On the achievable rate of stationary fading channels [Elektronische Ressource] / Meik Dörpinghaus

Doerpinghaus

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• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2011
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

OntheAchievableRateof
StationaryFadingChannels
Von der Fakulta¨t fu¨ r Elektrotechnik und Informationstechnik
derRheinisch-Westfa¨lischenTechnischenHochschuleAachen
zurErlangungdesakademischenGrades
einesDoktorsderIngenieurwissenschaften
genehmigteDissertation
vorgelegtvon
Diplom-IngenieurMeikDo¨rpinghaus
ausGummersbach
Berichter: Prof. Dr.-Ing. GerdAscheid
Prof. Dr. techn. HelmutBo¨lcskei
Prof. Dr. sc. techn. HeinrichMeyr
Tag der mu¨ ndlichen Pru¨ fung:
15.04.2010
DieseDissertationistaufdenInternetseitender
Hochschulbibliothekonlineverfu¨gbar.Acknowledgements
The work presented in this book is the result of my Ph.D. thesisthathasbeencarried
out during my time as a research assistant at the Institute forIntegratedSignalPro-
cessing Systems at RWTH Aachen University. Throughout this time I had the oppor-
tunity to work, discuss, and collaborate with many brilliantpeople.Theircomments,
thoughts,andalsocriticismhasbeenverybeneficialduringthecourseofthisworkand
helped me to learn, understand, and apply the fundamental concepts of information
andcommunicationtheory.
ThereareanumberofpeopleIwishtothankmakingallthispossible. FirstIthank
my advisors Prof. Heinrich Meyr and Prof. Gerd Ascheid. The given work was initi-
atedbytheirintriguingquestion’Whatcanwegainbyiterativelyenhancingthechan-
nel estimation using reliability information on data symbols?’. Prof. Meyr and Prof.
Ascheid gave me the freedom and time to follow my ideas to use information theory
to find answers to the given question. I want to thank them for their support over
the years. Their continuous encouragement and faith in my abilities have been very
motivating. Especially, Iwould liketo thankProf. Meyrfor veryvaluablediscussions
which have beenparticularly fruitful by bringing together his deepknowledge ones-
timationanddetectiontheoryandmythoughts andideasininformationtheory.
Furthermore,IthankProf. HelmutBol¨ cskei,foracceptingtotaketheefforttoread
and referee my thesis. In addition, I appreciate that he invited me to the Communi-
cation Theory Group at ETH Zurich in June 2007. This exciting stay in Zurich gave
me invaluable insights and the opportunity to discuss with Giuseppe Durisi, Ulrich
Schuster,andVeniaminMorgenshtern. Besidesthefactthatallofthemareoutstanding
researchers, I would like to thank them for their friendly welcome andtheiropenness
insharingtheirknowledge. WithVeniaminIhavediscussedmyapproachofbounding
theachievablerateofastationaryRayleighflat-fadingchannelusingmeansofrandom
matrix theory. Although we did not came up with a solution, this collaboration has
beenrewardingasweunderstandtheunderlyingproblems. Duringthesediscussions
IlearnedalotfromVeniaminwhohasadeepknowledgeinrandommatrixtheory.
Furthermore, I have to thank Giuseppe and Uli for discussing several aspects of the
capacity of noncoherent fading channels during my stay at ETH. In addition, I grace-
fullythankGiuseppeDurisi, with whom Idiscussedlarge parts of mythesis whenhe
came to Aachen in June 2009. By pinpointing weaknesses in some of my proofs, his
commentsandcriticshaveenhancedthepresentworkalot.
34
IalsothankProf.RudolfMatharforinterestingdiscussionsonthepartsregarding
discreteinputdistributions coveredinChapter9. Thispartoftheworkemergedafter
atalkonCapacity-AchievingDiscreteSignalingoverAdditiveNoiseChannelsgivenbyhim
on the UMIC day in 2007. A few weeks later I discussed the application of this ap-
proachtothescenarioofastationary Rayleighflat-fadingchannelwithhim, resulting
inanISITpublication.
Inaddition,IthankmycolleaguesattheInstituteforIntegratedSignal Processing
Systems for apleasantworking environment. EspeciallyIwouldlike tothankAdrian
Ispas,LarsSchmitt,SusanneGodtmann,MartinSenst,andDanZhangformanyhelp-
fulandinspiringdiscussions. SpecialthanksareduetoAdrianIspaswithwhomIhad
endlessdiscussionsaboutthematerialinthepresentmanuscriptespeciallyduringthe
endofmythesis. Thanksfortakingthetimefornumerousdiscussionsregardingvari-
ousaspectsofthepresentmaterialandthanksforyourdetailedfeedback.
Lastbutnotleast,Ithankmyparentsfortheircontinuoussupportduringmystud-
ies enabling all this. Lastly, I am particularly indebted to my girlfriend Anke, for her
patience and her encouragement which essentially contributes to the success of this
work.
Aachen,August2010 MeikDo¨rpinghausContents
1Introduction 1
