24 GHz Patch Antenna Array Design for RADAR

24 GHz Patch Antenna Array Design
for RADAR
Karl Nordin
Sina Shamekhi
Department of Electrical and Information Technology
Faculty of Engineering, LTH, Lund University
SE-221 00 Lund, Sweden
Advisor:
Buon Kiong Lau
Examiner:
Mats Gustafsson
June 29, 2016
Printed in Sweden
E-huset, Lund, 2016
Abstract
Radar is a technology that is widely used in many diverse areas; from monitoring
space down to ocean surveillance, with many more applications in between. The
technology existed before, but was mainly developed in secret by several nations
during World War II. Radar technology uses radio waves to detect various kinds
of objects and can determine their range, velocity and orientation. It is, therefore,
an very attractive technology to be used for surveillance applications.
The main goal with the thesis is to create a non-expensive, fast and efficient
people detecting device that can be used for surveillance applications. The device
should be able to detect the position of people in the area under surveillance.
The motivation for using radar technology is that it is unaffected by poor weather
conditions or low visibility, unlike visual based surveillance systems.
Three different configurations of 24 GHz Frequency-Modulated Continuous
Wave (FMCW) patch antenna arrays were designed, manufactured and tested
with an existing radar. Different signal processing algorithms, so called Directionof-Arrival (DOA) methods, were also implemented in order to process the data
from the radar. The antenna array configurations showed good results, with one
of them showing a more robust performance overall.
Keywords:
Direction-of-Arrival (DOA), Frequency-Modulated Continuous Wave (FMCW),
Patch Antenna Array, Radar
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Acknowledgments
We would like to express our gratitude for all the people that have been involved
in helping and supporting us during the work of this thesis:
Our supervisor, Professor Buon Kiong Lau at the Faculty of Enginnering, LTH,
for his valuable and wise reflections, which have been very helpful for finishing this
work.
Our examiner, Professor Mats Gustafsson at the Faculty of Enginnering, LTH,
for all his helpful comments.
Alexander Bondarik, PhD student at the Faculty of Enginnering, LTH, for
helping us with the simulation software and the S-parameter measurements.
Our industrial supervisor Carl-Axel Alm for his encouragements throughout
the whole project and for giving us valuable and helpful insights, which we needed
and appreciate very much.
Johan Wennersten, for helping us implementing the algorithms and providing
with valuable knowledge.
Last but not least, the whole PCNI team for making our stay very enjoyable
and making us feel welcome. Thank you!
Lund, June 29, 2016
Karl Nordin & Sina Shamekhi
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Table of Contents
1
2
Introduction
1.1 Background . . . . .
1.2 Thesis Goal . . . . .
1.3 Thesis Work Division
1.4 Outline . . . . . . .
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Theory of Radar
2.1 Introduction to Radar Technology . . . . . . . . . . . . . . . . . . .
2.2 Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Pulsed Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4
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2.3.1
Maximum Unambiguous Range
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2.3.2
Range Resolution
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2.3.3
Usable Range
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Continuous Wave (CW) Radar . . . . . . . . . . . . . . . . . . . . .
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2.4.1
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Frequency-Modulated Continuous Wave (FMCW) Radar
Theory of Antenna and Propagation
3.1 Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . . .
3.2
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3.1.1
The Far Field and the Near Field
3.1.2
Beamwidth, Gain and Effective Aperture
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3.1.3
Bandwidth and Fractional Bandwidth
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Propagation Aspects . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.2.1
Wave Propagation Parameters
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3.2.2
The Friis Transmission Equation
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3.2.3
The Radar Range Equation
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3.2.4
Radar Cross-Section
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3.3
Antenna Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5
Microstrip Patch Antennas . . . . . . . . . . . . . . . . . . . . . . .
3.3.1
3.4.1
Antenna Array Synthesis and Design Methods
Virtual Array
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3.5.1
Input Resistance
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3.5.2
Guide to Design a Microstrip Fed Patch Antenna
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Range and Direction-of-Arrival Estimation Algorithms
4.1 The Fourier Transform . . . . . . . . . . . . . . . .
4.2 Introduction to Direction-of-Arrival Algorithms . . .
4.3 Array Synthesis Beamformers . . . . . . . . . . . .
4.4 Adaptive Direction-of-Arrival Algorithms . . . . . .
4.5 Capon/MVDR Beamformer . . . . . . . . . . . . .
4.6 Subspace Methods . . . . . . . . . . . . . . . . . .
4.6.1
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MUSIC Algorithm
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Software and Hardware Tools
5.1 Computer Simulation Technology (CST) . . . . . . . . . . . . . . .
5.2 INRAS Radarbook Description . . . . . . . . . . . . . . . . . . . . .
5.3 Verification of the Signal Processing Algorithms . . . . . . . . . . .
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5.3.1
Implementation of Direction-of-Arrival Algorithms
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5.3.2
Verification of Direction-of-Arrival Algorithms Using INRAS Frontend
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Proposal of Antenna Array Design
6.1 Azimuth-Elevation Visualization . . . . . . . . . . . . . . . . . . . .
6.2 Proposed Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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7
Simulation Results of Antenna Array Element
7.1 Design of 24 GHz Single Patch Antenna . . . . . . . . . . . . . . . .
7.2 Design of 4x1 Linear Patch Antenna Array . . . . . . . . . . . . . .
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7.2.1
7.3
7.4
7.5
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Feeding Network
Final Design
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7.3.1
First Design Configuration
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7.3.2
Second Design Configuration
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7.3.3
Third Design Configuration
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7.3.4
Final Design Configuration
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Simulation of 24 GHz Single Patch Antenna . . . . . . . . . . . . .
Simulation of 4x1 Linear Patch Antenna Array . . . . . . . . . . . .
Measurement Results
8.1 Manufactured Patch Antenna Arrays . .
8.2 Calibration . . . . . . . . . . . . . . . .
8.3 Measurement of S-Parameters . . . . . .
8.4 Tests with Direction-of-Arrival Algorithms
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8.4.1
Test Scenario One
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8.4.2
Test Scenario Two
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Discussion
9.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Direction-of-Arrival Algorithms . . . . . . . . . . . . . . . . . . . . .
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9.3.1
Implementation of MIMO
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9.3.2
Covariance Matrix Estimation Problems and Implications
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10 Conclusions
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11 Further Work
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References
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List of Figures
2.1
2.2
2.3
2.4
2.5
The radar transmits radio waves and receives an echo from the target. 6
Transmit and receive waveform envelopes for a pulsed radar system. .
7
Block diagram of a FMCW radar system [22]. . . . . . . . . . . . .
9
FMCW radar ranging with sawtooth modulation [22]. . . . . . . . . 10
FMCW radar ranging with triangular modulation [22]. . . . . . . . . 11
3.1
One of NASA’s big Deep Space Network (DSN) antennas located in
Goldstone, California [16]. . . . . . . . . . . . . . . . . . . . . . . .
3.2 Different arrangements of an antenna array [17]. . . . . . . . . . . .
3.3 Radiation patterns of λ/2 with different weights a. The radiation that
is not in the main lobe is called sides lobes. Broadside corresponds to
90◦ [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Radiation pattern when d exceeds the λ/2 criterion. As expected,
several maxima is present in different angels. These maximas are
called grating lobes. Broadside corresponds to 90◦ [17]. . . . . . . .
3.5 This figure shows the implication of the radiating properties of the
element to an array factor gain, the dotted line is the gain of a element.
This effect can be used to counter the high gain in the grating lobes
if a narrow-beam element is used [17]. . . . . . . . . . . . . . . . . .
3.6 This figure shows the difference between uniform and Dolph-Chebyshev
weights in a 21 element linear array. The acceptable side lobe level
is set to -30dB. The difference between the nearest sidelobe is clearly
visible [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 The beam pattern of the receiving array, the transmitting array and
the virtual array. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 A rectangular patch antenna. . . . . . . . . . . . . . . . . . . . . .
z
3.9 This shows the configuration of the electric field in the active T M010
mode. a is the width of the patch and b is the length [9]. . . . . . .
3.10 Resistance normalized at different y-positions. . . . . . . . . . . . .
3.11 A transmission line used as a quarter-wave impedance transformer. .
4.1
4.2
The frequency spectrum of a rectangular window [11]. . . . . . . . .
The frequency spectrum of a Chebyshev window, side lobe attenuation
is set to 100 dB [11]. . . . . . . . . . . . . . . . . . . . . . . . . . .
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4.3
4.4
The frequency spectrum of the Hanning window [11]. . . . . . . . .
Different antenna synthesis filters with a linear array of 8 antennas. .
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5.1
5.2
5.3
The INRAS frontend connected to the Radarbook. . . . . . . . . . .
Overall frontend architecture. . . . . . . . . . . . . . . . . . . . . .
A scheme explaining how the Fourier transformers are conducted to
get the range and Doppler frequency. These are performed individually
by each antenna [18]. . . . . . . . . . . . . . . . . . . . . . . . . . .
Flow chart explaining how the data processing is performed. Reflectivity is calculated by averaging all fast chirps instead of a single slow
one. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The downcoverted baseband signal received by the Radarbook, sampling rate is set to 0.5 MS/s. . . . . . . . . . . . . . . . . . . . . .
The frequency response of the received data using Chebyshev window
with 100 dB sidelobe suppression. . . . . . . . . . . . . . . . . . . .
The phase of the frequency spectrum. . . . . . . . . . . . . . . . . .
The Doppler frequency of a stationary range bin, chirp repetition rate
is set to 512 µs and a total of 128 chirps is measured. . . . . . . . .
Grid representation of the beamforming conducted on the range bin.
Illustration of the INRAS antennas with 2 Tx arrays and 8 Rx arrays.
During testing only 1 Tx array element was used. . . . . . . . . . . .
Picture of the area tested with the INRAS antennas. The person in
the picture is holding up an octahedral radar reflector. . . . . . . . .
Target map with the reflections shown, the received power (in dB
scale) is normalized by the strongest hit. . . . . . . . . . . . . . . .
The power spectrum for the Sum-and-Delay algorithm. . . . . . . . .
The power spectrum for the Capon/MVDR algorithm. . . . . . . . .
The power spectrum for the MUSIC algorithm. . . . . . . . . . . . .
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Array Factor pattern for 2 × 8 rectangular array. . . . . . . . . . . .
Array Factor pattern for 2 × 8 rhomboid array. . . . . . . . . . . . .
Array Factor pattern for 4 × 4 rectangular array. . . . . . . . . . . .
Array Factor pattern for 4 × 4 rhomboid array. . . . . . . . . . . . .
Total gain for the 2 × 8 rhomboid broadside array. . . . . . . . . . .
Total gain for the 4 × 4 rhomboid broadside array. . . . . . . . . . .
Total gain for the 4x4 rhomboid array. Beam steered in the direction
φ = 0°, θ = 70°. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total gain for the 4 × 4 rhomboid array. Beam steered in the direction
φ = 60°, θ = 70°. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The proposed designs and how the virtual arrays are created. . . . .
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5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.1
7.2
7.3
7.4
Single patch antenna with microstrip feed line [1]. . . . . . . . . . .
Ground plane consisting of 12 µm thick annealed copper. . . . . . .
Substrate consisting of 0.25 mm RO4350B with the dielectric constant
r = 3.48. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The patch consisting of 12 µm annealed copper added on top of the
substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
First the empty space is created and then the microstrip line is added
to the patch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The final design of the 24 GHz patch antenna. . . . . . . . . . . . .
4x1 linear patch antenna array. . . . . . . . . . . . . . . . . . . . . .
The feeding network for the 4x1 linear patch antenna array. . . . . .
First design configuration. . . . . . . . . . . . . . . . . . . . . . . .
Second design configuration. . . . . . . . . . . . . . . . . . . . . . .
Third design configuration. . . . . . . . . . . . . . . . . . . . . . . .
Final design configuration. . . . . . . . . . . . . . . . . . . . . . . .
Final design configuration with two extra antenna arrays used for
TDMA application. . . . . . . . . . . . . . . . . . . . . . . . . . . .
S11 of the 24 GHz single patch antenna. . . . . . . . . . . . . . . .
Z11 of the 24 GHz single patch antenna. . . . . . . . . . . . . . . .
Directivity of the 24 GHz single patch antenna. The dBi range is -32.9
dBi - 7.14 dBi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S11 of the 4x1 linear patch antenna array. . . . . . . . . . . . . . . .
Z11 of the 4x1 linear patch antenna array. . . . . . . . . . . . . . . .
Crosstalk of two λ/2-spaced antenna array elements. . . . . . . . . .
Directivity of the 4x1 linear patch antenna array in the azimuthelevation plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Directivity of the 4x1 linear patch antenna array. The dBi range is
-28.2 dBi - 11.8 dBi. . . . . . . . . . . . . . . . . . . . . . . . . . .
Picture of the manufactured antenna arrays. . . . . . . . . . . . . .
Picture of the backside with soldered rigid flex cables. . . . . . . . .
Measurement of S-parameters using the network analyzer. . . . . . .
S11 measurement of the 4x1 linear patch antenna array. . . . . . . .
Crosstalk measurement of two λ/2-spaced antenna array elements. .
The INRAS Radarbook with the frontend connected to the antenna
board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The reflector located R = 5.5 m from the radar with an azimuth angle
of φ = −43° and an elevation angle of θ = 100° relative to the radar.
Power spectrum of the Sum-and-Delay beamformer. . . . . . . . . .
Pseudo power spectrum of the Capon/MVDR algorithm. . . . . . . .
Pseudo power spectrum of the MUSIC algorithm. . . . . . . . . . . .
Power spectrum of the Sum-and-Delay beamformer. . . . . . . . . .
Pseudo power spectrum of the Capon/MVDR algorithm. . . . . . . .
Pseudo power spectrum of the MUSIC algorithm. . . . . . . . . . . .
The second reflector located R = 5.3 m from the radar with an azimuth angle of φ = 22° and an elevation angle of θ = 101° relative to
the radar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Power spectrum of the Sum-and-Delay beamformer. . . . . . . . . .
Pseudo power spectrum of the Capon/MVDR algorithm. . . . . . . .
Pseudo power spectrum of the MUSIC algorithm. . . . . . . . . . . .
Power spectrum of the Sum-and-Delay beamformer. . . . . . . . . .
Pseudo power spectrum of the Capon/MVDR algorithm. . . . . . . .
Pseudo power spectrum of the MUSIC algorithm. . . . . . . . . . . .
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List of Tables
2.1
Radar frequency bands (in some definitions the mm band is classified
from 30-300 GHz; therefore, including the V- and W bands and part
of the Ka band) [4, 22]. . . . . . . . . . . . . . . . . . . . . . . . .
6
5.1
INRAS antenna parameters [12]. . . . . . . . . . . . . . . . . . . . .
48
8.1
8.2
Calibration coefficients calculated for 2 × 8 rhomboid configuration. .
Calibration coefficients calculated for 4 × 4 rhomboid configuration. .
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xiv
Chapter
1
Introduction
RAdio Detection And Ranging (RADAR) [4] is a technology that is used in numerous diverse applications, such as air traffic control, meteorological monitoring,
astronomy, ocean surveillance, guided missile target location systems, automotive
safety and many more. It is used to detect various kind of objects and has the
ability to determine their range, velocity and orientation.
The earliest significant achievements in radar technology were made during
World War II along with many other technological advancements. This is also
where the term "radar" was coined by two U.S. Navy officers Samuel M. Tucker
and F.R. Furth in 1940. Radar technology has since then grown fast and is today
not exclusive to the military but also used in commercial applications such as
weather monitoring, traffic speed control and air traffic control [4].
