Wavefield modeling and signal processing for sensor arrays of arbitrary geometry

136 Pages·2013·1.18 MB·English

by  Mário Jorge Costa

Department of Signal Processing and Acoustics
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ISBN 978-952-60-5346-2 BUSINESS +
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H ISSN-L 1799-4934
S ISSN 1799-4934 ART +
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F ISSN 1799-4942 (pdf) DESIGN +
M ARCHITECTURE
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DOCTORAL s DISSERTATIONS
DISSERTATIONS ity
Aalto University publication series
DOCTORAL DISSERTATIONS 149/2013
Wavefield modeling and signal
processing for sensor arrays of
arbitrary geometry
Mário Jorge Costa
A doctoral dissertation completed for the degree of Doctor of
Science in Technology to be defended, with the permission of the
Aalto University School of Electrical Engineering, at a public
examination held at the lecture hall S4 of the school on 1 November
2013 at 12 o'clock noon.
Aalto University
School of Electrical Engineering
Department of Signal Processing and Acoustics
Supervising professor
Academy Prof. Visa Koivunen

Thesis advisor
Academy Prof. Visa Koivunen

Preliminary examiners
Prof. Marius Pesavento, Technische Universität Darmstadt, Germany
Associate Prof. Mats Bengtsson, Kungliga Tekniska Högskolan,
Sweden

Opponents
PPrrooff.. ALe. eL eSew Sinwdilnedhluerhsutr, sUt,n Uivneirvseirtys itCya oliff oCranliiafo arnt iIarv aint eIr, vUinSeA, USA
PPrrooff.. MMaarriiuuss PPeessaavveennttoo,, TTeecchhnniisscchhee UUnniivveerrssiittäätt DDaarrmmssttaaddtt,, GGeerrmmaannyy
Aalto University publication series
DOCTORAL DISSERTATIONS 149/2013

© Mário Jorge Costa

ISBN 978-952-60-5346-2
ISBN 978-952-60-5347-9 (pdf)
ISSN-L 1799-4934
ISSN 1799-4934 (printed)
ISSN 1799-4942 (pdf)
http://urn.fi/URN:ISBN:978-952-60-5347-9

Unigrafia Oy
Helsinki 2013

Finland
Abstract
Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi
Author
Mário Jorge Costa
Name of the doctoral dissertation
Wavefield modeling and signal processing for sensor arrays of arbitrary geometry
Publisher School of Electrical Engineering
Unit Department of Signal Processing and Acoustics
Series Aalto University publication series DOCTORAL DISSERTATIONS 149/2013
Field of research Signal Processing for Communications
Manuscript submitted 7 June 2013 Date of the defence 1 November 2013
Permission to publish granted (date) 11 September 2013 Language English
Monograph Article dissertation (summary + original articles)
Abstract
Sensor arrays and related signal processing methods are key technologies in many areas of
engineering including wireless communication systems, radar and sonar as well as in
biomedical applications. Sensor arrays are a collection of sensors that are placed at distinct
locations in order to sense physical phenomena or synthesize wavefields. Spatial processing
from the multichannel output of the sensor array is a typical task. Such processing is useful in
areas including wireless communications, radar, surveillance and indoor positioning.
In this dissertation, fundamental theory and practical methods of wavefield modeling for
radio-frequency array processing applications are developed. Also, computationally-efficient
high-resolution and optimal signal processing methods for sensor arrays of arbitrary geometry
are proposed. Methods for taking into account array nonidealities are introduced as well.
Numerical results illustrating the performance of the proposed methods are given using real-
world antenna arrays.
Wavefield modeling and manifold separation for vector-fields such as completely polarized
electromagnetic wavefields and polarization sensitive arrays are proposed. Wavefield modeling
is used for writing the array output in terms of two independent parts, namely the sampling
matrix depending on the employed array including nonidealities and the coefficient vector
depending on the wavefield. The superexponentially decaying property of the sampling matrix
for polarization sensitive arrays is established. Two estimators of the sampling matrix from
calibration measurements are proposed and their statistical properties are established.
The array processing methods developed in this dissertation concentrate on polarimetric
beamforming as well as on high-resolution and optimal azimuth, elevation and polarization
parameter estimation. The proposed methods take into account array nonidealities such as
mutual coupling, cross-polarization effects and mounting platform reflections.
Computationally-efficient solutions based on polynomial rooting techniques and fast Fourier
transform are achieved without restricting the proposed methods to regular array geometries.
A novel expression for the Cramér-Rao bound in array processing that is tight for real-world
arrays with nonidealities in the asymptotic regime is also proposed.
A relationship between spherical harmonics and 2-D Fourier basis, called equivalence matrix,
is established. A novel fast spherical harmonic transform is proposed, and a one-to-one
mapping between spherical harmonic and 2-D Fourier spectra is found. Improvements to the
minimum number of samples on the sphere that are needed in order to avoid aliasing are also
proposed.
Keywords Sensor array signal processing, parameter estimation, beamforming, manifold
separation, harmonic analysis, array calibration, array nonidealities
ISBN (printed) 978-952-60-5346-2 ISBN (pdf) 978-952-60-5347-9
ISSN-L 1799-4934 ISSN (printed) 1799-4934 ISSN (pdf) 1799-4942
Location of publisher Helsinki Location of printing Helsinki Year 2013
Pages 204 urn http://urn.fi/URN:ISBN:978-952-60-5347-9

