A New Method for Reducing the Power Consumption of Portable Handsets in TDMA Mobile Systems

ANewMethodforReducingthePowerConsumption

ofPortableHandsetsinTDMAMobileSystems:ConditionalEqualization

LionelHussonandJean-ClaudeDany

Abstract—Intime-divisionmultiple-access(TDMA)systems,theautonomyofportablehandsetsisamajorconstraint.Weproposeanewmethod,conditionalequalization,whichminimizesthepowerconsumptionduetoequalizationbyequalizingonlywhenitismostneeded.

Ateachtimeslot,thereceiverestimatestheneedforequal-izationwithadeterministiccriterion.Theproposedcriteriausethresholds,chosentoprovideacompromisebetweenlossinperformanceandpercentageofsavedequalization.

Theperformanceofourmethodistheoreticallyanalyzedfortwo-pathRayleighfadingchannelsandsimulatedfortherec-ommendedCOST207channels.Conditionalequalizationcanensureadegradationintheaveragesignal-to-noiseratio(SNR),providingafixedbit-error-rate(BERwithanaverageSNR=9dBwithsystematicequalization),oflessthan0.5dBwhileprovidingagainof43%sparedequalizationforbadurban(BU),62%forhillyterrain(HT),79%fortypicalurban(TU),and98%forruralarea(RA)models,respectively.

Conditionalequalizationisshowntogreatlyimprovetheau-tonomyofthereceiverbydrasticallyreducingthepowercon-sumptionduetoequalization,withoutanoticeablelossintheperformance.

IndexTerms—Autonomyofportablehandsets,biterrorrate,equalization,evaluationofperformance,mobileradiochannels,time-divisionmultiple-access(TDMA).

Fig.1.Basebandequivalenttransmissionscheme.

andtoabstainfromusingitwhenthedistortionsduetothechannelareweak.

Thepaperisorganizedasfollows.AfterintroducinginSectionIIthenotationsandhypothesesusedinthispaper,wepresentinSectionIIIhowtheevaluationoftheperformanceofthereceiverintermsofprobabilityoferroriscarriedout.InSectionIV,weexplaintheprincipleofconditionalequalizationandwedisplaythetheoreticalperformanceofthisdeviceoveratwo-pathRayleighfadingchannel.SimulationresultsarethecoreofSectionV.Themethodisusedwithadecisionfeedbackequalizer(DFE)equalizeroverthechannelsrecommendedbytheCOST207finalreport.Weshowitsap-plicabilityanditsinterestforreducingthepowerconsumptionofportablehandsetsinTDMAsystems.Finally,SectionVIcontainstheconcludingremarks.

II.NOTATIONS

AND

I.INTRODUCTION

I

NMOBILEcommunicationsystems,thepropagationchan-nelimposesperturbationeffectsonthetransmissionlink(attenuation,distortions,andfluctuations).Ithasdirectcon-sequencesonthefunctionalitieswhichareneededinthetransmitterandthereceiver.Estimationofthechannelandequalizationareameansofobtainingtheperformancere-quiredinmobileradiotime-divisionmultiple-access(TDMA)systems.

Withthedevelopmentofmobilesystems,amajorconstraintisthedesiredsizeandautonomyoftheportablehandset.Sometechniquesareusedtominimizethepowerconsumption,suchascontrolofpowerorvocalactivitydetection.Inthisarticleweproposeadevicetolimittheconsumptionduetoequalization.Theideaistoadaptthepowerresourcesofthehandsetdependingonthequalityofthereceivedsignal.Itsprincipleistoresorttotheprocessingonlywhenitisneeded

ManuscriptreceivedDecember1,1995;revisedFebruary4,1999.

´´TheauthorsarewithServiceRadio´electricit´eetElectroniqueEcole

´Sup´erieured’Electricit´e(SUPELEC),F-91192Gif-sur-YvetteCedex,France.

PublisherItemIdentifierS0018-95(99)07384-3.