The simplest form of a radar system is made of a radio transmitter which sends
out electromagnetic pulses that bounce off an object and a receiver which collects
and processes the reflected waves. The physical aperture that is able to radiate or
receive these pulses is called an antenna (see Ch. 3).
Radars can be divided into two different classes [4]:
• Pulsed radars
• Continuous wave (CW) radars
Pulsed radars, which are the most common, transmit a sequence of pulses at a
certain frequency. They can use the same antenna for transmitting and receiving
the signal by using a transmit/receive (T/R) switch. This kind of radar setup is
called a monostatic radar. The CW radars transmit a continuous signal and uses
separate transmit and receive antennas. This is due to it being difficult to receive
a signal with full sensitivity through an antenna while it is transmitting. A radar
system which uses separate antennas that are well separated is called a bistatic
radar [6].
1.1 Background
There are many different applications where a people detecting device could be
of interest. One example is various traffic applications, such as counting and
detecting people on railroads. Modern surveillance cameras are widely used to
1
2
Introduction
monitor break-ins and prevent crime. However, under some conditions surveillance
cameras can have difficulty distinguishing between different objects. This can
happen when there is insufficient lighting, poor weather conditions, low visibility
or other factors. This is where radar technology can help the camera in detecting
objects. By the use of radar technology, the camera can respond to the signals
from the radar and attempt to detect an object where it otherwise would not be
able to.
1.2 Thesis Goal
The goal of the thesis is to investigate the opportunity of creating a non-expensive,
fast and efficient people detecting device with the help of radar technology. Different designs of state-of-the-art 24 GHz Frequency-Modulated Continuous Wave
(FMCW) patch antenna arrays will be designed and thereafter their properties and
performance will be investigated. The specific objective is to design the device to
simultaneously detect the position of one or more persons.
Can the radar can be precise enough to distinguish between human beings and
other objects? What happens if the objects are moving? Which design methods
are suitable to build a low cost radar system without sacrificing too much in
performance? Can more advanced methods using covariance matrix estimation
be used to get higher resolution and robust performance? In this work, we will
attempt to answer some of these questions.
1.3 Thesis Work Division
This thesis is written by Karl Nordin and Sina Shamekhi for the Department of
Electrical and Information Technology at the Faculty of Engineering, LTH, Lund
University.
For this thesis report, most of the work was divided between the two authors
as follows:
Karl Nordin worked primarily with implementing the different Direction-ofArrival (DOA) algorithms and wrote all sections concerning this topic as well as
part of the design work in Computer Simulation Technology (CST). Furthermore,
he wrote the chapters Software and Hardware Tools, Proposal of Antenna Array
Design and Further Work as well as the sections about antenna arrays and MIMO
technology.
Sina Shamekhi mainly worked with the simulations and designs in the software
program and wrote the Abstract, Introduction and chapters Theory of Radar and
Simulation Results of Antenna Array Element. Furthermore, he wrote the sections
about antenna characteristics and propagation aspects.
The two authors have jointly wrote the Acknowledgments, the chapters Measurement Results, Discussion and Conclusions, as well as discussed and worked
together to improve the language, the flow and the overall structure of the thesis.
Introduction
3
1.4 Outline
In Ch. 2 the general theory of radar is explained. Ch. 3 gives an introduction
to the theory of antenna and propagation aspects. Ch. 4 goes through different
signal processing methods, specifically Direction-of-Arrival (DOA) methods, that
are necessary to calculate the direction of the object(s) to be detected relative to
the radar. Ch. 5 describes the software and hardware tools that have been used.
Ch. 6 shows the proposed setup of antenna arrays and Ch. 7 goes through the
design as well as presents the simulation results. The measurement results are
presented in Ch. 8 followed by a discussion of the results in Ch. 9. Final thoughts
and conclusions are presented in Ch. 10, followed by several suggestions for further
work in Ch. 11.
4
Introduction
Chapter
2
Theory of Radar
In this chapter general theory of radar technology is presented as well as some
information about the different types of radar systems. Sec. 2.1 gives a short
introduction to radar technology with Sec. 2.2 presenting the frequency intervals
used for radar systems. The pulsed radar is described in Sec. 2.3 and finally Sec.
2.4 describes the continuous wave (CW) radar system.
2.1 Introduction to Radar Technology
RAdio Detection And Ranging (RADAR) is a system which uses radio waves to
detect various objects such as people, aircrafts, vehicles, ships and missiles. The
simplest form of a radar system consists of a radio transmitter and a receiver. The
transmitter radiates electromagnetic waves with a specific wavelength which are
reflected or scattered of objects and then collected by the receiver. In free space
the electromagnetic waves travel at the speed of light and by measuring the roundtrip time (the time from when an electromagnetic wave is transmitted, reflected
or scattered from an object and received), the range to the target can be obtained
[4, 6]. This is illustrated in Fig. 2.1, where it can be understood that the range to
target is given by [4]
R=
c0 t
2
(2.1)
where c0 is the speed of light in free space (3 · 108 m/s) and t is the round-trip
time.
5
6
Theory of Radar
Figure 2.1: The radar transmits radio waves and receives an echo
from the target.
2.2 Frequency Bands
Radars operate in a wide interval of frequencies; from 3 MHz up to 300 GHz. The
radar frequency interval is usually divided into different sub bands and is presented
in Table 2.1
Band
HF
VHF
UHF
L
S
C
X
Ku
K
Ka
V
W
mm
Frequency range
3-30 MHz
30-300 MHz
300-1000 MHz
1-2 GHz
2-4 GHz
4-8 GHz
8-12 GHz
12-18 GHz
18-27 GHz
27-40 GHz
40-75 GHz
75-110 GHz
110-300 GHz
Name
High Frequency
Very High Frequency
Ultra High Frequency
Long
Short
Compromise between X and S bands
X stands for "cross", as in "crosshairs"
Under K band
From the German word Kurz,
which means short
Above K band
Very short
W follows V
Millimeter wave band
Table 2.1: Radar frequency bands (in some definitions the mm band
is classified from 30-300 GHz; therefore, including the V- and
W bands and part of the Ka band) [4, 22].
Theory of Radar
7
2.3 Pulsed Radar
A pulsed radar system consists of a transmitter Tx that transmits a sequence
of pulses, a receiver Rx that amplifies and demodulates the received signals and
a duplexer that switches between the transmitter and receiver so that only one
antenna is used. The transmitter sends each pulse at the carrier frequency during
transmit time, waits for returning echo signals, and then sends out the next pulse.
The time from the start of one pulse to the beginning of the next is called the
pulse repetition time PRT. The number of pulses that are transmitted per second
is called the pulse repetition frequency PRF and is related to the PRT by [4]
1
(2.2)
P RT
Figure 2.2 shows the transmitted and received pulses. The pulse width is
denoted τp and the round-trip time t is the time it takes for the pulse to travel
the two-way direction between the radar and the target. The distance to target R
is then given by (2.1).
P RF =
Figure 2.2: Transmit and receive waveform envelopes for a pulsed
radar system.
2.3.1 Maximum Unambiguous Range
In pulsed radar systems the echo from a target must be detected before the next
transmitted pulse is generated. If the time for the received echo to return from a
target is greater than the pulse repetition period PRT, then there exists a range
ambiguity (an uncertainty in measuring range). The maximum unambiguous range
is defined as [4]
cP RT
c
=
(2.3)
2
2P RF
More advanced radar systems can avoid this problem by the use of multiple
PRFs either on the same single frequency with the PRT changing or simultaneously on different frequencies [4].
Ramb =
8
Theory of Radar
2.3.2 Range Resolution
The range resolution measures how well a pulsed radar distinguishes between two
targets, or more, that are close to each other. Two objects close to each other need
to be separated with at least half the pulse width in order for the radar to receive
two distinct echo signals. The range resolution is given by [22]
cτp
(2.4)
2
If the distance between two targets is smaller than the range resolution, then
the radar will only see one object [22].
∆R ≥
2.3.3 Usable Range
Pulsed radar systems usually use the same antenna for transmitting and receiving
signals (for monostatic radar setups). When the system is transmitting a pulse the
radar can not receive an echo signal. Therefore, the radar has a minimal usable
range, blind range, which is the minimum distance the target must have for the
radar to be able to detect it. The minimal usable range is given by [22]
c(τp + trecovery )
(2.5)
2
where trecovery is the time it takes for the system to switch on the receiver.
If the echo signal from a target arrives at the receiver too close to the next
transmit pulse, then it will prevent the entire pulse from entering the receiver
before it turns off for the next transmit pulse. The maximum usable range at
which the target can be located to guarantee that this does not occur is given by
(2.6) [4].
Rmin =
Rmax =
c(P RT − τp )
2
(2.6)
2.4 Continuous Wave (CW) Radar
Continuous Wave (CW) radar is a type of radar system where a signal with known
frequency is continuously transmitted. It differs from the pulsed radar system by
using a continuous signal and separate transmit and receive antennas.
The received echo signal from the object will either have the same frequency
as the transmitted signal or be shifted if the object is moving. This change in
frequency between the received and transmitted signal is known as the Doppler
effect [19]. The received frequency fr is related to the transmitted frequency ft
by [19]
1 + v/c
fr =
ft
(2.7)
1 − v/c
where c is the speed of light and v is the velocity of the moving object (in the
direction to or from the transmitter/receiver). The Doppler frequency fd is then
given by [19]
Theory of Radar
9
fd = fr − ft =
2v
ft
(c − v)
(2.8)
Since in most applications v c, it is possible to simplify (2.8) to [19]
2v
2v
ft =
(2.9)
c
λ
where λ is the wavelength of the signal that is transmitted.
This kind of radars that uses the Doppler effect without any modulation (so
called Doppler radars) can only detect moving objects, since stationary targets
will not cause any Doppler shift. Therefore, it is not possible to determine the
range to target; only the velocity of the moving object [19].
fd =
2.4.1 Frequency-Modulated Continuous Wave (FMCW) Radar
Frequency-Modulated Continuous Wave (FMCW) radar is a radar system where
a transmitted continuous signal with known frequency is varied up and down in
frequency over a fixed period of time by a modulating signal. The modulation in
frequency will allow for distance measurements along with speed measurements
[22].
The difference in frequency between the received and transmitted signal will
increase with delay and, therefore, also with distance. The received echo signals
from the target are mixed with the transmitted signal, which after demodulation
will give the range to target [22]. Figure 2.3 shows a block diagram of a FMCW
radar system.
Figure 2.3: Block diagram of a FMCW radar system [22].
10
Theory of Radar
The frequency modulation can be achieved with several different modulation
patterns, including:
• Triangle wave
• Sawtooth wave
• Square wave
• Sine wave
The basic principle behind the FMCW radar system using a sawtooth modulation
is shown in Figure 2.4.
Figure 2.4: FMCW radar ranging with sawtooth modulation [22].
As seen in Figure 2.4, the received signal (the green wave) is a exact copy
of the transmitted signal (the red wave) but shifted in time, i.e., to the right in
the figure. This results in a frequency difference, called the beat frequency ∆f ,
between the two signals which is proportional to the time delay ∆t. The time
delay is therefore a measure of the range to target. If there is a Doppler frequency
fD present, it will move the entire received signal either up (moving towards the
radar) or down (moving away from the radar) in frequency [22].
The distance to target can be obtained from the beat frequency. The slope of
the linear ramp in the figure is
df
Bsweep
=
dt
Tsweep
(2.10)
where Bsweep is the the swept bandwidth and Tsweep is the sweep time. Since the
beat frequency is proportional to the time delay, the following relation is true
∆f
Bsweep
=
∆t
Tsweep
(2.11)
The time delay is simply ∆t = 2R/c, which gives that the beat frequency is
Theory of Radar
11
∆f =
Bsweep
Bsweep 2R
∆t =
·
Tsweep
Tsweep
c
(2.12)
and the range to target is obtained as [22]
R=
cTsweep
∆f
2Bsweep
(2.13)
Using a sawtooth modulation gives the receiver no way of separating between
the frequency difference and the Doppler frequency. Therefore, the Doppler frequency will show up as a measurement error in the distance calculation. In many
applications this error is negligible [22].
To resolve the Doppler frequency, a modulation pattern with two frequency
slopes can be used. The triangle wave modulation is usually a popular choice. The
operation of this modulation is shown in Figure 2.5.
Figure 2.5: FMCW radar ranging with triangular modulation [22].
This modulation pattern gives the possibility of distance measurement on both
the rising and on the falling edge of the slope. The radar will measure the Doppler
frequency fD additional to the frequency difference. The frequency difference
will provide the distance information, while the Doppler frequency will provide
the velocity information. If there would be no Doppler frequency present, the
frequency difference during the rising edge ∆f1 would be equal to the frequency
difference during the falling edge ∆f2 . The radar will either measure the sum or
the difference of these two frequencies; depending on the direction of the movement
and the direction of the linear modulation [22]. In Figures 2.4 and 2.5, the received
echo signal is shifted down in frequency due to a Doppler shift.
The triangular modulation pattern makes it possible to determine the distance
more accurately, despite the shift caused by the Doppler frequency. The beat
frequency is given by the arithmetic mean of the two frequency differences at the
edges of the triangular pattern [22]
∆f =
∆f1 + ∆f2
2
(2.14)
12
Theory of Radar
and from Figure 2.5 it is easy to see that the Doppler frequency is [22]
|∆f1 − ∆f2 |
2
Using (2.14) in (2.13), the range is obtained as
fD =
R=
cTsweep
(∆f1 + ∆f2 )
4Bsweep
(2.15)
(2.16)
and the velocity of the moving object can be determined from using (2.15) in (2.9)
v=
c
c
fD =
|∆f1 − ∆f2 |
2f0
4f0
(2.17)
where f0 is the center frequency, i.e., the frequency that lies in the center of the
swept bandwidth Bsweep .
Another way using only the sawtooth wave is the method of using fast chirps.
If the chirps are being sent quick enough, the Doppler frequency will be present
as a low frequency on top of each range frequency as described. Since the Doppler
frequency is typically much lower than that of the reflected frequency, it will when
performing FFT (which is described in Sec. 5.3) stay in the same frequency bin.
This can be directly translated as a velocity using (2.17).
Chapter
3
Theory of Antenna and Propagation
This chapter gives an introduction to useful concepts in antenna theory and wave
propagation, such as antenna characteristics, radar cross section, antenna arrays,
patch antennas and more. The basic characteristics for antennas is described in
Sec. 3.1 with Sec. 3.2 describing the propagation aspects. Sec. 3.3 explains how
antennas can be coupled together to form antenna arrays, Sec. 3.4 goes through
the technique of Multiple-Input Multiple-Output (MIMO) antenna and Sec. 3.5
presents the microstrip patch antenna.
3.1 Antenna Characteristics
An antenna is a device that converts electrical power into electromagnetic waves,
and vice versa. They are used to radiate and receive radar signals and come in
many different shapes. Figure 3.1 shows one of NASA’s big Deep Space Network
(DSN) antennas located in Goldstone, California.
Figure 3.1: One of NASA’s big Deep Space Network (DSN) antennas located in Goldstone, California [16].
13
14
Theory of Antenna and Propagation
The electromagnetic field around the antenna is generated by connecting an
electronic oscillator to the antenna and thereby causing electrons to accelerate.
This creates an current that is accelerating back and forth at the frequency of
oscillation. Maxwell’s equations states that a change in an electric field induces a
magnetic field and from this an electromagnetic field is generated [6].
3.1.1 The Far Field and the Near Field
The curvature of the electromagnetic field lines depends on the distance from the
antenna. The waves propagate away from the antenna in a spherical shape. The
further the waves travel away from the antenna, the more planar they become.
The distance R at which the electromagnetic field is considered to be a plane wave
is given by [6]
R=
2D2
λ
(3.1)
where D is the largest dimension of the antenna and λ is the wavelength of the
radio wave. The electromagnetic wave is said to be in the far field when R ≥ 2D2 /λ
and in the near field when R < 2D2 /λ [6].
