DiscreteCommunicationSystems
StevanBerber
TheUniversityofAuckland
GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom
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Thisbookisdedicatedtoallauthorswhocommittedtowriteanoriginalbook intheirprofessionandpassedthroughademandingandexhaustingprocess fullofuncertaintiesandchallenges.
Preface
Acomunicationsystemisasetofdevicesthatworktogetherallowingthetransmissionof messagesatthedistance.Inthatsensethesystemcanbealsocalledatelecommunication systemthatallowsgenerationofamessageatonepointbymeansofatransmitterand itssufficientlyaccuratereproductionatanotherdistantpointbymeansofareceiver.A communicationnetworkcanbeconsideredasasetofcommunicationsystemsthatare inteconnectedandworkinsuchawaytoallowthetransmissionofmessagesbetweenany twoormorepointsbelongingtothenetwork.Themessagescanbeofvariousformsandtypes containingtheinformationcontentdefinedinthesenceofinformationtheory.Followingthese definitionswecansaythattheexistingtelecommunicationnetworkisthebiggestmachine everinvented.Itiscomposedofanenormouslyhighnumberofdevicesinterconnectedby transmissionmedia,whichworksynchronouslyallowingtransmisionofmessagesaroundthe globeandinthespace.
Wecansaythattheearlydevelopedworldterrestrialnetworkshavebeentwo-dimensional coveringthecontinentsandinterconnectingthembyunderseacablesthataredeployedinthe lasttwocenturies.Inthetwentiethcentury,duetothedeploymentofcommunicationsatellites, thisworldnetworkbecamethree-dimensionalandglobal,characterizedbythetransmission systemsofextremelyhighcapacity.Inaddition,tremendouseffortswereundertakenby themankindtodevelopwirelessmobilecommunicationsystemsasanintegralpartofthe globalstationaryhighcapacitytelecommunicationnetwork.Finally,thedevelopmentof thespacetechnologyrequirednewcommunicationdevicesthatareabletoachievedeep spacecommunications.Duetotheexistingtheoreticalandtechnologialadvancementin telecommunicaitonsystems’theoryandpractice,ithasbeenrelativellyeasytodevelopthe systemsforthiskindofcommunications.
Sincetheearlyattemptstodevelopanelectrictelecommunicationsysteminthenineteenth century,therehavebeentwo,Idaretosay,dreamsofus,telecomumunicationengineers andscientists.Thefirstdreamwastocommunicatewhileweareonthemove.Thatdream wasachievedbythedevelopmentofwirelessmobilecommunicationsystemsasintegral partsoftheglobalstationarytelecommunicationnetwork.Theseconddreamhasbeenand stillis,todevelopwirelesscommunicationsystemsthathavethetransmissioncapacity equivalenttothecapacityofthestationarynetwork.Thisdreamhasnotbeenachievedyet. However,wecannotsaythattheseconddreamwillnotbeachieved.Thedevelopmentofthe widebandradiosystemscancontributetothat.Inaddition,wecanbelieveinthepossible developmentofnewmeansofsignaltransmissionthatwillcontributetotheachievementof thisdream.
Thisbookaimstopresenttheoreticalbaseofdiscretecommunicationsystemsanddoesnot haveanyintentiontoaddressanyaspectofcommunicationnetworksdesign.Therefore,the contentsofthebookwillsolelyaddressproblemsofthedesignofacommunicationsystem
thatincludesatransmitter,atransmissionchannel,andareceiver.Fromthenetworkpointof view,thebookwillfocusonsocalledaphysicallayerdesign.Thesignalsprocessedinthe communicationsystemwillbepresentedintwodomains,thecontinuoustimedomainand thediscretetimedomainrepresentedbythecontinuousvariable t andthediscretevariable n,respectively.Todistinguishthetwosystemsinthisbook,thesystemoperatinginthe continuoustimedomainisnamed thedigitalsystem,whilethesystemoperatinginthediscrete timedomainisnamed thedicretesystem.
Thefirstobjectiveofwritingthisbookistopresentthefundamentaltheoryofdiscrete communicationsystemsthateverystudentstudyingcommunicationsystemsneedstoacquire andrelateittotheexistingtheoryofdigitalcommunicationsystems.Thesecondobective ofwritingthisbookistorelatetheacquiredtheoryandmathematicalmodelstothepractical simulation,emulation,anddesignofcommunicationsystemdevicesindigitalDSPandFPGA technology.
IhavebeenteachingcoursesinCommunicationSystems,DigitalCommunications, InformationTheory,andDigitalSignalProcessingforover20years.Inaddition,myresearch hasmainlybeeninthefieldofcommunicationsystemsandnetworks,whereIworkedonthe mathematicalmodelling,simulation,andimplementationofvarioustransmitterandreceiver structuresindigitaltechnology(primarilyDSPandFPGA)andtheirtestingfordifferent channels.Inoticedthatthetheoryofcontinuoustimecommunicationsystemsisimportant tounderstandoperationofthesystemsinthepresenceofnoiseandfading;however,itisnot sufficienttoworkonthedesignandimplementationofthecommunicationsystemblocksin modernDSPtechnology.
Forthatreason,Ibegantoworkonthetheoryofdiscretecommunicationsystems,primarily inmyresearch,wherethebuildingblocksinsidethetransceiverandthesimulated/emulated channelperformdiscretetimesignalprocessing.Inparallel,IwasupgradingmyDSPcourse reachingthepointoflecturingthediscretetimestochasticprocesses,whichare,amongthe otherthings,theessentialtheoreticalbackgroundforthediscretecommunicationsystems analysisanddesign.
Ihavealsonoticedthatthetheoreticalmodelsandstructuresoftransceiverbuildingblocks cannotbedirectlyusedassuchwhenwecometotheirdigitaldesign.However,theprinciples ofoperationwouldbepreservedinpractice.Duetothisfact,theinterestinthebookwillbe farreachingacrossnotonlystudents,butalsoresearchers,designengineers,andpractitioners intheindustry.
Thewritingofthisbookisadditionallymotivatedbymoderntrendsinthedesignof communicationsystems.Thedesignisbasedondigitaltechnology,primarilyonFPGA andDSPplatforms,whichisinextensiveusereplacinganaloghardwarethathasbeen traditionallyused,toimplementnecessarysignalprocessingfunctionsinsidethebasebandand intermediatefrequency(IF)transceiverblocks.Thesetrendswereheavilysupportedbythe advancesinthetheoryofdiscretetimesignalprocessing,primarilybythemathematicaltheory ofdiscretetimestochasticprocesses.Thesetrendswillcontinueinthefuturesupportedbythe everlastingincreaseintheprocessingabilityofdigitaltechnologyallowingthedevelopment ofsophisticatedcommunicationalgorithmswecouldnotdreamofinthepast.