1.1 PriorWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 ObjectivesandContributions . . . . . . . . . . . . . . . . . . . . . .... 5
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2Discrete-TimeFlat-FadingSystemModel 13
2.1 RayleighFadingandJakes’Model . . . . . . . . . . . . . . . . . . . ... 15
2.2 Matrix-Vector Notation . . . . . . . . . . . . . . . . . . . . . . . . . . ... 16
2.3 LimitationsoftheModel . . . . . . . . . . . . . . . . . . . . . . . . . . ..17
2.4 OperationalandInformationTheoreticCapacity . . . . . ......... 19
2.4.1 OutageCapacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3BoundsontheAchievableRateofaFlat-FadingChannel 23
!3.1 TheMutualInformationRateI (y;x) .................... 24
!3.2 TheReceivedSignalEntropyRateh (y) ................... 25
!3.2.1 LowerBoundonh(y) ......................... 25
!3.2.2 UpperBoundonh(y) ......................... 26
!3.3 TheEntropyRateh(y|x)............................ 26
!3.3.1 UpperBoundonh(y|x) ........................ 26
!3.3.2 LowerBoundonh(y|x)foraRectangularPSD . . . . . . . . . . 28
iii CONTENTS
3.3.2.1 DiscussionontheAssumptionofaRectangularPSD . . 33
3.4 TheAchievableRate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.1 UpperBound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.1.1 PeakPowerConstrainedInput. . . . . . . . . . . . . . . 34
3.4.1.2 GaussianInputDistribution . . . . . . . . . . . . . . . . 37
3.4.1.3 ModificationbasedonCoherentUpperBound . . . . . 38
3.4.2 LowerBound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.2.1 NoPeakPowerConstraint . . . . . . . . . . . . . . . . . 40
3.4.2.2 PeakPowerConstraint . . . . . . . . . . . . . . . . . . . 41
3.4.3 TightnessofBoundsontheAchievableRate . . . . . . . . . ... 41
3.4.3.1 AsymptoticallySmallChannelDynamics . . . . . . . . 42
3.4.3.2 GaussianInputs . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.4 TheAsymptoticHighSNRBehavior . . . . . . . . . . . . . . . . . 45
3.5 ComparisontoAsymptotesin[65] . . . . . . . . . . . . . . . . . . . ... 46
3.6 ComparisontoBoundsin[102]and[104] . . . . . . . . . . . . . . .... 47
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4BoundsontheAchievableRateofaFlat-FadingChanelBasedonPrediction52
!4.1 Calculationofh(y|x)basedonChannelPrediction . . . . . . . . . . . . 53
!4.2 UpperBoundonh(y) ............................. 56
!4.2.1 SimpleUpperBoundonh (y)..................... 56
!4.2.2 IdeasforanEnhancedUpperBoundonh(y)............ 56
4.3 UpperBoundontheAchievableRate . . . . . . . . . . . . . . . . . . ..60
4.3.1 ThePredictionErrorVariance . . . . . . . . . . . . . . . . . . . ..60
4.3.2 EffectofConstraintsontheInputDistribution . . . . ....... 63
4.4 ComparisontoBoundsgiveninChapter3 . . . . . . . . . . . . . . .... 64CONTENTS iii
4.4.1 NumericalEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . 64
!4.4.2 RelationofBoundsonh(y|x)..................... 66
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5PilotBasedSynchronizedDetection 69
5.1 SynchronizedDetection . . . . . . . . . . . . . . . . . . . . . . . . . . ..69
5.1.1 ChannelEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1.2 InterleavingandDetection/Decoding . . . . . . . . . . . . .... 73
5.2 AchievableRate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.1 ComparisontotheAchievableRatewithi.i.d.GaussianInputs . 80
5.2.2 OptimizedPilot-to-DataPowerRatio . . . . . . . . . . . . . ... 81
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6IterativeCode-AidedSynchronizedDetection 85
6.1 PrincipleofIterativeCode-AidedSynchronizedDetection . . . . . . . . 86
6.1.1 ModifiedChannelEstimationUnit . . . . . . . . . . . . . . . . . . 91
6.2 AchievableRatewithIterativeCode-AidedSynchronizedDetection... 92
6.2.1 Upper-BoundingApproachontheAchievableRate . . . . .... 93
6.2.2 TheChannelInterpolationSeparationInequality . . ........ 95
6.2.3 TheTermI(y ;x |y ,x )....................... 970 0 \0 \0
6.2.4 TheTermI(y ;x |y ).........................1000 \0 \0
6.2.4.1 CanI(y ;x |y )beexploitedbyusingthechanneles-0 \0 \0
timator in(6.13)? . . . . . . . . . . . . . . . . . . . . . . . 102
ˆ6.2.5 AnUpperBoundonI(x ;y |h ,x ) .................1020 0 0 \0
ˆ6.2.5.1 Calculationofh(y |x ,h ,x ) ...............1030 0 0 \0
ˆ6.2.5.2 UpperBoundonh(y |h ,x ) ...............1030 0 \0
ˆ6.2.5.3 DerivationofanUpperBoundonI(x ;y |h ,x )....1040 0 0 \0iv CONTENTS
6.2.5.4 TheInterpolationErrorVariance . . . . . . . . . . . . . . 105
6.2.6 ApproximativeUpperBoundontheAchievableRatewiththeIt-
erative Code-Aided Synchronized Detection based Receiver us-
ingtheModifiedChannelEstimator(6.19) . . . . . . . . . . . . . 108
6.2.7 NumericalE