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Wireless Communications
Over Rapidly Time-Varying
Channels
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Wireless Communications
Over Rapidly Time-Varying
Channels
Edited by
Franz Hlawatsch
Gerald Matz
AMSTERDAM•BOSTON•HEIDELBERG•LONDON
NEWYORK•OXFORD•PARIS•SANDIEGO
SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
AcademicPressisanimprintofElsevier
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Contributing Authors
PaoloBanelli,Universita` diPerugia(Perugia,Italy)
HelmutBo¨lcskei,ETHZurich(Zurich,Switzerland)
SibasishDas,QualcommInc.(SanDiego,CA,USA)
MinDong,UniversityofOntarioInstituteofTechnology(Oshawa,Ontario,Canada)
CharlotteDumard,FTWForschungszentrumTelekommunikationWien(Vienna,Austria)
GiuseppeDurisi,ChalmersUniversityofTechnology(Gothenburg,Switzerland)
FranzHlawatsch,ViennaUniversityofTechnology(Vienna,Austria)
YiHong,MonashUniversity(Clayton,Melbourne,Australia)
Sung-JunHwang,QualcommInc.(SantaClara,CA,USA)
CornelIoana,NationalPolytechnicInstituteofGrenoble(Grenoble,France)
JoakimJalde´n,RoyalInstituteofTechnology(KTH)(Stockholm,Sweden)
ArunP.Kannu,IndianInstituteofTechnology(Madras,Chennai,India)
GeertLeus,DelftUniversityofTechnology(Delft,TheNetherlands)
GeraldMatz,ViennaUniversityofTechnology(Vienna,Austria)
VeniaminI.Morgenshtern,ETHZurich(Zurich,Switzerland)
AntoniaPapandreou-Suppappola,ArizonaStateUniversity(Tempe,AZ,USA)
LucaRugini,Universita` diPerugia(Perugia,Italy)
BrianM.Sadler,ArmyResearchLaboratory(Adelphi,MD,USA)
PhilipSchniter,OhioStateUniversity(Columbus,OH,USA)
UlrichG.Schuster,RobertBoschGmbH(Stuttgart,Germany)
ShlomoShamai(Shitz),Technion–IsraelInstituteofTechnology(Haifa,Israel)
ZijianTang,TNODefence,SecurityandSafety(TheHague,TheNetherlands)
LangTong,CornellUniversity(Ithaca,NY,USA)
EmanueleViterbo,MonashUniversity(Clayton,Melbourne,Australia)
ThomasZemen,FTWForschungszentrumTelekommunikationWien(Vienna,Austria)
JunJasonZhang,ArizonaStateUniversity(Tempe,AZ,USA)
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About the Editors
FranzHlawatschreceivedtheDipl.-Ing.,Dr.techn.,andUniv.-Dozent(habilitation)degreesinelec-
tricalengineering/signalprocessingfromViennaUniversityofTechnology,Vienna,Austria,in1983,
1988,and1996,respectively.Since1983,hehasbeenwiththeInstituteofTelecommunications,Vienna
University of Technology, as an associate professor. During 1991–1992, as a recipient of an Erwin
Schro¨dinger Fellowship, he spent a sabbatical year with the Department of Electrical Engineering,
UniversityofRhodeIsland,Kingston,RI,USA.In1999,2000,and2001,heheldone-monthvisiting
professorpositionswithINP–ENSEEIHT/Te´SA(Toulouse,France)andIRCCyN(Nantes,France).He
(co)authoredabook,areviewpaperthatappearedintheIEEESignalProcessingMagazine,about180
refereedorinvitedscientificpapersandbookchapters,andthreepatents.Hecoeditedthreebooks.His
researchinterestsincludesignalprocessingforwirelesscommunications,statisticalsignalprocessing,
andcompressivesignalprocessing.Prof.HlawatschwasaTechnicalProgramCo-ChairofEUSIPCO
2004andhasservedonthetechnicalcommitteesofnumerousinternationalconferences.From2003to
2007,heservedasanassociateeditorfortheIEEETransactionsonSignalProcessing.Heiscurrently
servingasanassociateeditorfortheIEEETransactionsonInformationTheory.From2004to2009,
he was a member of the IEEE Signal Processing for Communications Technical Committee. He is
coauthorofapaperthatwonanIEEESignalProcessingSocietyYoungAuthorBestPaperAward.