Forthesereasons,itisnecessarytoteachstudentshowtousethediscretetimesignal processingtheoryandhowtoapplyitinthedesignofmoderncommunicationdevices.Even moreimportantistomakeavailablethetheoryofdiscretetimecommunicationsystemsto theresearchers,practicingengineers,anddesignersofcommunicationdevices.Thedesign ofthesedevicesisimpossiblewithoutdeepunderstandingofthetheoreticalprincipalsand conceptsrelatedtotheiroperationinthediscretetimedomain.Practicallyallmoderncommunicationdevices,likewirelessandcablemodems,TVmodems,consumerentertainment systems,satellitemodems,andsimilar,arebasedontheuseofdigitalprocessingtechnology andtheprinciplesofthediscretetimesignalprocessingtheory.Inadditiontothementioned mainpurposesofthebook,itisimportanttoapostrophizetheimportanceofthediscrete timesignalprocessingtheoryfortheresearchers,designers,andmanufacturersinthefield ofinstrumentationbecausethemainfunctionsofmoderninstrumentsareimplementedusing principlesofthediscretetimesignalprocessing.
Thisbookisthefirstofitskind.Nearlyallthebookswritteninthefieldofcommunication systemspresentsignalsandtheirprocessingincontinuoustimedomaintoexplainthe operationofacommunicationsystem.Inthisbook,thesignalsarepresentedindiscretetime domainforthemainbuildingblocksofacommunicationsystem.
Thebookisdedicatedtotheundergraduateandgraduatestudentsdoingcoursesin communicationsystemsandalsotothepracticingengineersworkingonthedesignof transceiversindiscretecommunicationsystems.Aone-semesterseniorlevelcourse,for studentswhohavehadpriorexposuretoclassicalanalogcommunicationsystemscovering passbandandbasebandsignaltransmission,canusematerialinChapters1–6,andChapter9 supportedwithrelatedcomplementaryChapters11–15,andChapter19andProjects1,2,or3.
Inafirst-yearpostgraduatelevelcourse,thefirstsixchaptersprovidethestudentswitha goodreviewofthedigitalanddiscretecommunicationsystemstheoryandthemainlecturing willcoverChapters2–5andChapters7–10,whichpresentthediscretecommunication systemsandtheirdesign,andrelatedProjects1–5.Thebackgroundtheoryforthiscourse iscontainedincomplementaryChapters13–18.
Forpracticingengineers,whoareexperiencedintheoryofdigitalcommunicationsystems, thematerialcoveredinSections2.2and2.3,Chapters3–5,andthenChapters7–10 supportedbycomplementaryChapters13–18isagoodbaseforunderstandingthevital conceptsindiscretecommunicationsystems.Allprojectsarerelevantforthem,inparticular Projects4and5.
Tomasterthetheory,eachchaptercontainsasetofproblemsforstudents’exercises.The solutionstoproblemsareinsideaseparatebookbelongingtotheSupplementaryMaterial. Majorityoftheproblemsolutionscanbeconfirmedusingavailablesoftwarepackages.
Thebookcontainstwoparts.Thefirstpartofthebookcontainstenchaptersandpresents essentialtheoryofthediscreteanddigitalcommunicationsystems,andoperationoftheir buildingblocks,atthefirstplacetheoperationofmodulatorsanddemodulators/detectors.Due totheimportanceofthetheoryofdiscreteandcontinuoustimesignalprocessing,forboththe deterministicandrandomsignals,ninechapterscontainingthistheoryareincorporatedinto thesecondpartofthebook.
Thedistinguishingfeaturesofthebookcanbesummarizedasfollows:
1.Thebookpresentsessentialtheoryandpracticeofthediscretecommunicationsystems design,basedonthetheoryofdiscretetimestochasticprocesses,andtheirrelationto theexistingtheoryofdigitalcommunicationsystems.
2.Basedonthepresentedorthogonalityprinciples,agenericstructureofacommunication system,basedoncorrelationdemodulationandoptimumdetection,isdevelopedand presentedintheformofmathematicaloperatorswithpreciselydefinedinputsand outputsandrelatedfunctions.
3.Duetotherandomnatureofthesignalsprocessed,startingwiththerandomly generatedmessagesatthetransmittersource,thetheoryofstochasticsignalprocessing isextensivelyandconsequentlyappliedtopresentthesignalsattheinputsand outputsofthesystemblocks.Thisapproachgivesanopportunitytothereaderto understandcompletesignalprocessingproceduresinsidethetransmitter,channel,and receiver.
4.Basedonthedevelopedgenericsystemstructure,thetraditionallydefinedphaseshift keying(PSK),frequencyshiftkeying(FSK),quadratureamplitudemodulation(QAM), orthogonalfrequencydivisionmultiplexing(OFDM),andcodedivisionmultipleaccess (CDMA)systemsarededucedasspecialcasesofthegenericsystem.Thesignals arepresentedinthetimeandfrequencydomain,whichrequiresprecisederivatives oftheiramplitudespectraldensityfunctions,correlationfunctions,andrelatedenergy andpowerspectraldensities.
5.HavinginmindthecontroversialnatureofthecontinuoustimewhiteGaussian noiseprocesshavingtheinfinitepower,aseparatechapterisdedicatedtothenoise discretizationbyintroducingnotionsofthenoiseentropyandthetruncatedGaussian densityfunctiontoavoidlimitationsinapplyingtheNyquistcriterion.
6.Thebookisself-sufficientbecauseitusesaunifiednotationwheneverispossible, bothinthemaintenchaptersexplainingcommunicationsystemstheoryandnine supplementarychaptersdealingwiththecontinuousanddiscretetimesignalprocessing forboththedeterministicandstochasticsignals.
7.Forthesakeofexplanationandclarity,thetheoryofdigitalcommunicationsystemsis presentedatcertainextentandrelatedtothemaintheoryofdiscretecommunication systems.Inthisway,thereadercanseecompletetheoryofmoderncommunication systems.
8.Theunifiednotationandunifiedterminologyallowcleardistinctionofthedeterministic signalsfromstochastic,powersignalsfromenergysignals,discretetimesignaland processesfromcontinuoustimesignalsandprocesses.Consequently,thisapproach allowsaneasywayofunderstandingtherelateddifferencesindefiningthecorrelation functions,powerandenergyspectraldensities,amplitude,andpowerspectraofthe mentionedsignalsandprocesses.
