Simulation and Design of an UWB Imaging System for Breast

Simulation and Design of an UWB Imaging System for Breast
Politecnico di Torino
Porto Institutional Repository
[Doctoral thesis] Simulation and Design of an UWB Imaging System for
Breast Cancer Detection
Original Citation:
Xiaolu Guo (2014). Simulation and Design of an UWB Imaging System for Breast Cancer Detection.
PhD thesis
Availability:
This version is available at : http://porto.polito.it/2540088/ since: April 2014
Published version:
DOI:10.6092/polito/porto/2540088
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POLITECNICO DI TORINO
SCUOLA DI DOTTORATO
Dottorato inIngegneria Elettronica e delle Comunicazioni – XXVI
ciclo
Tesi di Dottorato
Simulation and Design of an UWB
Imaging System for Breast Cancer
Detection
Xiaolu Guo
Tutore
prof. Maurizio Zamboni
Coordinatore del corso di dottorato
prof. Ivo Montrosset
April 2014
Summary
Breast cancer is the most frequently diagnosed cancer among women. In recent
years, the mortality rate due to this disease is greatly decreased thanks to both
enormous progress in cancer research, and screening campaigns which have allowed
the increase in the number of early diagnoses of the disease. In fact, if the tumor is
identified in its early stage, e.g. when it has a diameter of less than one centimeter,
the possibility of a cure can reach 93%. However, statistics show that more young
aged women are suffered breast cancer.
The goal of screening exams for early breast cancer detection is to find cancers
before they start to cause symptoms. Regular mass screening of all women at risk
is a good option to achieve that. Instead of meeting very high diagnostic standards,
it is expected to yield an early warning, not a definitive diagnosis. In the last
decades, X-ray mammography is the most efficient screening technique. However,
it uses ionizing radiation and, therefore, should not be used for frequent check-ups.
Besides, it requires significant breast compression, which is often painful. In this
scenario many alternative technologies were developed to overcome the limitations
of mammography. Among these possibilities, Magnetic Resonance Imaging (MRI)
is too expensive and time-consuming, Ultrasound is considered to be too operatordependent and low specificity, which are not suitable for mass screening. Microwave
imaging techniques, especially Ultra WideBand (UWB) radar imaging, is the most
interesting one. The reason of this interest relies on the fact that microwaves are
non-ionizing thus permitting frequent examinations. Moreover, it is potentially lowcost and more efficient for young women. Since it has been demonstrated in the
literatures that the dielectric constants between cancerous and healthy tissues are
quite different, the technique consists in illuminating these biological tissues with
microwave radiations by one or more antennas and analyzing the reflected signals.
An UWB imaging system consists of transmitters, receivers and antennas for
the RF part, the transmission channel and of a digital backend imaging unit for
processing the received signals. When an UWB pulse strikes the breast, the pulse is
reflected due to the dielectric discontinuity in tissues, the bigger the difference, the
bigger the backscatter. The reflected signals are acquired and processed to create
the energy maps. This thesis aims to develop an UWB system at high resolution for
II
the detection of carcinoma breast already in its initial phase. To favor the adoption
of this method in screening campaigns, it is necessary to replace the expensive and
bulky RF instrumentation used so far with ad-hoc designed circuits and systems.
In order to realize that, at the very beginning, the overall system environment must
be built and verified, which mainly consists of the transmission channel–the breast
model and the imaging unit. The used transmission channel data come from MRI
of the prone patient. In order to correctly use this numerical model, a simulator was
built, which was implemented in Matlab, according to the Finite-Difference-TimeDomain (FDTD) method. FDTD algorithm solves the electric and magnetic field
both in time and in space, thus, simulates the propagation of electromagnetic waves
in the breast model. To better understand the effect of the system non-idealities,
two 2D breast models are investigated, one is homogeneous, the other is heterogeneous. Moreover, the modeling takes into account all critical aspects, including
stability and medium dispersion. Given the types of tissues under examination, the
frequency dependence of tissue dielectric properties is incorporated into wideband
FDTD simulations using Debye dispersion parameters. A performed further study
is in the implementation of the boundary conditions. The Convolution Perfectly
Matched Layer (CPML) is used to implement the absorbing boundaries.
The objective of the imaging unit is to obtain an energy map representing the
amount of energy reflected from each point of the breast, by recombining the sampled
backscattered signals. For this purpose, the study has been carried out on various
beamforming in the literature. The basic idea is called as ”delay and sum”, which
is to align the received signals in such a way as to focus a given point in space and
then add up all the contributions, so as to obtain a constructive interference at that
point if this is a diseased tissue. In this work, Microwave Imaging via Space Time
(MIST) Beamforming algorithm is applied, which is based on the above principle
and add more elaborations of the signals in order to make the algorithm less sensitive
to propagation phenomena in the medium and to the non-idealities of the system.
It is divided into two distinct steps: the first step, called SKin Artifact Removal
(SKAR), takes care of removing the contributions from the signal caused by the
direct path between the transmitter and receiver, the reflection of skin, as they are
orders of magnitude higher compared to the reflections caused by cancers; the second
step, which is BEAmForming (BEAF), performs the algorithm of reconstruction by
forming a weighted combination of time delayed version of the calibrated reflected
signals.
As discussed above, more attention must be paid on the implementation of the
ad-hoc integration circuits. In this scenario, due to the strict requirements on the
RF receiver component, two different approaches of the implementation of the RF
front-end, Direct Conversion (DC) receiver and Coherent Equivalent Time Sampling
(CETS) receiver are compared. They are modeled behaviorally and the effects of
various impairments, such as thermal, jitter, and phase noise, as well as phase
III
inaccuracies, non-linearity, ADC quantization noise and distortion, on energy maps
and on quantitative metrics such as SCR and SMR are evaluated. Differential
Gaussian pulse is chosen as the exciting source. Results show that DC receiver
performs higher sensitivity to phase inaccuracies, which makes it less robust than
the CETS receiver. Another advantage of the CETS receiver is that it can work
in time domain with UWB pulses, other than in frequency domain with stepped
frequency continuous waves like the DC one, which reduces the acquisition time
without impacting the performance.
Based on the results of the behavioral simulations, low noise amplifier (LNA)
and Track and Hold Amplifier (THA) can be regarded as the most critical parts
for the proposed CETS receiver, as well as the UWB antenna. This work therefore
focuses on their hardware implementations. The LNA, which shows critical performance limitation at bandwidth and noise figure of receiver, has been developed based
on common-gate configuration. And the THA based on Switched Source Follower
(SSF) scheme has been presented and improved to obtain high input bandwidth,
high sampling rate, high linearity and low power consumption. LNA and THA
are implemented in CMOS 130 nm technology and the circuit performance evaluation has been taken place separately and together. The small size UWB wide-slot
antenna is designed and simulated in HFSS.
Finally, in order to evaluate the effect of the implemented transistor level components on system performance, a multi-resolution top-down system methodology
is applied. Therfore, the entire flow is analyzed for different levels of the RF frontend. Initially the system components are described behaviorally as ideal elements.
The main activity consists in the analysis and development of the entire frontend
system, observing and complementing each other blocks in a single flow simulation,
clear and well-defined in its various interfaces. To achieve that the receiver is modeled and analyzed using VHDL-AMS language block by block, moreover, the impact
of quantization, noise, jitter, and non-linearity is also evaluated. At last, the behavioral description of antenna, LNA and THA is replaced with a circuit-level one
without changing the rest of the system, which permits a system-level assessment
of low-level issues.
IV
Acknowledgements
First of all, I want to express my sincere gratitude to my supervisors Prof. Maurizio
Zamboni, Mariagrazia Graziano and Mario R. Casu, not only for their insightful
guidance, patience, support and invaluable assistance throughout this work, but
also for their help in my daily life over the past three years.
I would also like to show my gratitude to Marco and Azzurra for their help in
reviewing my thesis, as well as Marco Crepaldi for his technical advice and help
during my circuit design work.
I have received much help and support from numerous past and present members
of the UWB group, including Alessandro, Stefano, Matteo, Paolo, Franscesco and
Antonio. I want to say thank you so much guys, I am so happy to work with you.
My appreciation extends to all the students in the VLSI Lab, Awais, Ruiyu,
Juanchi, Manoj, Ali, Azhar, Abduwali and Matteo who kept me company with
their discussions and cheerful chats during the coffee break, and the rest of my
fellows whose names are missing due to space limitation.
Moreover, I would like to thank all my lovely friends, especially my roommates
and ”lunch group” members, for their companion, encouragement and support.
Finally, I would like to thank my family for their unconditional support and love
along these years. Thanks Mom, thanks Dad, your support means so much to me.
I have to say thank you to Yu Jian, for those moments of peace and well-being that
only you can give me.
V
Contents
Summary
II
Acknowledgements
V
1 Introduction
1.1 Mammography . . . . . . . . . . . .
1.2 alternative methods . . . . . . . . . .
1.2.1 Breast Ultrasound . . . . . .
1.2.2 Magnetic Resonance Imaging
1.2.3 Microwave Imaging . . . . . .
1.3 System overview . . . . . . . . . . .
1.4 Thesis outline . . . . . . . . . . . . .
2 UWB Imaging System
2.1 Transmission channel . . . . . . . . .
2.1.1 FDTD method . . . . . . . .
2.1.2 Breast model . . . . . . . . .
2.2 Front-end: Transceiver and Antenna
2.2.1 Transmitter . . . . . . . . . .
2.2.2 Receiver . . . . . . . . . . . .
2.2.3 Antenna . . . . . . . . . . . .
2.3 Algorithm and implementation . . .
2.3.1 Confocal Microwave Imaging .
2.3.2 MIST . . . . . . . . . . . . .
2.3.3 Quality factors . . . . . . . .
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3 System setting and verification
3.1 System parameters . . . . . . . . . . . . . . .
3.2 Source pulses . . . . . . . . . . . . . . . . . .
3.2.1 Modified Hermite Pulse (MHP) . . . .
3.2.2 Modulated and Modified Hermite Pulse
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3.3
3.4
3.2.3 Differential Gaussian pulse
System with homogeneous breast
3.3.1 Tumor size . . . . . . . . .
3.3.2 Tumor position . . . . . .
System with heterogeneous breast
(DG)
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4 Receiver comparison
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . .
4.2 Two different receiver architectures . . . . . . . .
4.2.1 Direct Conversion receiver . . . . . . . . .
4.2.2 CETS receiver . . . . . . . . . . . . . . . .
4.3 Methodology and simulation setting . . . . . . . .
4.4 Simulation results . . . . . . . . . . . . . . . . . .
4.4.1 DC receiver with SFCW approach . . . . .
4.4.2 CETS receiver with SFCW approach . . .
4.4.3 CETS receiver with time domain approach
4.4.4 Overall comparison . . . . . . . . . . . . .
5 Hardware Implementations
5.1 UWB antenna design . . . . . . . . . . .
5.1.1 UWB antenna requirements . . .
5.1.2 Antenna design . . . . . . . . . .
5.1.3 Results and discussion . . . . . .
5.2 Low Noise Amplifier . . . . . . . . . . .
5.2.1 Design consideration . . . . . . .
5.2.2 UWB LNA design . . . . . . . .
5.2.3 Simulation results and discussion
5.3 Track and Hold Amplifier . . . . . . . .
5.3.1 THA design . . . . . . . . . . . .
5.3.2 Simulation results . . . . . . . . .
6 System performance evaluation
6.1 Introduction . . . . . . . . . .
6.2 UWB imaging system building
6.2.1 Transmitter . . . . . .
6.2.2 Antenna . . . . . . . .
6.2.3 Channel model . . . .
6.2.4 Receiver . . . . . . . .
6.2.5 Imaging Unit . . . . .
6.3 Methodology . . . . . . . . .
6.4 Simulation results . . . . . . .
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7 Conclusion
130
Bibliography
132
VIII
List of Tables
2.1
2.2
2.3
2.4
3.1
3.2
3.3
4.1
4.2
4.3
5.1
5.2
5.3
5.4
5.5
5.6
6.1
6.2
The position of the E-field and H-field components in Yee cell. . . . . 15
Type of fabric and the corresponding average number . . . . . . . . . 28
Single-pole Debye parameters for the maximum, group1-high, group1median, group1-low, group3-high, group3-median, group3-low, and
minimum curves associated with normal breast tissue as well as skin
and muscle (valid for the 3-10 GHz band) [20]. . . . . . . . . . . . . . 30
Average breast tissue single-pole Debye parameters for each phantom. 33
Normalized tumor response with respect to different tumor size. . . . 57
System performance (SMR, SCR) as a function of the tumor’s size. . 61
system performance (SMR, SCR) as a function of the tumor’s position. 62
Parameters used in simulation. . . . . . . . . . . . . . . . . . . . . . . 77
SMR and SCR in the ideal case with different position. . . . . . . . . 78
SMR, SCR for the three scenarios. . . . . . . . . . . . . . . . . . . . 89
UWB Antenna design requirements for UWB transceiver. . . . . . . . 92
The dimension and parameter of proposed antenna in millimeters. . . 95
Researches in UWB LNA. . . . . . . . . . . . . . . . . . . . . . . . . 99
Dimension of LNA components. . . . . . . . . . . . . . . . . . . . . . 103
Summary of the simulated LNA performances. . . . . . . . . . . . . . 104
Dimension of THA components. . . . . . . . . . . . . . . . . . . . . . 110
Description of the simulation cases. . . . . . . . . . . . . . . . . . . . 121
Signal-to-Mean Ratio (SMR), Signal-to-Clutter Ratio (SCR), and tumor estimated position for the cases outlined in Table 6.1. . . . . . . 128
IX
List of Figures
1.1
A summary of the most actively pursued methods for image reconstruction from microwave measurements. . . . . . . . . . . . . . . .
1.2 An overview of breast cancer detection system. UWB pulses are
radiated against the breast and the echoes are acquired with a set of
transceivers and antennas. An imaging unit processes the data and
produces a map of reflected energy. Cancerous tissues have higher
dielectric constant, resulting in high reflected energy . . . . . . . . .
2.1 An overview of breast cancer detection system. . . . . . . . . . . . .
2.2 Anatomy of breast. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Standard Yee cell for FDTD. . . . . . . . . . . . . . . . . . . . . . .
2.4 Calculation flow chart of FDTD method. . . . . . . . . . . . . . . .
2.5 Schematic of a typical problem in the equation waves propagation,
where, in the region of interest analyzed, the radiated waves propagate
at finite in (a). The same problem but with the addition of a layer of
absorption (PML) to limit the area of analysis which does not create
reflections is shown in (b). . . . . . . . . . . . . . . . . . . . . . . .
2.6 MRI scans of the phantom in the repository UWCEM with Breast
ID: 012204. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 The seven tissue-type regions bounded by the curves in this graph
are labeled with the media numbers reported in Tab. 2.2. From top
to bottom, the curves correspond to the following eight cases: maximum, group1-high, group1-median, group1-low, group3-high, group3median, group3-low, and minimum [20]. . . . . . . . . . . . . . . . .
2.8 From top to bottom, the Cole-Cole and Debye (bold) curves correspond to the following eight cases: maximum, group1-high, group1median, group1-low, group3-high, group3-median, group3-low, and
minimum [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Dielectric constant–three dimensional model. . . . . . . . . . . . . .
2.10 Heterogeneous breast model. . . . . . . . . . . . . . . . . . . . . . .
2.11 Homogeneous breast model. . . . . . . . . . . . . . . . . . . . . . .
2.12 Block diagram of RF frontend. . . . . . . . . . . . . . . . . . . . . .
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2.13 Block diagram of the transmitter [27]. . . . . . . . . . . . . . . . . . .
2.14 Diagram of emission of a Hertzian dipole antenna [16]. . . . . . . . .
2.15 Possible configurations with Radar Microwave Imaging: (a) Monostatic, (b) Multistatic, (c) Bistatic. . . . . . . . . . . . . . . . . . . . .
2.16 An illustration of simple delay-and-sum beamforming. The received
signals are shown in the central panel. When the beamformer is
steered to location r0 (the actual location of tumor), the signals coherently sum, as shown by the left panel. When the beamformer is
steered to a location other than r0 , incoherent summation results, as
shown by the right panel [34]. . . . . . . . . . . . . . . . . . . . . . .
2.17 Structure of the reconstruction algorithm organized in two parts: skin
artifact removal (SKAR) and MIST beamforming (BEAF). . . . . . .
2.18 Block diagram illustrating the algorithm for removing the skin-breast
artifact from the backscattered signal received at the first of N antennas [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.19 Example of pulses before and after calibration. FDTD-computed
backscattered signals with and without tumor as received by one of
the antennas, with zoom on the late-time response, showing a difference between the two signals. (b) Signal after calibration, the skin
artifacts are removed. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.20 Block diagram illustrating the MIST beamforming process for location r in the breast [33]. . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Block scheme of imaging system and design flow. . . . . . . . . . . .
3.2 The reflection error versus time for different dimension of CPML [16].
3.3 The breast model in FDTD simulation. . . . . . . . . . . . . . . . . .
3.4 MHP used for simulations: a) time domain b) frequency domain [16].
3.5 MMHP used for simulations: a) time domain b) frequency domain. .
3.6 DG used for simulations: a) time domain b) frequency domain. . . . .
3.7 Propagation speed as function of frequency in case of homogeneous
breast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Backscattered responses with different tumor size at central position
of the breast model, (a) 1 mm (b) 2 mm (c) 3 mm (d) 4 mm. . . . . .
3.9 Calibration results with DG pulse, 4 mm tumor and middle tumor
position, homogeneous breast, the red lines are cases with tumor, the
blue lines are cases without tumor. . . . . . . . . . . . . . . . . . . .
3.10 Reconstruction results with MIST beamforming algorithm, with different tumor size at central position of the breast model, (a) 1 mm
(b) 2 mm (c) 3 mm (d) 4 mm. . . . . . . . . . . . . . . . . . . . . . .
3.11 The homogeneous breast model with three tested tumor positions. . .
3.12 Comparison of the backscattered responses for the different positions
of the tumor mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.13 Reconstruction results with MIST beamforming algorithm, with different tumor position, (a) near (b) middle (c) deep. . . . . . . . . .
3.14 The simulated heterogeneous breast model, 4 mm tumor is inserted
in the middle position. . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Backscattered responses with different kind of breast model. . . . .
3.16 Reconstruction results with MIST beamforming algorithm, with heterogeneous breast model, the tumor position is middle and size is
4 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 UWB imaging system design flow. Transmitted signals hit the breast
and the echoes are acquired with receivers. An imaging unit processes
the data and produces a map of reflected energy. . . . . . . . . . . .
4.2 Block diagrams of Direct Conversion (DC) receiver. . . . . . . . . .
4.3 Direct Conversion (DC) receiver behavioral model. . . . . . . . . .
4.4 Example of Coherent Equivalent-Time Sampling. Twenty-seven samples of the pulse are acquired in ten repetition periods (27 and 10 are
relatively prime). Samples are not acquired in order and need to be
sorted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Block diagrams of Coherent Equivalent Time Sampling (CETS) receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 CETS receiver behavioral model. . . . . . . . . . . . . . . . . . . .
4.7 Energy maps of the breast with the ideal receiver for different tumor
positions. Map (a) is for tumor placed near skin, (b) for tumor placed
in the middle of breast, (c) for tumor placed deep in breast. . . . .
4.8 DC receiver system performance (SMR a-b, SCR c-d) with different
signal power and ADC bits; results are reported both for ideal ADC
(a,c) and for ADC with nonlinearity (b,d). . . . . . . . . . . . . . .
4.9 DC receiver system performance with different signal transmitted
power and phase noise σpn ; results are reported both for a single
evaluation (a) and for an averaging on 100 trials (b). . . . . . . . .
4.10 DC receiver system performance (SMR, SCR) with different phase
mismatch with 15-bit ADC and -28dBm transmitted signal power;
results are reported both for a single evaluation (a) and for an averaging on 100 trials (b). . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 CETS receiver system performance (SMR, SCR) with SFCW approach with different signal power and ADC bits; results are reported
both for an ideal ADC (a) and for a nonlinear ADC (b). . . . . . .
4.12 CETS receiver system performance (SMR, SCR) with SFCW approach with different signal power, with 10-bit ADC and thermal
noise; results are reported both for a single evaluation (a) and for an
averaging on 100 trials (b). . . . . . . . . . . . . . . . . . . . . . . .
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4.13 CETS receiver system performance (SMR, SCR) with SFWC approach and with different rms jitter, with 10-bit ADC and -28dBm
transmitted signal power; results are reported both for a single evaluation (a) and for an averaging on 100 trials (b). . . . . . . . . . .
4.14 CETS receiver system performance (SMR, SCR) with different signal
power and ADC bits; results are reported for a nonlinear ADC. . .
4.15 CETS receiver system performance (SMR, SCR) in time domain with
different signal power and 10-bit ADC; results are reported both for
a single evaluation (a) and for an averaging on 100 trials (b). . . . .
4.16 CETS receiver system performance (SMR, SCR) in time domain with
different rms jitter, with 10-bit ADC and -10dBm transmitted signal
power; results are reported both for a single evaluation (a) and for an
averaging on 100 trials (b). . . . . . . . . . . . . . . . . . . . . . . .
4.17 Energy maps resulting from the system-level simulations with different receiver approaches and all the impairments. Maps (a)-(b) are for
DC with SFCW approach, (c)-(d) for CETS with SFCW approach,
(e)-(f) for CETS in time domain. The left column maps (a)-(c)-(e)
are without average, the right ones (b)-(d)-(f) are acquired 100 times
and averaged. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 The layout of the developed slot antenna. . . . . . . . . . . . . . . .
5.2 Overview of the slot antenna in HFSS. . . . . . . . . . . . . . . . .
5.3 Simulated return loss against frequency. . . . . . . . . . . . . . . .
5.4 Radiation pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Calculated electric field waveforms. . . . . . . . . . . . . . . . . . .
5.6 Typical inductor-degenerated common source LNA [73]. . . . . . . .
5.7 Typical common gate LNA. . . . . . . . . . . . . . . . . . . . . . .
5.8 Proposed differential UWB LNA. . . . . . . . . . . . . . . . . . . .
5.9 Simulated frequency response of the first stage. . . . . . . . . . . .
5.10 Simulated frequency response of the second stage. . . . . . . . . . .
5.11 Simulated performance of the proposed LNA: (a) Input and output
reflection coefficient (S11 and S22) of the UWB LNA versus frequency,
(b) Gain and reversal isolation (S21 and S12) of the UWB LNA versus
frequency and (c) Noise figure of the UWB LNA versus frequency. .
5.12 Simulated IIP3 of the proposed LNA versus frequency. . . . . . . .
5.13 Layout of the proposed LNA. . . . . . . . . . . . . . . . . . . . . .
5.14 Diagram of a simple circuit with THA differential switches in series
(a) and its differential version (b) [76] . . . . . . . . . . . . . . . . .
5.15 A switched source follower track and hold amplifier . . . . . . . . .
5.16 Proposed high linearity THA . . . . . . . . . . . . . . . . . . . . .
5.17 Diagram showing the circuit innovations made to the basic scheme of
Figure 5.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.18
5.19
5.20
5.21
5.22
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
THA transient simulation results . . . . . . . . . . . . . . . . . . .
THA AC simulation results . . . . . . . . . . . . . . . . . . . . . .
THA linearity performance in terms of SFDR. . . . . . . . . . . . .
Layout of the proposed THA. . . . . . . . . . . . . . . . . . . . . .
Transient simulation results with both LNA and THA . . . . . . . .
Block scheme of the portion of the system active when one UWB
pulse is sent, received and processed. TX is for transmitter, ANT. for
antenna, RX for receiver, and IU for Imaging Unit. . . . . . . . . .
Gray box encloses the architecture of the CETS-based receiver. All
mixed-signal and analog blocks have a VHDL-AMS description, but
LNA and THA also have a Spice transistor-level description. CETS
digital back-end block has a VHDL description. . . . . . . . . . . .
Images reconstructed using MIST. (a) Skin artifact removed by ideal
calibration and (b) by real calibration. The tumor is enclosed by a
contour level set to a value slightly lower than the maximum energy
found in the map. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Example of signals from case-1 simulation. The inset expands the
time region associated with the tumor information. . . . . . . . . .
Ensemble received and reordered signals (K=50) and average signal
in case-2, with thermal noise, jitter and quantization. Insets show
effectiveness of average in mitigating these effects, especially around
the time region where the small tumor information is present. . . .
ADMS simulation result showing the behavior of THA when tracking
and holding one of the received signals. . . . . . . . . . . . . . . . .
System metrics (SMR, SCR) as a function of tumor’s size. . . . . .
Energy maps resulting from the system-level simulations of the various cases outlined in Table 6.1 (energy unit is arbitrary). The tumor
can be easily identified in each of the reported maps, because it is
enclosed by a contour level that we set to a value slightly lower than
the maximum energy. . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 1
Introduction
Nowadays, breast cancer is the most common form of cancer affecting women worldwide. About 1/8 U.S. women (just under 12%), 1/12 Europe women and 1/40 Asia
women will develop invasive breast cancer over the course of her lifetime. All women
have the chances of developing breast cancer. The risk of developing breast cancer
increases with age beginning in the fourth decade of life. The probability of developing invasive breast cancer over the next decade is 0.4% for women aged 30-39,
1.5% for women aged 40-49, 2.8% for women aged 50-59, and 3.6% for women aged
60-69.
Recent research indicates that the five-year disease-free relative survival rate
was greater than 98% for women with a 20 mm or smaller invasive cancer (stage
I) which has not spread to lymph nodes yet, compared to 86% for stage II disease
(1-3 positive axillary lymph nodes and/or primary tumor size 21 to 50 mm) [1].
Therefore, early detection is believed to be crucial to reduce the breast cancer death
by finding cancers at smaller sizes and thus treating more effectively. Breast cancers
can be found by clinical breast exam or by a woman herself, but such tumors have
a median size of 20 to 25 mm [2]. Tumors with such sizes are more likely to be later
stage breast cancers that are logically have already spread to the axillary lymph
nodes and are likelier to be lethal. Hence detecting tumors at a nonpalpable early
stage becomes the philosophy that drives the development of breast cancer screening
technology. With advances in screening, diagnosis and treatment, the death rate for
breast cancer has declined considerably over the past decade.
In the literatures, there are different kinds of screening method for detecting
breast cancer such as X-ray mammography, ultrasound, Computed Tomography
(CT) and Magnetic Resonance Imaging (MRI). Currently the most widely used
method is X-ray mammography. In this chapter different breast cancer detection
screening methods will be introduced and compared.
1
1 – Introduction
1.1
Mammography
Nowadays, X-ray mammography is the most common screening method to detect
breast cancer in women who have no signs or symptoms of the disease. It uses
x-rays to produce images of the breast. In other words, mammography provides
information about breast morphology, normal anatomy, and gross pathology. The
overall procedure includes tightly compressing the breast between two parallel plates.
A x-ray pulse is then used to take the image. During the procedure, the breast is
flattened to evenly spread out the tissue. Consequently, the x-ray attenuation is
about the same within the overall region of the breast. In addition, the radiation
dosage absorbed by the breast is at a minimum value. The whole procedure takes
about 20 minutes. Film-screen mammography and digital mammography are the
two main types of mammography. The techniques for performing them are the same.
What differs is whether the images take the form of photographic films or of digital
files recorded directly onto a computer.
The effective of mammographic screening before age 50 years is less than at older
ages and the associated radiation risks are higher, due to the fact that younger
women have denser breasts that contain microcalcifications and have thick epithelial tissue, so as to absorb more of the radiation from the surface. Therefore, the
radiation logically penetrates less deeper into the breast tissue, which is the area
where malignant cancers are most likely to be found.
The researches showed that cancer detection with digital or film-screen mammography is similar in U.S. women aged 50 to 79 years going through screening
mammography. However, digital mammography is significantly better that film
mammography in screening women who are under age 50, or women of any age
who had very dense breasts [3]. Nevertheless, one of the obstacles to greater use
of digital mammography is its cost, it costs about 1.5 to 4 times more than film
mammography. The mammography that will talk about in the following is film
mammography. In women aged 50 years old, mammography’s sensitivity has been
estimated to range from 68% to over 90%, with most trials achieving sensitivities of
about 85%. In women aged 40-49, however, the sensitivity has been reported to be
about 62%. The specificity of mammography ranges between 82% and 97%.