Gerald Matz received the Dipl.-Ing. and Dr. techn. degrees in electrical engineering in 1994 and
2000, respectively, and the Habilitation degree for communication systems in 2004, all from Vienna
UniversityofTechnology,Vienna,Austria.Since1995,hehasbeenwiththeInstituteofTelecommu-
nications,ViennaUniversityofTechnology,wherehecurrentlyholdsatenuredpositionasassociate
professor. From March 2004 to February 2005, he was on leave as an Erwin Schro¨dinger Fellow
withtheLaboratoiredesSignauxetSyste`mes,EcoleSupe´rieured’Electricite´,France.Duringsummer
2007,hewasaguestresearcherwiththeCommunicationTheoryLabatETHZurich,Switzerland.He
hasdirectedoractivelyparticipatedinseveralresearchprojectsfundedbytheAustrianScienceFund
(FWF),theViennaScienceandTechnologyFund(WWTF),andtheEuropeanUnion.Hehaspublished
morethan140papersininternationaljournals,conferenceproceedings,andeditedbooks.Hisresearch
interestsincludewirelesscommunications,statisticalsignalprocessing,andinformationtheory.Prof.
MatzservesasamemberoftheIEEESignalProcessingSociety(SPS)TechnicalCommitteeonSignal
Processing for Communications and Networking and of the IEEE SPS Technical Committee on Sig-
nal Processing Theory and Methods. He was an associate editor for the IEEE Transactions of Signal
Processing(2006–2010),fortheIEEESignalProcessingLetters(2004–2008),andfortheEURASIP
journalSignalProcessing(2007–2010).HewasaTechnicalProgramCo-ChairofEUSIPCO2004and
has been on the Technical Program Committee of numerous international conferences. In 2006, he
receivedtheKardinalInnitzerMostPromisingYoungInvestigatorAward.
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Preface
Wireless communications has become a field of enormous scientific and economic interest. Recent
success stories include 2G and 3G cellular voice and data services (e.g., GSM and UMTS), wireless
local area networks (WiFi/IEEE 802.11x), wireless broadband access (WiMAX/IEEE 802.16x), and
digitalbroadcastsystems(DVB,DAB,DRM).Onthephysicallayerside,traditionaldesignstypically
assumethattheradiochannelremainsconstantforthedurationofadatablock.However,researchers
andsystemdesignersareincreasinglyshiftingtheirattentiontochannelsthatmayvarywithinablock.
In addition to time dispersion caused by multipath propagation, these rapidly time-varying channels
feature frequency dispersion resulting from the Doppler effect. They are, thus, often referred to as
being“doublydispersive.”
Historically,channelswithtimevariationandfrequencydispersionwerefirstconsideredmostlyin
the contextof ionospheric and troposphericcommunications and in radioastronomy. The theoretical
foundationsofrapidlytime-varyingchannelswereestablishedbyBello,Gallager,Kailath,Kennedy,
and others in the sixties of the twentieth century. More recently, rapidly time-varying channels have
becomeimportantinnovelapplicationscenarioswithpotentiallyhigheconomicrelevanceandsocietal
.impact.
User mobility, a source of significant Doppler frequency shifts, is an essential factor in today’s
cellular and broadband access systems. An extreme example is given by radio access links for
high-speedtrains.Channelswithrapidtimevariationarealsoencounteredincar-to-carandcar-to-
.
infrastructurecommunications,whicharebecomingincreasinglyimportant.
In advanced wireless networks, nodes may cooperate to achieve spatial diversity gains in a dis-
tributedmanner.Anexampleisthebasestationcooperationoption(alsoknownasnetworkMIMO
or cooperative multipoint transmission) in 3GPP Long Term Evolution. In such systems, the car-
rierfrequency offsetsof differentnodes accumulateand, togetherwith mobility-inducedDoppler
.
frequencyshifts,resultinchannelswithrapidtimevariation.
In underwater acoustic communications, the relative Doppler shifts are potentially much larger
thaninterrestrialradiosystemsbecausethespeedofsoundismuchsmallerthanthespeedoflight.
Furthermore,thesmallerpropagationspeedofacousticwavesresultsinlargerpropagationdelays.
Underwaterchannelsare,therefore,instancesofparticularlyharshdoublydispersivechannels.
Rapid channel variations induced by Doppler shifts provide an extra dimension that offers addi-
tionalgains.Atthesametime,doublydispersivechannelsposetoughdesignchallengesandnecessitate
the use of sophisticated methods to combat the detrimental effects of the channel and to realize the
additional gains. Thus, understanding the fundamental properties of doubly dispersive channels and
theresultingdesignparadigmswillbecomeessentialknow-howinthefuturewirelessarena.
This book explains the system-theoretic and information-theoretic foundations of doubly disper-
sivechannelsanddescribesthecurrentstateoftheartinalgorithmandsystemdesign.Itisintendedto
present a comprehensive and coherent discussion of the challenges and developments in the field,
which will help researchers and engineers understand and develop future wireless communication
technologies. Contributed by leading experts, the individual chapters of this book address the most
important aspects of the theory and methodology of wireless communications over rapidly time-
varying channels. Wireless transceiver design and modern techniques such as iterative turbo-style
xiii
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xiv Preface
detection, multicarrier (OFDM) modulation, and multiantenna (MIMO) processing are given special
attention.
