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Evaluation of UWB Beamformers in a Wireless Channeland Potential Microwave Implementations

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Evaluation of UWB Beamformers in a Wireless Channel
and Potential Microwave Implementations
by
Liang Liang
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Electrical And Computer Engineering
University of Toronto
c 2011 by Liang Liang
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Abstract
Evaluation of UWB Beamformers in a Wireless Channel and Potential Microwave
Implementations
Liang Liang
Master of Applied Science
Graduate Department of Electrical And Computer Engineering
University of Toronto
2011
Ultra-wideband (UWB) wireless communication is a topic of intense research. It has the
potential for superior performance over comparable narrowband wireless systems. UWB
wireless systems transmit pulses that have energy concentrated mainly from 3.1 GHz to
10.6 GHz. These pulses are transmitted at very low energy levels so as not to interfere
with many existing wireless systems that operate in the same band. UWB communication
systems can benefit significantly from beamforming networks where the received signal
strength depends on angle of arrival.
This thesis focuses on the characterization of a digital beamformer in a real wireless
channel. The beamformer is evaluated using various methods to judge its performance
impact on a real UWB communication system. An analog UWB beamformer in hardware
is derived by taking advantage of a simple microwave circuit realization. The analog UWB
beamformer is studied and its feasibility is evaluated.
ii
To my mommy and daddy
iii
Acknowledgements
I would like to express my deepest gratitude towards my supervisor, Sean Victor Hum,
for his invaluable guidance and support throughout my MASc study. He has been patient
and devoted to my work. It has been a great honour to be able to work with him and I
am looking forward to continue my study with him for PhD research. This thesis would
not have been possible without his help.
I would like to thank my friends and colleagues in Professor Hum’s research group,
Jonathan, Krishna, Derek, Asanee and Natalie. Thank you so much for the intriguing
technical discussions and always there to aid when I needed it. I would like to thank our
lab manager Tse for your helpful advice on many types of equipment and the occasional
chit-chats.
To my fellow graduate students, Alex, Michael, Neeraj, I have learnt a lot from you
throughout my time here and have always been there to lend a helping hand. To my
friends in the communications group, Chunpo, Hui, Lei, words simply can not describe
the times that it has been, so I can only say how much I appreciate it. It was truly
unforgettable.
I am deeply grateful for the unconditional love and support that my parents have
given me. None of this would have been possible without them. I am forever grateful.
Liang Liang
University of Toronto, 2010
iv
Contents
1 Introduction
1
1.1
Ultra-Wideband Wireless Communication . . . . . . . . . . . . . . . . .
1
1.2
Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2.1
Traditional Narrowband Beamforming . . . . . . . . . . . . . . .
4
1.2.2
Wideband Beamforming . . . . . . . . . . . . . . . . . . . . . . .
7
1.3
Motivation and Thesis Goals . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.4
Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2 Background
2.1
10
Realization of Beamfomers . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.1.1
Hardware Beamformers . . . . . . . . . . . . . . . . . . . . . . . .
11
2.1.2
Algorithmic Beamformers . . . . . . . . . . . . . . . . . . . . . .
13
2.2
Space-Time Processing and Review of an Ideal TTD beamformer . . . .
16
2.3
Derivation of the IIR Beamformer . . . . . . . . . . . . . . . . . . . . . .
18
2.3.1
22
Beamformer Characteristics . . . . . . . . . . . . . . . . . . . . .
3 UWB Beamformer Characterization
27
3.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.2
UWB Channel Sounding Techniques . . . . . . . . . . . . . . . . . . . .
28
3.2.1
Time Domain Sounding Technique . . . . . . . . . . . . . . . . .
28
3.2.2
Frequency Domain Sounding Technique . . . . . . . . . . . . . . .
29
v
3.3
UWB Antenna Array Description . . . . . . . . . . . . . . . . . . . . . .
30
3.4
Far-Field Pattern Characterization . . . . . . . . . . . . . . . . . . . . .
32
3.4.1
Setup and Measurement of Far-Field Pattern . . . . . . . . . . . .
33
3.4.2
Evaluation of Far-Field Pattern . . . . . . . . . . . . . . . . . . .
35
3.4.3
Far-Field Pattern Results . . . . . . . . . . . . . . . . . . . . . .
36
Interference Rejection Characterization . . . . . . . . . . . . . . . . . . .
37
3.5.1
Setup and Measurement of the Interference Rejection Experiment
38
3.5.2
Interference Rejection Evaluation . . . . . . . . . . . . . . . . . .
40
3.5.3
Interference Rejection Experiment Results . . . . . . . . . . . . .
42
Monte Carlo BER Simulations . . . . . . . . . . . . . . . . . . . . . . . .
44
3.6.1
Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.6.2
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . .
47
3.7
Beamformer Characterization Conclusions . . . . . . . . . . . . . . . . .
50
3.8
Sources of Errors in the Experiments . . . . . . . . . . . . . . . . . . . .
51
3.5
3.6
4 Potential Hardware Realization of a UWB Beamformer
57
4.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.2
Continuous-time Transfer Function . . . . . . . . . . . . . . . . . . . . .
58
4.2.1
Beam Characteristics . . . . . . . . . . . . . . . . . . . . . . . . .
63
Evaluation of Transfer Function Given Using S-parameters . . . . . . . .
66
4.3.1
70
4.3
4.4
Unit Cell Simulations . . . . . . . . . . . . . . . . . . . . . . . . .
Microwave Circuit Realization of the UWB Beamformer
. . . . . . . . .
73
4.4.1
Design of the In-Phase Wilkinson Power Divider . . . . . . . . . .
75
4.4.2
Design of the Out-of-Phase Wilkinson Power Divider . . . . . . .
76
4.4.3
Simulated Beam Characteristics of the Hardware Beamformer . .
82
4.4.4
Fabrication and Measurement of Wilkinson Power Dividers . . . .
87
4.4.5
Fabrication and Measurement of Out-Of-Phase Wilkinson Power
Dividers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
90
4.4.6
Calculated Beam Pattern Using Real Microwave Devices . . . . .
93
4.4.7
Feasibility Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
94
5 Conclusions
99
5.1
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A Fabrication and Measurements of BAVAs
103
A.1 Fabrication of BAVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.2 Measurement of BAVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
B CPW Wilkinson Power Divider Dimensions
112
Bibliography
113
vii
List of Acronyms
ADC
Analog-to-digital converter
ADS
Advanced Design System
AOA
Angle of arrival
AF
Array factor
AWGN
Additive white Gaussian noise
BAVA
Balanced Antipodal Vivaldi Antenna
BER
Bit-error-rate
BFM
Beamformer
BPSK
Binary phase shift keying
CPW
Coplanar waveguide
DSP
Digital signal processing
DUT
Device under test
EIRP
Equivalent isotropically radiated power
FDTD
Finite-difference time-domain
FIR
Finite impulse response
HFSS
High Frequency Structure Simulator (Ansoft)
IIR
Infinite impulse response
ISI
Inter-symbol-interference
LNA
Low-noise amplifier
MEMS
Micro-electro-mechanical system
viii
RX
Receiver
SIR
Signal-to-interference ratio
SNR
Signal-to-noise ratio
TTD
True-time-delay
TX
Transmitter
UWB
Ultra-wideband
VNA
Vector network analyzer
ix
List of Symbols
ω1
Spatial frequency
ω2
Temporal frequency
s1
Spatial frequency in s-domain
s2
Temporal frequency in s-domain
n1
Spatial domain index
n2
Time domain index
z1
Discrete spatial frequency in z-domain
z2
Discrete temporal frequency in z-domain
ψbf m
Angle in which a beamformer is set to
ψbf m
Angle in which the main lobe of the beamformer is pointed to
ψsource
Angle in which the desired signal is coming from
Δx
Spatial sampling period or array element spacing
Ts
Temporal sampling period
fs
Temporal sampling frequency
Eb,signal
Energy per bit of the desired signal
Eb,int
Energy per bit of the interference
N
Receiving arra size
R
Transmitted symbol rate
L
Downsample factor
sij
S-parameter of the ij th entry
x
List of Tables
1.1
Beamformer classification. . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3.1
Exponential curve parameters describing the fabricated BAVA. . . . . . .
32
3.2
Dimensions of optimized BAVA. . . . . . . . . . . . . . . . . . . . . . . .
32
3.3
Table of suppression levels (peak values in dB) from Figure 3.10. Values
in parentheses are the theoretical suppression levels assuming free space
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1 Fabricated CPW Wilkinson power divider dimensions in mm.
xi
44
. . . . . . 112
List of Figures
1.1
FCC spectral mask for indoor commercial UWB systems [1]. . . . . . . .
1.2
A narrowband beamformer with a phase shifter connected to each antenna
element in the array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
2
5
A planar wave impinging on an array of equally spaced N antenna elements
with inter-element spacing d. [Figure courtesy of Sean Victor Hum]. . . .
6
2.1
Received 2-D impulse signal from a linear array in the (t, x/c) domain. .
17
2.2
2-D spectrum of the received signal of an array of UWB receivers for
ψ = 10◦ and N = 30 antenna elements. . . . . . . . . . . . . . . . . . . .
17
2.3
A TTD UWB beamformer. . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.4
2-D beam pattern of a TTD beamformer in Figure 2.3 for N = 30 ideal
isotropic elements. The angle that the beamformer is set to ψbf m = 10◦ .
Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.5
Magnitude of 2-D transfer function (2.1). Colour scale in dB. . . . . . . .
20
2.6
First-order 2-D frequency-planar beam plane wave filter whose passband
vector is normal to [L1 , L2 ]. . . . . . . . . . . . . . . . . . . . . . . . . .
2.7
Signal flow graph implementing transfer function (2.5) and difference equation (2.9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8
20
23
2-D transfer function of (2.5). R = 0.01, Δx = 12 mm, ψbf m = 10◦ .
Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
24
2.9
2-D transfer function of the IIR beamformer spatially truncated to 30
elements with spacing 12 mm for isotropic antenna elements. ψbf m = 10◦ .
Color scale shown is in dB. . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.10 2-D transfer function of the IIR beamformer plotted with respect to angle
from broadside. ψbf m = 10◦ . Ideal isotropic antenna elements are used. .
25
2.11 Example of an array with a spatial downsample factor of L = 2. A unit
cell is defined in the dashed box in Figure 2.7. . . . . . . . . . . . . . . .
26
2.12 Spatially downsampled spectrum of a signal whose spectrum is shown in
Figure 2.2. Downsample factor L = 2. Colour scale in dB. . . . . . . . .
26
3.1
BAVA dimension definitions [2]. . . . . . . . . . . . . . . . . . . . . . . .
31
3.2
Fabricated BAVA array. . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.3
Measured and simulated |s11 | of the BAVAs. . . . . . . . . . . . . . . . .
33
3.4
Measured (solid) and simulated (dashed) BAVA array element coupling
values in a linear array with 12 mm spacing. . . . . . . . . . . . . . . . .
3.5
34
Far-field pattern measurement setup. Note that a synthetic array is formed
by displacing the array a distance Δx, the element spacing, in the direction
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6
35
Far-field gain pattern of IIR beamformer for ψbf m = 20◦ , from ideal calculations (solid red), measurements with coupling (solid black), and without
antenna coupling (dashed black). . . . . . . . . . . . . . . . . . . . . . .
37
3.7
UWB channel impulse response measurement setup. . . . . . . . . . . . .
39
3.8
Top view of the measured office environment. . . . . . . . . . . . . . . .
40
3.9
Interference rejection experiment setup. Signals can arrive directly from
four possible angles from broadside of the array ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }. 40
xiii
3.10 Time-domain output of the beamformer plotted for various beamformer
set AOAs. Red is the normalized received signal amplitude with no beamformers present all have the same peak. Black is the received signal with
the beamformer enabled and they are temporally offset for clarity. . . . .
43
3.11 Simulated UWB communication system. . . . . . . . . . . . . . . . . . .
45
3.12 BER of the simulated UWB communication system. N = 120, Δx = 12
mm, ψbf m = ψsource = 10◦ . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.13 BER of the simulated UWB communication system. N = 20, Δx = 72
mm, ψbf m = ψsource = 10◦ , with antenna coupling effect. See. Figure 3.14
for legend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.14 BER of the simulated UWB communication system. N = 8, Δx = 180
mm, ψbf m = ψsource = 10◦ , no antenna coupling effect. BER performance
is degraded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.15 BER of the simulated UWB communication system. N = 20, Δx = 72
mm, ψbf m = ψsource = 27◦ , with antenna coupling effect. The impact of
the beam squninting resulted no performance gain from the beamformer.
See Figure 3.14 for legend. . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.16 BER of the simulated UWB communication system. N = 20, Δx =
72 mm, ψsource = 27◦ , ψbf m = 22◦ with antenna coupling effect. See
Figure 3.14 for legend. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.17 Actual AOA ψbf
m , the angle of the main lobe, as a function of AOA of
the beamformer ψbf m for N = 30, Δx = 12 mm. . . . . . . . . . . . . . .
56
4.1
Unit cell from the signal flow graph in Figure 2.7. . . . . . . . . . . . . .
58
4.2
An RC network terminated by transmission lines. . . . . . . . . . . . . .
60
4.3
2-D transfer function given by equation (4.12) for ψbf m = 10◦ . Colour
4.4
scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
New unit cell of the new beamformer. . . . . . . . . . . . . . . . . . . . .
62
xiv
4.5
Far-field pattern of the new transfer function in Figure 4.3 . . . . . . . .
4.6
Far-field pattern of the digital IIR beamformer tuned ψbf m = 10◦ corresponding to Figure 2.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7
63
64
2-D transfer function given by equation (4.12) for ψbf m = 40◦ . Colour
scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.8
Far-field pattern of the new transfer function in Figure 4.7 . . . . . . . .
65
4.9
Location of the peak angle as a function of frequency for Figure 4.8 . . .
65
4.10 2-D transfer function for ψbf m = 40◦ spatially truncated to N = 30 elements. Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.11 Far-field gain pattern of the new beamformer whose transfer function is
shown in Figure 4.10 for ψbf m = 40◦ . . . . . . . . . . . . . . . . . . . . .
67
4.12 Generic unit cell port definition. Ports 4 and 5 of one cell are connected
to ports 2 and 3 of the next cell. Ports 2 and 3 of the first cell and ports
4 and 5 of the last cell are terminated in matched loads. . . . . . . . . .
67
4.13 Advanced Design System (ADS) unit cell simulation setup. . . . . . . . .
71
4.14 A signal delay matching scheme for the realization the IIR beamformer in
hardware. Cell I has a delay dcell which is compensated by a delay line
with delay dcell at port 1 of the next cell. . . . . . . . . . . . . . . . . . .
72
4.15 Layout of the Wilkinson realized in CPW form. . . . . . . . . . . . . . .
77
4.16 Simulated s-parameters of the Wilkinson power divider realized in CPW
form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.17 Simulated group delay of s21 and s31 of the CPW Wilkinson power divider. 78
4.18 Simulated phase balance of the CPW Wilkinson power divider. . . . . . .
78
4.19 Layout of the wideband phase inversion circuit. Radius of the stub is
16.5 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.20 Simulated s-parameters of the phase inversion circuit. . . . . . . . . . . .
80
4.21 Simulated group delay of the phase inversion circuit. . . . . . . . . . . .
80
xv
4.22 Simulated phase inversion characteristics of the phase inverter. . . . . . .
81
4.23 Layout of the out-of-phase Wilkinson power divider with the defined port
numbering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.24 Simulated s-parameters of the out-of-phase Wilkinson power divider. . .
83
4.25 Simulated group delay of the out-of-phase Wilkinson power divider. . . .
83
4.26 Simulated phase balance between the output ports of the out-of-phase
Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
4.27 Magnitude of ideal transfer function T F2 (s2 ) and simulated one obtained
from unit cell simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
4.28 Phase of ideal transfer function T F2 (s2 ) and simulated one obtained from
unit cell simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
4.29 2-D far-field pattern from 2.5 GHz to 3.5 GHz of the new beamformer with
simulated s-parameters of the in-phase and out-of-phase Wilkinson power
dividers. Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . .
86
4.30 Beam pattern for various frequencies in Figure 4.29. . . . . . . . . . . . .
87
4.31 Fabricated Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . .
88
4.32 Measured (solid) and simulated (dashed) s-parameters of the Wilkinson
power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
4.33 Measured (solid) and simulated (dashed) group delay of the Wilkinson
power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
4.34 Measured (solid) and simulated (dashed) phase balance of the Wilkinson
power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
4.35 Fabricated out-of-phase Wilkinson power divider. . . . . . . . . . . . . .
91
4.36 Measured (solid) and simulated (dashed) s-parameters of the out-of-phase
Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.37 Measured (solid) and simulated (dashed) group delay of the out-of-phase
Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . .
xvi
92
4.38 Measured (solid) and simulated (dashed) phase balance of the out-of-phase
Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
4.39 2-D far-field pattern of the beamformer using real in-phase and out-ofphase Wilkinson power dividers. Colour scale in dB. . . . . . . . . . . . .
94
4.40 Beam pattern for various frequencies of the beamformer with real in-phase
and out-of-phase Wilkinson power dividers. . . . . . . . . . . . . . . . . .
95
4.41 Magnitude of ideal transfer function T F2 (s2 ) versus the one obtained from
ADS unit cell simulation using real in-phase and out-of-phase Wilkinson
power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
4.42 Phase of ideal transfer function 2 versus the one obtained from ADS unit
cell simulation using real in-phase and out-of-phase Wilkinson power divider. 96
4.43 Cef f as a function of ψbf m . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
A.1 BAVA fabricated in two piece as shown. . . . . . . . . . . . . . . . . . . 104
A.2 |s11 | of all fabricated antennas and that of the simulated. . . . . . . . . . 106
A.3 Measured (solid) and simulated (dashed) 4-port s-parameters of the BAVA
array with element spacing 12 mm. . . . . . . . . . . . . . . . . . . . . . 107
A.4 E-plane cut for antenna 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.5 H-plane cut for antenna 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.6 E-plane cut for all fabricated antennas. . . . . . . . . . . . . . . . . . . . 110
A.7 H-plane cut for all fabricated antennas. . . . . . . . . . . . . . . . . . . . 111
B.1 (a) Wilkinson power divider with (b) cross section views. . . . . . . . . . 112
xvii
Your life is defined by its opportunities... even the ones you miss.
xviii
Chapter 1
Introduction
1.1
Ultra-Wideband Wireless Communication
Ultra-wideband signaling for wireless communications has received a lot of research attention in recent years. It is a fast emerging technology that has attractive features
with a large number of applications, including wireless personal area networks, sensor
networks, imaging systems, etc. The Federal Communications Commission (FCC) has
authorized unlicensed use of spectrum for UWB systems between 3.1 GHz to 10.6 GHz
with restricted equivalent isotropically radiated power (EIRP) below −41.3 dBm/MHz
and other frequencies are restricted to an even lower power of −75 dBm/MHz [1]. Figure 1.1 shows the FCC spectral mask for indoor commercial UWB systems. Due to
the restricted energy for transmission, UWB wireless systems have unique interference
challenges as the electromagnetic spectrum in the UWB band is already used by other
wireless systems. Moreover, multiple users could access the same physical channel and
transmitting in the same UWB band creating further interference. Furthermore, the
signal in the channel bounces off objects creating multipath which arrives at the receiver
from all directions making it difficult to decode the transmitted message. One way to
mitigate the multipath effects as well as interference from other wireless systems is to use
1
2
Chapter 1. Introduction
−40
UWB EIRP Emission Level [dBm]
−45
−50
−55
−60
−65
−70
−75
−80
1
2
3
4
Frequency [GHz]
5
6
7
8 9 10
Figure 1.1: FCC spectral mask for indoor commercial UWB systems [1].
beamformers where signals arriving from desired directions are enhanced while signals
arriving from undesired directions are attenuated. Research has shown, in a 2-D simulated environment, that UWB beamformers can be used to significantly improve system
performance. Specifically, they have been shown to decrease the bit-error-rate (BER) and
increase the channel capacity by orders of magnitude [3]. Beamformers offer a promising solution to address the interference and multipath issues of a wireless channel. This
thesis presents work on some quantitative measures of the behaviour of beamformers in
a real wireless communication channel.