High-quality, two view screening mammography is able to find the relatively
small breast cancers, with median size 1.0 to 1.5 cm. Because of its important role
in detecting tumor earlier, mammography has played a substantial role in reducing
the mortality rate by 20% in the last decade [4]. However, x-ray mammography has
the following shortages:
• Radiation exposure. As with all x-ray examinations, there is some radiation
exposure, although mammography uses low energy ionizing x-rays at low radiation doses to create an image, frequently repeated x-rays still may cause
2
1.2 – alternative methods
cancer.
• High false positive. False-positive results occur when radiologists decide mammograms are odd but no cancer is actually present. On the whole, screening
mammograms misdiagnose about 12 percent of breast cancers that are present
at the time of screening. It may lead to anxiety and other forms of psychological distress in affected women. The additional imaging studies and invasive
procedures (such as biopsy or fine-needle aspiration) required to exclude cancer can also be costly and cause physical discomfort. False-positive results
and accompanying additional imaging studies are more common in younger
women.
• High false negative. Up to 20% false-negative rates, false-negative results occur
when mammograms appear normal even though breast cancer is present. The
main cause of false-negative results is high breast density. Breasts contain
both dense fibroglandular tissue and fatty tissue. Fatty tissue appears dark on
a mammogram, whereas fibroglandular tissue appears as white areas. Since
fibroglandular tissue has similar density with tumors, it is harder to detect
tumor in women with denser breasts. This phenomena appear more often
among younger women than older women. False-negative results can lead to
delays in treatment and a false sense of security for influenced women.
• Overdiagnosis and overtreatment. Screening mammograms can find cancers
and cases of ductal carcinoma in situ (DCIS, a noninvasive tumor in which
abnormal cells that may become cancerous build up in the lining of breast
ducts) that need to be treated. However, some cases of DCIS will never cause
symptoms which may bring out ”overdiagnosis”, the subsequently unnecessary
treatment is called as ”overtreatment”.
Other potential harms, such as pain caused by the procedure, exist but are
thought to have tolerable effect on mammography use. All of these limitations and
their associated potential for harm, along with the additional health risks associated with x-ray’s ionizing radiation, give impetus to the development of alternative
techniques of breast cancer detection.
1.2
alternative methods
In this section, several important alternative methods are introduced.
3
1 – Introduction
1.2.1
Breast Ultrasound
Ultrasound, also known as sonography, uses ultrasound waves to profile a part of the
body. Ultrasound waves are high-frequency sound waves that reflect at boundaries
between tissues with different acoustic properties. The depth of these boundaries
is related to the time intervals of reflection arrivals. The echoes are converted into
a black and white image and displayed on a computer screen. Thus, the image
of tissue boundaries can be mapped. Ultrasound helps distinguish between cysts
(fluid-filled sacs) and solid masses and sometimes can help telling the difference between benign and cancerous tumors. It holds promise as a method for detection of
cancers in women with dense breast tissue, which is often problematic with conventional X-ray mammography [4]. Ultrasound has also assumed an important role in
breast imaging, as an adjunct to serial evaluation of benign masses, palpable mass
evaluation, and diagnostic mammography for biopsy guidance [4]. In the last few
years, great steps have been made in improving image quality and resolution of all
ultrasound machines. These improvements were benefited from the new transducer
design technology and advances in electronic signal processing.
This test is not painful and does not expose you to radiation. Unfortunately, even
though ultrasound is also a valid and low-cost method for breast imaging, it is just
a complementary method, the use of ultrasound instead of mammograms for breast
cancer screening is not suggested. Normally, it is used to target a specific area of
concern found on the mammogram. Its major limitation is that breast fat and most
cancer cells have similar acoustic properties, which reduces the detection efficiency.
Also, its imaging results are highly operator-dependent, as the vast majority of
ultrasound procedures are executed using hand-held devices.
1.2.2
Magnetic Resonance Imaging
MR images are created by acquiring the signals generated after radio frequency
excitation of nuclear particles in tissue exposed to a strong magnetic field [4]. The
signals have characteristics that vary according to tissue type. Magnetic resonance
imaging (MRI) relies on the interaction of RF energy and strong magnetic fields
with the magnetic properties of certain atoms to produce high resolution images. In
MRI, a strong magnet is first employed to align the protons of the hydrogen (also
possibly phosphorus or sodium) atoms, and then pulsed RF energy is used to tip the
protons out of alignment. Once the RF pulse ends, as the individual protons return
to alignment and begin to precess at different rates, they transmit an RF signal that
is detected by antennas in the MR device. Imaging is possible because these return
signals vary in intensity and phase based on the strength of the magnetic field, the
frequency and pattern of the RF pulses, and the properties of the tissue. The tissue
properties at each location can be mapped to form high resolution 3D images by
4
1.2 – alternative methods
encoding location information using magnetic field gradients and different sequences
of RF pulses.
If a suspected area exhibits contrast agent uptake, the probability that it is malignant is very big, it may or may not be a tumor. Conversely, its specificity is
better. Further imaging or biopsy may be needed to confirm the suspicion. MRI is
also used to image breast tissue near implants, where x-ray mammography is poor.
Despite the fact that MRI is more sensitive in detecting cancers than mammography, ultrasound, or clinical breast exam, it has higher false positive rate. These false
positive findings have to be checked out to know that cancer is not present, which
means coming back for further tests and/or biopsies. The studies have shown that
MRI had a specificity of only 95.4 percent, compared to 96, 99.3, and 99.8 percent
for ultrasound, clinical breast exam and mammography, respectively. Another important drawback is its higher cost and more time-consuming than mammography.
Moreover, it is uncomfortable during the examination, the patient should be able to
remain perfectly still. All these above shortcomings severely limit the widespread
application as a early breast imaging technique.
1.2.3
Microwave Imaging
The shortcomings of these techniques have motivated the search for better alternatives. The microwave imaging approach has the potential for a much higher sensitivity in detecting tumors and higher specificity in differentiating malignant and
benign tumors, as it benefits from the significant dielectric contrast between malignant and healthy tissues at microwave frequencies (between 2:1 and 10:1) [5][4],
whereas for X-rays the contrast is only a few percent.
Microwave imaging is safe without using ionizing radiations, relatively comfortable without compressing breast. Considering real implementation, the test instrumentation is mature, compact, thus it is potentially cheaper than X-ray mammography and MRI. It is potentially more efficient with younger patients. One of the main
reason for the unsolved breast cancer problem is lack of efficiency of early detection.
The growing speed of the tumor from 10 mm is fast and the chances of survival are
better than 90% if malignant growth is removed before it reaches a size of about
1.5 cm in any given direction. This implies frequently repeated examinations of all
women above the age of 45-50 years. Mass screening method is a good solution for
that, it need not meet very high diagnostic standards, just an early warning, not a
definitive diagnosis [6]. To meet the requirement of mass screening, the examination should be cheap, safe and easy to operate, otherwise, it is difficult for patient
to persist doing that. The existing breast imaging methods as introduced above, of
which X-ray mammography and MRI are most common, are not suitable for mass
screening. X-ray mammography is not safe for frequently tests as it uses ionizing
5
1 – Introduction
radiation, Besides, it requires significant breast compression, which is often uncomfortable and even painful. Ultrasound on the other hand is too operator-dependent
and of low specificity. MRI is considered to be too expensive and time-consuming.
It is reasonable to assume that microwave breast cancer imaging for massscreening purposes should aim at the sensitivity levels of mammography and the
specificity levels of MRI in order to be competitive to both and yet have the advantage of being a cheaper and safer modality. At this time, extensive research and
development is being carried out worldwide toward microwave imaging systems,
which could achieve this goal.
During the past several decades, many microwave imaging techniques, including passive, hybrid and active approaches, have been explored for breast cancer
detection. From the basic concepts of each approach, researchers have investigated
different techniques to achieve a suitable system for breast cancer detection. The
investigated techniques are illustrated in Figure 1.1.
Microwave Imaging
Passive
Active
Hybrid
Thermagraphy
Tomography
Radar Imaging
Figure 1.1. A summary of the most actively pursued methods for image reconstruction from microwave measurements.
The passive approaches detect malignant tumors based on the contrast between
the temperatures of the cancerous tissue to that of the normal one [9]. The radiometers are used to measure the temperature differences. Under the illumination of the
microwave radiation the tumor shows a greater increase in temperature compared
with healthy breast tissue [7][8]. The main challenge to this method is to detect
a very low level power radiated by tumors, which causes technical problems. The
other difficulty comes from the temperature distribution inside the body. It is hard
to distinguish between a cool target close to the skin and a hot target located deep
in the breast [10].
Hybrid (acoustic) microwave imaging systems use microwaves to rapidly illuminate the selected areas in the breast and ultrasound transducers are used to detect
6
1.2 – alternative methods
the pressure waves generated by the expansion of the heated tissues [9]. The heterogeneity (asymmetric nature) of breast is a major challenge being faced by this
technique, since the microwave energy illuminated on the breast surface results in a
non-uniform response being received that requires complicated algorithms to generate the image. The received heat energy which is called as thermal acoustic signals
includes responses from all kind of tissues, such as breast skin, breast tissues and
tumor. The reflected skin signals are much stronger than small tumors due to the
high conductivity of skin and the smaller distance between acoustic sensors and skin.
Moreover, because of the heterogeneity nature of the breast, the speed of the received acoustic signal is non-uniform, and therefore causing a problem in accurately
determining the time of the acoustic pulse generated at a particular location [10].
All these factors make it difficult to approximate the tumor location in the breast.
Unlike passive and hybrid techniques, as discussed above, the active approaches
rely on the significant electrical properties contrast between malignant and normal
breast tissues at microwave frequencies, and two different types of technique have
achieved promising results: microwave tomography and ultra-wideband (UWB) microwave imaging.
Tomography
The goal of microwave tomography is to use the scattered signals to reconstruct
the complete dielectric profile of the breast. The narrowband signals are applied
and the reflected signals received by antennas are used to create a trace of electrical
properties of the breast, using algorithms that basically match measurements of the
microwave signal scattered by the breast to results computed with a model. The
existence of tumors reduces the strength of the scattered signal, which results in areas
of increased permittivity and conductivity on images. This method requires solving
both forward scattering problem and nonlinear ill-conditioned inverse scattering
problem iteratively, until the computed and the measured data are close enough.
The tomographic approach has shown significant promise in both detecting small
tumors and also differentiating between malignant and benign tissue for lesions as
small as 1 cm in diameter. Several research groups are working on this approach
[11][12].
UWB radar imaging
Ultra-wideband (UWB) radar technique was introduced by S.C. Hagness in 1998.
The key point of the technique is time shifting and summing (synthetic focusing) of
scattered waveforms, thereby determines the location of microwave scatterers within
the breast. One of the advantages of UWB microwave imaging systems is that they
receive and process the reflected data in a very wide frequency band that can be
7
1 – Introduction
up to 10 GHz. The large bandwidth allows the UWB radar to obtain more information about the possible surrounding targets and detect, identify, and locate only
the most desired target among others. This fine spatial resolution makes the ultra
wideband radar beneficial for medical applications. The properties of short UWB
pulse indicate that the UWB signal can penetrate a great variety of breast tissues.
However, since the length of UWB pulse has the same order of magnitude with the
potential objects, UWB radar scattered pulses are changed by the electrical characteristics and target structure. Those changes in pulse waveform provide valuable
information such as material properties and shape about the objects. Discrimination of object using higher order signal processing of impulse signals can distinguish
between materials that would not be otherwise distinguishable by the narrowband
signals, at the expense of complex signal processing.
Rather than using the tomographic approach of reconstructing the entire dielectric profile of the breast, which carries more information, UWB radar imaging uses
the following beamforming algorithm to build the image of scatterers distribution
only. Hence, the big advantage of radar-based imaging over the tomographic imaging
is its less computational complex and robust signal processing.
1.3
System overview
Since the microwave technique allows to obtain a compromise between resolution and
penetration depth. Moreover the development of a low cost system is theoretically
possible using this technology. An high resolution breast cancer detection system
would be developed using this method. The diagram of the system is shown in
Figure 2.1. It consists of channel model breast, RF front-end transceiver and antenna
array, and back-end imaging reconstruction unit. The working flow of the system
is the following: the powerful transmitter generates UWB pulse and radiates to
breast by transmitting antenna. Due to the difference in dielectric properties of the
breast tissues, the wave scatters at each dielectric discontinuity. Consequently, the
backscattered pulse acquired by a highly sensitive receiver contains information on
the presence and position of the scatter, in the form of the magnitude and arrival
time of the reflected pulse. The energy map of the breast can be reconstructed and
the tumor can be identified by processing a set of obtained data from antenna array
in the following imaging reconstruction unit.
8
1.4 – Thesis outline
Reconstructed
image
Backscattered signal
Set of
antennas
and trans
ceivers
Tumor
Generated
pulse
Safe
tissue
Backscattered signal
Imaging
Unit
Bus
TX
RX
Antenna
Figure 1.2. An overview of breast cancer detection system. UWB pulses
are radiated against the breast and the echoes are acquired with a set of
transceivers and antennas. An imaging unit processes the data and produces
a map of reflected energy. Cancerous tissues have higher dielectric constant,
resulting in high reflected energy
1.4
Thesis outline
There are four primary topics of interest discussed in this thesis, including the
microwave breast cancer detection system analysis, microwave imaging system verification, hardware modeling and design, and simulation performances of the overall
system. The thesis work begins with Chapter2 which describes the system modeling
and design environment, the numerical transmission channel, breast model, is built,
the front-end components are introduced and the imaging reconstruction algorithm
is analyzed. Chapter 3 presents the system feasibility of the system environment
by setting proper system parameters. In Chapter 4, UWB receivers for this specific
application are proposed and modeled behaviorally, followed by circuit impairments
consideration of each individual radar receiver components. In Chapter 5, UWB
antenna and some other circuit design in 0.13 µm CMOS are presented. Chapter
6 illustrates the influence of the designed hardware components on system performance evaluation. A multi-resolution environment is built to evaluate the influence
of various non-idealities of front-end components. Finally, the conclusion is given in
Chapter 7.
9
Chapter 2
UWB Imaging System
The main UWB microwave imaging system components are shown in Figure 2.1. Antennas, transmitters, and receivers are arranged in an anatomically shaped support
places in close proximity to a patient’s breast. Transmitting antennas are activated
in turn, while receiving antennas can be activated all at once or one by one (multistatic vs monostatic approach). Receivers acquire antenna signals and send digitized
data to the front-end interface, which collects and prepare them for the elaboration
performed by the imaging unit. During the processing first the contribution of skin
reflection that is typically larger than tumor information is eliminated, and then
all signals are realignd so as to focus them on a single point of the breast volume.
The energy reflected by that point is computed and the procedure repeated for all
image points, according to the chosen resolution. To speed up the computation,
specialized hardware accelerators cooperate with a standard microprocessor. The
image is finally displayed on a standard PC screen.
Apart from the transmission channel, the breast, the imaging system can be
ideally partitioned in two main components, the RF part that generates and acquires
the UWB signal, which we term as front-end, and the part that processes the data
and produces the image of reflected energy, termed as back-end. In the following
they are introduced one by one.
2.1
Transmission channel
First of all, it is important to understand which tissues compose the breast, an
example of the breast anatomy is shown in Figure 2.2. It includes adipose tissues
(fat), glandular tissues, skin, nipple and chest wall. The glandular tissue, which
appears white or ”dense”, as defined by radiologists, is represented in the breast
together with the adipose tissue, or fat, which appears dark in contrast during the
mammographic, or ”ray”, always using the language of radiologists.
10
2.1 – Transmission channel
!
"
#$
%
#&"
Figure 2.1.
'
'
An overview of breast cancer detection system.
In order to analyze the performance of the imaging system under development,
simulations of the channel transmission, the breast must be carried out. To achieve
that, a numerical study model should be built and simulated to imitate the microwave propagation in the breast. Several key electromagnetic simulation techniques have been developed over recent years, including the Method of Moments
(MoM), Finite Element (FEM) and Finite Difference Time Domain (FDTD) solutions [13]. MOM method is not proper for general three-dimensional (3D) structures,
whereas FEM and FDTD simulation methods are true 3D field solver which can be
used for any type of 3D structure. In contrast to MOM and FEM algorithms, which
work in the frequency domain and solve Maxwell’s equations implicitly, FDTD algorithms work in the time domain and solve Maxwell’s equations in a fully clear way.
For a FDTD analysis, simulated targets are placed within a ”box” with defined borders, to truncate the analysis space and define the simulation domain. The volume
of the simulation domain is filled by discrete elements, known as ”Yee” cells. FDTD
employs a time-stepping algorithm, which updates the field values across the mesh
cell time-step by time-step, hereby explicitly following the EM waves as they propagate through the structure. The required time to implement a basic FDTD solver
is at least an order of magnitude less work than either an FEM or MoM solver.
Thanks to the above properties, FDTD modeling is frequently used in many
applications like radar signature technology, radiation antenna analysis, wireless
communication devices examination and digital interconnections. In 1998, Hagness
et al introduced FDTD modeling for breast cancer detection using ultra wide-band
radar techniques [4].
11
2 – UWB Imaging System
fat
skin
chest
wall
nipple
glandular
Figure 2.2.
2.1.1
Anatomy of breast.
FDTD method
FDTD method is easy to understand and easy to implement in software, which are
given by, FDTD is a time-domain technique, when a broadband pulse (such as a
Gaussian pulse) is used as the source, the response of the system over a wide range
of frequencies can be obtained with a single simulation. It processes Maxwell’s curl
equations with differential form. In the following, the basis of the FDTD numerical
technique for solving Maxwell’s curl equations directly in the time domain on a
space grid will be described. Maxwell’s curl equations are given by equations (2.1)
and (2.2):
∂D
+J
(2.1)
∇×H =
∂t
∇×E =−
where
E is the electric field;
12
∂B
− Jm
∂t
(2.2)
2.1 – Transmission channel
H is the magnetic field;
B is the magnetic flux density;
D is the electric flux density;
J is the electric current density;
Jm is the equivalent magnetic current density.
Moreover, in linear, isotropic, non-dispersive materials, we can define the following proportions:
D = εE = εr ε0 E,
B = µH = µr µ0 H,
J = σE,
Jm = σm H
(2.3)
where
ε represents the electric permittivity;
εr represents the relative electric permittivity;
ε0 represents the free-space electric permittivity;
µ represents the magnetic permeability;
µr represents the relative magnetic permeability;
µ0 represents the free-space magnetic permeability;
σ represents the electrical conductivity;
σm represents the magnetic conductivity.
In the Cartesian coordinate system, equation (2.1) and (2.2) can be written as:
∂Hz ∂Hy
∂Ex
−
=ε
+ σEx
∂y
∂z
∂t
∂Hx ∂Hz
∂Ey
−
=ε
+ σEy
∂z
∂x
∂t
∂Ez
∂Hy ∂Hx
−
=ε
+ σEz
∂x
∂y
∂t
(2.4)
∂Ez ∂Ey
∂Hx
−
= −µ
− σm Hx
∂y
∂z
∂t
∂Hy
∂Ex ∂Ez
−
= −µ
− σm Hy
∂z
∂x
∂t
∂Ey ∂Ex
∂Hz
−
= −µ
− σm Hz
∂x
∂y
∂t
(2.5)
and,
It can be seen that the change in the E-field in time (the time derivative) is
dependent on the change in the H-field across space (the curl) when Maxwell’s
differential equations (2.1) and (2.2) are examined. This leads to the basic FDTD
time-stepping relation that, at any point in space, the updated value of the E-field
in time is dependent on the stored value of the E-field and the numerical curl of
the local distribution of the H-field in space [14]. The H-field is time-stepped in a
13
2 – UWB Imaging System
similar manner. At any point in space, the updated value of the H-field in time
is dependent on the stored value of the H-field and the numerical curl of the local
distribution of the E-field in space. Iterating the E-field and H-field update results in
a marching-in-time process wherein sampled-data of the continuous electromagnetic
waves under consideration propagate in a numerical grid stored in the computer
memory.
Now the difference discrete of equation (2.4) and (2.5) are taken into consideration. f (x,y,z,t) represents the arbitrary component of E-field or H-field, its discrete
sample in time and space domain can be represented as in equation (2.6).
f (x,y,z,t) = f (i∆x,j∆y,k∆z,n∆t) = f n (i,j,k)
(2.6)
where the subscripts i, j and k are integers representing spatial grid locations in the
x, y and z direction respectively, and ∆x, ∆y and ∆z are, respectively, the lattice
space increments in the corresponding directions. Besides, the superscript n is an
integer representing the increment of the time step ∆t.
Then, the central-difference approximation of f (x,y,z,t) about the first-order
partial derivative of time and space domain can be described as in equation 2.7.
f n (i + 21 ,j,k) − f n (i − 21 ,j,k)
∂f (x,y,z,t)
|x=i∆x ≈
∂x
∆x
f n (i,j + 12 ,k) − f n (i,j − 12 ,k)
∂f (x,y,z,t)
|y=j∆y ≈
∂y
∆y
1
n
f (i,j,k + 2 ) − f n (i,j,k − 12 )
∂f (x,y,z,t)
|z=k∆z ≈
∂z
∆z
1
1
∂f (x,y,z,t)
f n+ 2 (i,j,k) − f n− 2 (i,j,k)
|t=n∆t ≈
∂t
∆t
(2.7)
Yee lattice
However, to better understand the FDTD algorithm, the basic Yee lattice is analyzed
in detail. Figure 2.3 illustrates the standard Yee cell used for FDTD. It is possible
to observe that every electric field component (E) is surrounded by four magnetic
component (H), likewise, every electric magnetic component (H) is surrounded
by four electric component (E). A three-dimensional space lattice is composed of
a multiplicity of such Yee cells. An electromagnetic wave interaction structure is
mapped into the space lattice by assigning appropriate values of permittivity to each
electric field component (E), and permeability to each magnetic field component
(H). Besides, electric and magnetic fields are sampled alternatively in the time
sequence, with a sampling interval between them equal to half the time-step. In
this way the Maxwell’s curl equations become the explicit differential equations
after discretization and can be solved by iterating in time without the necessary to
14
2.1 – Transmission channel
execute matrix inversion operations. As a consequence, FDTD method can solve
the electromagnetic field spatial distribution at each time, step by step, by applying
proper initial values.
Figure 2.3.
Standard Yee cell for FDTD.
In Yee cell, the relationships between the grid points for the E-field and Hfield components and the time step are shown in Table 2.1. The Yee algorithm
also centers its E and H components in time in what is normally called a leapfrog
arrangement. All of E computations in the modeled space are completed and stored
in memory for a particular time point using previously stored H data. Then all of
the H computations in the space are completed and stored in memory using the
E data just computed. The cycle begins again with the re-computation of the H
components based on the newly obtained E. This process continues until timestepping is concluded. The calculation flow is shown in Figure 2.4.
electromagnetic fields
Ex
Ey
Ez
Hx
Hy
Hz
Table 2.1.
x-axis y-axis z-axis
i + 21
j
k
1
i
j+2
k
i
j
k + 21
i
j + 12 k + 21
1
i+ 2
j
k + 21
i + 21 j + 12
k
time t sample.
n
n
n
n + 12
n + 12
n + 12
The position of the E-field and H-field components in Yee cell.
15
2 – UWB Imaging System
Supposing known E values
throughout space at time t1,
t1 = t0 = n Δt
Calculating H values throughout
space at time t2,
t2 = t1 + Δt/2
Calculating E values throughout
space at time t1,
t1 = t2 + Δt/2
Figure 2.4.
Calculation flow chart of FDTD method.
Accordingly, the finite difference equations corresponding to (2.4) and (2.5), can
be written as in equations (2.8) and (2.9) (supposing the observing point (x,y,z) is
the grid point of Ex and Hx , which mean (i + 1/2,j,k) at (n + 1/2)∆t and (i,j +
1/2,k + 1/2) at n∆t, respectively).
n+1/2
Hz
n+1/2
(i + 21 ,j + 12 ,k) − Hz
∆y
n+1/2
(i + 12 ,j − 12 ,k)
n+1/2
(i + 12 ,j,k + 21 ) − Hy
(i + 12 ,j,k − 12 )
∆z
n+1
E (i + 21 ,j,k) − Exn (i + 12 ,j,k)
1
)
= ε(i + ,j,k)( x
2
∆t
1
1
n+ 1
+σ(i + ,j,k)Ex 2 (i + ,j,k)
2
2
−
Hy
(2.8)
Ezn (i,j + 1,k + 12 ) − Ezn (i,j,k + 21 ) Eyn (i,j + 21 ,k + 1) − Eyn (i,j + 12 ,k)
−
∆y
∆z
n+1/2
1
1 Hx
= −µ(i,j + ,k + )(
2
2
n−1/2
(i,j + 12 ,k + 12 ) − Hx
(i,j + 12 ,k + 21 )
)
∆t
1
1
1
1
−σm (i,j + ,k + )Hxn (i,j + ,k + )
2
2
2
2
16
(2.9)
2.1 – Transmission channel
In the following (equation 2.10), the semi-implicit approximation method is applied.
Since Ex values at time-step n + 1/2 and Hx values at time-step n are not assumed
to be stored in the computer’s memory (only the previous values of Ex at time-step
n and Hx at time-step n − 1/2 are assumed to be stored in memory), a simple
arithmetic average is taken between the stored values of Ex at time-step n and the
yet-to-be computed new values of Ex at time-step n + 1, and similarly an average
is taken between the stored values of Hx at time-step n − 1/2 and the yet-to-be
computed new values of Hx at time-step n + 1/2.
n−1/2
n+1/2
Hxn (i,j
(i,j + 12 ,k + 12 )
(i,j + 12 ,k + 21 ) + Hx
2
n+1
Ex (i + 12 ,j,k) + Exn (i + 12 ,j,k)
1
n+1/2
Ex
(i + ,j,k) =
2
2
Hx
1
1
+ ,k + ) =
2
2
(2.10)
Equation (2.8) can be written equivalently as:
1
1
Exn+1 (i + ,j,k) = CA(m) · Exn (i + ,j,k)
2
2
n+1/2
n+1/2
Hz
(i + 12 ,j + 12 ,k) − Hz
(i + 12 ,j − 12 ,k)
+ CB(m) · [
∆y
n+1/2
−
Hy
n+1/2
(i + 12 ,j,k + 21 ) − Hy
∆z
(i + 12 ,j,k − 12 )
]
(2.11)
where
CA(m) =
CB(m) =
ε(m)
∆t
ε(m)
∆t
−
+
σ(m)
2
σ(m)
2
1
ε(m)
∆t
+
σ(m)
2
=−
=
1−
1+
1
σ(m)∆t
2ε(m)
σ(m)∆t
2ε(m)
∆t
ε(m)
+ σ(m)∆t
2ε(m)
(2.12)
(2.13)
where m = (i + 1/2,j,k). Similarly, the other two equations in (2.4) can be written
as:
1
1
Eyn+1 (i,j + ,k) = CA(m) · Eyn (i,j + ,k)
2
2
n+1/2
n+1/2
Hx
(i,j + 12 ,k + 21 ) − Hx
(i,j + 12 ,k − 21 )
+ CB(m) · [
∆z
n+1/2
n+1/2
1
1
Hz
(i + 2 ,j + 2 ,k) − Hz
(i − 21 ,j + 12 ,k)
−
]
(2.14)
∆x
17
2 – UWB Imaging System
where m = (i,j + 1/2,k), and
1
1
Ezn+1 (i,j,k + ) = CA(m) · Ezn (i,j,k + )
2
2
n+1/2
n+1/2
Hy
(i + 12 ,j,k + 21 ) − Hy
(i − 12 ,j,k + 21 )
+ CB(m) · [
∆x
n+1/2
n+1/2
1
1
Hx
(i,j + 2 ,k + 2 ) − Hx
(i,j − 12 ,k + 12 )
−
]
(2.15)
∆y
where m = (i,j,k + 1/2).