In the introductory chapter, Chapter 1, we discuss the properties and mathematical charac-
terization of doubly dispersive channels. Further topics addressed include propagation effects,
system-theoretic aspects, stochastic channel characterizations, parsimonious channel models, and
measurementprinciples.
Chapter 2, by G. Durisi, V. Morgenshtern, H. Bo¨lcskei, U. Schuster, and S. Shamai, discusses
information-theoreticaspectsofrandomtime-varyingchannels,includingMIMOchannels.Thischap-
ter focuses on noncoherent channel capacity (i.e., channel capacity in the absence of channel state
information)inthelarge-bandwidthandhigh-SNRregimes.
Chapter3,byE.ViterboandY.Hong,addressesthedesignofchannelcodesforfast-fadingchan-
nels,usingmethodsfromalgebraicnumbertheoryandlatticetheory.Thespheredecoderisdiscussed
asanefficientmeanstorecoverthetransmittedcodewords.
Chapter 4, by G. Leus, Z. Tang, and P. Banelli, considers the estimation of rapidly time-varying
channels in single-carrier and multicarrier communication systems. A block-based approach is
adoptedthatbuildsonabasisexpansionmodelforthechannelandthetransmissionofdedicatedpilot
(training)symbols.
Chapter 5, by M. Dong, B. M. Sadler, and L. Tong, complements Chapter 4 by discussing train-
ing designs for the estimation of time-varying channels. The optimization of the number, placement,
and power of pilot symbols is studied for various system configurations (single carrier, multicarrier,
multiantenna)andperformancecriteria.
Chapter6,byP.Schniter,S.-J.Hwang,S.Das,andA.P.Kannu,presentsequalizationtechniques
for doubly dispersive channels. Both coherent and noncoherent detection are addressed, using linear
andtree-searchmethods,iterativeapproaches,andjointdetection-estimationschemes.
Chapter7,byL.Rugini,P.Banelli,andG.Leus,isdedicatedtoorthogonalfrequencydivisionmulti-
plex(OFDM)transmissionsovertime-varyingchannels.Thischapterdiscussesmethodsforequalizing
intercarrierinterferenceandforchannelestimationandcommentsontherelevanceofthesemethods
toexistingstandards.
Chapter8,byC.Dumard,J.Jalde´n,andT.Zemen,considersamultiusersystememployingmultiple
antennas and a multicarrier CDMA transmission format. An iterative (turbo) receiver is developed,
whichperformsestimationofthetime-varyingchannels,multiuserseparation,andchanneldecoding,
withcomplexityreductionsduetoKrylovsubspaceandspheredecodingtechniques.
The final chapter, Chapter 9, by A. Papandreou-Suppappola, C. Ioana, and J. J. Zhang, discusses
wideband channels that are more suitably characterized in terms of Doppler scaling than in terms
of Doppler shifts. Theoretical considerations and advanced receiver designs are exemplified by an
underwateracousticcommunicationsystem.
Wewouldliketothankallpeoplewhocontributedtothisbookinonewayoranother.Weareespe-
ciallygratefultothechapterauthorsfortheirexpertiseandhardwork,andforacceptingtheconstraints
ofapredefined,commonnotation.WethankTimPittsofElsevierforinvitingustoeditthisbook.Tim
andhiscolleagues—MelanieBenson,SusanLi,MelissaRead,andNaomiRobertson—providedmuch
appreciatedassistanceduringthevariousstagesofthisproject.Finally,weacknowledgesupportbythe
Austrian Science Fund (FWF) under Grants S10603 (Statistical Inference) and S10606 (Information
Networks)withintheNationalResearchNetworkSISE.