Acknowledgments
Manypeoplehavecontributed,eitherdirectlyorindirectly,tothisdisser-
tation. The research work presented herein has been carried out under
thesupervisionofAcademyProf.VisaKoivunenattheDepartmentofSig-
nalProcessingandAcoustics,AaltoUniversity(formerSignalProcessing
Laboratory, Helsinki University of Technology) during the years 2008-
2013. The statistical signal processing group is led by Prof. Koivunen
anditispartofSMARAD(SmartRadiosandWirelessResearch), acen-
ter of excellence in research appointed by the Academy of Finland. This
research work has also included an external-researcher position at the
NokiaResearchCenterfromJanuarytoJuly2011.
Firstandforemost, Iwouldliketoexpressmydeepestgratitudetomy
supervisor Academy Prof. Visa Koivunen. The guidance, constructive
criticism, and technical insight that have been given by Prof. Koivunen
aretrulyremarkable. Secondly,Iwouldliketoexpressmysinceregrati-
tudetoDr. AndreasRichterforallthediscussionswehad. Mostofthese
discussionsweretechnicalbutsomeofthemwerelesspragmatic,though
still extremely helpful. Both Prof. Koivunen and Dr. Richter have pro-
vided valuable guidance and insight throughout the research work, and
I have learned so much from them. Dr. Fabio Belloni is also acknowl-
edged here for the great discussions during the course of this research.
I am also indebted to Prof. Carlos Lima for all the useful advices and
helpincontactingProf. Koivunen,allowingmetocontinuemystudiesin
this outstanding research group. Nokia Foundation and Ulla Tuominen
Foundationalsodeservemygratitudeforthefinancialsupport.
IwouldliketothankthepreliminaryexaminersProf. MariusPesavento
and Associate Prof. Mats Bengtsson. Their comments and suggestions
have helped to improve the quality and clarity of the dissertation. The
timeandefforttheyhaveputinreviewingthisdissertationisalsohighly
i
Acknowledgments
acknowledged.
Many thanks to my current and former colleagues at the Department
of Signal Processing and Acoustics. It has been a great learning experi-
enceworkingwithsuchexceptionalpeople. TheyincludeDr. JussiSalmi,
Dr. TraianAbrudan, Dr. SachinChaudhari, Dr. AlexandraOborina, Dr.
Jarmo Lunden, Dr. Jan Eriksson, Dr. Esa Ollila, Dr. Hyon-Jung Kim-
Ollila, Jan Oksanen, Marian Micaˇ, Adriana Chis, Pramod Mathecken,
TaneliRiihonen,TuomasAittomäki,Mei-YenCheong,AzadehHaghparast,
Jayaprakash Rajasekharan, Hassan Naseri, among others. Dr. Stefan
Werner,Prof.RistoWichman,Prof.SergiyVorobyov,andAbdullahAzremi
also deserve my gratitude. The help of secretaries Mirja Lemetyinen,
Heidi Koponen, and Marja Leppäharju in all the bureaucratic issues is
greatlyappreciated. Also,specialthankstomygoodfriendsVarunSingh,
JakubGronicz,andJavierMartinez.
My family has had an important role during these years. I thank my
parentsforhavingtaughtmetheimportanceofintegrityandhumanistic
values. My sisters deserve my gratitude for all the good advices. I also
thankmyuncleJoséMárioforhispersistenceinteachingmetheimpor-
tance,andbeauty,oflínguaLusófona. Finally,IthankSusanaforhelping
meunderstandingthathappinessisattainedthroughcommitmenttono-
bleideals.
Espoo,September19,2013,
MárioJorgeCosta
ii
Contents
Acknowledgments i
Contents iii
Listofpublications vii