9.Thetextofthebookisaccompaniedbysolutionsofabout300problemsandfivedesign projectswiththedefinedprojects’topicsandtasks.
Thebookchaptersarecloselyinterconnected.Theirrelationshipispresentedhereinthe formofadiagram.Themainchapters,presentingthetheoryofcommunicationsystems,are inthemiddleofthediagram.Thechapterscontainingthetheoryofsignalsamplingand reconstruction,andnecessarytheoryindiscretetimesignalprocessing,areonthelefthand side.Thechapterscontainingthetheoryofthecontinuoustimesignalprocessingareonthe righthandside.Thechaptersontheleftandrightcontainthetheoryofboththedeterministic andstochasticsignals,whichareextensivelyusedinexplainingthetheoryofcommunication systemsinthemiddlechapters.Chapters16–18,atthebottomofthediagram,containthe essentialtheoryofdigitalfiltersandmultiratesignalprocessingthatisrelevantfornearlyall chaptersofthebookandinparticularforChapters7and10.Thechaptersonthediagramare interconnectedbytheinputarrowandoutputdiamondlines,whichshowwhatthenecessary backgroundtheoryforachapterisandwherethetheoryofachaptercanbeused,respectively. Wewillapostrophizetheimportanceofsomeoftheseconnectionsforeachchapter.
Chapter1introducesthesubjectofthebook,definesthemaintermsincommunication systemsthatwillbeusedinthebookchapters,andpresentsthemainobjectivesofthe bookwritingfromthecommunicationsystemstheorypointofview.Thechapterpresents variousclassificationsofsignalsandsystemsandtheoreticalconceptsrelatedtothesignal conversionsintimedomainthatwillbeusedinthesubsequentchapters.Thesignals areclassifiedusingvariouscriteriaincludingperiodicityandsymmetry,continuityand discreteness,powerandenergyproperties,randomness,andphysicalrealizabilityofsignals. Theanalog-to-digital(AD)anddigital-to-analog(DA)conversions,andtheirplacesand importanceintheprocessingofsignalsinrelationtotheapplicationindiscreteanddigital communicationsystems,arebrieflyexplained.Thefinalcontentsreturnbacktothedefinition ofthesignalsrelatedtothecontinuityanddiscretenessintimeandintheirvalues,duetothe importanceofdistinguishingtheminthetheoreticalanalysisanddesignofdigitalanddiscrete communicationsystems.ThetermsdefinedinthischapterareusedinChapters4and6–10. Therelationofthechaptertootherchaptersispresentedinthediagram.
Chapter2isdedicatedtotheprincipleofdiscretetimesignalsorthogonalizationbecause theorthogonalsignalsarewidelyusedintelecommunicationtheoryandpractice,likethe carriersofbasebandsignals,subcarriersinOFDMsystems,andthespreadingsequencesin spread-spectrumandCDMAsystems.Theorthonormaldiscretebasisfunctionsaredefined, andtheprocedureofthevectorrepresentationofsignalsisdemonstrated.TheGram-Schmidt orthogonalizationprocedureandconstructionofthespacediagramarepresentedindetail. Basedonorthonormalsignals,thesignalsynthesizersandanalysersaretheoreticallyfounded, whichcanbeusedtoformthediscretetimetransmittersandreceivers.Understandingofthis chapterisaprerequisitetounderstandChapters4–10becausetheorthonormalsignalsdefined inthischapterwillbeusedthroughoutthebook.Inaddition,thecontentsofChapters5,6,7, 12,and15arerelatedtotheuseoftheorthogonalsignals,whichcontributetounderstanding ofthischapterfromthepracticalpointofview.
Chapter3containsthetheoryofdiscretetimestochasticprocesses,includingtheir mathematicalpresentationinthetimeandfrequencydomain.Thetypicalprocesses,relevant forthediscretecommunicationsystemsdesign,includingGaussianprocess,whitenoise, binary,andharmonicprocesses,arepresented.Acomprehensiveanalysisofstationary andergodicprocessesandthelineartimeinvariant(LTI)systemswithstochasticinputs
ispresentedinthischapter.Theprocessesareanalysedintermsoftheirautocorrelation functions(ACFs)andpowerspectraldensitiesthatarerelatedbytheWiener-Khintchine theorem.Thechapterisplacedatthebeginningofthebookbecauseitscontentsareconsidered asaprerequisiteforthechaptersthatfollow,inparticular,forthechapterrelatedtothetheory ofdiscretecommunicationsystems.Auniquenotationusedinthischapterisusedintherest ofthebook,whichmakesthebooktobeself-sufficient.Forbookreaders,itishighlyadvisable toreadthischapterfirstandacquireitsnotation.Thetheorypresentedinthischapterisan unavoidablebaseforChapters2–10tounderstandrelationshipsbetweenthecontinuousand thediscretetimesignalprocessingneededinanyanalysisofcommunicationsystems.
Chapter4addressedtheissuesrelatedtothetheoryofnoiseincommunicationsystems. TheproblemofdiscretizationofthewhiteGaussiannoiseprocessisraisedduetothe noisestrictdefinitionimplyingthatithastheoreticallyinfinitepower.Ifwestartwiththis definition,itwouldbeimpossibletogeneratediscretenoiseprocessbecausethesampling theoremrequiresthatthesampledsignalmustbephysicallyrealizable,i.e.thesamplednoise needstohaveafinitepower.Toovercomethisproblem,thenoiseentropyisdefinedasan additionalmeasureofthenoiseproperties,andthetruncatedGaussianprobabilitydensity functionisusedtodefinethedistributionofnoiseamplitudes.Additionoftheentropyand truncateddensityfunctiontothenoiseautocorrelationandpowerspectraldensity(PSD) functionsallowedmathematicalmodellingofthediscretenoisesourceandthedesignofboth basebandandbandpassnoisegeneratorsandregenerators.Thedevelopednoisetheoryand designednoisegeneratorsareessentialforthetheoreticalexplanationoftheoperationof digitalanddiscretecommunicationssystems,theirdesign,simulation,emulation,andtesting. ThischapterisincloserelationswithChapters3,19,13,16,and17.Thepresentedapproach forthenoisecharacterizationisanattempttoovercomecontroversialinterpretationsofthe whiteGaussiannoisethatcanbefoundintheexistingbooksincommunicationtheoryand signalprocessing.