3.1.2 Beamwidth, Gain and Effective Aperture
Antennas can be either directional or omni-directional. For directional antennas,
like satellite television dishes, the radiation is focused over a narrow field of view
and most of the gain is present in only one direction [6]. Omni-directional antennas
radiate in all directions and therefore the gain is not concentrated in one specific
direction. Examples of omni-directional antennas are cellular phone antennas, the
dipole antenna and AM/FM broadcast antennas [6].
The point at which the main beam gain has dropped 3 dB from maximum gain
is called the antenna beamwidth [6]. The half-power beamwidths in the electric
and magnetic field planes are denoted ΘE and ΘH and the antenna gain for a
directional antenna is approximately given by [6]
4π
GdB ' 10 log ρ
(3.2)
ΘH ΘE
where ρ is the antenna efficiency and usually ≥ 90%.
A cross section of the electromagnetic field is intercepted by the antenna and
can be expressed by the effective aperture. The effective aperture is closely related
to the antenna gain by [6]
Aef f =
Gλ2
4π
(3.3)
where G = 10GdB /10 . The effective aperture is not a representative of the physical
area of an antenna and can be larger in some cases, for example, the dipole antenna
[6]. It is often used as a performance parameter for radar systems since it is directly
linked to the 3 dB angular resolution ∆θ given in (3.4) [6].
Theory of Antenna and Propagation
∆θ =
15
λ
2Aef f
(3.4)
3.1.3 Bandwidth and Fractional Bandwidth
The bandwidth of an antenna describes the interval of frequencies over which
the antenna radiates or receives energy properly and can be expressed in many
different ways.
A very common way to determine if the antenna is narrowband or wideband
is to express the frequency range as a fraction of the center frequency fc , so called
the fractional bandwidth FBW and is defined as [3]
F BW =
fh − fl
fc
(3.5)
where the center frequency fc = (fl + fh )/2 lies between the lower frequency fl
and the higher frequency fh . The fractional bandwidth is often expressed as a
percentage, where the maximum limit is 200 %. Narrowband antennas normally
have a FBW of a few percentage, where wideband antennas have a FBW of 20 %
or more. Antennas with a FBW higher than 50 % are classified as ultra-wideband
antennas [3].
3.2 Propagation Aspects
The propagation aspects of the antenna depend on several different factors such as
power, gain, efficiency and more. Some of these aspects are described more closely
below in the following subsections 3.2.1 - 3.2.4.
3.2.1 Wave Propagation Parameters
The properties of the medium in which the electric and magnetic field lines propagate determines their velocity and the rate at which they form. These properties are determined by the parameters permittivity , permeability µ and loss
tangent σ. Since most radars are used in free space, these parameters become
0 = 8.854 · 10−12 (F/m), µ0 = 4 · π · 10−7 (H/m) and σ ≈ 0 (S/m). The wave
√
velocity is then given by 1/ 0 µ0 ≈ c0 (m/s) [6].
3.2.2 The Friis Transmission Equation
If the power input for a transmit antenna Ptx is known and the distance to a
receive antenna is R, then the power transmitted to the receive antenna Prx is
given by the Friis transmission equation [6]
Prx = Ptx Gtx Grx
λ
4πR
2
(3.6)
16
Theory of Antenna and Propagation
where Gtx and Grx are the antenna gains for the transmit and receive antennas
(assumes matched and polarization matched antennas). The Friis transmission
equation can be used to model the performance of radio communication [6].
3.2.3 The Radar Range Equation
The radar range equation is used to measure the performance of a radar system
and is given by (3.7) [6]
4
Rmax
=
Pave Gtx Arx ρrx σnEi (n)e(2αRmax )
(4π)2 kT0 Fn Bn τ Fr (SN R)1 Ls
(3.7)
where:
Rmax is the maximum range (m)
Pave is the average transmit power (W)
Gtx is the transmit antenna gain
Arx is the receive antenna effective aperture (m2 )
ρrx is the receive antenna efficiency
σ is the radar cross section of the target (m2 )
n is the number of received pulses integrated
Ei (n) is the integration efficiency
α is the attenuation constant of the propagation medium
k is Boltzmann’s constant, 1.38 · 10−23 J/K
T0 is the standard temperature, 290 K
Fn is the receiver noise figure
Bn is the system noise bandwidth (Hz)
τ is the pulse width (s)
Fr is the pulse repetition frequency (Hz)
(SN R)1 is the single-pulse signal-to-noise ratio requirement
Ls is the miscellaneous system losses
The average transmit power Pave is related to the duty cycle τ Fr of the transmitter by [6]
Pave = Pt τ Fr
(3.8)
where Pt is the root-mean square power of a single pulse. The receive antenna
effective aperture Arx and efficiency ρrx are related to the receive antenna gain
Grx in this equation by [6]
Grx λ20
(3.9)
4π
where λ0 is the center wavelength of the system. Impedance mismatch losses,
ohmic losses and other losses are all included in the antenna efficiency. For most
short-range radar systems used in free space the attenuation constant α is 0,
making the term e(2αRmax ) = 1 [6].
Two factors determine the single-pulse signal-to-noise ratio (SN R)1 : the specified probability of detection Pd and the probability of false alarm Pf a . Common
values are Pd = 0.95 and Pf a = 10−6 , making the (SN R)1 = 13.4 dB [6].
Arx ρrx =
Theory of Antenna and Propagation
17
In many cases the gain for the transmit antenna and receive antenna are equal,
Gtx = Grx = G [6]. Assuming e(2αRmax ) = 1 and substituting (3.8) and (3.9) into
(3.7), the radar range equation is simplified into
4
Rmax
=
Pt G2 λ20 σnEi (n)
(4π)3 kT0 Fn Bn (SN R)1 Ls
(3.10)
3.2.4 Radar Cross-Section
Radar Cross-Section (RCS), denoted σ, is a measure of how detectable an object
is with radar [22]. A large RCS is an indication that the target is easily detectable
and a low value makes it more hard to detect. The radar cross-section is defined
as [22]
Sr
(3.11)
σ = 4πr2
St
where Sr is the scattered power density seen at a distance r away from the target
and St is the power density intercepted by the target. The RCS has the unit of
m2 and is therefore an area. The maximum RCS for a perfectly spherical shape is
σmax = πr2 , where r is the radius of the sphere. This shows that the RCS is not
equal to the geometric area of the object [22].
There are several variables that affects the RCS but the main two are:
• Size and geometry
• Material
As a general rule, the larger an object is the greater is its RCS. A typical shape
with a low RCS is a flat surface or a geometry which minimizes the reflected energy
back to the transmitter. For materials, it depends on how much of the received
power that is reflected and how much that is absorbed by the target. If a target has
a metal surface, it usually has a very high reflection compared to other dielectric
materials. Metal objects can also work as mirrors, creating false targets and giving
several peak reflections from the signal originating from the same object.
3.3 Antenna Array
Antennas can be coupled together to form an array which can be used to enhance
the directional gain. The phase and amplitude can be modulated so that the
direction of the resulting beam can be controlled [17]. This means that controlling
the amplitude and phase of each element in the array can be equivalent of a
mechanically rotating antenna but without the need of moving parts, which can
be of benefit and important in our design. Depending on the configuration of the
arrays, different characteristics are set. The most common is the Uniform Linear
Array (ULA) that has a equidistant grid of antenna elements along a line [17].
This array can also be expanded to a two-dimensional structure with equidistant
length, which is called a Uniform Rectangular Array (URA). The URA has one
more degree of freedom which makes it possible to control the φ- and θ-directions,
18
Theory of Antenna and Propagation
compared to the ULA which can only control the θ-direction. Other common
configurations use circular/spherical symmetry, but they are disregarded since
they are inefficient in using space, which in our case is limited.
Figure 3.2: Different arrangements of an antenna array [17].
Electronically steering of the array is achieved by proper phase shifts of the
signals transmitted by different antennas. In certain directions the phases will
add constructively and in other they will add destructively. This is an effect of the
Fourier transform; a translation in space corresponds to a rotation of the phase
in the frequency domain. The radiation vector F describes the power density of
the radiated far field in the θ- and φ-directions for an individual antenna. The
total radiation vector containing all contributions for each antenna Ftot , can be
written as Ftot = A(k)F(k), where F(k) is the radiation vector and A(k) is the
array factor and is expressed as following in a n-length linear array [17]
A(k) = a0 ejk·d0 + a1 ejk·d1 + a2 ejk·d2 + a3 ejk·d3 + · · · + an ejk·dn
(3.12)
where k is the wave number, an are the weights for the corresponding element and
dn is the position of the element. To avoid grating lobes, the distance between
the element should be set to be smaller or greater than λ/2. The pattern of the
antenna array factor is only correct when the radiating element is isotropic, which
is not the case in real antennas. The total radiation pattern and the total power
gain is given by [17]
2
Utot (θ, φ) = |A(θ, φ)| U (θ, φ)
2
Gtot (θ, φ) = |A(θ, φ)| G(θ, φ)
(3.13)
where U (θ, φ) and G(θ, φ) are the radiation pattern and power gain of the radiating
element.
Theory of Antenna and Propagation
Figure 3.3: Radiation patterns of λ/2 with different weights a.
The radiation that is not in the main lobe is called sides lobes.
Broadside corresponds to 90◦ [17].
Figure 3.4: Radiation pattern when d exceeds the λ/2 criterion. As
expected, several maxima is present in different angels. These
maximas are called grating lobes. Broadside corresponds to 90◦
[17].
Figure 3.5: This figure shows the implication of the radiating properties of the element to an array factor gain, the dotted line is
the gain of a element. This effect can be used to counter the
high gain in the grating lobes if a narrow-beam element is used
[17].
19
20
Theory of Antenna and Propagation
For ULAs, the array factor in (3.12) has the form of a sinc-function [17]
sin N2ψ
(3.14)
A(ψ) =
N sin ψ2
where ψ = kd cos(φ). This array factor is the spatial analog of a low-pass FIR
filter in discrete time with a rectangular window function. This is only true if the
weights are equal on each element [17].
3.3.1 Antenna Array Synthesis and Design Methods
As described in Sec. 3.3, the amplitude and phase difference between antenna
elements give different radiation patterns. As mentioned in the previous section,
the method of synthesising the patterns is equivalent to designing FIR filters. It is
optimal to have the main beam in the broadside direction to maximize the effective
angular resolution given in (3.3). This implies that the phases are the same on each
element if a ULA with spacing of λ/2 is used. The first side lobe levels from (3.14)
reach a constant level approximately -13 dB of the main lobe, independent of the
number of elements in the ULA. In many applications these gain levels of the side
lobes are not acceptable. Since this problem is similar to a rectangular window
function, this function can be modified by the use of different weight functions.
There exist many different narrow beam low-sidelobe design methods.
The three standard methods other than the uniform weighting is DolphChebyshev, Taylor-one-parameter and binomial distribution [17]. Since the contribution of any other weight will smear out the main lobe, thus making it to
become wider. Dolph-Chebyshev weights were chosen since that method will for a
given side lobe level create the narrowest main lobe, which is desirable to reduce
the range of the radiation in elevation and to be maximized between −20° to 20°.
This method is constructed using Chebyshev polynomials. The mth Chebyshev
polynomial is [17]
Tm (x) = cos(m arccos(x))
The Dolph-Chebyshev array factor is then created by [17]
ψ
W (ψ) = TN =1 (x), x = x0 cos
2
(3.15)
(3.16)
The level of the side lobes which will be created depends on x0 and can be determined by [17]
arccosh(Ra )
x0 = cosh
(3.17)
N −1
where Ra = Wmain /Wsidelobe is the ratio between the height of the main lobe
relative to the side lobes in absolute value. The broadening of the main beam can
be expressed as [17]
∆φ3dB =
50.76◦ λ
b, 0◦ < φ0 < 180◦
sin φ0 N d
(3.18)
Theory of Antenna and Propagation
21
where b is the broadening factor, which is 1 for a uniform weight array and for a
Dolph-Chebyshev array it is expressed as [17]
b=
6(R + 12)
155
(3.19)
where R = 20log10 (Ra ).
Figure 3.6: This figure shows the difference between uniform and
Dolph-Chebyshev weights in a 21 element linear array. The acceptable side lobe level is set to -30dB. The difference between
the nearest sidelobe is clearly visible [17].
3.4 MIMO
Multiple-Input Multiple-Output (MIMO) is a new technique of using antennas
where there are more than one antenna used simultaneously at both the transmitter and receiver, and where the transmit antennas can radiate independent
signals [15]. The main use of MIMO today is in wireless communication where it
has been an essential element in, e.g., 802.11ac (WiFi-standard), HSPA+ (3G),
WiMAX (4G) and the more commonly used Long Term Evolution (LTE) (4G)
[15]. MIMO is an attractive method in wireless communications because it enhances the system performance by allowing the achievable data rate to grow linear
with the number of antennas used. One challenge with using MIMO is to be able
to distinguish signals between the different Tx-signals. There are several methods
that can be used to implement MIMO such as Space Division Multiple Access
(SDMA), Time Division Multiple Access (TDMA) and Code Division Multiple
Access (CDMA). Since the frontend used only had support for TDMA, which is
the simplest method, this is the one that was used in this thesis work.
These advantages of MIMO can also be exploited in the radar case where more
than one transmit and one receive antenna is used; each transmit antenna radiates
an arbitrary waveform which is independent of the other transmit antennas [15].
The receiving signal can receive the waveforms and because of the independence of
the signal, several output signals can be distinguished from each receive antenna.
This means that if the number of transmitting antennas is M and the number of
receiving antennas is N , the total number of signals is M × N . This will create
what is called a Virtual array, which will be further discussed in the next section.
22
Theory of Antenna and Propagation
The MIMO setting can be used to increase the spatial resolution by the creation
of the virtual array that has a larger aperture than the non-virtual array. The
main improvement is the enhanced signal quality, which can be described as an
improvement in the signal to interference plus noise (SINR). MIMO radar systems
are divided into two different subcategories, bi-static and mono-static, which have
been mentioned briefly. In the mono-static case the radar antennas are collocated
and thus see the same RCS of the target. For the bi-static case the RCS is
not equal from every transmit antenna, which means that they are distributed
in a certain pattern. This setup requires more complex data processing as each
transmit antenna looks at the target from a different perspective.
The transmitted signal is assumed to be narrowband, i.e., f0 BW and that
the propagation is non-dispersive. Under these conditions, the baseband signal is
described by [15]
Mt
X
e−j2πf0 τm (θ) xm (n) = a(θ)∗ x(n),
n = 1, . . . , N
(3.20)
m=1
where f0 is the carrier frequency and τm (θ) is the time needed by the signal
emitted via the mth transmit antenna to arrive at the target. *-operator means
the conjugate transpose. a(θ) denotes the target location parameter for each
element and is given by [15]
a(θ) = [ej2πf0 τ1 (θ)
ej2πf0 τ2 (θ)
ej2πf0 τMt (θ) ]T
···
(3.21)
and
x(n) = [x1 (n) x2 (n)
···
xMt (n)]T
(3.22)
For the received signal at the mth antenna let [15]
y(n) = [y1 (n) y2 (n)
···
yMr (n)]T ,
n = 1, . . . , N
(3.23)
and let
b(θ) = [ej2πf0 τ˜1 (θ)
ej2πf0 τ˜2 (θ)
···
˜ t (θ) T
ej2πf0 τM
]
(3.24)
where τ˜m (θ) describes the time needed by the reflected signal at θ to arrive at the
mth receive antenna.
