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ANovelInterferenceSuppressionAlgorithmBasedonIrregularWaveletPacketTransforminDSSSSatelliteCommunicationSystemYanghuiTong,FangjunLiu,DaoxingGuoandHengWangPLAUniversityofScienceandTechnology,Nanjing,Jiangsu,Chinaemail:1024276863@qq.
comKeywords:satellitecommunications,DSSS,waveletpackettransform,Optimumwaveletbase,interferencesuppressionAbstract:Inrecentyear,theDirectSequenceSpreadSpectrum(DSSS)technologyhasbeenintroducedasanattractiveapproachtoguaranteeanti-interferencecapabilityinsatellitecommunicationsystem.
However,duetothelimitationoftheDSSS,thesystemperformancehasbeengreatlydeterioratedwhileastronginterferenceisoutofthetoleranceofthesystem.
Meanwhile,whatthewaveletpackettransformsisideallysuitablefortheinterferencedetectionandsuppressionofDSSSsatellitecommunicationsystembyexploitingitsexcellentlocaltime-frequencydomainanalysiscapability.
Inthispaper,anovelalgorithmhasbeenputforwardtoachievingpositionandinterferencesuppressionthroughcombingthesub-bandpowerratiowithminimumpowerthresholdswhicharebasedontheanalysisontheoptimalwaveletpacketdecomposition.
Simulationresultshowsthattheproposedinterferencesuppressionalgorithmsignificantlyimprovestheanti-jammingcapabilityofDSSSsatellitecommunicationsystemcomparedwiththetraditionalFFTalgorithm.
IntroductionWiththeadventoftheinformationage,therequirementsofaccessingtoinformationareincreasinglyurgent.
Duetotheanti-interferencecapacitiesofdirectsequencespreadspectrum(DSSS)systems,ithasbeenwidelyusedinboththemilitaryandcivilcommunications.
However,theanti-interferencecapabilityofDSSSsystemislimitedbytheprocessinggain.
Theperformanceofthesystemlargelydegradeswhentheinterferencepowerisgreaterthanthejammingmargin.
Itisofgreatsignificanttoemploysignalprocessingtechniquestoimprovetheanti-jammingperformanceofDSSSsystem.
Currently,thesignalprocessingtechniquesisusedinthespreadspectrumsystemwhichisincludetimedomainprocessingtechniques[1,2]andtransformdomainprocessingstructures[3,4].
Timedomainprocessingtechniquescaneliminatethenarrowbandinterference(NBI)completelybecauseitestimatestheinterferenceexactlyandextractfromthereceivesignaltoleavetheinterferencefreeDSSSsignal.
Butitisnecessaryforconvergencetimetoreachtheoptimalsolution.
Soitissuitableforslow-alteredinterference.
Ontheotherhand,thechanginginterferencecanbequicklytrackedbythetransformdomainsuppression.
ThetransformdomainprocessingstructuresadoptthemethodsliketheFouriertransform,wavelettransformandwaveletpackettransform,andtoconvertatime-domainsignalintothetransformdomain.
Itutilizesthedifferentfeaturesbetweentheinterferencesignalandthedesiredsignalinthefrequencydomaintomakeadistinction.
Itusestherelevantsuppressionmethodtoeliminatetheinterferencesignals.
Therefore,thetransformdomainprocessingtechniquesareabletotrackandcapturedynamicinterferencequicklyandadaptively.
Waveletpackettransformisverysuitableforinterferencedetectionandsuppressioninthedirectsequencespreadspectrumsystemsbecauseofitsexcellentlocaltimeandfrequencydomainanalysiscapabilities.
Thedifficultyofusingwaveletpackettoachieveinterferencesuppressionismainlyreflectedintwoaspects:Thefirstoneisabouthowtocarryoutwaveletpacketdecompositiononthereceivedsignal.
Thesecondoneisabouthowtolocateinterferenceonthebasisofwavelettreeandtochooseappropriatealgorithmsforachievinginterferencesuppression.
Asisknowntoall,thewaveletpacketdecompositionusuallyincludesregulardecompositionwithuniformsub-bandandoptimalwaveletpacketdecompositionwithunevensub-band[5,6].
Thecommoninterferencelocatingmethodsbasedonwaveletpacketincludesub-bandpowerrationodepositioning[7],adaptivethresholdpositioning[8]andsoon.
Anewmethodforinterferencesuppressionhasbeenputforwardbasedontheoptimumwaveletpacketdecomposition.
Firstly,locatetheinterferencebyusingsub-bandpowerratiosothatsub-bandhigh-powerinterferencecanbesuppressed.
Then,makefurtherjudgmentsandsuppressiononthenon-suppressedsub-bandbyusingtheminimumpowerthresholdmethodinordertohaveabettereliminateresidualinterference.
SystemmodelTheinterferencesuppressionandnoisesuppressionmodel,whichisbuiltbasedonwaveletpacket,whichisshowninFig.
1.
Thesignalfromthegroundreceiverusuallyincludesspreadspectrumsignalcomponent,narrowbandinterferenceandnoisecomponents.