TheProject3intheSupplementaryMaterialpresentsthedesignofnoisegeneratorsand theirapplicationincommunicationsystem.
Chapter5isavitalpartofthisbookpresentingagenericcommunicationsystem operatingindiscretetimedomain,whichisbasedonimplementationoftheorthogonal modulators,correlationdemodulators,andoptimumdetectors.Basedondefinitionofthe signalsynthesizersandanalysersinChapter2,thisgenericdiscretesystemisdeveloped tobeusedtodeducethepracticalsystemsasitsspecialcases.Thesignalsynthesizer istransferredintoadiscretetransmitter,andthesignalanalyserisusedasacorrelation receiverfollowedbyanoptimumdetector.Thesystemstructureispresentedintermsof mathematicaloperatorsandsupportedbyexactmathematicalexpressionsbasedonthetheory ofstochasticprocessespresentedinChapters3and19.Thelikelihoodfunctionisderived, andthemaximumlikelihoodruleisappliedtospecifythedecisionprocessandconstructthe optimumdetector.Anexamplemultilevelsystemisdeducedasaspecialcaseofthegeneric system,andthebiterrorprobabilityexpressionisderived.Forthesakeofcontinuityand completenessinpresentingcommunicationsystemstheory,agenericdigitalcommunication systemisdevelopedandrelatedtoitsdiscretecounterpart.Notwithstandingthatthegeneric modelisdevelopedfortheassumedcorrelationreceiverthesamemodelcanbeeasilyreplaced withthematchedfilterreceiver.Duetothesimplicityofthisreplacement,thematchedfilter
receiversarenotanalysedinthebook.Inaddition,theresultsofthischapterareneededatthe firstplaceinChapters6–8,anditsprerequisitechaptersaremostlysupplementarychaptersas showninthediagram.
Chapter6presentsmathematicalmodelsofthebasebandandbandpassdigitalcommunicationsystemsbasedonthebinaryandquaternaryphaseshiftkeying(BPSKandQPSK),FSK, andQAMmethods.Itisdedicatedtothereaderswhoarenotfamiliaratallwiththedigital communicationssystems.Thesystemsarededucedasspecialcasesofthegenericsystem structurepresentedinSection5.8.2.Thesystemsareuniquelypresentedusingmathematical operatorsastheirblocks,followedbydetailedderivativesforsignalsintimeandfrequency domainatthevitalpointsofthesystems’transmitters,receivers,andthenoisegenerators, usingtheconceptsofboththestochastic(continuousanddiscrete)signalprocessingfrom Chapters3,4,5,and19andthedeterministic(continuousanddiscrete)signalprocessingfrom Chapters2and11–15.Thevitalcharacteristicsofthesystemanditsblocksareexpressedin termsoftheamplitudespectraldensity,ACFs,powerandenergyspectraldensities,andthebit errorprobability.ThetheoreticalresultsobtainedareheavilyusedinthesubsequentChapters 7,8,9,and10.Projects1and2aremainlyrelatedtothischapter.
WemostlyusedthenotionofACFandPSDtoexpressinputsandoutputsofthe signalprocessingblocksinthetransceiver.Forthesakeofunderstanding,themathematical derivativesarepresentedindetailshowingseveralsteps,whichcannotbefoundinotherbooks incommunicationtheory.Aspecificattentionismadetothepowerandenergycalculationof thesignalsinbothfrequencyandtimedomain.
Frommodulationmethodspointofview,Chapter7isthecentralpartofthebookbecause itpresentstheoperationoftransceiverblocksthatprocesspurediscretetimesignals.The inputsforthischapterareallpreviouschaptersandsucceedingChapters11–15andChapters 17and19.Thischapterpresentsmathematicalmodelsofthediscretebasebandandbandpass communicationsystemsbasedonBPSKandQPSK,FSK,andQAMmodulationmethods. TheoperationofIFsystemsispresentedwhereallprocessingisperformedinthediscrete timedomain.Thesystemsarededucedasspecialcasesfromthegenericsystemstructure presentedinSection5.6.4,Figure5.6.4,thatisbasedonapplicationoforthonormalbasis functionspresentedinChapter2,whichconfirmsthebasicideaofthisbookthattheexisting communicationsystemsarespecialcasesofthegenericsystem.Theideawillbefurther demonstratedonthedevelopmentofcomplexcommunicationssystems,likeOFDMand CDMA,aspresentedinChapter8.Theblockschematicsofanalysedsystemsarepresented usingmathematicaloperators,followedbydetailedmathematicalexpressionsforsignalsin discretetimedomainatthevitalpointsofthesystem’sstructureusingtheconceptsofboth thediscretestochasticanddiscretedeterministicsignalprocessing.Thekeycharacteristicsof discretecommunicationsystemsandtheirblocksareexpressedintermsofamplitudespectral density,ACFs,powerandenergyspectraldensities,andthebiterrorprobability.
Chapter8presentsmodernmultiuserandmulticarriercommunicationsystemsbasedon theCDMAandOFDMtechnology.Theanalog,digital,anddiscreteOFDMsystemsare separatelypresentedandinterrelatedfromthetheoreticalandpracticalpointofview.A precisemathematicalmodelofthediscretebasebandandIFblocksispresented,including theproceduresofsignalmappingandthediscreteFouriertransform(DFT)application,and thenrelatedtothemodelofanalogradio-frequencyblocktomakethewholeOFDMsystem.
Thebasictheoryofbinaryandnon-binaryCDMAsystemoperationispresented.Tosupport deepertheoreticalunderstandingoftheCDMAsystemoperationanddesign,Project4inthe SupplementaryMaterialdemonstratestheprocedureofmathematicalmodelling,simulation, anddesignofthissysteminFPGAtechnologyandpresentsrequireddevelopmenttools.The fundamentalconceptsthatareneededtosupportunderstandingofthischapterarepresented inChapters1–7incommunicationtheoryandChapters11–17inthetheoryofprocessing deterministicsignals.
Chapter9presentsthefundamentalsofinformationtheory,whicharerequiredfor understandingoftheinformationmeasure,entropy,andlimitsinsignaltransmissionincluding thedefinitionandderivationofthecommunicationchannelcapacity.Theproofofcoding theoremisseparatelypresented.Thechaptercontainsapartthatdefinestheentropyof continuousanddiscreteGaussiananduniformstochasticprocesses.Theresultsofthisunique analysisareessentialtounderstandthenotionofcontinuousanddiscretewhiteGaussiannoise processespresentedinChapter4.Theblockandconvolutionalcodes,includingharddecision Viterbialgorithm,arepresented.Thetheoryofiterativeandturbochannelcodingispresented inProject5intheSupplementaryMaterial,whereseveraltopicsaredefinedandtherelated solutionsareoffered.Thebackgroundtheorythatsupportstheunderstandingofthischapter canbefoundmainlyinChapters1–7andChapters11–15.