1.2
Beamforming
A beamformer is a component in a communication system that provides angle-dependent
spatial discrimination. It can operate in either a transmitting or receiving mode. There
are two major components in a beamformer. The first component is an array of antennas
used for transmitting an outgoing series of signals or for sampling the received signals
in time and space. The second major component is a beamforming network that is
Chapter 1. Introduction
3
connected to the array of antenna elements. Angle-dependent spatial discrimination is
achieved by the appropriate design of the beamforming network. For a beamformer in the
receive mode, the beamforming network appropriately weights the received signals from
all antennas in the array such that the signals arriving from a desired angle is enhanced
while signals arriving from other angles are attenuated as much as possible. Similarly,
for a beamformer in transmit mode, the signal at the desired angle is enhanced while the
signals transmitted to other angles are attenuated.
A beamformer is also a multi-dimensional spatial filter. When a 1-D linear array of
antenna elements is used, this spatial filter is a 2-D filter whose transfer characteristic
depends on both temporal frequency and spatial frequency. It has a corresponding 2-D
transfer function in the spectral domain, as well as an impulse response in time and
space. The 2-D transfer function has a corresponding beam pattern that determines the
amount of spatial discrimination that is experienced by a signal as a function of angle.
There are several main properties of a beamformer:
• transmitting or receiving mode (or both)
• narrowband or wideband
• adaptive or fixed
• hardware or software
• digital or analog
Although a beamformer in general can be used in a transmitter or a receiver, this thesis
focuses on receiving beamformers. The bandwidth of the beamformer is determined by
the bandwidth of the antenna elements and the bandwidth of the beamforming network.
The beamformer is considered to be adaptive when the beam pattern of the beamforming
network is made to be tunable. The beamforming network can be realized in hardware
or in software, both implementing a designed algorithm to process the signals. The
4
Chapter 1. Introduction
Digital
Analog
Delay & Sum Algorithmic
Table 1.1: Beamformer classification.
beamforming network in hardware can be made to process the signals in digital form
by utilizing a digital signal processing (DSP) platform or in analog form by using the
appropriate analog signal processing circuits.
Since the focus of the thesis is on receiving, ultra-wideband, adaptive beamformers, the implementation can be classified into one of the following categories listed in
Table 1.1. Digital beamformers typically employ finite impulse response (FIR) filters
where a delay and sum architecture is used. The digital beamformers can implement
a wideband beamforming mathematical algorithm realized either using software or on
a hardware DSP platform. Analog beamformers typically employ a delay and sum approach and use a true-time-delay (TTD) architecture whereby signals received from an
array are delayed appropriately prior being coherently summed. Such architecture is
described in detail in later sections. The particular beamformer of interest in this thesis is an adaptive wideband receiving beamformer that is digital and algorithmic. This
beamformer has a low computational complexity for digital implementations, and also
lends itself to a simple microwave analog circuit topology that could be realized. Since
few others have realized analog beamformers of this form, a potential analog version of
the proposed digital beamformer is investigated in this thesis.
1.2.1
Traditional Narrowband Beamforming
When multiple antennas are arranged in an array, its far-field pattern can be calculated
using classical array theory and it is the basis of a spatial filter. A typical narrowband
beamforming network is shown in Figure 1.2, which is shown here in the receiving mode.
Each antenna in the array is connected to a phase shifter whose value depends on the
5
Chapter 1. Introduction
Figure 1.2: A narrowband beamformer with a phase shifter connected to each antenna
element in the array.
desired angle of the main lobe. At the desired angle, measured from the broadside
direction of the array, the signals from each element in the antenna array add in-phase
and they constructively interfere at the beamformer output. Signals received from this
direction are the strongest. At other angles, the signals from the antenna elements do
not add in-phase. The signal strength at these angles is much weaker compared to angles
where the signals constructively interfere.
The far-field pattern of an uniform array of antenna elements is the product of two
patterns – the antenna element pattern and the array factor (AF) pattern. The antenna
element pattern is typically fixed. The array factor pattern depends on many factors:
frequency, array geometry and amplitude and phase of the weight elements in the beamformer. Consider Figure 1.3, which shows a linear array of antenna elements spaced with
inter-element distance d. θ is defined with respect to the axis of the array. The array
factor pattern P (θ) is computed as
P (θ) = a0 + a1 ejβd cos θ + a2 ejβ2d cos θ + ... + aN −1 ejβ(N −1)d cos θ
N
−1
=
am ejβmd cos θ ,
(1.1)
m=0
where β is the free space propagation constant, am is the amplitude weighting of each
6
Chapter 1. Introduction
Figure 1.3: A planar wave impinging on an array of equally spaced N antenna elements
with inter-element spacing d. [Figure courtesy of Sean Victor Hum].
antenna element and N is the total number of antennas. Since β =
2π
λ
=
2πf
c
is dependent
on temporal frequency f (where c is the speed of light), the shape of the array factor
pattern changes as a function of frequency. Moreover, it can be easily shown that the
angle of the main lobe, θmax , for uniform amplitude weights where am = 1, must satisfy
2πf
d cos θmax + Δφ = 0,
c
(1.2)
where Δφ is the uniform phase difference between two adjacent phase shifters. It is clear
from this equation that as f changes, Δφ needs to track linearly with frequency in order
to have a constant θmax . Most microwave phase shifters do not have this property, and
consequently the angle of the main lobe shifts. This implies that if a wideband signal
was received using this beamformer, the main lobe of the receiver can not point to a set
direction for all frequencies, which can result in signal loss. Different amplitude weighting
distributions would produce different array factor patterns. Side-lobe levels can also be
controlled by using different amplitude distributions.
An ideal wideband beamformer would have its far-field pattern independent of frequency. Particularly, the shape and angle of the main lobe would remain unchanged as
frequency is swept. However, in practice, a frequency-independent far-field pattern can
Chapter 1. Introduction
7
only be achieved within a limited bandwidth. Reconfigurable wideband beamforming is
difficult to achieve in general, and is discussed in the next section.
1.2.2
Wideband Beamforming
Wideband beamforming refers the frequency-invariant property of the pattern associated
with a beamformer. However, with a fixed aperture size, it is difficult to maintain a
constant beam shape over the entire UWB frequency spectrum. Hence, in this thesis, a
particular characteristic of the beam pattern, namely the direction of the main lobe, is
considered to be a measure of a beamformer’s bandwidth. If the angle of the main lobe
does not vary significantly as frequency is swept, then the beamformer is considered to
be wideband. There are two approaches to achieve wideband beamforming. The first
approach is to use a true-time-delay (TTD) architecture. This architecture works by
using TTD elements connected to each antenna to compensate for the delay of the signal
between two adjacent antenna elements. When all the signals are delay-matched, the
signals from each antenna element are then summed coherently to produce a signal with
a much larger strength. The beamformer can be made adaptive if the TTD elements
themselves can be tuned. The second approach to achieve wideband beamforming is
to appropriately design an algorithm to process the signal from each antenna. This
signal processor is the beamforming network. The advantage of this approach is that a
wide variety of far-field patterns can be achieved as different algorithms would achieve
different far-field patterns. The designed algorithm would allow for trade off between
performance characteristics such as beam width, bandwidth, complexity, etc. In practice,
the algorithms are typically realized on a DSP platform after the signals have been
digitalized by analog-to-digital converters (ADCs). In Chapter 2, the details of these two
approaches are discussed.
Chapter 1. Introduction
1.3
8
Motivation and Thesis Goals
UWB beamformers offer promising potential in providing interference and noise rejection
in a real radio channel. Beamformers can also provide a level of protection against multipath effects while dynamically adapting to changes in the channel environment. The
beamformer of particular interest in this thesis is an algorithmic infinite impulse response
(IIR) beamformer, which is described in detail in Chapter 2. Previous work has shown
that this beamformer was capable of providing significant improvements to the performance of a communication system [3]. However, the performance of the beamformer
was characterized in a 2-D simulated environment which is not sufficient to capture the
abundance of multipath reflections and scattering in a real three-dimensional channel.
In addition, ideal transmitters and receiver arrays were used which does not capture the
effects of real UWB antennas and element coupling in the receiving array. Finally, UWB
beamformers have been not been characterized in real radio channels. It is, in part, the
goal of this thesis to characterize beamformers in a real radio channel to assess their effectiveness in combating the multipath effects and interference from other UWB wireless
users in the same channel.
Wideband beamformers that are also reconfigurable are difficult to realize in hardware. Although they exist in literature, as shown in the literature survey in Chapter 2,
they all typically deployed in the true-time-delay (TTD) architecture which is typically
realized in hardware in an integrated circuit form. Hardware tunable wideband beamformers have not been widely explored as the wide bandwidth and tunability properties
over such wide frequency range pose a very challenging research problem. In addition to
the characterization of beamformers in a real radio channel, it is the goal of this thesis
to propose the design of a potential hardware realization of an analog wideband tunable
beamformer. This potential hardware realization of the beamformer does not employ
a true-time-delay architecture and differs in architecture compared to others presented
in literature. The analog microwave beamformer would have the features of the digital
Chapter 1. Introduction
9
beamformer with no analog-to-digital converters and the systolic array of DSP hardware
associated with the digital beamformer.
1.4
Thesis Outline
The chapters in this thesis are outlined as follows. Chapter 2 provides an overview of
how the beamformers are realized followed by a detailed derivation of the beamformer
to be characterized. Chapter 3 begins by describing how the wireless UWB channel was
characterized, followed by assessment of the performance parameters of the beamformer
using a variety of methods, namely, far-field pattern measurement, interference rejection experiment and Monte Carlo bit-error-rate (BER) simulations. Chapter 4 focuses
on a potential hardware realization of this particular beamformer. A feasibility study
is included followed by simulations and measurements of the potential beamformer in
hardware. Chapter 5 concludes this thesis by drawing conclusions about the beamformer
and describes future work that can be done in this area.
Chapter 2
Background
In this chapter, some background information related to the different types of beamformers is presented. A beamformer can be categorized into two main types – ones that
employ a TTD architecture and ones that employ a signal processing architecture to
realize an algorithm as the means to achieve beamforming. The beamformer of interest
in this thesis is of the algorithmic type, though later in the thesis a physical realization of
this beamformer is presented. Its mathematical derivation is presented in this chapter.
The properties of the beamformer resulting from its derivation are summarized.
2.1
Realization of Beamfomers
Beamformers can be realized in hardware or in software. Hardware beamformers typically
consist of a TTD architecture using tunable TTD elements. The algorithmic type of
beamformers that do not employ a TTD architecture typically are realized on a DSP
platform to leverage the flexible implementations of various signal processing techniques.
References to these beamformers are discussed in the following sections.
10
Chapter 2. Background
2.1.1
11
Hardware Beamformers
UWB beamformers realized in hardware typically utilize a TTD architecture where tunable delay devices are employed. After signal delays are properly compensated by the
tunable delay devices, a coherent summation is performed of all the signals from each antenna element such that the signals are added constructively, creating the desired signal
with a larger amplitude. However, the design of accurate tunable delays devices with precision delay control is not trivial. The tunability of the delay devices is achieved mainly in
two ways: changing the speed of signal propagation in the device or changing the physical
length of the device. Tunable delay devices can be realized in many forms – hardware
integrated circuits, RF microwave distributed circuits or simply lumped elements. This
section summarizes a representative set of realized UWB beamformers employing a TTD
architecture.
TTD elements can be realized by using distributed micro-electro-mechanical system
(MEMS) transmission lines in an integrated circuit form. [4] realizes TTD elements
by placing MEMS-actuated bridges periodically over a section of a coplanar waveguide
(CPW) transmission line. The MEMS bridges are placed across the center conductor
and connected the two ground planes of the CPW transmission line. The MEMS bridges
increase the capacitance per unit length of the transmission line as they are only a few
microns in height. Tunability is achieved by applying a DC voltage to the center conductor causing the MEMS bridges to bend towards it, changing the effective capacitance
per unit length. Hence, the group velocity of the signal propagating on the transmission
is changed and a tunable delay device is realized.
Artificial transmission lines can also be synthesized using tunable inductances [5].
The variable inductance is achieved by placing a second coil in close proximity with the
primary coil whose inductance is the per unit inductance of the artificial transmission
line. The current in the second coil is controlled by loading it with varactor diodes whose
capacitance can be changed by a control voltage. The current in the second coil changes
Chapter 2. Background
12
the mutual inductance between the primary and secondary coils which in turn changes
the self inductance of the primary coil. Since the inductance of the transmission line is
changed, the group velocity of signal propagation is changed as well.
The previous two references have shown that the group velocity of the signal can
be modified on a transmission line to change the signal delay. [6] realizes a wideband
beamformer by using electronically-controlled trombone lines where a signal experiences
a path of different lengths depending on which switches and amplifiers are turned on. The
characteristic impedance of the transmission line remains the same as the inductance and
capacitance per unit length do not change. The beamformer in this work conceptually
used a TTD architecture, however, it employed clever derivative of this architecture by
sharing signal delay paths to save chip area while relaxing the required maximum delay
of the TTD elements.
The wideband beamformers shown so far are in an integrated circuit form. The TTD
elements can also be realized using optical devices. [7] develops a TTD fiber-optic UWB
beamformer utilizing a tunable wavelength laser and dispersive fiber prism whose delay
depends on the wavelength of the light in the fiber. A receiving array of eight broadband
spiral antenna elements modulates an array of Mach-Zehnder modulators. The output
light from an optical port has an intensity that is proportional to the amplitude of the
modulating voltage waveform. The modulated light from the array of Mach-Zehnder
modulators is fed into an array of dispersive fibers whose optical signal delay depends
on the wavelength of the tunable laser. The wavelength of the light is tuned such that
the desired amount of delay is generated by the fibers. Signals were combined optically
and PIN photodiodes were used to convert the optical signals back to electrical signals
for more processing. A TTD UWB beamformer implemented using optical components
is then realized.
Chapter 2. Background
2.1.2
13
Algorithmic Beamformers
Many different types of algorithms exist in the literature for implementing wideband
beamforming, each having their own unique characteristics. These algorithms are typically implemented solely in software as they can be very complex. In this section, a survey
of different types of algorithmic beamformers and their architectures are summarized.
[8] describes a procedure to design a beamforming algorithm to produce a beam
pattern that is frequency invariant. This method is derived from an ideal continuous array
of sensors, whose required frequency response can be calculated given a particular beam
pattern. The continuous array of sensors is then discretized for practical implementations.
This method produces a beam pattern that is virtually independent of frequency by
utilizing frequency dilation properties of a linear array. [9] gives examples of how to
design the algorithm. [10] develops a multi-rate and a single-rate method to realize the
algorithm on a DSP platform. Although it is possible to realize the frequency invariant
beam pattern using this design approach, its complexity for multidimensional arrays
increases significantly [9].
Wideband beamforming can also be achieved by a direct optimization of the coefficients of the FIR filters connected to the receiving array of antennas elements [11]. In a
conventional narrowband beamforming network in equation (1.1), the beam pattern P (θ)
is a linear combination of the received signal governed by a set of complex weights am .
However, instead of having a fixed complex weighting, the weights can be made to be
dependent on frequency such that the beam pattern is as close to the desired one as possible. For instance, let am,n be the complex weight at the mth antenna element at frequency
n ffs , where n is the frequency index and fs is the sampling frequency. The set of am,n
are the optimization variables subject to constraints given by the desired beam pattern.
Such optimization problems can be done via available convex optimization methods [12].
However, for large sensor sizes, the number of variables for optimization is extremely
large.
Chapter 2. Background
14
Beamspace adaptive arrays are another method to achieve adaptive wideband beamformers [13, 14]. In this architecture, the sampled digital signals from each antenna
element in the receiving array are fed to an array of beamformers, which are individually
realized by a FIR fan filter consisting of delay and sum circuits with variable coefficients.
The design techniques for FIR fan filters for wideband beamforming are readily available and examples are given [14, 15]. Each beamformer in the array forms a beam in
a particular direction with one beam designated as the primary beam and the rest are
designated as so-called auxiliary beams. The auxiliary beams cover all possible directions
where interference and noise could arrive. The overall system output is a linear combination of the outputs from all beamformers. The weights associated with the output from
each beamformer are adaptively determined based on the direction and the strength of
the interference in the environment with the goal of minimizing the received interference.
The process to find the optimal weights is iterative [13].
The discussion so far is limited to beamforming by using FIR filters which can be
implemented in the form of a delay and sum architecture. FIR filters have only zeros in
the transfer function while IIR filters can have both zeros and poles. It is well known
that an IIR filter provides steeper rolloff characteristics than an FIR filter of the same
order. A beamformer whose transfer function is IIR would have a lower order for same
rolloff characteristics compared to a FIR beamformer. [16] describes a method to design a
multidimensional IIR beamformer. This paper uses a network resonance design approach
where a 3-D transfer function Ta (kx , ky , ω) has a resonance (the passband of the transfer
function) on a plane in the (kx , ky , ω) domain, which is the 3-D Fourier transform of the
(x, y, t) domain. A second transfer function Tb (kx , ky , ω) is designed in the same way. The
overall 3-D transfer function T (kx , ky , ω) = Ta (kx , ky , ω)Tb (kx , ky , ω) has a passband that
is a line defined by the intersection of passbands (planes) of Ta and Tb . This forms a highly
selective beam in 3-D that can be tuned to any angle by changing the line of intersection.
To discretize such a transfer function in both space and time, a 3-D bilinear transform is
Chapter 2. Background
15
applied to T so that the overall transfer function can be realized using discrete sensors in
two dimensions of space and digitally processed in discrete time. More complex shapes
can be designed using the network resonance concept. [17] considers a cone-shaped beam
designed using this approach.
[3] shows a wideband receiving beamformer using the network resonance concept approach discussed above. It is an IIR filter with poles in the spatio-temporal frequency
domain. Network resonance can also be synthesized using FIR techniques as well. However, the IIR nature of this beamformer allows for a lower complexity compared to FIR
beamformers for the same rolloff characteristics. This beamformer is completely characterized by a few parameters and no complicated design procedure is necessary. The
coefficients are algebraically defined and hence the beam is readily steerable to any angle. It will be shown in a later section that the beam angle can be set with only one
parameter. Furthermore, it will be shown in later sections that this beamformer has a
simple signal flow graph whose circuit topology is simple to realize in both digital and
analog form.