Thereceivedsignal()rkcanbeexpressedas:rkskJknk=++(1)Inthisformula,the()skdenotesspreadspectrumcommunicationsignalusingtheBPSKmodulation,()Jkpresentsthenarrow-bandinterferencesignals,()nkdenotestheadditivewhiteGaussiannoisesignalwithameanzeroandthevariance2σ.
Thus,thesignal()skbasedondirectsequencespreadspectrumsystemcanbeexpressedas:00cosskPskPNkkωφ=+(2)Inthisequationabove,Prepresentspowerlevelofthespreadspectrumsignal,()0skisthebinaryinformationbits,()PNkisthespreadingsequence,0ωiscarrierfrequency,φisthephase.
SatellitetransponderUplinkInformationinputInformationoutputinterferenceWaveletpackettransformOrientationandinterferencesuppressionWaveletpacketAntitransformTransformdomainsignalprocessingFig.
1SchematicofDSSSinterferencesuppressionsatellitecommunicationbasedonwaveletpackettransformWaveletpacketanalysisbasisofsignalWaveletpackettransformhasanexcellenttime-frequencylocalizationfeaturesandmulti-resolutionanalysisability.
Whentheinterferencechangesinreal-time,theinterferencewillbelocatedquicklyandefficientlyinalimitedsub-bandandthenitwillbeeliminatedthroughtherelevantsuppressionalgorithm.
ThetransformprocessofWaveletpacketisdefinedusingthefollowingsequenceoffunctionswithrecursion:2212222nnnnkZkZUthkUtkUtgkUtk+∈∈==∑∑(3)Inthisformula,()0Utisthescalingfunctionof()tφ,()1Utisthemotherwaveletof()tψ,(){},nUtnZ∈isknownasWaveletPacketGroupof()0Ut,(){},hkkZ∈and{}11,kgkhLkkZrespectivelyrepresentsalow-passfiltercoefficientgroupandhigh-passfiltersetofcoefficientsofquadraturemirrorfiltersQMFwithsupportinglengthL,andsatisfythefollowingcondition:()()(),222abkZkZhkahkbhkδ∈∈==∑∑(4)Waveletpacketneedstobediscretedforpracticalapplications.
AfollowingrecursivediscretewaveletpackettransformwasgivenbyC.
K.
Chui[9]:2121122nnllkznnllkzSihikSkSigikSk+∈++∈=*=*∑∑(5)Thecorrespondinginversediscretewaveletpackettransformisasfollows:2221122nnlllkzkzSihikSkgikSk++∈∈=+∑∑(6)Inthisformula,lrepresentsthecorrespondinglayersofwaveletpacketdecomposition,nindicatesthelateralnodespositionofthecorrespondinglevel;nlSrepresentsthedecompositionsequenceofnodenatthelayerofl.
Thereceivedsignalcanbeseparatedtoauniformornon-uniformspectralsub-bandbymakinguseofwaveletpackettransform.
WaveletpacketdecompositionoftheDSsignalTheoptimumwaveletpacketbaseisfoundoutbytheruleofenergycompactinthispaper,thespecificstepsareasfollows:(1)MakeuseofM-arywaveletpackettodecomposethereceivedspreadspectrumsignaltogainaM-aryruleswaveletpacketdecompositiontree.
Thenumberofnodescontainedineverylayeris()1LM.
(2)EachnodeusesastandardenergycompactGtoanalyze:1221/MMkkGσσ==∏(7)2σisthecoefficientvarianceofnodeNoflayeri()1iL≤≤,2kσisthecoefficientvarianceofthechildnodekNwhosenumberisMandparentnodeisNofthelayer1i+.
Thethresholdis_ThECM,ifthestandardGsatisfiesthecondition_GThECM>,itindicatesthattheenergyofchildnodekNisunevensoitneedkeepondecomposing;ifthestandardGsatisfiesthecondition_GThECM≤,itindicatesthattheenergyofchildnodekNisevenandthemostpartsofitsfrequencybandarecomposedofspreadspectrumsignalelementorinterferenceelement,sointhiscasethenodewillnolongermakefurtherdecomposition.
Itisworthnoticingthatitneedstomakeinterferencejudgmentoftheleafnodesthatareoutofbreakingdownatthetimeofinterferencepositionandsuppressiontoavoidtheinfluenceofinterferencecomponentsonsystemperformance.
(3)Ifthenodeneedsfurtherdecomposition,doingwaveletpackettransformagainisnecessarytohavethechildnodekNofthelayer2i+,andthenrepeatstep(1)inasimilaroperationuntilthedecompositionachievesthegivenmaximumnumberofscaleL(Atthistimeitcorrespondstothemaximumfrequencyresolution),thenodesstopdecomposing,andwewillgetanoptimumwaveletpacketbase,thediagramshowninFig.
2isanexcellentexample.
(0,0)(1,0)(1,1)(2,0)(2,1)(3,0)(3,1)(4,0)(4,1)(4,2)(4,3)16π416ππ01ω816πFig.
2Diagramofoptimalwaveletpacketdecompositiontree(decompositionlevelof4)andthecorrespondingrangebandwidthdecompositionTheinterferencepositioningandsuppressionalgorithmonthebasisofwaveletpackettransform.
