0.008
0.006
0.004
0.002
0
0
2
4
6
Distance (cm)
8
10
(c) Tongue(back)
Figure 5.13: Delta responses for large movement with electrical parameters taken from
values at different frequencies
60
5.4. VOCAL TRACT MEASUREMENTS FOR LARGE MOVEMENT
Dk1 and n=1 and n=0 represent two extreme states of the vocal tract. Note that each
measurement was repeated 20 times, and the mean and standard deviation of the responses
are computed, indicating repeatability.
Figures 5.14-5.17 compare delta responses of measurements and FDTD simulation with
the detailed model for two extreme vocal states. Note that all simulated curves have
been shifted by an identical amount to achieve the best fit for the lip movement case in
(a), removing any static differences due to source position. Also, the RMS delay distance
dc for measurements has been computed and is indicated as a vertical line in the plots.
Although Figures 5.14-5.16 look similar (a cluster of energy appears over some range), the
important observation is that moving incrementally deeper parts of the vocal tract leads
to energy in the delta response at a longer delay and a weaker level, strongly suggesting
that the features of interest are responsible for the energy measured in the delta response.
Figure 5.14 plots the case of lip movement where the two states are open mouth (3 cm
diameter) and closed mouth with the tongue resting on the bottom of the mouth. As can
be seen, the responses for the measured and simulated vocal tract are very similar, with a
slightly higher response for the measurement. Also, the measurement is quite repeatable,
evidenced by the low standard deviation.
Figure 5.15 shows the result for an open mouth (3 cm), where the two states are the tip
of the tongue resting on the bottom of the mouth versus touching the roof of the mouth.
Both measurement and simulation show a shift of the response to the right relative to
case (a) and good agreement in level.
Figure 5.16 depicts the result for the back of the tongue up or down with a mouth opening
of 3 cm diameter. For a lowered tongue, the state of the vocal tract is that of the vowel
“ah” and for raised that of the initial g on “gah.” Care is taken to keep the tongue and jaw
as still as possible for the two states. Both measurement and simulation show significant
energy coming from between 3-6 cm, roughly corresponding to the distance to the back
of the tongue. Both the unexpected measured energy for distance less than 3 cm, as well
as the increased standard deviation, are likely due to the difficulty of keeping the mouth
completely still while changing the back of the tongue.
Figure 5.17 shows the mean delta response for the three cases for a longer observation
time, allowing assessment of the impact of more distant environmental features (such as
nearby equipment) on the measurement. The plot suggests that environmental scatterers
impact the delta response weakly compared with vocal tract changes.
61
0.35
Mean
Std
Simulation
0.3
d = 2.3 cm
|h(τ)|
0.25
c
0.2
0.15
0.1
0.05
0
0
2
4
6
Distance (cm)
8
10
Figure 5.14: Time-domain delta response for lips
0.09
Mean
Std
Simulation
0.08
0.07
d = 2.6 cm
c
|h(τ)|
0.06
0.05
0.04
0.03
0.02
0.01
0
0
2
4
6
Distance (cm)
8
10
Figure 5.15: Time-domain delta response for tongue tip
62
5.4. VOCAL TRACT MEASUREMENTS FOR LARGE MOVEMENT
0.018
Mean
Std
Simulation
0.016
0.014
dc = 3.3 cm
|h(τ)|
0.012
0.01
0.008
0.006
0.004
0.002
0
0
2
4
6
Distance (cm)
8
10
Figure 5.16: Time-domain delta response for tongue back
0.35
Mean(Lips)
Mean(Tongue Tip)
Mean(Tongue Back)
0.3
|h(τ)|
0.25
0.2
0.15
0.1
0.05
0
0
10
20
Distance (cm)
30
40
Figure 5.17: Time-domain delta response with long time
5.5
63
UWB Speech-Recognition Experiment
This section describes sensing of actual speech with the prototype setup. Figure 5.18(a)
depicts an example delta response for two repeated vocalizations of the word “five” spaced
by 1 s. Figure 5.18(b) is another delta response example for two repeated vocalizations
of the word “seven”.
During periods of silence at the start and end of the record, minimal change leads to a
delta response with low amplitude and random phase. During vocalization, the weakly
modulated return signal can be identified, and significant information about the state of
the mouth and vocal tract is obtained.
To test of the potential of speech sensing with UWB, a simple speech recognition experiment was conducted. This experiment was performed using actual measured responses
only, since the vocal tract model is insufficient to simulate detailed movement of the
tongue and mouth. Although recognition of phonological segments [74] such as vowels
and consonants is a future goal of this effort, this requires extensive work to identify the
main features of interest in UWB speech responses and how they are connected to speech
processes.
In this thesis only simple whole-word recognition by template matching is considered,
where a dictionary is formed by recording the UWB response of several words spoken
(m,p)
many times each, where Dkn is the delta response of the mth word and pth trial. Next,
the UWB response of a new vocalization is recorded, denoted Dkn , and compared with the
dictionary. Recognition is accomplished by minimizing a simple sliding distance metric,
in which the recognized word index is
P
(m,p) 2
k,n |Dkn − Dk,n+i |
m = arg min min min q P
,
(5.6)
P
m
p
i
(m,p) 2
2
( k,n |Dkn | )( k,n |Dkn | )
where the sums span the ranges n ∈ [1, N] and k ∈ [1, NF ], and N and NF are the number
of time and frequency samples, respectively.
Table 5.1 shows the results of a speech recognition experiment involving speaking the
integers “zero” through “nine,” where 30 trials of each word are stored in the dictionary
as shown in Figure 5.19 (a). After recording the complete dictionary, each word on the
left column is spoken 25 times, and tabulated are the number of times it is matched with
each word in the dictionary as shown in Figure 5.19 (b). The poorest performance occurs
for “six,” possibly due to the fact that its vocalization is very short yielding a rather weak
signature. The average rate of recognition mismatch is low (around 7%). This is quite
encouraging, given the simplicity of the algorithm.
The effect of the environment on speech recognition was checked by applying a time-gate
filter to the measurements to remove signals arriving after 2 ns, thus excluding objects
64
5.5. UWB SPEECH-RECOGNITION EXPERIMENT
Phase
10
9
9
8
8
Frequency,GHz
Frequency,GHz
Magnitude
10
7
6
5
7
6
5
4
4
3
3
2
0
2
0
5
Time (s)
5
Time (s)
(a) Word “five”
Phase
10
9
9
8
8
Frequency,GHz
Frequency,GHz
Magnitude
10
7
6
5
7
6
5
4
4
3
3
2
0
5
2
0
Time (s)
5
Time (s)
(b) Word “Seven”
Figure 5.18: Delta response of two repeated vocalization of the words five and seven
65
Figure 5.19: Speech-recognition experiment
more than 30 cm away. The effect was that the words “two”, “six”, and “eight” were
recognized correctly for 23, 19, and 24 of the trials (the other words were unaffected),
indicating no improvement in the algorithm, and suggesting very little impact of environmental scatterers. This supports the observation in Section 5.4 that distant scatterers
have a minor impact on the measured delta response.
5.6
Summary
This chapter has explored the feasibility of speech sensing using the models developed
in Chapter 4. First, the detailed FDTD model was employed to optimize placement of
Table
Word
0
1
2
3
4
5
6
7
8
9
5.1:
0
21
0
1
0
1
0
1
0
0
0
Example
1 2
0 1
25 0
0 24
0 0
0 0
0 0
0 0
0 0
0 0
0 0
speech recognition experiment
3 4 5 6 7 8 9
0 3 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
25 0 0 0 0 0 0
0 24 0 0 0 0 0
0 0 23 1 0 1 0
0 3 0 18 1 1 1
0 0 3 0 22 0 0
0 0 0 0 0 25 0
0 0 0 0 0 0 25
66
5.6. SUMMARY
the UWB sensor to maximize coupling of UWB signals with the mouth. Time variation
of the vocal tract was characterized by defining the delta response that removes static
effects due to antenna and environmental reflections. Delta responses of the models in
Chapter 4 were simulated for large movement of the lips and tongue, indicating that these
movements can be sensed and that simple waveguide models are likely to be sufficient.
Next, direct measurement of the vocal tract delta responses was presented, showing the
same effects as those observed in simulation and suggesting that the features of interest
are responsible for the energy measured in the delta responses. A proof-of-concept UWB
speech-recognition experiment was presented suggesting that speech detection with the
proposed method is possible.
6. SPEECH SENSING: MULTIMODE WAVEGUIDE MODELING
67
Chapter 6
Speech Sensing: Multimode
Waveguide Modeling
As was demonstrated in Chapter 5, the simple flat-face circular waveguide model may be
sufficient for modeling UWB propagation in the human vocal tract. Although the FDTD
simulations gave high modeling accuracy for both the detailed and flat-face models, the
simulation time is quite long, inhibiting the ability to perform reconstruction of vocal
tract parameters based on the measured UWB returns. This chapter develops a simplified
waveguide model for the vocal tract that reduces the required simulation time by orders of
magnitude, making it more appropriate for estimating vocal tract parameters from UWB
means responses.
Assuming that the permittivity of the surrounding tissue is high compared to air, the
tangential E fields are modeled as being approximately 0 inside the body tissue (fields
are confined to the air channel of the vocal tract), and these tissues are replaced with
perfect electrical conductor (PEC) surfaces. The vocal tract is thus modeled as a cascaded
series of PEC sections, where each section has common length L and distinct diameter
di as shown in Figure 6.1. Each section should represent the dimensions (cross sectional
area) of the corresponding parameter of natural vocal tract as closely as possible. The
response of the complete waveguide can be found using a transmission-line model, where
multiple modes (propagating and evanscent) may be present on each section. Modes
on each section are found using closed-form analysis giving field profiles and propagation
constants. Transmission and reflection coefficients at discontinuities are found using modematching. Finally sections are cascaded to get the complete response using S parameter
analysis.
68
6.1. PRINCIPLES OF THE MODE MATCHING TECHNIQUE
Figure 6.1: Vocal tract segmentation
6.1
Principles of the Mode Matching Technique
The theory described below is well known and is summarized in [75]. In applying the
modal analysis method, the waveguide device is broken up into a series of sections that
are joined by step discontinuities as is shown in Figure 6.2 where the total transverse
electric and magnetic fields in waveguide 1 can be expressed as a sum of TM (e-type) and
TE (h-type) model fields [76].
Tangential (x and y-directed) field in the waveguide 1 can be written as
(1)
E t (x, y)
=
N1
X
(1) (1)
(a(1)
n + bn )en (x, y),
(6.1)
n=1
(1)
H t (x, y)
N1
X
(1) (1)
=
(a(1)
n − bn )hn (x, y),
(6.2)
n=1
(k)
(k)
where an and bn are respectively the incident and reflected modal amplitudes of the
(k)
nth mode in the kth section, and e(k)
n and hn are the normalized vectorial electric and
magnetic field profiles of the tangential components for the nth mode in the kth section,
and N1 is the maximum number of modes considered [77].
Similarly, the field in waveguide 2 can be written as
(2)
E t (x, y)
=
N1
X
n=1
(2) (2)
(a(2)
n + bn )en (x, y),
(6.3)
69
Figure 6.2: Mode matching at discontinuity
(2)
H t (x, y)
=
N1
X
(2)
(2)
(−a(2)
n + bn )hn (x, y).
(6.4)
n=1
6.1.1
Transverse Field Expressions
For a circular waveguide, the transverse magnetic field (TM) is given by
Ez = Jm (kρ ρ)
(
sin mφ
cos mφ
)
ejkz z ,
(6.5)
the dispersion relation is defined by
kz2 + kρ2 = ω 2 µ,
(6.6)
and the transverse field components are obtained by the following equations
Eρ
Eφ
Hρ
Hφ
)
sin mφ
ejkz z
cos mφ
(
)
cos mφ
m
ikz
Jm (kρ ρ)
ejkz z
=
ω 2 µ − kz2 ρ
− sin mφ
(
)
−iω m
cos mφ
=
Jm (kρ ρ)
ejkz z
2
2
ω µ − kz ρ
− sin mφ
(
)
sin mφ
iωkρ
0
J (kρ ρ)
ejkz z ,
=
ω 2 µ − kz2 m
cos mφ
ikz kρ
0
=
Jm (kρ )
2
2
ω µ − kz
(
(6.7)
(6.8)
(6.9)
(6.10)
70
where the prime on the Bessel function denotes derivative with respect to its argument.
The boundary condition of vanishing Ez and Eφ at ρ = a gives the guidance condition
Jm (kρ ρ) = 0.
(6.11)
Let xmn denote the nth root of the mth order Bessel function such that Jm (xmn ) = 0. We
find from the guidance condition (6.11) and the dispersion relation (6.6)
kz =
p
ω 2 µ − (xmn /a)2 .
