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MOBILE RADIO
CHANNELS
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MOBILE RADIO
CHANNELS
Second Edition
MatthiasPa¨tzold
UniversityofAgder,Norway
A John Wiley & Sons, Ltd., Publication
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Thiseditionfirstpublished2012
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LibraryofCongressCataloging-in-PublicationData
Pa¨tzold,Matthias,professorofmobilecommunications.
Mobileradiochannels/MatthiasPa¨tzold.–2nded.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-51747-5(cloth)
1.Mobilecommunicationsystems. 2.Radiowavepropagation. 3.Radioresourcemanagement
(Wirelesscommunications). I.Title.
TK5103.2.P3852012
621.3845–dc23
2011015882
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:978-0-470-51747-5
ePDFISBN:978-1-119-97412-3
oBookISBN:978-1-119-97411-6
ePubISBN:978-1-119-97525-0
MobiISBN:978-1-119-97526-7
Typesetin10/12ptTimesbyAptaraInc.,NewDelhi,India
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Contents
PrefacetotheSecondEdition xi
ListofAcronyms xv
ListofSymbols xix
1 Introduction 1
1.1 TheEvolutionofMobileRadioSystems 1
1.2 BasicKnowledgeofMobileRadioChannels 8
1.3 StructureofthisBook 12
2 RandomVariables,StochasticProcesses,andDeterministicSignals 17
2.1 RandomVariables 17
2.1.1 BasicDefinitionsofProbabilityTheory 17
2.1.2 ImportantProbabilityDensityFunctions 24
2.1.3 FunctionsofRandomVariables 35
2.2 StochasticProcesses 37
2.2.1 StationaryProcesses 40
2.2.2 ErgodicProcesses 42
2.2.3 Level-CrossingRateandAverageDurationofFades 43
2.2.4 LinearSystemswithStochasticInputs 45
2.3 DeterministicSignals 48
2.3.1 DeterministicContinuous-TimeSignals 48
2.3.2 DeterministicDiscrete-TimeSignals 50
2.4 FurtherReading 52
Appendix2.A DerivationofRice’sGeneralFormulafortheLevel-CrossingRate 52
3 RayleighandRiceChannels 55
3.1 SystemTheoreticalDescriptionofMultipathChannels 56
3.2 FormalDescriptionofRayleighandRiceChannels 61
3.3 ElementaryPropertiesofRayleighandRiceChannels 62
3.3.1 AutocorrelationFunctionandSpectrumoftheComplexEnvelope 62
3.3.2 AutocorrelationFunctionandSpectrumoftheEnvelope 65
3.3.3 AutocorrelationFunctionandSpectrumoftheSquaredEnvelope 67
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3.4 StatisticalPropertiesofRayleighandRiceChannels 69
3.4.1 ProbabilityDensityFunctionoftheEnvelopeandthePhase 70
3.4.2 ProbabilityDensityFunctionoftheSquaredEnvelope 72
3.4.3 Level-CrossingRateandAverageDurationofFades 73
3.4.4 TheStatisticsoftheFadingIntervalsofRayleighChannels 77
3.5 FurtherReading 84
Appendix3.A DerivationoftheJakesPowerSpectralDensityandthe
CorrespondingAutocorrelationFunction 84
Appendix3.B DerivationoftheAutocorrelationFunctionoftheEnvelope 88
Appendix3.C DerivationoftheAutocovarianceSpectrumoftheEnvelopeUnder
IsotropicScatteringConditions 90
Appendix3.D DerivationoftheLevel-CrossingRateofRiceProcesseswith
DifferentSpectralShapesoftheUnderlyingGaussianRandom
Processes 91
4 IntroductiontoSum-of-SinusoidsChannelModels 95
4.1 PrincipleofDeterministicChannelModelling 96
4.2 ElementaryPropertiesofDeterministicSum-of-SinusoidsProcesses 102
4.3 StatisticalPropertiesofDeterministicSum-of-SinusoidsProcesses 107
4.3.1 ProbabilityDensityFunctionoftheEnvelopeandthePhase 108
4.3.2 Level-CrossingRateandAverageDurationofFades 115
4.3.3 StatisticsoftheFadingIntervalsatLowSignalLevels 120
