MODELING AND DESIGN OF ULTRA-WIDEBAND ARRAYS Matteo Ciattaglia Advisor Gaetano ...

132 Pages·2007·5.04 MB·English

MODELING AND DESIGN

OF ULTRA-WIDEBAND ARRAYS

Matteo Ciattaglia

Advisor

Gaetano Marrocco
UNIVERSITÀ DEGLI STUDI DI ROMA TOR VERGATA
FACOLTÀ DI INGEGNERIA
Dipartimento di Informatica, Sistemi e Produzione

________________

Dottorato di Ricerca in
GEOINFORMAZIONE

Modeling and Design of Ultra-Wideband Arrays

Tesi di Dottorato di

Matteo Ciattaglia

Relatore

Gaetano Marrocco

________________

Ciclo XIX
Anno Accademico 2005-2006
2Vanità delle vanità, dice Qoèlet,
vanità delle vanità, tutto è vanità.
3Quale utilità ricava l’uomo da tutto l’affanno
per cui fatica sotto il sole?
Qoèlet 1, 2-3
…to my wife…
Contents
1 Introduction 7
2 UWB Generalities 9
2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Communications and antennas networks . . . . . . . . . 13
2.3.2 Position location and tracking . . . . . . . . . . . . . . . 14
2.3.3 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 The domain of Time 19
3.1 Domain of Analysis and Synthesis . . . . . . . . . . . . . . . . . 19
3.2 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Gaussian Waveforms . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Hermite Functions . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Radon Transform . . . . . . . . . . . . . . . . . . . . . . 24
3.2.4 Transient waveform representation . . . . . . . . . . . . 25
3.2.5 Convolution and Deconvolution . . . . . . . . . . . . . . 27
4 Pulsed arrays 29
4.1 The principle of pattern convolution . . . . . . . . . . . . . . . . 29
4.2 Pulsed vs. Monochromatic Arrays . . . . . . . . . . . . . . . . . 30
4.3 Requirements for the characterization of pulsed arrays . . . . . . 34
5 Efficient Characterization of Radiating Elements 37
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2 Aperture Antennas . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2.1 TD aperture effective height . . . . . . . . . . . . . . . . 39
5.2.2 Numericalrepresentationsoftheapertureimpulseresponse 40
5.2.3 Approximate calculation of time domain effective height 42
5.2.4 Discussion about numerical complexity . . . . . . . . . . 45
5.2.5 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . 46
3
4 CONTENTS
5.3 Directive antennas . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.3.1 Statement of the problem . . . . . . . . . . . . . . . . . 53
5.3.2 Hermite processing of the time-varying field . . . . . . . 53
5.3.3 Impulse response . . . . . . . . . . . . . . . . . . . . . . 57
5.3.4 Computational Issues . . . . . . . . . . . . . . . . . . . . 57
5.3.5 Numerical Examples . . . . . . . . . . . . . . . . . . . . 59
6 TD Analysis of Couplings in Pulsed Arrays 71
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Basic definitions: impulse response operator and TD array factor 72
6.3 TD active array factor and active element factor . . . . . . . . . 74
6.4 Investigation on coupling echoes . . . . . . . . . . . . . . . . . . 75
6.4.1 Coupling for Dirac pulse input signals . . . . . . . . . . . 76
6.4.2 Coupling for finite-duration pulses . . . . . . . . . . . . . 80
6.5 A fullwave example . . . . . . . . . . . . . . . . . . . . . . . . . 85
7 Synthesis of Pulsed Arrays 91
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Definition of the TD synthesis problem . . . . . . . . . . . . . . 93
7.3 Intersection finding problem . . . . . . . . . . . . . . . . . . . . 95
7.4 Alternating projections . . . . . . . . . . . . . . . . . . . . . . . 95
7.5 Radon inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6 Excitation Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.7 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . 102
7.7.1 Single monocycle pulse . . . . . . . . . . . . . . . . . . . 102
7.7.2 Simultaneous monocycle pulses . . . . . . . . . . . . . . 107
8 Conclusions 111
A Details on aperture effective height 113
A.1 Details on the definition of TD aperture effective height . . . . . 113
A.2 Calculation of the hR integral in (5.10) . . . . . . . . . . . . . 113
p,∞
A.3 Modal space factors . . . . . . . . . . . . . . . . . . . . . . . . . 114
A.3.1 Modal space factors for rectangular apertures . . . . . . 114
A.3.2 Modal space factors for circular apertures . . . . . . . . 115
List of Acronyms
Acronym Meaning
AH Associated Hermite
AHF2 Two-Dimensional Associated Hermite Functions
CDMA Code Division Multiple Access
CF Complete Fitting
CRH Circular Ridged Horn
DS Direct Sequence
EIRP Effective Isotropic Radiated Power
EM Electromagnetics
FCC Federal Communications Commission
FD Frequency Domain
FDTD Finite Difference Time Domain
FF Far Field
FDMA Frequency Division Multiple Access
GPS Global Positioning System
HR Hermite Rodriguez
IF Incomplete Fitting
LTI Linear Time Invariant
ME Moment Expansion
N2F Near To Far Field
NB Narrowband
NF Near Field
OFDM Orthogonal Frequency DivisionMultiplexing
PSD Power Spectral Density
RF Radio Frequency
SEM Singularity Expansion Method
SLL Side Lobe Level
SVD Singular Value Decomposition
TD Time Domain
TE Transverse Electric
TM Transverse Magnetic
UWB Ultra Wide Band
5