HYPOTHESES[1],[2]

Letusconsideranarrow-bandsignalaroundfrequency

(2)

where

,and

denotesthecorrespondingrollofffactor.Themobile

radiochannelresponseiswrittenas

(3)

0018–95/99$10.00©1999IEEE

HUSSONANDDANY:NEWMETHODFORREDUCINGPOWERCONSUMPTION1937

Fig.2.Basebandequivalentmodel.

Thereceivedsignalisthesignaltransmittedthroughthemobileradiochannelaffectedbyanadditionalwhite

Gaussiannoise

,havingtwo-sideddensitythebaseband

equivalentfiltertothewholetransmissionscheme(emission,

channel,andreceptionfiltering)and

istheadditivenoisecorrespondingto

afterthereceptionfiltering(seeFig.2).Theglobalresponse,includingpulsefiltering,isexpressedas

correspondstoacosinefilter.

Thereceivedsignalaftersamplingattime

(5)

thatwedenote

is(7)

with

and

thpath,

isthenoisevariance

(10)

where

th

path.TheaverageSNRisthendefinedby

where

iscom-putedbytheaverageofoverallthepossiblechannel

responsesasfollows:

(12)

Detailsofthiscomputationcanbefoundin[2],[3],and[4].

InthecaseofRayleighfadingchannelswith

multipathswithidenticalaveragepartialSNR

0xe

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Fig.3.EffectsofISIexample:two-pathchannelwithssn=+Aandn01=+A.

B.PerformanceintheAbsenceofEqualization

Inordertopresentthewayperformanceisevaluatedwhennoequalizationisled,wefirstexplainwhatwemeanbynoequalization.Thereceiverdoesnotresorttoanytechniquetoeliminatethedistortionsduetothechannel.Thissituationisusuallycalledreceptioninthepresenceofintersymbolinterference(ISI)[5].

Thechannelisestimatedbythereceiver.Inthefollowing,weconsideraperfectestimationofthechannel.Theestimationofthechannelenablesustodecidewhichcoefficient

correspondstothepathhavingthegreatestenergy.Thereceptionsystemmakesadecisioninrelationtothispath.Thereceivedsignalcanbewrittenas

(14)

where

correspondstothepathwiththegreatestenergy(alsocalledtheprincipalpath).

Inthisexpression,thefirstpartcorrespondstothepartofthesignalwhichistransmittedthroughtheprincipalpath,thesecondpartistheportionofthesignaltransmittedbytheotherpathswhichcausesISI,andthelastpartistheadditivenoise.Thereceivermakesitsdecisionsrelativetotheprincipalpath,withoutconsideringtheremainingpaths.Thesignalisdividedbythecoefficientofthispath,

sym-bol.Intheconsideredbinarymodulationwheretheemitted

symbolsarereal,thedecisionismadeontherealpartof

.Thecontributionoftheotherpathsofthechannelis

theirprojectiononthedirectiondefinedbythegreatestenergypath.Let

,theconditionalerrorprobabilityisgivenby

(19)

Detailsofthecomputationofthisprobabilityaregivenin[2].Inthegeneralcase,thisprobabilitycannotbeexpressedasafunctionexclusivelydependingon

and

(20)

where

is

evaluatedbyconsideringallthepossibleoccurrencesofthechannel.Thisleadstoanaveragingoverthevariables

whichare

uniformlydistributedover

.Inthecaseofatwo-pathchannel,theaveragebit-error

probabilityfunction

iscomputedby(22)

Extensiveanalyticalcomputationofthisprobabilitycanbefoundin[2].

C.ComparisonofPerformanceforTwo-PathFadingChannelsFig.4representstheaveragebiterrorrate(BER)withoptimumequalization[6]andwithoutanyequalizationinthecaseofaRayleighfadingchannelwithtwoindependentpathsofequalaverageenergies.Theinterestofequalizationisillustratedbytheimportantimprovementintheperformance.