Correspondingly, equation (2.9) and the other two equations in (2.5) can be
written as:
1
1
1
1
Hxn+1/2 (i,j + ,k + ) = CP (m) · Hxn−1/2 (i,j + ,k + )
2
2
2
2
Ezn (i,j + 1,k + 12 ) − Ezn (i,j,k + 12 )
− CQ(m) · [
∆y
1
n
n
Ey (i,j + 2 ,k + 1) − Ey (i,j + 12 ,k)
]
(2.16)
−
∆z
1
1
1
1
Hyn+1/2 (i + ,j,k + ) = CP (m) · Hyn−1/2 (i + ,j,k + )
2
2
2
2
Exn (i + 12 ,j,k + 1) − Ezn (i + 12 ,j,k)
− CQ(m) · [
∆z
1
n
n
Ez (i + 1,j,k + 2 ) − Ez (i,j,k + 12 )
]
(2.17)
−
∆x
1
1
1
1
Hzn+1/2 (i + ,j + ,k) = CP (m) · Hzn−1/2 (i + ,j + ,k)
2
2
2
2
Eyn (i + 1,j + 12 ,k) − Eyn (i,j + 12 ,k)
− CQ(m) · [
∆x
1
n
n
Ex (i + 2 ,j + 1,k) − Ex (i + 12 ,j,k)
−
]
(2.18)
∆y
where
CP (m) =
CQ(m) =
µ(m)
∆t
µ(m)
∆t
−
+
σm (m)
2
σm (m)
2
1
µ(m)
∆t
+
σm (m)
2
18
σm (m)∆t
2µ(m)
σm (m)∆t
2µ(m)
(2.19)
∆t
µ(m)
(m)∆t
+ σm2ε(m)
(2.20)
1−
=
=
1+
1
2.1 – Transmission channel
where the label m is (i,j + 1/2,k + 1/2), (i + 1/2,j,k + 1/2), (i + 1/2,j + 1/2,k)
successively.
The finite-difference systems of (2.11), (2.14), (2.15), (2.16), (2.17) and (2.18)
can be simplified if applied to a two-dimensional (2D) case. For 2D cases, if all
physical quantities are not related to z-axis, all partial derivatives of the fields with
respect to z are equal to zero, ∂/∂z = 0. From (2.4) and (2.5) two independent sets
can be identified, the sets of (Ez ,Hx ,Hy ) components called T M wave and the sets
of (Hz ,Ex ,Ey ) components called T E wave.
On the basis of the above 3D condition, their finite difference schemes can be
expressed in the following forms. For T E wave, Hx = Hy = Ez = 0, FDTD
equations become:
1
1
Exn+1 (i + ,j) = CA(m) · Exn (i + ,j)
2
2
n+1/2
n+1/2
Hz
(i + 12 ,j + 12 ) − Hz
(i + 12 ,j − 12 )
+ CB(m) · [
](2.21)
∆y
1
1
Eyn+1 (i,j + ) = CA(m) · Eyn (i,j + )
2
2
n+1/2
n+1/2
Hz
(i + 12 ,j + 12 ) − Hz
(i − 12 ,j + 12 )
− CB(m) · [
](2.22)
∆x
1
1
1
1
Hzn+1/2 (i + ,j + ) = CP (m) · Hzn−1/2 (i + ,j + )
2
2
2
2
Eyn (i + 1,j + 12 ) − Eyn (i,j + 12 )
− CQ(m) · [
∆x
Exn (i + 12 ,j + 1) − Exn (i + 12 ,j)
−
]
∆y
(2.23)
For T M wave, Ex = Ey = Hz = 0, FDTD equations become:
1
1
Hxn+1/2 (i,j + ) = CP (m) · Hxn−1/2 (i,j + )
2
2
Ezn (i,j + 1) − Ezn (i,j)
− CQ(m) · [
]
∆y
1
1
Hyn+1/2 (i + ,j) = CP (m) · Hyn−1/2 (i + ,j)
2
2
Ezn (i + 1,j,k + 12 ) − Ezn (i,j,k + 12 )
+ CQ(m) · [
]
∆x
19
(2.24)
(2.25)
2 – UWB Imaging System
Ezn+1 (i,j) = CA(m) · Ezn (i,j)
n+1/2
n+1/2
(i + 12 ,j) − Hy
(i − 12 ,j)
+ CB(m) · [
∆x
n+1/2
n+1/2
1
Hx
(i,j + 2 ) − Hx
(i,j − 12 )
−
]
∆y
Hy
(2.26)
where, the coefficients CA, CB, CP , CQ are the same of equations (2.11) (2.18),
and m is the same with the grid position of the left-hand side of the corresponding
equations.
The T M wave propagation will be used when 2D breast model is applied.
FDTD source
For FDTD simulations, correct modeling of sources is essential. There are two kinds
of sources, voltage sources and current sources. Another classification of FDTD
methods is possible based on the source modeling. Replaced source method, implemented by replacing the calculated component on a Yee-cell edge by the source
at every time-step. Added source method, achieved by adding the source to the
FDTD calculated component. Replaced sources may give rise to reflections of waves
propagating back to the source location, while added sources act transparently to
these incoming waves [15].
The modeling of FDTD voltage source is straightforward, due to the fact that the
electric field E appears explicitly in the standard FDTD equations. The operation of
replacing and adding to E with a source E is therefore explicit. However, modeling
FDTD current sources is more complex because current is usually not explicitly
included in the FDTD equations. The problem of where should the current source
be placed in the Yee cell, and how should the current source be included in the
FDTD equations should be taken into account.
In this application, current source is used as the FDTD source. The current
source in the FDTD formulation is located on the edge of a Yee cell and added
to the current density J in Maxwell’s equation (2.1). Therefore, J in equation
(2.1) becomes σE + Js rather than σE, where Js is the z-axis source current density
averaged over the entire FDTD source cell. Considering T M wave, instead of (2.26),
the electric field can be expressed as,
Ezn+1 (i,j) = CA(m) · Ezn (i,j)
n+1/2
n+1/2
(i − 12 ,j)
(i + 21 ,j) − Hy
+ CB(m) · [
∆x
n+1/2
n+1/2
1
Hx
(i,j + 2 ) − Hx
(i,j − 12 )
+ Jsn+1/2 (i,j)]
−
∆y
Hy
20
(2.27)
2.1 – Transmission channel
Other FDTD expressions in T M wave are unaffected by the current source. For
more details please refer to [16].
CPML
Due to the limited amount of computer memory, FDTD computation only can be
executed within finite computational domain. In order to model the electromagnetic scattering process efficiently and accurately, the artificial boundaries must be
inserted into the simulation space. Meanwhile, attentions must be taken to minimize
errors introduced by such boundaries. Instead of using highly effective absorbing
boundary conditions (ABCs) to simulate an infinite unbounded computational domain, such as first and second order Mur ABC and Liao ABC, a special absorbing
”material”, called a perfectly matched layer (PML) is applied to implement absorbing boundaries in most modern FDTD implementations [17]. PML can provide
orders-of-magnitude lower reflections than Mur and Liao ABC, but at the expense
of added complexity. It is implemented by setting a kind of special medium layer at
the FDTD truncation border, the wave impedance of this media is totally matched
with the adjacent media, thus, the incident wave goes through the interface and
goes into PML layer without any reflection. Moreover, due to the fact that PML
layer is lossy medium, the transmitted wave which enters PML layer will attenuate
rapidly. Even though PML has limited thickness, it still exhibits good absorbing
effect for incident waves.
Since 1994, the original PML formulation has been modified and extended to
the uniaxial PML (UPML), the convolutional PML (CPML), and the higher-order
PML [18]. CPML is chosen as our absorbing boundary condition, due to its increased
ability to absorb evanescent waves, therefore the absorbing layer can in theory be
placed closer to a simulated scattering or radiating structure. CPML constructs the
PML from an anisotropic, dispersive material, it does not require the fields to be
split and can be implemented in a relatively straightforward manner. Authors in [19]
have proved its effectiveness, besides, as compared to termination with a traditional
formulation of the PML, the CPML technique has lead to a four-fold reduction in
memory.
Figure 2.5 shows the schematic of a typical problem of equation waves propagation, where, in the region of interest analyzed, the radiated waves propagate at
infinite (Figure 2.5 (a)). The same problem but with the addition of a layer of
absorption (PML) to limit the area of analysis which does not create reflections is
shown in Figure 2.5 (b).
In order to better understand the CPML technique, the general PML formulations are introduced first. Here, for sake of example, a lossy medium is assumed.
21
2 – UWB Imaging System
Figure 2.5. Schematic of a typical problem in the equation waves propagation,
where, in the region of interest analyzed, the radiated waves propagate at finite in
(a). The same problem but with the addition of a layer of absorption (PML) to
limit the area of analysis which does not create reflections is shown in (b).
The x-projection of Ampere’s law is thus specified as [19]:
jωεEx + σEx =
1 ∂Hz
1 ∂Hy
−
sy ∂y
sz ∂z
(2.28)
where si are the stretched coordinate metrics, which was originally proposed by
Berenger in [18]:
σi
si = 1 +
,(i = x, y or z)
(2.29)
jωε0
Next, equation (2.28) is transformed to the time domain.
ε
∂Ex
∂Hz
∂Hy
+ σEx = 1 + sy (t) ∗
− sz (t) ∗
∂t
∂y
∂z
(2.30)
where si (t) is the inverse Laplace transform of s−1
i .
The CPML technique is based on the writing of the PML model in the form of
a convolution in time and on the introduction of memory variables to not have to
explicitly store all the past states of the medium to carry out the convolution, but
rather to calculate this convolution in a recursive way. The main idea of the CPML
technique consists of making a choice for si more general than that of equation(2.29)
by introducing not only σi , but also two other real variables αi ≥ 0 and κi ≥ 1 such
that:
σi
,(i = x, y or z)
(2.31)
si = κi +
αi + jωε0
22
2.1 – Transmission channel
In the particular case of κi = 1 and αi = 0, we get the classical PML coordinate
transformation. Using Laplace transform theory, equation (2.30) becomes:
ε
∂Ex
1 ∂Hz
1 ∂Hx
∂Hz
1 ∂Hx
+ σEx =
−
+ ζy (t) ∗
− ζz (t) ∗
∂t
κy ∂y
κz ∂z
∂y
κz ∂z
(2.32)
The discrete impulse response for ζi (t) is defined as
Z (m+1)∆t
Z (m+1)∆t
σ
σi
−( i + α )τ
ζi (τ )dτ = −
Z0i (m) =
e ε0 κi ε0 dτ
ε0κ2i m∆t
m∆t
σ
−( κi +α) m∆t
ε
= ai e
where
ai =
(2.33)
0
i
σ
σi
−( κi +αi ) ∆t
−1
σ0
i
(e
)
2
(σi κi + αi κi )
(2.34)
Using (2.33) and (2.34), (2.32) is discretized in both space and time according to a
staggered Yee-scheme, leading to:
ε
Exn+1 (i + 1/2,j,k) − Exn (i + 1/2,j,k
E n+1 (i + 1/2,j,k) + Exn (i + 1/2,j,k
+σ x
∆t
2
n+1/2
n+1/2
Hz
(i + 1/2,j + 1/2,k) − Hz
(i + 1/2,j − 1/2,k)
=
κy ∆y
n+1/2
−
+
−
N
−1
X
m=0
N
−1
X
Hy
n−m+1/2
Z0y (m)
Hz
Hy
m=0
n−m+1/2
(i + 1/2,j + 1/2,k) − Hz
∆y
n−m+1/2
Z0z (m)
n+1/2
(i + 1/2,j,k + 1/2) − Hy
κz ∆z
(i + 1/2,j − 1/2,k)
n−m+1/2
(i + 1/2,j,k + 1/2) − Hy
∆z
(i + 1/2,j,k − 1/2)
(i + 1/2,j,k − 1/2)
(2.35)
Due to the simple exponential form of Z0i (m), sums in (2.35) can be performed
recursively using the recursive convolution method.
ε
Exn+1 (i + 1/2,j,k) − Exn (i + 1/2,j,k)
E n+1 (i + 1/2,j,k) + Exn (i + 1/2,j,k)
+σ x
∆t
2
n+1/2
n+1/2
Hz
(i + 1/2,j + 1/2,k) − Hz
(i + 1/2,j − 1/2,k)
=
κy ∆y
n+1/2
−
Hy
n+1/2
(i + 1/2,j,k + 1/2) − Hy
(i + 1/2,j,k − 1/2)
κz ∆z
n+1/2
+Ψexy (i + 1/2,j,k) − Ψn+1/2
(i + 1/2,j,k)
exz
(2.36)
23
2 – UWB Imaging System
where
Ψn+1/2
(i + 1/2,j,k) = by Ψn−1/2
(i + 1/2,j,k)
exy
exy
n+ 21
+ ay (Hz
n+ 12
(i + 1/2,j + 1/2,k) − Hz
(i + 1/2,j − 1/2,k))/∆y
(2.37)
(i + 1/2,j,k)
(i + 1/2,j,k) = bz Ψn−1/2
Ψn+1/2
exz
exz
n+ 21
+ az (Hy
n+ 12
(i + 1/2,j + 1/2,k) − Hy
(i + 1/2,j − 1/2,k))/∆z
(2.38)
σ
−( κi +ai ) ∆t
ε
bi = e
i
0
,(i = x, y, or z)
(2.39)
This scheme is second-order accurate and is stable within the Courant limit for all
positive real values of σi and αi and for all real values of κi ≥ 1 .
The convolution terms are updated at each time step synchronously with the
normal FDTD algorithm and, to reduce the errors of reflection in space discrete,
the constitutive parameters (σi , αi , κi ) are scaled along the respective axes. In this
way, the constitutive parameters have a one-dimensional variation, also ai and bi are
one-dimensional functions that can be calculated in advance and stored in a vector,
saving memory. The explicit update of the electric field (2.11) becomes:
1
1
Exn+1 (i + ,j,k) = CA(m) · Exn (i + ,j,k)
2
2
n+1/2
n+1/2
Hz
(i + 12 ,j + 12 ,k) − Hz
(i + 12 ,j − 12 ,k)
+ CB(m) · [
κy ∆y
n+1/2
n+1/2
(i + 12 ,j,k + 21 ) − Hy
(i + 12 ,j,k − 12 )
−
κz ∆z
n+1/2
+ Ψexy (i + 1/2,j,k) − Ψn+1/2
(i + 1/2,j,k)]
exz
Hy
(2.40)
Similar expressions are derived for the remaining electric and magnetic fields.
The basic structure of the CPML setting was displayed in Figure 2.5 (b). In
FDTD computational region, Maxwell’s equations are solved by standard FDTD
algorithm, correspondingly, the computational region is surrounded by CPML layer,
in which the equations are solved by the algorithms introduced above. The reflection
coefficient is an important parameter for the evaluation of the CPML performance,
it can be calculated as follows [16],
R(θ) = e−2ησd cos θ
24
(2.41)
2.1 – Transmission channel
where θ is the angle of incidence of the incident wave relative to the PML interface
surface, d is the CPML layer thickness, η is wave impedance, σ is the conductivity
in PML layer.
From (2.41) we know that R(θ) is a function of layer thickness and layer conductivity. In a FDTD simulation, R(θ) is taken as a reflection of error, so the bigger
the product of d and σ, the smaller value of R(θ), the better performance of the
CPML.
Due to the discrete nature of the FDTD algorithm, the discontinuities due to
sampling artifacts must be compensated in some way. The change of the conductivity in PML layer is represented according to the following formula,
σ(x) = (x/d)m σmax
(2.42)
The conductivity grows from a zero value at the inner edge to a maximum value
σmax at the outer edge. It grows linearly when m = 1 and grows exponentially when
m > 1. Combining the polynomial variation of the conductivity from (2.42) and
(2.41) we obtain
R(θ) = e−2ησmax d cos θ/(m+1)
(2.43)
In (2.43), a large m allows to obtain a distribution of σ(x) flat near the interface
of the CPML while for small m there is a more rapid growth σ(x) inside of the
absorbing layer. Generally, a value of 3 ≤ m ≤ 4 allows to obtain good performance
for most FDTD simulations [16].
With these assumptions, the parameters of a PML may easily be calculated to
obtain a specific value of error, according to the following formula.
σmax = −
(m + 1) ln[R(0)]
2ηd
(2.44)
By balancing the parameters in equation (2.45) an optimal efficiency of the
CPML minimizing the discretization errors is obtained. Getting a low value of
σmax , it is possible to obtain a great reflection from the PEC wall set as boundary
condition.
In this case, using dispersive materials, the CPML parameters must be suitably chosen to optimize the performance of our computational model, such as layer
thickness and sigma attenuation factor. Following the literature [14] various tests
to evaluate the correct values for the design were performed.
To sum up, the design flow for CPML can be organized as following:
• As a first choice we opted for an error of reflection R(0), which brings us to
write the following equation for calculating the optimal loss coefficient:
σopt = −
0.8(m + 1)
√
η0 ∆ εr,ef f µr,ef f
25
(2.45)
2 – UWB Imaging System
where εr,ef f and µr,ef f are the average value of the material parameters present
at the edge of the main calculation area, and ∆ is the space interval.
• The second parameter to be chosen is the thickness of the layer d. Based on the
selected σmax and typical values of m, κmax and αmax , σ(x) can be expressed
as a function of d, which is the coefficient in the expression of ai and bi .
• Choosing a value of σmax different from the optimal one to evaluate how further
we can go to improve the performance.
These aspects will be evaluated from the practical point of view later.
Grid size and Stability
As FDTD technique represents Maxwell’s curl equations with a set of finite difference
equations, which means replacing the original solutions of electromagnetic partial
differential equations with the solutions of finite difference equations. This kind
of replacement is meaningful if and only if the solutions of the discrete difference
equations are convergent and stable. Thus the limitation of time and space discrete
intervals should be considered, from the stability and convergence of Maxwell’s
equations point of view.
For computational stability, it is necessary to satisfy the Courant stability conditions, in other words, the relationship between space interval ∆x, ∆y, ∆z and time
interval ∆t:
c∆t ≤ q
1
1
(∆x)2
+
1
(∆y)2
+
1
(∆z)2
(2.46)
√
where c = 1/ εµ is the light speed in medium. This requirement puts a limitation
on ∆t for the chosen ∆x, ∆y and ∆z.
Square Yee cells are adopted in this work for simplicity with ∆x = ∆y = ∆z = ∆.
Authors in [16] introduced a Courant stability factor S to deal in a formal way with
the time step choice. This factor is common to all numerical methods that have to
deal with partial differential equations and must always be less than or equal to one
to ensure stability. In 2D case the Courant factor is assumed to be 0.5, so, the time
step ∆t can be expressed as [16],
∆t =
∆
2c
(2.47)
The value of spatial grid ∆ in the FDTD grid is chosen to sufficiently sample
the shortest wavelength in the system (normally determined by the bandwidth of
the source), which means that over one increment the electromagnetic field does
26
2.1 – Transmission channel
not change significantly, and to accurately model the smallest dimension and/or
physical and electromagnetic phenomenon in the simulated materials (such as skin
depth, exchange length or domain wall width in a magnetic material). This means
that, to have meaningful results, the linear dimension of the grid must be only
a fraction of the wavelength (generally chosen between λ/10 and λ/20). In this
application, for example, the considered maximum wave frequency is 10.6 GHz, in
free space, the calculated minimum wavelength is about 30 mm, thus, the space
interval must be smaller than 3 mm to obtain the accurate results.
2.1.2
Breast model
The ”UWCEM Numerical Breast Phantom Repository ” contains a fairly large number of numerical models of the breast anatomy derived from MRI scans with the
patient in the prone position. They are used to investigate the methods for prevention of breast cancer and its treatment applications [20] [21]. Breast with ID:
012204 is selected as the investigated channel model, whose sagittal slice from the
3D numerical breast phantom is demonstrated in Figure 2.6. According to the radiographic density, this breast is classified as scattered fibroglandular who has 25-50%
glandular tissue [20].
Figure 2.6. MRI scans of the phantom in the repository UWCEM with
Breast ID: 012204.
The phantom is comprised of a 3D grid of cubic voxels, where each voxel is
0.5 mm × 0.5 mm × 0.5 mm. The breast model consists of a roughly 1.5-mm-thick
27
2 – UWB Imaging System
skin layer, a 1.5-cm-thick subcutaneous fat layer at the base of the breast, and a
0.5-cm-thick muscle chest wall.
The included mediums in the breast model are illustrated in Table. 2.2, they are
termed by media numbers. Except the skin and muscle medium, the normal breast
tissues in the breast phantom are categorized into seven tissue types, ranging from
the highest-water-content fibroconnective/glandular tissue with the highest dielectric properties (media number = 1.1), to the lowest-water-content fatty tissue with
the lowest dielectric properties (media number = 3.3). There is also a transitional
region with media number 2 which represents intermediate dielectric properties [20].
The dielectric properties information for each voxel of the breast interior are given.
tissue type
media number.
external Environment
-1
skin
-2
muscle
-4
glandular1
1.1
grandular2
1.2
glandular3
1.3
transitional
2
fat1
3.1
fat2
3.2
fat3
3.2
Table 2.2.
Type of fabric and the corresponding average number [20]
As microwave imaging technique for breast cancer detection application is based
on the principle that the dielectric properties contrast between malignant tissue and
normal tissue is significant, recently published data in [22] [23], based on a large
clinical study, report the realistic dispersive dielectric properties of normal breast
tissue in the extremely wide frequency range of 0.5 to 20 GHz, and suggest that
the contrast between healthy and malignant breast tissues might be not as high as
previously believed.
Dispersive medium
Since most human tissues are dispersive medium, it is necessary to take the dispersive effect into account to approach the actual case. In this study, the dispersive
properties of breast tissues were also included in our FDTD breast models. The
dispersive breast is modeled by setting different dispersive electrical properties for
the breast fat, the skin, the chest wall and the tumor.
28
2.1 – Transmission channel
80
8
70
6
3.1
4
3.2
3.3
60
1.1
50
1.2
40
1.3
2
4
6
Effective conductivity (S/m)
Dielectric Constant
Figure 2.7 shows the eight wideband dielectric properties curves that serve as
upper and lower bounds on each of the seven types of normal breast tissue listed in
Table 2.2 from 0.5 to 20 GHz [20] [22].
8
30
20
2
10
0
5
10
Frequency (GHz)
15
20
40
2
35
1
30
25
0
16
3.1
3.2
3.3
18
20
1.1
1.2
20
1.3
15
10
2
5
0
5
10
15
Frequency (GHz)
20
Figure 2.7. The seven tissue-type regions bounded by the curves in
this graph are labeled with the media numbers reported in Tab. 2.2.
From top to bottom, the curves correspond to the following eight cases:
maximum, group1-high, group1-median, group1-low, group3-high, group3median, group3-low, and minimum [20].
The frequency dependence of tissue dielectric properties is more promptly incorporated into wideband FDTD simulations using Debye dispersion parameters
rather than Cole-Cole parameters [20]. The frequency dependence of the dielectric
constant, ε(ω) , and the conductivity, σ(ω), over the band of interest (3 GHz to
10 GHz) was accurately modeled using single-pole Debye dispersion equations of the
following form:
σ
εs − ε∞
σs
= ε∞ +
−j
(2.48)
ε(ω) − j
ωε0
1 + jωτ
ωε0
In this model, ω is the angular frequency, σ/ωε0 is the frequency-dependent dielectric
loss, ε∞ defines the relative permittivity at infinite frequency, εs is the static relative
permittivity, σs is the static conductivity, and τ is the relaxation time constant.
τ can be approximated by a single known spatially independent value since the
relaxation time constant in the microwave frequency range is similar (e.g., on the
order of 10 ps) for various different biological tissues [24]. Consequently, there are
three unknowns for this equation (ε∞ , εs and σs ) at every voxel within the volume.
These three model parameters can be estimated from the experimental data.
Here, in Table 2.3, the parameters for single-pole Debye models over the 3-10 GHz
band are presented, which are used in the above introduced FDTD simulations
29
2 – UWB Imaging System
[16]. A constant relaxation time constant τ = 13 ps for all tissue types is used,
∆ε = εs − ε∞ .
ε∞
minimum
2.309
group3-low
2.848
group3-median 3.116
group3-high
3.987
group1-low
12.99
group1-median 13.81
group1-high
14.20
maximum
23.20
skin
15.93
muscle
21.66
∆ε τ (ps) σs (s/m)
0.092 13.00
0.005
1.104 13.00
0.005
1.592 13.00
0.050
3.545 13.00
0.080
24.40 13.00
0.397
35.55 13.00
0.738
40.49 13.00
0.824
46.05 13.00
1.306
23.83 13.00
0.831
33.24 13.00
0.886
Table 2.3. Single-pole Debye parameters for the maximum, group1-high,
group1-median, group1-low, group3-high, group3-median, group3-low, and minimum curves associated with normal breast tissue as well as skin and muscle (valid
for the 3-10 GHz band) [20].
Figure 2.8 shows the single-pole Debye curves for normal breast tissue along with
their corresponding Cole-Cole curves, to illustrate the accuracy of the Debye models
over the 3-10 GHz band. Debye parameters for specific voxels within the breast were
computed using a weighted average based on the p value of a specific voxel [16]. It
is possible to note that the weighted averages are applied to the Debye parameters
themselves rather than the frequency-specific dielectric constant and conductivity
[20].
Investigated breast model
Figure 2.9 shows the result of three-dimensional (3D) pre-processing at a given
frequency of 8 GHz.
However, as the first step, a two dimensional (2D) breast model was used as our
channel model, which is shown in Figure 2.10. It is the sagittal slice of the 3D breast
model of Figure 2.9. The chest wall was included, and the model was terminated by
a complementary perfectly matched layer (CPML). A fake tumor (the black square)
is inserted in the FDTD models, while the Debye parameters for the tumor are
ε∞ = 3.9, ∆ε = 50.1, τ = 13 ps and σs = 0.7 S/m. A conformal array consisting of
9 antenna elements is located on the surface of the naturally flattened breast, the
antenna in the FDTD model is the hertzian dipole antenna which is modeled as an
electric current sources [16].
30
80
8
70
6
3.1
4
3.2
3.3
60
1.1
50
1.2
40
1.3
2
4
6
Dielectric Constant
Dielectric Constant
2.1 – Transmission channel
8
30
20
2
10
0
80
8
70
6
3.1
4
3.2
3.3
60
1.1
50
1.2
40
1.3
2
4
6
8
30
20
2
10
5
10
15
Frequency (GHz)
20
0
5
10
15
Frequency (GHz)
20
Figure 2.8. From top to bottom, the Cole-Cole and Debye (bold) curves correspond to the following eight cases: maximum, group1-high, group1-median,
group1-low, group3-high, group3-median, group3-low, and minimum [20].
Figure 2.9.
Dielectric constant–three dimensional model.
Another breast model was created using the average properties technique, with
the same size and shape with above heterogeneous breast, but with constant breast
tissue [25]. The ideal model is used to decouple the effect of a complex breast
31
2 – UWB Imaging System
Figure 2.10.
Heterogeneous breast model.
from the effect of system non-idealities when we evaluate the system functionality.
The real model is used for a final assessment, when we evaluate the two effects
combined. Figure 2.11 depicts this homogeneous breast model. Table 2.4 shows the
spatial averages of the Debye parameters for each phantom in our application.
Figure 2.11.
Homogeneous breast model.
32
2.2 – Front-end: Transceiver and Antenna
skin
normal tissues
muscle
tumor
Table 2.4.
ε∞ ∆ε τ (ps)
4
33 13.00
7
3
13.00
4
50 13.00
3.9 50.1 13.00
σs (s/m)
1.1
0.15
0.7
0.7
Average breast tissue single-pole Debye parameters for each phantom.
As mentioned above, the spatial grid resolution for FDTD simulation is 0.5 mm,
which is accurate enough for the breast modeling. Using the 2D model, combined
with equation (2.47), the calculated time step is 0.834 ps, which is about 1200 GHz
sampling frequency.
2.2
Front-end: Transceiver and Antenna
The aim of the front-end is data transmission and acquisition. The UWB imaging
system is expected to be suitable for long term, continuous monitoring purposes,
so that low cost is one of the important characteristic to promote the development
of microwave imaging techniques for breast cancer detection. Even experiments
with standard RF instruments have proved that the microwave imaging technique
is capable of detecting small tumors [26]. The required experimental instruments,
like Vector Network Analyzer and the switching network, are bulky and expensive,
so they should be replaced by low cost integrated circuits and systems.