(6.12)
For transverse electric field (TE) waves solutions, we have
Hz = Jm (kρ ρ)
(
sin mφ
cos mφ
)
eikz z ,
(6.13)
with the dispersion relation
kz2 + kρ2 = ω 2 µ,
(6.14)
and the transverse field components are defined as
Hρ
Hφ
Eρ
Eφ
)
sin mφ
ejkz z
cos mφ
(
)
cos mφ
ikz
m
=
Jm (kρ ρ)
ejkz z
ω 2 µ − kz2 ρ
− sin mφ
(
)
cos mφ
m
iω
Jm (kρ ρ)
ejkz z
=
ω 2 µ − kz2 ρ
− sin mφ
(
)
sin mφ
−iωkρ 0
=
Jm (kρ ρ)
ejkz z .
2
2
ω µ − kz
cos mφ
ikz kρ
0
Jm (kρ ρ)
=
2
2
ω µ − kz
(
(6.15)
(6.16)
(6.17)
(6.18)
The boundary condition of vanishing Ez and Eφ at ρ = a gives the guidance condition
0
Jm (kρ ρ) = 0.
0
(6.19)
Let xmn denote the nth root of the derivative of the mth order Bessel function such that
0
0
Jm (xmn ) = 0. We find from the guidance condition (6.19) and the dispersion relation
(6.14)
71
kz =
6.1.2
p
ω 2 µ − (x0mn /a)2 .
(6.20)
The Scattering Matrix
The evaluation of the generalized scattering matrix for the step discontinuity is based
on enforcement of the continuity of the tangential electric and magnetic field over the
discontinuity interface. The boundary conditions to be satisfied for PEC walls are
(1)
(2)
E t (x, y) = E t (x, y)
(1)
(2)
H t (x, y) = H t (x, y)
(i)
∀(x, y) ∈ α
(6.21)
∀(x, y) ∈ β,
(6.22)
(i)
where E t and H t are the transverse electric and magnetic fields tangential at the
boundary, α = S1 ∪ S2 , β = S1 ∩ S2 , and S1 and S2 are the set of points in the cross
sectional areas of waveguides 1 and 2 respectively.
N1
X
(a(1)
n
+
(1)
b(1)
n )en (x, y)
n=1
N1
X
N2
X
(2) (2)
(a(2)
=
n + bn )en (x, y)
in α
(6.23)
in β
(6.24)
n=1
(a1n
−
(1)
b1n )hn (x, y)
=
N2
X
(2)
(−a2n + b2n )hn (x, y)
n=1
n=1
(1)
(1)
(2)
(2)
hE (1) , hm iα = hE (2) , hm iα ,
hE (1) , hm iα = hE (2) , hm iα ,
(1)
(2)
he(1)
iβ = he(1)
iβ ,
m ,H
m ,H
(1)
(2)
he(2)
iβ = he(2)
iβ
m ,H
m ,H
m = 1, 2, 3, ...N1
(6.25)
m = 1, 2, 3, ...N2
(6.26)
m = 1, 2, 3, ...N1
m = 1, 2, 3, ...N2
(6.27)
(6.28)
where
he, hiα =
Z
α
Defining
e × h dA.
(6.29)
72
A(r,s)
α,mn
=
Z
(s)
α
e(r)
m × hn dA,
(6.30)
equations (6.25)-(6.28) can be expanded as
N1
X
(a(1)
n
+
b(1)
n )
n=1
N1
X
|
(a(1)
n
+
b(1)
n )
n=1
N1
X
Z
(a(1)
n
−
b(1)
n )
n=1
Z
β
|
(a1n
−
b1n )
n=1
×
{z
(1)
hm dA
α
e(1)
n
×
{z
(2)
hm dA
×
{z
(1)
hn dA
}
e(2)
m
(1)
hn dA
β
|
×
{z
T (2,1)
Aβ,mn
which result in the matrix equations

Aα(1,1)T −Aα(2,1)T
 (1,2)T
 Aα
−Aα(2,2)T

(1,2)
 A(1,1)
Aβ
 β
(2,1)
(2,2)
Aβ
Aβ
|
{z
A1
(a(2)
n
+
b(2)
n )
=
N2
X
(1)
e(2)
n × hm dA
α
|
{z
}
(6.31)
T (2,1)
(a(2)
n
+
b(2)
n )
n=1
N2
X
Z
Aα
(−a(2)
n
Z
(2)
e(2)
n × hm dA
α
|
{z
}
(6.32)
T (2,2)
Aα,mn
+
b(2)
n )
n=1
Aβ,mn
T (1,1)
Z
=
N2
X
n=1
}
T (1,2)
Aα,mn
e(1)
m
=
}
T (1,1)
Aα
Z
|
N1
X
α
e(1)
n
Z
(2)
e(1)
m × hn dA
β
{z
}
|
(6.33)
T (1,2)
Aβ,mn
=
N2
X
(−a2n
+
b2n )
n=1
}
Z
(2)
e(2)
m × hn dA
β
{z
}
|
(6.34)
T (2,2)
Aβ,mn


−Aα(1,1)T Aα(2,1)T
 " (1) # 
 −Aα(1,2)T Aα(2,2)T
 a


(1,2)
 a(2) =  A(1,1)
Aβ


β
| {z }
(2,1)
(2,2)
Aβ
Aβ
a
|
}
{z
A2

 " (1) #
 b

 b(2) .

| {z }
(6.35)
b
}
A1 a = A2 b
The generalized scattering matrix characterizing transmission and reflection of modes at
the discontinuity is found as
−1
b = A2 A1 a.
| {z }
(6.36)
S
The obtained S-matrix is slightly different from the usual one in the circuit theory since
it relates both propagating and evanescent modes. Therefore, it contains information for
73
Figure 6.3: Cascading two port scattering matrices
both the power and the fields existing around the discontinuity. Note that if Nf modes
are retained at each interface, the S-parameter matrix characterizing that junction has
2Nf ports (Nf to the left and Nf to the right of the junction).
6.2
Cascading S-Parameters
Since the vocal tract has multiple sections for a non-homogeneous case, obtaining the
response of the whole vocal tract requires the sections to be cascaded. Figure 6.3 illustrates
the concept of reducing the two scattering matrices into a single effective scattering matrix.
It is assumed that the two 2-ports are characterized by S L and S R , respectively, indicating
the left and right structures. Port 2 of the left structure is connected to Port 1 of the
right structure. The effective scattering matrix, S T , describes the interactions between
Port 1 of the left structure and Port 2 of the right structure. For the left section, the
S-parameters are given by
"
b(1)
b(2)
#
=
"
S L11 S L12
S L21 S L22
#"
a(1)
a(2)
#
(6.37)
b(1) = S L11 a(1) + S L12 a(2)
(6.38)
b(2) = S L21 a(1) + S L22 a(2) .
(6.39)
Analogous equations may be written for the right matrix, and relating the wave amplitudes
at Port 1 of the right structure to those at Port 2 of the left structure
a(2) = S R11 b(2) + S R12 a(3)
(6.40)
b(3) = S R21 b(2) + S R22 a(3) .
(6.41)
74
6.3. SCATTERING MATRIX OF A UNIFORM SECTION
Substituting (6.40) into (6.39)
i
h
b(2) = S L21 a(1) + S L22 S R11 b(2) + S R12 b(3)
(6.42)
h
i
I − S L22 S R11 b(2) = S L21 a(1) + S R12 a(3)
i
h
i−1 h
b(2) = I − S L22 S R11
S L21 a(1) + S R12 a(3) .
(6.43)
Substituting (6.39) into (6.40),
h
i
a(2) = S R11 S L21 a(1) + S L22 a(2) + S R12 a(3)
(6.44)
i
h
I − S R11 S L22 a(2) = S R11 S L21 a(1) + S R12 a(3)
i
h
i−1 h
(2)
(1)
(3)
.
a
= I − S R11 S L22
S R11 S L21 a + S R12 a
(6.45)
Now, substituting (6.45) and (6.43) into (6.38) and (6.41),
(1)
b
h
i−1 h
i
(1)
(3)
= S L11 a + S L12 I − S R11 S L22
S R11 S L21 a + S R12 a
h
i−1
o
h
i−1
n
= S L11 + S L12 I − S R11 S L22 S R11 S L21 a(1) +S L12 I − S R11 S L22 S R12 a(3) .
|
|
{z
}
{z
}
(1)
ST11
ST12
(6.46)
(3)
a
i
h
i−1 h
(1)
(3)
+ S R22 a(3)
= S R21 I − S L22 S R11
S L21 a + S R12 a
h
i−1
n
h
i−1
o
= S R21 I − S L22 S R11 S L21 a(1) + S R21 I − S L22 S R11 S R12 + S R22 a(3) .
|
|
{z
}
{z
}
ST21
ST22
(6.47)
6.3
Scattering Matrix of a Uniform Section
Each discontinuity or transition of the vocal tract is connected to the next with a uniform
section of length L with the scattering matrix
n o
S 11
=0
(6.48)
k`
75
Figure 6.4: Thick iris in a circular waveguide
n
S 21
o
k`
n
= S 12
n
S 22
o
o
k`
k`
= δk` e−jγk L
(6.49)
= 0,
(6.50)
where γk is the complex propagation constant of the kth mode and L is the section length.
6.4
Mode Matching Validation
A comparison of the implementation of the mode matching equations presented here and
a similar published implementation in [78] was performed. The number of modes retained
was 40 and the structure depicted in Figure 6.4 was excited with the T E11 mode. Table
6.1 gives the resulting reflection coefficient for the iris with a=0.50175 in, b=0.25 in,
and different values of L for f=9 GHz. Good agreement is seen for the two different
implementations.
Table 6.1: Comparison of the reflection coefficient S11 as a function of L
Modal expansion [78]
Mode matching
L(inch)
S11 Magnitude S11 Phase S11 Magnitude S11 Phase
0.00500
0.00800
0.05000
0.10000
0.20000
0.50000
1.00000
0.864
0.872
0.934
0.965
0.989
0.999
1.000
149.4
150.1
155.6
158.5
160.9
161.7
161.8
0.86467
0.87285
0.93398
0.96555
0.98951
0.99965
1.00000
149.47639
150.20477
155.63172
158.57496
160.93680
161.98428
162.02150
76
6.5. VOCAL TRACT S-PARAMETER
Figure 6.5: Vocal tract as two port networks
6.5
Vocal Tract S-Parameter
Although a reduced-order model for the vocal tract has been developed based on mode
matching, the vocal tract needs to be illuminated by a distant antenna that excites
multiple modes in the first waveguide section. Here, a method for computing the Sparameters of a block is developed that captures the connection of signals present at the
antenna terminals and the forward and reverse traveling modes in the first waveguide
section. These S-parameters can be extracted directly from FDTD simulations of the
UWB antenna in the presence of a uniform waveguide.
The basic problem is shown in Figure 6.5. The port at Plane 1 is the input of the UWB
antenna and the port at Plane 2 represents the input to the first section of the vocal tract
waveguide model. Note that at Plane 2, a2 and b2 are vectors of signals associated with
the left and right traveling modes in the first waveguide section, while a1 and b1 at plane
1 are scalars for the usual incident and reflected waves at the antenna. The goal is to
compute the waves b1 and b2 that result in response to the input waves a1 and a2 , or
"
b1
b2
#
=
"
S11 S 12
S 21 S 22
#"
a1
a2
#
.
(6.51)
S 22 and S 21 represent modal reflection looking out of the mouth and transmission from
the various modes from the mouth to antenna. These quantities are found by exciting a
point source in the waveguide in an FDTD simulation that is placed to excite all modes
of interest. Left and right traveling modes are extracted by finding the complex modal
amplitude at Planes 3 and 4 in Figure 6.5, solving a set of linear equations to obtain left
and right traveling waves, and then shifting the reference plane to Plane 2.
77
Figure 6.6: Incident and reflection wave coefficient at plane inside the vocal tract
Figure 6.6 shows a detailed representation of the operation to be performed, where a(z)
and b(z) are the complex amplitudes of the left and right traveling waves and x(z) is the
total mode complex amplitude for a single (but arbitrary) mode at position z.
Total mode amplitude is related to the forward and reverse traveling waves by
x(z1 ) = a(z1 ) + b(z1 )
(6.52)
x(z2 ) = a(z2 ) + b(z2 ).
(6.53)
Propagation of the mode is given by the propagation constant kz , allowing the relations
a(z1 ) = a(z2 )e−jkz ∆z
(6.54)
b(z1 ) = b(z2 )ejkz ∆z
(6.55)
to be written. Substitution of (6.54) and (6.55) into (6.52) yields
x(z1 ) = a(z2 )e−jkz ∆z + b(z2 )ejkz ∆z .