4.3.4 StationarityandErgodicityofSum-of-SinusoidsProcesses 122
4.4 ClassesofSum-of-SinusoidsProcesses 123
4.5 BasicsofSum-of-CisoidsChannelModels 126
4.5.1 ElementaryPropertiesofStochasticSum-of-CisoidsProcesses 127
4.5.2 ProbabilityDensityFunctionoftheEnvelopeandPhase 129
4.6 CriteriaforthePerformanceEvaluation 135
4.7 FurtherReading 135
Appendix4.A DerivationoftheAutocorrelationFunctionoftheSquaredEnvelope
ofComplexDeterministicGaussianProcesses 136
Appendix4.B DerivationoftheExactSolutionoftheLevel-CrossingRateandthe
AverageDurationofFadesofDeterministicRiceProcesses 137
5 ParametrizationofSum-of-SinusoidsChannelModels 149
5.1 MethodsforComputingtheDopplerFrequenciesandGains 151
5.1.1 MethodofEqualDistances(MED) 151
5.1.2 Mean-Square-ErrorMethod(MSEM) 157
5.1.3 MethodofEqualAreas(MEA) 162
5.1.4 MonteCarloMethod(MCM) 170
5.1.5 JakesMethod(JM) 178
5.1.6 L -NormMethod(LPNM) 189
p
5.1.7 MethodofExactDopplerSpread(MEDS) 201
5.1.8 RandomizedMethodofExactDopplerSpread(RMEDS) 205
5.1.9 MethodofExactDopplerSpreadwithSetPartitioning(MEDS-SP) 207
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Contents vii
5.2 MethodsforComputingthePhases 212
5.3 FadingIntervalsofDeterministicRayleighProcesses 214
5.4 ParametrizationofSum-of-CisoidsChannelModels 222
5.4.1 ProblemDescription 222
5.4.2 ExtendedMethodofExactDopplerSpread(EMEDS) 222
5.4.3 L -NormMethod(LPNM) 224
p
5.4.4 GeneralizedMethodofEqualAreas(GMEA) 225
5.4.5 PerformanceAnalysis 228
5.5 ConcludingRemarksandFurtherReading 234
Appendix5.A AnalysisoftheRelativeModelErrorbyUsingtheMonteCarlo
Method 236
Appendix5.B ProofoftheConvergenceoftheSampleMeanAutocorrelation
FunctionbyUsingtheMEDS-SP 238
Appendix5.C ProofoftheConditionforUncorrelatedInphaseandQuadrature
ComponentsofSOCProcesses 239
6 Frequency-NonselectiveChannelModels 241
6.1 TheExtendedSuzukiProcessofTypeI 243
6.1.1 ModellingandAnalysisofShort-TermFading 243
6.1.2 ModellingandAnalysisofLong-TermFading 254
6.1.3 TheStochasticExtendedSuzukiProcessofTypeI 257
6.1.4 TheDeterministicExtendedSuzukiProcessofTypeI 262
6.1.5 ApplicationsandSimulationResults 265
6.2 TheExtendedSuzukiProcessofTypeII 268
6.2.1 ModellingandAnalysisofShort-TermFading 269
6.2.2 TheStochasticExtendedSuzukiProcessofTypeII 279
6.2.3 TheDeterministicExtendedSuzukiProcessofTypeII 283
6.2.4 ApplicationsandSimulationResults 287
6.3 TheGeneralizedRiceProcess 290
6.3.1 TheStochasticGeneralizedRiceProcess 291
6.3.2 TheDeterministicGeneralizedRiceProcess 295
6.3.3 ApplicationsandSimulationResults 298
6.4 TheModifiedLooModel 300
6.4.1 TheStochasticModifiedLooModel 300
6.4.2 TheDeterministicModifiedLooModel 311
6.4.3 ApplicationsandSimulationResults 317
6.5 ModellingofNonstationaryLandMobileSatelliteChannels 319
6.5.1 Lutz’sTwo-StateChannelModel 320
6.5.2 M-StateChannelModels 322
6.5.3 ModellingofNonstationaryReal-WorldLMSChannels 323
7 Frequency-SelectiveChannelModels 335
7.1 TheEllipseModelofParsonsandBajwa 336
7.2 SystemTheoreticalDescriptionofFrequency-SelectiveChannels 338
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7.3 Frequency-SelectiveStochasticChannelModels 342
7.3.1 CorrelationFunctions 342
7.3.2 TheWSSUSModelAccordingtoBello 344
7.3.3 TheCOST207ChannelModels 352
7.3.4 TheHIPERLAN/2ChannelModels 358
7.4 Frequency-SelectiveSum-of-SinusoidsChannelModels 358
7.4.1 SystemFunctionsofSum-of-SinusoidsUncorrelatedScattering
(SOSUS)Models 358