The received data vector can then be described by the following equation [15]
y(n) =
K
X
βk bc (θk )a∗ (θk )x(n)
+
(n),
n = 1, . . . , N
(3.25)
k=1
where K is the number of targets that reflect the signals back to the radar
receiver, βk are complex amplitudes proportional to the RCS of the targets and
θk are the location parameters of the target. (n) is the interference plus noise
term and (.)c denotes the complex conjugate. The interesting information in the
received data vector is the βk and θk for each target k. In simpler words, each
target’s RCS and its relative orientation in space.
Theory of Antenna and Propagation
23
As often described in array signal processing, the assumption that the target is
described as a point is in our scenario not a fully valid approximation; each human
can provide several points and a walking human is not a uniform moving point
object since different body parts such as arms, torso and legs have different relative
speeds, which can induce errors in a simplistic target model. The characteristic
signature of a walking human could also be exploited to confirm that a target is
human by analyzing the Doppler spectrum to identify these different speeds, which
are characteristics of a walking human [15].
3.4.1 Virtual Array
The MIMO concept says that a received data vector is MT × MR large. This data
matrix can be interpreted, as mentioned before, as a virtual array. This virtual
array is created by a convolution between the receiving antenna arrays and the
transmitting array. The received signal can be expressed as following for each
sampling point
z(t) =
X
H(δ)s(t − δ)
+
(n)
(3.26)
δ
where H(δ) is the delay for each antenna element, The summation in (3.26) is over
the delays δ, which correspond to different range cells. In the far field the delay
has the following structure
(3.27)
Hm,n ∝ eik·(yn +xm )
where k is the wave vector and yn , xm are the positions of the transmitters and
receivers phase centers, respectively. The structure of H gives more spatial separation than the size of the actual array, the effective aperture is increased which
is described by the virtual array. For a ULA the virtual array phase centers can
be constructed by convoluting the location of the real transmitter and receiver
location. This can be described by the following equation
vec(H) = aR (k) ⊗ aTT (k)
(3.28)
(aR )n = eikyn
(aT )m = e
ikxm
H represents the antenna aperture and the number of elements is thus increased
in size to MT × MR number of elements. The vec()-operator converts the matrix
arguments into a vector by stacking rows together, which then can be used by
beamformers [15].
An example can easily be constructed, for instance, given by the following
linear array when the antennas are using both receive and transmit mode
Tx
array
Rx
array
=
gives
the
{1
=
2
{1
1
1 1}
{1
1
1 1}
virtual array
3 4
3
2
1}
(3.29)
24
Theory of Antenna and Propagation
This means that the spatial sampling is more than one on several locations and
the overall aperture has been increased by 75 %. Since the received data matrix
has more than one vector that has the same time delay, this is not optimal in
angular resolution which is proportional to the spatial sampling points. The array
can easily be changed so that the virtual array is at different spatial locations. A
3 Tx and 3 Rx array could be placed in the following manner to achieve this
Tx
array
=
{1
Rx
array
=
{1
1
1 0
0
0
0 1
0
gives
{1
1
the
1 1
0
0 0
0}
0
1 0
0}
(3.30)
virtual array
1
1
1 1
1}
This will give a total of MT x MR = 9 element array, which is an increase of the
aperture by 300 %. This gives a significant reduction of the beamwidth and greatly
enhances the angular resolution. This can easily be converted to an rectangular
array by doing the convolution in two directions [15].
Beam Patterns
0
Gain (dB)
Receiver Array Pattern
Transmitter Array Pattern
Virtual Array Pattern
−10
−20
−30
0
20
40
60
80
100
120
Ang (°), broadside = 90°
140
160
Figure 3.7: The beam pattern of the receiving array, the transmitting
array and the virtual array.
180
Theory of Antenna and Propagation
25
3.5 Microstrip Patch Antennas
The most attractive variation of the microstrip antenna is the patch antenna. It
consists of an antenna element pattern in metal trace, a "patch" of metal, mounted
on top of a dielectric substrate, with a metal layer on the opposite side of the
substrate forming the ground plane.
Figure 3.8 shows a rectangular patch antenna with the width W , the length L
and the thickness t. The patch lies on top of a substrate with a dielectric constant
of r and height h. The rectangular geometry is the most common shape used for
patch antennas.
Figure 3.8: A rectangular patch antenna.
The patch antenna is inexpensive to manufacture and its simple physical dimensions makes it easily implementable on a PCB using lithographic manufacturing methods. It is mainly used in the Ultra High Frequency (UHF) band since
the size of the patch is directly related to the wavelength. The shape of the patch
is very flexible and common ones are square, rectangular, circular and elliptical.
These have the advantage of the ability to have polarization diversity, which can
be realized by designing the feed structure and patch geometry in different ways.
The drawbacks of the patch antenna is low bandwidth, not very good radiation
efficiency, low power handling and relatively low gain. However, large arrays of
patch antennas can be formed to compensate for the relatively low gain.
There are two approaches for modeling and analyzing the patch antenna:
• Transmission line model
• Cavity model
The interesting region is the one between the patch and the ground plane, which
is filled by the dielectric material. This is valid as long as the thickness of the
patch is t λ. This section describes the cavity model for the patch antenna and
Maxwell’s equation takes this form in the region [9]
26
Theory of Antenna and Propagation
∇ × E = −jωµ0 H
∇·E=0
∇ × H = J + jωE
∇·H=0
(3.31)
The boundary conditions can be simplified to Perfect Electric Conductor (PEC) on
the conductor surfaces and Perfect Magnetic Conductor (PMC) on the four sides
z
of the approximate cavity. The mode responsible for the radiation is the T M010
[9].
The magnetic currents along the x-axis at y = 0 and y = b is responsible for the
radiation. The radiation is equivalent as from two magnetic current slots in both
the cavity model and the transmission line model. With this model, the total
radiation pattern is derived from multiplying the array factor with the electric
field.
Figure 3.9: This shows the configuration of the electric field in the
z
active T M010
-mode. a is the width of the patch and b is the
length [9].
z
The EM-field of the resonant T M010
mode in the cavity is described by [9]
πx Ez (x) = E0 sin
L
πx (3.32)
jE0
Hy (x) =
cos
η
L
where η is the free space impedance.
3.5.1 Input Resistance
Input resistance Rin of a patch antenna is estimated from the following at resonance frequency [2]
πy 0
(3.33)
Rin (y = y0 ) = Rin (y = 0) cos2
L
where y0 is the inset feed distance and Rin (y = 0) is the resistance at the edge of
the patch.
Theory of Antenna and Propagation
27
This is important in the design of the feed network to the patch since to obtain
an optimal antenna good matching is required. The resistance in the center, where
there is a node in the E-field, is zero and the maximum is at the edge where the
theoretical model predicts a resistance going to infinity but in realistic cases the
resistance is between 200 Ω − 400 Ω. There are several methods of feeding a patch
antenna. The simplest are the direct coupled such as microstrip feed and coaxial
feeding, which are simple to design. There are also indirect coupling techniques
such as proximity or aperture coupled which are exploiting different layers in the
PCB [9]. These methods were not considered since they are more difficult to
implement.
The normalized input resistance can be plotted as a function of y, as shown
in Figure 3.10.
Rin (y=y0 )/Rin (y=0)
Normalized input resistance as a function of y
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
y0 /L
0.8
1
Figure 3.10: Resistance normalized at different y-positions.
Quarter-Wave Impedance Transformer
The impedance of the feed to the patch is usually 50 Ω and since the patch has
much higher impedance (if microstrip feed line is used), there is a mismatch in
impedance. A very common way to resolve this mismatch is the use of the quarterwave impedance transformer, which is a component that is exactly one quarter of
a wavelength long. It can be a transmission line or a waveguide and is terminated
in some known impedance. Figure 3.11 shows a transmission line used as a quarter
wave transformer.
28
Theory of Antenna and Propagation
Figure 3.11: A transmission line used as a quarter-wave impedance
transformer.
The relation between the input impedance Zin , the characteristic impedance
Z0 and the load impedance ZL is
Zin =
Z02
ZL
(3.34)
For instance, if the load is 100 Ω and it needs to be matched to a 50 Ω input, then
a transmission line with the characteristic impedance of
√
Z02
→ Z0 = 50 · 100 ≈ 70.71Ω
100
should be used to achieve impedance matching [9].
50 =
(3.35)
3.5.2 Guide to Design a Microstrip Fed Patch Antenna
Start by approximating the length of the patch, when using a substrate with the
dielectric constant r and free space wavelength λ0 , by using the following formula
[9]
L=
λ0
r + 1
(3.36)
This is a good first guess as long as a thin substrate is used (d < 0.015λ). A thicker
substrate will degrade the efficiency of the patch. There are more complex formulas
which are in most cases not necessary since fine tuning is still needed, which is
easiest to achieve in a simulation tool. Width can be tapered to suit different
needs, but to achieve maximum bandwidth, the width should be approximate 1.5
times the length, W = 1.5L. The thickness of the ground plane and the patch is
usually not critically important. Input resistance is affected by changes in width;
the impedance increases when the width is decreasing [9].
The other important thing is the impedance matching, which is done by inserting the microstrip on the width of the patch. The closer to the center the
patch is fed, the lower impedance is seen, as described in (3.33). This is easiest
done in simulations to ensure that good matching has been achieved. An attractive alternative is to use the quarter-wave impedance transformer at the input to
decrease the resistance without having to cut too far into the patch [9].
Chapter
4
Range and Direction-of-Arrival Estimation
Algorithms
This chapter goes through the different signal processing algorithms, called
Direction-of-Arrival (DOA) algorithms, used for calculating the direction of the
targets (sources of reflected waves for the transmitted radar signal) relative to
where the radar is located. Sec. 4.1 gives an introduction to the Fourier Transform,
which is used to obtain information about range and speed from the radar system.
Sec. 4.2 presents the concept of the DOA algorithms with Sec. 4.3-4.6 going into
further details.
4.1 The Fourier Transform
Fourier transform is one of the fundamental tools of signal processing and is very
useful, especially in FMCW-radars where the information about range and speed
are obtained from the frequency response. The estimation of target range and
speed, and even direction of arrival, can be achieved by performing different Fourier
transforms, though other methods are also available. A simple version of baseband
data is described by the following model derived from (2.13) and (4.2)
s(n) = Aej (2π(
Bn
N
) 2R
c )
(4.1)
where B is the bandwidth, N is the number of samples, R is the range to target
and c is the speed of light.
To get the received power from the range R, the Discrete Fourier Transform
(DFT) is used since it gives the range and corresponding magnitude directly. The
definition of DFT is the following when there are N samples in a sequence of
complex numbers [21]
Xk =
N
−1
X
xn e
−2πjkn
N
(4.2)
n=0
The algorithm used for the Fourier transform is the Fast Fourier Transform
(FFT). The main reason is that it reduces the complexity of DFT from O(N 2 ) to
O(N log(N )), where N is the data size. It is considered by many as one of the
most important numerical algorithms [21]. When performing FFT, one will get N
29
30
Range and Direction-of-Arrival Estimation Algorithms
data points (in frequency domain) that are uniformly distributed between 0 and
F s/2, where F s is the sample rate.
The range resolution is given by the relation c/2B, where B is the bandwidth
that can at maximum be 250 MHz by legal reasons [13] for the center frequency
of 24 GHz and this corresponds to a resolution in range of 0.6 meters. This is a
fundamental limit as long as no more bandwidth can be used. Several techniques
can be applied to improve the performance of the FFT. The ones that are used
include the addition of a window function and zero padding the data.
Window functions are frequently used when using DFT. Since the sampled
data in time has to be of finite length, the abrupt edges gives rise to leakage to
neighboring frequencies. The rectangular window, which is basically the same as
using no window, gives the smallest mainlobe, but at the expense of introducing
noise in the neighboring frequency channels. Since the dynamic range of radar is
large, the presence of a strong signal will make signals with less power, especially
those from farther away, to be appear below the noise level of the strong signal.
This trade off is very similar to the one experienced when synthesizing antenna
array patterns since the basic mathematics is the same. For high attenuation of
spectral leakage to the neighboring frequency bins, the trick is to shape the time
samples with non-rectangular windows, as can be seen in Figures 4.2 and 4.3.
This is necessary to detect weak radar hits in the presence of, e.g., a jammer or a
interferer [21].
The windows which have good sidelobe level attenuation are the Hanning or
Chebyshev windows [11]. Chebyshev, gives as mentioned in Sec. 3.3.1, the lowest
closest sidelobe level. Hanning gives not as good attenuation to the closest sidelobe
but has the advantage that the sidelobe level will attenuate monotonically away
from the mainlobe, which is not the case for the Chebyshev window. Figures
4.1-4.3 show the effect of the windows on a sinusoidal signal.
Figure 4.1: The frequency spectrum of a rectangular window [11].
Range and Direction-of-Arrival Estimation Algorithms
31
Figure 4.2: The frequency spectrum of a Chebyshev window, side
lobe attenuation is set to 100 dB [11].
Figure 4.3: The frequency spectrum of the Hanning window [11].
Another important method when performing FFT is zero-padding. This is
to add a long series of samples with zero after the received signal. This results
in an increase in the amount of frequency bins produced by the FFT. The sincinterpolation on the signal will give higher accuracy, but the resolution of the FFT
is unchanged, as the frequencies between the bins cannot be distinguished. The
peak frequency of the signal is more likely to get into the right bin. It often also
makes the FFT more efficient because of performing FFT on a sequence with 2n
points will speed up FFT computation, since efficient FFT algorithms for those
lengths exist.
4.2 Introduction to Direction-of-Arrival Algorithms
The antenna array receives signals from all directions, but a signal from a given
direction will arrive at each array element at a different time, which depends on
the element positions. Conventional phased arrays process most of the directional
information in radiofrequency (RF) using different amplitude and phase weighting
32
Range and Direction-of-Arrival Estimation Algorithms
components such as MEMS phase shifters which are complex to implement. The
focus of this thesis work is to implement a simple solution in the RF part of the circuitry in favor of exploiting the digital part. This approach could result in cheaper
future systems since the rate of development in the digital domain is much higher
than the RF counterpart. Moreover, doing the Direction-of-Arrival processing in
the digital domain gives a lot of flexibility, which is not possible in the RF domain,
as it is able to suit different needs such as operating in different environments by
adapting the algorithms for maximum performance for each environment with the
same hardware.
Signal processing has an entire field dedicated to this kind of work, array
processing. An array can be defined as a set of sensors, usually sound or electromagnetic, that are spatially separated. The main goals of array processing are to
[21]:
• Determine the number and locations of sources (emitters)
• Enhance the SNR
• Track the sources
All of these goals are highly relevant to radar systems since an object is considered
an emitter since it reflects the signal that is transmitted by the radar. There is a
gap between the idealized mathematical and the physical world and there are five
assumptions which are essential for many array processing models, but are hard
to achieve [21]:
• Uniform propagation and non-dispersive medium
• Radius of the propagation is much greater that the array size, i.e., plane
wave (far field) propagation assumption
• Presence of zero mean white noise and zero signal correlation
• Perfect calibration and no coupling between the sensors
• Narrowband signal assumption
The signal model is usually expressed as (which is identical to (3.25) shown
for MIMO-antennas)
X = A(θ)S + N
Where:
• X is the vector of signals received by the array sensors
• A is the steering vector for each angle of arrival θ
• S is the signal vector
• N is the vector containing all the noise
(4.3)
Range and Direction-of-Arrival Estimation Algorithms
33
for M snapshots [21].
The simplest case of beamforming uses the same methodology of antenna array
design and applies the complex weights as described by (3.12). The basic idea is to
create a matrix which sweeps the angle θ in M directions which can be formulated
as [7]



F = (F(ω1 · · · F (ωM )) = 

1
ejω1
..
