IntroductiontoCommunicationPrinciplesCourseName:IntroductiontoCommunicationPrinciplesCourseCode:EI211CourseInstructor:DianguangMaText:DigitalandAnalogCommunicationSystems,6thed.byLeonW.CouchII,ISBN0-13-081223-4Contents:Chapters1–4.IntroductiontoCommunication1AbouttheTextThisbookcoverstheessentialsneededfortheunderstandingofwireandwirelesscommunicationsystemsandincludesadoptedstandards.TheseessentialsareHowcommunicationsystemswork:chapters1through5.Theeffectofnoise:chapter6and7.Wireandwirelesscommunicationsystems:chapter8.Thisbookisidealforeitheraone-semesteroratwo-semestercourse.Foraone-semestercourse,thebasicsofhowcommunicationsystemsworkmaybetaughtbyusingthefirstfivechapters(withselectedreadingsfromchapter8).Foratwo-semestercourse,thewholebookisused.Thisbookcoverspracticalaspectsofcommunicationsystemsdevelopedfromasoundtheoreticalbasis.Thisbookincludesover550problems.AbouttheTextThisbookcovers2AbouttheAuthorLeonW.Couch,IIProfessorEmeritusandAssociateChairmanElectricalandComputerEngineeringDepartmentUniversityofFloridacouch@AbouttheAuthorLeonW.Couch,3CHAPTER1INTRODUCTIONCHAPTER1INTRODUCTION4ChapterObjectivesHowcommunicationsystemsworkFrequencyallocationandpropagationcharacteristicsComputersolutions(MATLABandMATHCAD)InformationmeasureCodingperformanceChapterObjectivesHowcommunic5WhatisaCommunicationSystem?Communicationsystemsaredesignedtotransmitinformation.Communicationsystemdesignershavefourmainconcerns:Selectionoftheinformation-bearingwaveformBandwidthandpowerofthewaveformEffectofsystemnoiseonthereceivedinformationCostofthesystemWhatisaCommunicationSystem61-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalinformationsourceproducesafinitesetofpossiblemessages.1-2DIGITALANDANALOGSOURCES71-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanaloginformationsourceproducesmessagesthataredefinedonacontinuum.1-2DIGITALANDANALOGSOURCES81-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalcommunicationsystemtransfersinformationfromadigitalsourcetothesink.1-2DIGITALANDANALOGSOURCES91-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanalogcommunicationsystemtransfersinformationfromananalogsourcetothesink.CommunicationNetwork1-2DIGITALANDANALOGSOURCES101-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalwaveformisafunctionoftimethatcanhaveonlyadiscretesetofvalues.1-2DIGITALANDANALOGSOURCES111-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanalogwaveformisafunctionoftimethatcanhasacontinuousrangeofvalues.1-2DIGITALANDANALOGSOURCES121-3DETERMINISTICANDRANDOMWAVEFORMSAdeterministicwaveformcanbemodeledasacompletespecifiedfunctionoftime.1-3DETERMINISTICANDRANDOMW131-3DETERMINISTICANDRANDOMWAVEFORMSArandomwaveform(orstochasticwaveform)cannotbecompletespecifiedasafunctionoftimeandmustbemodeledprobabilistically.1-3DETERMINISTICANDRANDOMW141-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMAllcommunicationsystemsinvolvesthreemainsubsystems:thetransmitter,thechannel,andthereceiver.Theinformation(message)maybeinanalogordigitalformanditmayrepresentaudio,video,orothertypeofinformation.Theyarebasebandsignals.Thesignalprocessingblockatthetransmitterconditionsthesourceformoreefficienttransmission.Thesignalprocessorprovidessource/channelcoding.1-6BLOCKDIAGRAMOfACOMMUNI151-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMThetransmittercarriercircuit(modulator)convertstheprocessedbasebandsignalintoafrequencybandthatisappropriateforthetransmissionmediumofthechannel.Itisneededwhenthetransmissionchannelislocatedinabandaroundfc>>0.Inthiscase,s(t)issaidtobebandpass.Channelsmaybeclassifiedintotwocategories:wireandwireless.Thechannelnoisemayarisefromnaturalelectricaldisturbances(e.g.,lighting)orfromartificialsources(e.g.,switchingcircuitsofanearbycomputer).1-6BLOCKDIAGRAMOfACOMMUNI161-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMThechannelmaycontainactiveamplifyingdevices(e.g.,transponders).Thechannelmayprovideundesirablemultipathsbetweenitsinputandoutputthathavedifferenttimedelaysandattenuationcharacteristics.Thesecharacteristicsmayvarywithtime,whichmakesthesignalfade.Thereceivercarriercircuits(demodulator)takesthecorruptedsignalatthechanneloutputandconvertsittoabasebandsignal.Thesignalprocessingblockatthereceiver“cleansup”thissignalanddeliversanestimateofthesourceinformationtotheinformationsink.1-6BLOCKDIAGRAMOfACOMMUNI171-7FREQUENCYALLOCATIONSWirelesscommunicationsystemsoftenusetheatmosphereforthetransmissionchannel.Here,interferenceandpropagationconditionsarestronglydependentonthetransmissionfrequency.Toprovidesomesemblanceoforderandtominimizeinterference,governmentregulationsspecifiesthemodulationtype,bandwidth,power,andtypeofinformationthatausercantransmitoverdesignatedfrequencyband.FrequencyassignmentsandtechnicalstandardsaresetinternationallybytheInternationalTelecommunicationsUnion(ITU).EachmembernationoftheITUretainssovereigntyoverthespectralusageandstandardsadoptedinitsterritory.However,eachnationisexpectedtoabidebytheoverallfrequencyplanandstandardsthatareadoptedbytheITU.1-7FREQUENCYALLOCATIONSWirel181-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS191-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS201-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS211-8PROPAGATIONOFELECTROMAGNETICWAVESWirelesscommunicationsystemsoftenusetheatmosphereforthetransmissionchannel.Here,interferenceandpropagationconditionsarestronglydependentonthetransmissionfrequency.Toprovidesomesemblanceoforderandtominimizeinterference,governmentregulationsspecifiesthemodulationtype,bandwidth,power,andtypeofinformationthatausercantransmitoverdesignatedfrequencyband.FrequencyassignmentsandtechnicalstandardsaresetinternationallybytheInternationalTelecommunicationsUnion(ITU).EachmembernationoftheITUretainssovereigntyoverthespectralusageandstandardsadoptedinitsterritory.However,eachnationisexpectedtoabidebytheoverallfrequencyplanandstandardsthatareadoptedbytheITU.1-8PROPAGATIONOFELECTROMAGN221-8PROPAGATIONOFELECTROMAGNETICWAVESThepropagationcharacteristicsofelectromagneticwavesusedinsoftwirechannelsarehighlydependentonthefrequency.Theelectromagneticspectrummaybedividedintothreebroadbandsthathaveonofthreedominantpropagationcharacteristics:groundwave,skywave,andlineofsight(LOS).Ground-wavepropagation(below2MHz):theelectromagneticwavetendstofollowthecontouroftheEarth,i.e.,diffractionofthewavecausesittopropagatealongthesurfaceoftheEarth.1-8PROPAGATIONOFELECTROMAGN231-8PROPAGATIONOFELECTROMAGNETICWAVESThelowestradiofrequencythatcanbeuseddependsonhowlongyouwanttomaketheantenna.Forefficientradiation,theantennaneedstobelongerthanonetenthofawavelength.