This topology is the beamformer of interest in this thesis. This digital beamformer
does not employ a TTD architecture nor does it have a complex design procedure associated with some of the beamformers in literature with FIR filters. It does not need
expensive integrated circuit typically associated with hardware TTD beamformers. The
hardware version of this beamformer, described in detailed in Chapter 4, has a very
simple microwave circuit topology which can be readily implemented in planar form.
Furthermore, previous work has shown that this particular beamformer is capable of improving system performance by many orders of magnitude [3]. However, the performance
was evaluated in a simulated 2-D environment. In this thesis, the performance of this
beamformer will be characterized in a real wireless UWB channel and conclusions will be
drawn based on its impact on a real wireless communication system. This beamformer
will be referred to as the “IIR beamformer” for the remainder of this thesis. Its properties
Chapter 2. Background
16
are reviewed in the next section in order to gain an appreciation of the beamformer.
2.2
Space-Time Processing and Review of an Ideal
TTD beamformer
It is important to be familiar with the two-dimensional spectrum of a broadband signal
received by an one-dimensional linear array of antenna elements as this multi-dimensional
signal is to be processed by beamformers for the remainder of this thesis. The spectrum
of the input is to be multiplied by the 2-D transfer functions of beamformers to obtain the
desired signal. The characteristics of an ideal TTD beamformer are also reviewed as its
architecture is often employed in hardware UWB beamformers, as seen in Section 2.1.1,
and this beamformer type which will serve as a reference for performance comparison to
the IIR beamformer later on this thesis.
When an impinging impulse signal arriving from angle ψ, defined with respect to
broadside of the array, the 2-D signal in the (t, x/c) domain is shown in Figure 2.1,
where x is the axis of the receiving linear array and c is the speed of light. Let α be the
angle in which the straight line makes with the x = x/c axis as shown in Figure 2.1.
The relationship between dt and dx is dt = dx sin(ψ)
. It is easy to see that tan(α) =
c
dt
dt dx
= dx
= sinc ψ (c) = sin ψ. Hence, α = tan−1 [sin ψ] defines the space-time angle
dx
dx
of incoming wave with respect to the x -axis. The 2-D Fourier transform of the received
signal in Figure 2.1 has a region of support inclined at the same angle as the space-time
angle α. Figure 2.2 shows the 2-D spectrum of the received signal by having N = 30element in the receiving array for ψ = 10◦ .
Figure 2.3 shows the architecture of an ideal TTD UWB beamformer in the receiving
mode. Each antenna element in the array is connected to a TTD device, shown here as a
piece of ideal transmission line which is also called a TTD phase shifter. The lengths of
these transmission lines are determined by the position of the antenna that it is connected
17
Chapter 2. Background
Figure 2.1: Received 2-D impulse signal from a linear array in the (t, x/c) domain.
Figure 2.2: 2-D spectrum of the received signal of an array of UWB receivers for ψ = 10◦
and N = 30 antenna elements.
to and the angle of the impinging UWB wave. The amount of delay for the mth delay
element is governed by dm = mΔx/c sin(ψT T D ), where Δx is the element spacing, ψT T D
is the desired beamforming angle with respect to broadside of the array and c is the
speed of light in free space. When the delays are properly compensated in this fashion,
a coherent sum is performed and all the signals add constructively at the output of the
18
Chapter 2. Background
Figure 2.3: A TTD UWB beamformer.
beamformer.
Figure 2.4 shows the 2-D beam pattern of a 30-element TTD beamformer when the
desired beam angle is set to 10◦ . Its wideband characteristics are clearly visible in this
figure as its main lobe points to the same direction, ψT T D = 10◦ , for all frequencies.
However, it is clear from the figure that the shape of the beam pattern does change
with frequency as expected as the phase at each frequency differs. Nevertheless, this
beamformer is considered to be wideband due to its squint-free property of its main lobe.
2.3
Derivation of the IIR Beamformer
The particular beamformer of interest in this thesis is described below. Its derivation
comes from the network resonance approach [3] where a fictitious 2-D analog circuit is
resonant at a particular set of frequencies. The first-order 2-D fictitious circuit is shown
19
Chapter 2. Background
in Figure 2.6 whose transfer function T (s1 , s2 ) is given by
T (s1 , s2 ) =
R
Y (s1 , s2 )
,
≡
R + s 1 L1 + s 2 L 2
W (s1 , s2 )
(2.1)
where W (s1 , s2 ) and Y (s1 , s2 ) are the 2-D Laplace transforms of the input and output
respectively. The frequencies s2 = jω2 , s1 = jω1 represent the temporal frequency and
spatial frequency, ko sin(ψ), respectively, where ko is the free space wavenumber and ψ
is the angle of arrival of the incoming broadband wave with respect to the broadside
direction of the array. The magnitude of transfer function (2.1) is shown in Figure 2.5.
This transfer function achieves unity when the frequencies (ω1 , ω2 ) satisfy
ω1 L1 + ω2 L2 = 0,
(2.2)
Figure 2.4: 2-D beam pattern of a TTD beamformer in Figure 2.3 for N = 30 ideal
isotropic elements. The angle that the beamformer is set to ψbf m = 10◦ . Colour scale in
dB.
Chapter 2. Background
20
Figure 2.5: Magnitude of 2-D transfer function (2.1). Colour scale in dB.
which is a straight line in the (ω1 , ω2 ) that makes an angle α with the ω2 axis, given by
α = tan−1 (L2 /L1 ). This line is the passband of the 2-D filter over which the beamformer
exhibits high spatial selectivity and broad bandwidth. Note that transfer function (2.1)
describes a passive circuit and its transfer function is meaningful for only positive inductances L1 and L2 . Hence for positive L1 and L2 , it is clear from equation (2.2) that either
ω1 or ω2 must be negative in order to satisfy this equation. This implies that the beamformer can only scan in one quadrant, i.e. from 0◦ to 90◦ , as measured from broadside.
The other quadrant can be scanned by reversing the spatial order of the received signals.
Figure 2.6: First-order 2-D frequency-planar beam plane wave filter whose passband
vector is normal to [L1 , L2 ].
The 2-D continuous transfer function given by equation (2.1) can not be realized easily
21
Chapter 2. Background
since a continuous array of sensors is needed (continuous s1 ). Here, both dimensions are
discretized so that the signal is sampled digitally in time and spatially using discrete
sensors. A standard 2-D bilinear transform [18] of equation (2.1) is found by setting,
s1
s2
1 − z1−1
2
=
Δx 1 + z1−1
1 − z2−1
2
,
=
cTs 1 + z2−1
(2.3)
(2.4)
where Δx and Ts is the spatial and temporal sampling period respectively and c is the
speed of light. It is worth noting here that the discretization in the time (s2 ) domain
is not necessary if the signal can be processed in the continuous-time domain. However,
for now we consider the discrete-space and discrete-time version of the beamformer. The
discrete 2-D transfer function is given by
H(z1 , z2 ) = α
(1 + z1−1 )(1 + z2−1 )
,
1 + b10 z1−1 + b01 z2−1 + b11 z1−1 z2−1
(2.5)
where
bij =
α =
R+
2
(−1)i L1
Δx
2
R + Δx
L1
R
R+
2
L
Δx 1
+
+
+
2
(−1)j L2
cTs
2
L
cTs 2
.
2
L
cTs 2
(2.6)
(2.7)
Here, z1 and z2 represent spatial and temporal frequencies respectively in the z-domain,
respectively. The bij coefficients are functions of the original parameters of the continuous transfer function, R, Δx and Ts . The R parameter is used to set the 3 dB rolloff
frequencies in the first-order circuit, analogous to the 3 dB frequency of a first-order lowpass RC circuit. The smaller the value of R, the lower the frequency is, in this case, the
sharper the main lobe of the beamformer becomes. These bij coefficients mathematically
set the angle to which the beamformer is tuned, ψbf m . The spatial sampling period, Δx,
22
Chapter 2. Background
is the antenna spacing in a linear array of antenna elements.
Since both the signals have been spatially and temporally discretized, one can use
a DSP platform with a discrete array of sensors to realize this 2-D transfer function.
Transfer function (2.5) can be re-arranged as
W (z1 , z2 )(1 + z1−1 )(1 + z2−1 ) = Y (z1 , z2 )(1 + b10 z1−1 + b01 z2−1 + b11 z1−1 z2−1 ),
(2.8)
and it can be written as a difference equation given by
y(n1 , n2 ) =
1 1
w(n1 − i, n2 − j) −
i=0 j=0
1 1
bij y(n1 − i, n2 − j),
i=0 j=0
i+j=0
(2.9)
where n1 and n2 are the spatial and temporal indices, respectively, and w(n1 , n2 ) is the
2-D discrete-time discrete-space input to the beamformer.
Figure 2.7 shows the signal flow graph that realizes equation (2.9). Defined in the
dashed box is a unit cell which processes the signal from the current antenna, previous
antenna and the outputs from the previous unit cell. Each antenna is connected to
one unit cell. The progression of the signal from one unit cell to the next implements
the spatial feedback loop that corresponds to the spatial feedback in equation (2.9). A
temporal feedback loop clearly exists at the output of the unit cell. Hence this 2-D filter
is of the IIR type in both space and time.
2.3.1
Beamformer Characteristics
In this section, the receiving beam pattern of the IIR beamformer is studied. Figure 2.8
shows the ideal 2-D transfer function (2.5) in the Nyquist square |ω1 | < ωs1 /2 and
|ω2 | < ωs2 /2. For low spatial and temporal frequencies, this discrete 2-D transfer function
approximates the original continuous transfer function shown in Figure 2.5 very well. In
this region, the passband approximates a straight line in the (ω1 , ω2 ) domain where
Chapter 2. Background
23
Figure 2.7: Signal flow graph implementing transfer function (2.5) and difference equation
(2.9).
the beam shape and pointing angle is not a strong function of temporal frequency. In
practice, only a finite number of antenna elements and unit cells can be realized. Thus,
the array is truncated by a spatial rectangular window. As a result, the ideal sharp peak
in Figure 2.8 are spread to a broader width and energy is spilled into adjacent spatial
frequencies, as shown in Figure 2.9. The spatial windowing effect is clearly visible in this
figure as sidelobes. Mapping the spatial frequencies in terms of angle from broadside
gives a 2-D far-field pattern shown in Figure 2.10. Here, the beam squinting is clearly
visible as the direction of main lobe is a function of temporal frequency.
One can downsample the inputs in the spatial domain to reduce the number of
required antenna elements in the receiving array, alleviating potential hardware constraints and costs. However, aliasing occurs if the signal is spatially undersampled,
Chapter 2. Background
24
Figure 2.8: 2-D transfer function of (2.5). R = 0.01, Δx = 12 mm, ψbf m = 10◦ . Colour
scale in dB.
Figure 2.9: 2-D transfer function of the IIR beamformer spatially truncated to 30 elements with spacing 12 mm for isotropic antenna elements. ψbf m = 10◦ . Color scale
shown is in dB.
defined when the sampling period is greater than the Nyquist period. This leads to
repetitions in the spectrum of the signal in the frequency domain. For a downsample
factor of L, the received signal the w(n1 , n2 ) have a corresponding downsampled signal
Chapter 2. Background
25
Figure 2.10: 2-D transfer function of the IIR beamformer plotted with respect to angle
from broadside. ψbf m = 10◦ . Ideal isotropic antenna elements are used.
ŵ(n1 , n2 ) = w(n1 L, n2 ) for n1 = kL, k ∈ Z and ŵ(n1 , n2 ) = 0 otherwise. Hence the
unit cells at index n1 = kL are connected to antennas while the rest of the unit cells
are fed with zero-inputs. Figure 2.11 shows an example to illustrate the mechanism in
which the spatial downsampling occurs for downsampling factor of L = 2. The new 2-D
input spectrum to the beamformer is same as the original spectrum except that duplicate
copies of the original spectrum appears an extra L − 1 times in the Nyquist square, as
shown in Figure 2.12 for L = 2. This downsampled input spectrum is then multiplied by
the transfer function shown in Figure 2.9. Clearly, the spatially aliased components in
Figure 2.12 lie in the stop band region of Figure 2.9. Thus, those aliased frequency components are not expected to make significant contributions for reasonable downsampling
factors, which is why spatial downsampling can be exploited by this type of beamformer.
26
Chapter 2. Background
Figure 2.11: Example of an array with a spatial downsample factor of L = 2. A unit cell
is defined in the dashed box in Figure 2.7.
Figure 2.12: Spatially downsampled spectrum of a signal whose spectrum is shown in
Figure 2.2. Downsample factor L = 2. Colour scale in dB.
Chapter 3
UWB Beamformer Characterization
3.1
Motivation
Previous work has characterized the performance of the IIR beamformer described in
Chapter 2 in a simulated environment [3]. An array of ideal field samplers was used that
neglected the effects of a real array of UWB antennas, such as the frequency-dependent
pattern of the antennas, mutual coupling between elements and impedance matching.
These non-ideal effects, which are not captured by the simulations in [3], can degrade
the performance of the IIR beamformer in real life. Furthermore, the performance of
the IIR beamformer was evaluated in a 2-D simulated environment. This 2-D model is
not sufficient in capturing all the realistic effects that exist in a radio channel as there
are considerably more multipath effects and scattering fields from objects in the third
dimension.
It is the goal of this chapter to characterize the digital IIR beamformer in a real
wireless UWB channel. There are several challenges to overcome in order to characterize
the performance of the beamformer. First, an array of real UWB antennas must be
designed and fabricated. The antennas are to be arranged in a linear array so that
realistic effects of the antenna array are captured in the performance assessment of the
27
Chapter 3. UWB Beamformer Characterization
28
IIR beamformer. Next, the impulse response of a wireless channel over an ultra-wide
bandwidth needs to be measured. By knowing the impulse response, the channel output
can be determined given any excitation via convolution.
The IIR beamformer is characterized using three different methods. The first method
measures its far-field pattern with realistic UWB antennas. The second method measures
the interference rejection capability of the beamformer when multiple users are transmitting at the same time. The third method measures the improvement in bit-error-rate
(BER) of a wireless communication system with and without the beamformer in place.
The improvement in BER is also compared to that achieved by an ideal TTD beamformer as this architecture is often employed in hardware realizations of beamformers, as
discussed in Chapter 2.
3.2
UWB Channel Sounding Techniques
An office environment is one type of channel that is often used in many of UWB applications. Short-range applications such as Wireless Personal Networks, Wireless HDTV
and Wireless USB could all have an office environment as its communication channel.
Hence, an indoor office channel was chosen to be characterized for the experiments in
this chapter. There are two main approaches to excite a wireless channel for it to be
characterized – one is in the time domain while the other is in the frequency domain.
There are a number of advantages to both approaches and they are summarized here.
3.2.1
Time Domain Sounding Technique
The simplest approach to measure a channel’s impulse response is to send a short pulse
in time whose bandwidth covers the entire frequency range of interest [19]. The received
signal in time is a good approximation of wideband impulse response of the channel.
A high speed oscilloscope can be used to capture the received signal whose spectrum
Chapter 3. UWB Beamformer Characterization
29
is a close approximation to the channel’s frequency response over the excited signal
bandwidth. The most attractive aspect of this direct measurement system is its lack
of complexity. The frequency response of the channel can be displayed in real time on
the oscilloscope via a simple Fourier transform. However, this direct approach is rarely
used in practice because very high instantaneous pulse energy is needed to have a decent
range.
One method often used in practice is to use a modulated pseudo-random bit sequence
to excite the channel. A well-known property of maximal length pseudo-random bit
sequences is that the autocorrelation is a close approximation to a delta function. Hence,
this property can be used to measure the impulse response of an UWB channel [20, 21, 22].
The impulse response of the channel can be obtained by taking the cross correlation of
the input and output of the channel. This approach is attractive because the total
transmitted energy can be increased by using a longer pseudo-random sequence and the
post-processing gain allows for more dynamic range and a lower noise floor. However,
more sophisticated equipments are needed to measure the channel’s impulse response.
An arbitrary waveform generator is needed to produce the desired pseudo-random bit
sequence. Modulators are needed to modulate the baseband signal up to (and potentially
down from) the carrier frequency and a high-speed RF sampling oscilloscope is needed
to capture the received signal for post-processing.
3.2.2
Frequency Domain Sounding Technique
A vector network analyzer (VNA) can be used to directly measure the frequency response of a device under test (DUT). At each frequency point, the VNA evaluates the
s-parameters of the DUT and s21 is taken to be the transfer function of the DUT. In
an UWB channel measurement, the wireless channel with the transmitting and receiving
antennas is the DUT. Many researchers have used this method to obtain the frequency
response of a wireless channel to compute the channel’s statistics [23, 24, 25]. To obtain
Chapter 3. UWB Beamformer Characterization
30
the measured s21 from the VNA of the DUT, the VNA is calibrated such that the measured s-parameters do not include the effects of the test cables connected to the VNA.
The advantage of this method is that it is simple to set up. Only one instrument is required to obtain the frequency response of the channel. However, long cables are needed
between the transmitting and receiving antennas limiting the length of the channel that
can be measured. The channel must also remain stationary over the sweep time of the
instrument. Since a small office environment is to be characterized, the channel length
of an office is not exceedingly long and cables with such lengths are readily available.
Hence, this frequency domain method is chosen for the characterization of an indoor
office channel.
3.3
UWB Antenna Array Description
An array of UWB antennas was fabricated in order to measure the characteristics of
the beamformer with real UWB antennas. The type of UWB antenna chosen was a
balanced antipodal Vivaldi antenna (BAVA) which was originally designed for breast
cancer detection [2]. Vivaldi antennas are non-resonant traveling type of antenna where
the guided wave transitions smoothly to a free-space wave. It has an extremely wide
impedance bandwidth, ranging from approximately 2.4 GHz to in excess of 10 GHz and
it has low dispersion compared to other types of UWB antennas [26]. A detailed study of
the effects of the dimensions of the BAVA is presented in [2]. The authors of [2] designed
the BAVA to be submerged in canola oil which exhibits a dielectric constant of 2.5. In
this work, the dimensions of the BAVA were modified to operate in free space for use in
wireless communication.
The BAVA was simulated in a finite-difference time-domain (FDTD) simulator called
SEMCAD. The dimensions of the BAVA were numerically optimized to minimize |s11 | of
the antenna over the widest frequency range. The dimensional parameters are defined in
Chapter 3. UWB Beamformer Characterization
31
Figure 3.1. Each curve describing the exponential section of the BAVA can be described
using an equation in the form Z = ±AeP (x−B) + C. Table 3.1 describes the set of
equations defining the curved boundaries of the BAVA. The optimized BAVA dimension
parameters are shown in Table 3.2. A photograph of the fabricated array of BAVAs is
shown in Figure 3.2.
Figure 3.1: BAVA dimension definitions [2].
Figure 3.2: Fabricated BAVA array.