The block diagram of the proposed front-end is shown in Figure 2.12. It is
composed of the array of transceivers and antennas. Transceivers are the chain that
connects the antennas on one side and signal processing section on the other side. In
this specific application, the purpose of the hardware is to send a pulse train toward
the breast through antenna, detect and sample the particular type of reflected pulse
train, caused by the interface between the different breast tissues, and then convert
it to digital signal. Based on the radar configuration, a circulator or switch may
need to select between connecting the antenna to the transmitter and to the receiver.
Moreover, the isolation between transmitter and receiver can not be ignored.
2.2.1
Transmitter
The transmitter part is conceptually simple. It works as a pulse generator, and
should be able to generate any type of sub-nanosecond pulse in the band chosen
for application to breast cancer detection. Ideally, it is modeled in Matlab as a
single source point in FDTD simulation. An integrated and flexible CMOS UWB
33
2 – UWB Imaging System
TX
Digital
Blocks
Pulse CK
RX
Figure 2.12.
Block diagram of RF frontend.
transmitter architecture based on the distributed-waveform generator technique have
proposed and developed [27] [28]. The block diagram is presented in Figure 2.13.
Figure 2.13.
Block diagram of the transmitter [27].
34
2.2 – Front-end: Transceiver and Antenna
2.2.2
Receiver
The receiver is an important block and a design challenge in our microwave imaging
application, as the requirements of the receiver are very strict in this application,
given that it has to satisfy the input matching with the antenna, minimize the noise
distortion within the specific ultra-wide bandwidth (up to 10 GHz), while achieving
at the same time very large dynamic ranges. Similarly to the transmitter, the
receiver is modeled as a perfect cell under ideal condition. The focus will be focused
on the implementation of the receiver part later.
2.2.3
Antenna
Antennas are located around and close to the breast, and each antenna is connected
to a transceiver pair. In the ideal model that we use as a reference, the antenna
is ideally modeled as a hertzian dipole during FDTD simulation [16]. Figure 2.14
shows the ideal radiation pattern of the typical Hertzian dipole antenna. In addition,
a custom-designed slot antenna was also experimented, as will be discussed later on.
Figure 2.14.
Diagram of emission of a Hertzian dipole antenna [16].
35
2 – UWB Imaging System
2.3
Algorithm and implementation
The aim of the image reconstruction unit is, starting from the sampled reflected
signals, to recombine this values in order to obtain an energy map representing the
amount of energy backscattered from each point of the breast.
Depending on how the backscattered energy is acquired, there are several different approaches to UWB radar imaging. These approaches can be divided into
three categories: monostatic, bistatic, and multistatic. In the monostatic case, the
transmitting antenna itself acquires the backscattered signal. Often the transmitting antenna is moved across the breast to produce a synthetic aperture. In the
bistatic configuration, two antennas are used, a single transmitting antenna and a
single receiving antenna. At last, in the multistatic approach, the tissue is illuminated by one transmitting antenna while the backscattered signals are recorded at
several antennas placed at different positions around the breast [29]. Figure 2.15
explains better these configurations. Multistatic and Bistatic configurations offer
better performance at the expense of increased implementation complexity.
Figure 2.15. Possible configurations with Radar Microwave Imaging: (a) Monostatic, (b) Multistatic, (c) Bistatic.
Based on different radar configurations, various imaging algorithms have been
proposed, like Confocal Microwave Imaging(CMI) [5], Time Reversal(TR) [30], Generalized Likelihood Ratio Test(GLRT) [31], multistatic adaptive microwave imaging(MAMI) [29], delay-multiply-and-sum (DMAS) [32] and Microwave Imaging via
Space-Time(MIST) [33] [34]. The monostatic radar method is applied in this breast
cancer detection system for its simplicity; moreover, the MIST beamforming algorithm has proved to be a better technique for the application [35].
To better understand the imaging reconstruction process, CMI technique will
also be introduced, which is the most simple algorithm for detecting breast cancer.
36
2.3 – Algorithm and implementation
2.3.1
Confocal Microwave Imaging
Confocal Microwave Imaging employs a simple delay-and-sum (DAS) beamforming
algorithm. Figure 2.16 shows the basic principle of CMI, antenna array is located
around breast surface. The antennas detect all the points in breast, the delay types
are the same at the same points. The received signals at different antenna positions
are shown in the central panel. It is possible to see that the time delay of the received
pulse by different antennas is different, and the sum of all delayed waveforms gives
us an information about dielectric contrast in that point. When the beamformer
is steered to location r0 (the actual location of the tumor), the signals coherently
sum, as shown by the left panel, the resulting signal will be big. Correspondingly,
when the beamformer is steered to a location other than r0 , incoherent summation
results, as shown by the right panel, the energy will be smaller. More in detail, the
Figure 2.16. An illustration of simple delay-and-sum beamforming. The received
signals are shown in the central panel. When the beamformer is steered to location
r0 (the actual location of tumor), the signals coherently sum, as shown by the left
panel. When the beamformer is steered to a location other than r0 , incoherent
summation results, as shown by the right panel [34].
implementation of this algorithm can be divided into four steps [5].
1. Calibration. This is the first and fundamental step prior to performing tumor
detection, not only for CMI technique, but for all imaging techniques. The
goal of the calibration step is to remove the incident pulse and skin backscatter
37
2 – UWB Imaging System
from the recorded waveforms, as the response from the skin-breast interface is
orders of magnitude larger than the response from all other contributions and
may persist in time beyond the time at which the lesion response occurs. Supposing the distance between antenna and breast skin is identical, so the signals
recorded at various antenna locations have identical incident pulse and skin
backscatter content. Moreover, as the distance of antenna-to-skin is smaller
than the distance of antenna-to-tumor, the skin reflection appears earlier than
tumor information. The calibration operation is implemented generating a
calibration signal for each antenna by averaging the time response of every
other antenna. The calibration is completed subtracting the signal from the
corresponding antenna.
2. Integration. The next step in the signal processing is the integration of the
calibrated signals. The differentiated Gaussian excitation signal has a zerocrossing at its center point in time. The backscattered signal that would follow
after a specific time delay corresponding to the round-trip distance between
the antenna and the scatterer would also have a zero-crossing at its center
point. After integration, the signal would have a maximum at the center
point, allowing for the coherent addition of local maxima via straightforward
time-shifting.
3. Compensation. Compensation for radial spreading and/or path loss is applied
to the signals. Radial spreading correction accounts for the decrease in amplitude of a spherical wave as it expands, while path loss compensation corrects
for the reduction in signal strength due to propagation through lossy breast
tissue.
4. Image Reconstruction. It consists on calculating, for each pixel, its intensity.
First, the round trip time (τii ) from each antenna to the considered pixel
(|~r−~ri |) is calculated. In this calculation, the wave velocities (υ) of the different
covered mediums (air, skin, healthy breast tissue) are taken into account.
Then, the time-domain signals are time-shifted by an amount corresponding to
the calculated round-trip times. In this way, the information on the considered
pixel embedded in the various time-domain signals is aligned [35]. The roundtrip time is calculated by
2|~r − ~ri |
(2.49)
τii (~r) =
υ∆t
The intensity of a pixel in the reconstructed image is the square of the coherently summed values.
"N RX
#2
X
I(~r) =
wi aii (τii (~r))
(2.50)
i=1
38
2.3 – Algorithm and implementation
where the weights wi are introduced to compensate for the radial spreading of
each cylindrical wave as it propagates outward from the transmitting antenna.
However, this algorithm does not account for dispersive propagation effects and
offers limited capability for discriminating against artifacts and noise. In the following, MIST beamforming algorithm, along with an advanced algorithm for optimal
removal of skin artifacts are analyzed.
2.3.2
Since antennas may be located at slightly different (sub-millimeter) distances from
the skin, it is clear that the above introduced calibration procedure is effective as long
as each antenna has the same distance from the skin. More sophisticated algorithms
should be employed to estimate the correct distance and efficiently remove the skin
content.
The MIST imaging system can be divided into two main processing stages: preprocessing that eliminates the large reflection at the skin (skin artifact removal),
optimal beamforming (MIST beamforming). The structure of this MIST imaging
system is demonstrated in Figure 2.17, n is the number of antennas, n channels
are used in skin artifact removal part, and then MIST beamforming processes the
calibrated n signals and reconstructs the energy map, N is the antenna number.
Details of each of these stages are described below.
(t)
3
4
4
NO TUMOR
TUMOR
4.5
MIST
5
channel1
channel2
Reconstruction
algorithm
channeln
4.5
5
Figure 2.17. Structure of the reconstruction algorithm organized in two parts:
skin artifact removal (SKAR) and MIST beamforming (BEAF).
Skin Artifact Removal
Skin artifact removal (SKAR) is an algorithm for optimally removing artifacts in the
received signals due to backscatter from the skin-breast interface [33]. Compared
39
2 – UWB Imaging System
with the above mentioned calibration, this approach takes into account the local
variations in skin thickness and breast heterogeneity.
The general idea behind this approach is simple. It estimates the skin artifact at
each antenna as a filtered combination of the signals at all other antennas to compensate for channel-to-channel variation. The filter weights are chosen to minimize
the residual signal over the initial portion of the received data, which is dominated
by the backscatter from the skin interface. Figure 2.18 shows the block diagram of
this algorithm.
Figure 2.18. Block diagram illustrating the algorithm for removing the skin-breast
artifact from the backscattered signal received at the first of N antennas [35].
Without loss of generality, suppose that the skin-breast artifact is to be removed
from the first antenna. Considering an array of Nant receiving antennas, we denote
the nth received sample at the ith antenna as bi [n]. Starting to analyze the block
for the first antenna, the skin contribute on sample nth is estimated from a window
bi [n] of length 2J + 1 centered on the nth sample in each other Nant − 1 channel:
bi [n] = [bi [n−J],..,bi [n],..,bi [n+J]]T
T
T T
b2N [n] = [b2 [n] ,..,bN [n] ]
2 ≤ i ≤ Nant
(2.51)
(2.52)
Vector b2N [n] is obtained as the merging of windows from channel 2 to channel
Nant . The filter weights vector is denoted as qi and concatenation of coefficients
T T
from channels 2 through Nant is q = [q2T ....qN
] .
The residual part of signal is computed subtracting the sum from all filtered windows
to the n-sample of first antenna:
x1 [n] = b1 [n] − qT b2N [n]
40
(2.53)
2.3 – Algorithm and implementation
This operation is repeated for each channel. If received data are decomposed in skin
(s[n]) and residual (d[n]) contributions a distortion occurs in the residual part of
each signal:
x1 [n] =s1 [n] − qT s2N [n] + d1 [n] − qT d2N [n]
≈d1 [n] − qT d2N [n]
(2.54)
d2N [n] can be approximated by using x2N [n]. Taking into account this approximation, the compensation is performed using the following formula:
x̃1 [n] = x1 [n] + qT x2N [n]
(2.55)
In order to obtain the coefficients, a specific procedure is requested, and is reported here. Filter weights are chosen to satisfy the constraints of equation (2.56),
q = arg min
q
n0X
+m−1
|b1 [n] − qT b2N [n]|2
(2.56)
n=n0
where the time interval n = n0 to n0 +m−1 represents the initial portion of the data
record containing skin-breast artifact and no backscattered signals from lesions. In
other words, coefficients are chosen to nullify part of signal dominated by unwanted
skin reflection and direct path, delimited by n0 and n0 + m − 1. Solution to this kind
of problem requests a least square method solution. This minimization problem can
be solved by:
q = R−1 · p
(2.57)
n +m−1
1 0X
b2N [n]b1 [n]
p=
m n=n
(2.58)
0
R=
1
m
n0X
+m−1
b2N [n]bT2N [n]
(2.59)
n=n0
An issue with this kind of solution is that the signals in specified time interval
have high similarity, which leads to have matrix R ill-conditioned. Weights obtained
have large norm and amplify noise. To prevent this, low-rank approximation Rp is
used in place of R. Matrix inversion becomes:
Rp =
p
X
λi ui uTi
(2.60)
i=1
R−1
p
p
X
1
ui uTi
=
λ
i
i=1
41
(2.61)
2 – UWB Imaging System
where λi , 1 ≤ i ≤ p, are the p most significant R eigenvalues and ui , i ≤ i ≤ p, are
the corresponding eigenvectors.
Therefore, the design flow can be simply organized as follows:
1. Choosing the starting sample n0 and the number of the processed samples m.
It is correct to think that only these m samples will contain skin artifact.
2. Choosing a window has a length of 2J + 1 for theses m samples.
3. Calculating the filter weights and calibrating these chosen m samples to get
the residual parts of the received signals.
4. Compensating the calculated residual parts.
An example of the SKAR effect on the signal is shown in Figure 2.19. The
backscattered signals are from antenna, obtained by a FDTD simulation. The solid
pulse is acquired at the condition when tumor is inserted, the dotted pulse is without tumor. The zoomed part includes tumor information, it is invisible, as the
skin reflection part is too big. The bottom figure shows the pulses after the SKAR
application, it is possible to see that the big skin reflection parts are eliminated
and the tumor information part is kept and became clear (compare the superposition between two signals obtained in a case without tumor and with tumor). The
importance and effectiveness of this stage is therefore evident.
MIST Beamforming
Following the skin artifact removal, the calibrated signals x
e1 [n] to x
eN [n] are then
passed through the MIST beamformer.
The image of backscattered energy as a function of scan location is obtained by
applying a space-time beamformer designed for each scan location to the backscattered signals measured at each antenna. Figure 2.20 shows the space-time beamformer for each scan location forms a weighted combination of time-delayed versions
of the backscattered signals. The aim of this section is to design the beamformer to
keep the backscattered signals from the designed point while attenuating contributions from other locations.
Similarly to other beamforming techniques, the MIST beamforming algorithm,
or ”BEAF”, is based on time aligning of signals from different antennas in order to
adjust different round trips time (τi (r0 )) from antennas to a generic point r0 . In this
way, if a dielectric discontinuity, such as malignant tumor, exists at r0 , the timealigned signals add coherently and the energy response will be large. The MIST
block diagram is shown in Figure 2.20.
42
2.3 – Algorithm and implementation
Electric Field (V/m)
FDTD Simulation: Received Signal Before Calibration
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
NO TUMOR
TUMOR
0.00015
0.0001
5e-05
0
-5e-05
-0.0001
2 2.2 2.4 2.6 2.8 3 3.2
0
0.5
1
1.5
2
2.5
Time (ns)
3
3.5
4
(a)
FDTD Simulation: Received Signal After Calibration
Electric Field (V/m)
0.00015
NO TUMOR
TUMOR
0.0001
5e-05
0
-5e-05
-0.0001
-0.00015
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (ns)
(b)
Figure 2.19. Example of pulses before and after calibration. FDTD-computed
backscattered signals with and without tumor as received by one of the antennas,
with zoom on the late-time response, showing a difference between the two signals.
(b) Signal after calibration, the skin artifacts are removed.
Remembering that the distances between each antenna and point r0 may not
be the same. First of all, time-aligning is performed, as suggested in [33] [35], by
delaying the waveform by an integer number ni (r0 ):
ni (r0 ) = na −round(τi (r0 )) na ≥ round(max τi (r0 ))
i,r0
(2.62)
where na is the worst case round-trip over all channels and locations.
Then, the aligned signal is truncated by a window function g[n] to remove the
samples before na which are not useful for energy estimation.
(
1, n ≥ na
g[n] =
(2.63)
0, otherwise
43
2 – UWB Imaging System
Figure 2.20. Block diagram illustrating the MIST beamforming process
for location r in the breast [33].
Before summing the outputs, the FIR filters are needed to compensate the
frequency-dependent propagation effects, such as attenuation and dispersion of breast
tissues related to the path length. If wil is defined as the lth weight of ith filter, the
summed output from these filters can be expressed as [35]:
z[n,r0 ] =
N X
L
X
wil · x̃i [n − l − ni (r0 )]
(2.64)
i=1 l=0
where L is the number of weights in each channel. The calculation of filter weights
will be introduced later. It is necessary to notice that the performance will be better
with more filter weights, but the design complexity will increase too, so the weights
number must be chosen by carefully exploring this trade-off.
Before calculating the voxel energy, another window h with length of lh is defined
to choose the useful samples which contain the tumor information.
(
1, nh ≤ n ≤ nh + lh
h[n,r0 ] =
(2.65)
0, otherwise
Finally, the energy p(r0 ) is obtained as the sum of the squares of z[n] windowed
by h[n,r0 ]:
X
p(r0 ) =
|z[n]h[n,r0 ]|2
(2.66)
n
Weights of FIR filters can be computed in time-domain [33] [35] or frequencydomain [36] [37]. Frequency-domain approach is applied for its computationally
simplicity, as it does not require matrix inversion.
44
2.3 – Algorithm and implementation
The frequency resolution for weights design ∆ω is:
∆ω =
2π
LTs
(2.67)
As mentioned above, it is limited by maximum length of FIR filter L. Ts is the
sampling time interval.
The band of interest is composed of the set of K frequencies starting form a
lower bound ωl to an upper-bound ωh :
ωl = ω0 ≤ ωk ≤ ωK−1 = ωh
:
0≤k ≤K −1
(2.68)
Then, supposing to choose ωl and ωh multiple of frequency step ∆ω, K is equal to:
K=
ωh − ωl
+1
∆ω
(2.69)
For a monostatic configuration, the backscattered signal in frequency domain
Bi (ω) is:
Bi (ωk ) = I(ωk )Sii (ωk ,r0 )
(2.70)
where I(ωk ) is the portion of the transmitted signal belonging to the k th frequency
in UWB range of transmitted signal. Each value Sii (ωk ,r0 ) corresponds to the ideal
scattering value in frequency domain for each voxel. In a monostatic configuration
Sii (ωk ,r0 ) can be formulated by considering radial spreading, path loss and phase
shift. Depending on if the scanning is performed in 2D or 3D space, the formulas
are:
2
1
−α(ωk )|r0 −ri | −β(ωk )|r0 −ri |
e
e
Sii (ωk ,r0 ) =
|r0 − ri |
2
1
−α(ωk )|r0 −ri | −β(ωk )|r0 −ri |
Sii (ωk ,r0 ) =
e
e
|r0 − ri |0.5
3D
(2.71)
2D
α(ω) is attenuation factor for path loss and β(ω) is phase constant for phase shift.
They are functions of dielectric properties of the medium considering also dielectric
losses (the same used in FDTD simulation algorithms) [35].
Since the filter weights are designed to have unit gain and linear phase response,
the following relationship is obtained.
I(ωk )
M
X
Sii (ωk ,r0 )ejωk bτi (r0 )/Ts cTs Wi∗ [k,r0 ] = e−jωk τ0
(2.72)
i=1
The linear phase term ejωk bτi (r0 )/Ts cTs represents the coarse time alignment, while
τ0 = (L − 1)Ts /2 is the average time delay introduced by the filters.
45
2 – UWB Imaging System
The above formula can be divided into two parts, one is V(ωk ,r0 ) which denotes
combination of pulse shape, propagation and coarse time alignment effects, the other
is W[k,r0 ] that is the vector of weights associated to each signal at a given frequency.
S̃ii (ωk ,r0 ) = Sii (ωk ,r0 )ejωk bτi (r0 )/Ts cTs
V(ωk ,r0 ) = I(ωk ){S̃ii (ωk ,r0 )}N
i=1
W[k,r0 ] = {[Wi [k,r0 ]}N
i=1
(2.73)
(2.74)
Formula (2.72) can be rewritten as:
WH [k,r0 ]V(ωk ,r0 ) = e−jωk τ0
(2.75)
Therefore, the weights calculated by this frequency-domain method can be expressed
as:
V(ωk ,r0 )ejωk τ0
W[k,r0 ] = H
(2.76)
V (ωk ,r0 )V(ωk ,r0 )
However, this result is prone to amplify noise because weights can become very
large when VH (r0 ,ωk )V(r0 ,ωk ) is small. This situation occurs, particularly at higher
frequencies and deeper locations, due to greater attenuation values for Sii (ωk ,r0 ).
This problem was studied and discussed in [37], a penalized least-squares approach
was applied. Basically, equation (2.75) is solved as:
W[k,r0 ] = arg min {|WH [k,r0 ]V(ωk ,r0 ) − e−jωk τ0 |2 +
W[k,r0 ]
(2.77)
ξWH [k,r0 ]Λ[k,r0 ]W[k,r0 ]}
Second term controls noise gain, where matrix Λ[k,r0 ] represents the penalty structure and ξ is positive parameter, it is used to scale the impact of penalty. Various
kind of matrix Λ[k,r0 ] can be chosen to perform this operation. As discussed in [37]
and verified in [35], in a comparison between identity matrix, diagonal matrix and
square diagonal matrix, the second one resulted to be the best choice for the case
in analysis. The calculated weights are:
Wi [k,r0 ] =
Vi (ωk ,r0 )ejωk τ0
,
P
|Vi (ωk ,r0 )|(ξ + N
j=1 |Vjj (ωk ,r0 )|)
Λii [k,r0 ] = |Vi [k,r0 ]|
(2.78)
Finally, FIR filter weights are computed by performing IFFT of Wi [k,r0 ] to
produce a set of vectors of size L.
For other skin artifact removal and beamforming algorithms, please refer to [35].
46
2.3 – Algorithm and implementation
2.3.3
Quality factors
To evaluate the results obtained during the simulation, it is not sufficient to observe
the reconstructed map. Quality factors are used for the evaluation of performance
in addition to the observation of the outcomes.
• SMR - Ratio between maximum value into the backscattered energy matrix in
case of tumor (recT ) and average inbreast energy points recT,ave . The formula
is:
max(recT )
(2.79)
SMR = 10 · log
recT,ave
The maximum energy value is supposed to be the tumor response. If this is
not true, this value become meaningless.
• SCR - The maximum value of backscattered energy in the tumor region (recT )
0
divided by the maximum value found elsewhere (recT ). The formula is:
SCR = 10 · log
max(recT )
0
recT
(2.80)
• MAXPOS - Maximum energy position in the map: if the maximum point is
near to theoretical, the beamformer has detected tumor.
For the definitions presented here, the tumor can be thought as detected if and only
if SMR and SCR are greater than 10 dB and 0 dB, respectively, as well an energy
peak appears at the correct tumor position.
47
Chapter 3
System setting and verification
The purpose in this chapter is to build the entire system using the models developed
in previous chapters, that is, the transmitter for pulse generation, the antennas for
transmitting and receiving signals, the 2D channel model represented by the breast
and the surrounding environment, the receiver, and the imaging unit(IU), and then
to analyze the system feasibility. In this chapter, all simulations are ideally performed by Matlab, in other words, the transmitters, receivers and antennas are
included in FDTD simulation. Therefore, the block scheme and design flow is illustrated in Figure 3.1.
CHANNEL MODEL
Figure 3.1.
IU
Block scheme of imaging system and design flow.
48
3.1 – System parameters
3.1
System parameters
Before performing any simulation, the system parameters should be defined. Firstly,
the parameters of the 2D numerical breast model are organized here: the effective
breast size is 158 mm×176 mm, the depth of the skin layer is 1.5 mm, the spatial
grid resolution is 0.5 mm, the FDTD time step is 0.834 ps, the sampling frequency
is around 1200 GHz. After that, the performance of the Convolution Perfect Match
Layer (CPML) is evaluated. Based on the defined breast model parameters, the
suitable setting for CPML can be found. A set of simulations have been performed
to choose the optimal CPML parameters for the specific 2D breast model, especially
the thickness of the CPML absorbing layer d [16]. To this end, a coefficient, error
relative to the reference solution, was computed as a function of time using [16]:
n
(i,j)|/|Eref,max (i,j)|
Rel.errorn (i,j) = |E n (i,j) − Eref
(3.1)
where E n (i,j) represents the time-dependent discrete electric field computed within
n
the working volume, Eref
(i,j) represents the same discrete electric field computed
by the reference problem, and Eref,max (i,j) represents the maximum value of the
electric field in the given reference probe point over the full time simulation.
The reflection error versus time for different dimension of CPML is illustrated
in Figure 3.2. It is possible to observe that d = 16 is a good choice to compromise
the performance and execution time (refer to [16] for more details).
Moreover, the effect of antenna and transceiver is also included in FDTD simulation, both of them are ideally modeled. Figure 3.3 presents the proposed FDTD
simulation environment, a conformal dipole antenna and transceiver array consisting
of 9 elements modeled as electric-current sources is located around the surface of
the breast, the distance between each antenna and skin is 2 mm. A 16-layer CPML
surrounds the breast model. A small square in the breast is a fake tumor, which
is inserted in the numerical model during the FDTD simulation. The tumor size
selection will be analyzed later.
As introduced in Chapter 2, SKAR calibration and MIST beamforming algorithm
are used to reconstruct a microwave scattering image of the interior of the breast.
First of all, since UWB pulses are applied, based on the Nyquist criterion, the
sampling frequency must be greater than two times signal frequency (10.6 GHz),
therefore, the sampling frequency of beamformer is set to be 50 GHz [33]. The
grid resolution of beamforming is 1 mm, which must be a multiple of FDTD spatial
resolution. Based on them, other design parameters for SKAR and MIST beamforing
are evaluated [35].
Furthermore, in order to process the reflected signals from FDTD simulation,
the signals are decimated from a sampling frequency of 1200 GHz to 50 GHz.
49
3 – System setting and verification
Relative error for different PML size
6 cell PML
10 cell PML
16 cell PML
20 cell PML
−3
10
−4
Relative error
10
−5
10
−6
10
−7
10
0
0.2
0.4
0.6
Time [s]
Figure 3.2.
0.8
1
−9
x 10
The reflection error versus time for different dimension of CPML [16].
Figure 3.3.
The breast model in FDTD simulation.
50
3.2 – Source pulses
3.2
Source pulses
In this section, the last important component for executing the imaging system
simulation, the exciting source, is introduced. As the characteristic of radar imaging
approach, the signal bandwidth related to the resolution and penetration depth. The
higher the signal frequency, the higher the radar profile resolution, but the more
attenuation displayed by the body tissues, impairing the capability of detecting a
deeper target. Consequently, penetration depth and spatial resolution need to be
properly balanced by the choice of the operating frequencies. This discussion is
important because different types of UWB signals generate different backscattered
responses and then it is possible to obtain imaging reconstructions with different
properties.
In UWB waveforms, impulsive type pulses typically have a wavelength less than
1 ns and a bandwidth greater than gigahertz. A brief discussion about three commonly used impulse types for breast cancer detection application is included here.
3.2.1
Modified Hermite Pulse (MHP)
The Modified Hermitian Pulse (MHP) are defined as [38]:
2 /4τ 2
hn (t) = kn e−t
he,n (t)
(3.2)
The value kn defines the energy of the signal, n defines the derivative order of the
polynomial, τ represents the width time of the pulse and the sequence is orthogonal.
The MHP has the following properties [38] [39]:
• The duration of the pulse is roughly the same for all values of n.
• The bandwidth of the pulse is approximately the same for all values of n.
• The pulses are mutually orthogonal.
• The pulses do not have a DC component equal to zero, and in fact the lowfrequency component is relatively significant.
• The number of steps for the coordinate zero is equal to n.
Figure 3.4 represents the first-order (n = 1) MHP signals in time domain and frequency domain, the pulse width τ is equal to 150 ps. The spectral analysis shows a
center frequency equal to 750MHz and a 3 dB bandwidth extends to 1.2 GHz. This
MHP pulse is a relative low frequency source, which can achieve high penetration
depth, but low range resolution.
51
3 – System setting and verification
Source Pulse
1
0.8
0.6
Amplitude [V]
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.5
1
1.5
2
2.5
Time [s]
−9
x 10
(a)
X: 7.501e+08
Y: 0
Frequency response
0
Normalized amplitude magnitude (dB)
−1
−2
X: 1.227e+09
Y: −3
−3
−4
−5
−6
−7
−8
−9
−10
0
0.5
1
1.5
Frequency (Hz)
2
2.5
3
9
x 10
(b)
Figure 3.4.
MHP used for simulations: a) time domain b) frequency domain [16].
52
3.2 – Source pulses
3.2.2
Modulated and Modified Hermite Pulse (MMHP)
The Modulated and Modified Hermite Pulses (MMHP) are another candidate model
for the UWB signals, which are used to investigate the effect of excitation pulses
on the microwave imaging qualities. It was designed in [30] in order to obtain high
resolution map using Time Reversal algorithm. As suggested by the name, they
are obtained by performing a modulation of MHP sequence. The obtained MMHP
pulses are expressed as,
√
pn (t) = 2hn cos(2πfc t + φr )
(3.3)
The modulation carrier is fc and φr is a phase term.