HUSSONANDDANY:NEWMETHODFORREDUCINGPOWERCONSUMPTION1939

Fig.4.AverageBERforRayleighfadingchannelwithtwopathsofequalaverageenergies,(---)optimum:analyticalmatchedfilterbound,(—)noequalization:analyticalcomputation,(+)noequalization:MonteCarlosimulation.

Fig.5.Principleofconditionalequalization.

Inthefollowing,wedescribeaprocessing,conditionalequalization,whichleadstoaperformanceclosetothatob-tainedwithasystematicequalizationandwhichconsiderablydecreasestheaveragenumberofprocessingsinthereceiver.

IV.CONDITIONALEQUALIZATION

Thepurposeofconditionalequalizationistosavethehandsetresourcesbyresortingtothecompleteprocessingoftheequalizeronlyinthemostseveredistortioncases,i.e.,thatimplythedegradationintheperformance.

Ateachtimeslot,thereceiverestimates,onitsown,theneedtoresorttoequalization.Theproposedmethoddoesnotneedanyadditivesignalingonthenetwork.Whenthechannelisconsideredasweaklydispersivebythereceiver,theprocessingislimitedtoadivisionofthedemodulatedsignalbythegreater

energypathcoefficient

,followedbyadecisionontherealpart(Fig.5.).

Thisdeviceimpliesthedefinitionofacriterionintendedtomakeapartitionbetweenweaklydispersivechannelsanddispersivechannels.Weproposedeterministiccriteriawhichenablethereceivertodecideateachtimeslotifequalizationshouldbeusedornot.Inthissectionwedescribethetwoproposedcriteriaandanalyzetheiranalyticalperformanceinthecaseofatwo-pathRayleighfadingchannel,whichisachannelusuallyconsideredasrepresentativeofmobileradiotransmissionsandwhichallowsanalyticalcomputa-tion.

A.DefinitionofaCriterion:C1

Wedefineacriterion(denotedbyC1)basedonthepaths’energies.

Fig.6.DomainsforthecomputationoftheaverageerrorprobabilitywhenusingC1.Foreachdomaintherelatedconditionalprobabilityfunctionisdisplayed.

CriterionC1:Iftheenergyofapathisfargreaterthanthe

totalenergyoftheotherpaths,thispathisconsideredaspredominantandnoequaliza-tionisused.

Thispredominancycanbeexpressedbythefollowing.Ifcanbefoundsuchthat,thenthepathispredominant.

Thiscriterioniseasytoimplementinthereceiverasitsconsistsofthefollowingprocessing:computingtheenergyofeach(formerlyestimated)path,thendeterminingtheprincipalpath,and,finally,checkingifthesumoftheenergiesoftheotherpathsislessthanarelevantthreshold.Theadditionalcomplexityofthiscriterionis,consequently,verysmall[2].Inthecaseofatwo-pathchannelthiscriterionisexpressedby

noequalization

.

Tocomputetheaverageerrorprobability,wemustoperatetheintegrationoftheconditionalprobabilityoferroron

and

dependent.Theotherpartcorrespondingtothe

equalizationcaseisobtainedbyintegratingtherelatedfunction

(9),whichisindependentof

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Fig.7.Percentageofnoequalization,P(󰀋),inthecaseofaRayleighfadingchannelwithtwopathsofequalaverageenergieswithC1.

isuniformly

distributedover

whenusingthesymmetriesofthecomputation.Thecompleteanalyticalexpressionsoftheseintegralsareexplicatedin[2].

2)CorrespondenceBetweentheChoiceof

corre-spondingtodifferentpercentagesofavoidedequalizationsinthecaseofaRayleighfadingchannelwithtwopathsofequalaverageenergies.

ForagivenaverageBERof8

,thenthepathispredominant.

ThecomplexityofimplementationofthiscriterionisgreaterthanthecomplexityofC1becauseofthecomputationoftheprojectionsovertheprincipalpathoftheotherpaths.However,thiscomplexityislowenoughtobeusedpracticallyinthereceiver[2].Inthecaseofatwo-pathchannel,thiscriterionisexpressedby

noequalization

otherwise

.