7.4.2 CorrelationFunctionsandPowerSpectralDensitiesof
SOSUSModels 364
7.4.3 DelayPowerSpectralDensity,DopplerPowerSpectralDensity,
andCharacteristicQuantitiesofSOSUSModels 368
7.4.4 DeterminationoftheModelParametersofSOSUSModels 372
7.4.5 SimulationModelsfortheCOST207ChannelModels 376
7.5 MethodsforModellingofGivenPowerDelayProfiles 378
7.5.1 ProblemDescription 379
7.5.2 MethodsfortheComputationoftheDiscretePropagationDelaysand
thePathGains 381
7.5.3 ComparisonoftheParameterComputationMethods 391
7.5.4 ApplicationstoMeasuredPowerDelayProfiles 393
7.6 PerfectModellingandSimulationofMeasuredWidebandMobileRadio
Channels 396
7.6.1 TheSum-of-CisoidsUncorrelatedScattering(SOCUS)Model 396
7.6.2 ThePrincipleofPerfectChannelModelling 403
7.6.3 ApplicationtoaMeasuredWidebandIndoorChannel 404
7.7 FurtherReading 406
Appendix7.A SpecificationoftheL-PathCOST207ChannelModels 409
Appendix7.B SpecificationoftheL-PathHIPERLAN/2ChannelModels 413
8 MIMOChannelModels 417
8.1 TheGeneralizedPrincipleofDeterministicChannelModelling 418
8.2 TheOne-RingMIMOChannelModel 421
8.2.1 TheGeometricalOne-RingScatteringModel 422
8.2.2 TheReferenceModelfortheOne-RingMIMOChannelModel 423
8.2.3 SimulationModelsfortheOne-RingMIMOChannelModel 429
8.2.4 ParameterComputationMethods 433
8.2.5 PerformanceEvaluation 434
8.2.6 SimulationResults 436
8.3 TheTwo-RingMIMOChannelModel 438
8.3.1 TheGeometricalTwo-RingScatteringModel 439
8.3.2 TheReferenceModelfortheTwo-RingMIMOChannelModel 440
8.3.3 SimulationModelsfortheTwo-RingMIMOChannelModel 445
8.3.4 IsotropicandNon-IsotropicScatteringScenarios 449
8.3.5 ParameterComputationMethods 451
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Contents ix
8.4 TheEllipticalMIMOChannelModel 457
8.4.1 TheGeometricalEllipticalScatteringModel 458
8.4.2 TheReferenceModelfortheEllipticalMIMOChannelModel 459
8.4.3 SimulationModelsfortheEllipticalMIMOChannelModel 463
8.4.4 ModelExtensions 466
8.5 FurtherReading 469
Appendix8.A ProofofErgodicity 472
9 High-SpeedChannelSimulators 475
9.1 Discrete-TimeDeterministicProcesses 476
9.2 RealizationofDiscrete-TimeDeterministicProcesses 478
9.2.1 Look-UpTableSystem 478
9.2.2 MatrixSystem 481
9.2.3 ShiftRegisterSystem 483
9.3 PropertiesofDiscrete-TimeDeterministicProcesses 484
9.3.1 ElementaryPropertiesofDiscrete-TimeDeterministicProcesses 484
9.3.2 StatisticalPropertiesofDiscrete-TimeDeterministicProcesses 491
9.4 RealizationComplexityandSimulationSpeed 500
9.5 ComparisonoftheSum-of-SinusoidsMethodwiththeFilterMethod 502
9.6 FurtherReading 505
10 SelectedTopicsinMobileRadioChannelModelling 507
10.1 DesignofMultipleUncorrelatedRayleighFadingWaveforms 507
10.1.1 ProblemDescription 508
10.1.2 GeneralizedMethodofExactDopplerSpread(GMEDS ) 511
q
10.1.3 RelatedParameterComputationMethods 516
10.1.4 TheEffectofFiniteSimulationTimeontheCross-Correlation
Properties 518
10.1.5 FurtherReading 520
10.2 SpatialChannelModelsforShadowFading 521
10.2.1 TheReferenceModelforShadowFading 522
10.2.2 TheSimulationModelforShadowFading 523
10.2.3 CorrelationModelsforShadowFading 527
10.2.4 FurtherReading 535
10.3 FrequencyHoppingMobileRadioChannels 536
10.3.1 TheReferenceModelforFrequencyHoppingChannels 536
10.3.2 TheSimulationModelforFrequencyHoppingChannels 538
10.3.3 PerformanceAnalysis 540
10.3.4 SimulationResults 544
10.3.5 FurtherReading 544
Appendix10.ADerivationoftheSpatialAutocorrelationFunctionofLognormal