Thestepspresenttheinterferencesuppressionmethodofcombiningthesub-bandpowerratiowiththeminimumthresholdinthisarticleareasfollows:(1)Readtheleafnodeleavesofoptimalwaveletpackettree,lookfordoubleleavesnodeswhichhavethesameparentnode,andprocessthosedoubleleavesnodeswiththesub-bandpowerratiointerferencepositioningsuppression.
Thenusetheminimumthresholdtojudgetheexistenceoftheresidualinterference,ifthereisinterference,thenthecoefficientofthisleaveissetaszerodirectly;(2)Searchforsingleleafnodeswhichhavedifferentparentnodes.
Accordingtotheprocessofoptimalwaveletpacketdecomposition,theremaybeinterferenceleftonthedecomposedsingleleafnodes.
Inordertoachievebetterinhibitoryeffect,readcoefficientsofallleafnodesandcalculatethevariancefirstly,thenmakeuseofthemedianinthevariancecollectiontojudgethoseleaves.
Ifthevarianceoftheleavesisgreaterthanthemedian,itindicatesthatinterferenceexistsinthesingleleafnode,thenthecoefficientofthisleaveshouldbesetaszerodirectly,otherwise,thereisnointerferenceinthissingleleafnode,whichavoidstheinfluencewhenthesingleleafnodeisaffectedbyinterference.
Atthesametime,italsoensuresthatmostoftheusefulsignalsareundamaged;(3)TransformtheprocessedwaveletpackettreeinverselybyadoptingM-arywaveletpacketandobtainthespreadspectrumsignalthroughinterferencesuppression,thenmakedespreading,demodulationandothersubsequentprocessing.
ThesimulationresultsandanalysisInthesimulationprocess,theDSsystemusesapseudo-randomsequenceoflength32tospread,modulationschemeisBPSKmodulation,waveletpacketdecompositiontakesgenerationfunctionofdb16(Daubechieswavelets),MofM-Arytakestwo,thechannelofAWGNistaken.
Becausethespreadingcodelengthis32,thesystemhasacertainanti-interferencetolerance,inordertoreflecttheperformanceofthealgorithmforinterferencesuppressionwell,jamming-to-signalratio(JSR)mustbegreaterthan15.
051dB()()1010log3215.
051dB*=,jamming-to-signalratioisfrom20to50dBinsimulationprocess.
Themaximumdecompositionlevelofwaveletpackettreeis5,whatisneededtosatisfyboththesuppressionperformanceandthecomplexofdecomposition.
Thenormalizeddigitalfrequenciesoftwo-toneinterferencetospreadingrateare0.
314and1.
57,phasein[]0,2πisuniform.
FromtheFig.
3,itcanbeseenthattheinterferencefortheDSsystemposesaseriousdeterioration,itcannotcommunicateproperlywithoutsuppression,whilethetransformdomainprocessingstructurescaneffectivelyimprovetheperformanceofthesystem.
Furthermore,thenovelinterferencesuppressionalgorithmbasedonirregularwaveletpackettransformofcombiningthesub-bandpowerratioandtheminimumthresholdvaluehasthebetterinhibitoryeffectthanthetraditionalFFTinterferencesuppression.
FromtheFig.
4,inthesameconditionthatthesignal-to-noiseratio(SNR)is8dB,whenSNRislow,theperformanceofthenovelinterferencesuppressionalgorithmbasedonirregularwaveletpackettransformofcombiningthesub-bandpowerratioandtheminimumthresholdvalueisclosewiththetraditionalFFTinterferencesuppression.
ButastheSNRincreases,theanti-interferenceeffectofthelatterissignificantlybetterthantheformer.
2025303540455010-410-310-210-1100JSR[dB]PbNointerferencesuppressionFFTinterferencesuppressionAcombinedsuppressionofthesub-bandpowerratioandtheminimumthresholdvalueOnlythepresenceofnoise12345678910-510-410-310-210-1100SNR[dB]PbNointerferencesuppressionFFTinterferencesuppressionAcombinedsuppressionofthesub-bandpowerratioandtheminimumthresholdvalueOnlythepresenceofnoiseFig.
3TheBERperformancecomparisonofFig.
4TheBERperformancecomparisonofvariousalgorithmsindifferentjamming-to-variousalgorithmsindifferentsignal-to-signalratioandtwo-toneinterferencenoiseratioandtwo-toneinterference(SNR=8dB)(JSR=30dB)ConclusionAnovelinterferencesuppressionalgorithmthatirregularwaveletpacketstransformbycombiningthesub-bandpowerratioandtheminimumthresholdisproposedinthispaper.
Ourproposedalgorithmlimitstheinterferencetoafewnumberofsub-bandstoavoiddamagetotheusefulsignalwhilethoroughlyeliminatestheresidualinterferencewiththeassistanceofsub-bandpowerratiosuppression.
Simulationresultsrevealsthatinterferenceareeffectivelylocatedandsuppressedeventhroughunderthescenarioofstronginterference,whichsignificantlyenhancetheanti-interferenceabilityofDSSSsatellitecommunicationsystem.
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