1)ErrorProbability:WeconsideraRayleighfadingchan-nelwithtwopathsandanoptimalequalizationconditionallytoC2.AsinthecaseofC1,toevaluatetheaverageerrorprobabilityweintegratetheconditionalprobabilityonthe

HUSSONANDDANY:NEWMETHODFORREDUCINGPOWERCONSUMPTION1941

Fig.9.Domainsofcomputationfortheaverageerrorprobabilitywhen󰀋function=jcos(󰀒is)j2displayed.

<1.Foreachdomain,therelatedconditionalprobabilityFig.10.Domainsofcomputationfortheaverageerrorprobabilitywhen󰀋=functionjcos(󰀒is)j2displayed.

>1.Foreachdomain,therelatedconditionalprobabilityvariables.However,fortheintegrationdepending

on

.

Then

noequalization

otherwise

,thenwecanrepresent

thecomputationrelatedtothiscaseonthe

noequalization

andPercentageofEqual-ization:Thepercentageofnoequalizationforatwo-pathRayleighfadingchannelcanbecomputedby

10

(performanceofsystematicequalizationataverageSNR

10.ItexplicitlyshowsthatC2enables

ustoreachbetterperformancethanC1foragivenpercentageofnoequalization.Inaddition,itshowsthatbelow50%of

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Fig.11.PercentageofsparedequalizationP(󰀋)inthecaseofaRayleighfadingchannelwithtwopathsofequalaverageenergieswiththecriterionC2.

Fig.12.AverageperformanceofconditionalequalizationwithcriterionC2andoptimalequalization.Optimumequalizationused:(a)100%(󰀋=0),(b)65%(󰀋=0:05),(c)50%(󰀋=0:1),(d)35%(󰀋=0:2),and(e)0%(󰀋=1)oftime.

Fig.13.ComparisonbetweenC1C2onatwo-pathRayleighfadingchannel.DegradationinperformanceforconditionaloptimalequalizationcomparedtoasystematicequalizationwithaaverageBERfixedto811003.

savedequalizations,thedegradationisrelativelylow(lessthan1dB).

Thesetheoreticalresultsshowthatusingconditionalequal-

Fig.14.ProfilefortheTUcase,six-tapmodel.

Fig.15.ProfilefortheBUcase,six-tapmodel.

izationwitharelevantcriterionenablesthesavingofagreatpercentageofpowerconsumptionandthesavingoftimespentintheequalizerwithalimiteddamagetotheBERperformance.Consequently,conditionalequalizationappearsasapromisingtechniqueforincreasingtheautonomyofportablehandsets.

V.APPLICATIONTOMOBILERADIOCHANNELS

Inthissection,wepresenttheresultsofsimulationsoftheproposedmethodforthechannelsrecommendedbytheCOST207[7],[8],usingaDFEinsteadofanoptimalequalizer.WeanalyzetheperformanceandshowtheapplicabilityandtheefficiencyofconditionalequalizationforTDMAmobileradiosystems.

A.COST207Channels

Simulationsofthispaperarebasedonthesix-tapprofilesproposedbytheCOST207group[7]forsimulationsovermobileradiochannels.Theproposedmodelsdescribefourdifferentenvironments:typicalurban(TU),badurban(BU),hillyterrain(HT),andruralarea(RA).Figs.14–17representtheaveragerelativepowerofthesixtapscorrespondingtotheWSSUSmodelforeachenvironment.ExceptforthefirsttapoftheRAmodel,whichfollowsaRicedistributiontypicalof

HUSSONANDDANY:NEWMETHODFORREDUCINGPOWERCONSUMPTION1943

Fig.16.ProfilefortheHTcase,six-tapmodel.

Fig.17.ProfilefortheRAcase,six-tapmodel.

thepresenceofaline-of-sight(LOS)propagation,allthetapsfollowaRayleighdistribution,characteristicofanonline-of-sight(NLOS)propagation.