(6.56)
Solving (6.53) and (6.56) for a(z2 ) and b(z2 ) yields
b(z2 ) =
x(z1 ) − x(z2 )e−jkz ∆z
ejkz ∆z − e−jkz ∆z
a(z2 ) = x(z2 ) − b(z2 ).
(6.57)
(6.58)
78
6.6. VOCAL TRACT SHAPE ESTIMATION
0
S11 (Antenna)
S11 (Antenna/Head)
S21 (Antenna/Head)
Transmission/Return loss (dB)
−5
−10
−15
−20
−25
−30
−35
−40
2
4
6
Frequency (GHz)
8
10
Figure 6.7: Scattering parameters of the vocal tract represented as two port network for
T E11 mode
Values of a and b at the opening of the mouth at z=0 are found as
a(0) = a(z2 )e−jkz z2
(6.59)
b(0) = b(z2 )ejkz z2 .
(6.60)
Total mode amplitude can be extracted as
RR
E F DT D (x, y, z, t) × hm (x, y)ẑdA
x(z) = A RR
,
e
(x,
y)
×
h
(x,
y)ẑdA
m
m
A
(6.61)
where EF DT D is the FDTD transverse electric field, and em (x, y) and hm (x, y) are the
transverse modal pattern.
Using Equation (6.61), S21 is calculated and the simulation result is shown in Figure 6.7.
Note that below 9.12 GHz, a mouth radius of 2 cm, means purely evanescent modes in
the first waveguide section, as described by Equation 5.4 for T E11 mode.
6.6
Vocal Tract Shape Estimation
Estimation of the state of vocal tract from measured UWB responses requires inverse
scattering methods for waveguides. The development of direct inverse scattering methods
for our problem is challenging, due to the presence of multiple propagating and evanescent
79
modes that contribute to the scattered signal. In this section, a first step in this direction
is considered where the response is compared with a library of simulated responses for
all possible parameters at a given level of parameter quantization. The results indicate
that although features in the vocal tract can be estimated, estimating parameters beyond
significant obstructions is quite difficult, possibly requiring transmission (as opposed to
reflective) measurements. The vocal tract is modeled as a cascaded series of perfect
electrical conductor (PEC) circular waveguides, where the ith section has common length
L and distinct diameter di . For the interface from the ith to jth section, the multimode
(propagating and evanescent) S-parameters are found using the mode-matching technique,
where the assumption that the waveguides have a common axis is used, allowing the
required integrations to be performed rapidly in closed form [79].
Estimation of the waveguide parameters from the frequency-dependent multi-mode reflection coefficient is performed by computing a library of responses for all possible
combinations of di . Given the response, the unknown set of diameters is found by
comparing that response against all library entries, and the parameters from the closest
match is declared the state of the waveguide. Note that generating the library requires
the efficient mode-matching procedure, since FDTD simulations would be far too time
intensive.
As a tractable example, a 4-section waveguide is considered, where the diameter of the
first section (do ) is assumed to be known (4 cm) and the cascaded chain is terminated at
the right in a short circuit for all modes (Γ = −1). The possible di are quantized at 20
levels ranging from 0 to 4 cm.
Figure 6.8 depicts a typical reconstruction, where the UWB response for 35 frequencies
equally spaced from 3 to 10 GHz is computed, mode-matching computations are performed
using 2 modes (70 indices) which are stored and compared with the library, and additive
white Gaussian noise (AWGN) is added to obtain a measurement SNR of 30 dB. This
example illustrates one problem that is observed when performing inverse-scattering of
waveguides, or namely that estimating waveguide features past an obstruction is difficult.
Note that in the case of no obstruction, estimating waveguide features give a good results
as shown in Figure 6.9.
The accuracy of this method is investigated by defining the weighted reconstruction error
as
v
u PNs
ˆ 2
u
i=1 | wi (di − di) |
Err = t P
Ns
2
j=1 | wj dmax |
(6.62)
where Ns is the number of sections to be estimated (one less than the physical number of
sections), dmax is the maximum diameter of the cascaded sections, and wi is the weight of
80
6.6. VOCAL TRACT SHAPE ESTIMATION
1.5
Re(Sest )
Im(Sest )
Re(Sact )
Im(Sact )
Amplitude
1
0.5
0
-0.5
-1
-1.5
0
10
20 30 40 50 60
Frequency, Mode Index
70
(a) Response
Radius (cm)
4
Est
Act
3.5
3
2.5
2
1.5
1
0.5
0
0
2
4
6
8
Length (cm)
10
12
(b) Reconstruction
Figure 6.8: Vocal tract reconstruction using a library lookup based method: (a) matched
response, (b) estimated waveguide parameters
81
2
Re(Sest )
Im(Sest )
Re(Sact )
Im(Sact )
1.5
Amplitude
1
0.5
0
-0.5
-1
-1.5
0
10
20 30 40 50 60
Frequency, Mode Index
70
(a) Response
Radius (cm)
4
3.5
3
2.5
2
1.5
1
0.5
0
Estimated
Actual
0
2
4
6
8
Length (cm)
10
12
(b) Reconstruction
Figure 6.9: Vocal tract reconstruction using a library lookup based method: (a) matched
response, (b) estimated waveguide parameters
82
6.7. SUMMARY
(a) vs. Upper Frequency (2 modes)
Freq
Mean(Erra)
Std(Erra)
Mean (Errw)
Std(Errw)
6 GHz
33.1
19.7
15.6
11.2
10 GHz
23.3
18.3
8.2
6.8
20 GHz
19.4
17.0
5.1
3.9
(b) vs. Number of Modes (10 GHz)
Modes
Mean(Erra)
Std(Erra)
Mean (Errw)
Std(Errw)
1
21.7
18.4
7.1
5.9
2
29.7
19.1
10.4
7.9
10
25.1
18.8
7.7
6.3
Table 6.2: Percent error performance
the ith section. The absolute error Erra is computed assuming wi = 1, placing equal error
Qj−1
on all sections. The weighted error Errw is computed assuming wj = i=1
di /dmax , where
dmax = maxi di , reducing the weight for sections after obstructions, which are expected
to be difficult or even impossible to estimate.
Table 6.2 lists the mean and standard deviation of the errors for 100 Monte-Carlo simulations, where various frequency ranges and number of compared lowest-order modes
are considered. The results indicate that whereas increasing the upper frequency can
improve the estimation performance, using more than the lowest order mode does not
appear particularly helpful. This latter effect is likely due to the fact that only one mode
is not evanescent for the size of the waveguide under consideration.
6.7
Summary
This chapter explored the mode matching method for analyzing the vocal tract with the
purpose of reducing the modeling complexity of UWB propagation in the vocal tract.
In applying the modal analysis method, the vocal tract is broken up into a series of
uniform sections separated by transitions. The structure is conveniently analyzed using a
transmission line model employing S parameters. The generalized scattering matrices
employed relate both propagating and evanescent modes. The method was used to
implement a simple inverse-scattering procedure for waveguides based on library look up,
indicating that such reduced-order models are promising for reconstruction of vocal tract
parameters based on UWB response. A method for extracting the S parameter coupling
to the antenna was also presented. Estimation of the vocal tract shape from the measured
return response with inverse scattering methods is also conducted with the results indicate
that although features in the vocal tract can be estimated, estimating parameters beyond
significant obstructions is quite difficult, possibly requiring transmission (as opposed to
reflective) measurements.
7. BODY AREA NETWORK: NUMERICAL METHODS
83
Chapter 7
Body Area Network: Numerical
Methods
Body area networks (BANs) are an emerging paradigm for wireless communications
where communicating nodes are placed on, near, or inside the body which have several
applications in biomedicine, sports, emergency response, and consumer electronics [22].
Remote health monitoring of patients, for example, requires wireless sensors placed on the
patient’s body to monitor pulse, respiration, blood pressure, etc. Although such sensors
can be connected by wired links, wireless BANs employing RF and microwave propagation
provide more freedom of movement for the user. However, designing wireless BAN systems
that are robust, efficient, and high performance is challenging since the body forms an
integral part of the antennas and propagation channel. An important goal is to develop
modeling strategies for BANs that can accurately capture the effects of the body, yet
are computationally efficient, allowing rapid implementation and simulation. Note that
the modeling situation for BANs is quite different from sensing applications. For sensing
applications, coupling of the radiated fields with the body should be enhanced, whereas
for BANs, it is usually desirable to mitigate the effect of the body on propagation.
BAN communication is most challenging when two communicating nodes are shadowed
from each other due to the presence of the body. In [80] it was identified that propagation
between two shadowed BAN nodes can occur due to waves penetrating through the
body or creeping around the body, but that the creeping waves dominate in most cases.
BAN characterization has been achieved by measurements [24, 81, 82], as well as detailed
simulations [80]. Although studies successfully assess BAN communications for a specific
type of antenna and environment, an important drawback of these approaches is that
the observations are antenna and environment specific, possibly limiting the generality
of the results. Ideally, characterization of the BAN channel should consider propagation
mechanisms due to the body alone, allowing arbitrary antennas and environments to be
84
Figure 7.1: Two-step procedure for body area modeling
modeled.
An analytical model that was presented and experimentally verified in [83] that provides a
useful initial solution to accurate and simple BAN modeling, where the body is assumed
to be an infinite lossy circular dielectric cylinder. This chapter provides an improved
method for modeling BAN propagation that has a similar strategy and complexity to
the simple model in [83]. In order to derive the electric fields around the human torso
resulting from a point source, the two step procedure from [83] depicted in Figure 7.1 is
followed. First, the problem of radiated fields from a linear current source located outside
the torso model is solved. Second, the line source solution is converted to a point source
solution by performing an inverse Fourier transform of the line source solution along the
spectral (propagation constant) dimension. Not only is the point source a reasonable
approximation of a small dipole, but also it represents the Green’s function that may be
used to find the response for arbitrary antennas.
This chapter extends the result of [83] in two ways. First, the analysis of the circular
dielectric cylinder is extended to arbitrary transmit and receive polarization. However,
comparisons with measurements (Chapter 8) indicate that the circular shape is too
simplistic to model the body in some cases. Second, an efficient surface-based methodof-moments technique is developed that allows a cylinder with arbitrary cross section to
be modeled, significantly improving accuracy in some cases. Note that comparison of the
models with measurements is considered in Chapter 8.
85
Figure 7.2: Circular cylinder excited with a line current source
7.1
Circular Cylinder BAN Model (Closed-Form Solution)
In this section, the modeling strategy in [83] is extended to arbitrary polarization. The
solution is simplified by using properties of waveguides that are also satisfied by the
structure of the BAN model. The body is modeled as a lossy circular dielectric cylinder
centered at the origin with (complex) permittivity r1 , radius a, and infinite extent in the
z direction, embedded in an infinite medium with dielectric constant r2 . Wave number
and intrinsic impedance for region i are ki and ηi , respectively.
7.1.1
Incident Fields
The cylinder is excited with a line current source centered at polar coordinates ρ = ρ0
and φ = φ0 as shown in Figure 7.2, or
J=−
4j
(aρ ρ̂0 + aφ φ̂0 + az ẑ) exp(−jkz z),
µ
(7.1)
where the sinusoidal variation in z is included to allow a line-to-point transformation as
well as model oblique far-field plane wave sources. Polar unit vectors at the source can
be written in terms of polar unit vectors at observation point (ρ, φ) as
ρ̂0 = ρ̂ cos(φ − φ0 ) − φ̂ sin(φ − φ0 ),
φ̂0 = φ̂ cos(φ − φ0 ) + ρ̂ sin(φ − φ0 ).
(7.2)
86
7.1. CIRCULAR CYLINDER BAN MODEL (CLOSED-FORM SOLUTION)
The vector potential of the incident field (field present in absence of the scatterer) is
(2)
Ainc = −
µH0 (kρ2 R)
J
4j
(2)
= H0 (kρ2 R){ρ̂[aρ cos(φ − φ0 ) + aφ sin(φ − φ0 )]
+ φ̂[aφ cos(φ − φ0 ) − aρ sin(φ − φ0 )] + ẑaz } exp(−jkz z),
(7.3)
p
2
where kz2 + kρi
= ki2 and R = ρ2 + ρ02 − 2ρρ0 cos(φ − φ0 ). In order to enforce continutity
of tangential (φ̂ and ẑ) electric and magnetic field on the surface of the scatterer, the
incident field needs to be written in terms of polar functions that are centered at the
origin (axis of the scatterer), requiring
(2)
H0 (kρ2 R) =
X
n
H (2) (kρ2 ρ0 )Jn (kρ2 ρ) exp[jn(φ − φ0 )],
{z
}
|n
{z
}|
Qn
Fn
(7.4)
valid for ρ < ρ0 , which is suitable for applying the boundary conditions since in this case
fields are only observed on the surface of the scatter, and the current at ρ0 is assumed to
be outside of this. Although the exact expression requires summation for n ∈ [−∞, ∞],
in practice the summation is truncated to a finite number of terms n ∈ [−N, N] for
numerical computation.