Authors in [30] have indicated that MMHP has more oscillations than MHP
with the same pulse width. Unlike MHP, MMHP has zero DC component, but, as
the same as MHP, both the duration and bandwidth remain the same for pulses of
different orders. Figure 3.5 displays the time domain and frequency domain of this
MMHP signals with τ = 40 ps, fc = 8 GHz, n = 8. Figure 3.5 (b) shows that more
spectral components go up to a maximum frequency of 18GHz.
A higher signal frequency of MMHP allows to obtain a higher spatial resolution
compared to the case MHP and a greater sensitivity is in the tumor masses of small
dimensions. However, due to the lower frequency of the main lobe respect to the
following differential gaussian pulse, an higher penetration depth but less resolution
is obtained, as possible to verify in [16].
3.2.3
Differential Gaussian pulse (DG)
Differential gaussian pulse is the most frequently used impulse type in literature for
UWB applications [40] [33]. It has a zero-crossing at its center point in time. This
pulse is obtained modulating the Gaussian Monocycle pulse and the equation is [16]:
t − t22
· e 4τ
(3.4)
τ
Figure 3.6 shows the time domain and frequency domain of this differential gaussian
pulse with a full width at half maximum τ = 110 ps, and the center frequency fc =
6 GHz, actually it has a significant energy between 1 and 11 GHz.
This DG pulse has indeed a high center frequency that allows a modest penetration capacity within the tissue and a good spatial resolution, and a deviation value
of high standard, which allows to reduce the sensitivity is to the clutter. Ultimately
should get a response such as to enable, the algorithm reconstruction, the creation
of a map with a good compromise between spatial resolution and contrast.
From [35] and [16], it is possible to conclude that differential gaussian pulse is
more suitable for the specific breast model. It works as the exciting source for the
following analysis.
yDG (t) = sin(2πfc t) ·
53
3 – System setting and verification
Source Pulse
1
0.8
0.6
Amplitude [V]
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.5
1
1.5
2
Time [s]
2.5
−9
x 10
(a)
Frequency response
X: 1.478e+09
Y: 0
0
Normalized amplitude magnitude (dB)
−1
−2
−3
X: 1.815e+10
Y: −4.163
−4
−5
−6
−7
−8
−9
−10
0
0.5
1
1.5
Frequency (Hz)
2
2.5
10
x 10
(b)
Figure 3.5.
MMHP used for simulations: a) time domain b) frequency domain.
54
3.2 – Source pulses
Source Pulse
1
0.8
0.6
0.4
Amplitude [V]
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.5
1
1.5
2
2.5
Time [s]
−9
x 10
(a)
Frequency response
0
X: 6e+09
Y: 0
Normalized amplitude magnitude (dB)
−1
−2
X: 7.7e+09
Y: −2.999
−3
−4
−5
−6
−7
−8
−9
−10
0
2
4
6
Frequency (Hz)
8
10
12
9
x 10
(b)
Figure 3.6.
DG used for simulations: a) time domain b) frequency domain.
55
3 – System setting and verification
3.3
System with homogeneous breast
Now, with above defined system parameter, firstly, the system performance with
homogeneous breast is evaluated, which means the dielectric properties of the breast
tissue is constant. The functionality of the beamforming algorithm can be verified.
The influence of different tumor sizes and tumor positions on the system performance
are analyzed.
Before any simulation, an important coefficient should be defined, the propagation speed, which is highly related to determining tumor position. Due to the
position of the dielectric discontinuity is expressed by the time delay in the obtained
backscattered waveforms. The distance is then computed using the equation, distance=time × velocity, where the time is the pulse round trip time, and the velocity
can be calculated based on the Debye parameters in Chapter 2 by the following
equaiton:
p
(3.5)
vp = c · / Re(εr )
Where c is the light speed in free space, 3 · 108 m/s, and εr is frequency dependent.
The plot of the calculated propagation speed versus frequency is shown in Figure 3.7.
The propagation speed is 0.95 · 108 m/s at 6 GHz frequency, which is the central
frequency of the applied differential gaussian pulse.
Figure 3.7.
Propagation speed as function of frequency in case of homogeneous breast.
56
3.3 – System with homogeneous breast
3.3.1
Tumor size
The size of the modeled tumor is determined by various factors and has to be
carefully chosen. First of all, given that the microwave imaging technique is proposed
as a complementary approach to mammography to be used in screening campaigns,
an early-stage detection is the target. The size of an early-stage tumor can be defined
by reference to the current practice in mammography. Mammography for breast
cancer, whose sensitivity depends a lot on the density of the breast tissue, can find
tumors with the median size 1 cm to 1.5 cm effectively. Furthermore, studies have
shown that 5 mm tumors were found approximately 40% of the time, and the median
size at which breast cancers become operationally detectable by mammography is
approximately 7 mm [41]. Based on these facts, the upper limit for early-stage
detection can be set to around 5 mm and the target for an UWB microwave system
to less than 5 mm.
The system performance for tumor sizes of 1 mm, 2 mm, 3 mm and 4 mm due
to the homogeneous breast model is evaluated. To better understand the system
performance influenced by tumor size, the tumors are placed in the middle of the
breast model, at depth of 88 mm. The exciting source is differential gaussian pulse
(Figure 3.6). The normalized tumor response is shown in the Table 3.1, which is
defined as the peak-to-peak amplitude of the tumor backscattered response divided
by the peak-to-peak amplitude of the illuminating pulse. The reflected pulses are
shown in Figure 3.8 at antenna 5, it is possible to see that the skin reflections are
the same for different tumor size conditions, the tumor information appear within
the time intervals 1.5 ns to 2.5 ns, which are zoomed in each figures.
The biggest response is acquired with 4 mm tumor and the smallest with 1 mm
tumor. Consequently, the image qualities with 4 mm tumor embedded after reconstruction algorithm should be the best.
Tumor diameter (mm)
1
2
3
4
Table 3.1.
Tumor response (dB)
-95.2
-83.4
-79.3
-79.0
Normalized tumor response with respect to different tumor size.
Before shown the reconstructed energy maps, the pulses after SKAR calibration
are presented in Figure 3.9.
The energy maps are demonstrated by Figure 3.10, which are reconstructed by
MIST beamforming algorithm. Combining with Table 3.2 which gives the simulated
system performance under the ideal analysis condition as a function of the tumor’s
57
3 – System setting and verification
FDTD simulation: Reflected pulse
0.3
1mm tumor size
0.2
0.2
0.1
0.1
Electric field (V/m)
Electric field (V/m)
0.3
0
−5
3 x 10
−0.1
1
−0.2
0
2mm tumor size
0
−5
10 x 10
−0.1
2mm tumor size
5
−0.2
0
−1
−0.3
−0.4
0
1mm tumor size
2
FDTD simulation: Reflected pulse
−0.3
−2
1.8
1
2
2.2
2
Time (s)
3
2.4
−9
x 10
−5
1.8
−0.4
0
4
−9
1
FDTD simulation: Reflected pulse
0.3
3mm tumor size
0.2
0.2
0.1
0.1
0
−4
1.5 x 10
−0.1
0.5
0
−0.5
−0.3
−0.4
0
3mm tumor size
1
−0.2
1
4
−9
x 10
FDTD simulation: Reflected pulse
4mm tumor size
0
−4
1.5 x 10
−0.1
1.8
2
Time (s)
2
2.2
0.5
−0.2
0
−0.5
−1
2.4
−9
x 10
3
4
−9
x 10
(c)
−0.4
0
4mm tumor size
1
−0.3
−1
3
2.4
−9
x 10
(b)
Electric field (V/m)
Electric field (V/m)
0.3
2.2
2
Time (s)
x 10
(a)
2
1
1.8
2
Time (s)
2
2.2
3
2.4
−9
x 10
4
−9
x 10
(d)
Figure 3.8. Backscattered responses with different tumor size at central position
of the breast model, (a) 1 mm (b) 2 mm (c) 3 mm (d) 4 mm.
58
3.3 – System with homogeneous breast
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 3.9. Calibration results with DG pulse, 4 mm tumor and middle tumor
position, homogeneous breast, the red lines are cases with tumor, the blue lines
are cases without tumor.
59
3 – System setting and verification
size, it is possible to see that the applied MIST beamforming algorithm is not able
to detect tumor with 1 mm size inside this specific breast model, and it shows much
better results with 4 mm tumor inserted. Therefore, 4 mm is chosen as the designed
tumor size, since the influence of the hardware implementations and heterogeneous
breast model for the following verifications should be taken into account.
(a)
(b)
(c)
(d)
Figure 3.10. Reconstruction results with MIST beamforming algorithm,
with different tumor size at central position of the breast model, (a) 1 mm
(b) 2 mm (c) 3 mm (d) 4 mm.
3.3.2
Tumor position
The tumor position influence on system performance with 4 mm tumor size are
evaluated, not only from reflection pulses point of view, but also from imaging
quality point of view. Three different tumor positions are chosen, namely, near,
60
3.3 – System with homogeneous breast
Tumor size (mm)
1
2
3
4
Table 3.2.
SMR (dB)
13.2
15.7
17.6
17.5
SCR (dB) Max. Pos (mm, mm)
-6.3
(153,39)
4.2
(89,88)
7.2
(88,88)
7.8
(89,88)
System performance (SMR, SCR) as a function of the tumor’s size.
middle and deep. The tumor central positions are (88 mm, 44 mm), (88 mm, 88 mm)
and (88 mm, 131 mm) respectively, as displayed in Figure 3.11.
(88, 131)
deep
(88, 88)
middle
(88, 44)
near
Figure 3.11.
The homogeneous breast model with three tested tumor positions.
Figure 3.12 shows the backscattered responses for different tumor positions. In
order to observe and compare tumor information parts easily, the skin artifact parts
from the actual reflected waves are subtracted. The tumor information are clearly
separated in time. The amplitude of the response from deep position tumor is small
due to more tissue attenuation during wave propagation.
The quantitative values of SMR and SCR after beamforming for different tumor
positions are tabulated in Table 3.3 and energy maps are graphed in Figure 3.13.
The first column in Table 3.3 is the real tumor position, and the fourth column is
the simulated maximum energy point, which represents examined tumor position.
The skin artifact removal and imaging reconstruction algorithm are working well,
61
3 – System setting and verification
−3
1
x 10
Reflected pulses with different tumor positions
Near Pos
Middle Pos
Deep Pos
Amplitude (V)
0.5
0
−0.5
−1
−1.5
0
1
2
Time (s)
3
4
−9
x 10
Figure 3.12. Comparison of the backscattered responses for the different
positions of the tumor mass.
as the tumors corresponding to the energy peaks are clearly identified. Moreover,
as seen from Figure 3.13 (a), more clutters near tumor appear, the skin contributes
more distortion. SMR value for the deep tumor condition is quite small, but the
energy peak still can be recognized in Figure 3.13 (c). The reason is that the
amplitude of tumor reflection is smaller with larger attenuation and the distortion
from breast wall.
Tumor Pos. (mm, mm) SMR (dB)
near (88,44)
15.2
middle (88,88)
17.5
deep (88, 131)
12.0
Table 3.3.
SCR (dB) Max. Pos. (mm, mm)
2.6
(88,46)
7.8
(89,88)
1.9
(89, 131)
system performance (SMR, SCR) as a function of the tumor’s position.
62
3.3 – System with homogeneous breast
(a)
(b)
(c)
Figure 3.13. Reconstruction results with MIST beamforming algorithm, with
different tumor position, (a) near (b) middle (c) deep.
63
3 – System setting and verification
3.4
System with heterogeneous breast
At last, the ideal homogeneous breast model is replaced by the real heterogeneous
model. This type of simulation uses signals obtained by real breast phantom FDTD
simulation. The pulse in an heterogeneous breast propagates in different ways depending on the tissue that are going through.
The middle position tumor with 4 mm size is inserted. First of all, the heterogeneous breast is shown again in Figure 3.14. It is possible to observe that there
are many glandular tissues around tumor, which have high dielectric properties and
may add noise. Moreover, each dielectric discontinuity generates a reflection that
adds to clutter response.
In this heterogeneous condition, as each kind of tissue has unique εr value, we
use average propagation speed to approximate the wave propagation behavior in the
breast. The average propagation speed was computed using the average dielectric
constant of the breast tissues [35]. The average propagation speed is 0.86 · 108 m/s
at 6 GHz central frequency of the applied differential gaussian pulse.
Figure 3.14. The simulated heterogeneous breast model, 4 mm tumor is
inserted in the middle position.
Figure 3.15 displays the backscattered response from antenna 5 with heterogenous breast, as well as the pulse from the same antenna with homogeneous breast
model. The exciting sources are differential gaussian pulse in Figure 3.6. They are
different even at skin reflection part and in the enlarged late time part. The tumor
64
3.4 – System with heterogeneous breast
information is not as clear as homogeneous one because of clutter responses. Figure 3.16 shows the reconstructed results with MIST beamforming algorithm. Even
though the clutters are quite clear, the tumor can be detected. The calculated SMR
is 12.7 dB, SCR is 1.2 dB.
0.3
Reflected pulses with different breast model
Homo breast
Hetero breast
0.2
Amplitude (V)
0.1
0
−3
1.5 x 10
−0.1
1
−0.2
0.5
−0.3
0
−0.5
−0.4
−0.5
0
Figure 3.15.
Homo breast
Hetero breast
−1
1
1.5
2
2
Time (s)
2.5
3
3
3.5
−9
x 10
4
−9
x 10
Backscattered responses with different kind of breast model.
All above illustrated simulations have proved the functionality of the proposed
UWB radar imaging system for breast cancer detection. The more detailed explanations of the results were shown in [16][35].
65
3 – System setting and verification
Figure 3.16. Reconstruction results with MIST beamforming algorithm, with
heterogeneous breast model, the tumor position is middle and size is 4 mm.
66
Chapter 4
Receiver comparison
4.1
Motivation
In the previous chapters, the front-end block influence is ignored, it is ideally modeled as a point in FDTD simulation. In this chapter, the discuss will be focused on
the front-end block. The system design flow is shown in Figure 4.1, all the components, the transmitter, antenna and receiver are presented. The goal is to define
a system-level and architectural solution suitable for the diagnosis application. It
is achieved by first proposing a suitable receiver structure, then modeling it and
inserting it into the system to evaluate its performance in terms of the system-level
performance.
TX
ANT.
CHANNEL MODEL
ANT.
RX
IU
Figure 4.1. UWB imaging system design flow. Transmitted signals hit the breast
and the echoes are acquired with receivers. An imaging unit processes the data and
produces a map of reflected energy.
Microwaves may be transmitted as continuous waves, in impulses, by stepped
frequencies, pure oscillating sinusoids or as a combination of these methods. Hence,
depending on the operating principle, two common radar approaches, impulse radar
and Stepped Frequency Continuous Wave (SFCW) radar, are explored. Impulse
67
4 – Receiver comparison
radar is a time domain operation, which transmits a single narrow pulse (less than
a few nano-seconds), associated with a wide spectrum of signals [42][43]. The time
delayed received waveform is then sampled, which, in general, imposes severe constrains on the Analog-to-Digital conversion process. On the other hand, SFCW
radar is a frequency domain method, whose waveform is implemented by transmitting a series of single frequency tones separated by a fixed frequency value ∆f .
At each frequency the amplitude and phase of the received signal is sampled and
recorded. Therefore, compared to impulse approach, the SFCW approach requires
additional time to transmit and receive N pulses needed to obtain the equivalent
wide bandwidth of a single narrow pulse. An additional Inverse Fast Fourier Transform (IFFT) has to be applied to transform the received signals into the time domain
synthesizd pulse [44]. The SFCW approach can achieve fine range resolution while
maintaining a narrow instantaneous bandwidth which alleviates the ADC requirements. In this chapter, both of them are applied and compared. While accurate
electromagnetic simulations and experiments carried out using bulky and expensive
RF measurement tools (e.g. vector network analyzers and the like) have proved
the validity of the microwave breast cancer detection system, if this method should
become suitable for mass screening programs, RF instruments have to be replaced
with low-cost and ad-hoc CMOS circuits that integrate the main functionalities in
a small chip.
In this thesis, the RF receiver part is described with particular detail because
it is the most critical building block. The receiver function is acquire the reflected
signals, convert them to digital codes and to send them to the processor. Therefore,
the receiver requirements are very strict in this specific application. One of the
design challenges that have to be faced is the large dynamics of the received signal,
whose maximum amplitude is determined by a large skin reflection. The tumor
backscatter is instead a small amplitude signal, which emerges from the background
due to the dielectric contrast, but with a magnitude that can be 70 dB smaller than
skin reflection. This can be seen in the FDTD simulation results in Chapter 3.
On the other hand, high sampling frequency is another design challenge, as the
bandwidth of the excited source is as high as 10 GHz in our application, based on
Nyquist criterion, the sampling frequency is at least two times the signal frequency,
so at least 20 GHz is needed. Therefore, high resolution and high sampling frequency
requirement significantly tightens the ADC design constraints.
Since two radar approaches are considered, there are two candidates for the
implementation of integrated receiver. One is the direct conversion (DC) receiver,
the most popular architecture in narrowband system [45], which has been proposed
in this application with SFCW radar approach [46][47]. The other is the UWB
receiver based on Coherent Equivalent Time Sampling (CETS) method [48][49].
Both can handle time domain UWB signals and frequency-stepped continuous waves,
which is proposed here for the first time in this context.
68
4.2 – Two different receiver architectures
The contributions of this chapter are the following:
1) models of receivers are built behaviorally, by using formulas to represent all their
signal processing functions (such as voltage gain, mixing, sampling, etc.) as well
as the related non-idealities considered (such as nonlinearity, noise, quantization
noise, phase inaccuracy, jitter, etc.). The effect of various circuit impairments is
understood and demonstrated with the help of evaluating the performance of the
receiver within the breast cancer detection system. Moreover, the performance of
DC receiver and CETS receiver with different radar approaches are compared for the
first time. The qualities of receivers are ultimately judged with respect to systemlevel parameters Signal-to-Mean Ratio (SMR) and Signal-to-Clutter Ratio (SCR),
as well as energy maps.
2) The fact that the DC receiver is very sensitive to I/Q phase mismatch and phase
noise from local oscillator is shown, hence confirming the results reported in [46]
under different simulation conditions. Instead, the CETS receiver is more robust to
its non-idealities, primarily jitter of the Phase-locked-loops clock and thermal noise,
both in case of the time domain single UWB pulse or SFCW sinusoidal signal series.
3) The possibility of saving acquisition time and obtaining even more accuracy with
CETS receiver using the time domain radar approach is shown.
4.2
Two different receiver architectures
The main aim here is to develop simple and accurate analytic models of the two
receiver candidates with relevant circuit non-idealities. Next, based on these models,
the system-level analysis of the entire microwave breast cancer detection system will
be performed to explore the receiver design tradeoffs.
4.2.1
Direct Conversion receiver
Figure 4.2 shows the general structure of a RF frontend direct conversion (DC)
receiver, in which only one down-conversion component mixer is used to obtain
zero-IF signals [45]. As mentioned before, monostatic radar method is applied, only
one antenna need be used, the UWB circulator alternately switches the antenna
between transmitter and receiver and provides isolation between them.
The basic work flow of the DC receiver is the following: the received RF signal
after antenna and circulator is amplified by the low-noise-amplifier (LNA); the amplified RF signal is mixed with in-phase and quadrature local oscillator (LO) signals
which are set to be the same frequency of the transmitted RF signal; consequently,
the output signals after the mixers contain the desired baseband signal and an undesired signal at twice the RF signal frequency which will be removed by the following
low-pass-filters (LPFs); finally the Analog-to-Digital converters (ADCs) are used to
69
4 – Receiver comparison
Figure 4.2.
Block diagrams of Direct Conversion (DC) receiver.
quantize the analog complex baseband signal.
In order to make the receiver more realistic, our focus is not only on the functionality implementation of receiver, but also on the modeling techniques of various
impairments. The main specific attributes of LNA are conversion gain, thermal
noise and nonlinearity. Besides the mixer gain, nonlinearity and thermal noise,
the quadrature mixer mainly contributes to the critical In-phase/Quadrature mismatches. Phase noise is the most important impairment in the local oscillator. The
main architecture specific non-idealities of ADC are quantization noise and nonlinearity. The behavioral model of DC receiver is shown in Figure 4.3, complex
baseband equivalent models are used. The main source of noise is the thermal noise
which is specified by the cascaded overall noise figure (NF) while the distortions are
expressed by overall saturation and nonlinearity.
Figure 4.3.
Direct Conversion (DC) receiver behavioral model.
The non-ideal antenna is modeled as a 2-port network, with s-parameters as a
function of frequency [50], with the insertion loss at transmitting mode and receiving
mode, (S21 ant (ω)). Non-ideal circulator influences are modeled with insertion loss
from transmitter to antenna, (S21 cc (ω)), the attenuation to the signal as it travels from antenna to receiver, (S32 cc (ω)), and the transmitter-to-receiver coupling,
70
4.2 – Two different receiver architectures
(S31 cc (ω)), respectively. The received signal Sin rf,i after antenna and circulator can
be expressed as:
Sin rf,i = AT X |T Fall (ωi )|cos ωi t + 6 T Fall (ωi )
(4.1)
+ AT X |S31 cc (ωi )|cos ωi t + 6 S31 cc (ωi ) .
where supposing that the transmitted signal is a single tone sinusoidal wave with
frequency fi , as required by the SFCW radar approach, AT X is the signal amplitude at the transmitter. T Fall (ω) = S21 cc (ω)S21 ant (ω)S21 ant (ω)S32 cc (ω)T F (ω).
T F (ω) = |T F (ω)|exp(j 6 T F (ω)) is the transfer function of our channel model breast
which includes both antenna-skin-antenna path and antenna-tumor-antenna path.
After the multiplication with the positive complex LO frequency ejωi t and passing
through the low pass filters hlpf (t), the real signal Sin rf,i is transferred into the ideal
baseband complex signals, which is given by the following mathematic expression.
Sin bb,i = AT X |T Fall (ωi )|ej
6 T Fall (ωi )
+ AT X |S31 circ (ωi )|ej
6 S31
circ (ωi )
.
(4.2)
Unfortunately, the down-conversion part (mixers and LO block) includes two
impairments, phase noise that comes from LO circuit and I/Q phase mismatch
that comes from the In-phase and Quadrature channels phase imbalance. As the
tumor position information is included in the time delay of the echoed signals, phase
inaccuracies are more critical in this application. A simple model can be realized by
changing the ideal LO complex signal expression ejωi t into,
φDM
+ ∆φ)
2
φDM
+ ∆φ).
−
2
LOi = cos(ωi t + φCM +
+ jsin(ωi t + φCM
(4.3)
where φCM , common-mode error, represents the phase mismatch between the received RF signals and LO signals, φDM , differential-mode error, represents the phase
mismatch between the In-phase and Quadrature components of the LO, both of them
are systematic errors and frequency dependent, and are modeled as Gaussian ran2
dom variables with zero mean and variance σpm
. ∆φ represents the phase noise, it
is a random error, and we model it as Gaussian stochastic process with zero mean
2
and variance σpn
.
Consequently, the distorted complex baseband signal Sbb φ,i can be expressed as
Sbb φ,i = Sin bb,i e−j(φCM +∆φ) cos(
φDM
).
2
(4.4)
The overall receiver nonlinearity can be modeled straightforwardly using the
power series equation [51]. Therefore the baseband equivalent nonlinearity model
71
4 – Receiver comparison
can be expressed as,
Ybb φ,i = G1 · Sbb φ,i + G2 · |Sbb φ,i |2 (1 + j)
+ G3 · |Sbb φ,i |3 ej
6 Sbb
φ,i
.
(4.5)
where the higher order terms above third order are usually not taken into account.
G1 is the linear conversion gain, G2 and G3 are the coefficients of the second-order
and third-order nonlinearity specified by IIP2 and IIP3 [51], respectively. In case of
0
high input power, a simple saturation is applied, the signal after that will be Ybb φ,i .
Then, the thermal white noise source no,eq is added, which is modeled as additive
white gaussian noise (AWGN), with the equivalent output noise power given by,
Pnoise = KT B · F · G12 .
(4.6)
where K is Boltzmann’s constant, T is temperature, B is the noise bandwidth after
low pass filter and F is the overall noise factor.
Finally, the analog signal is converted to digital code by ADC. There are two
steps, first, the signal will come through the nonlinearity distortion part of ADC
whose contribution is reflected by integral nonlinearity (INL) rather than IIP2 and
IIP3. The non-uniform quantization level is modeled like [52]. Then, ideal quantization, which includes inherent quantization noise is applied. The final data before
signal processing is expressed as,
0
YQ i = [Ybb φ,i + no,eq ]q .
(4.7)
[·]q means quantization.
The flicker noise and DC offset are not modeled, as presented in [47], the autozeroing and chopper stabilization techniques are applied to ignore their influences.
4.2.2
CETS receiver
In this breast cancer detection field, tumor information is much weaker than skin
artifact due to the radial spreading of the pulse energy, the path loss and the lossy
breast tissue, therefore, it is important to use a high dynamic range receiver to
capture the variation in the received analog signals. However the high Nyquist
sampling frequency leads to severe constraints in the implementation of ADC.
The proposed CETS receiver is based on the Coherent Equivalent-Time Sampling
technique, the work principle is that N samples are taken out of M identical pulses.
The properties of the CETS receiver can be summarized as follows:
• The input pulses are periodic
72
4.2 – Two different receiver architectures
• The equivalent sampling frequency is much greater than Nyquist frequency
based on the N and M choice
• The digital backend is necessary to sort the sampled signals
• Average technique is used to reduce the random noise effect
Therefore, compared to conventional Nyquist sampling technique, CETS method
can alleviate the sampling frequency requirements for ADC by sampling the periodic
signal at a much lower frequency [48][49][53].
In this case the normal acquisition of a single pulse is achieved by gathering
samples from different received pulses. Assuming each pulse is repeated M times
every Tpulse time units, the overall acquisition time equals to M Tpulse , N samples
are taken out of these M identical pulses, this causes the pulses to be sampled at a
real-time sampling frequency of
fs = (M Tpulse /N )−1
(4.8)
the corresponding equivalent sampling frequency is
feq = (Tpulse /N )−1
(4.9)
which can be much higher than Nyquist sampling. The technique can severely relaxes the trade-off between the sampling rate and quantization resolution by choosing appropriate M and N values.
Figure 4.4 shows an example of CETS technique, the pulse is repeated 10 times,
and 27 samples are acquired. After sorting there are 27 samples in one single pulse,
the equivalent sampling frequency is therefore 27 times larger than the pulse frequency and the real sampling frequency is only 2.7 times the pulse frequency which
simplifies the circuit design of the ADC.
Figure 4.5 depicts the architecture of the CETS receiver. The received signal
as the one in DC receiver is amplified by LNA and then directly sampled by track
and hold amplifier at a relatively low sampling frequency, and quantized by ADC.
A time to digital converter measures the time offset between transmitted clock and
sampling clock. The sampling clock is synthesized by a phase-locked loop (PLL)
and locked to the pulse repetition clock of the transmitter with the correct M/N
ratio. The N samples are not acquired in order and therefore the digital back-end
sorts them. The receiver can acquire the same signal multiple times (K) and average
them to reduce the effect of random noise.
Let us focus on the block diagram of Figure 4.6 representing the behavioral
model of the CETS receiver. Similarly to the DC receiver, the model includes
the main ideal receiver functionality as well as the following imperfections: thermal
noise and distortions generated in the very front-end components, ADC quantization
73
4 – Receiver comparison
1 st pulse
2 nd
3
1
23
6
4
2
9 th
...
25
10 th
27
24
5
26
26
18
7
10
15
23
1 20
12 4
16
T equiv
8 27 19 11 3 22 14 6 25 17 9
2
24
T sample
21
5
13
T pulse
Figure 4.4. Example of Coherent Equivalent-Time Sampling. Twenty-seven samples of the pulse are acquired in ten repetition periods (27 and 10 are relatively
prime). Samples are not acquired in order and need to be sorted.
Figure 4.5.
Block diagrams of Coherent Equivalent Time Sampling (CETS) receiver.