Figure 3.3 shows the measured and simulated |s11 | of all the fabricated BAVAs when
each of them are isolated. The measured |s11 | values are very close to simulated values for
Chapter 3. UWB Beamformer Characterization
Curve
Et
Ef
Ea
A
W ts−W g
2(eP t∗Lt −1)
Af
W ts+W a
2(eP a∗La −1)
32
P
B
C
Pt
0
Wg/2 - At
Pf Lt+Lts Wts/2 - Af
Pa Lt+Lts -Wts/2 - Aa
Table 3.1: Exponential curve parameters describing the fabricated BAVA.
Parameter Value [mm]
Wts
2.24
Wg
10
Ws
2
Wa
56
W
76
Pa
0.05
Pt
-0.15
Pf
0.4
Af
0.1
Lt
23
La
60
Lts
1
Table 3.2: Dimensions of optimized BAVA.
all four fabricated BAVAs. The measured (solid curves) and simulated (dashed curves)
coupling values when the BAVAs are arranged in a linear array with 12 mm spacing
are shown in Figure 3.4. The coupling values between adjacent antennas are quite high,
averaging at about −10 dB from 3 GHz to 10 GHz. The measured full 4-port s-parameters
of the BAVA array and the measured far-field pattern of each antenna are included in
Appendix A along with the detailed fabrication steps.
3.4
Far-Field Pattern Characterization
The first method to characterize the beamformer is to measure its far-field pattern with
a real receiving antenna array. The aim is to verify that the far-field pattern of the
beamformer is not affected significantly by the real UWB antennas. Particularly, the
33
Chapter 3. UWB Beamformer Characterization
0
−5
−10
−15
|s11| [dB]
−20
−25
−30
−35
−40
−45
−50
Antenna 1
Antenna 2
Antenna 3
Antenna 4
Simulated
2
4
6
8
Frequency [GHz]
10
12
Figure 3.3: Measured and simulated |s11 | of the BAVAs.
mutual coupling between the antenna elements could distort the far-field pattern of the
beamformer.
3.4.1
Setup and Measurement of Far-Field Pattern
Figure 3.5 shows the far-field pattern measurement setup. A four-element linear array
of BAVAs with 12 mm element spacing was placed in an anechoic chamber. 12 mm
was chosen as the antenna spacing to avoid spatial aliasing of the received signal, as it
satisfies the Nyquist sampling period of 15 mm assuming a maximum frequency of 10 GHz
is used for communication. A VNA measured the complex transmission coefficient s21
between the transmitter and the receiver. This coefficient is a function of the angle
of incidence and antenna position. A synthetic array of N -elements can be created by
34
Chapter 3. UWB Beamformer Characterization
0
−5
−10
S−Parameters [dB]
−15
−20
−25
−30
−35
|s21|
−40
|s31|
|s41|
−45
−50
|s32|
2
3
4
5
6
7
Frequency [GHz]
8
9
10
Figure 3.4: Measured (solid) and simulated (dashed) BAVA array element coupling values
in a linear array with 12 mm spacing.
moving the four fabricated antennas to the appropriate distances, effectively creating
an array size that is larger than the size of the physical array, hence saving fabrication
time and cost. A synthetic array with reasonable size had to be chosen subject to a
reasonably directive beam pattern of the beamformer and the physical constraints of
moving the fabricated antenna elements in the anechoic chamber on a rotating platform.
A 16-element synthetic array was found to be a good compromise and was implemented
by moving the four antennas to the appropriate positions 15 times. Each time, the entire
array is moved by the element spacing of Δx = 12 mm, as shown in Figure 3.5.
One receiving antenna (#2) was connected to the VNA while the remaining three
acted as dummy antennas connected to matched loads. Hence, the antenna coupling
effect due to dummy antennas #1, #3 and #4 was included in the measured complex
gain. The antenna coupling effect from more distant elements was not considered because
35
Chapter 3. UWB Beamformer Characterization
it was expected that the immediately adjacent elements would dominate the coupling
effect while elements further away would not contribute significantly. Furthermore, in
spatially downsampled configurations shown in later sections, the element spacing is much
greater than 12 mm and the effects of non-adjacent elements are even less pronounced.
3.4.2
Evaluation of Far-Field Pattern
For a given measured transmission coefficient, the excitation to the IIR beamformer, for
the mth antenna element at a particular angle from broadside ψ is
Em (t, ω, ψ) = Am (ω, ψ) cos(ωt + γm (ω, ψ))
(3.1)
for m = 1, 2, ..., 16. Am (ω, ψ) and γm (ω, ψ) are the measured magnitude and phase of the
complex gain s21 at frequency ω and angle ψ. Two sets data for Am (ω, ψ) and γm (ω, φ)
are measured corresponding to cases with and without dummy elements in place. When
there are no dummy antenna elements present, then the measured complex gain is that of
a purely synthetic 16-element array. Likewise, when the three remaining dummy elements
Figure 3.5: Far-field pattern measurement setup. Note that a synthetic array is formed
by displacing the array a distance Δx, the element spacing, in the direction shown.
Chapter 3. UWB Beamformer Characterization
36
are present, then the measured complex gain includes mutual coupling effects.
To compute the far-field pattern of beamformer, the input Em (t) is the input to
the difference equation (3.1), all of which is computed and processed in MATLAB. The
output y(n1 , n2 ) is computed for each angle of incidence of the signal ψ ∈ (−90◦ , 90◦ )
in equation (3.1) and the amplitude of the output sinusoid is known. This amplitude
variation as a function of angle is the far-field pattern of the beamformer at a particular
frequency.
3.4.3
Far-Field Pattern Results
Figure 3.6 shows the measured far-field gain pattern for three cases with the IIR beamformer tuned to ψbf m = 20◦ with N = 16-element array spaced at 12 mm. The solid
red curve is the gain pattern of the IIR beamformer assuming ideal field samplers with
isotropic patterns and no mutual coupling. The dashed black curve is the gain pattern
from a purely synthetic 16-element array. The solid black curve is the gain pattern that
includes element coupling effects. The gain of the uncoupled case with a purely synthetic
array is higher than the gain of the coupled case. This behaviour is expected and is
likely caused by the significant mutual coupling between adjacent elements as well as a
degradation in the active impedance match, both of which reduce the measured gain.
The total measured pattern is expected to be the pattern of the beamformer multiplied
by the antenna element pattern. The gain difference between the ideal (red) curve and
the curve without antenna coupling (dashed black) is expected to be the BAVA gain as
shown in Figure A.5 at 20◦ from broadside. The difference in gain of the red the curve
and the dashed black curve approximately corresponds to measured gain at 20◦ from
broadside in Figure A.5.
The measured far-field pattern (black curves) are for the worse case mutual coupling
scenario as the antennas are at only 12 mm apart. Overall, the general shape of all the
plots are still very close to each other across a wide range of frequencies. This show
37
Chapter 3. UWB Beamformer Characterization
4.4 GHz
20
20
10
10
Gain [dBi]
Gain [dBi]
3.2 GHz
0
−10
−20
−10
−20
−50
0
ψ°
5.6 GHz
50
20
20
10
10
Gain [dBi]
Gain [dBi]
0
0
−10
−20
−50
0
ψ°
6.8 GHz
50
−50
0
ψ°
50
0
−10
−20
−50
0
ψ°
50
Figure 3.6: Far-field gain pattern of IIR beamformer for ψbf m = 20◦ , from ideal calculations (solid red), measurements with coupling (solid black), and without antenna
coupling (dashed black).
that even with worst case antenna spacing, the beam characteristics are not sensitive
to mutual coupling between the antenna elements. Thanks to the gain provided by the
BAVA elements, the gain of the beamformer with real antennas is more than that of the
beamformer alone. The introduction of the real antenna elements as the receiving array
does not significantly degrade the pattern shape and the real antennas have added gain to
the beamformer, proving that real antennas are well-suited for this digital beamformer.
3.5
Interference Rejection Characterization
Of significant interest is the beamformer’s interference rejection capability in a multi-user
environment as multiple UWB users could be transmitting in the same channel causing
Chapter 3. UWB Beamformer Characterization
38
interference with one another. This experiment characterizes the interference rejection
capability of the beamformer in the time-domain where multiple users simultaneously
transmit wideband signals causing interference. The interference rejection capability
of the IIR beamformer in a real radio channel with rich multipath effects is unknown.
The far-field pattern of the IIR beamformer has been shown to be very robust even
with real UWB antennas with significant antenna element coupling. The beam pattern
characterization described in the previous experiment was in the frequency domain where
far-field pattern characteristics are examined at discrete points in frequency. Hence, the
interference rejection capability is assessed in the time-domain in this experiment.
3.5.1
Setup and Measurement of the Interference Rejection Experiment
The interference rejection experiment setup is shown in Figure 3.7. In this setup, a
VNA was used to acquire the impulse response in the frequency domain of an office
environment from 2 GHz to 10 GHz, which is shown in Figure 3.8 where RX is the centre
of the receiving array. The transfer function was taken to be the measured s21 . An inverse
Fourier transform was applied to obtain the channel’s bandpass impulse response. This
method has the advantage of being simple to set up and capable of obtaining highly
accurate measurements. During the data acquisition process, nothing in the vicinity of
the channel was moving and the channel was assumed to be stationary. Measurements
were checked for repeatability. The VNA was calibrated so that the measured frequency
response only included the antennas and the wireless channel. Furthermore, the RMS
delay spread of the measured channel impulse response was checked against that of the
reported in the literature for a small office channel environment. The RMS delay spread
in the measurements was approximately 10 ns which is consistent with the lower bound
reported for indoor channels [19]. Similar to the far-field pattern measurement setup, the
same three dummy antenna elements were in place to capture element coupling effects
Chapter 3. UWB Beamformer Characterization
39
in the measurements.
Figure 3.7: UWB channel impulse response measurement setup.
The receiver array was placed on an arm of a scanner capable of moving within a
span of 1.5 m spatial window to an accuracy of a few microns. 12 mm element spacing
was used, satisfying the spatial Nyquist period of 15 mm for a maximum frequency of
10 GHz. Up to a 120-element (1.5 m) synthetic array could be realized on the positioner.
A computer script was written to control the position of the antenna array and captured
the measured s21 from the VNA at proper positions.
The angle of arrival (AOA) is defined with respect to the broadside direction of the
receiver array. One transmitter is moved to four different positions so that impinging
signals from four different AOAs could be produced ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }. The
interference rejection simulation setup is shown in Figure 3.9.
40
Chapter 3. UWB Beamformer Characterization
Figure 3.8: Top view of the measured office environment.
Figure 3.9: Interference rejection experiment setup. Signals can arrive directly from four
possible angles from broadside of the array ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }.
3.5.2
Interference Rejection Evaluation
The received signal at the mth antenna element, rm (t), in the receiving array is derived
from the measured impulse response from each transmitter. It is the superposition of the
Chapter 3. UWB Beamformer Characterization
41
signals from each of the transmitter convolved with the corresponding impulse response.
rm (t) is expressed as
rm (t) =
3
hmi (t) ∗ si (t),
(3.2)
i=0
where hmi (t) is the measured impulse response from the ith transmitter to the mth antenna
element and is the inverse Fourier transform of the measured s21 , si (t) is the signal transmitted by the ith transmitter and ∗ denotes linear convolution. A multi-user interference
scenario is created when each transmitter emits a broadband pulse, si (t) = δ(t − iTd )
delayed by Td , such that the received signal rm (t) is the superposition of the delayed
impulse responses from each transmitter,
rm (t) =
3
hmi (t − iTd ).
(3.3)
i=0
A small amount of delay Td is introduced to temporally separate the received pulses from
such that received pulse from a single transmitter can be clearly shown, but in practice
the signals can overlap and still be resolved by the beamformer.
It is expected that when there is no beamformer at the receiver, the received signal
would consist of four peaks corresponding to the four transmitted pulses. The amplitudes
of the four received peaks are solely determined by the channel response. Since the
channel responses differ, the received four peak amplitudes may differ. Thus, in equation
(3.3), hmi (t) is normalized to unity before the received signals are summed such that
when there is no beamformer exist at the receiver, the four received peaks all have the
same amplitude. This serves as a base for comparison to the case when the beamformer
is enabled at the receiver. The amount of attenuation of the received signal is then solely
caused by the beamformer, a direct measurement of the wideband interference rejection
capability of the beamformer in the multipath radio channel.
Chapter 3. UWB Beamformer Characterization
3.5.3
42
Interference Rejection Experiment Results
A 120-element receiving array with 12 mm element spacing was used in this experiment.
When the beamformer was set to the first transmitter located at broadside of the receiving
array ψbf m = ψsource = 0◦ in Figure 3.10(a), the received signal from that direction had
the highest peak as expected. Similarly, for ψbf m = ψsource ∈ {10◦ , 20◦ , 27◦ }, the received
signal amplitude had the highest peak when the beamformer was tuned to them, as shown
in Figures 3.10(b), 3.10(c), 3.10(d) respectively. The suppression levels are summarized in
Table 3.3. The suppression levels of the signals are measured relative to the highest peak
of the received signal. Values in parentheses in this table are the theoretical suppression
levels in an ideal channel.
It is clear that the signals arriving from angles that were not where the beamformer
is tuned to experienced a great deal of attenuation. The transmitters were spatially
separated by only 10◦ (7◦ for the last transmitter) and provided on average of approximately 9.4 dB suppression for adjacent transmitters. The further it is from the tuned
angle of the beamformer, the greater the attenuation is experienced by the signal. This
behaviour is expected as the gain of the far-field pattern of the beamformer quickly drops
when deviated from the tuned angle.
Note that the receiving array and the beamformer is in the azimuth plane, therefore no
spatial discrimination is provided in the elevation plane other than the antenna pattern
itself. Hence the signals bouncing off the ground or ceiling arriving at the receiver in the
elevation plane are not spatially filtered by the beamformer. However, the beamformer
still provides significant spatial discrimination overall.
It is also worth noting that the measured suppression levels are not expected to be
the same as the suppressions level from the measured far-field pattern. The far-field
pattern is in the frequency domain and its gain varies across frequency. This wideband
interference rejection levels includes the gain and pattern variations for all frequencies.
Furthermore, this interference rejection experiment was performed in a multipath rich
43
Chapter 3. UWB Beamformer Characterization
real radio channel where the signals can arrive from any angle, perturbing the received
peak level. Hence, the measured interference rejection levels can only compared to the
far-field pattern on a first-order basis.
To capture the effect of the beamformer more rigorously as a part of a communication
system, Monte Carlo BER tests of an UWB communication system are performed in the
next section, with and without the beamformer to gauge its performance.
1
1
X: 0.3997
Y: 1
0.8
Received Signal [au]
Received Signal [au]
X: 0.0792
Y: 1
0.6
X: 0.3989
Y: 0.3066
0.4
X: 0.7209
Y: 0.1223
0.2
0
0
0.5
0.6
0.4
X: 0.7209
Y: 0.332
X: 0.0794
Y: 0.3004
X: 1.043
Y: 0.2418
0.2
X: 1.043
Y: 0.0947
1
0.8
0
1.5
0
0.5
Time [μ s]
1
(a) IIR beamformer tuned to ψbf m = 0◦
(b) IIR beamformer tuned to ψbf m = 10◦
1
1
X: 1.042
Y: 1
0.8
Received Signal [au]
Received Signal [au]
X: 0.7212
Y: 1
X: 1.043
Y: 0.646
0.6
0.4
X: 0.3997
Y: 0.265
0
X: 0.0839
Y: 0.7518
0.8
0.6
X: 0.7211
Y: 0.3016
0.4
X: 0.4031
Y: 0.2194
X: 0.0833
Y: 0.1562
0.2
0
1.5
Time [μ s]
0.2
0.5
1
Time [μ s]
(c) IIR beamformer tuned to ψbf m = 20◦
1.5
0
0
0.5
1
1.5
Time [μ s]
(d) IIR beamformer tuned to ψbf m = 27◦
Figure 3.10: Time-domain output of the beamformer plotted for various beamformer set
AOAs. Red is the normalized received signal amplitude with no beamformers present all
have the same peak. Black is the received signal with the beamformer enabled and they
are temporally offset for clarity.
Chapter 3. UWB Beamformer Characterization
44
Tx Location
1
2
3
4
◦
0
0
-10.3 (-30.4) -18.3 (-36.0) -20.5 (-38.3)
◦
10
-10.5 (-20.4)
0
-9.6 (-13.5) -12.3 (-19.5)
20◦
-16.1 (-22.8) -11.5 (-20.3)
0
-3.8 (-5.0)
◦
27
-2.5 (-23.6) -13.3 (-22.2) -10.4 (-13.9)
0
Table 3.3: Table of suppression levels (peak values in dB) from Figure 3.10. Values in
parentheses are the theoretical suppression levels assuming free space channel.
3.6
Monte Carlo BER Simulations
The goal of the Monte Carlo BER simulations is to assess the improvement in BER
that can be provided by the beamformer in a multi-user scenario by using real measured
channel responses. Previous work has shown that this beamformer lowered the BER
of the received signal in an UWB wireless system by several orders of magnitude [3].
However, the performance of the beamformer was shown in a simulated two-dimensional
environment with an isotropic transmitter and an ideal array of field samplers as the
receiving array. Realistic effects of the UWB antenna as a transmitter and antenna
element coupling in the receiving array were not captured. Furthermore, the simulated
nature of the 2-D channel was not adequate to capture the effects of abundant multipath
and scattered fields in a real channel, especially when the simulation was in only two
dimensions.
In this experiment, one user transmitted the desired signal while the others acted
as interferers, emulating interference signals generated by other UWB users in the same
channel. The amount of interference rejection capability of this experiment is captured
in the improvement of the BER of the received signal. When the beamformer is tuned to
the desired transmitter, the BER is expected to be much lower compared to that when
no beamforming is present. The effects of the IIR beamformer on the BER curves are
studied in detail in different beamformer configurations. In addition, since many modern
UWB beamformers implemented in hardware utilize the TTD architecture, it will be
used as the reference to gauge the performance of the IIR beamformer.
45
Chapter 3. UWB Beamformer Characterization
3.6.1
Simulation Setup
Figure 3.11 shows the simulated UWB communication system. The locations of the four
transmitters are the same as the one described in the interference rejection experiment
shown in Figure 3.9. The generated random bits are fed into a pulse shaper to convert
the bits to pulse shapes that represent the bits. A raised cosine was used as the pulse
shape, which is given by,
2Wo sinc(2Wo t)
cos(2π(W − Wo t))
,
1 − 4(W − Wo )t2
(3.4)
where W is the desired bandwidth, Wo = 1/2T represents the minimum Nyquist bandwidth for the rectangular spectrum and W − Wo is the excess bandwidth. T = 250 ps
and W = 1.7Wo is used to produce a frequency content from approximately 2 GHz to
10 GHz. The signal from the pulse shaper is then sent through a channel whose impulse
response is that of the measured ones from the interference rejection experiment. The
impulse response from each transmitter to each antenna element in the receiving array
is known. This received signal is then passed through a matched filter, the output of
which is decoded assuming a perfect symbol timing recovery. Since a multi-user scenario
environment is desired, one of the AOAs, ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }, is selected to be the
desired signal source while the transmitters located at the three remaining AOAs acted
Figure 3.11: Simulated UWB communication system.