Circular functions in (7.3) can be expanded as complex exponentials, or
i 1
1 h j(φ−φ0 )
−j(φ−φ0 )
cos(φ − φ ) =
e
+e
= [Q1 + Q−1 ]
2
2
h
i
1
1 j(φ−φ0 )
−j(φ−φ0 )
0
e
−e
= [Q1 − Q−1 ],
sin(φ − φ ) =
2j
2j
0
(7.5)
(7.6)
and substitution yields
Ainc =
X
n
n a
aφ
ρ
Fn Qn ρ̂
(Q1 + Q−1 ) + (Q1 − Q−1 )
2
2j
aφ
aρ
+φ̂
(Q1 + Q−1 ) − (Q1 − Q−1 )
2
2j
−jkz z
+ẑaz e
.
(7.7)
The expression under the summation is expanded, allowing the summation to be distributed to the individual terms and the Q functions to be combined according to Qn Q±1 =
Qn±1 . Shifting each summation by one transforms Qn±1 back to Qn and the Fn to Fn∓1 .
87
Combining into a single sum gives
Ainc =
1X
ρ̂ [jaρ (Fn−1 + Fn+1 ) + aφ (Fn−1 − Fn+1 )]
2j n
+φ̂ [jaφ (Fn−1 + Fn+1 ) − aρ (Fn−1 − Fn+1 )]
+ẑj2az Fn Ψ
1 Xn
=
ρ̂ [Fn−1 (aφ + jaρ ) + Fn+1 (−aφ + jaρ )]
{z
}
|
2j n
Xn
+φ̂ [Fn−1 (−aρ + jaφ ) + Fn+1 (aρ + jaφ )]
|
{z
}
Yn
o
+ẑj2az Fn Ψ
0
where Ψ = e−jkz z ejn(φ−φ ) , or
Ainc =
(7.8)
1 X
0
[ρ̂Xn + φ̂Yn + ẑj2az Fn ]e−jkz z ejn(φ−φ ) .
{z
}
2j n |
A
(7.9)
Incident eletric field is found as
Einc
∞
1 ω X
=
[∇(∇ · A) + k22 A].
2j jk22 n=−∞
(7.10)
The divergence operation is evaluated as
∂Aρ Aρ 1 ∂Aφ ∂Az
+
+
+
∂ρ
ρ
ρ ∂φ
∂z
Xn
n
0
= Xn +
+ j Yn + 2kz az Fn Ψ,
ρ
ρ
{z
}
|
Tn
(7.11)
∇·A=
where {·}0 =
∂{·}
.
∂ρ
(7.12)
Evaluating the gradient,
1 ∂G
∂G
∂G
+ φ̂
+ ẑ
∇G = ρ̂
∂ρ
ρ ∂φ
∂z
jn
0
∇(∇ · A) = ρ̂Tn + φ̂ Tn − ẑjkz Tn Ψ,
ρ
(7.13)
(7.14)
yielding
Einc = Se
X
ρ̂
Tn0
+
k22 Xn
n
where
Tn0 = Xn00 +
+ φ̂
jn
Tn + k22 Yn
ρ
+ ẑj
2k22 az Fn
− kz Tn
ρXn0 − Xn jn(ρYn0 − Yn )
+
+ 2kz az Fn0
ρ2
ρ2
Ψ,
(7.15)
(7.16)
88
and Se = − 2kω2 . If we remove the − 4j
term in (7.1) to give unit current for unit a, the
µ
2
η2
µω
. Incident magnetic field is found as
solution instead requires Se = 8jk2 = −j 8k
2
2
1
(∇ × Ainc ),
(7.17)
2jµ
1 X
1 ∂Az
∂Aρ ∂Az
∂Aφ 1
∂Aφ
1 ∂Aρ
=
ρ̂
+ φ̂
+ ẑ
,
−
−
+ Aφ −
2jµ n
ρ ∂φ
∂z
∂z
∂ρ
∂ρ
ρ
ρ ∂φ
Hinc =
(7.18)
X
2n
1
jn
= Sh
ρ̂ − az Fn +jkz Yn + φ̂ (−jkz Xn − 2jaz Fn0 )+ ẑ Yn0 + Yn − Xn Ψ,
ρ
ρ
ρ
n
(7.19)
where Sh =
7.1.2
ω
.
2jη2 k2
Removing the − 4j
term to scale for unit current, we have Sh = 1/8.
µ
Scattered Fields
Since we have e−jkz z variation of the fields, the scenario is analogous to waveguide modes
where transverse-directed (ρ̂, φ̂) fields can be written in terms of ẑ-directed fields only.
This is convenient, since for each term in the cylindrical mode series, we will have only
four unknowns: scattered Ez and Hz outside the cylinder and total Ez and Hz inside the
cylinder. Also, for each mode, we will have four equations arising from continuity of Ez ,
Hz , Eφ , and Hφ , thus producing a unique solution to the problem.
Analogous to a waveguide with e−jkz z variation, transverse fields are given by
j
(kη∇T × ẑHz + kz ∇T Ez ) ,
kρ2
j k
∇T × ẑEz − kz ∇T Hz ,
HT = 2
kρ η
ET = −
where the transverse-only curl and gradient are
∂Az
1 ∂Az
− φ̂
∇T × ẑAz = ρ̂
ρ ∂φ
∂ρ
1 ∂G
∂G
+ φ̂
.
∇T G = ρ̂
∂ρ
ρ ∂φ
(7.20)
(7.21)
(7.22)
(7.23)
Inside the scatterer, arbitrary total field Ez and Hz can be represented with the polar
expansion
Ez,1 =
X
An Jn (kρ1 ρ)Ψ
(7.24)
Bn Jn (kρ1 ρ)Ψ,
(7.25)
n
Hz,1 =
X
n
89
where scalars An and Bn remain to be determined. Substituting (7.24) and (7.25) into
(7.20) and (7.21) results in
j
∂Hz
∂Ez
1 ∂Hz
1 ∂Ez
= − 2 k1 η1 ρ̂
− φ̂
+ kz ρ̂
+ φ̂
kρ1
ρ ∂φ
∂ρ
∂ρ
ρ ∂φ
n
X
jnk1 η1
j
Bn Jn (kρ1 ρ) + kz kρ1 An Jn0 (kρ1 ρ) +
ρ̂
=− 2
kρ1 n
ρ
jnkz
0
φ̂
An Jn (kρ1 ρ) − k1 η1 kρ1 Bn Jn (kρ1 ρ) Ψ
ρ
ET,1
(7.26)
(7.27)
and
HT,1
k1
1 ∂Ez
∂Ez
∂Hz
1 ∂Hz
j
ρ̂
− φ̂
− kz ρ̂
+ φ̂
= 2
kρ1 η1
ρ ∂φ
∂ρ
∂ρ
φ ∂φ
j jnk1
An Jn (kρ1 ρ) − kz kρ1 Bn Jn0 (kρ1 ρ) +
= 2 ρ̂
kρ1
η1 ρ
jnkz
k1 kρ1
0
φ̂ −
Bn Jn (kρ1 ρ) −
An Jn (kρ1 ρ) Ψ.
ρ
η1
(7.28)
(7.29)
Outside the scatterer, arbitrary outward traveling scattered field can be represented as
Ez,2 =
X
Cn Hn(2) (kρ2 ρ)Ψ
(7.30)
Dn Hn(2) (kρ2 ρ)Ψ,
(7.31)
n
Hz,2 =
X
n
where again the scalars Cn and Dn will be determined by the boundary conditions.
Transverse scattered field is found in the same way as with total field inside the scatterer,
giving
ET,2
HT,2
j X n jnk2 η2
(2)
(2) 0
ρ̂
=− 2
Dn Hn (kρ2 ρ) + kz kρ2 Cn Hn (kρ2 ρ) +
kρ2 n
ρ
o
jnkz
(2)
(2) 0
Cn Hn (kρ2 ρ) − k2 η2 kρ2 Dn Hn (kρ2 ρ) Ψ
φ̂
ρ
j
jnk2
(2)
(2) 0
= 2 {ρ̂
Cn Hn (kρ2 ρ) − kz kρ2 Dn Hn (kρ2 ρ) +
kρ2
η2 ρ
jnkz
k2 kρ2
(2)
(2) 0
φ̂ −
Dn Hn (kρ2 ρ) −
Cn Hn (kρ2 ρ) }Ψ.
ρ
η2
(7.32)
(7.33)
90
7.1.3
Determination of Unknown Coefficients
The unknown coefficients An , Bn , Cn , and Dn are found by equating total tangential field
on the boundary at ρ = a, or
Ez,inc + Ez,2 = Ez,1
(7.34)
Hz,inc + Hz,2 = Hz,1
(7.35)
Eφ,inc + Eφ,2 = Eφ,1
(7.36)
Hφ,inc + Hφ,2 = Hφ,1 .
(7.37)
The only way each of these equations to be satisfied for all φ is to have equality for each
modal term (fixed value of n). For Ez ,
Se [−jkz Tn + k22 2jaz Fn ] + Cn Hn(2) (kρ2 a) = An Jn (kρ1 a).
(7.38)
For Eφ ,
j jnkz
jnTn
2
(2)
(2) 0
+ k2 Y n ] − 2
Cn Hn (kρ2 a) − k2 η2 kρ2 Dn Hn (kρ2 a) =
Se [
a
kρ2
a
j jnkz
0
An Jn (kρ1 a) − k1 η1 kρ1 Bn Jn (kρ1 a) .
− 2
kρ1
a
(7.39)
For Hz ,
1
jn
0
Sh Yn + Yn − Xn + Dn Hn(2) (kρ2 a) = Bn Jn (kρ1 a).
a
a
(7.40)
For Hφ ,
Sh [−jkz Xn −
2jaz Fn0 ]
jnkz
k2 kρ2
j
(2)
(2) 0
Dn Hn (kρ2 a) −
Cn Hn (kρ2 a) =
+ 2 −
kρ2
a
η2
jnkz
k1 kρ1
j
0
−
An Jn (kρ1 a) .
Bn Jn (kρ1 a) −
2
kρ1
a
η1
(7.41)
For each value of n, a matrix equation of the form
Z[An Bn Cn Dn ]T = [Ez,inc,n Eφ,inc,n Hz,inc,n Hφ,inc,n ]T
(7.42)
is formed and inverted to obtain the unknown coefficients. These coefficients can then
be plugged back into the previous expressions to obtain field both inside and outside the
scatterer. Note that outside the scatterer, incident field must be added to scattered field
to obtain total field.
91
7.1.4
Non-singular Expression for Incident Field
Note that the modal expansion (7.4) assumes an observation radial distance ρ that is less
than the radial distance of the source current. Although a different modal expansion can
be used for ρ > ρ0 , these modal expansions exhibit singular behavior near ρ = ρ0 , which
unfortunately is the most interesting case for on-body communication.
The singular behavior is avoided by only using the modal expansion for enforcing the
boundary condition and obtaining the unknown coefficients An , Bn , Cn , and Dn . Once
these are found, incident field outside the scatterer is obtained by using the simple direct
form of the incident vector potential in (7.3), which is only singular when both ρ and φ
of source and observation are coincident.