Chapter10presentspracticalaspectsofdiscretecommunicationsystemsdesignindigital technology,primarilyinDSPandFPGA.Thesystemsarepresentedatthelevelofblock schematicsapostrophizingthemainissuesintheirdesignanddiscussingexpectedadvantages anddisadvantagesofthesystems’designindigitaltechnology.Designsofsystemsbased ontheQPSKandQAMmodulationareseparatelypresented.Theoperationofeachdesigned systemisexplainedusingtherelatedtheoreticalstructureofthesystem,whichallowedaclear understandingoftherelationshipsbetweenthesystem’stheoreticalmodelanditspractical design.Thestructuresofthefirst,second,andthirdgenerationofthediscretetransceiver designsarepresented.ThischapterrelaysonthetheoreticalprinciplespresentedinChapters 5–9.Duetothesizeofthisbookwecouldnotgointodetailsofvariousdiscretesystem implementationsbasedonthemultiratesignalprocessingandapplicationofdigitalfiltersand bankoffiltersthatarepresentedinChapters16,17,and18.
Inadditiontothemaintenchapters,thebookcontainsninecomplementarychapters.These chaptersareaddedfortworeasons.Firstly,theycontainthebasictheoryofcontinuoustime anddiscretetimesignalprocessingthatisessentialfortheunderstandingofmathematical modelsandoperationsofthedigitalanddiscretetransceivers,whereweareusingthetheoryof deterministicandstochasticsignalprocessing.Secondly,thenotationoftheseninechaptersis preservedinthemainchapters,whichwillhelpstudentsandexpertstounderstandindepththe communicationsystemstheory.Therefore,eventhoughareadercanbeveryfamiliarwiththe contentoftheseninechapters,itisadvisabletoreadthembeforestartingtoworkonthemain tenchapters.Iamapostrophizingthisforoneadditionalsimplereason.Namely,weunified thenotationinallchaptersthatsimplifiesunderstandingoftheircontent.
Duetoimportanceoftheconceptofindependentvariablemodificationanddefinitionof LTIsystembasedonitsimpulseresponse,Chapter11presentsbasicdeterministicsignals andsystemsinthecontinuoustimedomain.Thesesignals,expressedintheformoffunctions andfunctionals,likeDirac’sdeltafunction,areusedinthewholebookforthedeterministic
andstochasticsignalanalysis.ThedefinitionoftheACFandexplanationoftheconvolution procedureinLTIsystemsarepresentedindetailduetotheirimportanceincommunication systemsanalysisandsynthesis.Alinearmodificationoftheindependentcontinuousvariable ispresentedforspecificcases,liketimeshift,timereversal,time,andamplitudescaling. ContentofthischapterisimportantinputtothecomprehensiveanalysisofLTIsystems dealingwiththedeterministicsignalsinChapter12,stochasticsignalsinChapters3and 19,andfortheanalysisofdiscretetimedeterministicsignalsinChapters14and15.
Chapter12presentsadetailedanalysisofcontinuoustimesignalsandsystemsinfrequency domain,includingthetheoryofFourierseriesandFouriertransforms,andpresentingkey examplesrelevantfortheanalysisandsynthesisofsignalsprocessedinadigitaltransceiver blocksofacommunicationsystem.Theamplitude,magnitude,phase,andpowerspectra aredefinedandcalculatedfortypicalsignalexamples.Inparticular,theFouriertransform ofperiodicsignalsispresentedduetoitsimportanceincommunicationsystemstheory andpractice.Usingauniquenotationthatdistinguishestheenergyandpowersignals,the correlation,power,orenergyspectraldensityfunctionsareinterrelatedbyprovingtheWinerKhintchinetheorem.AcomprehensiveanalysisoftheLTIsystem,usingconceptsofthe impulseresponse,systemcorrelationfunction,andPSD,bothforpowerandenergysignals,is presented.Thecontentofthischapterisofavitalimportanceforunderstandingmathematical presentationsoftransceiverblocksincommunicationssystemsanalysedinChapters1–9and alsoforacquiringthesignalprocessingtheoryinChapters13–15and19.
Chapter13presentsthetheoryoftransferringacontinuoustimesignalintodiscretetime formbysampling,andthenconvertingtheobtainedsamplestodigitalsignalsuitablefor processinginaprocessingmachineusingtheprocedureofasamplequantizingandcoding. Then,theprocedureofconvertingadigitallyprocessedsignalintodiscretesignalsamples andthereconstructionoftheinitialcontinuoustimesignalusingalow-passreconstruction filterispresented.ThepresentedtheorymakesamathematicalbaseofboththeADand DAconversionsthatareextensivelyusedinprocessingsignalsindiscretecommunication systems.ItwasshownthattheNyquistcriterionmustbefulfilledtoeliminatethesignal aliasinginfrequencydomain.Themathematicalmodeloftransferringcontinuoustimesignal intoitsdiscretetimeformandviceversaispresentedanddemonstratedonasinusoidal signal.TheseconceptspresentedinthischapterareusedinmainChapters4–8andalsoin complementaryChapters3and19.
Duetotheimportanceoftheconceptofindependentdiscretevariablemodificationand thedefinitionofdiscreteLTIsystems,Chapter14presentsbasicdeterministicdiscretetime signalsandsystems.Thesediscretesignals,expressedintheformoffunctions,including theKroneckerdeltafunctionanddiscreterectangularpulse,areusedinthewholebookforthe deterministicdiscretesignalanalysis.ThedefinitionoftheACFandtheexplanationofthe convolutionprocedureinLTIsystemsforthediscretetimesignalsarepresentedindetail duetotheirimportanceintheanalysisandsynthesisofdiscretecommunicationsystems.As such,thischapteriscloselyrelatedtobothChapter15andChapter3dealingwithdiscrete timedeterministicsignalprocessinginthefrequencydomainanddiscretetimestochastic processes,respectively.Thecontentofthischapterisimportantinputtothecomprehensive analysisofLTIsystemsdealingwiththestochasticsignals.
