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Adaptive Equalizer

Adaptive equalization is a technique used to combat inter-symbol interference in time-varying channels. Equalizers can be either preset or adaptive. Adaptive equalizers track changes in the time-varying channel to continuously adjust their filter characteristics. They operate in either a training mode, where a known training sequence is used, or a tracking mode, where decisions are used to generate error signals to update coefficients and track channel variations. Common adaptive algorithms include zero forcing, least mean squares, and recursive least squares.

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234 views24 pages

Adaptive Equalizer

Adaptive equalization is a technique used to combat inter-symbol interference in time-varying channels. Equalizers can be either preset or adaptive. Adaptive equalizers track changes in the time-varying channel to continuously adjust their filter characteristics. They operate in either a training mode, where a known training sequence is used, or a tracking mode, where decisions are used to generate error signals to update coefficients and track channel variations. Common adaptive algorithms include zero forcing, least mean squares, and recursive least squares.

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Hagos Gebretsadik
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ADAPTIVEEQUALIZATION

Preparedby Deepa.T,Asst.Prof./TCE

INTRODUCTIONTOEQUALIZATION Equalizationisatechniqueusedtocombatinter symbolinterference(ISI). AnEqualizerwithinareceivercompensatesfor theaveragerangeofexpectedchannelamplitude anddelaycharacteristics. Equalizersmustbeadaptiveasthechannelis generallyunknownandtimevarying. ISIhasbeenrecognizedasthemajorobstacleto highspeeddatatransmissionovermobileradio channels.

Equalizers
The goal of equalizers is to eliminate intersymbol interference (ISI) and the additive noise as much as possible. Intersymbol interference arises because of the spreading of a transmitted pulse due to the dispersive nature of the channel, which results in overlap of adjacent pulses. In Fig. 1, there is a fourlevel pulse amplitude modulated signal (PAM), x(t). This signal is transmitted through the channel with impulse response h(t). Then noise n(t) is added. The received signal r(t) is a distorted signal.

CategoriesofEqualization
Equalizersareusedtoovercomethe negativeeffectsofthechannel.In general,equalizationispartitioned intotwobroadcategories; 1. Maximumlikelihoodsequence estimation(MLSE) whichentails makingmeasurementofchannel impulseresponseandthen providingameansforadjustingthe receivertothetransmission environment. (Example:Viterbi equalization) 2. Equalizationwithfilters,usesfilters tocompansate thedistortedpulses. Thegeneralchannelandequalizer pairisshowninFigure.2.

Dependingonthetimenature
Thesetypeofequalizerscanbegroupedaspresetor adaptiveequalizers. Presetequalizersassumethatthechannelistimeinvariant andtrytofindH(f)anddesignequalizerdependingonH(f). TheexamplesoftheseADAPTIVEEQUALIZERSarezero forcingequalizer,minimummeansquareerrorequalizer, anddesicion feedbackequalizer. Adaptiveequalizersassumechannelistimevaryingchannel andtrytodesignequalizerfilterwhosefiltercoefficients arevaryingintimeaccordingtothechangeofchannel,and trytoeliminateISIandadditivenoiseateachtime.The implicitassumptionofadaptiveequalizersisthatthe channelisvaryingslowly.

BlockdiagramofAdaptive equalizer

Asthemobilefadingchannelsarerandomandtimevarying, equalizersmusttrackthetimevaryingcharacteristicsofthe mobilechannel,andthusarecalledadaptiveequalizers.

Workingprinciplesofadaptiveequalizers
Theworkingprinciplesofadaptiveequalizersareinthefollowing: Thereceivedsignalisappliedtoreceivefilter.Inhere,receivefilter isnotmatchedfilter.Becausewedonotknowthechannelimpulse response.Thereceivefilterinhereisjustalowpassfilterthat rejectsalloutofbandnoise. Theoutputofthereceiverfilterissampledatthesymbolrateor twicethesymbolrate. Sampledsignalisappliedtoadaptivetransversalfilterequalizer. TransversalfiltersareactuallyFIRdiscretetimefilters. Theobjectistoadaptthecoefficientstominimizethenoiseand intersymbol interference(dependingonthetypeofequalizer)at theoutput. Theadaptationoftheequalizerisdrivenbyanerrorsignal.

Operationmodeofadaptive equalizers
Therearetwomodesthatadaptiveequalizerswork; 1. DecisionDirectedMode:Thismeansthatthereceiverdecisions areusedtogeneratetheerrorsignal. 2. Decisiondirectedequalizeradjustmentiseffectiveintrackingslow variationsinthechannelresponse. However,thisapproachisnoteffectiveduringinitialacqusition . TrainingMode:Tomakeequalizersuitableintheinitialacqusition duration,atrainingsignalisneeded.In thismodeofoperation,the transmittergeneratesadatasymbolsequenceknowntothe receiver.Thereceivertherefore,substitutesthisknowntraining signalinplaceofthesliceroutput.Onceanagreedtimehas elapsed,thesliceroutputissubstitutedandtheactualdata transmissionbegins.

Operatingmodesofadaptive equalizer

1) Trainingmode

2) TrackingMode

Trainingmode
Initially,aknown,fixedlength trainingsequenceissentby thetransmittersothatthe receiversequalizermay averagetoapropersetting. Thetrainingsequenceisa pseudorandomsignalora fixed,prescribedbitpattern. Immediatelyfollowingthe trainingsequence,theuser dataissent.