Assuming a line current source at the origin
J = (x̂ax + ŷay + ẑaz ) exp(−jkz z),
(7.43)
vector potential of the radiated field is given by
Ainc = −
where R =
p
µ
(2)
(x̂ax + ŷay + ẑaz )H0 (kρ2 R) exp(−jkz z),
4j
(7.44)
x2 + y 2. We can find Einc directly in cartesian coordinates according to
Einc =
ω 2
∇(∇
·
A
)
+
k
A
,
inc
inc
2
jk22
(7.45)
which yields
Ex,inc
Ey,inc
Ez,inc
x2
kρ2
(2) 0
2 (2)
H0 (kρ2 R) + U
+ k2 H0 (kρ2 R) +
R
R
xkz kρ2 az (2) 0
ay kρ2 xyU
−j
H0 (kρ2 R)}e−jkz z
2
R
R
2
η2
y
k
ρ2
(2) 0
2 (2)
= {ay H0 (kρ2 R) + U
+ k2 H0 (kρ2 R) +
k2
R
R
ax kρ2 xyU
ykz kρ2 az (2) 0
−j
H0 (kρ2 R)}e−jkz z
2
R
R
η2
kz kρ2
(2)
(2) 0
2
2
=
(k2 − kz )az H0 (kρ2 R) − j
(xax + yay )H0 (kρ2 R) e−jkz z ,
k2
R
η2
= {ax
k2
(2)
(2)
(7.46)
(7.47)
(7.48)
where U = kρ2 H0 00 (kρ2 R) − (1/R)H0 0 (kρ2 R). If needed, incident magnetic field outside
the scatterer is found as
1
(7.49)
Hinc = (∇ × A),
µ
92
7.2. SURFACE-BASED NUMERICAL SOLUTION FOR BAN PROPAGATION
which gives
Hx,inc
Hy,inc
Hz,inc
j az kρ2 y (2) 0
(2)
=
H0 (kρ2 R) + jkz ay H0 (kρ2 R) e−jkz z
4
R
az kρ2 x (2) 0
j
(2)
H0 (kρ2 R) e−jkz z
= − jkz ax H0 (kρ2 R) +
4
R
j ay kρ2 x ax kρ2 y
(2)
=
H0 0 (kρ2 R)e−jkz z .
−
4
R
R
(7.50)
(7.51)
(7.52)
Note that these expressions are for a line source centered at the origin, which must be
translated to the polar coordinate (ρ0 , φ0 ). Also, the direction of the source in polar
coordinates (aρ , aφ ) must be converted to a Cartesian direction (ax , ay ) before using these
expressions.
7.2
Surface-based Numerical Solution for BAN Propagation
A major limitation of the model presented in [83] and in the previous section is the unrealistic circular cross-section of the body. Although arbitrary cross-section can be modeled
with FDTD, FEM, and volumetric method-of-moments (MOM), these methods can be
computationally expensive due to the high dielectric permittivity of the body coupled
with the need to segment the complete volume, where typically 8-10 cells per wavelength
are required for high accuracy. In this section, a surface based MOM simulation strategy
is developed, where only the surface of the lossy cylinder needs to be segmented, leading
to high accuracy and computational savings over volumetric methods.
Figure 7.3 depicts a lossy dielectric cylinder model of the body, whose shape varies only
in the xy plane and is infinite and homogeneous in the z-direction. The perimeter of
the object is defined by the contour C, whereas contour Cs encloses the line source and
contour C∞ recedes to infinity. It is required to calculate the field at an observation point
(x, y) in response to a point current source of arbitrary orientation having the current
density
J = δ(x − x0 )δ(y − y0 )δ(z − z0 )(ax x̂ + ay ŷ + az ẑ).
(7.53)
Like in the previous section, this problem is solved using the approach in [83], where first
the fields due to a line source with current density
J = δ(x − x0 )δ(y − y0 )(ax x̂ + ay ŷ + az ẑ) exp(−jkz z)
(7.54)
are obtained, which can then be transformed via Fourier techniques to find the point
source solution, as explained in Section 7.3.
93
Figure 7.3: Arbitrarily shaped biological body illuminated by electromagnetic wave
This simplified BAN propagation problem is solved by borrowing properties of waveguides
to identify the unique unknown field quantities, writing the governing surface integral
inside and outside the body boundary in terms of those unknowns, discretization the
surface integrals using the Method-of-Moments (MOM), and finally enforcing the proper
continuity conditions at the boundary.
7.2.1
Governing Equations
In a homogeneous region without sources, electric (E) and magentic (H) field satisfy
[∇2 + k 2 ]{E, H} = 0,
(7.55)
where k is the wavenumber of the medium.
Since the line source has exp(−jkz z) variation and the geometry is homogeneous in z, the
solutions for E and H must also have exp(−jkz z) variation. As in waveguide analysis,
this form allows fields transverse to the z direction to be written as
−j
(7.56)
E T = 2 (kη∇T × ẑHz + kz ∇T Ez ),
kρ
j k
(7.57)
H T = 2 ( ∇T × ẑEz − kz ∇T Hz ),
kρ η
where kρ2 = k 2 − kz2 , which means that Ez and Hz are the only unique unknowns, and in
the ith homogeneous region, the two-dimensional relationship
2
[∇2T + kρi
]{Ez , Hz } = 0
(7.58)
2
holds, where ∇T = x̂∂/∂x + ŷ∂/∂y is a two-dimensional transverse operator and kρi
=
2
2
ki − kz . The solution to the problem
2
[∇2T + kρi
]gi (ρ, ρ0 ) = δ(x − x0 )δ(y − y 0 )
(7.59)
94
is given by the usual two-dimensional scalar Green’s function
j (2)
gi (ρ, ρ0 ) = H0 (kρi |ρ − ρ0 |),
4
and combining (7.60) and (7.58) with Green’s theorem, yields
Z 0
0
0 ∂gi (ρ, ρ )
0 ∂Ezi (ρ )
Ezi (ρ) =
− gi (ρ, ρ )
d`0 ,
Ezi (ρ )
0
0
∂n
∂n
∂Si
(7.60)
(7.61)
where Ezi is Ez in the ith region, ∂Si is the contour formed by the boundary of the
homogeneous region Si , n̂0 is the normal vector on the contour at point ρ0 outward from
Si , and the same equation holds for Hz . For a region Si defined to lie inside multiple
unconnected boundaries, (7.61) still holds where ∂Si includes all boundaries and n̂0 is
always away from the medium Si . Note that the observation point in (7.61) must be
strictly inside Si .
Fields in Region 0 (outside the body) are found by writing (7.61), with closed contours
around the line source, around the body, and at infinity (far-field), as depicted in Figure 7.3. The contour Cs around the line source just yields fields radiated by that source
in free space, and the contour integral at infinity vanishes, leaving
inc
scat
(ρ) + Ez0
(ρ)
Ez0 (ρ) = Ez0
I 0
0
scat
0 ∂g0 (ρ, ρ )
0 ∂Ez0 (ρ )
Ez0 (ρ) = −
Ez0 (ρ )
− g0 (ρ, ρ )
d`0 ,
0
0
∂n
∂n
C
s
s
(7.62)
(7.63)
where n̂0s is the outward normal direction from the scatterer (the body) and the sign
change comes from n̂0s = −n̂0 in Region 0. Fields in Region 1 (inside the body) are given
by the single contour integral
I 0
0
0 ∂g1 (ρ, ρ )
0 ∂Ez1 (ρ )
− g1 (ρ, ρ )
d`0 .
(7.64)
Ez1 (ρ )
Ez1 (ρ) =
0
0
∂ns
∂ns
C
7.2.2
Incident Fields
Incident electric and magnetic fields for the line current source are given by
i
η0 n h (2) 0
x2 kρ0
(2)
Exinc =
ax H0 (kρ0 R) + U
+ k22 H0 (kρ0 R)
4k0
R
R
o
xkz kρ0 az (2) 0
ay kρ0 xyU
−
j
H
(k
R)
e−jkz z
+
ρ0
0
R2
R
i
η0 n h (2) 0
y 2 kρ0
(2)
Eyinc =
ay H0 (kρ0 R) + U
+ k22 H0 (kρ0 R)
4k0
R
R
o
ykz kρ0 az (2) 0
ax kρ0 xyU
−
j
H
(k
R)
e−jkz z
+
ρ0
0
2
R
R
η0 n 2
(2)
inc
(k0 − kz2 )az H0 (kρ0 R)
Ez =
4k0
o
kz kρ0
(2)
−j
(xax + yay )H0 0 (kρ0 R) e−jkz z ,
R
(7.65)
(7.66)
(7.67)
95
(2) 00
(2)
(kρ0 R) − (1/R)H0 0 (kρ0 R), and
j az kρ0 y (2) 0
(2)
inc
Hx =
H0 (kρ0 R) + jkz ay H0 (kρ0 R) e−jkz z
4
R
az kρ0 x (2) 0
j
(2)
inc
H0 (kρ0 R) e−jkz z
Hy = − jkz ax H0 (kρ0 R)+
4
R
j ay kρ0 x ax kρ0 y
(2)
Hzinc =
H0 0 (kρ0 R)e−jkz z ,
−
4
R
R
where U = kρ0 H0
(7.68)
(7.69)
(7.70)
and R = |ρ − ρ0 |, where ρ0 is the coordinate of the line source.
7.2.3
Boundary Conditions
Solving the governing equations requires enforcing the proper continuity conditions at the
z
z
boundary. Although Hz0 = Hz1 and Ez0 = Ez1 on C, the normal derivatives ∂H
and ∂E
∂ns
∂ns
may be discontinuous on the boundary.
Let n̂ = n̂s be the outward normal of the scatterer (orthogonal to ẑ) and `ˆ = ẑ × n̂ be the
vector tangential to the surface. The transverse field components satisfy the conditions
n̂ × E T 0 = n̂ × E T 1
(7.71)
n̂ · (0 E T 0 ) = n̂ · (1 E T 1 )
(7.72)
n̂ × H T 0 = n̂ × H T 1
(7.73)
n̂ · H T 0 = n̂ · H T 1 ,
(7.74)
where E T 0 , H T 0 and E T 1 , H T 1 represent the transverse component of the fields just
outside and just inside the scatterer respectively. Substituting Equation (7.56) and (7.57)
into Equation (7.71) and (7.73) yields,
1
1
(k1 η1 n̂ × ∇T × ẑHz1 + kz n̂ × ∇T Ez1 ) = 2 (k0 η0 n̂ × ∇T × ẑHz0 + kz n̂ × ∇T Ez ) (7.75)
2
kρ1
kρ0
and
1 k0
1 k1
( n̂ × ∇T × ẑEz1 − kz n̂ × ∇T Hz1 ) = 2 ( n̂ × ∇T × ẑEz0 − kz n̂ × ∇T Hz0 ). (7.76)
2
kρ1 η1
kρ0 η0
Also substituting Equation (7.56) and (7.57) into Equation (7.72) and (7.74) yields,
0
1
(k0 η0 n̂ · ∇T × ẑHz0 + kz n̂ · ∇T Ez0 ) = 2 (k1 η1 n̂ · ∇T × ẑHz1 + kz n̂ · ∇T Ez1 ) (7.77)
2
kρ0
kρ1
and
1 k1
1 k0
n̂
·
∇
×
ẑE
−
k
n̂
·
∇
H
)
=
(
( n̂ · ∇T × ẑEz1 − kz n̂ · ∇T Hz1 ).
T
z0
z
T
z0
2
2
kρ0
η0
kρ1
η1
(7.78)
96
The required operations
∂f
∂n
∂f
n̂ × (∇T f ) = ẑ
∂`
∂f
n̂ · (∇T × ẑf ) =
∂`
∂f
n̂ · (∇T f ) =
∂n
are easily derived, where f is an arbitrary function. Thus, equations (7.75)-(7.78)
n̂ × (∇T × ẑf ) = −ẑ
2 kρ1
∂Hz0
∂Hz1
∂Ez0 ∂Ez1
k
η
= k1 η1
−k
−kz
0 0
z
2
kρ0
∂n
∂`
∂n
∂`
2 2
kρ1
η1
∂Hz0
∂Hz1
∂Ez0 ∂Ez1
k
η
= k1 η1
+k
+kz
0
0
z
2 2
kρ0 η0
∂`
∂n
∂`
∂n
2 kρ1 k0 ∂Ez0
k1 ∂Ez1
∂Hz0
∂Hz1
=
+ kz
+ kz
2
kρ0 η0 ∂n
∂`
η1 ∂n
∂`
2 kρ1 k0 ∂Ez0
k1 ∂Ez1
∂Hz0
∂Hz1
=
− kz
− kz
,
2
kρ0 η0 ∂`
∂n
η1 ∂`
∂n
(7.79)
(7.80)
(7.81)
(7.82)
give
(7.83)
(7.84)
(7.85)
(7.86)
z
z
and ∂E
must be equal on the two
respectively. Note that the tangential derivatives ∂H
∂`
∂`
sides of the interface, since everywhere on the contour Hz0 = Hz1 and Ez0 = Ez1 . Using
this fact the tangential derivatives can be eliminated from the equations, yielding
∂Hz0
∂Hz1
= ch,1
∂n
∂n
∂Ez0
∂Ez1
ce,0
= ce,1
,
∂n
∂n
ch,0
(7.87)
(7.88)
where
1
2
k
η
−
k
β
,
i
i
z
2
kρi
−1 1
k1
1
k0
− 2 ,
− 2
β=
2
2
kρ0
η0 kρ1
η1
kρ0
kρ1
ch,i =
(7.89)
(7.90)
and ce,i = ch,i /ηi2 . Therefore, we only need to retain z-directed fields and normal derivatives on the outside surface as the unique unknowns, and substitute (7.87)-(7.88) for
fields on the inside boundary. Also, note that since governing equations and boundary
conditions for Ez and Hz are uncoupled, they can be solved for separately.