.
ej(M −1)ω1
···
..
.
···
1
ejωM
..
.
ej(M −1)ωM





(4.4)
where ωn denotes the phase-delay for element M when scanning in the direction
θ.
To perform a scan in an arbitrary direction, a steering weight can be multiplied
to each antenna element to change the scan direction. The scan direction can be
expanded to both azimuth φ and elevation θ. Such a scan is equal to how a phased
array is steered, but done in the digital domain with the sampled baseband data,
both azimuth φ and elevation θ. The steering vector is a change of phase of the
signal to each element, which is shown in (3.12). For a planar array with elements
positioned in the xy-plane, the weight vector wnd can be expressed in terms of the
steering vector as [21]
wnd = ejkd ·rn = ej
2π
λ
sin(θd )(cos φd xn + sin φd yn )
(4.5)
4.3 Array Synthesis Beamformers
The same array design methods and concepts can be used on the digital domain as
if it would be implemented in the analog realm using RF components. To look in
the angular direction θ, a vector of phase shifts is multiplied to the signal of each
individual antenna element which will steer the beam. As the case of designing a
phased array, different weight functions can be added to each element as a window
function to improve certain aspects.
There are several beamforming methods described in Sec. 3.3.1 and their pros
and cons are described. In more general terms, there are two aspects that are in
most cases a trade-off one has to choose:
• Mainlobe beamwidth
• Sidelobe levels
For maximum resolution in the mainlobe direction, uniform weights should be
used. Uniform weights has its first sidelobe at only -13 dB, which is far too big in
most radar scenarios since the dynamic range can be as high as 50 dB [21]. Any
change of the amplitude will cause widening of the main beam, but the dynamic
range can be increased.
The three synthesis methods which reduces sidelobes, Dolph-Chebyshev, Taylor one-parameter and binomial distributions are briefly described in the following.
34
Range and Direction-of-Arrival Estimation Algorithms
Binominal has no sidelobes but a huge main lobe which probably deteriorates the
resolution too much with respect to what one can gain. The Taylor one-parameter
method is desirable in radar applications due to its decaying sidelobes, because
it can be easier to detect signals which can be determined to be false targets appearing in the sidelobes [2]. The difference between Dolph-Chebyshev and Taylor
one-parameter is that there is a slightly larger mainlobe beamwidth in the Taylor
case with the same level on the closest sidelobe, this effect is shown in Figure 4.4.
Gain (dB)
Comparison between different array synthesis algorithms
0
Taylor one parameter, R = 40
Dolph-Chebyshev, R = 40
Binominal
−20
−40
−60
−80
0
20
40
60
80
100
120
Ang (°), broadside = 90°
140
160
180
Figure 4.4: Different antenna synthesis filters with a linear array of
8 antennas.
The angular resolution deteriorates the farther the angle is from broadside and
above 60° the resolution is restricted. This resolution limit is set by the number of
antennas used. By increasing the number of elements in the array, the maximum
angle resolvable from the broadside is increased, as described by [2].
4.4 Adaptive Direction-of-Arrival Algorithms
The algorithms described are functions implemented by using techniques from array pattern synthesis. These methods are crude since they do not adapt to the
current environment. The main problem that arises is the sidelobes, which will
give rise to false targets and create noise in different scan angles that severely
degrades the resolution capability in that direction. Array processing has developed methods which adapt the beampattern to the current environment by using
the raw data to compute optimal weights for that data. These methods can improve performance and suppress noise that occurs. The different methods can be
explained in two major categories [14]:
Range and Direction-of-Arrival Estimation Algorithms
35
• Spectral-based techniques
– Beamforming technique
– Subspace methods
• Parametric-based techniques
– Stochastic approach
– Deterministic approach
Spectral-based techniques use modified spectrum functions of the parameters of
interest. The location of the highest separable peaks are noted as the directions
of arrival (DOAs). Parametric techniques uses a simultaneous search of all the
parameters of interest. This method is usually more accurate but at the expense
of an increased computational complexity. This work will only focus on spectralbased techniques since they are easier to implement. The parametric solutions can
be simplified if a ULA/URA is used and for these arrays it is possible to create an
efficient parametric search [14].
The beamforming techniques discussed in the last section can be expanded to
cover adaptive methods, where one of the simplest is Minimum Variance Distortionless Response (MVDR) algorithm, also known as Capon beamformer after its
inventor J. Capon. There are several subspace methods such as MUSIC (MUltiple
SIgnal Classifaction) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques). Due to time limitation, only the MUSIC algorithm
is evaluated in this work [14].
4.5 Capon/MVDR Beamformer
The conventional beamformer works well when pointing the main beam in the
signal direction, which yields the highest peak power in that specific direction. It
does not work equally well when having more than one signal, which is almost
always the case in radar application due to clutter and several targets. It will
find well separated targets with high RCS. Capon beamformer overcomes this by
using the available degrees of freedom (DOF) to look a target in the direction and
at the same time steer nulls to directions of other targets and clutter. Since the
environment to be optimized changes with different scan angles, this method is
adaptive. In particular, all the DOFs except one is used to minimize the output
power while at the same time the magnitude of the beampattern at the scan angle
is maintained. Mathematically, this is expressed as [7]
minimize
P (w) subject
to wH a(θ) = 1
(4.6)
where P (w) is the output power at the beamformer. Capon beamformer weights
are calculated based on the spatial covariance matrix, which is estimated from
multiple time samples of the array signal outputs. More details of this matrix is
given in the following. The signal model (4.3) contains signal as well as noise. The
noise received is in many cases uncorrelated with each other and with this signal,
36
Range and Direction-of-Arrival Estimation Algorithms
however, the signals that originate from the same source are correlated. This property can be used to efficiently extract the DOA information. This is done by the
concept of cross-covariance information, which is stored in the spatial covariance
matrix. The spatial covariance matrix is defined as (4.7), where replacing x(t)
with (4.3) yields the expression on the right hand side of (4.7) [7]
2
Rxx = E{x(t)xH (t)} = ARxx AH + σN
IM
(4.7)
2
where σN
is the common variance of the noise. In practice, the exact covariance
matrix is hard to estimate, since it has to be estimated with a finite number of
data points. The most common estimator of the covariance matrix is the following
[7]
Rxx ≈ R̂ =
N
1
1 X
x(tn )xH (tn ) = XH X
N n=1
N
(4.8)
The covariance matrix is fundamental to many DOA-algorithms that are used; the
difference is how they extract information from the estimated covariance matrix.
The weight vector for the Capon beamformer is expressed as [7]
wCapon =
R̂−1
xx a(θ)
aH (θ)R̂−1
xx a(θ)
(4.9)
The term aH (θ)R̂−1
xx a(θ) is known as the power spectrum of the Capon beamformer, which is the normalization constant to get the correct power spectrum.
The Capon weights should give an increase in resolution compared with the
weights for conventional beamformers. The price to pay is that the inverse of the
estimated correlation matrix needs to be calculated [5].
4.6 Subspace Methods
Subspace-based techniques are based on certain properties of the matrix space of
Rxx [21]:
• The space, spanned by its eigenvectors, can be divided into two orthogonal
subspaces: the signal subspace and the noise subspace
• The steering vectors correspond to the signal subspace
• The noise subspace is spanned by the eigenvectors connected with the
smaller eigenvalues of the correlation matrix
• The signal subspace is spanned by the eigenvectors connected with the larger
eigenvalues
Range and Direction-of-Arrival Estimation Algorithms
37
4.6.1 MUSIC Algorithm
MUSIC is one of the first proposed methods whose sole use is for DOA-estimation,
which was discovered by P.O. Schmidt in 1977 [20]. It uses eigenvalue decomposition of the correlation matrix Rxx , which assumes the following data model, the
same as (4.7), [7]
(4.10)
2
Rxx = ARxx AH + σN
IM
2
where σN
is the common variance of the noise and IM is the identity matrix of
rank M. The assumption is made that the eigenvalues of the correlation matrix
satisfies the following relation [7]
(4.11)
|Rxx − λi IM | = 0
Combining (4.10) and (4.11) gives the following relation, if ARxx A has eigenvalues ei , then they can be expressed as ei = λi −σ 2 . The eigenvalues of ARxx AH
have the properties that they are positive semidefinite with rank d (number of signals with the derivation given in [21]). This implies that M − d of the eigenvalues
are in the proximity of 0. That means that the M − d of the eigenvalues of Rxx
are equal to the noise common variance, which will be the smallest when doing
the eigenvalue decomposition. This leads to that the array steering vector a(θ) is
perpendicular to the eigenvectors of the noise subspace. An effect of this is that
aH (θ)Vn VnH a(θ) = 0, where Vn contains the M − d noise eigenvectors, arbitrary
steering angle θ to the DOA of the incoming signal [7].
The MUSIC spectrum is defined by [7]
H
PM U SIC (θ) =
1
aH Vn VnH a(θ)
(4.12)
The MUSIC algorithm steps can be roughly described as follows [7]:
• Calculate the estimated covariance matrix using (4.8)
• Perform eigendecomposition on R̂xx
• Estimate the multiplicity k of the smallest eigenvalue λmin , then estimate
the number of signals as d = M − k, where M is the number of eigenvalues
found in the estimated covariance matrix R̂xx
• Compute PM U SIC (θ) using the approximated noise corresponding eigenvectors as Vn
• The d largest peaks in the PM U SIC (θ) is the DOA estimates of the d incoming signals, since these peaks indicates that these scanned directions are
orthogonal to the noise.
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Range and Direction-of-Arrival Estimation Algorithms
Chapter
5
Software and Hardware Tools
In this chapter, the software and hardware tools used in this thesis are described.
The chapter begins with Sec. 5.1 giving a short introduction to the software
program Computer Simulation Technology Studio Suite (CST Studio Suite), that
is used for antenna design and simulations. Thereafter, the frontend used for the
radar system, the INRAS Radarbook, is described in Sec. 5.2. The verification of
the DOA-Algorithms, mentioned in the previous chapter, is given in Sec. 5.3.
5.1 Computer Simulation Technology (CST)
Computer Simulation Technology Studio Suite (CST Studio Suite) is a high performance software program that offers a wide variety of tools designed for the
simulation of 3D electromagnetic fields. It consists of several modules aimed at
different areas of applications, including [8]:
• CST MICROWAVE STUDIO (3D EM simulation for high frequency components)
• CST EM STUDIO (simulation of static and low frequency components)
• CST PCB STUDIO (PCBs and packages)
• CST CABLE STUDIO (analysis of cable harnesses)
• CST MPHYSICS STUDIO (thermal and mechanical stress analysis)
• CST PARTICLE STUDIO (simulation of charged particles)
• CST DESIGN STUDIO (system and circuit simulator)
To design and simulate the antennas, CST MICROWAVE STUDIO was used.
Firstly, one single patch antenna was designed and it was then used to form a
linear array consisting of four patch antennas. Finally, the patch antenna arrays
were put together in different configurations to obtain the final design.
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Software and Hardware Tools
5.2 INRAS Radarbook Description
The frontend used for our MIMO radar design is the INRAS Radarbook. It is
designed to be a highly flexible and a low cost signal processing and RF product.
Its indented primary use is CW radar with the frontend included. The frontend
consists of a digital and RF part.
The RF FMCW frontend that operates with the Radarbook consists of two
transmit (Tx) and eight receive (Rx) antennas. It can be seen in Figure 5.1, where
it is connected to the Radarbook.
Figure 5.1: The INRAS frontend connected to the Radarbook.
Figure 5.2 shows a block diagram of the overall frontend architecture. The
Analog Devices ADF5901 is a 24 GHz Tx Monolithic Microwave Integrated Circuit
(MMIC) that consists of a Voltage Controlled Oscillator (VCO) and a 2-channel
Power Amplifier (PA) output. The MMIC is connected to the ADF4159, which
is a fractional-N frequency synthesizer used to generate the FMCW signal for the
transmitter. The Rx channel is provided by ADF5904 combined with an additional
Wilkinson divider. The Rx architecture is a 4-channel down-converter. Note that
no I-Q channel down-conversion is performed.
Software and Hardware Tools
41
Figure 5.2: Overall frontend architecture.
The baseband block is built with a Cyclone III and a ARM Tegra 2 processor
module. The design is made to provide a powerful processing unit suited for
the high bandwidth data streams for real-time radar data signal processing. The
computer interface is either Ethernet or USB version 3.0. It is connected using
Matlab interface and the timing unit is fully programmable [12].
The frequency can be set to sweep between 23.7 GHz and 24.3 GHz. The
ramp up time can be set and the number of chirps for range-Doppler processing
can be controlled as well. This gives a big degree of freedom to try different
configurations. The analog signal processing composes of a 12-bit ADC. The ADC
has a maximum sample rate of 80 MSPS and samples the channels sequentially,
thus giving each channel a maximum of 20 MSPS for each receive channel. An
AAF (Anti-Aliasing Filter) is used before sampling to avoid aliasing frequencies
[12].
The FMCW radar can be configured into mainly two setups, depending on if
range-Doppler is needed or not. It is programmed for a precise timing between
the chirps on each Tx antenna, to ensure no phase differences between each chirp
measurement, so that a virtual array can be constructed. The requirement is the
same when using the range-Doppler configuration, as precise timing between each
chirp is crucial.
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Software and Hardware Tools
5.3 Verification of the Signal Processing Algorithms
The Radarbook receives the data from the Analog-Digital Converter (ADC), which
gives the time domain baseband data. Since the ADC is sampling the antennas
in a serial format the phase needs to be calibrated to give the correct data. The
Radarbook has already been calibrated by INRAS when using their antennas,
which fixes the errors that have occurred in the device. The calibrated data contains all the information which is needed to get a picture of the environment. The
implementation is described by Figure 5.3 and a flow chart of the data processing
is shown in Figure 5.4. Figures 5.5-5.6 show an example of the sampled data in
time and frequency domain to give a grasp of the form of the incoming data.
Figure 5.3: A scheme explaining how the Fourier transformers are
conducted to get the range and Doppler frequency. These are
performed individually by each antenna [18].
Software and Hardware Tools
Figure 5.4: Flow chart explaining how the data processing is performed. Reflectivity is calculated by averaging all fast chirps
instead of a single slow one.
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Software and Hardware Tools
Sampled baseband data
·10−2
Rx1
Rx2
Rx3
Rx4
Rx5
Rx6
Rx7
Rx8
Magnitude
5
0
−5
0
50
100
150
200
16 bits Sample points
250
300
Figure 5.5: The downcoverted baseband signal received by the
Radarbook, sampling rate is set to 0.5 MS/s.
Frequency spectrum of the baseband signal
Received Signal (dBV)
−20
Rx1
Rx2
Rx3
Rx4
Rx5
Rx6
Rx7
Rx8
−40
−60
−80
−100
0
0.2 0.4 0.6 0.8
1 1.2 1.4 1.6 1.8
Frequency (Hz)
2
2.2 2.4
·105
Figure 5.6: The frequency response of the received data using
Chebyshev window with 100 dB sidelobe suppression.
Software and Hardware Tools
45
As can be seen in Figures 5.5-5.6, the signal has a strong low frequency component, which likely comes from noise generated in the device, i.e., crosstalk and
self-mixing. This causes a problem in the estimation of the covariance matrix,
which will be biased by this noise component. This low frequency part needs to be
filtered out to get a good estimation. However, since the information is processed
in the frequency domain, the low frequency component can be easily filtered out.
The frequency of the received signal is directly proportional to the distance,
as discussed in the Sec. 2.4.1. The received data is ∆f in (2.13). The received
power corresponds to the RCS of that particular frequency. A peak in the received
signals means that there is a strong reflection at the distance corresponding to that
frequency.