Processes 545
Appendix10.BDerivationoftheLevel-CrossingRateofSpatialLognormal
Processes 546
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Appendix10.CDerivationoftheLevel-CrossingRateofSum-of-Sinusoids
ShadowingSimulators 546
Appendix10.DApplicationoftheMethodofEqualAreas(MEA)onthe
GudmundsonCorrelationModel 548
Appendix10.EDerivationoftheTime-FrequencyCross-CorrelationFunctionof
FrequencyHoppingChannels 549
Appendix10.F ParametrizationofFrequencyHoppingChannelSimulators 551
References 553
Index 571
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Preface to the Second Edition
Withthisbookatyourfingertips,you,thereader,andIhavesomethingincommon.Weshare
thesameinterestinmobileradiochannels.Thisareaattractedmyinterestfirstinautumn1992
whenImovedfromindustrytoacademiatofindachallengeinmylifeandtopursueascientific
career. Since then, I consider myself as a student of the mobile radio channel who lives for
modelling,analyzing,andsimulatingthem.Whilethefirsteditionofthisbookresultedfrom
myteachingandresearchactivitiesattheTechnicalUniversityofHamburg-Harburg(TUHH),
Germany,thepresentsecondeditionisentirelyanoutcomeofmyworkattheUniversityof
Agder,Norway.
Tosharemypassionwiththereader,myobjectivewastowriteacomprehensivebookthat
beginswiththebasicsandmovesgraduallytoadvancedresearchtopics.Thismakesthepresent
edition of interest to beginners and experts alike. It is addressed especially to mobile radio
engineers, telecommunication engineers, and physicists working in industry or in research
institutesintherapidlygrowingwirelessandmobilecommunicationsmarket.Inadditionto
that, it is also suitable for experts who have a professional interest in subjects dealing with
mobileradiochannelissues.Last,butnotleast,thisbookisalsoaddressedtoMaster’sstudents
specializinginmobileradiocommunications.
The study of this book assumes prior basic knowledge of statistics and systems theory.
Master’sstudentsingeneralhavesufficientbackgroundknowledgeintheseareas.Tosimplify
comprehension,allfundamentalmathematicaltools,whicharerelevantfortheobjectivesof
this book, are recapitulated at the beginning. Starting from this basic knowledge, nearly all
statements made in this book are derived in detail, so that a high degree of mathematical
transparency and explicitness can be achieved. Thanks to sufficient guidance and help, it is
guaranteed that the interested reader can verify the results with reasonable effort. Longer
derivationsinterruptingtheflowofthetexthavebeenrelegatedtotheappendices.Muchem-
phasishasbeenplacedontheconfirmationofthetheoreticalresultsbynumericalsimulations.
To illustrate the theoretical and experimental results, a large number of figures have been
included. Their multiple interpretations and meanings enrich the reader’s understanding of
thetext.Theuseofabbreviationshasingeneralbeenavoided,whichinmyexperienceeases
readabilityconsiderably.Furthermore,alargenumberofreferencesareprovidedleadingthe
readertofurthersourcesforthealmostinexhaustibletopicofmobileradiochannelmodelling.
(cid:2)
AhugesetofselectedMATLABR -programsforsimulatingandanalyzingthemobileradio
channel models has been made available for free downloading at the companion website
www.wiley.com/go/paetzold.Theyprovidevaluablesupportinsimulatingthechannelmodels
andgivepracticalguidelinesforapplyingthepowerfulanalysistoolsdescribedinthebook.