7.2.4
Discretization
Discretization of the problem is accomplished using the usual MOM procedure, where the
closed contour C consists of N straight-line segments, and a typical segment is depicted
97
e
ρen+1 = (xen+1, yn+1
)
n̂s,n
Free Space
`n
k = k0
ˆ
ρn = (xn, yn)
`n
ρen = (xen, yne )
Body
k = k1
0
C
Figure 7.4: The nth segment for the Method-of-Moments discretization procedure. Order
of the endpoints is chosen so that when moving to the next endpoint, the outward normal
of the scatterer n̂s points to the right.
in Figure 7.4, where ρ0 = (x0 , y 0) is a coordinate along the contour, and `n , ρen = (xen , yne ),
ρn = (xn , yn ), and n̂s,n are the length, first endpoint, midpoint, and (body) outward
normal, of the nth segment, respectively. Segments are connected such that n̂s,n points
to the right when moving from ρen to ρen+1 , i.e. the segments go counter-clockwise around
the scatterer.
To find Ez and
∂Ez
,
∂n
these unknowns are expanded in Region 0 as
Ez0 (x, y) =
∂Ez0 (x, y)
=
∂ns
N
X
n=1
N
X
an fn (x, y),
(7.91)
bn fn (x, y),
(7.92)
n=1
where the point ρ = (x, y) lies on the contour C, and fn (x, y) is a pulse function giving
1 when (x, y) lies on segment n and 0 otherwise. Substituting into (7.62) and applying
point matching at (xm , ym ),
N
X
an δmn =
inc
Ez0
(xm , ym )
n=1
−
N
X
n=1
an Q(0)
mn
+
N
X
(0)
bn Smn
,
(7.93)
n=1
where
Q(0)
mn
=
(0)
Smn
Z
`n
0
=
Z
∂g0 [xm , ym ; xn (`0 ), yn (`0 )] 0
d`
∂n0s
`n
g0 [xm , ym ; xn (`0 ), yn (`0 )]d`0 ,
(7.94)
(7.95)
0
and x and y along the contour segment are given by pn (`0 ) = (pen+1 − pen )`0 + pen , with
p ∈ {x, y}. The derivative of the Green’s function in (7.94) can be evaluated directly as
(2)
jkρi H0 0 (kρi R)
∂gi
=
[ns,n,x (x0 − x) + ns,n,y (y 0 − y)],
∂n0s
4
R
where n̂s,n = ns,n,x x̂ + ns,n,y ŷ and R = |ρ − ρ0 |.
(7.96)
98
n̂s,m = ŷ
Free Space
k = k0
ρm = (0, 0)
`ˆm
−`m /2
x̂
`m /2
Body
k = k1
Figure 7.5: Integration path for case of m = n, where segment is rotated and translated
to the origin for convenience.
For m 6= n, we can approximate integrals in (7.93)-(7.95) as the integrand evaluted at the
midpoint times the length of the segment, or
Q(0)
mn ≈
∂g0 [xm , ym ; xn , yn ]
`n
∂n0s
(0)
Smn
≈ g0 (xm , ym ; xn , yn )`n .
(7.97)
(7.98)
For higher accuracy, multipoint numerical quadrature methods can also be applied.
For the case of m = n, the observation point is on the source segment, and the integral
must be evaluated. Figure 7.5 depicts the integration path for the case of m = n where
the segment has been rotated to align with the x-axis and translated to have its midpoint
at the origin. We have
Z
j `m /2 (2)
(0)
H (kρ0 |x0 |)dx0
(7.99)
Smm =
4 −`m /2 0
Z
j `m /2 (2)
=
H0 (kρ0 x0 )dx0
(7.100)
2 0
Z kρ0 `m /2
j
(2)
H0 (u)du,
(7.101)
=
2kρ0 0
which can be evaluated using the indefinite integral
Z
(2)
s(u) = H0 (u)du,
(7.102)
1
(2)
(2)
(2)
= uH0 (u) + πu[T0 (u)H1 (u) − T1 (u)H0 (u)]
2
where T0 (u) and T1 (u) are the Struve functions [84]
2
u3
u5
T0 (u) =
u − 2 2 + 2 2 2 − ...
π
1 ·3
1 ·3 ·5
2
4
u
u6
2 u
−
+
− ... .
T1 (u) =
π 12 ·3 12 ·32 ·5 12 ·32 ·52 ·7
(7.103)
(7.104)
Since limu→0 s(u) = 0, we have
(0)
Smm
=
j
s(kρ0 `m /2).
2kρ0
(7.105)
99
(0)
For the evaluation of Qmm , we avoid direct integration of the higher order singularity by
changing the contour to be that depicted in Figure 7.6, chosen such that the observation
point at the middle of the interval is inside the complete contour C, and let ∆ → 0. Along
Free Space
k = k0
n̂s,m = ŷ
(0, 0)
C1
C3
∆
−`m /2
n̂s,m = −ρ̂
`m /2
x̂
Body
k = k1
C2
Figure 7.6: Integration path for observing fields in Region 0 for the singular case of m = n,
where segment is rotated and translated to the origin for convenience.
(0)
C1 , the contribution to Qmm is
j
lim
y→0 4
Z
−∆
−`m /2
(2)
H0 0 (kρ0 R)
kρ0 y
dx,
R
(7.106)
p
where R = x2 + y 2, and (7.106) vanishes as does the contribution on C3 . Thus, only
the integral on C2 has a contribution, and recognizing n̂s,m = −ρ̂,
Z 0
(2)
∂H
(k
ρ)
j
ρ0
0
∆dφ,
(7.107)
Q(0)
=
−
lim
mm
∆→0 4 φ=−π
∂ρ
ρ=∆
Z 0
j
2 ∂ ln(kρ0 ρ) = − lim
∆dφ
(7.108)
∆→0 4 φ=−π jπ
∂ρ
ρ=∆
1
=− ,
(7.109)
2
where the integral was performed from −π to 0 to ensure that d` = ∆dφ is positive and
the logarithm came from the small argument approximation of the Hankel function.
In a similar way, the surface integral inside the body (7.64) is evaluated according to
N
X
an δmn =
n=1
where
Q(1)
mn
=
(1)
Smn
=
N
X
an Q(1)
mn
n=1
Z
`n
0
ce,0
ce,1
−
N
X
(1)
bn Smn
,
(7.110)
n=1
∂g1 [xm , ym ; xn (`0 ), yn (`0 )] 0
d` ,
∂n0s
Z `n
g1 [xm , ym; xn (`0 ), yn (`0 )]d`0 ,
(7.111)
(7.112)
0
where (7.88) was combined with (7.92) to obtain
quadrature can be used as before.
∂Ez1
.
∂ns
For m 6= n, single point numerical
(2)
Q(1)
mn
(1)
Smn
jkρ1 `n H0 0 (kρ1 Rmn )
[nx,n (xn − xm ) + ny,n (yn − ym )]
=
4
Rmn
j`n (2)
H (kρ1 Rmn ).
=
4 0
(7.113)
(7.114)
100
n̂s,m = ρ̂
n̂s,m = ŷ
C2
C1
C3
∆
−`m /2
Free Space
k = k0
x̂
`m /2
(0, 0)
Body
k = k1
Figure 7.7: Integration path for observing fields in Region 1 for the singular case of m = n,
where segment is rotated and translated to the origin for convenience.
For the case of m = n, only the integral on C2 has a contribution as shown in Figure 7.7,
and recognizing n̂s,m = ρ̂
Q(1)
mm
j
= lim
∆→0 4
j
= lim
∆→0 4
1
= ,
2
Z
π
φ=0
Z
π
φ=0
(2)
∂H0 (kρ0 ρ) ∂ρ
∆dφ,
ρ=∆
2 ∂ ln(kρ0 ρ) ∆dφ
jπ
∂ρ
ρ=∆
(7.115)
(7.116)
(7.117)
where the integral was performed from 0 to π to ensure that d` = ∆dφ is positive, and
(1)
Smm
j
=
4
j
=
2
Z
−`m /2
`m /2
Z
`m /2
0
j
=
2kρ1
Z
0
(2)
H0 (kρ1 |x0 |)dx0
(2)
H0 (kρ1 x0 )dx0
kρ1 `m /2
(2)
H0 (u)du,
(7.118)
(7.119)
(7.120)
which can be evaluated as before, thus
(1)
Smm
=
jce,0
s(kρ1 `m /2).
2kρ1 ce,1
(7.121)
Summarizing, (7.93) and (7.110) characterize the system, which can be written in matrix
form as
#" # " #
"
I + Q(0) −S (0)
a
v
=
,
(7.122)
(1)
(1)
b
0
I −Q
S
where vm = Ezinc (xm , ym ), and (7.122) can be inverted to find a and b. Scattered Ez
outside the body is given by
scat
Ez0
(ρ) = −
N
X
n=1
an Q(0)
n (ρ) +
N
X
n=1
bn Sn(0) (ρ),
(7.123)
101
where
Q(0)
n (ρ)
Sn(0) (ρ)
=
=
Z
Z
`n
0
`n
∂g0 [x, y; xn (`0 ), yn (`0 )] 0
d` ,
∂n0s
(7.124)
g0 [x, y; xn (`0 ), yn (`0 )]d`0 .
(7.125)
0
Total field inside the body is given as
scat
Ez1
(ρ)
=−
N
X
n=1
an Q(1)
n (ρ)
+
N
X
bn Sn(1) (ρ),
(7.126)
n=1
where
Q(1)
n (ρ)
Sn(1) (ρ)
=
=
Z
Z
`n
0
∂g1 [x, y; xn (`0 ), yn (`0 )] 0
d` ,
∂n0s
(7.127)
g1 [x, y; xn (`0 ), yn (`0 )]d`0 .
(7.128)
`n
0
The procedure for finding Hz is identical to that for Ez , by simply making the substitutions
Ez (x, y) → Hz (x, y),
(7.129)
Ezinc (xm , ym ) → Hzinc (xm , ym ),
(7.130)
ce,0 /ce,1 → ch,0 /ch,1 ,
(7.131)
in the above development.
After solution of Ez and Hz , transverse fields are given by (7.56) and (7.57), which in
component form are
j
∂Hz
∂Ez
Ex = − 2 kη
,
(7.132)
+ kz
kρ
∂y
∂x
∂Ez
∂Hz
j
,
(7.133)
− kη
Ey = − 2 kz
kρ
∂y
∂x
∂Hz
j k ∂Ez
,
(7.134)
+ kz
Hx = 2
kρ η ∂y
∂x
∂Hz
k ∂Ez
j
.
(7.135)
−
Hy = 2 k z
kρ
∂y
η ∂x
Transverse scattered field outside the body is found by substituting (7.126) and the
analogous expression for Hz into (7.132)-(7.135). In this case, derivatives with respect to
(0)
(0)
x or y can be transferred to Qn (ρ), and Sn (ρ), or
N
N
(0)
(0)
scat
X
∂Qn (ρ) X ∂Sn (ρ)
∂Ez0
(ρ)
=−
an
+
bn
,
∂p
∂p
∂p
n=1
n=1
(7.136)
102
7.3. POINT SOURCE
where p ∈ {x, y},
(0)
∂Qn (ρ)
=
∂p
(0)
∂Sn (ρ)
=
∂p
Z
Z
`n
0
`n
0
∂ 2 g0 [x, y; xn (`0 ), yn (`0 )] 0
d` ,
∂n0s ∂p
(7.137)
∂g0 [x, ym ; xn (`0 ), yn (`0 )] 0
d` ,
∂p
(7.138)
and
jkρ0 n
∂ 2 g0
(2)
(2)
[ns,n,x (x − x0 ) + ns,n,y (y − y 0)] × [Rkρ0 H0 00 (kρ0 R) − H0 0 (kρ0 R)]
=−
0
∂ns ∂p
4
(2)
H0 0 (kρ0 R) (p − p0 )
,
(7.139)
+
n
×
s,n,p
R3
R
(2)
∂g0
jkρ H0 0 (kρ R)
=
(p − p0 ).
(7.140)
∂p
4
R
7.3
Point Source
The electric and magnetic fields due to a line source near the lossy torso model derived in
the previous sections can be transformed to a point source, using the Fourier relationship
1
δ(z − z0 ) =
2π
Z
∞
e−jkz z ejkz z0 dkz .
(7.141)
−∞
Since the system is linear, the response to the point source can be written as a superposition of the responses due to line sources that make up the point source, or
1
E Point (x, y, z) =
2π
Z
∞
E Line (x, y, kz )e−jkz z dkz .