Chapter15presentsadetailedanalysisofdeterministicdiscretetimesignalsandsystems infrequencydomain,includingthetheoryofdiscreteFourierseries,discretetimeFourier transform(DTFT),andDFT,andkeyexamplesrelevantfortheanalysisandsynthesis ofsignalsprocessedinthediscretetransceiverblocksofacommunicationsystem.The amplitude,magnitude,phase,andpowerspectraaredefinedandcalculatedfortypicalsignals relevantforcommunicationsystems.Usingauniquenotation,whichdistinguishestheenergy andpowersignals,thecorrelation,power,orenergyspectraldensityfunctionsareinterrelated byprovingtheWiner-Khintchinetheorem.AcomprehensiveanalysisoftheLTIsystems, usingtheconceptsofimpulseresponses,correlation,andconvolution,bothforpowerand energysignals,ispresented.Thepresentedtheoryisvitalforunderstandingmathematical modellingoftransceiverblocksincommunicationsystemspresentedinChapters4–10.The chapterfinisheswiththe z-transformcontainingthetheoryrequiredtounderstandthecontents ofChapters16,17,and18thataredealingwithdigitalfiltersandmultiratesignalprocessing.
Chapter16presentsthetheoreticalbaseofthedigitalfiltersincludingtheissuesrelatedto theirdesigns.Basiccharacteristicsandstructuresofthefiniteimpulseresponse(FIR)andthe infiniteimpulseresponse(IIF)filtersarepresentedanddiscussed.Themethodsoffilterdesign andrelatedalgorithms,whicharebasedonbilineartransformationmethod,windowedFourier series,andalgorithmsbasedoniterativeoptimization,arepresented.Thechapterservesas anintroductiontoChapters17and18andisrelevantforunderstandingChapters1,2,4,and 7–10.ItisimportanttoacquiretheknowledgefromChapters13to15toreadthischapter.
Chapter17presentsthemultiratesignalprocessingstaringwiththeexplanationofthe upsamplinganddownsamplingproceduresonadiscretesignalintimedomain.Theoperations ofadownsampler(decimator)andanupsampler(interpolator)areanalysedinthefrequency domainemphasizingtheproblemofpossiblealiasing.Complexsystemsthatincludeboththe upsamplinganddownsamplingareanalysed,andtheproblemofthecomplexityreductionis mentioned.Theoperationofsystemsthatcombineaninterpolatorandaninterpolationfilter, andadecimatorandadecimationlow-pass(LP)filter,ispresentedintimeandfrequency domain.Inparticular,theproblemofreducingcomplexityofamultiratesystemisaddressed, andapoly-phasedecompositionforboththeFIRandIIFfiltersisofferedasanefficient solution.ThecontentofthischapterisrelevantforunderstandingChapters4–8and10.The prerequisitesforthischapterareChapters13–15and16.
Chapter18,whichisbasedontheoryinChapters16and17,andchaptersrelatedtothe discretetimesignalprocessing,presentsthetheoreticaldescriptionandprincipalsofoperation oftheanalysisandsynthesisfilterbanks,whichisessentialmaterialforunderstandingmodern designofthetransceiversthatarebasedonthediscretetimesignalprocessing.Thestructure ofaquadraturemirrorfilter(QMF)bankispresented,andtheoperationoftheanalysisand synthesiscomponentfiltersisexplained.Theconditionforaperfectreconstructionoftwochannelfilterbanksisderived.Basedonatwo-channelQMFfilterbank,theprocedure ofmakingmultichannelQMFbankispresented.Thetheorypresentedinthischapteris importantinthedesignofmodulatorsanddemodulatorsindiscretecommunicationsystems.
Chapter19containsthetheoryofcontinuoustimestochasticprocesses,includingtheir mathematicalpresentationinthetimeandfrequencydomain.Thetypicalprocessesrelevant forthecommunicationsystemstheory,includingGaussianprocess,whitenoise,binary, andharmonicprocesses,areanalysedinthetimeandfrequencydomain.Acomprehensive
analysisofstationaryandergodicprocessesandtheLTIsystemswithstochasticinputsis presented.TheprocessesareanalysedintermsoftheirACFsandpowerspectraldensities. Thenotationusedinthischaptercomplieswiththenotationusedinotherchaptersof thebook.Forthebookreaderswhoarenotfamiliarwiththecontinuoustimestochastic processes,itishighlyadvisabletoreadthischapterandacquireitsnotation,duetoits importanceforunderstandingthecontentofChapters1–9.Theprerequisitesforthischapter areChapters11and12.
ThebookcontainstheSupplementaryMaterialthatiscomposedoftwoparts:theSolutions oftheProblemsandResearchProjectswithofferedsolutions.Tomasterthetheory,key chapterscontainasetofproblemsforstudents’exercises.Thesolutionstotheproblemsare insideaseparatebookbelongingtotheSupplementaryMaterialforthereaders.Inaddition tothesolvedproblems,thebookcontainsseveralreal-worldcasestudiesintheformof projectsrelatedtotheadvancedmodellinganddesignsofmoderncommunicationsystems basedondigitalanddiscretetimesignalprocessingandapplicationofmoderntechnologies likeDSPandFPGA.Thepurposeoftheprojectsistwo-fold:firstly,thereaderwillreinforce understandingofthetheorylearnedand,secondly,understandtheimportanceoftheoretical knowledgeforthepracticaldesign,whereexactmathematicalformsneedtobeusedto implementfunctionsofacommunicationsystem’sblocksindigitalprocessingtechnology likeDSPorFPGA,i.e.theexactmathematicalexpressionsareusuallydirectlytransferredinto preciselinesofcode.Theprojectscontaintwoparts:thefirstpartdefinesTopicsandTasks tobesuppliedtotheprojectexecutors,students,forexample,andthesecondpartcontains theofferedsolutionsoftheproject.Theimplementationofthesystemsdefinedintheprojects canbeperformedusingsimulationtoolslikeMATLABorsoftwaredevelopmenttoolsused fordesignsinDSPandFPGAtechnologies.Aprojectisnotalaboratoryexercisebutaselfcontainedpieceofresearchworkrelatedtoaparticularbookchapter,andassuchcanbea partofonesemesterprojectinsidethecourseindiscreteanddigitalcommunicationsystems.
Insummary,thebookcontainsthetheoryofdiscreteanddigitalcommunicationsystems andpracticaladvicesrelatedtotheirdesign.Thebookincludestheessentialbackground theoryindeterministicandstochasticsignalprocessing,withanemphasisonthediscrete timesignalprocessing,withtheadoptedunifiednotationsandthedefinitionoftermstobe directlyusedinthemainchaptersofthebookrelatedtothecommunicationsystemstheory.