Chapter 3. UWB Beamformer Characterization
46
as interference sources. The signal-to-interference ratio (SIR) in dB is defined as
SIRdB = 10 log10
Eb,signal
Eb,int
(3.5)
where Eb,signal and Eb,int are the energy per bit of the desired signal and total energy
per bit of all interferers respectively, measured at the receiver. Both quantities include
the effects of multipath captured in the measured channel response. A constant additive
white Gaussian noise (AWGN) of power Eb /No = 10 dB is added to the received signal to model the superposition of independent noise sources, including but not limited
to, analog-to-digital converters quantization noise, background noise from environment
picked up by the UWB antennas, and the thermal noise in the receiver equipment.
Different array configurations of the beamformer were studied. The following parameters were varied to study their impact on the system performance:
• Number of antenna elements, N
• Antenna spacing, Δx
• Angle of arrival of received signal, ψsource
• Symbol rate, R
• Effect of mutual coupling
A minimum number of antenna elements N is desired to reduce the cost of the receiver
hardware. The beam squint of the main lobe of the beamformer for high ψbf m is expected
to negatively impact the BER performance for such angles. ψsource ∈ {10◦ , 27◦ } was tested
to assess the impact of the beam squinting and the performance results were compared
to a TTD beamformer, which does not suffer from beam squinting. The close proximity
of the antenna elements yields relatively high mutual coupling, which may also reduce
the BER performance, hence cases with and without antenna coupling effect were also
compared.
Chapter 3. UWB Beamformer Characterization
3.6.2
47
Simulation Results
Effect of Antenna Coupling, Symbol Rate and Bilinear Warping
Two symbol transmission (bit) rates were simulated, R ∈ {1, 2} Gb/s, with binary phase
shift keying (BPSK) as the modulation format. Figure 3.12 shows the receiver BER
curves as a function of SIR for the array configuration with N = 120 elements, Δx =
12 mm and ψbf m = ψsource = 10◦ . In Figure 3.12(a), the two circled curves shows the
receiver BER for the two transmission rates when no beamformer was employed. The
BER quickly drops and saturates on a floor as the SIR is increased. This behaviour is
expected as at high SIRs, the power of the interfering signal is negligible compared to
the signal power and the only source of decoding error is the added AWGN noise and the
multipath effects causing inter-symbol-interference (ISI), both of which are independent
of SIR. When either IIR or TTD beamformers are used, the BER floor is pushed to
a much lower level, showing that beamformers are very effective in rejecting multipath
interference. For the same BER, a much higher SIR is needed at the receiver when
beamformers are not used, showing an improvement in SIR provided by the beamformer.
Higher symbol rates yielded a higher BER as expected due to higher ISI. The performance
of both of the two beamformers are reasonably close despite that the IIR beamformer
suffers from the effects of bilinear warping at high frequencies as shown in Figure 2.10.
Figure 3.12(b) shows the BER curves when the antenna mutual coupling effect is
introduced. For the TTD beamformer, the coupling worsens the BER by approximately
3 dB for both symbol rates. For the IIR beamformer, the coupling effects did not change
the BER significantly for both symbol rates. For symbol rate R = 2 Gb/s, the coupling effect has caused the BER to be increased slightly at high SIR. The reason for
this behaviour is thought to be the following. At low SIRs, the power from the interference signal dominates the contributions to decoding errors, while at high SIRs, the ISI
dominates the decoding errors while ISI is higher when antenna coupling is present.
Chapter 3. UWB Beamformer Characterization
48
The mutual coupling effect is the worst in this configuration as the element spacing is
the smallest at 12 mm. Despite this, the IIR beamformer provided significant improvements compared to no beamforming at the receiver. Its performance is comparable to
that of the TTD beamformer despite that the IIR beamformer has warping effects.
Effect of Spatial Downsampling
The input can be downsampled in the spatial domain to reduced the number of required
antenna elements. The mechanism to spatially downsample is described in Figure 2.11,
where every L − 1 input is zeroed between every Lth cell.
Figure 3.13 shows the BER performance of the two beamformers with the two symbol
rates at downsampling factor L = 6, where the number of antenna elements has reduced
to N = 120/6 = 20 and element spacing increased to Δx = 72 = 6 × 12 mm. In this
downsampled case, both beamformers still offer significant improvement in BER relatively
to the no beamforming case with only 20 elements. For symbol rate R = 1 Gb/s, the IIR
beamformer provides about 2 orders of magnitude improvement in BER compared to no
beamforming. For a symbol rate of R = 2 Gb/s, the IIR beamformer provides over an
order of magnitude of improvement. The TTD beamformer performs moderately better
for the lower symbol rate as the main lobe of the TTD beamformer does not point to
a different direction as a function of frequency. The higher the symbol rate, the higher
the ISI in the received signal, makes the frequency invariant nature of the receiver more
important to receive error-free symbols.
With the antenna elements spaced at 72 mm, the effect of the element coupling is much
less than when elements were placed at only 12 mm. It was found that further decreasing
the number of elements degrades the BER. Figure 3.14 shows the spatial downsampling
factor of L = 15 with N = 8 antenna elements spaced at Δx = 180 = 15 × 12 mm.
At this high downsampling factor, the original received spectrum is folded in the spatial
domain 14 times. Figure 2.12 shows an example of the 2-D spectrum for downsample
Chapter 3. UWB Beamformer Characterization
49
factor L = 2, where the signals is only folded 1 time. For L = 15, a great deal of the
spatially aliased components of the original signal fall back to be within the passband
(main lobe) of the beamformer, contributing significantly to decoding errors.
Effect of Angle of Arrival
The IIR beamformer suffers from beam squinting resulting from the 2-D bilinear transform of the transfer function. The actual angle that the main lobe of the IIR beamformer
points, ψbf
m , is different from the angle in which the beamformer is set to, ψbf m . For
each ψbf m , ψbf
m depends on frequency. The higher that ψbf m is set to, the worse the
beam squinting becomes. Figure 3.17 shows the actual angle of the main lobe, ψbf
m
as a function of the angle that the beamformer is set to, ψbf m . At ψbf m = 27◦ , ψbf
m
ranges from approximately 31◦ to 61◦ in the frequency range of 2.5 GHz to 8 GHz. This
squint is expected to negatively impact the BER performance of the beamformer. To
quantitatively capture this effect, Figure 3.15 shows the BER for ψsource = ψbf m = 27◦ .
The performance in BER in this case has degraded significantly and the BER is higher
compared to no beamforming at all, rendering the IIR beamformer useless.
However, this effect can be mitigated by pre-tuning the ψbf m of the beamformer to
an angle such that, at the center frequency of 6 GHz, the beamformer is tuned to ψsource .
◦
Figure 3.17 shows that for ψbf m = 22◦ corresponds to ψbf
m = 27 at 6 GHz. With
this configuration, Figure 3.16 shows the BER performance when beamformer is pretuned to 22◦ . The performance in BER is now improved significantly and comparable
to the performance achieved by the TTD beamformer. This shows that the pre-tuning
is effective in addressing the beam squinting. The pre-tune angles can be calculated or
stored as a look-up-table in a real communication system.
Chapter 3. UWB Beamformer Characterization
3.7
50
Beamformer Characterization Conclusions
The IIR beamformer has been characterized with real antenna array using three different
methods. The first method was the measurement of the beamformer’s far-field pattern
using real UWB antenna as the receiving array. It was shown that the measured gain
of the beamformer with real antennas was higher than that of the beamformer alone as
the antenna elements provided gain of its own. Despite being in the worest coupling
scenario with element spacing of 12 mm, the measured far-field pattern agreed closely
with the ideal pattern. This showed that the real UWB antenna array is well-suited for
the beamformer.
The second method to characterize the beamformer was to assess its wideband interference rejection capability in a real radio channel. Multiple users were placed at different
angles of arrival where each user transmitted a wideband pulse. The IIR beamformer was
placed at the receiver to observe the signal attenuation level based on angle of arrival.
It was shown that the beamformer provided an excellent spatially selectivity despite the
fact the beamformer was implemented in the azimuth plane while signals arriving from
the elevation plane were not spatially discriminated by the beamformer. The interference
rejection capability of the beamformer was shown to be excellent even in the multipath
rich environment of a real radio channel. This also showed the beamformer’s effectiveness
in mitigating multipath effects.
The third method was to assess the performance of the beamformer is in terms of
BER of a wireless communication system. BER simulations were conducted with multiple
users transmitting in the same physical channel causing interference with one another.
The impact of the beamformer on BER in a realistic UWB communication system was
assessed for different beamformer configurations, namely, symbol rate, element spacing,
angle of arrival and antenna coupling. It was shown that even in the case with the
highest antenna coupling values, the BER did not degrade significantly. Quantitatively,
the improvement in BER is consistent with that is seen in earlier reported work [3],
Chapter 3. UWB Beamformer Characterization
51
despite the fact that the simulated conditions in a 2-D channel are very different from
that the measuredno channel. Different symbol rates and pulse shapes were used and
the beamformer still yielded a significant improvement in BER in a real radio channel.
The spatial downsampling mechanism was proven to be effective, reducing the number
of required antenna elements by a factor of 6 from 120 elements to 20 elements. For
higher ψbf m , the BER was worse compared to angles that are closer to broadside due
to bilinear transform in the beamformer’s transfer function. Strategically pre-tuning the
beamformer was shown to mitigate the effect of the beam squinting and lowered the BER
to a level that was comparable to that of a TTD beamformer.
The analysis of the IIR beamformer has shown its promising potential. In the next
chapter, a potential hardware realization of this digital beamformer is discussed in detail.
Real physical microwave circuits are fabricated to assess the feasibility of the hardware
beamformer.
3.8
Sources of Errors in the Experiments
The errors in the experiment mainly reside in the measured UWB frequency response
of the channel in the anechoic chamber and in the office environment. In the anechoic
chamber, the four BAVAs were placed on a rotating platform and its gain is measured
as a function of frequency and position. Accurate angular and linear alignment of the
BAVAs was required. A great deal of effort was spent to align the antennas. However,
there could still be some errors left leading to distortion in the measured far-field patterns
of the beamformer.
During the frequency response acquisition of the office environment, the measured s21
from a VNA is taken to be the transfer function of the UWB channel. Any stochastic
process in the channel would result in errors in the simulated BER. Hence, multiple
acquisitions over the same channel were carried out and checked for repeatability and
Chapter 3. UWB Beamformer Characterization
52
consistency. It is difficult to comment exactly the type of errors that would result in
the measurement from a particular VNA. However, the s-parameter measurement from
a modern network analyzer is extremely accurate and is considered to be trustworthy.
Moreover, the measured impulse response of the small office channel was compared to
that of the response of other small office environment, the mean excess delay and the
RMS delay spread were all in the expected range of a typical office environment.
53
Chapter 3. UWB Beamformer Characterization
0
10
−1
BER
10
−2
10
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
(a) No antenna coupling effect.
TTD Bfm Rate 1 Gb/s
TTD Bfm Rate 2 Gb/s
IIR Bfm Rate 1 Gb/s
IIR Bfm Rate 2 Gb/s
No Bfm Rate 1 Gb/s
No Bfm Rate 2 Gb/s
0
10
−1
BER
10
−2
10
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
(b) With antenna coupling effect.
Figure 3.12: BER of the simulated UWB communication system. N = 120, Δx = 12
mm, ψbf m = ψsource = 10◦ .
54
Chapter 3. UWB Beamformer Characterization
0
10
−1
BER
10
−2
10
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
Figure 3.13: BER of the simulated UWB communication system. N = 20, Δx = 72 mm,
ψbf m = ψsource = 10◦ , with antenna coupling effect. See. Figure 3.14 for legend.
0
10
−1
BER
10
−2
10
TTD Bfm Rate 1 Gb/s
TTD Bfm Rate 2 Gb/s
IIR Bfm Rate 1 Gb/s
IIR Bfm Rate 2 Gb/s
No Bfm Rate 1 Gb/s
No Bfm Rate 2 Gb/s
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
Figure 3.14: BER of the simulated UWB communication system. N = 8, Δx = 180 mm,
ψbf m = ψsource = 10◦ , no antenna coupling effect. BER performance is degraded.
55
Chapter 3. UWB Beamformer Characterization
0
10
−1
BER
10
−2
10
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
Figure 3.15: BER of the simulated UWB communication system. N = 20, Δx = 72 mm,
ψbf m = ψsource = 27◦ , with antenna coupling effect. The impact of the beam squninting
resulted no performance gain from the beamformer. See Figure 3.14 for legend.
0
10
−1
BER
10
−2
10
−3
10
−4
10
−20
−15
−10
−5
0
SIR [dB]
5
10
15
20
Figure 3.16: BER of the simulated UWB communication system. N = 20, Δx = 72 mm,
ψsource = 27◦ , ψbf m = 22◦ with antenna coupling effect. See Figure 3.14 for legend.
Chapter 3. UWB Beamformer Characterization
56
Figure 3.17: Actual AOA ψbf
m , the angle of the main lobe, as a function of AOA of the
beamformer ψbf m for N = 30, Δx = 12 mm.
Chapter 4
Potential Hardware Realization of a
UWB Beamformer
In Chapter 3, the performance of the IIR beamformer was evaluated using three different methods to assess its capabilities. It was shown that the beamformer is robust
against mutual coupling and it can improve the BER of an UWB communication system
by several orders of magnitude. In this chapter, a potential realization of a hardware
UWB beamformer, which processes the received signal in the continuous-time domain,
is studied. A detailed feasibility analysis is also conducted to assess the performance of
such a beamformer using real physical components.
4.1
Motivation
To realize the IIR beamformer algorithm using conventional DSP techniques, one would
need an array of ADCs as shown in Figure 2.7. These ADCs need to sample the signals
at radio frequencies in order to prevent aliasing. Since the upper frequency of the UWB
band is at approximately 10 GHz, the sampling frequency must be at least 20 GHz to
prevent aliasing. Flash ADCs are typically used for such a high sampling rate and they
are very expensive and consume a lot of power [27]. Furthermore, a massive systolic
57
Chapter 4. Potential Hardware Realization of a UWB Beamformer 58
Figure 4.1: Unit cell from the signal flow graph in Figure 2.7.
array needs to be built [28] in order to realize this beamformer in digital form which,
while more efficient than other DSP implementations, still requires a tremendous number
of calculations per second. The realization of the signal flow graph is possible without
the need for digitization and it could be implemented using RF microwave circuits in
the continuous-time domain. The resulting beamformer would then have all the features
of the digital IIR beamformer but with a lower cost and lower power requirements than
present DSP technologies allow.
4.2
Continuous-time Transfer Function
Figure 4.1 shows signal flow graph of the unit cell with the defined port numbers. There
are only two unique transfer functions in the unit cell to be realized, T F1 (z2 ) and T F2 (z2 ).
They correspond to the transfer functions from port 1 to 4 (T F1 (z2 )), port 2 to 4 (T F1 (z2 ))
Chapter 4. Potential Hardware Realization of a UWB Beamformer 59
and port 3 to 4 (T F2 (z2 )). They can be derived as
1 + z2−1
1 + b01 z2−1
b10 + b11 z2−1
.
T F2 (z2 ) = −
1 + b01 z2−1
T F1 (z2 ) =
(4.1)
(4.2)
If an analog circuit can realize the above two transfer functions exactly, then one would
arrive at the desired response exactly. In practice, an analog circuit can only approximate
the transfer functions. The resistor R in circuit Figure 2.6 only controls the passband
width of the transfer function. It is desired for it to be as small as possible in order to
achieve the sharpest beam. Taking the limit as R → 0 in equation (2.6),
b11 = −1 and
(4.3)
b01 = −b10 .
(4.4)
From now on, the value of the bij coefficients are to be taken as such. Hence the angle
the beamformer is set to, ψbf m , can be considered to be a function of b01 only.
The goal is to find a new transfer function that can be easily realized by simple RF
microwave circuits. The following derivation of the new transfer function was found to
be the simplest for realization. Consider bilinear transformed versions of equations (4.1)
and (4.2). Substituting
z2−1 =
1 − s2 T2s
,
1 + s2 T2s
(4.5)
where Ts = 1/fs is the temporal sampling period, the two new transfer functions T F1 (s2 )
and T F2 (s2 ) are now in the continuous-time Laplace domain s2 ,
T F1 (s2 ) =
2
1 + b01
T F2 (s2 ) = −1 +
s2
s2
1
Ts 1−b01
2 1+b01
2
Ts 1−b01
2 1+b01
+1
(4.6)
+1
.
(4.7)
Chapter 4. Potential Hardware Realization of a UWB Beamformer 60
Figure 4.2: An RC network terminated by transmission lines.
The two new transfer functions are in the form of a low-pass resistor-capacitor (RC)
network which easily can be realized by RC network connected to a transmission line
as shown in Figure 4.2. The transfer function of the circuit, taken to be its s21 , can be
shown to be
T Fshc (s2 ) ≡ s21 (s2 ) =
where Ref f =
R+Z0
2+R/Z0
2/(2 +
R
)
Z0
s2 CRef f + 1
,
(4.8)
, C is the shunt capacitance, R is the series resistance and Z0 is
the characteristic impedance of two transmission lines feeding the circuit. A small Ref f
R+Z0
Ts 1−b01
is desired such that C 2+R/Z
is
comparable
to
in equations (4.6) and (4.7).
2 1+b01
0
The variable gain term 1+b2 01 is the voltage gain of the signal and it is dependent on
ψbf m . For ease of fabrication R is set to be zero allowing Ref f to be the smallest possible
value of 25 Ω. Hence, for R = 0 and Z0 = 50 Ω, the transfer function is simply
T Fshc (s2 ) =
1
,
s2 (25)C + 1
(4.9)
which is the form of the desired low-pass network in equations (4.6) and (4.7) with
C=
1 Ts 1 − b01
.
25 2 1 + b01
(4.10)
For each angle that the IIR beamformer is set to, ψbf m , there is a corresponding value
for b01 given by equation (2.6), which has a corresponding value for C given by equation
(4.10). Hence, ψbf m can changed by varying C. An electronically tunable capacitance,
such as a varactor diode, can be used to tune C which in turn tunes ψbf m .
With the new definitions of the two transfer functions (4.6) and (4.7), the new 2-D
Chapter 4. Potential Hardware Realization of a UWB Beamformer 61
transfer function is derived as follows. The relationship between the output y(n1 , s2 ) and
the input w(n1 , s2 ) can be written as
y(n1 , s2 ) = (w(n1 , s2 ) + w(n1 , s))T F1 (s2 ) + y(n1 − 1, s2 )T F2 (s2 ),
(4.11)
where n1 is the spatial index and s2 is the continuous temporal frequency in the Laplace
domain. It follows that the new 2-D transfer function is given by
Y (z1 , s2 )
(1 + z1−1 )
= T F1 (s2 )
W (z1 , s2 )
1 − z1−1 T F2 (s2 )
(4.12)
where T F1 (s2 ) and T F2 (s2 ) are given in equations (4.6) and (4.7) respectively. Note that
T F1 (s2 ) only modifies the magnitude and the phase of the overall transfer function in the
s2 domain. It does not have any effect on where the passband of the transfer function
is located. Hence, for simplicity, T F1 (s2 ) can be set to 1. The gain term 1+b2 01 in
equation (4.6) and corresponding need for an amplifier to realize it are now eliminated.