Listofabbreviations ix
Listofsymbols xi
1. Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectivesandscope . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Dissertationstructure . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Summaryofthepublications . . . . . . . . . . . . . . . . . . 6
2. Arrayprocessingmodels 11
2.1 Signalmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Idealarraymodelsandreal-worldarrays . . . . . . . . . . . 18
3. Arrayprocessinginthefaceofnonidealities 23
3.1 Auto-calibrationtechniques . . . . . . . . . . . . . . . . . . . 23
3.2 Uncertaintysetsonthearraysteeringvector . . . . . . . . . 25
3.3 Arraycalibrationmeasurements . . . . . . . . . . . . . . . . 27
3.4 Localinterpolationofthearraycalibrationmatrix . . . . . . 30
3.5 Arraymappingtechniques . . . . . . . . . . . . . . . . . . . . 31
3.5.1 Arrayinterpolationbasedonvirtualarrays . . . . . . 31
3.5.2 Phase-modeexcitationandbeamspacetransform . . 32
3.6 Wavefieldmodelingandmanifoldseparation-summary . . 35
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
iii
Contents
4. Wavefieldmodelingandmanifoldseparation 39
4.1 Wavefieldmodelingandmanifoldseparationforscalar-fields 40
4.1.1 Relationship to local interpolation of the array cali-
brationmatrix . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.2 Relationshiptoarraymappingtechniques. . . . . . . 43
4.2 Wavefieldmodelingandmanifoldseparationforvector-fields 45
4.3 Samplingmatrixestimation . . . . . . . . . . . . . . . . . . . 50
4.3.1 Least-squaresestimator . . . . . . . . . . . . . . . . . 50
4.3.2 Discretevectorsphericalharmonictransform. . . . . 52
4.4 Equivalencematrix . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.1 Conceptsanddefinitions . . . . . . . . . . . . . . . . . 58
4.4.2 Wavefield modeling and manifold separation based
on2-DFourierbasis . . . . . . . . . . . . . . . . . . . 60
4.4.3 Relationshiptoeffectiveaperturedistributionfunction 65
4.4.4 Fastvectorsphericalharmonictransformby2-DFFT 66
4.5 Arraycalibrationexample . . . . . . . . . . . . . . . . . . . . 68
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5. Signalprocessingmethodsforarbitraryarraygeometries 75
5.1 Beamformingtechniques . . . . . . . . . . . . . . . . . . . . . 76
5.1.1 Conventionalbeamformer . . . . . . . . . . . . . . . . 77
5.1.2 Caponbeamformer . . . . . . . . . . . . . . . . . . . . 78
5.2 Subspacemethods . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.1 Multiplesignalclassification(MUSIC) . . . . . . . . . 82
5.2.2 Root-MUSIC . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.3 Weightedsubspacefitting(WSF) . . . . . . . . . . . . 86
5.3 StochasticCRBforreal-worldantennaarrays . . . . . . . . 87
5.4 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . . 88
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6. Conclusions 93
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Futureresearch . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A. Appendix 97
A.1 Derivationofexpression(4.25) . . . . . . . . . . . . . . . . . 97
A.2 Closed-formexpressionfortheequivalencematrix . . . . . . 99
A.3 Derivationofexpressions(4.45)and(4.46). . . . . . . . . . . 100
Bibliography 101
iv
Contents
Errata 117
Publications 119
v