Acknowlegements
Thisbookhastwoorigins.Firstly,thebookoriginatesfromcoursesinCommunication Systems,DigitalCommunications,andDigitalSignalProcessingthatmycolleaguesKevin Sowerby,BernardGuillemin,MarkAndrews,andmyselfweredevelopingandteachingat theUniversityofAuckland.Ithankthemallfortheirenormoushelpbecausetheirideas greatlyinfluencedmythinkingabouthowthesecoursesshouldbetaught.Secondly,the contentofthebookhasbeeninspiredbymyresearchindigitalanddiscretecommunication systemsconductedattheDepartmentofElectrical,Computer,andSoftwareEngineeringat theUniversityofAuckland.IamgratefultomyDepartment,Faculty,andtheUniversitythat madeanenvironmentwherethebookwritingwaspossible.
IamthankfultothestaffatOxfordUniversityPress,inparticularHarrietKonishi, FrancescaMcMahonandSumintraGaur,fortheirsupportandperfectcooperationduring thepreparationofthebookmanuscript.Itwasmygreatestpleasuretoworkwiththem.
Specialthanksforsupportandencouragementgotomybelovedfamily;mywifeZorka, sonPavle,anddaughtersAnaandMarinawiththeirfamilies.
ListofSymbols,Functions,Operators,andAbbreviations
1IntroductiontoCommunicationSystems 1
1.1CommunicationSystemsandNetworks1
1.2ClassificationofSignalsandSystems4
1.2.1ClassificationofSignalswithRespecttoTimeandValue5
1.2.2PeriodicandSymmetricSignals8
1.2.3DeterministicandStochasticSignals9
1.2.4ClassificationofSignalswithRespecttoPowerandEnergy9
1.2.5ClassificationofSignalswithRespecttoRealizability10
1.2.6ClassificationofSystems11
1.3ConversionsofAnalogueandDigitalSignals13
1.3.1Analogue-to-DigitalConversion14
1.3.2Digital-to-AnalogueConversion15
1.3.3ApplicationofSignalsinDigitalandDiscreteCommunicationSystems17
2OrthogonalSignalsandtheOrthogonalizationProcedure 18
2.1Introduction18
2.2GeometricRepresentationofSignals19
2.2.1OrthonormalBasisFunctions19
2.2.2VectorRepresentationofSignals24
2.3TheGram–SchmidtOrthogonalizationProcedure26
2.4Continuous-TimeOrthogonalSignals35
2.4.1Continuous-TimeVersusDiscrete-TimeBasisSignals35
2.4.2OrthonormalSignals36
2.4.3TheGram–SchmidtOrthogonalizationProcedure37
2.5OrthogonalSignalsinCodeDivisionMultipleAccessCommunicationSystems38 Problems42
3Discrete-TimeStochasticProcesses 56
3.1DefinitionandAnalysisofDiscrete-TimeStochasticProcesses56
3.1.1Introduction56
3.1.2DefinitionofaStochasticProcess57
3.1.3MathematicalAnalysisofStochasticProcesses59
3.2StatisticalPropertiesofStochasticProcesses61
3.2.1First-OrderStatistics61
3.2.2Second-OrderStatistics63
3.2.3Higher-OrderStatistics72
3.2.4TypesofDiscrete-TimeStochasticProcesses72
3.3TheStationarityofDiscrete-TimeStochasticProcesses75
3.3.1TheStationarityofOneDiscrete-TimeStochasticProcess75
3.3.2PropertiesoftheAutocorrelationFunction81
3.3.3TheStationarityofTwoDiscrete-TimeStochasticProcesses83
3.4ErgodicProcesses84
3.4.1EnsembleAveragesandTimeAverages84
3.4.2ErgodicProcesses85
3.4.3EstimateoftheMeanacrosstheEnsembleofRealizationsof X (n)85
3.4.4EstimateoftheMeanacrossarealizationof X (n)86
3.4.5EstimateoftheMeanofanErgodicProcess X (n)87
3.4.6SummaryofErgodicStochasticProcesses88
3.5TheFrequency-DomainRepresentationofDiscrete-TimeStochasticProcesses89
3.5.1Continuous-TimeStochasticProcessesintheFrequencyDomain90
3.5.2Discrete-TimeStochasticProcessesintheFrequencyDomain91
3.5.3Cross-SpectrumFunctions92
3.6TypicalStochasticProcesses94
3.6.1NoiseProcesses94
3.6.2GeneralGaussianNoiseProcesses96
3.6.3HarmonicProcesses98
3.6.4StochasticBinaryProcesses101
3.7LinearSystemswithStationaryRandomInputs103
3.7.1AnLTISystemwithStationaryRandomInputsintheTimeDomain104
3.7.2Frequency-DomainAnalysisofanLTISystem108
3.8Summary112 Problems112
4NoiseProcessesinDiscreteCommunicationSystems 121
4.1GaussianNoiseProcessesintheContinuous-TimeDomain121
4.1.1ContinuousWhiteGaussianNoiseProcesses121
4.1.2TheEntropyofWhiteGaussianNoiseProcesses126
4.1.3TruncatedGaussianNoiseProcesses128
4.1.4ConcludingNotesonGaussianNoiseProcesses131
4.2GaussianNoiseProcessesintheDiscrete-TimeDomain133
4.2.1WhiteGaussianNoiseProcesseswithDiscrete-Timeand Continuous-ValuedSamples133
4.2.2Discrete-TimeWhiteGaussianNoiseProcesseswith Discrete-ValuedSamples139
4.2.3WhiteGaussianNoiseProcesseswithQuantizedSamples inaStrictlyLimitedInterval140
4.2.4Band-LimitedContinuous-andDiscrete-TimeSignalsandNoise141
4.3OperationofaBasebandNoiseGenerator143
4.3.1Band-LimitedContinuous-TimeNoiseGenerators143
4.3.2Band-LimitedDiscrete-TimeNoiseGenerators144
4.3.3SpectralAnalysisofContinuous-TimeBasebandNoise147
4.3.4SpectralAnalysisofDiscrete-TimeBasebandNoise148
4.4OperationofaBandpassNoiseGenerator151
4.4.1IdealBandpassContinuous-TimeGaussianNoise151
4.4.2IdealBandpassDiscreteGaussianNoise154
4.4.3ModulatorsandDemodulatorsofIdealBandpassDiscrete GaussianNoise156
4.5PracticalDesignofaBand-LimitedDiscrete-TimeNoiseModulator162