74
4.2 – Two different receiver architectures
noise and INL. Besides these parameters, the architecture unavoidable impairment
random timing jitter produced in PLL has also been involved, which is an undesired
perturbation or uncertainty in the timing of events.
Figure 4.6.
CETS receiver behavioral model.
Since the periodic signal can be both a tone and a periodically repeated UWB
pulse (e.g. generated by an UWB transmitter like in [28]), the CETS receiver can
work both in SFCW mode and in time-domain. In the first case, amplitude and
phase of the received signal are computed by the digital back-end. To permit an
easier comparison with the DC receiver, we report the model equations with sinusoidal signals.
The incoming time domain RF signal Sin rf,i is directly sampled by THA which is
modeled as an ideal switch controlled by the sampling clock from PLL. Considering
the presence of Root Mean Square (RMS) timing jitter, the rising or falling edge of
the sampling clock is deviated with a time deviation j from its ideal position. The
noisy sampled signal can be written as,
Sin (tjit,i ) = Sin rf,i (tjit,i )
(4.10)
where tjit,i (m) = mTs +ji (m), tjit,i is the real sampling clock with jitter influence,
Ts is the real sampling period, m is the mth sample, ji (m) is the mth jitter value for
the ith signal, which is modeled as gaussian random variable with zero mean and
2
variance σjit
.
Meanwhile, linear conversion gain and AM-AM nonlinearity are modeled using
the power series equation.
Yin (tjit,i ) = G1 · Sin (tjit,i ) + G2 · (Sin (tjit,i ))2
+ G3 · (Sin (tjit,i ))3
(4.11)
Before converting the signal from ADC, thermal noise is added, whose equivalent
power is proportional to the signal bandwidth and the overall cascaded noise factor.
Since there are not filters in this receiver, the multi GHz signal bandwidth makes
thermal noise quite huge in contrast to the case in DC receiver whose noise is filtered
75
4 – Receiver comparison
by LPF. Hence, averaging technique is usually applied to alleviate the influence of
random noises, like thermal noise and jitter.
0
YQ [K] = [Yin (tjit,i ) + no,eq ]q .
(4.12)
The digital signal YQ is therefore the input data of the following digital processing.
In addition, the CETS receiver is insensitive to DC offset and flicker noise, because
it works at high frequency.
4.3
Methodology and simulation setting
In this chapter the performance of three different system combinations are evaluated,
namely DC receiver working with SFCW radar approach, CETS receiver working
with SFCW approach and CETS receiver working with impulse time domain radar
approach.
Two dimensional electromagnetic breast model is used as the channel model in
the system simulations that includes the influence of dispersion and attenuation,
as described in previous chapters. A 4-mm diameter tumor with high dielectric
properties is inserted in the breast model [54] [4].
For the impulse radar approach the transmitted signals are short UWB pulses.
The pulse characteristics must be chosen accordingly to the range resolution and
penetration depth, the differential gaussian pulse with a central frequency of about
6 GHz and full width at half maximum equal to 110 ps is used as in [40] [33]. Since
the pulse has a significant energy in a 10 GHz bandwidth, the complete system
should be able to process an operational bandwidth from 1 GHz to 11 GHz. Use
of the SFCW technology results in a system transmitting a single sinusoidal tone
starting from 1GHz and stoping at 11GHz, with a fixed frequency step 125 MHz.
Consequently, 81 tones are required to cover the equivalent wide bandwidth of a
single narrow pulse.
Below these radar specifications are translated into radar functional requirements, range resolution Sr and unambiguous range Runabm [44].
Sr =
υ
,
2B
Runabm =
υ
2∆f
(4.13)
where υ is the wave speed in the medium, B is the bandwidth (10 GHz in our case),
and ∆f is the frequency step (125 MHz). The average propagation velocity is less
than 108 cm/s, which results in Sr and Runabm about 4.7 mm and 40 cm respectively.
These values are sufficient to detect the 4 mm-diameter tumor.
Receiver model equations, electromagnetic breast model, and beamforming algorithm are implemented in Matlab. In order to make these three scenarios more
comparable, most of the receivers parameters are set equal in all configurations. The
76
4.3 – Methodology and simulation setting
Param.
DC
CETS–Freq.
Power supply (V)
1.2
1.2
signal BW (GHz)
1-11
1-11
total gain (dB)
40
40
noise figure (dB)
10
10
IIP2 (dBm)
20
20
1dB compression point (dBm)
-30
-30
antenna S11 (dB)
-10
-10
circulator S21/S32 (dB)
-5
-5
circulator S31 (dB)
-18
-18
INL (LSB)
2
2
noise BW (Hz)
100K
10G
TX power (dBm)
-50 to -18
-50 to -14
ADC bits
11 to 17
7 to 12
phase noise (deg)
0 to 0.21
NA
phase mismatch (deg)
0 to 6
NA
RMS jitter (ps)
NA
0 to 6
K (iterations)
1 or 100
1 or 100
Table 4.1.
CETS–Time
1.2
1-11
40
10
20
-30
-10
-5
-18
2
10G
-50 to -2
7 to 12
NA
NA
0 to 6
1 or 100
Parameters used in simulation.
high conversion gain is required to amplify the input signals, especially the weak
tumor information, but it can not be too high to avoid ADC saturation which will
cause distortion, especially the strong skin reflection. According to [46], 40dB gain
and 10dB noise figure for two receivers are chosen. The 1-dB compression point is
set to -30dBm which indicates around -20dBm IIP3 value. The in-band return loss
S11 of UWB antenna is set to be -10dB [55], transmitter-to-receiver isolation and
the insertion loss of circulator are set to -18dB and -5dB respectively [56].
The number of bits (NoB) of the ADC, must be chosen accordingly to two
opposite requirements: on the one hand it’s better to keep it as low as possible
for cost and power consumption reasons, on the other hand, the high resolution is
needed to have less quantization noise and to improve receiver accuracy. Therefore,
due to the different sampling frequency, the ADC resolution of DC receiver is swept
from 11bit to 17bit, but only 8bit to 12bit for CETS receiver. The maximum INL
value is set to be 2 times the Least Significant Bit (LSB) value [57][58]. Furthermore,
the standard deviation of the phase mismatch, phase noise and rms jitter are swept
from 0 to 6 degree, 0 to 0.2 degree, and 0 to 6ps respectively.
These parameters are summarized in Table 4.1. The strategy is to fix the values of
each common parameters and to choose the appropriate values for other parameters
77
4 – Receiver comparison
by sweeping the values of each individual non-ideality considered as an independent
and additive noise source.
The effects of the impairments on the receiver performance are characterized in
terms of the overall detection system performance, in other words, imaging quality
which is specified by visual inspection of the energy maps reconstructed by imaging algorithm [59][33] and SMR/SCR. As defined in Chapter 2, the tumor can be
detected if and only if SMR and SCR are greater than 10 dB and 0 dB, an energy
peak appears at the correct tumor position. The coming reported SMR/SCR results
for each scenarios with random non-idealities are the average from at least 20 times
repeated Matlab simulations.
Before any evaluation, the system feasibility is verified. If the effect of all the
impairments in Table 4.1 is not considered—i.e. all noise sources, mismatches, nonlinearity, and quantization are removed—a system with ideal receiver is obtained.
However the 40 dB gain may cause ADC saturation of the skin reflection part in
the received signal, this saturation is unavoidable. Without loss of generality, we
consider tumors with in three different locations, at (7.0 cm,5.2 cm), (8.8 cm,8.8 cm)
and (11.7 cm,12.6 cm), corresponding to a position close to the skin, in the middle of
the breast and deep in the breast. It is possible to verify that in this ideal case these
three scenarios yield the same results. The values of SMR and SCR are tabulated in
Table 4.2, and energy maps are graphed in Figure 4.7. The built system works well
as the tumors corresponding to the energy peaks (enclosed by a circle) are clearly
identified. Moreover, as seen from Figure 4.7 (a), more clutters near tumor appear,
due to the skin distortion. SMR value for the deep tumor condition is quite small,
but the energy peak still can be recognized in Figure 4.7 (c), the reason is that the
amplitude of tumor reflection is smaller with larger attenuation, and the distortion
from breast wall. In theory, receiver parameters do not depend on tumor position
as the tumor information happens at different time delay.
Tumor Pos.
(7.0 cm, 5.2 cm)
(8.8 cm, 8.8 cm)
(11.7 cm, 12.7 cm)
Table 4.2.
SMR(dB) SCR(dB) Max. Energy Pos.
15.8
2.3
(7.0 cm, 5.1 cm)
16.5
7.0
(8.8 cm, 8.8 cm)
11.6
2.6
(11.7 cm, 12.8 cm)
SMR and SCR in the ideal case with different position.
Since the focus in this chapter is to compare different receivers, to better assess
the influence, the middle position tumor is used in the following simulations. Results
reported in the next section, where all the impairments are considered, can be
compared to the ideal case to evaluate the performance degradation.
78
4.3 – Methodology and simulation setting
(a) tumor near skin
(b) tumor in the middle
(c) tumor in the deep
Figure 4.7. Energy maps of the breast with the ideal receiver for different tumor
positions. Map (a) is for tumor placed near skin, (b) for tumor placed in the middle
of breast, (c) for tumor placed deep in breast.
79
4 – Receiver comparison
4.4
Simulation results
In order to choose the suitable values for the parameters of each receiver and thereby
compare the performance of three scenarios, the effectiveness of these main impairments on the receiver performance are demonstrated in this section. They are
evaluated in terms of system-level parameters such as SMR and SCR.
4.4.1
DC receiver with SFCW approach
The most critical impairments for DC receiver are ADC resolution, phase noise and
phase mismatch. Their influences are presented one by one.
ADC
As highlighted in the previous section, ADC has two main limitations, ADC resolution and nonlinearity. We set all the fixed parameters in Table 4.1 to the nominal
value. In this evaluation, all the non-idealities are not considered, except ADC
and saturation. Figure 4.8(a) shows the evaluation of system performance at different transmitted power with different ADC resolution, which changes from 11 to
17bit. Considering the region of low resolution, the SMR and SCR values increase
with transmitted power. Considering instead the region at low power, the impact of
quantization noise is evident as SMR/SCR values improve obviously when ADC resolution increases. The curves indicate that the performance benefit of using higher
ADC resolution is negligible when ADC bits is bigger than 15-bit.
Figure 4.8(b) and (c) depict the overall performance with additional ADC nonlinearity INL. Compared to Figure 4.8(a) and (c), the values in Figure 4.8(b) and
(d) have at least 1dB and 2dB decrease respectively, moreover, ADC nonlinearity
has stronger influence at low power and low resolution. However, the selected 15-bit
ADC reaches the optimum performance for transmitted power between -35dBm and
-20dBm. Consequently, this power range and a 15-bit ADC is used for the following
analyses.
Phase Noise
In this analysis we evaluate the effect of transmitted power and phase noise variance
2
σpn
. Simulations are run for values of σpn between 0 and 0.210 . Results are obtained
using ADC quantization of 15bit with all other impairments set to their nominal
value as in Table 4.1, like thermal noise, nonlinearity and saturation, while, phase
mismatch is not considered yet.
Figure 4.9(a) shows the results when K is set to 1 (no iterations). SMR and
SCR are sensitive to the variance of phase noise during 0.150 and 0.030 , there is a
80
4.4 – Simulation results
(a)
(b)
(c)
(d)
Figure 4.8. DC receiver system performance (SMR a-b, SCR c-d) with different
signal power and ADC bits; results are reported both for ideal ADC (a,c) and for
ADC with nonlinearity (b,d).
81
4 – Receiver comparison
decrement of 2 dB when σpn increases from 0.090 to 0.150 and an increment of 2 dB
increase when σpn is 0.060 smaller than 0.090 . The overall system performance is
mainly influenced by phase noise, but comparing the blue line(phase noise excluded)
in Figure 4.9(a) with Figure 4.8(b) and (d), we see that thermal noise have clear
influence when transmitted power is less than -35dBm. In the high power part,
bigger than -18dBm, the nonlinearity limits the performance.
As defined in Section 4.3, in order to make the three scenarios comparable, we
also apply the average technique to DC receiver. Figure 4.9(b) shows the results
with K = 100 iterations, which prove that the random thermal noise and phase
noise can be reduced by an average operation. However, this operation increases
the data acquisition time which will be discussed later. Considering a real circuit
implementation, a value of 0.10 as phase noise standard deviation is chosen, the
corresponding maximum SMR value is about 14dB without average.
(a)
(b)
Figure 4.9. DC receiver system performance with different signal transmitted
power and phase noise σpn ; results are reported both for a single evaluation (a)
and for an averaging on 100 trials (b).
Phase Mismatch
Common mode and differential mode phase mismatch are then added to the model,
with standard deviation σpm sweeping from 0 to 60 , while the other impairments
left untouched. -28 dBm is chosen as the transmitted power, which is the value that
optimizes performance. Figure 4.10 shows the results with and without average,
we see that SMR and SCR values decrease when phase mismatch increases. In
addition, since the phase mismatch is a systematic error, comparing Figure 4.10(a)
and (b), it can be observe that, even with 100 times average, the phase mismatch
82
4.4 – Simulation results
influence on system performance can not be alleviated. The overall performance
improvement is determined by the averaging of thermal noise and phase noise. As a
result, σpm greater than 20 can cause more than 1 dB SMR decrease. As a guideline
for designers, phase mismatches must be kept well below this limit.
(a)
(b)
Figure 4.10. DC receiver system performance (SMR, SCR) with different phase
mismatch with 15-bit ADC and -28dBm transmitted signal power; results are
reported both for a single evaluation (a) and for an averaging on 100 trials (b).
4.4.2
CETS receiver with SFCW approach
Considering the results obtained for the DC receiver, the critical impairments in
CETS receiver should be ADC resolution, thermal noise and jitter. Concerning
thermal noise, there is no mixer and filter in CETS receiver, the receiver will work
in the whole input signal bandwidth, in our specific case 10GHz, therefore, much
more influence from thermal noise than in DC receiver is expected.
ADC
Figure 4.11 shows the values of SMR and SCR as a function of transmitted power,
with ADC resolution changing from 7 bit to 12 bit. Thermal noise and jitter are not
included now, K is set to one iteration. The difference between Figure 4.11(a) and
Figure 4.11(b) is the presence of the ADC nonlinearity, as can be seen there is only
a small difference in system performance, indicating that the effect of ADC INL is
negligible at these ADC resolution levels. However, the results demonstrate that
the system performance is good enough when ADC resolution is bigger than 9-bit in
the range of -35 dBm and -22 dBm transmitted power. In addition, the performance
83
4 – Receiver comparison
starts to be strongly limited by nonlinearity, especially saturation, when transmitted
power is larger than -22dBm.
ADC sampling frequency might be relatively high, thus, based on the technique
design constraints, 10-bit is the perfect choice. With a resolution of 10 bit, SMR
and SCR are bigger than 15 dB and 5 dB respectively, between -35 dBm and -22 dBm
power range.
(a)
(b)
Figure 4.11. CETS receiver system performance (SMR, SCR) with SFCW approach with different signal power and ADC bits; results are reported both for an
ideal ADC (a) and for a nonlinear ADC (b).
Thermal noise
The simulation results of the CETS receiver with 10-bit ADC and additional thermal
noise are presented in Figure 4.12(a). It is possible to see that the influence of
thermal noise is significant, especially at low power, since the system does not work
if the signal power is less than -30 dBm. Actually, the thermal noise influence is less
than in the case we are about to examine (CETS in time domain). This is caused
by the FFT operation after the ADC which behaves as a bandpass filter centered
around the given frequency.
The results after enough average time (100 times here) in Figure 4.12(b) proves
the perfect functionality of the average technique in reducing random noise. The
SMR and SCR reductions in low power part are due to the ADC quantization noise
and ADC nonlinearity. It is therefore a necessary to implement averaging technique
in this kind of receiver and application. Figure 4.12(b) illustrates that the ideal
working power range still is from -35 dBm to -22 dBm, in order to keep consistent
84
4.4 – Simulation results
with the above DC receiver, -28 dBm is chosen as our transmitted power for our
following evaluation.
(a)
(b)
Figure 4.12. CETS receiver system performance (SMR, SCR) with SFCW approach with different signal power, with 10-bit ADC and thermal noise; results are
reported both for a single evaluation (a) and for an averaging on 100 trials (b).
Jitter
Simulations are performed sweeping the rms timing jitter variance, from 0 to 6
picoseconds. The simulation results in Figure 4.13(a) are referred to the case without
average. The depicted curves present the results with -28 dBm as the transmitted
power, and 10-bit as ADC resolution. Here, the impact of jitter is obvious since SMR
and SCR decrease dramatically and approach the working threshold values when rms
jitter variance is 2 ps. However, results with 100 times average are quite good, as
shown by curves in Figure 4.11(b), which prove the CETS receiver is considerably
robust to jitter influence. PLL with 2 ps rms jitter can be achieved, as shown in [60].
4.4.3
CETS receiver with time domain approach
In this scenario, instead of transmitting a series tones of variable frequency, a single
gaussian pulse with ultra-wide-band is transmitted.
ADC
Since the ADC resolution for the CETS receiver has already been decided in previous
simulations, the focus of this analysis will be put on the performance with this 10-bit
85
4 – Receiver comparison
SMR/SCR VS. rms jitter
15
SMR/SCR VS. rms jitter @100avg
15
@10bit @−28dBm
SMR
SMR/SCR(dB)
SMR/SCR(dB)
@10bit @−28dBm
10
SMR
5
SCR
0
−5
0
10
SCR
5
0
1
2
3
4
rms jitter σjit (ps)
5
−5
0
6
1
(a)
2
3
4
rms jitter σjit (ps)
5
6
(b)
Figure 4.13. CETS receiver system performance (SMR, SCR) with SFWC
approach and with different rms jitter, with 10-bit ADC and -28dBm transmitted signal power; results are reported both for a single evaluation (a) and
for an averaging on 100 trials (b).
SCR VS. Nonlinear ADC bits
SMR VS. Nonlinear ADC bits
17
8
16
6
15
4
SCR (dB)
SMR (dB)
14
13
12
7
8
9
10
11
12
11
10
9
8
−50
−40
2
7
8
9
10
11
12
0
−2
−4
−6
−50
−30
−20
−10
Transmitted Power (dBm)
(a)
−40
−30
−20
−10
Transmitted Power (dBm)
(b)
Figure 4.14. CETS receiver system performance (SMR, SCR) with different signal
power and ADC bits; results are reported for a nonlinear ADC.
ADC. The transmitted signal level is scaled from -50dBm to -2dBm as defined in
Section 4.3. As can be seen from Figure 4.14, 10-bit is also a good choice in this
kind of application when transmitted power is greater than -20dBm, based on the
rule that SMR is meaningful if and only if the corresponding SCR is bigger than
0dB.
86
4.4 – Simulation results
Thermal noise
In this specific application, thermal noise is expected to be the big performance
degradation contribution, because the noise without filter is added to the time domain signals directly before quantization; moreover, the sampled digital signals after
resorting are processed by imaging reconstruction algorithm directly, without any
further processing step, like FFT in CETS receiver with SFCW approach.
Figure 4.15 (a) proves this hypothesis, the noise influence is significant. The
system starts working if and only if transmitted power is bigger than -10 dBm without average. After 100 times average, Thermal noise is dramatically reduced, the
working threshold power becomes -30 dBm, the SMR and SCR values increase monotonically with the power to 16 dB and 5 dB respectively. Figure 4.15 (b) indicates
that the needed power for good performance is at least -20dBm.
Note that, unlike the previous two scenarios, nonlinearity and saturation exhibit
less impact on the system performance at high signal power. Since the reflected pulse
is a combination of skin reflection and tumor response in time, the skin reflection
appears early and performs strong, on the contrary, tumor information appears later
in time and behaves much weaker. Most of the distortions are due to the strong skin
response and are display common to all the received signals at different antennas,
as the same distance between antennas and skin is applied, and they are effectively
removed by the following skin artifact calibration [33].
PTX VS. SMR/SCR @100avg
SMR
15
SMR/SCR (dB)
@10bit
10
SCR
5
0
−5
−50
(a)
−40
−30
−20
−10
Transmitted Power (dBm)
(b)
Figure 4.15. CETS receiver system performance (SMR, SCR) in time domain
with different signal power and 10-bit ADC; results are reported both for a single
evaluation (a) and for an averaging on 100 trials (b).
87
4 – Receiver comparison
Jitter
RMS jitter is now included in the model, and varied from 0 to 6 picoseconds. Results
are shown in Figure 4.16, which are obtained using -10 dBm transmitted power, 10bit ADC and 100 iterations. As expected, results with averaging (b) are way better
than those obtained after a single trial (a), proving that jitter influence can be
removed in CETS even with a time domain approach.
SMR/SCR VS. rms jitter
15
SMR/SCR VS. rms jitter @100avg
15
@10bit @−10dBm
SMR
SMR/SCR (dB)
SMR/SCR (dB)
@10bit @−10dBm
SMR
10
5
SCR
0
−5
0
1
2
3
4
rms jitter σjit (ps)
10
SCR
5
0
5
−5
0
6
(a)
1
2
3
4
rms jitter σjit (ps)
5
6
(b)
Figure 4.16. CETS receiver system performance (SMR, SCR) in time domain with
different rms jitter, with 10-bit ADC and -10dBm transmitted signal power; results
are reported both for a single evaluation (a) and for an averaging on 100 trials (b).
4.4.4
Overall comparison
The simulated quantitative results (SMR, SCR) for three different scenarios (DC,
CETS receiver at frequency mode and CETS at time mode) are summarized in
Table 4.3, along with selected receiver parameters. The corresponding energy maps
generated by imaging algorithm are illustrated in Figure 4.17, the maximum energy
peaks are enclosed.
For the DC receiver with SFCW approach, the results are obtained under the
condition of phase mismatch equal to 20 , transmitted power is -28 dBm, ADC resolution is 15-bit, phase noise is 0.10 , the total gain of receiver is 40 dB, a NF is
10 dB, S11 of antenna is -10 dB, insertion loss and isolation of circulator is -2 dB and
-18 dB respectively and the IIP2 and IIP3 are 20 dBm and -20 dBm respectively.
Compared to the ideal case, SMR and SCR without average decrease by 3.7 dB and
3.7 dB, respectively. Maps are in Figures 4.17 (a)-(b), it is clearly to see that averaging removes many clutters from the image, the tumor is evident. So in conclusion,
88
4.4 – Simulation results
DC receiver needs averaging to achieve high performance but averaging increases
the data acquisition time.
Results for the CETS receiver with SFCW approach are obtained with 2 ps RMS
jitter, 10 bits ADC, -28 dBm transmitted power. The energy map in Figure 4.17 (c)
shows a lot of clutters, the energy peak appears in many places, tumor is hard to
be identified, while SMR and SCR values tell us the same results. On the contrary
averaging improves results and seems to be more effective than in the DC case, as
SMR and SCR decrease by only 0.2 dB and 1.0 dB about the ideal case.
Concerning CETS in time domain, the receiver parameters are set equal to the
SFCW case except for the 10 GHz effective noise bandwidth. The quantitative
results indicate that the tumor can not be detected without average, we can not
identify the tumor from the map in Figure 4.17 (e) either. The map after averaging
in Figure 4.17 (f) is instead very clear. Performance results are the closest to the
ideal case: SMR decreases by 0.3 dB, and by 0.7 dB for SCR.
At last, another comparison parameter for the three scenarios is considered, data
acquisition time. For CETS in time domain with 8 ns pulse repetition time and 251
pulses required for a single acquisition, the total acquisition time with averaging
is only 200 µs. The same time is needed for one frequency tone in case of CETS
with SFCW, but 81 frequencies are acquired, leading to a total acquisition time
of 17 ms. The baseband filter with 100 KHz bandwidth used in DC receiver may
have around 4 µs rise time, therefore it is reasonable to assume 10 µs acquisition
time for each frequency. The acquisition time for 81 tones is thus about 800 µs, and
as a consequence the total capture time is about 80 ms in case of 100 iterations.
Therefore, the proposed CETS receiver working with impulse radar approach can
obtain better results with less acquisition time.
ideal
no avg
SMR
16.5
SCR
7.0
DC
CETS–Freq.
no avg avg no avg avg
12.8
15.2
10.2
16.3
3.3
5.6
-0.6
6.0
Table 4.3.
CETS–Time
no avg avg
9.0
16.2
-1.5
6.3
SMR, SCR for the three scenarios.
89
4 – Receiver comparison
(a) DC RX NO AVG
(b) DC RX AVG
(c) CETS RX FREQ NO AVG
(d) CETS RX FREQ AVG
(e) CETS RX TIME NO AVG
(f) CETS RX TIME AVG
Figure 4.17. Energy maps resulting from the system-level simulations with different receiver approaches and all the impairments. Maps (a)-(b) are for DC with
SFCW approach, (c)-(d) for CETS with SFCW approach, (e)-(f) for CETS in
time domain. The left column maps (a)-(c)-(e) are without average, the right ones
(b)-(d)-(f) are acquired 100 times and averaged.
90
Chapter 5
Hardware Implementations
Considering the receiver requirements on bandwidth, resolution and sampling frequency, the most critical blocks in the proposed CETS receiver are LNA and THA.
In this chapter, specific LNA and THA are designed for the CETS receiver in 130 nm
UMC CMOS technology. Moreover, an UWB slot antenna with HFSS software is
designed.
5.1
UWB antenna design
The primary goal of this section is to develop a planar, directional and physically
compact UWB antenna for breast cancer detection system.
5.1.1
UWB antenna requirements
The antenna is developed keeping in mind a broad range of possible applications
that can be achieved using this time domain impulse UWB radar transceiver. In
addition to the parameters described above, the UWB antenna design faces some
additional challenges as compared to other narrowband antennas.
First of all, even though the proposed signal bandwidth is 10 GHz in behavioral
system simulation, after considering the complexity of the practical hardware design,
the standard Ultra Wideband bandwidth 3.1-10.6 GHz is the designed bandwidth
range. Consequently, an Ultra Wideband antenna must be operable over the entire
3.1-10.6 GHz frequency range which implies that the UWB antenna must achieve
an impedance bandwidth of at least 7.5 GHz. Moreover, due to the very low transmission power spectral density of the UWB signals, high radiation efficiency for the
antenna is required, which means that all types of losses, including dielectric and
return loss should be kept very low. Another important parameter which must be
91
5 – Hardware Implementations
Physical Profile
Operational Bandwidth
Radiation Efficiency
Radiation Pattern
Directivity and Gain
Group Delay
Table 5.1.
Compact, preferably conformal, Low cost of manufacture
3.1-10.6 GHz
High, S11 < -10dB in the entire band
Directional, Stable over the entire frequency range
High
Constant throughout the operational bandwidth
UWB Antenna design requirements for UWB transceiver.
taken care of in the case of UWB antennas is the group delay. It gives an indication of the average time delay the input UWB signal suffers at each frequency. For
distortion less signal transmission UWB antennas must have a constant group delay over the entire operational bandwidth. In narrowband antennas constant group
delay is naturally achieved. The antenna requirements for the UWB transceiver are
summarized in the Table 4.1.
5.1.2
Antenna design
The selection of an UWB antenna topology depends on the particular application for
which it will be used. A wide variety of UWB antennas are available in literature
for different UWB applications in which several antennas for microwave imaging
system have been proposed, such as stacked patch antenna[61], Vivaldi[62], horn
[55], monopole [63] and also other more antennas are designed and investigated in
order to get the proper antenna. Although the popular pyramidal horn antennas is
commercially available with an operational frequency band of 1-18 GHz, the large
dimensions and high cost make this kind of antenna improper for breast cancer
imaging applications.
Therefore, in this section, a wide slot antenna is investigated in which the slot
width and length are comparable. The generic form of this configuration has been
proposed in [64]. Slot antennas are well-known for their wide bandwidth and small
size. In the following, a numerical study of a specific realization of this design is
presented, wherein the antenna is customized to centimeter-scale dimensions for
operation in the microwave frequency range from 3.1 to 10.6 GHz.
Figure 5.1 displays the top-view and side-view of the proposed wide-slot antenna.