To get the angle information of the hit, a DOA-algorithm needs to be implemented at the corresponding frequency. The angular information is stored in the
phase difference between the Rx-antennas at the same frequency when applying
DOA-algorithms.
Complex phase (°)
Frequency spectrum of the baseband signal
Rx1
Rx2
Rx3
Rx4
Rx5
Rx6
Rx7
Rx8
100
0
−100
3
3.5
4
4.5
5
5.5
6
Frequency (Hz)
6.5
7
7.5
·104
Figure 5.7: The phase of the frequency spectrum.
To get the velocity map of the target, a sample of chirps needs to be compared,
the Doppler frequency can be seen as an added frequency on top of the bins. The
resolution depends on the amount of chirps processed and the respective timing
between the chirps. A big number of chirps will take time to process and during
the sampling time, the velocity could have changed or it could have moved to the
adjacent frequency bin, which will give wrong results. In practise this gives a tradeoff between resolution and the possibility to detect fast moving targets. Since the
goal is to measure people, a high resolution of low velocities is preferable since the
speed of a walking human is around 1.5 meters per second, which according to
(2.17), corresponds to a Doppler frequency of 120 Hz at the center frequency 24
GHz. That means that choosing the correct weight function for the FFT is critical
in order to achieve good resolution between slow movements and stationary targets.
Doppler shifts of a stationary scene with a Chebyshev 100 dB side lobe level is
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Software and Hardware Tools
shown in Figure 5.8.
Doppler Frequency
−80
−100
dBV
−120
−140
−160
−180
−1,000−800 −600 −400 −200
0
200 400 600 800 1,000
Frequency (Hz)
Figure 5.8: The Doppler frequency of a stationary range bin, chirp
repetition rate is set to 512 µs and a total of 128 chirps is
measured.
5.3.1 Implementation of Direction-of-Arrival Algorithms
The beamformers are implemented in the frequency domain by sweeping the scan
direction in the desired (φ, θ) angles and creating a grid for each frequency bin.
Each grid point represents the total power after the signal from each antenna has
been multiplied by a complex delay, described by (4.5), and summed. This is done
for each frequency bin to calculate the angular power distribution of that bin. To
calculate the range information, the total power of the different range bins needs to
be compared. Note that the subspace methods are not considered as beamforming
since they calculate the power spectrum based on orthogonality of subspaces and
do not provide beamforming weights. The 2D angular grid for a given range bin
is shown in Figure 5.9.
Since the interest in this thesis work is to be able to only have a limited
scan range in the θ (elevation) direction, the angles of interest are defined to
be from approximately -20 to 20 degrees in elevation and 30 to 150 degrees in
azimuth. This limitation is imposed as a recommendation as the resolution of the
considered arrays outside this 2D angular sector is poor, especially in elevation.
This limitation is even worse when it comes to the 4 × 4 array, since the antenna
element spacing is larger and the grating lobes also exist in the azimuth plane.
For unambiguous direction estimation in the azimuth, the maximum range is thus
limited to 60-120 degrees.
Software and Hardware Tools
47
Figure 5.9: Grid representation of the beamforming conducted on
the range bin.
5.3.2 Verification of Direction-of-Arrival Algorithms Using INRAS Frontend
To verify the algorithms, tests were conducted on the original INRAS antennas
(from Analog Devices). The antenna parameters are shown in Table 5.1 and an
illustration of the antennas is shown in Figure 5.10. The INRAS antennas follow
an amplitude tapered patch antenna array design which lowers the level of the
side lobes in the elevation plane. There is a λ/2 spacing between the two Tx
antenna elements. It was not designed to benefit from MIMO virtual array since
the virtual array is not used to create a larger effective aperture, thus only SingleInput Multiple-Output (SIMO) measurements were conducted. Since it is a ULA
design, only azimuth DOA could be measured.
A simple case where a reflector was measured in a stationary scene is shown
in Figure 5.11. The target is a reflector located 10 meter from the radar with
open terrain and a parking lot behind. The azimuth angle of the target is φ = 0°
(broadside direction for the INRAS antenna configuration).
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Software and Hardware Tools
Parameter
G
∆S
∆ΘH
∆ΘV
Name
Realized gain
Sidelobe suppression
Horizontal 3 dB beamwidth
Vertical 3 dB beamwidth
Value
15.8 dBi
-18 dB
76.5°
12.8°
Table 5.1: INRAS antenna parameters [12].
Figure 5.10: Illustration of the INRAS antennas with 2 Tx arrays
and 8 Rx arrays. During testing only 1 Tx array element was
used.
Software and Hardware Tools
Figure 5.11: Picture of the area tested with the INRAS antennas.
The person in the picture is holding up an octahedral radar
reflector.
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Software and Hardware Tools
Figure 5.12: Target map with the reflections shown, the received
power (in dB scale) is normalized by the strongest hit.
To get a good overview over the performance of the different DOA-algorithms,
the range bin that contains the most power was extracted and the power distribution in azimuth angle is plotted for the different methods. The results are
summarized in Figures 5.13-5.15. As can be seen in Figure 5.6 and discussed earlier, to get a good estimate of the covariance matrix, the received signal should
be filtered by a Butterworth high-pass filter with a cut-off frequency of 50 kHz
to suppress the low frequency noise. Based on the number of larger eigenvalues
in the covariance matrices, the first 5 eigenvalues were assumed to represent the
signal subspace in the MUSIC algorithm.
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51
Sum-and-Delay Spectrum
Uniform
Dolph-Chebyshev, - 30 dB
dBm
−100
−110
−120
−130
−100 −80 −60 −40 −20
0
20
40
60
80
100
Ang (°)
Figure 5.13: The power spectrum for the Sum-and-Delay algorithm.
Capon/MVDR Spectrum
−100
dBm
−110
−120
−130
−100 −80 −60 −40 −20
0
20
40
60
80
Ang (°)
Figure 5.14: The power spectrum for the Capon/MVDR algorithm.
100
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Software and Hardware Tools
MUSIC Spectrum
−80
dBm
−100
−120
−140
−100 −80 −60 −40 −20
0
20
40
60
80
100
Ang (°)
Figure 5.15: The power spectrum for the MUSIC algorithm.
It can be seen from Figures 5.13-5.15 that the algorithms seem to work properly, especially the Sum-and-Delay as it is performing exactly according to theory.
The methods using the covariance matrix are harder to verify but they seem to
be correctly implemented. There are several correlated signals in the received
spectrum, which is one of the reasons that only three of the eight eigenvectors
is assumed to be the noise subspace. The Capon beamformer is a more robust
method and seems to be working well. These methods are seen to have a narrower
3 dB beamwidth compared to the conventional Sum-and-Delay. For more accurate
resolution measurements two targets of similar RCS should be conducted, and this
will be studied when testing the patch antenna array designed in this work The
fundamental problem for the adaptive methods using the covariance matrix is that
the signals from all frequency bins are being combined and evaluated at the same
time, which can cause phantom target originating from reflections occurring only
in some bins to appear. Moreover, the filtering of the baseband signal may need
to be improved beyond a simple high pass filter.
Chapter
6
Proposal of Antenna Array Design
This chapter explains the different setups of antenna array placements with Sec.
6.1 showing the array factor pattern and the total gain for the different setups and
Sec. 6.2 describing the proposed design with its corresponding virtual array.
6.1 Azimuth-Elevation Visualization
The goal of this thesis is, as formulated in the introduction, to investigate an
already existing 1D array design (i.e. INRAS antennas) to try to get a good idea
of how to create the new design of the 2D array. The INRAS frontend card,
which supports 2 Tx and 8 Rx antennas, is used for MIMO by using TDMA.
Since a uniform rectangular 2D array will require the use of single patch antenna
elements, which have too low gain and too wide main beam in the elevation plane,
problems with ground reflections can be expected. The array factor can be used
to calculate the array pattern for an arbitrarily arranged array and to analyze
which weight function would be optimal for Delay-and-Sum beam-steering. The
resolution of the beam-steering is given by the effective aperture, which is described
by (3.4). The resolution requirement becomes more difficult when both azimuth
and elevation DOAs need to be distinguished. Since the pattern will be nonsymmetrical, the angular resolution will change depending on the direction of the
plane that is separating the objects. This is the case since a Uniform Rectangular
Array (URA) or arrays of similar shapes are not symmetric along an arbitrary line
crossing the array center, unlike a circular symmetric array.
In the linear case, the beamwidth is easily calculated by the length of the
array projected in a certain direction. The effective aperture is d(Me − 1) cos(θ),
where Me is the number of elements in the virtual array, d is the distance between
adjacent elements and θ is the projection angle. This is true for a URA aligned
on the x-y plane as well as when looking along the x-z or y-z plane.
It is not possible for the antenna implementation in this thesis to use a URAdesign, due to physical restrictions in the placement of the array antenna element.
Therefore, inspired by designs given in [10], a rhomboid shape is proposed because
of its similar performance to a URA and that it is possible to circumvent the physical restrictions in the element placement. Since the resolution in the azimuthal
direction is more important and the limitation of the maximum use of 2 Tx and
8 Rx, the two following array geometries are proposed. Since the number of vir-
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Proposal of Antenna Array Design
tual array elements is 16, a smart design would be to have a symmetric number
of elements in both dimensions for the different designs. The array elements are
placed in the y-z plane (vertical plane), consistent to the expected orientation of
the array in the intended radar application. It should be noted that at this point,
the array elements are assumed to be single-patch elements. The first two arrays
use λ/2 element spacing in both y- and z-directions for a total of 2 × 8 element
patterns (with the top row of elements in the second arrays shifted to the right
by one element), while the second group of two arrays use λ/2 or λ spacing in
the y-direction and λ in z-direction for a total of 4 × 4 elements (with the fourth
array having shifted rows of elements). These arrays are visualized in the left subplots of Figures 6.1-6.4. The array factors (assuming isotropic elements) for the
broadside scan angle are provided in the right subplots of Figures 6.1-6.4. Since
the scan angle is limited in the elevation, a design with grating lobes present is
proposed. By using the patch antenna array design, effects of the grating lobes
giving false detections is reduced since the array element has a narrow main beam
in the elevation plane, which is effectively multiplied to the array factor to obtain
the actual array pattern.
Figure 6.1: Array Factor pattern for 2 × 8 rectangular array.
Proposal of Antenna Array Design
Figure 6.2: Array Factor pattern for 2 × 8 rhomboid array.
Figure 6.3: Array Factor pattern for 4 × 4 rectangular array.
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Proposal of Antenna Array Design
Figure 6.4: Array Factor pattern for 4 × 4 rhomboid array.
To get the full picture of the radiation pattern, one need to look at the actual
array pattern given by (3.13). To get a good picture of how this affects the array
factor that assumes isotropic element patterns, the total gain of the actual array
pattern is shown in Figures 6.5-6.8. The case with λ-spacing in the array setups are
given to visualize that the dampening of the grating lobes may not be sufficient,
since a target with high RCS will cause false detections if located in the grating
lobes. Chebyshev array pattern can be implemented to decrease the sidelobes,
which is more useful for the 2 × 8 arrays, since it does not affect the grating lobes
in the 4 × 4 configurations.
Figure 6.5: Total gain for the 2 × 8 rhomboid broadside array.
Proposal of Antenna Array Design
Figure 6.6: Total gain for the 4 × 4 rhomboid broadside array.
Figure 6.7: Total gain for the 4x4 rhomboid array. Beam steered in
the direction φ = 0°, θ = 70°.
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Proposal of Antenna Array Design
Figure 6.8: Total gain for the 4 × 4 rhomboid array. Beam steered
in the direction φ = 60°, θ = 70°.
Proposal of Antenna Array Design
59
6.2 Proposed Design
The two proposed designs are shown in Figure 6.2 and Figure 6.4. The virtual
array needs to be formed using equation (3.28). The proposed designs that include
virtual array elements are shown in Figure 6.9, where the dots represent the actual
antenna array elements and the crosses represent the convoluted virtual arrays,
where the left Tx-antenna array is used to synthesize the virtual arrays. In Figure
6.9, the first configuration shows the 4 × 4 rhomboid design and the second one
shows the 2 × 8 rhomboid design.
Figure 6.9: The proposed designs and how the virtual arrays are
created.
The distance between the Tx and Rx arrays is not relevant when calculating
the virtual array. As seen in Figure 5.10, the Tx and Rx arrays are not well
separated in the original INRAS arrays and this is probably one of the reasons
why a strong low frequency signal component was seen in the verification test of
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Proposal of Antenna Array Design
the INRAS Radarbook system. In Figure 5.6 it is obvious that the low frequency
component magnitude is a function of the distance from the transmitting antenna,
since Tx 1 is positioned closest and Tx 8 is positioned furthest away. Rx to Tx
isolation is thus important with regard to several factors such as to get a good
covariance matrix estimation and not to saturate the Low Noise Amplifier (LNA)
in the input stage of the Rx array, causing non-linear effects to distort the received
signal that is of interest or even causing stability issues in the input stage.
The design is then realized using CST and the final design is shown in Figure
7.12 in Ch. 7.
Chapter
7
Simulation Results of Antenna Array
Element
This chapter goes through the process of designing the antenna array elements and
the simulations of these. Firstly, the process of designing the 24 GHz single patch
antenna is described in Sec. 7.1. Thereafter, in Sec. 7.2, using the single patch
antenna, the 4×1 linear patch antenna array is designed. Finally, multiple antenna
arrays are put together to obtain the final design in Sec. 7.3. After the design
process is described, the simulation results are presented in Sec. 7.4-7.5. The
software program that was used for this design process is Computer Simulation
Technology Studio Suite (CST Studio Suite), which is described in Sec. 5.1. All
the simulations were made with the frequency domain solver in CST.
7.1 Design of 24 GHz Single Patch Antenna
The rectangular patch antenna was designed with the help from a CST tutorial [1].
The patch antenna that was designed is shown in Figure 7.1 with the dimensions
W and L. The ground plane and substrate were defined to be twice as large as
the patch antenna, i.e. 2W and 2L. The dimensions of the patch antenna were
calculated according to the guide described in Sec. 3.5.2 as a first approach. The
antenna is fed with a microstrip line where Wf and Lf are the dimensions of the
microstrip line, g is the gap distance between the microstrip line and the patch
antenna and d is the inset feed distance. These dimensions, including those of the
patch antenna, were not finally determined at this point, but subject to change
during the simulations to obtain the best performance.
The ground plane was defined as annealed copper with a thickness of 12 µm
and is shown in Figure 7.2. The substrate chosen was Rogers RO4350B with the
dielectric constant of r = 3.48, since its material properties are suitable for high
frequency applications such as 24 GHz patch antennas. The substrate was located
on top of the ground plane with a height of 0.25 mm and can be seen in Figure
7.3.
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Simulation Results of Antenna Array Element
Figure 7.1: Single patch antenna with microstrip feed line [1].
Figure 7.2: Ground plane consisting of 12 µm thick annealed copper.
Simulation Results of Antenna Array Element
63
Figure 7.3: Substrate consisting of 0.25 mm RO4350B with the
dielectric constant r = 3.48.
Thereafter, the patch was created on top of the substrate with the same material and thickness as the ground plane. Figure 7.4 shows the patch added on top
of the substrate.
Figure 7.4: The patch consisting of 12 µm annealed copper added
on top of the substrate.
After the patch was defined, the microstrip feed line needed to be created.
To do this, first an empty space was created (see Figure 7.5a) and then the microstrip feed line was added as shown in Figure 7.5b. This created a gap between
the antenna and the microstrip line. The final designed patch antenna with the
microstrip feed line is shown in Figure 7.6.
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Simulation Results of Antenna Array Element
(a) Empty space created on the patch.
(b) Microstrip line added to the patch.