4.6DesignofanOrdinaryBand-LimitedDiscrete-TimeNoiseModulator166 Problems168
5OperationofaDiscreteCommunicationSystem 172
5.1StructureofaDiscreteSystem172
5.2OperationofaDiscreteMessageSource172
5.3OperationofaDiscreteModulator176
5.4AdditiveWhiteGaussianNoiseChannelsinaDiscrete-TimeDomain178
5.5CorrelationDemodulators180
5.5.1OperationofaCorrelator180
5.5.2StatisticalCharacterizationofCorrelatorOutput185
5.5.3SignalConstellation189
5.6OptimumDetectors190
5.6.1TheMaximumLikelihoodEstimatorofaTransmittedSignal190
5.6.2ApplicationoftheMaximumLikelihoodRule194
5.6.3DesignofanOptimumDetector194
5.6.4GenericStructureofaDiscreteCommunicationSystem198
5.7MultilevelSystemswithaBinarySource198
5.7.1TransmitterOperation201
5.7.2RadioFrequencyBlocksandAdditiveWhiteGaussian NoiseWaveformChannels202
5.7.3OperationofaBandpassNoiseGenerator203
5.7.4Intermediate-FrequencyOptimumReceivers204
5.7.5Intermediate-FrequencyOptimumDetectors207
5.8OperationofaDigitalCommunicationSystem207
5.8.1DigitalversusDiscreteCommunicationSystems207
5.8.2GenericStructureofaDigitalCommunicationSystem208
Appendix:OperationofaCorrelatorinthePresenceofDiscreteWhite GaussianNoise212
6DigitalBandpassModulationMethods 215
6.1Introduction215
6.2CoherentBinaryPhase-ShiftKeyingSystems220
6.2.1OperationofaBinaryPhase-ShiftKeyingSystem220
6.2.2TransmitterOperation221
6.2.2.1ModulatingSignalPresentation221
6.2.2.2ModulatedSignalsinTimeandFrequencyDomains224
6.2.3ReceiverOperation231
6.2.3.1CorrelationDemodulatorOperation231
6.2.3.2OperationoftheOptimumDetector,andStructure oftheReceiver233
6.2.3.3BitErrorProbabilityCalculation238
6.3Quadriphase-ShiftKeying245
6.3.1OperationofaQuadraturePhase-ShiftKeyingSystem245
6.3.2TransmitterOperation246
6.3.2.1ModulatingSignalsinTimeandFrequencyDomains246
6.3.2.2ModulatedSignalsintheTimeDomain250
6.3.2.3ModulatedSignalsintheFrequencyDomain253
6.3.2.4ThePowerSpectralDensityofSignalsinaQuadriphase-Shift KeyingSystem253
6.3.3ReceiverOperation256
6.3.3.1OperationoftheCorrelationDemodulatorandthe OptimumDetector256
6.3.3.2BitErrorProbabilityCalculation257
6.3.3.3SignalAnalysisandTransceiverStructureinaQuadrature Phase-ShiftKeyingSystem259
6.4CoherentBinaryFrequency-ShiftKeyingwithaContinuousPhase260
6.4.1OperationofaBinaryFrequency-ShiftKeyingSystem260
6.4.2TransmitterOperation262
6.4.2.1ModulatingSignalsinTimeandFrequencyDomains262
6.4.2.2ModulatedSignalsintheTimeDomainandthe Signal-SpaceDiagram263
6.4.2.3ModulatingandModulatedSignalsinTimeandFrequency Domains264
6.4.2.4ModulatedSignalsintheFrequencyDomain270
6.4.3ReceiverOperation272
6.4.3.1OperationofaCorrelationDemodulator272
6.4.3.2OperationofanOptimumDetector274
6.4.3.3CalculationoftheBitErrorProbability276
6.4.3.4DesignofaTransceiverforaBinaryFrequency-Shift KeyingSignal278
6.5 M -aryQuadratureAmplitudeModulation280
6.5.1SystemOperation280
6.5.2TransmitterOperation282
6.5.3ReceiverOperation285
AppendixA:DensitiesoftheCorrelationVariables X 1 and X 2 inaQuadrature Phase-ShiftKeyingSystem289
AppendixB:DerivativesofDensityFunctionsforaBinaryFrequency-Shift KeyingSystem290
AppendixC:PreciseDerivationoftheBitErrorProbabilityforaBinary Frequency-ShiftKeyingSystem292
AppendixD:PowerSpectralDensityofaQuadratureComponentina Frequency-ShiftKeyingSignal294 Problems296 7DiscreteBandpassModulationMethods 305
7.1Introduction305
7.2CoherentBinaryPhase-ShiftKeyingSystems308
7.2.1OperationofaBinaryPhase-ShiftKeyingSystem308
7.2.2TransmitterOperation309
7.2.2.1PresentationofaModulatingSignal309
7.2.2.2ModulatedSignalsinTimeandFrequencyDomains312
7.2.2.3ThePowerSpectralDensityofBinaryPhase-ShiftKeying ModulatedSignals316
7.2.3ReceiverOperation319
7.2.3.1OperationofaCorrelationDemodulator319
7.2.3.2OperationofanOptimumDetector,andStructureofaReceiver321
7.2.3.3CalculationoftheBitErrorProbability326
7.3Quadriphase-ShiftKeying328
7.3.1SystemOperation328
7.3.2TransmitterOperation330
7.3.2.1ModulatingSignalsinTimeandFrequencyDomains330
7.3.2.2ModulatedSignalsintheTimeDomain333
7.3.2.3ModulatedSignalsintheFrequencyDomain336
7.3.3ReceiverOperation338
7.3.3.1OperationoftheCorrelationDemodulatorandthe OptimumDetector338
7.3.3.2CalculationoftheBitErrorProbability340
7.3.3.3SignalAnalysisandStructureoftheTransceiverina Quadriphase-ShiftKeyingSystem341
7.4CoherentBinaryFrequency-ShiftKeyingwithContinuousPhase343
7.4.1OperationofaBinaryFrequency-ShiftKeyingSystem343
7.4.2TransmitterOperation345
7.4.2.1ModulatingSignalsinTimeandFrequencyDomains345
7.4.2.2ModulatedSignalAnalysisintheTimeDomainanda Signal-SpaceDiagram346
7.4.2.3ModulatedSignalAnalysisinTimeandFrequencyDomains349
7.4.2.4ModulatedSignalsintheFrequencyDomain356
7.4.3ReceiverOperation358
7.4.3.1OperationoftheCorrelationDemodulator358