(7.142)
−∞
The integration in (7.142) is performed numerically using the parabolic contour integral
shown in Figure 7.8 together with Simpsons rule in the complex plane to avoid a singularity
when kz = k0 , the free space wave number. The complex wave number kz is defined as
kz = Re {kz } + jIm {kz } ,
where
"
Im {kz } = d 1 −
Re {kz } − k0
k0
(7.143)
2 #
,
(7.144)
and d should be selected carefully to avoid evaluation too close to the singularity. Here,
d is selected to be 0.1 and integration is performed from kz = 0 to 2k0 .
103
Figure 7.8: A parabolic contour integral around singularity kz = k0
7.4
Numerical Methods Validation
The closed-form solution for the circular cylinder and MOM solution for a cylinder with
arbitrary cross section are validated by comparing with FDTD simulations and with each
other. Here, a specific example is shown indicating that the two methods work correctly.
A cylinder of radius 1.0λ0 and relative permittivity of r = 2 is used as validation
target model, where the low permittivity is needed to keep the number of FDTD cells
manageable. An FDTD simulation domain size of 10λ0 × 10λ0 was used, discretized into
400×400 cells in the x and y directions, respectively. The PML was 10 cells thick on
all sides with a quadratic conductivity gradient and normal reflection coefficient of 10−5.
The simulations were run for 400 sinusoidal periods with 500 steps per period to ensure
high accuracy. The source was placed at φ0 = 0 and ρ0 = 1.5λ0 .
The comparison for different orientation of receive/transmit sensor/source are shown in
Figures 7.9, 7.10, 7.11 and 7.12 where Ez , Eρ and Eφ are compared at fixed observation
radius ρ = 1.6λ0 for different observation angle φ.
7.5
Summary
This chapter introduced body area networks (BANs), which are an important emerging
communications paradigm, and identified the need for efficient but accurate models for
BANs.
Two models were introduced that represent the body as an infinite lossy dielectric cylinder.
In the first case, an existing analysis was extended to the case of arbitrary source and
receive polarization, but a limitation of the approach is the unrealistic circular shape.
In the second case, an efficient simulation method for arbitrary cross section was developed
based on a surface method of moments solution. Note that in each case, the line source
solution is transformed to a point source by applying a Fourier transform.
The two methods were validated numerically by comparing with 2D FDTD simulations
104
7.5. SUMMARY
15
MOM
FDTD
Closed Form
Relative Channel Gain (dB)
10
5
0
−5
−10
−15
−20
−25
−30
0
100
200
°
φ
300
400
Figure 7.9: Channel comparison of Ez in response to a z-directed line source
30
MOM
FDTD
Closed Form
20
10
0
−10
−20
0
100
200
φ°
300
400
Figure 7.10: Channel comparison of Eρ in response to a ρ-directed line source
105
30
MOM
FDTD
Closed Form
20
10
0
−10
−20
−30
0
100
200
φ°
300
400
Figure 7.11: Channel comparison of Eφ in response to a φ-directed line source
20
MOM
FDTD
Closed Form
10
0
−10
−20
−30
−40
−50
0
100
200
φ°
300
400
Figure 7.12: Channel comparison of Eρ in response to a φ-directed line source
106
7.5. SUMMARY
of a line source. The results indicate that the methods are in agreement with FDTD as
well as each other. These methods will be compared with direct BAN measurements in
Chapter 8.
8. BODY AREA NETWORK: MODELING AND EXPERIMENTAL VALIDATION
107
Chapter 8
Body Area Network: Modeling and
Experimental Validation
In the previous chapter, closed-form and numerical methods for the prediction of BAN
channel characteristics were developed. In this chapter, predictions of the two models
are compared, where in the case of the moment method solution, a realistic torso model
based on a superquadratic ellipse is developed.
In addition to model comparisons, measurements are performed in a compact anechoic
chamber and in a large outdoor field, allowing the accuracy of the models to be compared
with BAN propagation on a real subject. The results indicate that these simple models
can provide sufficient accuracy in most cases.
8.1
Human Torso Models
In order to correctly quantify path loss around the human body, the human torso shape
should be accurately identified. A camera-based measurement system shown in Figure
8.1 is used in this work to measure the torso, where the subject stands on a circular
disk that is rotated to different angles, and at each angle, a photo is taken. Lengths in
the photos are calibrated by marking a known distance on the wall behind the subject,
allowing length D 0 for different rotations to be computed.
The computation of D 0 from relative distances in a photo is performed as follows, as shown
in Figure 8.1. The distances D1 , d2 , and d3 are measured, where D1 is an arbitrary distance
measured on the wall. In the photos, the ratio D/D1 is easily computed by dividing the
apparent width D of the subject (in pixels) by the apparent width D1 marked on the wall
(also in pixels).
108
8.1. HUMAN TORSO MODELS
D1
D
Wall
d2
D'
Subject
Marked point
on wall
d1
Camera
Figure 8.1: Camera-based torso measurement
Considering the geometry from Figure 8.1, the actual width D 0 is given by
d1 − d2
D =
d1
0
D
D1
D1 .
(8.1)
Ideally the camera should be as far from the subject and wall as possible to reduce
shadowing error. In this work, d1 =5 m, d2 =50 cm, and D1 =70 cm was used.
The torso measurement result for the subject in this work is shown in Figure 8.2 having
axial lengths a=1.55λ0 and b=1.19λ0 . Although the shape of the torso is roughly elliptical,
a better approximation is possible using a superquadratic ellipse, which provides more
flexibility in defining the body shape, given by
1.5
Measured
Superquadratic
1
λ
0.5
0
−0.5
−1
−1.5
−2
−1.5
−1
−0.5
0
λ
0.5
1
1.5
Figure 8.2: Measured torso of the subject
2
109
2
2
2
0
0
0
−2
−2
0
(a)
2
−2
−2
0
(b)
2
−2
−2
0
(c)
2
Figure 8.3: Human torso model for (a) circular, (b) elliptical and (c) superquadtratic
shape
x − x0 m y − y0 m
(8.2)
a + b = 1,
where a and b are the axial lengths, m is the exponent, and x0 and y0 are the center.
The exponent m = 2.35 that was used in Figure 8.2 provid good fit of the measured torso
with the superquadratic model. Three models depicted in Figure 8.3 were implemented
and compared to the measurements. For all models, relative permittivity r = 45.5−j10.9
was chosen to match average properties of fat (15%) and muscle (85%) at 2.55 GHz [66].
Also, the source was placed at φ0 = 0 and ρ0 = 1 cm for ẑ and φ̂ polarization and
ρ0 = 3 cm for ρ̂ polarization, corresponding to positions used in subsequent measurements.
The model parameters are as follows:
• Circular model: For the circular shape model shown in Figure 8.3(a), the radius
is chosen to be r= 1.42λ0 in order to have the same perimeter as the subject.
• Elliptical model: Figure 8.3(b) shows an elliptical model which has the same
perimeter length as the measured torso, while keeping the ratio of axial lengths a
and b constant. This leads to a = 1.59λ0 , b = 1.22λ0 .
• Superquadratic model: Figure 8.3(c) shows the superquadtratic model of axial
length a = 1.55λ0 , b=1.19λ0 and m=2.35, chosen to match the measured subject.
For each model, Ez , Eρ and Eφ fields were computed at different observation angle angle
φ.
8.1.1
Field Around the Torso Model
The electric field intensity as a function of angle φ at 2.55 GHz for z − z, ρ − ρ and φ − φ
polarization is shown in Figures 8.4, 8.5 and 8.6 respectively, where p1 − p2 polarization
refers to p1 -directed field in response to a p2 directed point current.
110
40
Superquadtratic
Elliptical
Circular
20
0
−20
−40
−60
−80
−100
0
100
200
φ°
300
400
Figure 8.4: Model comparison of Ez in response to a z-directed point source
The simulations show that the propagation loss around the torso decays nearly exponentially with distance (observation angle) and can be sensitive to the shape of the model,
especially for cross polarization as shown in Figures 8.7 and 8.8. Also, these figures show
some fluctuations (partial nulls) in the shadow region near the back of the torso which is
explained by the interference of clockwise and counter-clockwise creeping waves.
8.1.2
Field Inside and Outside Torso Model
Figure 8.9 shows the simulated field propagating into and around the human torso model
with a point source located at 1 cm outside the model for z-oriented point source. On
the right side of Figure 8.9, the electric field away from the model decays proportionally
with the square of the distance as expected in free space.
Figure 8.10 shows that the electric field inside the torso model decays exponentially
with distance [83] for a z-oriented point source. Actually, for high frequency, the fields
around the body will result from diffraction around the surface of the body rather than
penetration through the body, because the skin depth is proportional to the square root
of the wavelength of the operating frequency.
111
40
Superquadtratic
Elliptical
Circular
30
20
10
0
−10
−20
−30
−40
−50
0
100
200
φ°
300
400
Figure 8.5: Model comparison of Eρ in response to a ρ-directed point source
40
Superquadtratic
Elliptical
Circular
20
0
−20
−40
−60
−80
−100
0
100
200
φ°
300
400
Figure 8.6: Model comparison of Eφ in response to a φ-directed point source
112
20
Superquadtratic
Elliptical
Circular
10
0
−10
−20
−30
−40
−50
−60
0
100
200
φ°
300
400
Figure 8.7: Model comparison of Eρ in response to a φ-directed point source
20
Superquadtratic
Elliptical
Circular
10
0
−10
−20
−30
−40
−50
−60
0
100
200
φ°
300
400
Figure 8.8: Model comparison of Eφ in response to a ρ-directed point source
113
80
Torso model
60
Source
Power (dB)
40
20
0
−20
−40
−60
−2
−1
0
λ (m)
1
2
Figure 8.9: Electric field as a function of observation radius
60
−1.5
40
−1
λ (m)
0
0
Power (dB)
20
−0.5
0.5
−20
1
−40
1.5
−1.5
−1
−0.5
0
λ (m)
0.5
1
1.5
Figure 8.10: Field around and into a lossy human model
114
8.2. BAN MEASUREMENT SETUP
Figure 8.11: BAN measurement setup
8.2
BAN Measurement Setup
This section explains the measurement equipment, antennas, and scenarios used for
experimental validation of the BAN model.
8.2.1
Network Analyzer-Based System
Measurements of the BAN channel were performed with a Rohde&Schwarz ZVB20 vector
network analyzer connected to the antennas via 3 m instrument grade SMA cables (MiniCircuits CBL-10FT-SMS+) and 20 dBm transmit power as shown in Figure 8.11. During
the measurements, the subject placed his hands over his head to reduce the influence of
the arms. In this work, one antenna was placed above the left hip of the subject and
the other antenna starting above the right hip and moved in 1 cm increments around the
waist toward the other antenna. Automated measurements of S21 were performed by using
the LAN interface of the network analyzer controlled with MATLAB. S21 was measured
for each transmit position and the data was saved in a file for each transmit/receive
source/sensor combination.
8.2.2
BAN Antenna
Figure 8.13 depicts the antennas that were used for the measurement, which are 1.5 cm
monopoles. The monopoles were intentionally chosen to be short (approximately λ/8)
compared to the wavelength λ at 2.55 GHz, thus approximating a point transmit current
and a point receive field sensor. The matching efficiency of the short monopoles is between
0.1 and 0.5 depending on the orientation relative to the body as shown in Figure 8.12,
115
−0.5
−1
ρ−orinented source
φ−orinented source
z−orinented source
−2
−2.5
S
11
(dB)
−1.5
−3
−3.5
−4
−4.5
0
50
°
100
150
φ
Figure 8.12: Reflection coefficient of the short monopoles used in measurements, indicating
matching efficiency
but it is estimated that the maximum additional link loss of 20 dB does not significantly
hinder the short range BAN measurements.
Antennas were attached to the body by sewing them onto small Velcro patches and
attaching these to an ordinary back-support Velcro band worn around the waist. To
allow all combinations of the three transmit and receive polarizations to be measured,
two antennas were constructed with right angle cable connections (ρ̂ polarization) and
two with straight connections (φ̂ and ẑ polarization). A long Velcro measuring tape was
also constructed, which when attached to the waist strap allowed the antennas to be
positioned with ±1 mm accuracy.
Figure 8.13: Antennas for the BAN measurement
116
8.2. BAN MEASUREMENT SETUP
Figure 8.14: Anechoic chamber measurement with subject
During the measurements, when the antennas were very close to each other (<3 cm),
accurate placement was difficult due to the overlap of the Velcro bands, so some variation
from the ideal response is expected. The circumference of the subject from the two
extreme points above the hip was 47 cm. The thickness of the clothes and Velcro band
together was estimated as 0.5 cm. The distance between the body and the antenna can
significantly influence the pathloss and needs to be carefully determined. The additional
displacement of the antennas from the body was 2.5 cm for ρ̂ oriented and 0.5 cm for ẑ
and φ̂ oriented monopoles.