Figure 4.3 shows the 2-D transfer function (4.12) for ψbf m = 10◦ . For the IIR digital
beamformer in the same configuration, shown in Figure 2.8, it is clear the new transfer
function does not suffer from the effects of the bilinear warping as its passband is almost
a straight line, similar to the ideal analog transfer function shown in Figure 2.5.
The potential microwave circuit design for the unit cell has a simple topology shown
in Figure 4.4. In this new unit cell, the transfer functions from port 1 to 4, from port 2 to
4 and from port 1 to 5 is are all assumed to be all-pass functions. The transfer function
from port 3 to 4 is that described by equation (4.7). Devices in dashed lines are the
power dividers and combiners needed to add and divide signals. A wideband Wilkinson
power divider could be used to realize such device. A shunt variable capacitor C is
connected to the transmission line followed by a voltage amplifier with gain value of 2 as
required by equation (4.7). A wideband 180◦ phase shifter is also needed to realize the −1
multiplicative constant. This unit cell requires very little hardware and is simple to build.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 62
Figure 4.3: 2-D transfer function given by equation (4.12) for ψbf m = 10◦ . Colour scale
in dB.
Figure 4.4: New unit cell of the new beamformer.
An array of such unit cells connected would have the desired beamforming capability.
The beam characteristics of this circuit network are summarized in the following section.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 63
0
3 GHz
4 GHz
5 GHz
6 GHz
7 GHz
8 GHz
9 GHz
−10
−20
[dB]
−30
−40
−50
−60
−70
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.5: Far-field pattern of the new transfer function in Figure 4.3
4.2.1
Beam Characteristics
Figure 4.5 shows the far-field pattern of the new beamformer tuned to ψbf m = 10◦
corresponding to the transfer function plotted in Figure 4.3, assuming the microwave
networks used to realize the transfer function are ideal.
There is virtually no beam squinting and the angle of the main lobe points to 10◦
for all frequencies within the UWB band. Figure 4.6 shows the far-field pattern for the
IIR beamformer also tuned to 10◦ . Comparing these two figures, it is clear that the new
beamformer suffers much less beam squinting compared to the IIR beamformer. When
the new beamformer is set to ψbf m = 40◦ , Figure 4.7 shows its transfer function with the
corresponding far-field pattern shown in Figure 4.8, where a slight beam squinting of the
main lobe can be observed.
Figure 4.9 shows the angle of the main lobe as a function of frequency for ψbf m = 40◦ .
The main lobe squints slightly towards the broadside direction as frequency is increased.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 64
0
3 GHz
4 GHz
5 GHz
6 GHz
7 GHz
8 GHz
9 GHz
−10
−20
[dB]
−30
−40
−50
−60
−70
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.6: Far-field pattern of the digital IIR beamformer tuned ψbf m = 10◦ corresponding to Figure 2.8.
Figure 4.7: 2-D transfer function given by equation (4.12) for ψbf m = 40◦ . Colour scale
in dB.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 65
0
3 GHz
4 GHz
5 GHz
6 GHz
7 GHz
8 GHz
9 GHz
−10
−20
[dB]
−30
−40
−50
−60
−70
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.8: Far-field pattern of the new transfer function in Figure 4.7
40
39
Angle of peak [deg]
38
37
36
35
34
33
3
4
5
6
Frequency [GHz]
7
8
9
Figure 4.9: Location of the peak angle as a function of frequency for Figure 4.8
Chapter 4. Potential Hardware Realization of a UWB Beamformer 66
In practice, only a limited number of unit cells can be realized, spatially truncating the array. Figure 4.10 shows the transfer function for N = 30 elements spaced at
Δx = 12 mm with ψbf m = 40◦ and capacitance C = 0.514 pF. The effect of the spatial
truncation is apparent in this figure, manifesting itself as side-lobes. Figure 4.11 shows
the corresponding far-field gain pattern of the beamformer in the same configuration.
The angle of the main lobe shifts towards the broadside direction as frequency is swept
from 3 GHz to 9 GHz. The beamformer produces a variable antenna gain ranging from
15 dBi to 20 dBi across the UWB frequency band.
Figure 4.10: 2-D transfer function for ψbf m = 40◦ spatially truncated to N = 30 elements.
Colour scale in dB.
4.3
Evaluation of Transfer Function Given Using Sparameters
Given an arbitrary set of 5-port s-parameters of an unit cell, it is desired to calculate its
2-D transfer function to calculate its beam pattern. The 5-port s-parameters of the unit
Chapter 4. Potential Hardware Realization of a UWB Beamformer 67
20
3 GHz
4 GHz
5 GHz
6 GHz
7 GHz
8 GHz
9 GHz
Gain [dBi]
10
0
−10
−20
−30
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.11: Far-field gain pattern of the new beamformer whose transfer function is
shown in Figure 4.10 for ψbf m = 40◦ .
Figure 4.12: Generic unit cell port definition. Ports 4 and 5 of one cell are connected to
ports 2 and 3 of the next cell. Ports 2 and 3 of the first cell and ports 4 and 5 of the last
cell are terminated in matched loads.
cell can obtained from any sources – ideal theoretical calculated s-parameters, simulated
5-port parameters from software or measured 5-port parameters. Figure 4.12 shows how
+
the cells are cascaded. Let vn,p
denote the traveling voltage into the pth port of cell n.
−
Likewise, let vn,p
denote the voltage traveling wave out of the pth port of cell n. For the
Chapter 4. Potential Hardware Realization of a UWB Beamformer 68
first cell, at a particular frequency, the system of equations governing the traveling waves
at its nodes are written as
+
−
vI,2
= v0,5
= 0 for the first cell, n = 0
−
+
+
+
+
+
vI,2
= s21 vI,1
+ s22 vI,2
+ s23 vI,3
+ s24 vI,4
+ s25 vI,4
+
−
vI,3
= v0,4
= 0 for the first cell, n = 0
−
+
+
+
+
+
vI,3
= s31 vI,1
+ s32 vI,2
+ s33 vI,3
+ s34 vI,4
+ s35 vI,5
+
−
vI,4
= vII
3
−
+
+
+
+
+
vI,4
= s41 vI,1
+ s42 vI,2
+ s43 vI,3
+ s44 vI,4
+ s45 vI,5
+
−
vI,5
= vII
2
−
+
+
+
+
+
vI,5
= s51 vI,1
+ s52 vI,2
+ s53 vI,3
+ s54 vI,4
+ s55 vI,5
.
(4.13)
where cell n = 0 index is used to denote a dummy zero-input cell at the input of the
beamformer. Similarly, the equations governing the traveling voltages at the ports of cell
II are
+
−
= vI,5
vII,2
−
+
+
+
+
+
vII,2
= s21 vII,1
+ s22 vII,2
+ s23 vII,3
+ s24 vII,4
+ s25 vII,4
+
−
vII,3
= vI,4
−
+
+
+
+
+
vII,3
= s31 vII,1
+ s32 vII,2
+ s33 vII,3
+ s34 vII,4
+ s35 vII,5
+
−
vII,4
= vIII
3
set to 0 if last cell, n = N
−
+
+
+
+
+
vII,4
= s41 vII,1
+ s42 vII,2
+ s43 vII,3
+ s44 vII,4
+ s45 vII,5
+
−
vII,5
= vIII
2
set to 0 if last cell, n = N
−
+
+
+
+
+
vII,5
= s51 vII,1
+ s52 vII,2
+ s53 vII,3
+ s54 vII,4
+ s55 vII,5
.
(4.14)
The system of equations for each unit cell can be arranged as written above. These
Chapter 4. Potential Hardware Realization of a UWB Beamformer 69
sets of equations can be arranged in a matrix form Av = B, where a matrix A contain
the 5-port s-parameters values of the unit cell, v is a column vector of the traveling
voltage waves in and out of the nodes of each unit cell and matrix B is a column vector
containing the excitations to each unit cell.
The following example shows the value of A, v and B assuming only two unit cells
are connected. A MATLAB algorithm is written to generate the A, v and B vectors for
the generic case when N unit cells are cascaded as shown in Figure 4.12.
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
A=⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
s22
s32
s42
s52
0
0
0
0
1
0
0
0
0
0
0
0
s23
s33
s43
s53
0
0
0
0
0
1
0
0
0
0
0
0
s24
s34
s44
s54
0
0
0
0
0
0
1
0
0
0
0
0
s25
s35
s45
s55
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
s22
s32
s42
s52
0
0
0
0
1
0
0
0
0
0
0
0
s23
s33
s43
s53
0
0
0
0
0
1
0
0
0
0
0
0
s24
s34
s44
s54
0
0
0
0
0
0
1
0
0
0
0
0
s25
s35
s45
s55
0
0
0
0
0
0
0
1
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
v=⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
−1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
vI,2
+
vI,3
+
vI,4
+
vI,5
+
vII,2
+
vII,3
+
vII,4
+
vII,5
−
vI,2
−
vI,3
−
vI,4
−
vI,5
−
vII,2
−
vII,3
−
vII,4
−
vII,5
0
−1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−1
0
0
0
0
0
0
0
0
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟ (4.15)
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
(4.16)
Chapter 4. Potential Hardware Realization of a UWB Beamformer 70
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
B=⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
+
−s21 vI,1
+
−s31 vI,1
+
−s41 vI,1
+
−s51 vI,1
+
−s21 vII,1
+
−s31 vII,1
+
−s41 vII,1
+
−s51 vII,1
0
..
.
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
(4.17)
0
+
To obtain the 2-D frequency response of an array of unit cells, vI,1
(s2 ) = 1 for all
frequencies, which corresponds to a spatial impulse. Matrix A and column vector B are
known given the 5-port s-parameters of the unit cell and the excitation to the unit cells.
v can be calculated via a matrix inversion of A given by
v = A−1 B.
(4.18)
Hence, the traveling waves at all nodes in the circuit are known. The 2-D output is taken
at port 4 for all unit cells,
Y (n1 , s2 ) = vn+4 (s2 ) + vn−4 (s2 ) n ∈ {I, II, III, IV, ..., N }
(4.19)
where N is the total number of unit cells calculated. This calculation is repeated for
each frequency of interest followed by a Fourier transform with respect to n1 in equation
(4.19), resulting in the 2-D transfer function in Figure 4.10.
4.3.1
Unit Cell Simulations
Previous sections have described the new beamformer with beam characteristics that are
highly desirable. A potential realizable microwave circuit of one unit cell is shown in
Figure 4.4. When the s-parameters of each component in the unit cell are known, the
overall 5-port s-parameters of the cell can be calculated. Hence, the overall transfer func-
Chapter 4. Potential Hardware Realization of a UWB Beamformer 71
tion and beam pattern can be calculated according to method described in the previous
section.
A simulation was set up in Agilent Advanced Design System (ADS) to compute the
overall 5-port s-parameters of the unit cell when the s-parameters of each individual
microwave components are known. Figure 4.13 shows the simulation setup in ADS. The
required microwave components are connected in the fashion as shown.
Figure 4.13: Advanced Design System (ADS) unit cell simulation setup.
The s-parameters of each component in Figure 4.13 can be obtained either from ideal,
simulated or measured data. Real RF microwave devices would have propagation delays
which do not exist in the ideal circuit shown in Figure 4.4. Thus, when real microwave
devices are employed, the delays of the signals must be matched before they are added. In
the actual microwave circuit fabrication, this delay matching can be achieved by adjusting
the lengths of transmission lines as necessary to match the delays of signals. Figure 4.14
shows the case when cell I has a delay of dcell seconds from the input ports 1, 2 and 3 to
the output ports 4 and 5. This delay can be compensated by adding a delay (transmission
line) at port 1 of the next cell as shown in this figure. By doing so, the input signals at
ports 1, 2 and 3 of cell II would all arrive at the same time. A similar delay with value
2dcell can be added at port 1 for cell III to match the delay from cells I and II.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 72
Figure 4.14: A signal delay matching scheme for the realization the IIR beamformer in
hardware. Cell I has a delay dcell which is compensated by a delay line with delay dcell
at port 1 of the next cell.
Four phase shifters with values φi for i ∈ {1, 2, 3, 4} are placed at proper locations
in Figure 4.13 in order to compensate for the delay by the real microwave devices. For
example, the ideal transfer function from port 1 to 5 is an all-pass function. However,
with a real power divider, there would be delay incurred between the input and output.
The purpose of φ1 phase shifter is to phase advance (or group advance the signal) the
output of the divider so that the transfer function from port 1 to 5 is an all-pass function
with no delay. In the actual realization of the unit cell, these delays are matched to
the same amount but it is more convenient in simulation to delay match the signal to
0 seconds. Similarly for φ2 , it is phase advanced with a value of twice the delay of the
power divider. These four phase shifters are implemented in ADS via an equation-based
2-port network with s21 = s12 = ejωd , where d is the required delay. This allows for
the calculation of the realistic response of the system, without having to introduce the
delay-compensation network discussed above for each unit cell. Instead, the delay-less
cells can simply be cascaded.
Port 3 in Figure 4.13 shows a balun with the phase of one output port is 180◦ out of
phase with respect to the other output port. This achieves the phase inversion needed in
Chapter 4. Potential Hardware Realization of a UWB Beamformer 73
equation (4.7). A voltage amplifier with a gain value of A is needed at port 4 because each
time the signal passes through a power divider, its voltage amplitude drops by a factor
√
of 1/ 2. Hence an amplifier is needed to scale the voltage back up to an appropriate
√
value with A = ( 2)3 . However, the microwave implementation of the amplifier was not
considered in this study.
Port 2 in Figure 4.13 is connected to a power divider with one output port terminated
in a matched load. The purpose of this power divider is to amplitude and phase match
the signal coming in from port 1 of the unit cell, as that signal has already passed through
a power divider. Since the transfer functions of the power dividers are expected to be
similar after fabrication, the signals can be expected to be reasonably amplitude and
phase matched before they are added by another power divider.
4.4
Microwave Circuit Realization of the UWB Beamformer
The initial focus of the microwave circuit realization of the beamformer was the development of the wideband microwave 3-port power dividers and baluns needed to realized the
beamformer. The impact of the non-ideal characteristics of these devices on the beamformer is unknown. Hence, before real devices were employed, ideal devices were first
used in the unit cell circuit shown in Figure 4.13 to develop a sense of tolerance levels
allowed in the non-ideal characteristics of real microwave devices. It was found that the
dispersion of the microwave circuits needs to be kept at minimum along with the port
reflection coefficient and port isolation. These three parameters largely determine the
performance of the beamformer and the quality of the corresponding beam pattern. With
this in mind, the microwave components were designed with priority given to these three
parameters.
Wideband power dividers that operate over the entire 3 GHz to 10 GHz UWB fre-
Chapter 4. Potential Hardware Realization of a UWB Beamformer 74
quency range are difficult to design. It would likely require multiple stages to cover the
entire frequency range. With the stringent requirements on the port reflection coefficient and output port isolation, the design of the power divider over such wide band of
frequencies is outside of scope of this thesis. However, a proof-of-concept beamformer
in hardware can be designed to show the principle of operation of the beamformer at a
lower centre frequency of 3 GHz and over a narrower bandwidth.
Different planar transmission line technologies were assessed for realizing the microwave combiners. It was determined that the quasi-TEM mode of a microstrip transmission line had too much dispersion, causing the beam pattern to distort significantly.
However, coplanar waveguide (CPW) transmission line have a much lower dispersion in
comparison. Furthermore, its uniplanar structure allowed for easy fabrication and also
facilitated the realization of a phase inversion circuit needed to realize the −1 term in
equation (4.7), which is discussed shortly. Hence, CPW topology was chosen as the form
to realize all microwave components.
Wideband power dividers are needed for the addition operators in equation (4.7). All
three ports of the power divider must have a low reflection coefficient. Poor impedance
matching would cause changes from the desired transfer function. Consider the all-pass
transfer function from port 2 to 4 in Figure 4.13 as an example. If the power divider
is perfectly impedance-matched at all three ports, then the transfer function from port
2 to 4 would simply be the product of each transfer function of the power dividers.
If high port reflection coefficients exist, then signals would bounce back and forth on
the transmission line connecting the components, creating poles in the overall transfer
function that disturbs the desired all-pass characteristic. Similarly, good port isolation
between the output ports of the power divider is desired. Poor port isolation would
disturb transfer function in the same manner.
There are many wideband power dividers in literature that have excellent performance
characteristics and they come in a variety of different sizes and forms. Various methods
Chapter 4. Potential Hardware Realization of a UWB Beamformer 75
have been developed to design power dividers with wideband features [29, 30, 31, 32],
but none possess characteristics that are suitable for the needs of the beamformer. The
design of a power divider is typically concerned with the port reflection coefficient, power
splitting ratio, port isolation and port phase balance and is not typically designed with
dispersion as a priority, which is an important and stringent parameter required by unit
cell of the beamformer.
A Wilkinson power divider was chosen as the candidate for the power divider as it has
many attractive properties. A good input reflection coefficient can be obtained over a
reasonably wide bandwidth. The power splitting ratio is constant over a wide bandwidth.
Port isolation is expected to be excellent but over a narrower bandwidth. A good port
reflection coefficient is expected to alleviate the requirement on the port isolation. A
multi-stage Wilkinson power divider can be designed but since each section is resonant,
it introduces a ripple in the group delay that contributes to dispersion. A single stage
Wilkinson power divider is chosen to show a proof-of-concept beamformer in hardware.
An out-of-phase power divider is needed for the phase inversion required in equation
(4.7). A phase inversion circuit is simple to realize by swapping signal and ground
conductors in CPW, changing the signal polarity. Because both the ground plane and
signal line are on the same plane, no complicated vias need to be drilled or plated.
By connecting a phase inversion circuit to one of the output ports of the Wilkinson
power divider, a balun can be created. The following section describes the simulated
and measured data for the Wilkinson power divider and out-of-phase Wilkinson power
divider.
4.4.1
Design of the In-Phase Wilkinson Power Divider
Figure 4.15 shows the structure of the Wilkinson power divider with the defined port
numbering. The design of this Wilkinson power divider was based on [33]. This circuit
consists of a CPW transmission line connected to a coupled CPW transmission line
Chapter 4. Potential Hardware Realization of a UWB Beamformer 76
for the quarter-wavelength transformer section. A 100 Ω resistor is connected between
the centre conductors of the output ports. The fabricated dimensions of the power
divider were numerically optimized to be within fabrication limits. The gap sizes of the
50 Ω CPW and the coupled CPW section and its length were modified for minimum
port reflection coefficient and high output port isolation over the widest frequency range
possible, centred at 3 GHz. The final dimensions of the CPW Wilkinson power divider
are included in Appendix B.
Figure 4.16 shows the simulated s-parameters of the Wilkinson power divider as
characterized by Ansoft High Frequency Structure Simulator (HFSS). Its |s21 | varies
only from −3.5 dB at 1 GHz to −3.1 dB at the centre frequency to −3.9 dB at 5 GHz.
|s11 |, |s22 | and |s33 | are excellent and are below −10 dB from 1 GHz to 4.5 GHz. The
port isolation, s32 , has the narrowest bandwidth. Its magnitude is less than −10 dB from
1.75 GHz to 4.25 GHz. This is to be expected as the quarter-wavelength transformer is
a narrow band structure and is relatively sensitive to frequency changes.