Figure 7.5: First the empty space is created and then the microstrip
line is added to the patch.
Figure 7.6: The final design of the 24 GHz patch antenna.
The dimensions of the final patch antenna design were:
• Width of the patch, W = 4.5 mm
• Length of the patch, L = 3.13 mm
• Width of the microstrip line, Wf = 0.1 mm
• Length of the microstrip line, Lf = 1.81 mm
• Distance of gap, g = 0.1 mm
• Inset feed distance, d = 0.75 mm
• Height of substrate, h = 0.25 mm
• Thickness of patch, t = 12 µm
Simulation Results of Antenna Array Element
65
7.2 Design of 4x1 Linear Patch Antenna Array
Continuing with the work on the single patch antenna, a 4 × 1 linear antenna
array was created and is shown in Figure 7.7. The dimensions of the two inner
patch antennas differ from the two outer ones. The inner patch antennas are
slightly wider and shorter due to it being desirable to have larger radiated power
in the center of the array. The inner patches have exactly the same dimensions as
described in the previous section, while the outer ones have the length L = 3.17
mm and the width W = 4 mm. The size of the ground plane and the substrate is
10 mm x 32 mm and the distance between each patch is λ/2 = 6.25 mm.
Figure 7.7: 4x1 linear patch antenna array.
7.2.1 Feeding Network
The patch antennas are fed through a feeding network where the power is divided
between two patch antennas, as seen in Figure 7.8. Due to impedance mismatch
between the patch antenna and the transmission line, a quarter-wave impedance
transformer is used. Typically the patch antenna has an impedance of 200 Ω or
more and the transmission line 50 Ω. The use of the quarter-wave impedance
transformer, as described in Sec. 3.5.1, is necessary in order to ensure there is
good impedance matching between the patch antennas and the transmission lines.
Figure 7.8: The feeding network for the 4x1 linear patch antenna
array.
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Simulation Results of Antenna Array Element
7.3 Final Design
After the 4 × 1 linear patch antenna array had been designed, multiple arrays
were put together in different configurations of 2-element Tx arrays and 8-element
Rx arrays to obtain the final design. These configurations were chosen based on
the theory of virtual array, as described in Sec. 3.4.1, in order to achieve good
performance. The corresponding virtual arrays are shown in Figure 6.9 in Ch. 6.
7.3.1 First Design Configuration
Figure 7.9 shows the first design configuration, where the horizontal element separation distance for the 2-element Tx arrays is λ/2 = 6.25 mm and the vertical
element separation distance is λ = 12.5 mm. The horizontal distance between the
8 Rx arrays is λ and the vertical distance is 2λ. The separation distance between
the Tx array and the Rx array is (Tx array center to Rx array center) 4λ, but this
distance is of no great importance to the performance.
Figure 7.9: First design configuration.
7.3.2 Second Design Configuration
The second configuration is shown in Figure 7.10, where the horizontal element
separation distance between the 2-element Tx array is λ/2 = 6.25 mm. There
is no vertical element separation in this case. The horizontal element separation
distance for the 8-element Rx array is λ/2 and the vertical element separation
distance is λ/2.
7.3.3 Third Design Configuration
The last configuration is a mix of the two first configurations. It consists of the
same Tx array placement as the second configuration and the same Rx array
placement as the first configuration. Figure 7.11 shows this configuration.
Simulation Results of Antenna Array Element
Figure 7.10: Second design configuration.
Figure 7.11: Third design configuration.
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Simulation Results of Antenna Array Element
7.3.4 Final Design Configuration
Putting the three above configurations together, the final design is obtained and
shown in Figure 7.12.
Figure 7.12: Final design configuration.
Final Design Configuration with Two Extra Antenna Arrays
Two more antenna arrays were added to the final design configuration, as shown
in Figure 7.13. The first extra antenna is located λ/2 in horizontal distance and λ
in vertical distance from its closest neighbour antenna. The second extra antenna
is located λ/2 in horizontal distance from its closest neighbour antenna. The
use of the extra antennas is desirable if the application of Time Division Multiple
Access (TDMA) is problematic; these extra antennas can be used to create multiple
virtual array elements on the same spatial location.
Figure 7.13: Final design configuration with two extra antenna arrays used for TDMA application.
7.4 Simulation of 24 GHz Single Patch Antenna
Figure 7.14 shows the S11 scattering parameter, also known as the reflection coefficient, for the 24 GHz single patch antenna. The S11 parameter shows how much
power that is reflected from the antenna and it can be seen from the figure that
the antenna reflects the least around f ≈ 24.1 GHz, with the S11 ≈ -40.6 dB.
The impedance bandwidth, B, is the frequency interval where the patch antenna has a reflection coefficient below a certain dB value. A very common value
Simulation Results of Antenna Array Element
69
is -10 dB; using this and Figure 7.14, the bandwidth is obtained as B ≈ 700 MHz.
Using (3.5), the fractional bandwidth is F BW ≈ 2.90 %.
S11 Simulation
0
S11 (dB)
−10
−20
−30
−40
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
25
Figure 7.14: S11 of the 24 GHz single patch antenna.
Figure 7.15 shows the Z11 impedance parameter, which describes the open
circuit input impedance of the system. The real part of this parameter is Re(Z11 )
≈ 105 Ω and the imaginary part is Im(Z11 ) ≈ -0.661 Ω for the operating frequency
f = 24.1 GHz.
Z11 Simulation
Re(Z11 )
Im(Z11 )
Z11 (Ω)
400
200
0
−200
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
Figure 7.15: Z11 of the 24 GHz single patch antenna.
25
70
Simulation Results of Antenna Array Element
The 3D simulation plot of the far field radiation pattern for the patch antenna
is shown in Figure 7.16. The directivity for the antenna is 7.14 dBi.
Figure 7.16: Directivity of the 24 GHz single patch antenna. The
dBi range is -32.9 dBi - 7.14 dBi.
7.5 Simulation of 4x1 Linear Patch Antenna Array
Figure 7.17 shows the S11 parameter for the 4×1 linear patch antenna array. From
the figure it can be seen that the patch antenna array reflects the least around the
frequency f ≈ 24.2 GHz, with the S11 ≈ -22.6 dB.
The bandwidth for the patch antenna array can be obtained from Figure 7.17
and is around B ≈ 1 GHz. Using (3.5), the fractional bandwidth is obtained as
F BW ≈ 4.13 %.
Figure 7.18 shows the Z11 impedance parameter for the 4 × 1 linear patch
antenna array. The figure shows that the real part of this parameter is Re(Z11 ) ≈
58.8 Ω and the imaginary part is Im(Z11 ) ≈ -3.21 Ω for the operating frequency
f = 24.2 GHz.
The crosstalk (or coupling coefficient) between two λ/2-spaced patch antenna
array elements is shown in Figure 7.19. It is around -29.2 dB at the operating
frequency for antennas 1 and 2. The S12 parameter shows how much power is
coupled into antenna 1 relative to the power input at antenna 2.
Figure 7.20 shows a 2D plot of the directivity for the 4×1 linear patch antenna
array and Figure 7.21 shows the corresponding 3D plot. The directivity for the
antenna array is 11.8 dBi.
Simulation Results of Antenna Array Element
71
S11 Simulation
0
S11 (dB)
−5
−10
−15
−20
−25
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
25
Figure 7.17: S11 of the 4x1 linear patch antenna array.
Z11 Simulation
80
Z11 (Ω)
60
Re(Z11 )
Im(Z11 )
40
20
0
−20
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
Figure 7.18: Z11 of the 4x1 linear patch antenna array.
25
72
Simulation Results of Antenna Array Element
Crosstalk Simulation
−20
S12 , S21 (dB)
S12
−25
−30
−35
−40
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
Figure 7.19: Crosstalk of two λ/2-spaced antenna array elements.
Figure 7.20: Directivity of the 4x1 linear patch antenna array in the
azimuth-elevation plane.
25
Simulation Results of Antenna Array Element
Figure 7.21: Directivity of the 4x1 linear patch antenna array. The
dBi range is -28.2 dBi - 11.8 dBi.
73
74
Simulation Results of Antenna Array Element
Chapter
8
Measurement Results
This chapter presents the manufactured final antenna array design and the measurement results. Sec. 8.1 shows the manufactured antenna arrays, Sec. 8.2 describes the calibration of this design, Sec. 8.3 goes through the S-parameter measurements, and Sec. 8.4 presents the results obtained with the different Directionof-Arrival (DOA) methods.
8.1 Manufactured Patch Antenna Arrays
The design was manufactured by Malmö Mönsterkort and the final manufactured
design is shown in Figure 8.1. This is the same design in CST, showed in Figure
7.12, that has been realized. Initially there were some problems regarding the
dimensions of the PCB (Printed Circuit Board) which did not meet the Design
Rule Check (DRC), but this problem was solved by increasing the size of the
mitered bends.
Figure 8.1: Picture of the manufactured antenna arrays.
A small miscalculation was that the microstrip line did not end in the via and
the last 0.1 millimeters had to be connected by soldering, which is not optimal
with regard to the feeding network design. The connectors used were ordinary
SMA connectors. Figure 8.2 shows the backside of the PCB, together with the
feed cables and SMA connectors.
75
76
Measurement Results
Figure 8.2: Picture of the backside with soldered rigid flex cables.
8.2 Calibration
Calibration of the arrays is done by the same method as calibrating the INRAS
frontend. The calibration data is derived for a single angle of incidence and the
mutual coupling between the elements is neglected. The simplest form is to put
an object at the broadside direction. Since the distance is roughly the same to
each element the phase should be equal. This means that the range, phase and
magnitude profile should be identical for each antenna. One of the Tx-antennas
was used as a reference.
This rudimentary procedure was performed for each Tx antenna in the 2 × 8
and 4 × 4 rhomboid array configurations with a reflector placed R = 5 m in the
direction φ = 0°, θ = 90°, i.e., straight in front of the radar. As a reference, antenna
4 was chosen in both configurations. The calibration coefficients are shown in Table
8.1 and Table 8.2.
Measurement Results
Antenna
1
2
3
4
5
6
7
8
Antenna
1
2
3
4
5
6
7
8
77
Real Part
-1.7561
0.8424
0.2781
1.0000
-1.0386
0.2948
0.0331
-0.4858
Real Part
1.6286
0.8533
0.2832
1.0000
1.0084
0.2356
0.0141
-0.5467
Imaginary Part
-0.0458
-0.5451
0.9942
0.0000
0.0267
0.9090
-1.1729
1.5525
Imaginary Part
-0.1086
-0.5546
0.09463
0.0000
0.0364
0.9561
-1.1229
-1.6575
Tx Antenna
1
1
1
1
1
1
1
1
Tx Antenna
2
2
2
2
2
2
2
2
Table 8.1: Calibration coefficients calculated for 2 × 8 rhomboid
configuration.
78
Measurement Results
Antenna
1
2
3
4
5
6
7
8
Antenna
1
2
3
4
5
6
7
8
Real Part
0.9679
0.8072
0.1602
1.0000
-1.0119
0.1754
0.7355
-0.7489
Real Part
0.2038
0.4538
0.5107
1.0000
-0.6410
0.0870
0.7427
-0.6882
Imaginary Part
-1.7614
-0.5671
1.0437
0.0000
0.5703
1.0123
-0.6136
0.4835
Imaginary Part
-1.6471
-0.7345
0.7576
0.0000
1.0024
0.0997
-0.4602
0.3591
Tx Antenna
1
1
1
1
1
1
1
1
Tx Antenna
2
2
2
2
2
2
2
2
Table 8.2: Calibration coefficients calculated for 4 × 4 rhomboid
configuration.
Measurement Results
79
8.3 Measurement of S-Parameters
To measure the S-parameters of the manufactured antenna arrays, a network analyzer was used. The network analyzer was the E8361A PNA Series Network
Analyzer by Agilent Technologies. The mutual coupling between two adjacent
elements in each antenna array was measured by connecting one antenna to port
1 of the analyzer and the other antenna to port 2, as seen in Figure 8.3.
Figure 8.4 shows the measured S11 parameter of the 4 × 1 linear patch antenna
array. There are three resonances where the antennas have a reflection coefficient
of below -10 dB, their center frequencies are f1 ≈ 23.5 GHz with a reflection
coefficient of S11 (f1 ) ≈ -21.5 Ω, f2 ≈ 24.1 GHz with a reflection coefficient of
S11 (f2 ) ≈ -24.7 Ω, and f3 ≈ 24.7 GHz with a reflection coefficient of S11 (f3 ) ≈
-12.4 Ω.
The measured crosstalk between two λ/2-spaced patch antenna arrays is shown
in Figure 8.5. The crosstalk is around -27.7 dB at the smallest reflecting frequency
f = 24.1 GHz.
Figure 8.3: Measurement of S-parameters using the network analyzer.
80
Measurement Results
S11 Measurement
0
S11 (dB)
−5
−10
−15
−20
−25
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
25
Figure 8.4: S11 measurement of the 4x1 linear patch antenna array.
Crosstalk Measurement
−20
S12
S12 , S21 (dB)
−22
−24
−26
−28
−30
23
23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8
Frequency (GHz)
Figure 8.5: Crosstalk measurement of two λ/2-spaced antenna array
elements.
25
Measurement Results
81
8.4 Tests with Direction-of-Arrival Algorithms
Two different tests were conducted to verify and measure the performance of the
manufactured arrays. The algorithms that were verified in Sec. 5.3 were tested
in both azimuth and elevation. This was conducted in an environment that was
clutter-free enough to get accurate measurements.
A target scene containing two stationary targets were measured and the different algorithms were implemented to see how well they could resolve the targets
with an angular separation. The first test scenario contained only one target and
the second test scenario contained two targets located at different azimuth and
elevation angles. Three different DOA methods were tested to evaluate their performance: Sum-and-Delay, Capon/MVDR and MUSIC. The power of the range
bin was then plotted in (φ, θ) space. The power spectrum of the Capon/MVDR
algorithm was not normalized to show the correct power. This is due to the used
butterworth bandpass filter, which was implemented to filter out the low frequency
signals that were not from the range bin of interest. In these methods the locations
of the spectrum peaks, which corresponds to incoming signals, are of interest.
Figure 8.6 shows the test setup with the INRAS Radarbook and frontend
connected to the antenna board via mini-SMP to SMA connectors.
Figure 8.6: The INRAS Radarbook with the frontend connected to
the antenna board.
82
Measurement Results
During the measurement tests, the bandwidth was increased to use the band
23.7 GHz - 24.3 GHz in order to ensure that performance of the antennas were
equivalent. This is due to the fact that not all of the antennas had a bandwidth
in the desired range 24 GHz - 24.25 GHz due to mismatches, but all of the tested
antennas had a bandwidth which was included the 23.7 GHz - 24.3 GHz range.
Due to lack of time, the intended (narrower) frequency range of 24 GHz - 24.25
GHz was not tested.
8.4.1 Test Scenario One
The first test scenario contained a reflector located R = 5.5 m from the radar
with an azimuth angle of φ = −43° relative to the radar, as shown in Figure 8.7.
The radar is located around 1 m above the ground and using simple algebra, the
elevation angle of the target relative to the radar is θ = arctan (1/5.5)+90° ≈ 100°.
Figure 8.7: The reflector located R = 5.5 m from the radar with an
azimuth angle of φ = −43° and an elevation angle of θ = 100°
relative to the radar.
Results with the 2 × 8 Rhomboid Array Configuration
Figures 8.8-8.10 show the results obtained with the 2 × 8 rhomboid configuration
for test scenario one, where the position of the reflector is marked with a red circle.
The range bin corresponding to the distance to the reflector was used to conduct
the DOA-algorithms in (φ, θ) space. The MUSIC algorithm assumed 7 impinging
signals corresponding to the seven highest eigenvalues of the estimated covariance
matrix.
