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1Anti-frequencyOffsetMethodforPrecisionSynchronizationonHighlyDynamicConditionBasedontheLeastSquaresAbstract:Howtoachieveprecisesynchronizationisatechnicalproblemthatmustbeaddressedintoday’smilitaryoperationsinthehighlydynamicconditions.Intheconditions,thebitrateoffsetandcarrierfrequencyoffsetwillaffecttheprecisesynchronizationaccuracy.AnimprovedPseudoNoise(PN)codephasemeasurementmethodbasedontheleastsquaresmethodisproposed,andtheprecisesynchronizationabilityofthismethodinhigh-dynamicconditionsisprovedbytheoreticalanalysisandsimulation.Thetheoreticalanalysisshowsthatthemethodcaneliminatetheimpactofcarrierfrequencyoffsetandbeofstronganti-noiseability.WhilethenumericalsimulationmanifeststhatthismethodisnotsensitivetobitrateoffsetwhenthelengthoftheselectedPNsequenceisnotverylong,andprovesthatitisofstronganti-frequencyoffset.Themeasurementresultsdemonstratethatthismethodnotonlyachievesahighmeasurementaccuracy,butalsopossessesgoodanti-noiseandanti-frequencyoffsetability.Keywords:Wirelesscommunication;PseudoNoise(PN)phaseestimate;Precisionsynchronization;Anti-frequencyoffset;Highlydynamiccondition;LeastSquares(LS)1IntroductionWiththecontinuousdevelopmentofwirelesscommunicationandnetwork,theprecisesynchronizationrequirementofthesystemishigherandhigher,suchastheAmericanGPS,ChineseBeidouPositioningSystem,AmericanTacticalTatgetingNetworkTechnologyandIntraFlightDataLinkNetworkTechnologyputforwardnewrequirementsonprecisesynchronizationtechnology,andoftenneedtoworkundertheconditionofhighdynamicandlownoiseratio.DirectSequenceSpreadSpectrum,becauseofitsgoodcorrelationandgoodanti-noiseability,isoftenusedintheprocessofsynchronouscommunicationsystem,especiallyinthefieldofaerospaceandmilitarycommunications,DirectSpreadSpectrumsignalusuallyappliedtocompletetherangeandpositioningwork[1,2].Bothsynchronousandranging,thephasemeasuringaccuracyofPNcodesequenceistheunderlyingfactorsofaffectingtheperformance,soalotofliteraturesdomanyresearchesonthephasemeasurementofthePNsequence[3-6].Forexample,literature[3]analysisoftheeffectofdeviationofphasemeasurementinthetimedomain,andsubsectioncross-correlationmethodisproposedtoimprovetheabilitytoresistfrequencydeviationofthesystem,butthearticledidn'tmentiontheerrorrangeofsystemaccuratesynchronizationintheend.Theliterature[4],withfastFouriertransformmethod,bytheprocessofcalculatingreferencesignalandtheinputsignalcorrelationspectrumachievesDSSSsignalPNcodephasemeasurement,thismethodisofhighefficiencyandwidelyused.Defectsofthemethodis,however,thatitmustincrease2thesamplingfrequencyinordertofurtherimprovetheaccuracyofphasemeasurement,leadingtoincreasethepointsofFFT,andincreasetheamountofcalculationandimplementationdifficulty.Theliterature[5]withthetwo-pointlinearinterpolationdealswithdatasofthepeakandthepeaktimesofthereferencesignalandtheinputsignalcorrelationspectruminordertoimprovethemeasurementprecision,butthealgorithmisstillnothighprecisioninpracticalapplication.Theliterature[6]usesthecorrelationspectrumanditsneighboringtwodatapointstodeterminequadraticinterpolationpolynomial,thencalculatethemaximumpointofinterpolationpolynomialtodeterminepreciselocationrelatedtospectralspectrumpeak,theeffectofimprovingthemeasuringaccuracyofDSSSsignalPNcodephasebythemethodisnotobvious,butnottheanalysisoftheeffectofdeviation,accordingtotheanalysisoftheliterature[3],however,thismethodislargelyaffectedbythefrequencydeviation,thisarticlealsoshowsthatitisnotsuitableforhighdynamicenvironmentthroughsimulation.Theliterature[7]proposesthatitusesDelay-LockedLoopSphasecurvelinearcharacteristicsofthemiddlesection,andusestheleastsquaremethodtogetprecisepseudo-codephasedifference,thismethodissimple,highprecision,canyetberegardedasakindofgoodaccuratesynchronizationmethod,butitalsodidnotconsidertheeffectsofdeviationinitsarticle.Theliterature[8]quantitativelyanalysestheeffectofthearbitrarychannelnon-idealfeaturesforpseudocoderangingzerovalue,thereceiverofthesoftwarehascarriedonthesimulationtotheanalysisresult,butithasnothingabouthowtosolvethepseudocoderangingintheconditionofhighdynamicproblems.Theliterature[9]solvestheproblemofalgorithmcomplexityincreasesduetocarrierphasemeasurementuncertaintybyusingtheresampling,butitdoesnotrelatetohowtoimprovethePNphasemeasurementaccuracy.Inhighdynamiccondition,forexample,satellitecommunication,spacecombatandsoon,synchronizationaccuracywillbeaffectedbythefrequencydeviationandtherateofmigration.Consideringthetwofactors,thispaperputsforwardanprecisemeasurementPNphasemethodbasedontheimprovedleastsquares,andshowsthemeasuringresultsundertheconditionofhighdynamicusingtheimprovedmethodthroughtheoreticalderivationandnumericalsimulation.2PNphasemeasurementmethodandthediscreteexpressionofthecross-correlationfunctionundertheconditionofhighdynamic2.1ThePNphasemeasurementmethodoftheleastsquaresTheliterature[7]putsforwardusingtheleastsquaremethodtomeasurethephaseofthereceivedPNsequence,thebasicideaistousethePNcoderelatedsymmetry,inordertoachievephasecurves.Asshowninfigure1andfigure2.3figure1relevantcurveun