8.2.3
Anechoic Chamber and Outdoor Measurement
A small anechoic chamber was constructed in this work for performing on-body measurements having dimensions 2.0 m for the width and length and 2.2 m for the height. The
floor was constructed as an open lattice of thin planks, allowing microwave absorber to
be placed between the planks and a human subject to stand over the absorber. The
walls, floor, and ceiling are covered with EPP-22 absorber material from Telemeter
Electronic GmbH, having a guaranteed normal reflection below -40 dB in the 2-4 GHz
band. Due to budget constraints, only the center 1.5m×1.5m area of each surface was
covered with absorber, which is estimated to be sufficient to remove the strongest specular
wall reflections. Figure 8.14 depicts the inside of the chamber with the human subject.
Although channels were measured with a broadband 2 to 5 GHz sweep, only the results
at 2.55 GHz are presented and analyzed in this thesis.
Outdoor measurements were also carried out at the Jacobs University campus as shown
in Figure 8.15. The campus is open area environment, where the nearest building from
117
Figure 8.15: Outdoor measurement with subject
the measurement point is 70 m. Measurements were performed by placing the network
analyzer as far as possible from the subject (' 2.5 m) and covering the network analyzer
with absorber to reduce the effect of reflections from the instrument. In addition, microwave absorber was placed on the ground around the subject as well as in front of the
human operator who controlled the network analyzer with a PC and a 10 m LAN cable.
In this case the measurement was carried out just for the ẑ polarization for comparison
with the anechoic chamber measurement.
8.3
Measurement Results
Measurement results are compared with the superquadratic model from Section 8.1. All
measurements are from the anechoic chamber unless otherwise noted. Figure 8.16 depicts
the result for ρ̂ oriented transmitter and receiver (antenna perpendicular to body). The
model is able to accurately predict the field decay with increasing separation, as well as
the presence of a small dip just before the most extreme separation.
Figure 8.18 shows the result for ẑ oriented transmitter and receiver (antenna parallel to
body), which exhibits very high shadowing. A floor is seen in the measured power in the
strongly shadowed region, apparently due to a specular wall reflection in the chamber.
This was checked by computing fields radiated from the transmit antenna to an image
of the receive antenna (on the opposite side of the wall) as shown in Figure 8.17 and
adding an additional 40 dB of loss for the absorber. The resulting curve in Figure 8.18
118
8.3. MEASUREMENT RESULTS
30
MOM
Indoor measurement
Normalised |Eρ| (dB)
20
10
0
−10
−20
−30
−40
−50
0
50
°
100
150
φ
Figure 8.16: Measurement and model comparison of Eρ in response to a ρ-directed point
source
is very close to the observed floor. Unfortunately, outdoor measurements of the same
polarization did not improve the accuracy of fit of the model, which could be resulting
from the absorber around the subject’s feet.
These result reveal that performing BAN measurements for regions with strong shadowing
can be difficult, since reflections can easily over shadow on-body propagation mechanisms.
Figure 8.17: Wall reflection with Anechoic chamber measurements: d1 = 68 cm, d2 =67
cm
119
40
MOM
Indoor measurement
Outdoor measurement
Modeled Wall
0
z
Normalised |E | (dB)
20
−20
−40
−60
−80
0
50
°
100
150
φ
Figure 8.18: Measurement and model comparison of Ez in response to a z-directed point
source
Figure 8.19 shows the result for the φ̂ oriented transmitter and receiver (antenna tangential
to body). This polarization also exhibits a high shadowing due to the body. The model
pathloss decay level is quite similar to the measured one at the initial separation but it is
not well predicted for larger separations except for the presence of dips that look similar
to measured ones.
Figure 8.20 shows the result for a cross-polarization measurement, which may be important for sensors that can be placed at arbitrary angle. Although agreement for the smaller
separation is reasonable, it is believed that the φ-oriented polarization becomes corrupted
by the cable being present around the body.
8.4
Summary
In this chapter a superquadratic ellipse model of the human body was proposed, whose
parameters were found for a human subject by means of a camera based measurement.
Two simplified models based on an elliptical and circular cross section were also considered. Fields around the torso were found to decay exponentially with distance for the
three models. Additionally, it was observed that the detailed torso shape can play an
important role for some polarizations. Next, accuracy of the superquadratic torso model
was investigated by direct measurements in an anechoic chamber and in an open outdoor
field.
120
8.4. SUMMARY
60
MOM
Indoor measurement
Normalised |Eφ| (dB)
40
20
0
−20
−40
−60
−80
0
50
φ°
100
150
Figure 8.19: Measurement and model comparison of Eφ in response to a φ-directed point
source
20
MOM
Indoor measurement
Normalised |Eρ| (dB)
10
0
−10
−20
−30
−40
−50
0
50
φ°
100
150
Figure 8.20: Measurement and model comparison of Eφ in response to a ρ-directed point
source
121
Comparison shows that for ρ̂ oriented transmitter and receiver, the model is able to
accurately predict the field decay with increasing separation and partial cancellation of
waves in the shadow region. Results for ẑ oriented transmitter and receiver indicate very
strong shadowing due to the body. Although the model is able to accurately predict initial
field decay with increasing separation. BAN measurement for the shadow region was not
possible in the compact anechoic chamber. Measurements in an open field unfortunately
did not remedy the problem.
Finally, for the measurements that showed reasonable agreement, the slight deviations
were probably due to the presence of the cables around the body.
9. CONCLUSION AND FUTURE WORK
123
Chapter 9
Conclusion and Future Work
Accurate and efficient electromagnetic modeling of antenna-body interactions was identified as a vital requirement for the determination of the distributed electromagnetic field in
and around the body. This thesis has considered two important and diverse applications,
speech sensing and body area networking. This concluding chapter summarizes the most
important results of the thesis and provides future extensions of this work.
In Chapter 2, the concept of speech sensing was introduced and highlighted for some
existing speech sensing techniques. The characteristics of UWB technology which were
used for speech sensing were discussed. The existing UWB sensing applications for heart
rate sensing, tumor detection and through wall imaging were highlighted as existing
applications of UWB technology. For UWB speech sensing, the hardware setup was
also presented.
The requirements of the UWB antenna used for tracking of speech production were
discussed in Chapter 3. A number of candidate UWB antennas and their suitability
for speech sensing were also investigated. The planar microstrip antenna, including the
broadband monopole antenna and Vivaldi antenna were simulated and optimized for the
application of interest. The response of the UWB antenna was measured for a stand alone
antenna, the antenna mounted in the prototype headset, and the antenna mounted in the
prototype headset in the presence of the subject. The result indicates that the headset
and subject change the response of the antenna, but this does not significantly reduce the
efficiency of the antenna.
In Chapter 4, full-wave modeling for the speech sensing application was discussed. A
detailed head-vocal tract model was designed using MakeHuman and Blender, where the
internal vocal tract model was developed using MRI images for the open and closed mouth.
A simple 3D flat-face stacked layer moder was presented to overcome the complexity in
generating the detailed head-vocal tract model. Also, a one-dimensional (1D) model was
presented which indicates the maximum receive power that one can expect the UWB
124
9.1. FUTURE WORK
sensor to experience.
Simulations and experimental validation of UWB speech sensing were presented in Chapter 5. The horizontal and vertical optimization of the UWB antenna placement to
maximize coupling of UWB signals with the mouth was studied. Delta responses of the
models in Chapter 4 were simulated for large movement of the lips and tongue, indicating
that these movements can be sensed and that simple waveguide models are likely to
be sufficient. The frequency-dependent tissue properties were also studied with results
indicating that the exact material parameters play a minor role in determinig the UWB
response when strong waveguiding effects are present.
Direct measurement of the vocal tract delta responses was presented in Chapter 5, showing
the same effects as those observed in simulation and suggesting that the features of interest
are responsible for the energy measured in the delta responses. A proof-of-concept UWB
speech-recognition experiment was presented indicating that speech detection with the
proposed method is possible.
In Chapter 6, principles of the mode matching technique were presented for analyzing the
vocal tract with the purpose reducing the modeling complexity of UWB propagation in
the vocal tract. A method for extracting S parameters coupling the antenna to the vocal
tract was also presented. Estimation of the vocal tract shape from the measured return
response with a simple inverse scattering method was explored.
Chapter 7 considered numerical methods used for BAN modeling. Two methods were
considered, one for a circular cylinder BAN model which was based on a closed-form
solution and the second method for a model with arbitrary shape based on the MOM.
The transformation from the line source solution to a point source was accomplished
by applying a Fourier transform. Comparisons were made of the numerical methods,
indicating that the methods are in agreement with each other.
In Chapter 8, modeling and experimental validation for BANs were discussed. A superquadratic ellipse model of the human body was proposed, whose parameters were
found for a human subject by means of a camera based measurement. Two simplified
models based on an elliptical and circular cross section were also considered. Fields around
and into the torso were studied. A BAN measurement setup was presented for a network
analyzer-based system and BAN antenna, and measurements were taken in an anechoic
chamber and outdoor field. Comparisons were made of the superquadratic ellipse model
and measurements, indicating reasonable agreement.
9.1
Future Work
This section considers near and long-term extensions of the work presented in the thesis.
9. CONCLUSION AND FUTURE WORK
125
Accurate modeling of antenna-body interactions in speech sensing is greatly affected by
the sensors used. In this thesis, omni directional UWB sensors were used for speech sensing. As a next possible step, it would be interesting to study improved sensors with a more
directional response which give better coupling with the mouth and throat. Furthermore,
it would be interesting to investigate transmissive sensors, multimode sensors (multiple
ports) or even ultrasonic sensors which can overcome the cutoff seen by microwaves.
Another possible speech sensing research direction is to continue to develop the waveguide
modeling strategy for the vocal tract. Specifically, the assumption of PEC walls should
be relaxed, more accurately representing human tissue. With this new research direction,
least-square fit may be used to do mode matching rather than using mode orthogonality,
which may not be satisfied.
As a more in-depth extension of speech sensing, it would be useful to study the detailed
connection between measured UWB responses and the features being sensed as a step
toward individual phoneme recognition. Fusion of UWB sensing data with audio/video
data is another research direction which may be fruitful. Speech sensing could also be
included into tools such as the virtual language tutor, allowing the tools to ’see’ the
position of the tongue and lips and provide useful feedback for language training.
Two-dimensional modeling of the human body torso has assumed that the torso is a
regular circular, elliptical, or superquadratic shape. Since the actual torso shape is more
complex than these shapes, it would be interesting to study more sophisticated torso
models and investigate their effects on the field behavior around the torso. Also, as
indicated in this thesis, the compact anechoic chamber has some practical limitations for
BAN measurements. Measurements in a larger chamber could be considered as a next
possible research direction which may gives answers about sensing in shadowed region and
what is the true reason for the floor seen in the data measured in the compact anechoic
chamber.
It would be interesting to consider and synthesize the response of other antenna types
rather than point source as the next step of accurate BANs modeling. Also, since the point
source/sensor was not totally achieved by the short dipole and the presense of cables may
corrupt the measurements, it would be interesting to develop fiber-optic sensing capability
and compare the results.
Finally, since it believed that the BAN models presented show good accuracy, it is now
of interest to use these models to find optimal antennas for the on-body channel with
the goals of efficiency, robustness, high performance and security. Another accurate BAN
research direction is to consider the combination of multiple simple BAN models to capture
the effects of arms and non-homogeneous shape in the z-direction.
A. PUBLICATIONS
127
Appendix A
Publications
Below are a list of publications resulting from the work in this thesis:
1. A. Eid and J. Wallace, “Ultra-wideband sensing of speech production,” IEEE Antennas and Propagation Society International Symposium (APS ’09), Charleston,
SC, June 1-5, 2009.
2. A. Eid and J. Wallace, “Ultrawideband Speech Sensing,”IEEE Antennas and Wireless Propagation Letters, vol. 8, pp. 1414-1417, 2009.
3. A. Eid, N. Murtaza and J. Wallace, “Green’s Function Models and Measurements for
Body Area Network (BAN) Channels,”IEEE International Conference on Wireless
Information Technology and Systems (ICWITS ’10), Honolulu, Hawaii, Aug. 28 Sept. 3, 2010.
4. A. Eid and J. Wallace, “Accurate Modeling of Body Area Network Channels Using
Surface-Based Method of Moments,”Submitted to IEEE Trans. Antennas Propag.,
2010.
128
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