Figures 4.17 and 4.18 shows the group delay and phase balance as a function of
frequency. It is desired that there be minimum variation in the group delay over a wide
range of frequency to minimize dispersion. Here, the group delay of both s21 and s31 only
varies by about 5 ps for from 2 GHz to 4.5 GHz. This amount of dispersion was found to
be tolerable as it was found previously that the tolerable dispersion was approximately
20 ps for the Wilkinson power divider. Phase balance, calculated to be ∠(s21 /s31 ), is
ideally zero for all frequencies as the signals are phase-balanced. Shown in the figure, the
phase variation is less than 1◦ .
4.4.2
Design of the Out-of-Phase Wilkinson Power Divider
A phase inversion circuit is needed to realized the inversion in equation (4.7). The
realization of microwave circuits in CPW form allows for convenient realization of a
phase inversion circuit as all the conductors are on the same layer. The signal polarity
Chapter 4. Potential Hardware Realization of a UWB Beamformer 77
Figure 4.15: Layout of the Wilkinson realized in CPW form.
0
−5
S−Parameters [dB]
−10
−15
−20
−25
|s11|
|s22|
−30
|s33|
|s21|
−35
|s32|
−40
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.16: Simulated s-parameters of the Wilkinson power divider realized in CPW
form.
can easily be inverted by swapping the signal and ground conductors. Figure 4.19 shows
the 2-port wideband phase inversion structure [34] with defined port numbering. CPW
transmission lines are used at the two ports so that it can be connected with the rest of the
Chapter 4. Potential Hardware Realization of a UWB Beamformer 78
X: 3
Y: 374.9
376
374
X: 3
Y: 373.7
Delay [ps]
372
370
368
366
364
Group Delay s21
Group Delay s31
362
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.17: Simulated group delay of s21 and s31 of the CPW Wilkinson power divider.
0.8
0.6
Phase Balance [Deg]
0.4
0.2
0
−0.2
−0.4
−0.6
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.18: Simulated phase balance of the CPW Wilkinson power divider.
microwave components. There are two ‘X’-crossings for each of the slotline of the CPW
to invert the signal polarity. A wideband quarter-wavelength radial stub is placed at the
two ‘X’-crossings to create a wideband open circuit that electromagnetically separates
the two ground planes to the left and right side of the radial stub. The radius of the stub
is 16.5 mm. Air bridges used for the ‘X’-crossings are as shown in the inset of Figure 4.19.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 79
Figure 4.20 shows the simulated s-parameters of this phase inverter. The transmission
coefficient s21 is very constant as a function of frequency, with the magnitude ranging
from −0.36 dB at 1 GHz to −1.8 dB at 5 GHz. s11 and s22 are excellent and they are
below −10 dB for all frequencies from 1 GHz to 5 GHz. Note that resonance contributed
by the wideband radial stubs is not centered at the design frequency of 3 GHz but instead
has been lowered by lengthening the stubs to a frequency such that the dispersion of s21
is kept at a minimum at the desired frequency. The reason for doing so is because the
system is dispersion sensitive and minimizing the group delay variation is more important
than minimizing reflections. Note that the port reflection coefficients are still very good
at frequencies around 3 GHz.
It is desired that the insertion phase of the phase inverter is exactly ±180◦ for all
frequencies. Figure 4.22 shows the phase characteristics of the phase inverter as a function
of frequency. A reference transmission line of the same length was used a phase reference
as shown in Figure 4.19. The phase differs from −180◦ by 10◦ from 2 GHz to 4 GHz,
which is deemed as acceptable for achieving a wideband signal inversion. The difference
of 10◦ is thought to be mostly contributed by the electrical length difference between the
reference transmission line and the phase inverter.
Figure 4.19: Layout of the wideband phase inversion circuit. Radius of the stub is
16.5 mm.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 80
0
X: 3
Y: −0.3577
X: 5
Y: −1.824
−5
S−Parameters [dB]
−10
−15
−20
−25
−30
|s11|
|s22|
−35
|s21|
−40
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.20: Simulated s-parameters of the phase inversion circuit.
315
310
305
Group Delay [ps]
300
295
290
285
280
275
270
265
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.21: Simulated group delay of the phase inversion circuit.
This phase inverter is then attached to one of the output ports of the CPW Wilkinson
power divider designed in the previous section [35]. The dimensions of the Wilkinson
power divider and that of the phase inverter are exactly the same as before. Figure 4.23
shows the HFSS design of the out-of-phase Wilkinson power divider with the phase
inverter attached at port 2. It is expected that the phase of port 2 is 180◦ out of phase
Chapter 4. Potential Hardware Realization of a UWB Beamformer 81
−160
−165
Insertion Phase [Deg]
−170
−175
−180
−185
−190
−195
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.22: Simulated phase inversion characteristics of the phase inverter.
with respect to port 3. Figure 4.24 shows the simulated s-parameters of the out-of-phase
Wilkinson power divider. The port reflection coefficient |s11 | is approximately −15 dB
at the centre design frequency of 3 GHz and it is below −10 dB from 1 GHz to 4 GHz.
The magnitudes of s22 and s33 are very low, staying between −15 dB and −20 dB for
most of the simulated frequencies. The port isolation, s32 , has the narrowest bandwidth
but it is still reasonably wideband as it is below −10 dB from 1.6 GHz to 4.6 GHz.
Figure 4.25 shows the simulated group delay of the out-of-phase Wilkinson power
divider. Group delays are computed for s21 and s31 of the device. At the design centre
frequency of 3 GHz, it has a delay of 569.5 ps for both output ports 2 and 3. For
frequencies close to 3 GHz, the device has a small amount of dispersion as there are slight
variations, approximately 5 ps, in both of its group delays. The large amount of group
delay can be compensated but the dispersion can not. Figure 4.26 shows relative phase
between the two output ports 2 and 3. In the vicinity of 3 GHz, from 2 GHz to 4 GHz,
the relative phase is fairly constant. However, it consistently differs by approximately
10◦ from −180◦ in that frequency range. This is thought to be attributed by the extra
length of the air bridge needed for the polarity inversion. The lengths of the output ports
Chapter 4. Potential Hardware Realization of a UWB Beamformer 82
were adjusted for the minimum variation in the relative phase and for it to be as close
as possible to −180◦ .
Figure 4.23: Layout of the out-of-phase Wilkinson power divider with the defined port
numbering.
It has been shown that the Wilkinson power divider and the out-of-phase Wilkinson power divider have excellent performance characteristics. Operation of fairly wideband devices (1 GHz) has been demonstrated. In the next section, the simulated sparameters of these two devices are used in ADS unit cell simulation to compute its
5-port s-parameters, which can be used to determine the beam pattern of the beamformer.
4.4.3
Simulated Beam Characteristics of the Hardware Beamformer
The simulated s-parameters of the Wilkinson power divider and the out-of-phase Wilkinson power divider are input into the ADS unit cell simulation for computation of the
5-port s-parameters of the unit cell. The circuit diagram of the unit cell is shown in Figure 4.13. Each square block represents a Wilkinson power divider whose s-parameters are
that of the simulated ones obtained from HFSS. The phase shifters are set to values where
Chapter 4. Potential Hardware Realization of a UWB Beamformer 83
0
−5
−10
S−Parameters [dB]
−15
−20
−25
−30
|s11|
−35
|s22|
−40
|s33|
|s21|
−45
−50
|s32|
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.24: Simulated s-parameters of the out-of-phase Wilkinson power divider.
620
600
Delay [ps]
580
X: 3
Y: 569.5
560
540
520
Group Delay s21
Group Delay s31
500
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.25: Simulated group delay of the out-of-phase Wilkinson power divider.
the phases of the signals are advanced such that there is no net delay. For example, phase
shifter φ1 is a 2-port equation based s-parameter block with s21 = s12 = ejω374×10
where ω is frequency in radians. Phase shifter φ2 has s21 = s12 = ejω2(374×10
−12 )
−12
,
, repre-
senting a phase advancement of 2 times that of a single Wilkinson power divider. Phase
shifter φ3 has a s21 = s12 = ejω(374+569.5)×10
−12
. The amplifier with a gain of A is set to
Chapter 4. Potential Hardware Realization of a UWB Beamformer 84
−150
−155
Phase Balance [Deg]
−160
−165
−170
−175
−180
−185
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.26: Simulated phase balance between the output ports of the out-of-phase
Wilkinson power divider.
√
( 2)3 to compensate for the voltage attenation of the signal due to the Wilkinson power
dividers.
For beamformer set to ψbf m = 40◦ corresponding to the ideal shunt capacitance
C = 0.514 pF, the 5-port s-parameters of the unit cell are calculated. Figure 4.27 shows
the ideal and simulated magnitude response of transfer function T F2 (s2 ) from 1 GHz to
5 GHz. The ideal transfer function T F2 (s2 ) is given by equation (4.7). The s43 of the
simulated unit cell is taken to be the simulated transfer function. Around the design
frequency of 3 GHz, the simulated |T F2 | is very close to the ideal one, fluctuating only
within 2 dB of the ideal curve even with the simulated s-parameters of the Wilkinson
power dividers. Figure 4.28 shows the ideal and simulated phase responses of T F2 (s2 ).
The phase between the ideal and simulated cases closely matched with each other around
the design frequency.
The simulated T F2 (s2 ) has frequencies with a magnitude response greater than unity
at some frequencies. At those frequencies, the impulse response of the beamformer is
not stable. It is easy to see that as the more unit cells are cascaded, the signal will get
Chapter 4. Potential Hardware Realization of a UWB Beamformer 85
6
4
2
|TF2| [dB]
0
−2
−4
−6
−8
−10
−12
−14
Ideal
Simulated
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.27: Magnitude of ideal transfer function T F2 (s2 ) and simulated one obtained
from unit cell simulation.
80
Ideal
Simulated
60
40
∠ TF2 [Deg]
20
0
−20
−40
−60
−80
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.28: Phase of ideal transfer function T F2 (s2 ) and simulated one obtained from
unit cell simulation.
amplified cell after cell, leading to instability. Hence, it is not meaningful to calculate
the response at those unstable frequencies and only the stable frequencies (2.5 GHz to
3.5 GHz) are calculated. Figure 4.29 shows the 2-D transfer function of the beamformer
in the frequency range from 2.5 GHz to 3.5 GHz for ψbf m = 40◦ and N = 15, using the
Chapter 4. Potential Hardware Realization of a UWB Beamformer 86
5-port s-parameters of the unit cell. This figure shows a good beam pattern whose main
lobe is centred at approximately 40◦ across a reasonably wide bandwidth of 1 GHz. A
slight variation in the peak the main lobe can be observed due to the variations of |T F2 |
across frequency, shown in Figure 4.27. To evaluate this gain variation, Figure 4.30 shows
the corresponding gain beam pattern, it offers a high gain between 11 dBi to 12.7 dBi
over 1 GHz of bandwidth.
Figure 4.29: 2-D far-field pattern from 2.5 GHz to 3.5 GHz of the new beamformer
with simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers.
Colour scale in dB.
Since the simulated response offers high gain over a reasonably wide bandwidth using
the simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers,
the next step is to evaluate whether real Wilkinson power dividers have sufficiently good
performance to achieve beamforming. The next section evaluates the performance of the
beamformer with fabricated Wilkinson power dividers to assess their feasibility of the
hardware UWB beamformer.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 87
15
2.5 GHz
3 GHz
3.5 GHz
10
Gain [dBi]
5
0
−5
−10
−15
−20
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.30: Beam pattern for various frequencies in Figure 4.29.
4.4.4
Fabrication and Measurement of Wilkinson Power Dividers
The simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers
offer promising performance. However, the beam pattern obtained in the previous section
was only based on the simulated s-parameters of the two power dividers. In this section,
a Wilkinson power divider is fabricated and its s-parameters are measured.
The Wilkinson power divider was fabricated using a milling machine to produce a
desired metal pattern. It was fabricated on Rogers RO4360 substrate with a dielectric
constant of 6.15. Three female SMA connectors were soldered at the ports of the power
divider so that its s-parameters can be measured using a PNA. A surface mount chip
resistor of 100 Ω was soldered between the output conductors of the power divider as the
isolation resistor. There were four air bridges soldered across the two ground planes at
the points of discontinuities to suppress the unwanted slotline mode from propagating on
the CPW transmission lines. Figure 4.31 shows the fabricated Wilkinson power divider.
The port numbering definitions are the same in both simulated and measured case.
Figure 4.32 shows the simulated and measured s-parameters of the Wilkinson power
Chapter 4. Potential Hardware Realization of a UWB Beamformer 88
divider, which matches very well. The measured |s21 | and |s31 | are slightly lower compare
to the simulated values as there are losses in the substrate in the fabricated device. The
higher the frequency, the more lossy the CPW transmission lines are. However, it isn’t
until 5 GHz that the loss is sufficiently large to reduce |s21 | by 2 dB.
Figure 4.31: Fabricated Wilkinson power divider.
Figure 4.33 shows the measured group delay of the device to check its dispersion
characteristics. The group delay is computed for both s21 and s31 . At the centre frequency
of 3 GHz, the group delay is 447.9 ps and varies by 25 ps as the frequency deviates ±1 GHz
away from the design frequency. 70 ps of delay is added in the simulated group delay
to account for the extra length of the SMA connectors soldered. This is not a source of
concern as it simply introduces an extra delay shifting the group delay higher and it does
not contribute to dispersion. Overall, the device has good dispersion characteristics in
simulations and measurements.
Figure 4.34 shows the measured phase balance between the two output ports of the
power divider. The phase balance is calculated to be ∠(s21 /s31 ) at each frequency. The
Chapter 4. Potential Hardware Realization of a UWB Beamformer 89
0
−5
S−Parameters [dB]
−10
−15
−20
−25
|s11|
|s22|
−30
|s33|
|s21|
−35
|s32|
−40
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.32: Measured (solid) and simulated (dashed) s-parameters of the Wilkinson
power divider.
520
500
480
X: 3.002
Y: 447.9
Delay [ps]
460
440
420
400
380
Group Delay s21
360
Group Delay s31
340
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.33: Measured (solid) and simulated (dashed) group delay of the Wilkinson power
divider.
phase balance is within 2.4◦ of the desired value over the frequency range of interest.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 90
4.4.5
Fabrication and Measurement of Out-Of-Phase Wilkinson
Power Dividers
Figure 4.35 shows the fabricated out-of-phase Wilkinson power divider. This out-of-phase
Wilkinson power divider was also fabricated on Rogers RO4360 substrate. The phase
inverter was attached at port 2 to invert the phase of the signal at this port relative to
port 3, creating a balun. The same 100 Ω isolation resistor was soldered between the
conductors at port 2 and port 3.
Figure 4.36 shows the simulated and the measured s-parameters of the out-of-phase
Wilkinson power divider. Overall, the s-parameters between the simulated and measured
match very well. The measured |s11 | has a better performance than the simulated one. In
addition, the measured isolation bandwidth, s32 , is better than the simulated bandwidth.
The measured |s21 | is slightly more lossy than the simulated one due to the loss in the
substrate. The measured |s22 | has a worse performance than |s33 | as the phase inverter
circuit is connected at port 2.
Figure 4.37 shows the measured group delay of s21 and s31 of the out-of-phase Wilkin-
2.5
Measured
Simulated
2
Phase Balance [Deg]
1.5
1
0.5
0
−0.5
−1
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.34: Measured (solid) and simulated (dashed) phase balance of the Wilkinson
power divider.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 91
Figure 4.35: Fabricated out-of-phase Wilkinson power divider.
0
−5
−10
S−Parameters [dB]
−15
−20
−25
−30
|s11|
−35
|s22|
−40
|s33|
|s21|
−45
−50
|s32|
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.36: Measured (solid) and simulated (dashed) s-parameters of the out-of-phase
Wilkinson power divider.
son power divider. Both curves match very well near the design frequency of 3 GHz with
a group delay of approximately 600 ps. As in the earlier case, the simulated group delay
is offset to match with the measured group delay. The fabricated out-of-phase power
Chapter 4. Potential Hardware Realization of a UWB Beamformer 92
divider is slightly more dispersive compared to the simulated one as there are fabrication imperfections. The measured group delay has 20 ps of variance from approximately
2 GHz to 3.5 GHz. The beamformer is expected to have the best performance within
this frequency range.
Figure 4.38 shows the measured phase balance of this out-of-phase Wilkinson power
divider. The ideal phase balance between output port 2 and port 3 is −180◦ across all
frequencies. Here, the measured performance is close to that of the ideal phase balance
from approximately 2 GHz to 4 GHz where it is relatively flat. It is only about 8.5◦
away from the ideal −180◦ in this frequency range. This phase balance error is thought
to be contributed mostly by the air bridges soldered in the phase inverter circuit at port
2. The air bridges were soldered to be as close to the ground plane as possible without
making contact with any other metal. However, there was still a gap left contributing to
the extra length that the signal must travel through.
700
680
660
Delay [ps]
640
620
600
580
560
540
Group Delay s21
520
500
Group Delay s31
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.37: Measured (solid) and simulated (dashed) group delay of the out-of-phase
Wilkinson power divider.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 93
−150
Measured
Simulated
−155
Phase Balance [Deg]
−160
−165
−170
−175
−180
−185
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.38: Measured (solid) and simulated (dashed) phase balance of the out-of-phase
Wilkinson power divider.
4.4.6
Calculated Beam Pattern Using Real Microwave Devices
The simulated and measured performance of both the in-phase and out-of-phase Wilkinson power dividers match very well with simulation results. One can expect that the
beamformer pattern obtained using the measured s-parameters of the two power dividers
to have similar characteristics as the one obtained by using simulated s-parameters. The
ADS unit cell simulation can compute the 5-port s-parameters given the measured sparameters of the two power dividers. Then, the beam pattern can be calculated for any
number of unit cells in cascade.
Figures 4.41 and 4.42 show the magnitude and phase of T F2 (s2 ) obtained from the
ADS unit cell simulation when the measured s-parameters of the power dividers are
used instead of simulated ones. |T F2 (s2 )| matches very well with the ideal one from
approximately 2.5 GHz to 4 GHz where it is the most flat. For frequencies outside of
this band, there are peaks in the magnitude of the transfer function that are greater
than unity. Those frequencies do not produce stable operation of the beamformer, as
discussed earlier, and are omitted from the frequency range considered for this proof-of-
Chapter 4. Potential Hardware Realization of a UWB Beamformer 94
Figure 4.39: 2-D far-field pattern of the beamformer using real in-phase and out-of-phase
Wilkinson power dividers. Colour scale in dB.
concept calculation. The phase of T F2 (s2 ) also matches closely with the ideal one near
the design frequency of 3 GHz shown in Figure 4.42.
