On the Optimum Detection of Digital Signals in the Presence of White Gaussian Noise.pdf

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1、336IRETRANSACTIONSONCOMMtJNICATIONSSYSTEMS,DecemberOntheOptimumDetectionofDigitalSignalsinthePresenceofWhiteGaussianNoise-AGeometricInterpretationandaStudyofThreeLBasicIDataTransmissionSystems*ANDH.DYMZ,MEMBER,IRESummary-Thispaperconsiderstheproblemofoptimallyde-introductio

2、ntothemoregeneraltreatmentwhereinthetectingdigitalwaveformsinthepresenceofadditivewhiteGaussiantransmittedsign:tlsarerepresentedintermsofaKar-noise.Atechniqueforrepresentingthetransmittedsignalsandhunen-Loeveexp:znsion.’Jtheadditivenoisewhichleadstoageometricinterpretationo

3、fthedetectionproblemispresentedonatutoriallevel.Subsequently,Theconceptsdevelopedintheearlyportionsofthethistechniqueisusedtoderivetheoptimumdetectorforeachofpaperareusedsubsequentlytoderivetheoptimumthreebasicdatatransmissionsystems:m-levelPhaseShiftKeyed,detectorforeachof

4、threesystemsmentionedabove(bothm-levelAmplitudeShiftKeyedandm-levelFrequencyShiftKeyed.undertheassumptionofphasezoherenceandphasein-Correspondingprobabilityoferrorcurvesarederived,comparedcoherence)andtoderivethecorrespondingexpressionsanddiscussedwithreasonabledetail.forth

5、eprobabilityoferror.SeveralsetsofcurvesarepresentedanddiscussedinreasonabledetailinthefinalI.INTRODUCTIONsectionsofthepaper.HISPAPERWASwrittentofulfilltwoobjectives.Inthecourseofthepresentation,referencestoad-Thefirstobjectiveistutorial;thepaperisintendedditionalarticlesand

6、booksonrelatedsubjectmatteraretoserveasanintroductiontosomeoftheideasofcited.However,appreciatingthedifficultyinvolvedinmodernstatisticalcommunicationtheory;inparticular,siftingthroughmanyreferenceseachwithitsownpeculiartheproblemofdetectingaknownsignalinawhitenoisenotation

7、,anefforthasbeenmadetowritethispaperasbackgroundwithminimumprobabilityoferrorisintro-acompleteunit.Accordingly,theoreticalresultswhichduced.Thesecondobjectiveistoanalyzeandcompareareutilizedwithinthebodyofthispa.perwithoutproofindetailtheperformanceofthreebasicdatatransmiss

8、ionarediscussedatlengthintheappendixes,which,withsystems,namely,m-levelPhaseShiftK