[Example]1-8PROPAGATIONOFELECTROMAGN241-8PROPAGATIONOFELECTROMAGNETICWAVESThelongwaveantenna(282meterhigh)usedtobroadcaston189kHzThetopofthelongwaveantennaThemastofthelongwaveantennaThewiretosupportthelongwaveantenna1-8PROPAGATIONOFELECTROMAGN251-8PROPAGATIONOFELECTROMAGNETICWAVESSky-wavepropagation(inthe2-to-30range):long-distancecoverageisobtainedbyreflectingthewaveattheionosphereandattheEarth’sboundaries.1-8PROPAGATIONOFELECTROMAGN261-8PROPAGATIONOFELECTROMAGNETICWAVESTheionizationiscausedbyultravioletradiationfromthesun,aswellascosmicrays.1-8PROPAGATIONOFELECTROMAGN271-8PROPAGATIONOFELECTROMAGNETICWAVESThecriticalfrequenciesoftheionospherearethehighestfrequenciescapableofbeingreflectedfromtheionizedregions.Thisisrelatedtothemaximumelectrondensitiesfortheseregions.1-8PROPAGATIONOFELECTROMAGN281-8PROPAGATIONOFELECTROMAGNETICWAVESTherefractionindexoftheionosphereisgivenbywhereNisthefreeelectrondensity(numberofelectronspercubicmeter).Inanionizedregionnislessthan1becauseNisgreaterthan0andoutsidetheionizedregionnisapproximatelyequalto1becauseNisapproximatelyequalto0.Intheionizedregion,thewavewillbebentaccordingtoShell’slaw:1-8PROPAGATIONOFELECTROMAGN291-8PROPAGATIONOFELECTROMAGNETICWAVESActually,intheionospherethewavesarerefracted(i.e.,bent)graduallyinaninvertedUshape.1-8PROPAGATIONOFELECTROMAGN301-8PROPAGATIONOFELECTROMAGNETICWAVESActually,intheionospherethewavesarerefracted(i.e.,bent)graduallyinaninvertedUshape.1-8PROPAGATIONOFELECTROMAGN311-8PROPAGATIONOFELECTROMAGNETICWAVESLOSpropagation(above30MHz):theelectromagneticwavepropagationinastraightline.Thereislittlerefractionbytheionosphere.Thesignalwillpropagatethroughtheionosphere.Thismodehasthedisadvantagethatforcommunicationbetweentwoterrestrial(Earth)stations,thesignalpathhastobeabovethehorizon.1-8PROPAGATIONOFELECTROMAGN321-8PROPAGATIONOFELECTROMAGNETICWAVESTheantennaneedtobeplacedontalltowerssothatthereceiverantennacan“see”thetransmittingantenna.What’sthedistancetotheradiohorizon?1-8PROPAGATIONOFELECTROMAGN331-8PROPAGATIONOFELECTROMAGNETICWAVES[Derivation]But1mi.=5280ft.,soifdandharemeasuredbymi.andft.,respectively1-8PROPAGATIONOFELECTROMAGN341-9INFORMATIONMEASURETheinformationsentfromadigitalsourcewhenthejthmessageistransmittedisgivenbywherePjistheprobabilityoftransmittingthejthmessage.Theaverageinformation(entropy)measureofadigitalsourceiswheremisthenumberofpossibledifferentmessages.ThesourcerateisgivenbywhereTisthetimerequiredtosendamessage.1-9INFORMATIONMEASURETheinf351-10CHANNELCAPACITYANDIDEALCOMMUNICATIONSYSTEMTheoptimumdigitalsystemmightbedefinedasthesystemthatminimizestheprobabilityofbiterroratthesystemoutputsubjecttoconstraintsontransmittedenergyandchannelbandwidth.Itispossibletoinventasystemwithnobiterrorattheoutputevenwehavenoiseintroducedintothechannel.Theoptimumanalogsystemmightbedefinedastheonethatachievesthelargestsignal-to-noiseratio(SNR)atthereceiveroutputsubjecttoconstraintsontransmittedenergyandchannelbandwidth.ItisimpossibletodesignasystemwithinfiniteSNRattheoutputwhennoiseisintroducedbythechannel.1-10CHANNELCAPACITYANDIDEA361-10CHANNELCAPACITYANDIDEALCOMMUNICATIONSYSTEMShannonshowedthat(forthecaseofsignalpluswhiteGaussiannoise)achannelcapacityC(bits/s)couldbecalculatedsuchthatiftherateofinformationR(bits/s)waslessthanC,theprobabilityoferrorwouldapproachzero.TheequationforCiswhereBisthechannelbandwidthinHz,andS/Nisthesignal-to-noisepowerratio(watts/watts,notdB)attheinputtothedigitalreceiver.Systemsapproachthisboundusuallyincorporateerror-correctioncoding.Nyquistshowedthatifapulserepresentsonebitofdata,noninterferencingpulsescouldbesentoverachannelnofasterthan2Bpulses/s.1-10CHANNELCAPACITYANDIDEA371-11CODINGIfthedataattheoutputofadigitalcommunicationsystemhaveerrorsthataretoofrequentforthedesireduse,theerrorscanoftenbereducedbytheuseoftwomaintechniques:automaticrepeatrequest(ARQ)andforwarderrorcorrection(FEC).InanARQsystem,whenareceivercircuitdetectserrorsinablockofdata,itrequeststhatthedatablockberetransmitted.InanFECsystem,thetransmitteddataareencodedsothatthereceivercancorrectaswellasdetecterrors.Theseproceduresarealsoclassifiedaschannelcodingbecausetheyareusedtocorrecterrorscausedbychannelnoise.