Figure 4.39 shows the 2-D far field-pattern of the beamformer using the measured sparameters of the two Wilkinson power dividers. This 2-D far-field pattern was calculated
for ψbf m = 40◦ and N = 15 unit cells. A highly directive beam is clearly visible in
this figure. Figure 4.40 shows the gain beam pattern of this beamformer for various
frequencies. It offers a very highly directive beam ranging from 10.6 dBi to 12.9 dBi,
aimed at approximately ψbf m = 40◦ over a 1.5 GHz bandwidth.
4.4.7
Feasibility Discussion
This proof-of-concept design has shown that an UWB beamformer could be realized by
using real physical components to achieve a highly directive tunable beam pattern and it
Chapter 4. Potential Hardware Realization of a UWB Beamformer 95
15
2.5 GHz
3 GHz
3.5 GHz
4 GHz
10
Gain [dBi]
5
0
−5
−10
−15
−20
−80
−60
−40
−20
0
20
Angle From Broadside ψ°
40
60
80
Figure 4.40: Beam pattern for various frequencies of the beamformer with real in-phase
and out-of-phase Wilkinson power dividers.
10
8
6
|TF2| [dB]
4
2
0
−2
−4
−6
−8
Ideal
Simulated
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.41: Magnitude of ideal transfer function T F2 (s2 ) versus the one obtained from
ADS unit cell simulation using real in-phase and out-of-phase Wilkinson power divider.
could potentially be used as a part of a real UWB wireless communication system. The
proof-of-concept beamformer has a good performance over about a 1.5 GHz bandwidth
from 2.5 GHz to approximately 4 GHz. Although it does not cover the entire UWB
Chapter 4. Potential Hardware Realization of a UWB Beamformer 96
100
Ideal
Simulated
80
60
∠ TF2 [Deg]
40
20
0
−20
−40
−60
−80
−100
1
1.5
2
2.5
3
3.5
Frequency [GHz]
4
4.5
5
Figure 4.42: Phase of ideal transfer function 2 versus the one obtained from ADS unit
cell simulation using real in-phase and out-of-phase Wilkinson power divider.
frequency range, it is still quite wideband. It meets the FCC definition of UWB transmission as it exceeds the absolute bandwidth of 500 MHz and the fractional bandwidth
of 20%. Throughout the design process of the proof-of-concept beamformer, some design
considerations have presented themselves and they are summarized here.
1. Wideband power dividers and baluns that operate over the entire UWB frequency
range need to have an excellent performance in order for the beamformer to operate
over a such wide frequency range. Furthermore, these devices must be designed
with dispersion as a priority in addition to keeping port reflection coefficient low
and output port isolation high. Designing such devices is very challenging.
2. The signal propagation delay needs to be matched within each unit cell in order
for the signals to be processed properly. This means that the lengths of the transmission lines need to be properly designed. In addition, the inputs of the unit cells
(port 1) must be properly delayed to compensate the delays of the previous cells,
as shown in Figure 4.14. Hence an extra piece of transmission line of appropriate
length is needed at the input of each unit cell.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 97
3. Two voltage amplifiers are needed to scale signal at the two nodes shown in Fig√
ure 4.13 of values 2 and ( 2)3 . While these gain values can be easily achieved
via an active amplifier, their dispersion characteristics must be controlled. Either
the dispersion of the amplifiers needs to be minimized or their dispersion must be
compensated by microwave circuits. The dispersion of an UWB low-noise amplifier
was measured to gather a sense of the dispersion characteristics of tpyical UWB
amplifiers in general. It showed a group delay variance of about 25 ps over the
UWB band, which is potentially tolerable by the analog beamformer.
4. A varactor diode can be used as the variable capacitor needed to tune ψbf m to a
desired angle, shown in Figure 4.13. A control voltage line must be routed to bias
the varactor in order for it to have the desired capacitance. A DC chock circuit
must be deployed so that the voltage bias line does not interfere with the RF signal
path. The non-ideal characteristics of a varactor diode is expect to distort the beam
pattern as the device inductance at high frequencies could be considerable.
5. Figure 4.43 shows the effect capacitance needed Cef f , which includes any parasitic
capacitance due to the device itself, soldering of its leads, etc. as a function of
the angle that the beamformer is set to ψbf m . The required effective capacitance
ranges from 0 pF (open circuit) to almost 1 pF. Depending on the manufacturing
process of the varactor diodes, such a small capacitance could be difficult to achieve
as the parasitic capacitance would increase the effective capacitance. The effective
capacitance as a function of the control voltage must be characterized.
Chapter 4. Potential Hardware Realization of a UWB Beamformer 98
0.8
0.7
0.6
Ceff [pF]
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
ψ°bfm
Figure 4.43: Cef f as a function of ψbf m .
80
Chapter 5
Conclusions
UWB is a fast growing technology that has attracted much research efforts as it is applicable for a wide variety of applications. In wireless communications in particular,
UWB signaling scheme offers a promising potential for extremely high data rates due to
the extremely wide bandwidth available for signal transmission. However, the transmit
power is restricted to a very low level to minimize interference with many existing communication systems that already operate within the UWB frequency band. This creates
a challenging research problem because the received signal power could be on the same
order of magnitude as the power of interfering signal. Furthermore, multiple UWB users
could be transmitting broadband signals in the same channel that create more interference making signal recovery even more difficult. The multipath in the channel further
degrades the quality of the received signal as multiple copies of the transmitted signal, all
with different amplitudes and phases are added. UWB beamformers provide a filtering
process based on the location of the transmitter, enhancing the desired signal arriving
from a desired direction and attenuate interference signals from other directions. The
work presented in this thesis has shown that UWB beamformers are effective tools in
combating interference and multipath issues.
In this thesis, an UWB IIR beamformer has been characterized in a real wireless UWB
99
Chapter 5. Conclusions
100
channel. The beamformer was characterized in three different methods – far-field pattern
with real array of UWB antennas, interference rejection capability and Monte Carlo BER
simulations. In the far-field pattern measurement of the beamformer, it was shown that
with real UWB antennas as the receiving array, the beam pattern is very robust even
in the worse case antenna coupling scenario. The measured far-field pattern was very
close to that of the ideal pattern in all cases. In the interference rejection experiment, it
was shown that the beamformer provided clear spatial discrimination based on the angle
of arrival of the received signal, clearing demonstrating its spatial selectivity in a real
wireless channel. The BER simulations have clearly shown the interference suppression
capability that the beamformer can provide in a real UWB communication system. The
BER floor was lowered by several orders of magnitude in many cases. Different beamformer configurations were tested to assess the impact of the beamformer’s parameters.
Limitations of the beamformer were also shown. The beamformer performance degrades
when it is scanned to large angles from broadside. It was shown that this undesired effect
can be mitigated by pre-tuning the beamformer to a different angle.
The design of a proof-of-concept hardware beamformer was proposed. This hardware beamformer processes the signal in the continuous-domain and does not have the
computational complexity associated with high-speed digital signal processing. Real
physical microwave components were fabricated in order to assess the feasibility of the
hardware beamformer. A few design considerations resulted from design processes of
the hardware beamformer – the beamformer placed rather stringent requirements on the
dispersion, port reflection coefficient and port isolation of the combining devices used in
the beamformer network. Despite such stringent requirements, it was shown that the
proof-of-concept beamformer had a good performance over 1.5 GHz of bandwidth with a
relatively narrowband Wilkinson power dividers. This showed that the beamformer was
potentially feasible to realize in hardware and could potentially be part of a real UWB
wireless communication system.
Chapter 5. Conclusions
5.1
101
Contributions
There are two major contributions listed below have resulted from this thesis:
• L. Liang and S. V. Hum, “Experimental characterization of UWB beamformers
based on multidimensional beam filters (in press),”, IEEE Transaction on Antennas
and Propagation, vol. 59, no. 1, January 2011.
• L. Liang and S. V. Hum, “Experimental Verification of an Adaptive UWB Beamformer Based on Multidimensional Filtering in a Real Radio Channel,” IEEE Antennas and Propagation Society International Symposium (AP-S 2010), July 2010.
5.2
Future Work
There are lot of aspects of the hardware beamformer that remain as future work. They
are outlined below.
1. In the derivation of the beamformer only a one-dimensional physical array size was
considered. This derivation can be extended to include another dimension to allow
for a 2-D physical array as the receiving array. Such a beam pattern would then be
a steerable pattern in all 3 dimensions. However, the complexity of the beamformer
would be increased as a more sophisticated interconnection between the networks
would be required, placing even greater constraints on the design of those networks.
2. Although the Wilkinson power divider provided an excellent performance over a
reasonably wide bandwidth, new UWB power dividers must be designed in order
for the beamformer to operate over the entire UWB frequency range. A balun must
also be designed to provide a balanced output signals over UWB frequencies. Such
wideband microwave devices are not trivial to design and were beyond the scope
of this MASc thesis. Since it was found that the dispersion plays an important
role in the performance of the beamformer, the dispersion characteristics must be
Chapter 5. Conclusions
102
a design priority in all the microwave components used in addition to the low port
reflection coefficient and high output port isolation.
3. A variable capacitor must be used in the realization of the hardware beamformer
as an ideal low-pass RC network is used in this thesis. A varactor diode is a good
candidate to generate the variable capacitance needed in the microwave circuit as it
is economically affordable. MEMs capacitors can be used as an alternative but are
relatively expensive and immature compared to varactor diodes. However, MEMs
capacitors are much more linear.
4. There are two voltage amplifiers needed in the microwave realization of the unit
cell. In the realization of the unit cell, these voltage amplifiers must be carefully
characterized for their gain and dispersion, since both could be function of frequency. Since the bandwidth of the UWB frequencies are very wide, the gain and
dispersion characteristics could vary significantly from one end of the spectrum to
another. A method to manage this must be developed.
5. A fabrication of an unit cell with the physical microwave components, varactor
diode and amplifiers is needed to measure its 5-port s-parameters, which can be
used to calculate the corresponding beam pattern of the beamformer and assess its
tunability over a wide frequency range. An array of unit cells can be fabricated
and cascaded to realize a full implementation of the UWB hardware beamformer.
Appendix A
Fabrication and Measurements of
BAVAs
A.1
Fabrication of BAVAs
A Rogers RT/duroid 6002 high frequency laminate (r = 2.94, tan δ = 0.0012 @ 10 GHz,
thickness h = 1.524 mm) was used as the substrate in the fabrication of the BAVA. This
substrate has very low loss and it is well-suited for the milling process where the copper
is removed from the substrates. The BAVAs were constructed in two pieces as shown
in Figure A.1. On the bottom piece (Piece 1), there are two layers of metal shown here
in red and blue on the opposite side of the substrate. The top piece (Piece 2) is to be
aligned and bonded to the bottom piece via a bonding film placed in between the two
substrates. A multipress machine was used to during this bonding process in which the
pressure and temperature was controlled to the specified values required by the bonding
specifications. The bonding procedure is outline below.
1. Apply constant pressure of 138 N/cm2 .
2. Increase temperature to 210◦ C for 30 minutes.
103
Appendix A. Fabrication and Measurements of BAVAs
104
3. Decrease temperature to below 70◦ C for curing.
4. Release pressure.
Figure A.1: BAVA fabricated in two piece as shown.
The exponential antenna patterns on each of the metal layers were fabricated via a
combination of etching and milling processes. The etching process is a chemical process
where the copper is removed using an acid solution. The metal pattern is produced by
placing a photoresistive mask with the same shape as the desired metal pattern but the
mask material is immune to the acid protecting the copper from dissolving the copper.
The etching process for copper removal and it was used to remove large areas of
copper. However, the etching process does not allow an accurate alignment between
metal layers. Hence the finer details of the metal pattern were produced by a milling
machine after the large amount of copper was removed. This allows for rapid fabrication
while maintaining the same high-precision fabrication offered by the milling machine.
The combination of etching and milling process is described below.
1. A course etching mask is created from the antenna design. The course mask only
has features and contours that approximate the overall shape of the actual design.
2. A photoresist was laminated on substrate.
Appendix A. Fabrication and Measurements of BAVAs
105
3. Ultraviolet was shone over the entire substrate which causes the photoresist to
harden. The remaining photoresist was washed away.
4. An acid washer then dissolves the unprotected copper leaving the desired metal
pattern.
5. Since etching process removed large areas of copper, the design was placed under
a milling machine to mill out the remaining finer details of the metal pattern.
Alignment holes wee made in the course mask such that when the design was placed
on the milling machine, the machine can use the alignment holes for positioning
references.
A.2
Measurement of BAVAs
Four BAVAs were fabricated using the same process and their characteristics were measured then compared to that of the simulated. The measured characteristics were:
• s11
• Absolute gain in the E-plane and H-plane.
• 4-port s-parameters in an array configuration.
Figure A.2 through Figure A.7 shows the measured s11 of all fabricated antennas
and measured 4-port s-parameters of the BAVAs arranged in a linear array with element
spacing of 12 mm, and the E and H plane antenna pattern cuts of the antennas. Note
that this element spacing produces the highest coupling values as the antennas elements
are at the smallest.
106
Appendix A. Fabrication and Measurements of BAVAs
0
−5
−10
−15
|s11| [dB]
−20
−25
−30
−35
−40
−45
−50
Antenna 1
Antenna 2
Antenna 3
Antenna 4
Simulated
2
4
6
8
Frequency [GHz]
10
12
Figure A.2: |s11 | of all fabricated antennas and that of the simulated.
107
Appendix A. Fabrication and Measurements of BAVAs
0
−5
−10
S−Parameters [dB]
−15
−20
−25
−30
−35
|s21|
−40
|s31|
|s41|
−45
−50
|s32|
2
3
4
5
6
7
Frequency [GHz]
8
9
10
8
9
10
(a)
0
−5
−10
S−Parameters [dB]
−15
−20
−25
−30
−35
−40
|s22|
|s33|
−45
−50
|s44|
2
3
4
5
6
7
Frequency [GHz]
(b)
Figure A.3: Measured (solid) and simulated (dashed) 4-port s-parameters of the BAVA
array with element spacing 12 mm.
108
Appendix A. Fabrication and Measurements of BAVAs
2 Ghz
2.5 Ghz
−10
−100
0
0
−10
−20
100
10
Gain [dBi]
0
−20
−100
°
−10
0
ψ°
5 Ghz
−10
−100
0
−10
−100
°
0
100
−20
Gain [dBi]
−10
−100
0
ψ°
100
−100
0
100
ψ
Simulated Directivity
Measured Gain
0
−10
−20
100
°
10
0
0
ψ°
6 Ghz
−10
ψ
7 Ghz
10
−100
0
°
ψ
6.5 Ghz
Gain [dBi]
−10
10
0
−20
100
0
−20
0
100
°
ψ
5.5 Ghz
Gain [dBi]
Gain [dBi]
Gain [dBi]
−10
100
10
10
0
0
ψ
4.5 Ghz
0
−20
100
10
−100
−100
°
Gain [dBi]
Gain [dBi]
Gain [dBi]
0
−20
−20
100
10
−100
−10
ψ
4 Ghz
10
−20
0
0
°
ψ
3.5 Ghz
−20
3 Ghz
10
Gain [dBi]
Gain [dBi]
10
−100
0
ψ°
100
Figure A.4: E-plane cut for antenna 1.
109
Appendix A. Fabrication and Measurements of BAVAs
2 Ghz
2.5 Ghz
−10
−100
−10
−100
0
ψ°
5 Ghz
−10
−100
−10
−100
Gain [dBi]
−10
−100
0
ψ°
100
−100
0
ψ°
6 Ghz
100
−100
0
ψ°
100
10
−10
−100
0
ψ°
7 Ghz
100
0
−10
−20
Simulated Directivity
Measured Gain
0
−10
−20
0
100
ψ°
4.5 Ghz
−10
10
0
−100
0
−20
0
100
ψ°
5.5 Ghz
0
−20
0
100
ψ°
6.5 Ghz
−10
10
Gain [dBi]
Gain [dBi]
Gain [dBi]
0
0
−20
100
10
10
Gain [dBi]
0
ψ°
4 Ghz
0
−20
100
10
−20
−100
Gain [dBi]
0
−20
−10
10
Gain [dBi]
Gain [dBi]
10
−20
0
−20
0
100
ψ°
3.5 Ghz
10
Gain [dBi]
0
−20
3 Ghz
10
Gain [dBi]
Gain [dBi]
10
−100
0
ψ°
100
Figure A.5: H-plane cut for antenna 1.
110
Appendix A. Fabrication and Measurements of BAVAs
2 Ghz
2.5 Ghz
−10
−100
−10
−100
0
ψ°
5 Ghz
−10
−100
−10
−100
−100
0
100
ψ°
4.5 Ghz
0
−10
−20
0
100
°
ψ
5.5 Ghz
−100
0
ψ°
6 Ghz
100
−100
0
ψ°
100
10
0
−10
−20
0
100
ψ°
6.5 Ghz
−10
10
Gain [dBi]
Gain [dBi]
Gain [dBi]
0
0
−20
100
10
−100
0
ψ°
7 Ghz
100
0
−10
−20
10
Gain [dBi]
10
Gain [dBi]
0
ψ°
4 Ghz
0
−20
100
10
0
−10
−20
−100
Gain [dBi]
0
−20
−10
10
Gain [dBi]
Gain [dBi]
10
−20
0
−20
0
100
ψ°
3.5 Ghz
10
Gain [dBi]
0
−20
3 Ghz
10
Gain [dBi]
Gain [dBi]
10
−100
0
ψ°
100
Antenna 1
Antenna 2
Antenna 3
Antenna 4
0
−10
−20
−100
0
ψ°
100
Figure A.6: E-plane cut for all fabricated antennas.
111
Appendix A. Fabrication and Measurements of BAVAs
2 Ghz
2.5 Ghz
−10
−100
−10
−100
0
ψ°
5 Ghz
−10
−100
−10
−100
−100
0
100
ψ°
4.5 Ghz
0
−10
−20
0
100
°
ψ
5.5 Ghz
−100
0
ψ°
6 Ghz
100
−100
0
ψ°
100
10
0
−10
−20
0
100
ψ°
6.5 Ghz
−10
10
Gain [dBi]
Gain [dBi]
Gain [dBi]
0
0
−20
100
10
−100
0
ψ°
7 Ghz
100
0
−10
−20
10
Gain [dBi]
10
Gain [dBi]
0
ψ°
4 Ghz
0
−20
100
10
0
−10
−20
−100
Gain [dBi]
0
−20
−10
10
Gain [dBi]
Gain [dBi]
10
−20
0
−20
0
100
ψ°
3.5 Ghz
10
Gain [dBi]
0
−20
3 Ghz
10
Gain [dBi]
Gain [dBi]
10
−100
0
ψ°
100
Antenna 1
Antenna 2
Antenna 3
Antenna 4
0
−10
−20
−100
0
ψ°
100
Figure A.7: H-plane cut for all fabricated antennas.
Appendix B
CPW Wilkinson Power Divider
Dimensions
The fabricated Wilkinson power divider is shown in Figure B.1 along with its cross section
views. The dimensions are defined in Table B.1.
(a)
(b)
Figure B.1: (a) Wilkinson power divider with (b) cross section views.
Dimension
h
G50
G70
W50 W70
Value
1.524 0.155 0.155 0.936 1.6
L70
S
15.196 0.8
Table B.1: Fabricated CPW Wilkinson power divider dimensions in mm.
112
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