A wide slot with comparable width W and length L is placed in the ground plain
on one side of the substrate with relative permittivity εr . The wide slot is fed
by a microstrip line with a fork-like tuning stub, which is printed on the opposite
side of the substrate and placed symmetrically with respect to the centerline of the
wide slot. The fork-like tuning stub consists of a straight section of length (L2 plus
92
5.1 – UWB antenna design
L4) and two branch sections of equal length. The space between the two branch
sections is W5. The widths of these sections are all the same and equal to that of
the microstrip line W3. By selecting proper dimensions of the fork-like tuning stub,
good impedance matching of the printed wide-slot antenna across a much enhanced
bandwidth can be obtained. In this case, 50 Ohm impedance matching is used.
L1
L3
W1
W
L W2
W5
W4
L4
L2
H
W3
Figure 5.1.
The layout of the developed slot antenna.
The first step in the design is to choose a suitable dielectric substrate of appropriate thickness and loss tangent. To begin with, the relationship between thickness
H and dielectric constant of the substrate should be compromised. The operation
bandwidth improves as the substrate thickness is increased, or the dielectric constant is reduced, but these trends are limited by an inductive impedance offset that
increases with thickness [65]. On the other hand, in order to minimize the antenna
size, the substrate dielectric constant should be bigger [64], which is an important
requirement of breast cancer application.
A logical approach, therefore, is to use a high dielectric constants and a thick
substrate. Rogers RT/duroid 6010/6010LM with relative permittivity εr = 10.2 and
dielectric loss tangent tan δ = 0.0023 is applied.
Next, based on this relative permittivity and height of substrate, in order to
obtain 50 Ohm impedance matching, the relationship between the microstrip line
width and the impedance can be calculated in two conditions.
When W/h ≤ 1
93
5 – Hardware Implementations
8h
W
+ 0.25 )
2π εre
W
h
εr + 1 εr − 1
h
W
+
[(1 + 12 )−0.5 + 0.04(1 − )2 ]
εre =
2
2
W
h
Zc =
η
√
ln(
(5.1)
When W/h ≥ 1
η W
W
Zc = √ [ + 1.393 + 0.677 ln( + 1.444)]
εre h
h
h
εr + 1 εr − 1
+
(1 + 12 )−0.5
εre =
2
2
W
(5.2)
Where εre is effective dielectric constant, εr is relative dielectric constant, Zc is
the characteristic impedance.
The slot antenna is designed and optimized using the CAD tool HFSS v10. During simulation, the ground plane and the microstrip line are assigned as the Perfect
E boundary. This type of boundary forces the electric field (E-Field) perpendicular
to the surface. Besides, Lumped port is applied as the excitation port. The excitation port is a type of boundary condition that permits energy to flow into and
out of a structure, and Lumped Port is useful for modeling internal port within a
structure. In order to find best values for different antenna parameters, a number
of simulations have been run within the given frequency range 2GHz to 12GHz in
HFSS. The best parameters found after parametric optimization in HFSS are listed
in Table 5.2. The layout of the antenna in HFSS is shown in Figure 5.2, the total
size is 22 mm × 19 mm × 1 mm.
5.1.3
Results and discussion
Reflection coefficient
First, the fundamental parameter impedance matching is simulated, which is used
to characterize the impedance bandwidth of an antenna. Figure 5.3 (a) depicts the
amplitude of the simulated return loss, for the -10 dB return loss, the measured maximum impedance bandwidth of the proposed antenna is from 2.5 GHz to 10.8 GHz,
which satisfy the good impedance matching requirement. The sharp nulls in the
plot correspond to the frequencies that attain the highest resonance. These points
indicate a near perfect match to 50 Ohm. Figure 5.3 (b) shows the corresponding
phase response of the antenna.
94
5.1 – UWB antenna design
Material Rogers RT/duroid 6010/6010LM εr = 10.2 tan δ = 0.0023
Height H
1 mm
Slot width W
17 mm
Slot length L
15.5 mm
Microstrip width W3
1 mm
L1
3.5 mm
L2
3 mm
L3
4.5 mm
L4
4 mm
W1
1 mm
W2
1 mm
W4
4 mm
W5
7 mm
S11 (dB)
0
-5
Table 5.2. The dimension and parameter of proposed antenna in millimeters. -10
-15
-20
-25
-30
S11 (rad)
0
4
3
2
1
0
-1
-2
-3
-4
0
Figure 5.2.
Overview of the slot antenna in HFSS.
(a)
Radiation pattern
An input matching is only one requirement for the antenna, radiation patterns are
also important over the full band of operation. Antenna radiation pattern demonstrates the radiation properties on antenna as a function of space coordinate. The
95
2
2
0
-5
-10
-15
-20
-25
-30
0.2
0
S11 (rad)
T
0.3
2
4
6
8
Frequency (GHz)
10
12
14
4
3
2
1
0
-1
-2
-3
-4
Amplitude (V)
S11 (dB)
5 – Hardware Implementations
0.1
0
-0.1
-0.2
-0.3
0
2
4
6
8
10
12
14
Frequency (GHz)
(a)
(b)
Figure 5.3.
Simulated return loss against frequency.
gain in the z direction (maximum gain direction in the radiation pattern) ranges
from 3.2 dBi to 5.9 dBi within the operating bandwidth of the antenna, and the
peak gain is at 9GHz. Typical radiation patterns is plotted in Figure 5.4.
Time domain analysis
In order to validate the efficiency of the antenna, the pulse base signal is excited
with Gaussian pulse. Figure 5.5 shows the radiated E field which is virtually place
probe in simulation to study the effect of radiated signal. It is proved that the
proposed antenna has good potential in transmitting UWB signals with minimum
distortion and late-time ringing. Furthermore, the time domain UWB pulse signal
received by the electric probe shows stable performance where the received pulse
signal is almost identical to the transmitted pulse signal.
The above results show that the proposed wide slot antenna has a good impedance
matching, well more than the entire UWB range (7.5 GHz). Furthermore, the wide
slot antenna has much smaller size than other type of antennas. Simulated radiation
patterns confirm good directional radiation performance over the entire UWB range.
96
0
0.2
5.2 – Low Noise Amplifier
Figure 5.4.
Radiation pattern.
Transmitted Signal Before Antenna
Transmitted Signal After Antenna
0.3
8
ncy (GHz)
10
12
14
Amplitude (V)
0.2
0.1
0
-0.1
-0.2
-0.3
8
10
12
14
0
0.2
ncy (GHz)
0.4
0.6
0.8
1
1.2
Time (ns)
b)
(c)
Figure 5.5.
5.2
Calculated electric field waveforms.
Low Noise Amplifier
As the first block in receiver, the purpose of the low-noise amplifier (LNA) is to
amplify the weak RF-signal while adding a minimum noise.
97
5 – Hardware Implementations
5.2.1
Design consideration
As discussed in Chapter 4, the main concern of the proposed CETS receiver in time
domain impulse radar approach is the influence of thermal noise. Based on the Friis’
formula, the cascaded noise figure and third-order intercept point IP3 of a receiver
can be expressed as:
FN − 1
F2 − 1 F3 − 1
+
+ ... +
G1
G1 G2
G1 G2 · · · GN
1
IP 3 = 1
G2 ···GN
G1
G1 G2
+ IP 32 + IP 33 + ... + G1IP
IP 31
3N
F = F1 +
(5.3)
where Fi , IP 3i and Gi (i = 1,2,...N ) are the noise figure, third-order intercept point
and gain of each individual component in the RF chain.
Therefore, the noise figure and gain of the first component in receiver, LNA, are
important. The overall noise figure of the receiver caused by the second component,
THA, is reduced by the gain of the LNA, as well as nonlinearity behavior. But the
high gain may cause a potential problem that strong signals in the bandwidth of the
amplifier may drive it into saturation and generate spurious frequencies.
To sum up, considering that the received pulse has ultra wide bandwidth (3.1 GHz
to 10.6 GHz) and small tumor information amplitude, the main specifications of LNA
are the following: the LNA input impedance must be matched as closely as possible
to the antenna characteristic impedance over the entire bandwidth to guarantee the
maximum power transfer; the LNA must exhibit the flat gain behavior over the
entire bandwidth with sharp roll-off at the upper and lower -3 dB frequencies to prevent out-of-band interference; the LNA must have a high conversion gain to amplify
the weak tumor information; the noise figure (NF) should be low enough to identify
important information from noise interference. Nevertheless, it must offer robust
RF performance (i.e., gain and dynamic range) over many gigahertz of bandwidth
(7.5 GHz) with levels of current consumption comparable to existing narrowband
amplifiers.
In recent times, many literatures have reported UWB LNA circuit designs with
various approaches to impedance matching and involving lower noise. Table 5.3
illustrates the recent researches in UWB LNA.
5.2.2
UWB LNA design
There are two popular architecture choices for input matching, common-source
topology and common-gate topology. Most reported common-source structure can
provide acceptable gain and input matching while dissipating rather low power.
However, these common-source UWB LNAs tend to show unacceptably high noise
figure (NF) at high frequencies (near 10 GHz) due to the strong cutoff frequency
98
5.2 – Low Noise Amplifier
Ref
[66]
[67]
[68]
[69]
[70]
Technology
Gain (dB)
0.13 µm CMOS
11
0.18 µm CMOS
9.5
0.18 µm CMOS
9.7
0.13 µm CMOS
15.1
0.13 µm CMOS
16
Table 5.3.
BW (GHz)
2-9.6
3.1-10.6
1.2-11.9
3.1-10.6
2.9-11
NF (dB)
3.6-4.8
5-5.6
4.5-5.1
2.1-2.53
3.8-4.0
S11 (dB)
< -9.5
< -8.6
< -11
< -9
< -10
Power (mW)
19
9.4
20
9
9.5
Researches in UWB LNA.
dependence [71]. Instead, common-gate topology is benefited from its better input matching, inherent wideband operating performance, good linearity and inputoutput isolation property [72].
Figure 5.6 and Figure 5.7 show a typical inductively degenerated common-source
LNA (CS-LNA) and a common-gate LNA (CG-LNA).
Figure 5.6.
Typical inductor-degenerated common source LNA [73].
The corresponding input impedance of Figure 5.6 can be expressed as,
Zin (s) =
m1 Ls
s2 + s (Ls g+L
+
g )Cgs1
1
(Ls +Lg )Cgs1
s/(Ls + Lg )
(5.4)
The corresponding input impedance of Figure 5.7 can be expressed as,
Zin (s) =
s2
s/Cgs1
+ s Cgm1
+ Ls C1gs1
gs1
99
(5.5)
5 – Hardware Implementations
Figure 5.7.
Typical common gate LNA.
Where Cgs1 is the parasitic gate-to-source capacitance of the input transistor.
As thermal noise is the most important impairment in the CETS receiver, more
attention being paid to it. The NF of the CS-LNA is generally superior to that
of the CG-LNA at lower frequency, because the CG-LNA’s NF is limited by 1/gm
input matching. But, the NF of CS-LNA is proportional to ω0 /ωT , while the NF of
CG-LNA is constant with respect to ω0 /ωT . Therefore, the CG-LNA outperforms
CS-LNA in the higher frequency.
Taking advantage of the common gate topology, as above mentioned, and taking
inspiration from a single-ended LNA in [70], a fully differential LNA is proposed.
The schematic is shown in Figure 5.8. Compared to [70], this LNA occupies less
area, one of the reasons is that two inductors in the original circuit are removed.
As the circuit in Figure 5.8 is a total symmetrical structure, it can be considered
as a single-side circuit when discuss it. The proposed common gate wide-band Low
Noise Amplifier (LNA) consists of three stages, a common-gate stage, a commonsource stage and an output buffer. The common-gate stage provides input matching
and wide-band noise. The second stage use cascode to extend the overall amplifier
bandwidth and gain and the output buffer is a source follower for measuring purposes.
The circuit has been designed with UMC CMOS 130 nm technology. All inductor,
resistors and capacitors are implemented on chip. Various pre-characterized active
and passive components that UMC makes available through their design library are
used.
The first stage is critical since it should match with source impedance to get
100
5.2 – Low Noise Amplifier
R1
R2
R1
R2
C4
C4
L2
L2
M1
M5
M3
OUT_N
M1
M5
IN_N
M3
IN_P
OUT_P
C2
C2
C1
M4
BIAS
L1
R5
M6
C1
M2
L1
R4
R4
M4
M2
R5
C3
Figure 5.8.
Proposed differential UWB LNA.
maximum power transfer and minimum reflection. Its noise figure must be kept
under control, because the overall noise is mostly determined in this stage. The
input impedance can be simplified as
Zin (s) = sL1/(1 + (gm1 + sCgs1 )sL1).
(5.6)
Where gm1 and Cgs1 are the transconductance and the parasitic capacitance of transistor M 1. Zin is determined by inductor L1 at low frequency and is close to 1/gm1
at high frequency. L1 provides a DC path for the first stage, and combines with
the parasitic capacitance Cgs1 , which resonates and determines the input matching
range and input impedance.
In addition, the gain of the first stage is determined by the size of M 1 and
R1. Input inductor L1 of 10 nH (with 7 GHz Self Resonant Frequency (SRF)) and
input transistor M 1 of 50 µm/0.12 µm are chosen to ensure the broad-band input
matching condition. Figure 5.9 plots the simulated frequency response of this first
stage. The optimal matching frequency is 1.2 GHz. The 3-dB bandwidth of the first
stage is 0.36 GHz-5 GHz with the maximum gain of 14.9 dB at 1 GHz.
The second stage is a simple cascode common-source stage, which provides highfrequency gain and determines higher 3-dB bandwidth of the LNA. The cascode
transistor M 3 is used for better isolation, higher frequency response and higher
gain. A series peaking inductor L2 will resonate with the parasitic capacitance of
M 3 and M 5 at high frequency. By optimizing the values of L2 and R2, the second
stage can compensate the gain roll-off from first stage at high frequencies. Hence the
101
5 – Hardware Implementations
16
14
Gain (dB)
12
10
8
6
4
2
0 8
10
Figure 5.9.
9
10
Frequency (Hz)
10
10
Simulated frequency response of the first stage.
flat frequency response is obtained over the whole frequency band of interest. L2 in
the second stage is 3.99 nH (with 14GHz SRF). Figure 5.10 displays the simulated
frequency response of the second stage. The maximum gain of the second stage is
17.7 dB at 10 GHz and 3-dB bandwidth is 5.9 GHz-11 GHz.
M 4 and M 5 compose the output buffer. The output buffer is a simple source
follower. In order to reduce the parasitic capacitance arisen from a large device, the
input device of this buffer must be reduced despite larger loss occurs. The width
and length of the input device M 5 are set to 20 µm and 0.12 µm, respectively. The
loss of the output buffer is 10 dB in this design for output impedance matching.
These three stages have the same bias voltage, which simplifies the bias circuit. The
dimensions of the circuit components are organized in the Table 5.4.
5.2.3
Simulation results and discussion
The LNA is simulated and designed in 0.13 µm CMOS technology with 1.2 V supply.
The circuit has been simulated under Cadence design framework. Figure 5.11 (a)
shows the input and output impedance matching performance (S11 and S22), which
is less than -10 dB over the bandwidth from 500 MHz to 12 GHz. The maximum
power gain with 50 Ω matched load is 17.2 dB and the reverse isolation is less than
-55 dB, as shown in Figure 5.11 (b).
102
5.2 – Low Noise Amplifier
19
18
Gain (dB)
17
16
15
14
13
12
11 8
10
Figure 5.10.
9
10
Frequency (Hz)
10
10
Simulated frequency response of the second stage.
Component
M1
M2
M3
M4
M5
M3
R1
R2
R3, R4, R5
C1, C2
C3, C4
L1
L2
Table 5.4.
value
unit
50/0.12 µm
34/0.12 µm
20/0.12 µm
30/0.12 µm
20/0.12 µm
4/0.12 µm
510
Ω
210
Ω
10
KΩ
10
pF
1
pF
12
nH
3.99
nH
Dimension of LNA components.
The simulated NF of the proposed LNA as a function of frequency is also presented in Figure 5.11 (c), which is improving with frequency. It is because the effect
103
5 – Hardware Implementations
of L1 on input matching and NF increases at high frequencies. This is also the
advantage of common-gate topology over other architectures like common-source or
cascode amplifiers, whose NF is increasing with frequency. In this LNA design, the
NF values range from 3.1 to 4 dB between 2 and 12 GHz.
Two-tone test with 250 MHz spacing at various frequencies is implemented to
examine the linearity performance of the proposed LNA. In the frequency range of
3-12 GHz, the IIP3 varies from -12 to -18 dBm, which is presented in Figure 5.12. As
proved in Chapter 4, the nonlinearity problem exhibited less impact on the system
performance in this specific application, given that the received reflected pulse is
a combination of skin reflection and tumor response in time, the skin reflection
appears early and performs strong, on the contrary, tumor information appears later
in time and behaves much weaker. Most of the distortions are due to the strong
skin response and display common to all the received signal at different antennas,
as the same distance between antennas and skin is applied, and they are effectively
removed by the following skin artifact calibration. Consequently, the requirement
on nonlinearity is not that stringent.
The layout of the proposed LNA is shown in Figure 5.13. The input and output
coupling capacitors occupy the majority area. Due to the reduction of the used
inductors, the chip area is saved. Power consumption is 11 mW at 1.2 V and the
chip area is 0.24 mm2 . The LNA performances are summarized in Table 5.5.
Table 5.5.
Summary of the simulated LNA performances.
parameter
value
Technology
UMC 0.13 µm CMOS
S11 (dB)
< -10
S22 (dB)
< -10
S12 (dB)
< -55
S21 (dB)
14.5−17.2
3dB bandwidth (GHz)
0.5−12
NF (dB)
3.1 − 4
IIP3 (dBm)
-15
Power consumption (mW)
11
Area (mm2 )
0.24
104
5.2 – Low Noise Amplifier
Input &Output Return Loss(dB)
0
S11
S22
−5
−10
−15
−20
−25
−30
−35
−40
0
2
4
6
8
Frequency(Hz)
10
12
9
x 10
(a)
20
−40
15
10
0
−60
2
4
6
8
Frequency (dB)
10
(b)
Reverse Isolation (dB)
Power Gain (dB)
S21
S12
−80
12
9
x 10
12
Noise Figure (dB)
10
8
6
4
2
0
2
4
6
8
Frequency (Hz)
10
12
9
x 10
(c)
Figure 5.11. Simulated performance of the proposed LNA: (a) Input and output
reflection coefficient (S11 and S22) of the UWB LNA versus frequency, (b) Gain
and reversal isolation (S21 and S12) of the UWB LNA versus frequency and (c)
Noise figure of the UWB LNA versus frequency.
105
5 – Hardware Implementations
Figure 5.12.
Simulated IIP3 of the proposed LNA versus frequency.
Figure 5.13.
Layout of the proposed LNA.
106
5.3 – Track and Hold Amplifier
5.3
Track and Hold Amplifier
As mentioned in previous chapters, high speed data acquisition systems require ultra
high-speed analog-to-digital converters (ADCs). The THA is a crucial building block
in ADCs since it makes a great impact on the dynamic performance of ADCs.
5.3.1
THA design
Based on some simple differences in architecture, the topologies of THA can be
classified as closed-loop topology, open-loop topology and distribute topology [74].
To achieve high speed operation, the open loop architecture switched source follower
(SSF) is chosen [75] [76]. Therefore, to understand the principle of the SSF circuit,
the simplest open-loop THA composes of two elements: a storage capacity and a
switch (implemented with a MOS transistor) controlled by a clock. The simple
circuits are illustrated in Figure 5.14.
(a)
(b)
CLK
CLK
Vin1
Vin1
M1
Vout
Vout1
M2
CH
CH
Vin2
Vout2
M1
CH
∆V
S2
Figure 5.14. Diagram of a simple circuit with THA differential switches
in series
(a) and its differential version (b) [76]
M2
S3
The circuit works at track mode when switch is on,
and hold mode when switch
S1
is off. Even though this topology is characterized by simplicity, two problems should
M3
be concerned: one is the low velocity due to on-resistance of the sampling transistor;
CH
the other is that the output voltage is lower than the supply voltage due to the fact
−
M1 transistor in
Vin on the
that a threshold voltage Vgs is necessary to turn
X track mode.
Consequently, the SSF structure was proposed to solve these problems, which is
+ is shown
R1
R2 high speed and high linearity. The single-side structure
characterized
by
in Figure 5.15. This circuit consists of a differential pair (QN and QP ), a current
tail IT , a switched source follower QSF and a hold capacitor CH . In track mode,
CLKP is high, the tail current IT flows through QSF and QP , transistor QSF acts
M1
Vout
M2
107
+
Vo
Vin
CH
I1
−
X
−
Vout
+
M3
M4
(a)
I2
5 – Hardware Implementations
as a source follower and the output voltage Vout is linearly dependent on the input
voltage Vin . In hold mode, CLKN is high, the tail current IT switches through
the load RL other than transistor QSF . The value of RL is chosen such that the
voltage drop IT RL turns off transistor QSF and the hold capacitor CH maintains
the sampling voltage [75].
5/
46)
9LQ
4
9RXW
&+
&/.1
41
43
&/.3
,7
Figure 5.15.
A switched source follower track and hold amplifier
The main specifications of the required THA in the microwave imaging application are high-frequency operation in track mode (up to 10GHz), high-speed when
moving from track to hold mode, and high linearity. In Figure 5.15, both the differential pair and the input buffer show highly linear behavior. There is inherent
distortion in the SSF, which limits the performance of THA. Therefore it is necessary
to improve the above existing architecture to suppress the effect of the distortion,
improve linearity without renouncing speed. The proposed THA architecture is
presented in Figure 5.16: differential circuits are used to solve the even harmonics
problem and the odd harmonics are still exist.
A fairly effective method, harmonic-canceling technique, is applied to reduce the
odd harmonics problem, which has been proved to be an effective way to increase
the linearity of an amplifier or buffer [77] [78]. To implement the harmonic canceling
technique, the nonlinearity of the input buffer is compensated by means of adding
small transistors M 3, M 4 and M 6.
In addition, if a standard source follower (QSF ) is used, its large input capacitance would cause a high aperture time. To guarantee low aperture time without
increasing power consumption, a modified source follower is proposed in Figure 5.17.
108
5.3 – Track and Hold Amplifier
R2
R1
M16
M12
outp
outn
M8
M7
C2
M2
M13
M14
M9
M5
TRACK
Va
vn
TRACK
HOLD
M4
M11
Vc
M3
M6
Figure 5.16.
M10
vp
HOLD
Vc
M15
C1
M1
Vb
Proposed high linearity THA
M 5 (in Figure 5.16) or M 7 and M 8 (in Figure 5.17) are added and controlled by
hold clock. In the track phase, M 12 and M 16 act as source follower. In the hold
phase, M 7 and M 8 switch off M 12 and M 16, respectively, and their currents are
deviated in M 10 and M 13.
vin
M1
vin
M1
vgs2
M5
vgs1
C1
C1
M2
M2
M3
M3
Vc
ID1
Vc
HOLD
HOLD
HOLD
TRACK
ID2
TRACK
d
Figure 5.17. Diagram showing the circuit innovations made to the basic
scheme of Figure 5.15
The THA is simulated and designed in 0.13 µm CMOS process under Cadence
design framework. The dimension of the circuit component are organized in the
Table 5.6.
109
5 – Hardware Implementations
Component
value
unit
M1, M2
11.3/0.12 µm
M3, M4
3/0.12
µm
M12, M16
80/0.12
µm
M10, M14
5/0.12
µm
M9, M13
20/0.12
µm
M11, M15
20/0.12
µm
M7, M8
80/0.12
µm
M5
43/0.12
µm
M6
8/0.12
µm
R1, R2
175
Ω
C1, C2
200
fF
Table 5.6.
5.3.2
Dimension of THA components.
Simulation results
First of all, stand-alone simulations have been carried out in Cadence design framework to verify the transient behavior of the THA in track and hold mode. Figure 5.18
shows the transient simulation results of THA, the red line is track clock which has a
period of 0.9ns, black one is the THA output with input frequency of 6GHz and the
dotted blue one is the output under the condition of track clock always ’1’ and hold
clock always ’0’ which shown as a reference. It is possible to see from Figure 5.18
that the circuit works very well in track and hold phases.
The simulated conversion gain of the proposed THA is shown in Figure 5.19. It
has maximum gain of -2.5 dB and a bandwidth of at least 12 GHz when the circuit
is operated in track mode.
The linearity of THA is characterized in terms of SFDR which is shown in Figure 5.20. In particular, the third harmonic distortion (the strongest) is less than
-50 dB from 0 to 10GHz, while the fifth and seventh harmonic distortion are less
than -65 and -70 dB, respectively. The layout of the proposed THA is shown in
Figure 5.21.
Since in the receiver THA directly follows LNA, Figure 5.22 shows the circuit
transient simulation results when both of them are simulated together. The track
clock period is 1.9 ns, input signal frequency is 4 GHz. The blue line is the LNA
input signal, the purple one is the output of LNA (input of THA) and the black one
is the differential output of THA. The signal is correctly amplified and held.
110
5.3 – Track and Hold Amplifier
0.6
Track−ck
THA−out1
THA−out2
Amplitude(V)
0.4
0.2
0
−0.2
−0.4
0
0.2
0.4
0.6
0.8
Time(s)
Figure 5.18.
1
−8
x 10
THA transient simulation results
−2
−2.5
Gain (dB)
−3
−3.5
−4
−4.5
−5
−5.5
−6
0
2
Figure 5.19.
4
6
8
Frequency (Hz)
10
THA AC simulation results
111
12
9
x 10
5 – Hardware Implementations
15.0
BW_buffer_high_linearity
SFDR5
BW_TH_total(track_mode)
SFDR3
SFDR7
100.0
90.0
13.0
80.0
12.0
70.0
11.0
10.0
60.0
0
2.0
Figure 5.20.
4.0
f_in(E9)
6.0
8.0
THA linearity performance in terms of SFDR.
112
50.0
10.0
SFDR
Bandwidth (E9)
14.0
110.0
5.3 – Track and Hold Amplifier
Figure 5.21.
Layout of the proposed THA.
113
5 – Hardware Implementations
0.6
LNA−in
LNA−out
THA−out
Track−ck
Amplitude (V)
0.4
0.2
0
−0.2
−0.4
0
0.2
0.4
0.6
0.8
Time (s)
Figure 5.22.
Transient simulation results with both LNA and THA
114
1
−8
x 10
Chapter 6
System performance evaluation
6.1
Introduction
In addition to present the circuit simulation results, the influence of the implemented
circuit components with respect to the system performance is evaluated in this
chapter. To achieve that, a multi-resolution methodology is applied. The first step
of this approach is an ideal model of the entire environment, which comprises breast,
antennas, transmitter, receiver and digital processing. High-level simulations with
such models determine an ideal result, which is a performance upper bound, as
illustrated in Chapter 3. Then, a progressive refinement of the design description
allows evaluating the impact of non-idealities on system-level performance.
Unlike the behavioral functional modeling way of receiver in Chapter 4, the
receiver is modeled block by block. Therefore, the designed circuit can be easily
substituted by its netlist form. As an example, a designer can evaluate by how much
a given system-level performance metric is influenced by circuit-level characteristics
of the receiver low-noise amplifier (LNA), all the other components being ideal. The
designer can then use this valuable feedback to optimize the design of the LNA.
Key to achieve this result is a multi-resolution environment for the co-simulation
of differently described components. Tools based on VHDL Analog and MixedSignal (AMS) hardware description languages, which can also co-simulate Spice-level
components, proved effective in complex designs [79][80][42][81].
In order to keep the consistent of the performance evaluation, some results replicate to Chapter 3 may reported. The main objective of this investigation is to assess
the functionality of an UWB imaging system for breast cancer detection. In particular, the critical components of an implementation that uses, for the most part,
ad-hoc CMOS integrated circuits are focused. To reach this goal, a simulation and
design environment according to the top-down, system-level approach that outlined
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6 – System performance evaluation
above is built. The starting point is an idealized Matlab model like the above chapters, which is the highest-level model to which the refined and less abstract models
of the system are compared. For such refined versions, Mentor Graphics’ ADMS
and its multi-resolution capability is leveraged [42]. ADMS allows to co-simulate
blocks described at behavioral-level with blocks described at transistor-level. Such
capability allows to test the effect at the system level of circuit-level aspects of the
most critical components, which are designed down to the layout level, as well as
the effect of noise, nonlinearity, and other impairments. The investigation ends with
the understanding through accurate simulations of the effect of the designed components. Therefore, fabricating the system and testing it is out of the scope of this
thesis in which the main contributions are illustrated in the following:
• A simulation environment of an UWB imaging system has been implemented
and presented again. Simulations use data from real measurements of breast
electrical parameters in the microwave frequency range.