FranzHlawatsch
GeraldMatz
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Notations and Symbols
Basic Notations
R,C,Z real/complex/integernumbers
√
j −1
∗
x complexconjugation
z−1 unitdelay
dx(t),x(cid:48)(t) differentiation/derivative
dt
(cid:104)x,y(cid:105) innerproduct
√
(cid:107)x(cid:107)= (cid:104)x,x(cid:105) norm
E =(cid:107)x(cid:107)2 energy
x
(x∗y)(t) continuous-timeconvolution
(x∗y)[n] discrete-timeconvolution
Re{·},Im{·} realpart,imaginarypart
L2(R) spaceofsquare-integrablefunctionsonR
l2(Z) spaceofsquare-summablefunctionsonZ
(cid:44) definition
(cid:100)x(cid:101) smallestintegernotlessthanx
(cid:98)x(cid:99) largestintegernotgreaterthanx
Basic Symbols
t continuoustime
f frequency(Hz)
τ continuoustime-delay
ν Dopplerfrequency(Hz)
α continuoustimescaleparameter
n discretetime
m discretetime-delay
θ normalizedfrequency
l discretefrequency
ξ normalizedDopplerfrequency
d discreteDopplerfrequency
κ discretescaleparameter
(cid:49)t,(cid:49)n,etc. lag/difference
x(t) continuous-timesignal
x[n] discrete-timesignal
xix
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xx Notations and Symbols
X(f) continuous-timeFouriertransform
X(θ) discrete-timeFouriertransform
X[l] discreteFouriertransform(DFT)
X(z) z-transform
f ,T samplingfrequency/period
s s
s(t),s[n] transmitsignal
w(t),w[n] whitechannelnoise
r(t),r[n] receivesignal
g(t),γ(t) transmit/receivepulse
b[i] informationbits
c[j] codedbits
L [j] log-likelihoodratio
c
a[k],a[k,l] transmitsymbols
y[k],y[k,l] demodulatedsymbols
z[k],z[k,l] noiseafterdemodulation
p[k],p[k,l] pilotsymbols
Transceiver and Channel Parameters
T ,N blocklength
0
B transmitbandwidth(Hz)
f carrierfrequency(Hz)
c
T symbolduration
R symbolrate
F subcarrierfrequencyspacing
T bitduration
b
R bitrate
b
(cid:53) interleaver
k symboltimeindex
l subcarrierfrequencyindex
A symbolalphabet
N size(cardinality)ofsymbolalphabet
a
P setofpilotlocationskor(k,l)
N numberofpilotsymbols
p
K numberoftransmittedsymbols
L numberofsubcarriers
N guardintervallength
g
L cyclicprefixlength
CP
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Notations and Symbols xxi
M ,M numberoftransmit/receiveantennas
T R
U numberofusers
ρ signal-to-noiseratio
I basisexpansionmodelorder
τ ,M maximumdelay(channellength)
max
ν ,D maximumDopplerfrequency
max
A Dopplerscalespread
s
T coherencetime
c
F coherencebandwidth
c
T stationaritytime
s
F stationaritybandwidth
s
Channel and Signal Representations
H channeloperator
h(t,τ),h[n,m] time-varyingimpulseresponse
H(f,ν),H[l,d] frequency-domainimpulseresponse
L (t,f),L [n,l] (time-frequency/time-varying)transferfunction
H H
S (τ,ν),S [m,d] (delay-Doppler)spreadingfunction
H H
F (τ,α),F [m,κ] widebandspreadingfunction
H H
C (τ,ν),C [m,d] scatteringfunction
H H
B (τ,α),B [m,κ] widebandscatteringfunction
H H
R ((cid:49)t,(cid:49)f),R [(cid:49)n,(cid:49)l] time-frequencycorrelationfunction
H H
A ((cid:49)t,(cid:49)f) ambiguityfunction
x
A ((cid:49)t,(cid:49)f) cross-ambiguityfunction
xy
Special Functions and Signals
ln(·) naturallogarithm
log(·),log (·) base-10logarithm
10
log (·) binarylogarithm
2
et,exp(t) exponentialfunction
ej2πft complexsinusoid
sin(·),cos(·),tan(·),cot(·) trigonometricfunctions
sinh(·),cosh(·),tanh(·),coth(·) hyperbolicfunctions
u(t),u[n] unitstep
1T(t),1N [n] indicatorfunction
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xxii Notations and Symbols
δ(t) Diracimpulse
δ[n] unitsample
δ Kroneckerdelta
ij
sign(·) signfunction
sinc(t)= sin(t) sincfunction
t
Vectors, Matrices, and Operators
x (column)vector
x,[x] ithelementofvectorx
i i
(cid:107)x(cid:107) normofx
(cid:107)x(cid:107) weightednormofx
W
A,(a ) matrix
ij
a ,[A] elementofmatrixA
ij ij
det{A} determinant
tr{A} trace
dim{x} dimension
A−1 inverse
A# pseudo-inverse
xT,AT transpose
xH,AH Hermitiantranspose
I identitymatrix
W DFTmatrix
U(cid:54)VH singularvaluedecomposition
U(cid:51)UH eigenvaluedecomposition
H linearoperator
H−1 inverseofH
∗
H adjoint
H# pseudo-inverse
I identityoperator
Probability, Random Variables, and Random Processes
Pr{E} probabilityofeventE
f(x) probabilitydensityfunction(pdf)
p(x) probabilitymassfunction(pmf)
f(x|y),p(x|y) conditionalpdf/pmf
F(x) cumulativedistributionfunction