(Thepurposeofsourcecodingistoextracttheessentialinformationfromthesourceandencodeitintodigitalformsothatitcanbesavedortransmittedusingdigitaltechniques.)Codinginvolvesaddingextra(redundant)bitstothedatastreamsothatthedecodercanreduceorcorrecterrorsattheoutputofthereceiver.1-11CODINGIfthedataatthe381-11CODINGCodingisamappingofkinputbinarysymbolsintonoutputbinarysymbols.Codesmaybeclassifiedintotwobroadcategories:blockcodesandconvolutioncodes.BlockCodesConvolutionCodes(n,k)(n,k,K)MemorylessMemoryR=k/n=1/4to7/8R=k/n=?to7/8.k=3toseveralhundredk,n=3to8,v=(k-1)K=2to601-11CODINGCodingisamapping391-11CODING1-11CODING401-11CODINGAllofthecodesachievetheircodinggainsattheexpenseofbandwidthexpansion(Trellis-codedmodulationisanexception).1-11CODINGAllofthecodesac41Homework11-1,1-4,1-5,1-9,1-15,1-16.Homework11-1,1-4,1-5,1-9,42IntroductiontoCommunicationPrinciplesCourseName:IntroductiontoCommunicationPrinciplesCourseCode:EI211CourseInstructor:DianguangMaText:DigitalandAnalogCommunicationSystems,6thed.byLeonW.CouchII,ISBN0-13-081223-4Contents:Chapters1–4.IntroductiontoCommunication43AbouttheTextThisbookcoverstheessentialsneededfortheunderstandingofwireandwirelesscommunicationsystemsandincludesadoptedstandards.TheseessentialsareHowcommunicationsystemswork:chapters1through5.Theeffectofnoise:chapter6and7.Wireandwirelesscommunicationsystems:chapter8.Thisbookisidealforeitheraone-semesteroratwo-semestercourse.Foraone-semestercourse,thebasicsofhowcommunicationsystemsworkmaybetaughtbyusingthefirstfivechapters(withselectedreadingsfromchapter8).Foratwo-semestercourse,thewholebookisused.Thisbookcoverspracticalaspectsofcommunicationsystemsdevelopedfromasoundtheoreticalbasis.Thisbookincludesover550problems.AbouttheTextThisbookcovers44AbouttheAuthorLeonW.Couch,IIProfessorEmeritusandAssociateChairmanElectricalandComputerEngineeringDepartmentUniversityofFloridacouch@AbouttheAuthorLeonW.Couch,45CHAPTER1INTRODUCTIONCHAPTER1INTRODUCTION46ChapterObjectivesHowcommunicationsystemsworkFrequencyallocationandpropagationcharacteristicsComputersolutions(MATLABandMATHCAD)InformationmeasureCodingperformanceChapterObjectivesHowcommunic47WhatisaCommunicationSystem?Communicationsystemsaredesignedtotransmitinformation.Communicationsystemdesignershavefourmainconcerns:Selectionoftheinformation-bearingwaveformBandwidthandpowerofthewaveformEffectofsystemnoiseonthereceivedinformationCostofthesystemWhatisaCommunicationSystem481-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalinformationsourceproducesafinitesetofpossiblemessages.1-2DIGITALANDANALOGSOURCES491-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanaloginformationsourceproducesmessagesthataredefinedonacontinuum.1-2DIGITALANDANALOGSOURCES501-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalcommunicationsystemtransfersinformationfromadigitalsourcetothesink.1-2DIGITALANDANALOGSOURCES511-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanalogcommunicationsystemtransfersinformationfromananalogsourcetothesink.CommunicationNetwork1-2DIGITALANDANALOGSOURCES521-2DIGITALANDANALOGSOURCESANDSYSTEMSAdigitalwaveformisafunctionoftimethatcanhaveonlyadiscretesetofvalues.1-2DIGITALANDANALOGSOURCES531-2DIGITALANDANALOGSOURCESANDSYSTEMSAnanalogwaveformisafunctionoftimethatcanhasacontinuousrangeofvalues.1-2DIGITALANDANALOGSOURCES541-3DETERMINISTICANDRANDOMWAVEFORMSAdeterministicwaveformcanbemodeledasacompletespecifiedfunctionoftime.1-3DETERMINISTICANDRANDOMW551-3DETERMINISTICANDRANDOMWAVEFORMSArandomwaveform(orstochasticwaveform)cannotbecompletespecifiedasafunctionoftimeandmustbemodeledprobabilistically.1-3DETERMINISTICANDRANDOMW561-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMAllcommunicationsystemsinvolvesthreemainsubsystems:thetransmitter,thechannel,andthereceiver.Theinformation(message)maybeinanalogordigitalformanditmayrepresentaudio,video,orothertypeofinformation.Theyarebasebandsignals.Thesignalprocessingblockatthetransmitterconditionsthesourceformoreefficienttransmission.Thesignalprocessorprovidessource/channelcoding.1-6BLOCKDIAGRAMOfACOMMUNI571-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMThetransmittercarriercircuit(modulator)convertstheprocessedbasebandsignalintoafrequencybandthatisappropriateforthetransmissionmediumofthechannel.Itisneededwhenthetransmissionchannelislocatedinabandaroundfc>>0.Inthiscase,s(t)issaidtobebandpass.Channelsmaybeclassifiedintotwocategories:wireandwireless.Thechannelnoisemayarisefromnaturalelectricaldisturbances(e.g.,lighting)orfromartificialsources(e.g.,switchingcircuitsofanearbycomputer).1-6BLOCKDIAGRAMOfACOMMUNI581-6BLOCKDIAGRAMOfACOMMUNICATIONSYSTEMThechannelmaycontainactiveamplifyingdevices(e.g.,transponders).Thechannelmayprovideundesirablemultipathsbetweenitsinputandoutputthathavedifferenttimedelaysandattenuationcharacteristics.Thesecharacteristicsmayvarywithtime,whichmakesthesignalfade.Thereceivercarriercircuits(demodulator)takesthecorruptedsignalatthechanneloutputandconvertsittoabasebandsignal.Thesignalprocessingblockatthereceiver“cleansup”thissignalanddeliversanestimateofthesourceinformationtotheinformationsink.1-6BLOCKDIAGRAMOfACOMMUNI591-7FREQUENCYALLOCATIONSWirelesscommunicationsystemsoftenusetheatmosphereforthetransmissionchannel.Here,interferenceandpropagationconditionsarestronglydependentonthetransmissionfrequency.Toprovidesomesemblanceoforderandtominimizeinterference,governmentregulationsspecifiesthemodulationtype,bandwidth,power,andtypeofinformationthatausercantransmitoverdesignatedfrequencyband.FrequencyassignmentsandtechnicalstandardsaresetinternationallybytheInternationalTelecommunicationsUnion(ITU).EachmembernationoftheITUretainssovereigntyoverthespectralusageandstandardsadoptedinitsterritory.However,eachnationisexpectedtoabidebytheoverallfrequencyplanandstandardsthatareadoptedbytheITU.1-7FREQUENCYALLOCATIONSWirel601-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS611-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS621-7FREQUENCYALLOCATIONS1-7FREQUENCYALLOCATIONS631-8PROPAGATIONOFELECTROMAGNETICWAVESWirelesscommunicationsystemsoftenusetheatmosphereforthetransmissionchannel.Here,interferenceandpropagationconditionsarestronglydependentonthetransmissionfrequency.Toprovidesomesemblanceoforderandtominimizeinterference,governmentregulationsspecifiesthemodulationtype,bandwidth,power,andtypeofinformationthatausercantransmitoverdesignatedfrequencyband.FrequencyassignmentsandtechnicalstandardsaresetinternationallybytheInternationalTelecommunicationsUnion(ITU).EachmembernationoftheITUretainssovereigntyoverthespectralusageandstandardsadoptedinitsterritory.However,eachnationisexpectedtoabidebytheoverallfrequencyplanandstandardsthatareadoptedbytheITU.1-8PROPAGATIONOFELECTROMAGN641-8PROPAGATIONOFELECTROMAGNETICWAVESThepropagationcharacteristicsofelectromagneticwavesusedinsoftwirechannelsarehighlydependentonthefrequency.Theelectromagneticspectrummaybedividedintothreebroadbandsthathaveonofthreedominantpropagationcharacteristics:groundwave,skywave,andlineofsight(LOS).Ground-wavepropagation(below2MHz):theelectromagneticwavetendstofollowthecontouroftheEarth,i.e.,diffractionofthewavecausesittopropagatealongthesurfaceoftheEarth.1-8PROPAGATIONOFELECTROMAGN651-8PROPAGATIONOFELECTROMAGNETICWAVESThelowestradiofrequencythatcanbeuseddependsonhowlongyouwanttomaketheantenna.Forefficientradiation,theantennaneedstobelongerthanonetenthofawavelength.[Example]1-8PROPAGATIONOFELECTROMAGN661-8PROPAGATIONOFELECTROMAGNETICWAVESThelongwaveantenna(282meterhigh)usedtobroadcaston189kHzThetopofthelongwaveantennaThemastofthelongwaveantennaThewiretosupportthelongwaveantenna1-8PROPAGATIONOFELECTROMAGN671-8PROPAGATIONOFELECTROMAGNETICWAVESSky-wavepropagation(inthe2-to-30range):long-distancecoverageisobtainedbyreflectingthewaveattheionosphereandattheEarth’sboundaries.1-8PROPAGATIONOFELECTROMAGN681-8PROPAGATIONOFELECTROMAGNETICWAVESTheionizationiscausedbyultravioletradiationfromthesun,aswellascosmicrays.1-8PROPAGATIONOFELECTROMAGN691-8PROPAGATIONOFELECTROMAGNETICWAVESThecriticalfrequenciesoftheionospherearethehighestfrequenciescapableofbeingreflectedfromtheionizedregions.Thisisrelatedtothemaximumelectrondensitiesfortheseregions.1-8PROPAGATIONOFELECTROMAGN701-8PROPAGATIONOFELECTROMAGNETICWAVESTherefractionindexoftheionosphereisgivenbywhereNisthefreeelectrondensity(numberofelectronspercubicmeter).Inanionizedregionnislessthan1becauseNisgreaterthan0andoutsidetheionizedregionnisapproximatelyequalto1becauseNisapproximatelyequalto0.Intheionizedregion,thewavewillbebentaccordingtoShell’slaw:1-8PROPAGATIONOFELECTROMAGN711-8PROPAGATIONOFELECTROMAGNETICWAVESActually,intheionospherethewavesarerefracted(i.e.,bent)graduallyinaninvertedUshape.1-8PROPAGATIONOFELECTROMAGN721-8PROPAGATIONOFELECTROMAGNETICWAVESActually,intheionospherethewavesarerefracted(i.e.,bent)graduallyinaninvertedUshape.1-8PROPAGATIONOFELECTROMAGN731-8PROPAGATIONOFELECTROMAGNETICWAVESLOSpropagation(above30MHz):theelectromagneticwavepropagationinastraightline.Thereislittlerefractionbytheionosphere.Thesignalwillpropagatethroughtheionosphere.Thismodehasthedisadvantagethatforcommunicationbetweentwoterrestrial(Earth)stations,thesignalpathhastobeabovethehorizon.1-8PROPAGATIONOFELECTROMAGN741-8PROPAGATIONOFELECTROMAGNETICWAVESTheantennaneedtobeplacedontalltowerssothatthereceiverantennacan“see”thetransmittingantenna.What’sthedistancetotheradiohorizon?1-8PROPAGATIONOFELECTROMAGN751-8PROPAGATIONOFELECTROMAGNETICWAVES[Derivation]But1mi.=5280ft.,soifdandharemeasuredbymi.andft.,respectively1-8PROPAGATIONOFELECTROMAGN761-9INFORMATIONMEASURETheinformationsentfromadigitalsourcewhenthejthmessageistransmittedisgivenbywherePjistheprobabilityoftransmittingthejthmessage.Theaverageinformation(entropy)measureofadigitalsourceiswheremisthenumberofpossibledifferentmessages.ThesourcerateisgivenbywhereTisthetimerequiredtosendamessage.1-9INFORMATIONMEASURETheinf771-10CHANNELCAPACITYANDIDEALCOMMUNICATIONSYSTEMTheoptimumdigitalsystemmightbedefinedasthesystemthatminimizestheprobabilityofbiterroratthesystemoutputsubjecttoconstraintsontransmittedenergyandchannelbandwidth.Itispossibletoinventasystemwithnobiterrorattheoutputevenwehavenoise