• A detailed implementation of an UWB imaging system for breast cancer detection along with its design methodology is outlined.
• A practical implementation has been proved that leverages existing technology
is feasible, and the effects of non-ideality of some components are evaluated
(UWB antennas and receiver elements like LNA and Track-and-Hold Amplifier) by means of accurate, full-system simulations. In particular, these effects
on the reconstructed 2D maps of UWB reflected energies are analyzed and
quantified with standard metrics.
The contributions are demonstrated in typical conditions (e.g. breast and tumor
size, image resolution). Exploring all possible parameter variations, albeit interesting, is more appropriate when the potential of the technique has to be demonstrated.
This is not the goal of this investigation, given that the microwave imaging capability
has already been proved with simulations and instrumentation tools.
6.2
UWB imaging system building
To build a simulation and design environment for the entire system, it is partitioned
in blocks again, as shown in Figure 6.1: the transmitter, the antenna, the channel
model (i.e. the breast and the surrounding environment), the receiver, and the IU
that performs image reconstruction.
The simplified scheme in Figure 6.1 reflects the portion of the system that is
active any time one pulse is sent, received, and processed. Depending on the position
of the antennas around the breast, the channel model is different. In the following,
the characteristics of the blocks in Figure 6.1 are succinctly described simply.
116
6.2 – UWB imaging system building
TX
ANT.
CHANNEL
MODEL
ANT.
RX
IU
Figure 6.1. Block scheme of the portion of the system active when one UWB pulse
is sent, received and processed. TX is for transmitter, ANT. for antenna, RX for
receiver, and IU for Imaging Unit.
6.2.1
Transmitter
The transmitter should offer a certain level of flexibility to generate UWB pulses with
different spectral characteristics. An integrated and flexible CMOS UWB transmitter architecture based on the distributed-waveform generator technique has been
proposed previously [28][43]. The transmitter synthesizes arbitrary UWB waveforms by delaying, weighting, and finally adding a set of ultra-short base pulses.
The transmitter uses a pre-emphasis technique to compensate for bandwidth limitations arising from the antenna or other circuit nonidealities. Post-layout simulations
show that generated signals like differential gaussian (DG), Modified Hermite Polynomial (MHP), and Modulated and Modified Hermite Polynomial (MMHP) pulses
differ by less than 2% from ideal pulses in terms of RMS error, even when the antenna is taken into account. In this chapter the results obtained with DG pulses
are reported, as the DG signal is the most often used in the literature [40][33]. The
pulse center frequency is 6 GHz and the pulse 3dB-bandwidth extends from 4.3 to
7.7 GHz.
6.2.2
Antenna
As mentioned previously, in the ideal model that used as a reference, the antenna
is ideally modeled as a hertzian dipole, but a custom-designed slot antenna is also
experimented. Moreover, the so-called monostatic approach is utilized. Since in
this approach each antenna transmits the pulse and receives the echo at the same
time, an antenna switch cannot be used. Instead, a circulator can be used for this
purpose (or a quasi-circulator, given that there is no power transfer from receiver to
transmitter), and integrated implementations in the working bandwidth have been
reported in the literature [82].
6.2.3
Channel model
The channel model is obtained from an electromagnetic model of the breast, which
is assumed surrounded by air. Two numerical breast phantoms are experimented:
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6 – System performance evaluation
an ideal model of a breast uniformly filled with adipose tissue, and a real model
with a mix of fat and fibroglandular tissue.
6.2.4
Receiver
In the imaging system, the maximum depth of investigation Smax is about 15 cm.
The pulse repetition period must be greater than the round-trip time of the UWB
pulse, Tpulse ≥ 2Smax /v, where v is the wave speed in the breast tissue, which is
about 0.95 · 1010 cm/s for the uniform breast model and 0.86 · 1010 cm/s for real
breast model. Therefore, the pulse repetition time should be big enough to make
sure the echoed pulse from the target will return before next pulse emission. As the
investigated scenario is CETS receiver works under time domain radar approach and
Eldo is best known for operating in the time domain, the simulation is quite slow
especially when its noisetran analysis is activated. In order to save the simulation
time, the pulse is repeated every 4 ns instead of 8 ns in Chapter ??. Furthermore, in
order to have a sufficient accuracy in the following imaging process, Tequiv = 4 ps is
used, which means that N = 1000 equivalent samples in one 4 ns period are acquired.
Moreover, parameter M , which determines the real sampling frequency, is limited
by the implementation of the following THA/ADC blocks. The choice of M = 251
results in Tsample = (251/1000) 4 ns = 1.004 ns, compatible with the chosen ADC
resolution.Each sample is acquired K = 50 times and averaged. It can be observed
that increasing K up to 50 results in increasingly better results. Beyond 50 the
advantage in terms of noise reduction is marginal and there is a negative impact on
the overall execution time of the measurement.
The gray box in the block scheme in Figure 6.2 encloses the CETS-based receiver. PLL, TDC and ADC are described behaviorally in VHDL-AMS (hence their
different coloring in Figure 6.2). PLL’s critical parameter is the jitter of the generated sampling clock, which we consider in its behavioral model. The RMS jitter
that a typical PLL can achieve is less than 0.2% of the operation period [83]. In
this system 0.2% is about 2 ps as selected in Chapter 4. The TDC is modeled as
an ideal 11-bit converter with 2 ps resolution, which can also be achieved in existing
technologies [84][85]. At the sampling frequency at stake, the ADC can be implemented with a resolution of 12 bits [86][87]. The different color of two blocks LNA
and THA in Figure 6.2 indicates that they are modeled both in VHDL-AMS and as
transistor-level components. The digital process block has been modeled in VHDL.
6.2.5
Imaging Unit
As usual, MIST beamforming algorithm is used to reconstruct the imaging. It is
implemented in Matlab. For comparison purpose, Figure 6.3 (a) is obtained with an
ideal calibration that subtracts, signal by signal, the response without tumor from
118
6.3 – Methodology
Figure 6.2. Gray box encloses the architecture of the CETS-based receiver.
All mixed-signal and analog blocks have a VHDL-AMS description, but LNA
and THA also have a Spice transistor-level description. CETS digital back-end
block has a VHDL description.
the response with tumor. The ideal calibration is of course not feasible in practice,
but the comparison of its results with those of a real calibration helps evaluate the
performance of the latter. Figure 6.3 (b) reports the result obtained with MIST
after the SKAR calibration introduced in [33]: the tumor is clearly evident and the
maximum energy of tumor response is in the same location of the ideal calibration
(88 mm, 88 mm). The standard metrics SMR and SCR are also used to evaluate the
effectiveness of imaging.
For the cases in Figure 6.3, SMR is 18.5 dB with ideal calibration and 16.7 dB
with real calibration. SCR is 8.33 dB with ideal calibration and 7.91 dB with real
calibration.
6.3
Methodology
To evaluate the performance of the UWB imaging system as progressed in the refinement of its description, a first ideal version is also implemented and referred as
golden case in the remainder of the thesis. Various refined versions are compared to
the golden case and this comparison is executed for the two breast models introduced
in Chapter 2. In both cases a 4-mm tumor is placed in the middle location within
the breast, corresponding to position (88 mm,88 mm) in the 2D map of dielectric
properties of the breast.
Firstly, the comparison of the golden case with ideal breast with seven other
refined cases are discussed, case-1 to case-7. Then the breast model is changed and
the golden case with real breast is compared with a final case, which is called as
case-8. Table 6.1 summarizes the various cases and their main features.
In the two golden cases, the entire system is modeled in Matlab, including FDTD
119
6 – System performance evaluation
(a)
(a)
(a)
(b)
(b)
Figure 6.3. Images reconstructed using MIST. (a) Skin artifact removed by ideal
calibration and (b) by real calibration. The tumor is enclosed by a contour level
set to a value slightly lower than the maximum energy found in the map.
channel model and back-end processing. To determine a performance upper bound,
noise sources and other non-idealities are ignored. For instance, the TDC and the
ADC in the golden cases have infinite resolution – 64-bits double precision numbers is
used – and have no saturation or input range limitations. The same holds for LNA,
THA and antennas, assumed as ideal components without bandwidth limitations
nor limits in dynamics determined by a finite supply voltage. Data fed to the image
reconstruction algorithm have highest resolution and accuracy. The MIST image in
120
(b)
6.3 – Methodology
Case
Description
golden
with
ideal breast
Matlab description of the imaging system, case of homogeneous breast, tumor in middle position.
case-1
Receiver blocks in behavioral VHDL-AMS, limited resolution and input range as well as saturation effects of
ADC (12 bits) and TDC (11 bits).
case-2
Like case-1, with AMS modeling of noise (thermal, clock
jitter), bandwidth limitations and non-linearity.
case-3
Like case-1, with custom-designed antenna.
case-4
Like case-1, with transistor-level LNA description.
case-5
Like case-1 with transistor-level THA description.
case-6
Like case-1, with both transistor-level LNA and THA.
case-7
Like case-2, with custom antenna, LNA, and THA.
golden with real Like golden case with ideal breast, but with a heterogebreast
neous breast model taken from [21].
case-8
Like case-7, but with heterogeneous breast model.
Table 6.1.
Description of the simulation cases.
Figure 6.3 (b), which commented on above, represents the energy map obtained in
the golden case with ideal breast.
The first refined version, case-1, has been obtained by removing from Matlab
the description of the receiver, and by building a VHDL-AMS model of it to be
run within ADMS. The rest of the system keeps being modeled in Matlab, and
file exchange acts as interface between Matlab and ADMS. In this version, all the
receiver blocks in Figure 6.2 are individually and behaviorally modeled. Every block
has its own VHDL-AMS entity and architecture, and together they form a structural
netlist. The structural description is a necessary step toward the refinement of the
description of the other cases in Table 6.1. Noise source and bandwidth limitations
are not considered yet, but a limited resolution and input range of ADC and TDC are
introduced. Saturation effects determined by the supply voltage are also modeled.
Simulations in case-2 to case-8 are evolutions of case-1. The effect of noise, finite
bandwidth and non-linearity are firstly considered. Then the substitute-and-play
approach described in [42] is applied to refine the description of the blocks. First the
hertzian dipole is replaced with a custom-designed slot antenna. The evaluations are
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6 – System performance evaluation
continued by replacing the VHDL-AMS models of LNA and THA with their Spicelevel description, one by one or combined. Finally all the non-idealities are put
together. This approach permits to keep the overall system architecture unchanged
across the multiple cases, to reuse the same testbench, and so to easily compare the
results.
Details about implementation of the blocks and modeling issues are reported in
the next section, together with the results of the simulations of the various cases.
6.4
Simulation results
The refinement of the description shows how the various non-ideal effects determine
a performance degradation with respect to the golden cases. The impact the reduction of abstraction has on performance qualitatively is determined, by visually
comparing the images obtained in the various cases to the golden images, and quantitatively, by comparing SMR and SCR values to the corresponding golden values.
Case-1: In case-1 all the blocks are still described behaviorally. The modeled
non-idealities are finite resolution of ADC and TDC, input range limits of ADC and
saturation effects. Assuming that the voltage cannot exceed the range from 0 V to
1.2 V in any point in the chain that goes from LNA to ADC. This range comes from
power supply limits of the technology that will be use in the next steps. The LNA
voltage gain is set to 5 (14 dB) and the THA gain to 1 (0 dB).
Figure 6.4 reports signals from case-1 simulations and shows the transmitted
pulse, the pulse at the input of the receiver, and the pulse at the output of the block
that models the LNA. The zoomed part is where the tumor information is.
The dynamic range of the signal is on the order of 70 dB, which has two consequences. First, the high gain needed to sense the small tumor information determines
a substantial distortion of the first part of the signal, which contains the large echo
of the skin back-scatter. The effect can be seen in the saturation of the LNA output in Figure 6.4. Since this distortion does not modify the part of the signal that
conveys the tumor information, it has little or no effect on performance.
The second consequence is that at least a 12-bit ADC is required, as referring to
the value defined in Chapter 4. The flexibility of VHDL-AMS allows to explore the
design space. Simulation experiments with a 12-bit and a 16-bit ADC model have
been executed. SCR and SMR metrics have been compared, and visually inspected
the energy maps. Since the difference is around 0.5 dB in terms of SCR and SMR
values, and the two maps are almost indistinguishable to the naked eye, a 12-bit
ADC is selected for this receiver.
SCR, SMR, and position of the tumor for case-1 are reported in Table 6.2, which
also reports all the values found in the various cases. Likewise, Figure 6.8 reports
122
6.4 – Simulation results
Transmitted Pulse
Received Pulse
LNA Output Pulse
1
Amplitude (V)
0.5
0
0.0015
0.001
0.0005
0
-0.0005
-0.001
-0.0015
-0.5
-1
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2
0
0.5
1
1.5
2
2.5
Time (ns)
3
3.5
4
Figure 6.4. Example of signals from case-1 simulation. The inset expands the time
region associated with the tumor information.
all the energy maps. By comparing case-1 to the golden case with ideal breast, the
impacts of ADC, TDC, and saturation are quantifies as about 1.0 dB in terms of
SCR and SMR. The maximum of the energy response is within the 4-mm tumor
region, albeit displaced by 1 mm compared to the golden case.
Case-2: In case-2 bandwidth limitations, thermal noise, clock jitter and nonlinearity are added, which are modeled in VHDL-AMS and parametrized to permit sensitivity analyses. The results obtained with the following parameters are
reported, which are reasonable and consistent with the state of the art: 3-dB bandwidth between 0.5 GHz and 10 GHz; LNA gain, noise figure, and third-order intercept points 14 dB, 5 dB, and -3 dBm, respectively; 150 fF for the KT/C noise of the
THA; 2 ps RMS jitter noise; standard value of input thermal noise at 300 K, modeled
as additive gaussian noise.
As stated above, the CETS acquisition is repeated K = 50 times and the samples
are averaged. Figure 6.5 shows the 50 sampled signals overlapped and the average
signal after reordering. Zoomed insets in Figure 6.5 show that averaging reduces the
effect of noise sources, particularly in the region around the small tumor information.
The TDC values obtained in K experiments are therefore averaged to minimize the
effect of PLL’s jitter.
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6 – System performance evaluation
Ensamble Received Signals
Average Signal
1.2
Amplitude (V)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
Time (ns)
3
3.5
4
Figure 6.5. Ensemble received and reordered signals (K=50) and average signal
in case-2, with thermal noise, jitter and quantization. Insets show effectiveness
of average in mitigating these effects, especially around the time region where the
small tumor information is present.
Results in Table 6.2 and Figure 6.8 show that the various impairments have small
effect. The tumor is clearly visible, but the clutter is more evident. SMR and SCR
are about 1 and 2.7 dB smaller than in golden case.
Case-3: In case-1 and case-2 the antenna is modeled as an ideal hertzian dipole,
which is replaced by a real microstrip slot antenna that was designed in Chapter 5
in this case.
To analyze separately the effect of the antenna, in case-3 noise sources and
all other linear and non-linear distortions of case-2 are removed. The antenna is
modeled as a 2-port network, with S-parameters [50] as a function of frequency,
and replaced in VHDL-AMS the ideal model with the refined one. The relationship
between antenna input pulse and output pulse is represented by the insertion loss
S21 , which is calculated by the following equation [50].
|S21 | =
p
(G(1 − |S22 |2 ))
(6.1)
where G is the antenna power gain, S22 is the same with S11 of the antenna, as
assuming antennas have the same characteristics in transmitting and receiving mode.
124
6.4 – Simulation results
Results in Figure 6.8 and Table 6.2 show the the effect of the antenna is very
small, if comparing SMR, SCR and the map to case-1 in which an ideal antenna is
used.
In addition, as mentioned in Section 6.2.2, the monostatic approach requires an
additional circulator or quasi-circulator with sufficient isolation between transmitter
and receiver in the whole bandwidth. The coupling between transmitter and receiver
of a non-ideal circulator is modeled. Results show that SMR has 0.3 dB reduction
and SCR has 0.03 dB reduction when the isolation is set to -18 dB. Therefore the
circulator that would be used must feature an isolation of -18 dB or better, which
can be easily achieved [82][88].
Case-4: Thanks to the flexibility offered by Mentor Graphics’ ADMS, the
VHDL-AMS behavioral model of the LNA can be replaced by a transistor-level
Spice netlist which will be exported from Cadence software. The entity declaration
does not change, nor does the structural description at the upper hierarchy level
The antenna in case-3 is single-ended, so a balance-unbalance (balun) transformer is required when connecting the antenna to the differential LNA. The balun
should cover the whole bandwidth and have small insertion and return losses. Several papers show an insertion loss smaller than 2 dB in a 7.5-GHz bandwidth [89]
[90]. This typical value is used as a model parameter of the balun when we evaluate
the system performance.
As shown in Section 5.2, the impedance mismatch (S11 and S22) of the designed
LNA is less than -10 dB from 500 MHz to 12 GHz, and the gain is between 14.5 and
17.2 dB. The noise figure ranges from 3.1 to 4 dB between 2 and 12 GHz. However,
the simulated nonlinearity parameter IIP3 is -16 dBm at 5 GHz. The nonlinearity
will mainly influence the skin backscattered part of the received pulses, because the
tumor information part is weak and so not influenced by nonlinearity. Since the
distorted skin-reflected part will be erased through a careful calibration, as shown
in Figure 3.10, there will be no effect of this distortion.
Full-system simulations are run as the other cases, both including and not including the LNA post-layout parasitic parameters. Results in Table 6.2 refer to the
case in which parasitics are included. The evaluated performance without parasitic
parameters shows a reduction of about 1.1 dB and 2.6 dB of SMR and SCR, respectively, compared to the golden case. When parasitics are taken into account, SMR
and SCR in Table 6.2 are 2.5 dB and 3.6 dB less than the golden case, respectively.
The map in Figure 6.8, accordingly, exhibits a more energetic clutter than in the
case without parasitics (not reported).
Case-5: Similarly to case-4, the THA behavioral model is replaced by the
transistor-level netlist of a circuit designed in the same 130 nm CMOS technology.
Figure 6.6 reports waveforms obtained from full-system simulations and shows
125
0.4
THA Output
0.2
0
-0.2
-0.4
1.6
1.2
0.8
0.4
0
THA Clock
40
42
44
46
48
Time (ns)
50
Voltage (mV)
THA Input
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
Voltage (mV)
1.5
1
0.5
0
-0.5
-1
-1.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
Voltage (V)
Voltage (V)
Voltage (V)
Voltage (V)
6 – System performance evaluation
52
54
(a)
1.6
1.2
0.8
0.4
0
45.5
THA Input
1.04mv
THA Output
0.8mv
THA Clock
46
46.5
47
Time (ns)
47.5
48
48.5
(b)
Figure 6.6. ADMS simulation result showing the behavior of THA when tracking
and holding one of the received signals.
that the received signal is correctly tracked and held by the THA. It also shows
that the sampling clock correctly drifts in time with respect to the pulse repetition
clock, hence permitting the acquisition of different samples as we exemplified in Figure 4.4. Figure 6.6 (b) is a zoom of Figure 6.6 (a) and shows the part of the signal
that contains the weak tumor information, also correctly sampled. The period of the
sampling clock is 1.004 ns, according to the specifications outlined in Section 6.2.4,
with 32 ps rise time and 28 ps fall time, as determined by the clock buffer. Figure 6.6
(b) shows that the gain of the THA in track phase is about 0.8/1.04=0.769, which
corresponds to -2.28 dB. More detailed AC simulations show that the gain is -2.5 dB
over a 12-GHz 3-dB input bandwidth (refer to Section 5.3). The output/input ratio
that one can measure in Figure 6.6 (a) is less than -2.5 dB due to the gain compression determined by nonlinearity. As stated above, however, the skin reflected part
of the pulse that causes nonlinearity effects will be eliminated through calibration.
The imaging performance has been assessed using the THA with post-layout
parasitic parameters as well as THA without parasitics, and the similar SMR is obtained and only 0.6-dB SCR reduction when parasitics are included. SMR and SCR
in Table 6.2 include parasitics and are close to the golden case values. Accordingly,
the map in Figure 6.8 has a clear energy peak. These results confirm that the CMOS
THA block works nearly as well as its ideal version.
Case-6: In case-6 both the LNA and THA VHDL-AMS models are replaced
with Spice netlists annotated with layout parasitics. As expected, the clutter in
Figure 6.8 is more evident. Likewise, SMR and SCR are worse than values obtained
126
6.4 – Simulation results
in case-4 and case-5, in which the two circuits were tested separately (see Table 6.2).
Still, the tumor is correctly identified.
Case-7: This is the worst among the cases of ideal breast, because the realistic
antenna, LNA and THA are all put together, and on top of that all noise and jitter
sources are enabled. It is pleased to observe that all the components combined
perform, at system-level, as well as when each is separately considered, even under
worst noise and jitter. SCR, SMR, and energy map are similar to previously analyzed
cases.
In this case, the effect of reducing the tumor size below 4 mm are also evaluated. The graphs in Figure 6.7 show the simulated system performance metrics
as a function of the tumor size. It is possible to see that the system performance
increases with the increase of tumor size. A tumor having a diameter as small as
2 mm yields 10.3 dB SMR and 1.5 dB SCR, which are values that make the tumor
hardly detectable.
14
SMR
12 SCR
10
8
dB
6
4
2
0
-2
-4
0.5
Figure 6.7.
1
1.5
2
2.5
3
Tumor size (mm)
3.5
4
4.5
System metrics (SMR, SCR) as a function of tumor’s size.
Golden case with real breast model: Results obtained in the golden case
with a real breast model are significantly different than those obtained in the golden
case with an ideal breast model. Tumor detection is more challenging, because
different tissues have different propagation velocity, which makes the alignment of
received signals a more complex task. A greater signal attenuation decreases the
dynamic response of the tumor mass, which calls for a very sensitive receiver. On
127
6 – System performance evaluation
Case
SMR
(dB)
SCR Tumor position
(dB)
(mm,mm)
golden ideal breast
case1
case2
case3
case4
case5
case6
case7
16.76
16.00
15.81
15.80
14.26
16.03
13.50
13.01
7.91
6.96
5.19
7.09
4.37
5.43
3.22
3.50
88,88
88,87
88,87
88,87
90,88
89,87
91,88
89,88
golden real breast
case8
13.11
13.06
2.44
1.98
82,84
86,82
Table 6.2. Signal-to-Mean Ratio (SMR), Signal-to-Clutter Ratio (SCR), and tumor estimated position for the cases outlined in Table 6.1.
top of that, each dielectric discontinuity generates a reflection that makes the clutter
response larger.
The map in Figure 6.8 exhibits a more evident clutter and more than one point
with a very high reflected energy. Consequently, SCR in Table 6.2 is small (2.4 dB).
SMR is still high, about 13 dB, which means that there is still a significantly
higher energy value in the tumor region than elsewhere. The tumor can still be
easily found, even though the estimated position is offset by 6 mm and 4 mm in the
two directions.
Since this is a golden case, the reduction of imaging performance with respect
to previous cases is determined by the more complex breast model and the MIST
limitations. Circuit-level effects are not yet considered.
Case-8: For sake of brevity, Results for all the intermediate cases as we did
for the uniform breast model are not reported. Instead, results for a case akin to
case-7 are reported, which is the worst case with ideal breast, with all sources of
non-idealities active, and with antenna, LNA, and THA circuits. Numerical results
in Table 6.2 are very close to the corresponding golden case with real breast, which
confirms that the effect of circuits and non-idealities is small. The reconstructed
map in Figure 6.8 shows that the tumor is still easily identified.
Given that the system performance metrics in this case of heterogeneous breast
are slightly worse than the performance in the homogeneous case, and based on the
results of Figure 6.7, is is possible to conclude that 4 mm is the limit size of a clearly
detectable tumor.
128
6.4 – Simulation results
Figure 6.8. Energy maps resulting from the system-level simulations of the various
cases outlined in Table 6.1 (energy unit is arbitrary). The tumor can be easily
identified in each of the reported maps, because it is enclosed by a contour level
that we set to a value slightly lower than the maximum energy.
129
Chapter 7
Conclusion
The work of this thesis aimed to develop an UWB imaging system for breast cancer
detection. The principle this diagnostic method relies on is the UWB microwave
radar imaging technique already used in ground-penetrating radar applications. It
is suited to breast cancer detection, because it is non-ionizing and so it can be repeated several times without incurring the problem of radiation typical of standard
methods like mammography, at the cost of a lower accuracy. Another advantage is
that it is potentially a lower-cost alternative to standard methods like the mentioned
mammography or other methods like magnetic resonance. Experiments with RF instrumentation proved this method capable of detecting small tumors, but adoption
in screening campaigns requires the replacement of RF tools with ad-hoc circuits
and systems: this is where the research conducted in my thesis fits in. In order
to do this, the overall simulation environment must be developed, which includes a
breast electromagnetic model obtained with an FDTD technique, antennas which
are put around the breast model and modeled as ideal dipoles, digital processing
which is used to reconstruct the breast image by a specific microwave imaging algorithm and UWB transmitters and receivers which connect to the antenna by means
of circulators. Initially all the system elements are described behaviorally and as
ideal components. The results of this system analysis reveal the functionality of
the imaging system, in the case of different breast model, different tumor size and
different tumor position. In addition, to save simulation time, the transfer functions
of the breast electromagnetic model were developed, and were verified to be able to
replace the time-domain model of real breasts reasonably.
Subsequently, the RF front-end was developed, especially the ad-hoc designed
receiver. The reason of this choice was that in this medical imaging application
the receiver was more important and difficult to implement than other parts, since
its requirements were quite strict, given that it had to cover the specific ultra-wide
bandwidth (from 3.1 to 10.6 GHz), while achieving very large dynamic ranges. There
were two candidates for the implementation of integrated receiver of the RF frontend:
130
one was the direct conversion (DC) receiver, the other was the coherent equivalent
time sampling (CETS) receiver. Primarily, the receivers were behaviorally modeled
and applied in the imaging system. Key impairments relating to the circuit design
were involved. The receivers performance was evaluated in terms of both qualitative
breast images and of specific quantitative metrics like SMR and SCR. In particular, the effects of transmitted signal power, analog-to-digital converter quantization,
noise, phase mismatches and non-linearity were evaluated. Considering the overall
behavior in terms of image quality, performance measured by SMR and SCR parameters, and data acquisition time. The CETS receiver was proved to outperform
the DC one, and was thus more suitable for this microwave breast cancer detection
application.
The aim of this work was also the hardware implementation. Two key elements
of the proposed CETS receiver, Low Noise Amplifier (LNA), and the Track-and-Hold
Amplifier (THA), have been designed and simulated in a CMOS 130 nm technology
using Cadence. The post-simulation results of the proposed LNA showed good
conversion gain and noise performance within the 3 dB bandwidth 2-12 GHz. The
designed THA achieved high linearity from 0 to 10 GHz and high sampling frequency
up to 4 GHz, which were suitable for this specific application. Moreover, an UWB
slot antenna was designed with HFSS software, it presented a less than -10 dB return
loss behavior from 2 GHz to 11 GHz.
Finally, in order to evaluate the system performance with these real designed
circuits, a different system environment was built, which was based on analog and
mixed-signal hardware description languages VHDL-AMS and on powerful tools like
Mentor Graphics’ ADMS. The system environment permitted to explore the refinement of this complex system in various design stages. To keep the consistency of
the system evaluation, the design flow started from a highly abstract description
of the system, and progressively refined it by replacing some of the most critical
blocks’ behavioral description with a lower-level description. The impacts of nonidealities like quantization, noise, jitter and input range limits on the performance
of the imaging system were evaluated. The effects at system-level of three critical
blocks were eventually determined, by replacing their behavioral description with
real transfer functions (antennas) or transistor level netlists obtained from previously designed in a 130 nm CMOS technology (LNA and THA). The simulation and
comparison results, which were obtained under both homogeneous breast model and
heterogeneous breast model, reveal that despite the design challenges that an UWB
imaging system poses, the system is capable of detecting a small 4 mm tumor, as
proved with accurate simulations on numerical breast phantoms.
131
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