Trackingmode
Whenthedataoftheusers arereceived,theadaptive algorithmoftheequalizer tracksthechangingchannel. Asaresultofthis,theadaptive equalizercontinuously changesthefilter characteristicsovertime. Equalizersarewidelyusedin TDMASystems.

trainingsequence(Contd..)
Thetrainingsequenceisdesignedtopermit anequalizeratthereceivertoacquirethe properfiltercoefficientsintheworst possiblechannelconditions.Thereforewhen thetrainingsequenceisfinished.Therefore filtercoefficientsareneartheiroptimal valuesforreceptionofuserdata.An adaptiveequalizeratthereceiverusesa recursivealgorithmtoevaluatethechannel andestimatefiltercoefficientsto compensateforthechannel.

BlockDiagramofAdaptiveEqualizer

AGenericAdaptiveEqualizer
TransversalfilterwithNdelayelements,N+1taps,andN+1tunable complexweights.Theseweightsareupdatedcontinuouslybyan adaptivealgorithm.

AlgorithmforAdaptive Equalization
Performancemeasuresforanalgorithm Rateofconvergence Misadjustment Computationalcomplexity Numericalproperties Factorsdominatethechoiceofanequalizationstructureandits algorithm Thecostofcomputingplatform Thepowerbudget Theradiopropagationcharacteristics

AlgorithmforAdaptive Equalization
Thespeedofthemobileunitdeterminesthechannelfadingrate andthe Dopperspread,whichisrelatedtothecoherenttimeofthe channel directly Thechoiceofalgorithm,anditscorrespondingrateofconvergence, dependsonthechanneldatarateandcoherenttime Thenumberoftapsusedintheequalizerdesigndependsonthe maximum expectedtimedelayspreadofthechannel Thecircuitcomplexityandprocessingtimeincreaseswiththe numberof tapsanddelayelements

AlgorithmforAdaptive Equalization
Threeclassicequalizeralgorithms:zeroforcing(ZF),leastmean squares (LMS),andrecursiveleastsquares(RLS)algorithms Summaryofalgorithms(seeTable1)

Conclusion
Summary
Linearequalizers:sufferfromnoiseenhancement DFE:Errorpropagation MLSE
Optimalmethod Viterbi equalizerimplementsMLSEwithmuchlower complexity

17

Summaryofalgorithms

Table1Comparisonofvariousalgorithmsforadaptiveequalization

Adaptivedecisionfeedback equalizer
AdaptiveDecisionFeedbackEqualizer Adecisionfeedbackequalizer(DFE)isanonlinear equalizerthatusespreviousdetectordecisionsto eliminatetheISIonpulsesthatarecurrentlybeing demodulated. ThebasicideaofaDFEisthatifthevaluesofthe symbolspreviouslydetectedareknown(pastdecisions areassumedtobecorrect),thentheISIcontributedby thesesymbolscanbecanceledouteactly theoutputof theforwardfilterbysubtractingpastsymbolsvalues withappropriateweighting.In

BlockdiagramofAdaptiveDFE

Adaptivedecisionfeedback equalizer(Contd..)
IfwelookatFig.18,weseethattheestimatedsignalsequence becomes,

{ci}sarecoefficientsoftheprecursorequalizer, {di}arecoefficientsofthepostcursor equalizer. NisthenumberofprecursorequalizercoefficientsandMisthenumberofpostcursor equalizercoefficients. AdaptiveDFEalgorithmissimilartostochasticgradientalgorithm,withtheimportant differencethattheinputtothecausalportionofthefilteristhedecisionsratherthan theoutputoftheprecursorequalizerfilter. Thisdifferencewillobviouslychangethedesiredtapcoefficientsaswellasreducethe noiseenhancementduetoequalization.

Adaptivedecisionfeedback equalizer(Contd..)

References
WirelessCommunications TheodoreS.Rappaport. MobileCommunicationEngineersTheoryandapplication WilliamC.Y.Lee. Cox,D.C.,AntennaDiversityPerformanceinMitigatingtheeffectsofPortable RadiotelephoneOrientationandMultipathPropagation, IEEETransactionsonCommunications,vol.62,No.9,pp.26952712,November1983. Jakes,W.C.,AComparisonofspecificspaceDiversityTechniqueforReductionofFast FadinginUHFMobileRadioSystems, IEEETransactionsonVehicularTechnology,Vol.VT20,No.4,pp.8193,November1971. Lemieux,J.F.,Tanany,M.,andHafez,H.M.,ExperimentalEvaluationof Space/Frequency/PolarizationDiversityintheIndoorWirelessChannel, IEEETransactionsonVehicularTechnology,Vol.40,No.3,pp.569574,August1993.

References
Rappaport,T.S.,andHawbaker,D.A,WidebandMicrowavePropagation ParametersUsingCircularFrequencyReuseEfficiencyfortheReverseChannel , IEEETransactionsonVehicularTechnology,Vol.40,No.2,pp.231242, February1992. Vaughan,R.,PolarizationDiversityinMobileCommunications, IEEETransactionsonVehicularTechnology,Vol.39,No.3,pp.177186,August 1990. Kozono,S.,BaseStationPolarizationDiversityReceptionforMobileRadio, IEEETransactionsonVehicularTechnology,Vol.VT33,No.4,pp.301306, November1985. Lee,W.C.Y,PolarizationDiversitySystemforMobileRadio, IEEETransactionsonCommunications,Vol.20,pp.912922,October1972.

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