Measurement Results
Figure 8.8: Power spectrum of the Sum-and-Delay beamformer.
Figure 8.9: Pseudo power spectrum of the Capon/MVDR algorithm.
83
84
Measurement Results
Figure 8.10: Pseudo power spectrum of the MUSIC algorithm.
Measurement Results
85
Results with the 4 × 4 Rhomboid Array Configuration
Figures 8.11-8.13 shows the results obtained with 4 × 4 rhomboid configuration for
test scenario one. The location of the reflector is marked in the figures with a red
circle.
Figure 8.11: Power spectrum of the Sum-and-Delay beamformer.
86
Measurement Results
Figure 8.12: Pseudo power spectrum of the Capon/MVDR algorithm.
Figure 8.13: Pseudo power spectrum of the MUSIC algorithm.
Measurement Results
87
8.4.2 Test Scenario Two
This scenario is similar to the first one, but in this case an additional reflector
was added and its azimuth angle was slightly decreased (relative to the array
broadside). The test scenario is shown in Figure 8.14, where the second reflector
is located R = 5.3 m from the radar with an azimuth angle of φ = 22° relative to
the radar. The elevation angle is θ = arctan (1/5.3) + 90° ≈ 101°, which is around
the same as for the first reflector.
This scenario did not just test the accuracy of the algoritms as was the case
for scenario one, but it also tested the resolution as well as the possible presence of
fake targets due to the grating and/or sidelobe effects from the targets interacting
with each other. The Capon/MVDR and MUSIC methods for the 2 × 8 array
seem to fail and gives large errors in the DOA-estimations.
Figure 8.14: The second reflector located R = 5.3 m from the
radar with an azimuth angle of φ = 22° and an elevation angle
of θ = 101° relative to the radar.
Results with the 2 × 8 Rhomboid Array Configuration
Figures 8.15-8.17 shows the results obtained with the 2×8 rhomboid configuration
for test scenario two. The position of the first reflector is marked with a red circle
and the position of the second reflector is marked with a blue circle.
88
Measurement Results
Figure 8.15: Power spectrum of the Sum-and-Delay beamformer.
Figure 8.16: Pseudo power spectrum of the Capon/MVDR algorithm.
Measurement Results
Figure 8.17: Pseudo power spectrum of the MUSIC algorithm.
89
90
Measurement Results
Results with the 4 × 4 Rhomboid Array Configuration
Figures 8.18-8.20 shows the results obtained with 4 × 4 rhomboid configuration
for test scenario two. The position of the first reflector is marked with a red circle
and the position of the second reflector is marked with a blue circle.
Figure 8.18: Power spectrum of the Sum-and-Delay beamformer.
Measurement Results
Figure 8.19: Pseudo power spectrum of the Capon/MVDR algorithm.
Figure 8.20: Pseudo power spectrum of the MUSIC algorithm.
91
92
Measurement Results
Chapter
9
Discussion
This chapter presents a discussion of the simulation results, the measurement
results and the effectiveness of the Direction-of-Arrival algorithms. The discussion
goes through the strengths and weaknesses of the thesis work and aims to explain
the differences between the simulation results and the actual measurement results.
The chapter starts with Sec. 9.1 explaining the results from the CST simulation,
followed by Sec. 9.2 with a discussion of the measurement results and a comparison
with the simulation results. Finally, Sec. 9.3 describes the test scenario results
obtained from the different DOA-algorithms.
9.1 Simulation Results
The aim was to create a patch antenna that radiates around the frequency f = 24
GHz, and from Figures 7.14 and 7.17 it can be seen that this is achieved successfully
in the simulations. Both the single patch antenna and the patch antenna array
radiates around the correct frequency with a reflection coefficient well below -10
dB, which is desirable. The single patch antenna has a much lower reflection
coefficient (S11 ≈ -40.6 dB) than the antenna array (S11 ≈ -22.6 dB) and hence
it radiates more power around its operating frequency (assuming similar radiation
efficiency).
Both the single patch antenna and the antenna array have bandwidths of
around 1 GHz, with the single patch antenna having a slightly smaller bandwidth
than the array. Their fractional bandwidths, which are less than 20 %, shows that
they are both narrowband antenna designs.
The impedance parameters are important when designing a patch antenna
since it gives information on how to model the antenna system. The impedance
consists of a real part and an imaginary part, Z = R+jX, where the real part is the
resistance and the imaginary part is the reactance. The real part at the operating
frequency shows which impedance transform one has to perform when designing
the feeding network, in order to achieve maximum power transfer. A positive
reactance means the antenna has inductive reactance and a negative reactance
means the antenna has capacitive reactance. The most desirable solution is to
have zero reactance X = 0 and a resistance of R = 50 Ω, since most standard RF
cables have an impedance of 50 Ω. Figures 7.15 and 7.18 show that the real part of
the impedance is around 105 Ω for the single patch antenna and around 58.8 Ω for
93
94
Discussion
the antenna array at their respective operating frequencies. This was considered
when designing the feeding network to ensure good impedance matching. In both
cases the imaginary part of the impedance is negative and close to zero, thus
showing a capacitive behaviour.
Since antenna elements will affect each other in antenna arrays, it is important
to have low crosstalk between them in order to ensure good performance. Figure
7.19 shows that the crosstalk between two λ/2-spaced elements in the antenna
arrays is around -29.2 dB for the operating frequency. For our applications, this is
quite a good value and the crosstalk is low enough to ensure stable performance.
In other applications, such as for phased arrays, the requirement can be much
higher.
Figures 7.16 and 7.21 shows that the directivity for the patch antenna is 7.14
dBi and 11.8 dBi for the antenna array, respectively. The directivity for a patch
antenna is usually between 5-8 dBi and for a 4 × 1 linear patch antenna array it
should be around 11-14 dBi. The simulations seem to give accurate results.
9.2 Measurement Results
The connectors that were used for the antennas were ordinary SMA connectors,
which were not optimized for 24 GHz frequency applications. The reason for this
was that connectors that are suited for operation at 24 GHz are very expensive.
Since many as 30 cables connectors were required, it was important to choose a
cheaper alternative. The differences between the regular and the higher frequency
connectors is in the insertion loss. Since the main aim for this prototype was
to test the different DOA-algorithms, the extra power loss only contributed to a
smaller maximum range, which should not affect the testing capability. A more
important aspect is that the Tx feed lines should be of same length in order to
get the correct phase information for the DOA-algorithms. Even if most of phase
problems could be fixed by a calibration, the equal length made the calibration
easier and more precise.
The measurement of the S-parameters, presented in Figure 8.4, resulted in
three resonant frequencies rather than one. There can be many reasons for why
this would occur. As mentioned before, the microstrip line did not end in the via
and the last 0.1 millimeters had to be connected by soldering. This solution was
not optimal and affects the impedance matching in the feeding network, which can
be the cause for the multiple resonant frequencies. However, all the resonances
are close to the operating frequency of 24 GHz and from Figure 8.4 it can be seen
that the antennas reflect the least around this frequency, which is desired.
Figure 8.5 shows that the measured crosstalk between two λ/2-spaced elements
in an antenna array is -27.7 dB at the smallest reflecting frequency f = 24.1 GHz,
which is low enough to ensure good performance. Taking into account the problem
of multiple resonances in the measured S11, the measured results appear to agree
reasonably well with the simulated results.
Discussion
95
9.3 Direction-of-Arrival Algorithms
The ultimate goal of this thesis was to test the performance of the DOA-algorithms
based on the different configurations in order to verify the effects of the array
patterns simulated in Sec. 6.1. Due to the lack of time, only two of the three
antenna configurations were tested.
The first observation was that the 2 × 8 array was more sensitive to errors in
the calibration, which caused the calibration to be recalculated several times to
get the algorithms to work with the virtual array. The 4 × 4 array did not suffer
to the same extent from these problems.
The algorithms seem to work very well for the 2 × 8 rhomboid array in the first
test scenario, as seen in Figures 8.8-8.10; the results are accurate with the correct
(φ, θ) angles identified in the spectrum and the methods seem to be working as
intended. Likewise, the results for the 4 × 4 array, as seen in Figures 8.11-8.13.
However, from the figures it can be seen that some false targets appear for the 4×4
array. For test scenario two with the 2 × 8 array, the Sum-and-Delay beamformer
works well, which can be seen in Figure 8.15, but the Capon/MVDR and MUSIC
methods fail as shown in Figure 8.16 and Figure 8.17. These two methods seem to
provide quite inaccurate results, which can be due to an incorrect implementation.
Errors could also arise from bad calibration in combination with distortions. For
example, the received baseband signal was observed to be distorted during a part
of the measurements; but without changing anything, just redoing the test seemed
to have fixed the problem. In the case of the 4 × 4 array in test scenario two, seen
in Figures 8.18-8.20, all three methods seem to work well, however, false targets
appear once more.
The methods that involve the estimation of covariance matrix suffered from
lack of robustness. When filtering was insufficient, which was the case when only
a high pass filter or no filter was used, the covariance matrix was severly distorted
and large errors occurred in the DOA-estimation. Since the Capon/MVDR algorithm is less sensitive to modeling errors, it is not as heavily affected as the MUSIC
algorithm. Another problem is that Capon/MVDR and MUSIC algorithms are
sensitive to coherent signals arising multipath propagation (for example, ground
reflection). The low number of antennas can also be the reason why the artifacts
occur since the DOFs are too few to be used effectively. Also, the crosstalk in the
model is assumed to be zero, however, in reality it is not the case, as shown by
the measured results in Figure 8.5.
The performance trade-offs between the different array configurations in the
test scenario are clearly visible; higher resolution with false targets appearing in
the grating lobes versus low resolution with no false targets (grating lobes). The
resolution is poor in the 2 × 8 array, where the spectrum peak is smeared out.
On the other hand, the 4 × 4 array has well performing resolution (more distinct
and narrow peak). Nevertheless, in the case of the 4 × 4 array, the results are
confusing due to the grating lobes giving false detections. The spectrum gives a
total of eight hits in scenario two, when the actual number of targets is two, and
as explained before this is due to the problem of ambiguity in the array factor.
96
Discussion
9.3.1 Implementation of MIMO
The original goal of MIMO as described in Sec. 5.2, was to run TDMA in real time.
This means that the switching between the two Tx-antennas takes place after each
fast chirp, thus enabling real time MIMO measurements where the Doppler-shift
also can be observed. Due to incorrectly working software for the frontend-board,
this was not possible. The MIMO operation had to instead be conducted in time
series; first a number of frames with fast chirps was sent by the first Tx antenna
and received for a couple of seconds followed by the same measurement for the
other Tx-antenna. The results can then be processed to synthesize a complete
virtual array (with both real and virtual elements) for DOA-estimation. This
approach limited our test cases to stationary scenes. The achieved results are good
considering the many sources of errors present in the system. Several errors were
present, such as the connectors being not specified for use at this frequency, which
could introduce phase errors (apart from increased and uneven attenuation). The
soldering and the not optimized antenna connections causes the S11 -parameter to
be noisy, which can be seen in Figure 8.4. The different attenuation and phase
between the TX-channels can be calibrated afterwords, making the design more
tolerant to imperfections in the DOA-estimation. Finally, the antenna board was
found to be not completely flat-surfaced and that is, together with the crude
calibration, recognized to be the main error sources in the DOA-estimation.
9.3.2 Covariance Matrix Estimation Problems and Implications
This problem arises since the model used assumes that the signals in the baseband
are the incoming signals, which is not always the case. The first step was to
remove the low frequency noise shown in Figure 5.6. When doing testing with the
manufactured array, it was seen that this step was not enough. Since all signals
that are not originating from the same distance do not need to be considered, this
insight needs to be somehow accounted for. In the processing of results, this was
done by using a Butterworth bandpass filter, which filtered out all signals except
the ones contained in the range bin of interest. However, this procedure distorts
the power spectrum, thus the spectrum is called a pseudo power spectrum. The
Capon/MVDR method seems to show the ground signal reflection to a greater
extent, which can be seen in Figure 8.19 and Figure 8.20. However, this bandpass
filtering approach is not a very efficient method and it only worked because the
target scene was known in advance. For usage in an unknown scenario, this method
needs to be improved. In the case of the MUSIC algorithm, the eigenvalues that
contain the signal need to be estimated. It was found that the number of signals
assumed should be larger than the number of targets in the test scenario, in order
to achieve better estimation performance. In the results section, the number of
eigenvalues that were assumed to be signals were iterated by how closely the
estimated DOA(s) represent the actual test scenario.
Chapter
10
Conclusions
In this work, a two dimensional patch antenna array was designed for use with
a FMCW-radar that implements MIMO operation for virtual array formation.
The intended application of the radar system is people and traffic detection and
measurement. To get the angular information of a target, different Direction-ofArrival (DOA) algorithms were implemented and their performances were analyzed in two different scenarios for both accuracy and resolution capabilities. The
evaluation was done on a custom-designed microstrip patch antenna array powered by a radar-frontend evaluation board. The measurements were successful and
the implemented algorithms worked, though the ones using information from the
covariance matrix, the Capon/MVDR and MUSIC algorithms, were found to be
unreliable and need to be investigated further to be useful in a radar system. The
conventional Sum-and-Delay beamformer performed very well, though for better
resolution between two separate targets in close proximity of each other, a larger
array than the 2x8 proposed in Figure 6.9 (with close enough spacing between the
antenna array elements to remove the grating lobes, unlike the 4 × 4 array) could
be implemented for better performance.
To conclude, using FMCW-radar for monitoring people and traffic can be done
according to our tests, if the necessary tracking and target counting algorithms
are added in combination with an array configuration with no grating lobe and
high enough resolution.
97
98
Conclusions
Chapter
11
Further Work
The estimation of the covariance matrix can be improved by several methods to
boost the performance of the Capon/MVDR and MUSIC algorithms. The information contained in the covariance matrix can be better structured by performing
preprocessing schemes, which are often implemented when these methods are used.
Two common ones are spatial smoothing and backward-forward averaging. In addition, the use of MUSIC and subspace algorithms require the number of signals
to be known. In practice, the number of signals need to be estimated by another
algorithm, e.g. via Akaike Information Criterion (AIC). The question is if these
methods can be implemented, considering that the system should be low cost, easy
to calibrate and integrated into a single chip. These are interesting topics that
could be further investigated.
One other topic that can be investigated is if the array can be optimized to
reduce the number of elements. This can be done by investigating the number of
antennas that are needed to get an acceptable resolution in real scenarios as well
as making the antennas more integrated with the output and input stages of the
frontend, in order to lower the attenuation in the RF-chain.
Since MIMO operation could not be implemented as intended, Doppler measurements could not be conducted. Since Doppler measurements contain information of the speed of the measured targets, this could not be measured. This
speed information can be exploited to filter out the stationary clutter by performing mean value subtraction. All stationary targets do not have the low frequency
Doppler-shift, which means that the mean value is constant for each chirp for the
entire chirp repetition interval. Removing the mean value will remove the signal
from stationary targets, since it should be relatively constant in all chirps. The
mean value subtraction will increase the SNR when there is a high amount of static
clutter in the target scene, especially when measuring indoors. The drawback is
that the stationary targets can not be seen, but to measure people and traffic, only
moving target are usually of interest. This can be a interesting topic for further
studies.
Some kind of tracking algorithm also needs to be implemented in order to to
filter out hits from the background of noise, clutter and interference. One example
is the Constant False Alarm Rate (CFAR) algorithm, which is a common form of
adaptive algorithm used in radar systems. In addition to this, a tracking algorithm
used to count and track people needs to be developed, if a full working product is
to be considered.
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100
Further Work
References
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