Chapter 1
Introduction
Several applications of UWB technology have been recently proposed for com-
munications, radar, precise positioning and tracking. The development of new
system components, in particular antennas, requires efficient modeling tools.
The extremely large bandwidths of the systems encourage the use of time-
domain formulations. In particular, the objective of my research activities
has been to develop efficient methods for the transient characterization of
pulsed arrays. Pulsed arrays consist of an arrangement of Ultra-Wideband
antennas sourced by baseband carrier-free input signals, usually with a pure
delay-line as beamforming network, in order to control the main lobe direction.
Their radiating performances are pretty different from narrowband arrays and
time-domain extensively replaces the conventional frequency domain way to
approach the array modeling. In the previous years, this new approach has
alreadypermittedfirstinvestigationsonsometopicsofpulsedarrays, likegrat-
ing lobes cancellation, side lobes mitigation and sparse array design. However
tools for the complete transient characterization of pulsed arrays still lack re-
quiring:
1. the efficient analysis of the isolated radiating elements that constitute
the array;
2. the analysis of the effects of their spatial displacement on the radiating
performances of the array;
3. the synthesis of their transient excitations to realize a desired far field of
the array.
Each of these subjects has been developed during my PhD activity research
and reported in the following chapters. After some historical notes on UWB
technology, Chapter 2 introduces the advantages of the technology as well
as its current and future applications. Chapter 3 compares the two possible
domains of analysis and synthesis of UWB systems and some ”tools” (most
7
8 Chapter 1. Introduction
used waveforms, transformations, operators, representations), useful in time-
domainanalysisandfrequentlyusedintherestofthework, areherepresented.
An introduction on pulsed arrays theory is provided in Chapter 4 and their
main features are briefly described.
Chapters 5 to 7 present innovative methods proposed and developed in
this research activity to characterize pulsed arrays following the three items
previously introduced.
The scope of the study presented in Chapter 5 was to develop suitable
representations of signals and electromagnetic fields to efficiently characterize
UWB antennas. In particular, two techniques for the efficient modeling of
radiating elements by means of suitable spatial and temporal expansions are
introduced. One technique is suitable for aperture antennas, the other for
antennas of more general shape, such as UWB dipoles, TEM horn and non
canonical-aperture horns. These expansions permit to capture the complete
spatialandtemporalbehavioroftheantenna(itseffectiveheight)byasmallset
of parameters thus expressing its response by semi-analytical representations.
The proposed techniques are suited to strengthen any existing time-domain
numericalsolverandtoperformmoreeasilyUWBarrayanalysisandsynthesis.
Chapter 6 presents a simple physical model of the time domain coupling for
UWB arrays aimed to identify the role of the scan angle, input signal duration,
repetition rate of the input pulse train and impulse response of the single
antenna. Expressions for the time domain active array and element patterns
are retrieved and an investigation on coupling echoes and their distorting effect
on the main signal permits to obtain conditions to reduce coupling even in
compact configurations with very small inter-element distances.
Chapter7, finally,presentsasynthesistechniquetocomputetheamplitude,
the transient behavior and the relative delay of the input signals of UWB
arrays in order to shape the radiated field in accordance to a given mask
in the angular and temporal domains. The technique extends the method
of alternating projections to the time domain array synthesis: in particular it
consistsofiterativeprojectionsoftheradiatedpatternontothedesiredpattern
maskandoftheobtainedexcitationsontoaphysicalsetofexcitations. Thanks
tothissecondprojection,theproposedtechniqueprovidesinputcurrentswhich
are physically realizable by means of a beamforming network which will be
shown in the chapter.
Eachtopicisdevelopedpresentingatheoreticalsectionandsomenumerical
examplestovalidatemethodsandinvestigatethephenomena,followedbysome
discussions on the results.