B.PerformanceofaConditionalDFEEqualizer[9],[10]Consideringthepreviousmodels,wecarriedoutsimulationsofconditionalequalizationwhenusingthemostefficientcrite-rion,C2.Theperformanceofaconditionaloptimalequalizerisstudiedin[2].Inthissection,wedisplaytheperformanceofaconditionalDFEequalizerwitheightforwardandsixbackwardcoefficients.Theusedmodulationis2ASK,withasymbolrateequaltotheGSMsymbolrate:270.833kbauds.Therolloffcoefficientofthepulseshapeissetat

leadingtodifferentpercentagesofavoided

equalizations.

Fig.21showsthat,intheRAcase,equalizationisuselessandshouldbeavoided.Inotherenvironmentsitappearsthat,formobileradiochannels,conditionalequalizationenablestosaveagreatpercentageofequalizationwithoutanimportant

Fig.18.AverageperformanceofconditionalequalizationintheTUcase.DFEequalizerused:(a)100%(󰀋=0),(b)49%(󰀋=0:05),(c)27%(󰀋=0:1),(d)17%(󰀋=0:15),and(e)0%(󰀋=1)oftime.

Fig.19.AverageperformanceofconditionalequalizationintheBUcase.DFEequalizerused:(a)100%(󰀋=0),(b)82%(󰀋=0:05),(c)65%(󰀋=0:1),(d)53%(󰀋=0:15),(e)36%(󰀋=0:25),(f)30%(󰀋=0:3),and(g)0%(󰀋=1)oftime.

Fig.20.AverageperformanceofconditionalequalizationintheHTcase.DFEequalizerused:(a)100%(󰀋=0),(b)66%(󰀋=0:05),(c)45%(󰀋=0:1),(d)35%(󰀋=0:15),(e)26%(󰀋=0:2),(f)18%(󰀋=0:3),and(g)0%(󰀋=1)oftime.

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Fig.21.AverageperformanceofconditionalequalizationintheRAcase.DFEequalizerused:(a)100%(󰀋=0)and(b)0%(󰀋=1)oftime.

lossofperformance.AvoidinghalfoftheequalizationsbyresortingtoC2leadstodegradationsoftheaverageSNR,fulfillingthesameperformanceassystematicequalizationat9dB,of0.6,0.2,and0.1dB,respectively,forHT,BU,andTUmodels.

Theseresultsshowthatconditionalequalizationcanbeusedprofitablyinpractice.Acompromisebetweenthedegradationsoftheperformanceandthepercentageofsavedequalizationsmustbedetermined.

Inordertouseconditionalequalizationinpractice,thethresholdusedinthedecisioncriterionmustbepreliminarilysetatafixedvalue.Fig.22displaysthedegradation,forafixedaverageBER,asafunctionofthisthresholdfortheTU,BU,HT,andRAchannels.Fig.23displaysthepercentageofsavedequalizationasafunctionofthethresholdforthesamechannels.Itcanbeseenthatforlowvaluesofthethreshold

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conditionalequalizationisstudiedin[2]and[11].Inthegeneralcase,theBERisincreasedinthepresenceoferrorsintheevaluationsofthecoefficientsofthechannel.Whenthereceiverdoesnotresorttothewholeprocessofequalization,thedegradationoftheBERisonlycausedbythepredominantcoefficient,whichleadstoabetterBERthananequalizationusingalltheimperfectcoefficientswhenthechannelisnotdispersive.Consequently,conditionalequalizationthataimsatreducingpowerconsumptionalsominimizestheeffectsoftheerrorsofchannelestimation.Thisistheareaofourfutureresearchworkanditisexpectedtoleadtofurtherpublications.

ACKNOWLEDGMENT

TheauthorswishtothankA.WautierandJ.colleaguesintheServiceRadio´electricit´eetElectronique´Antoine,their

de

Sup´elec,fortheirusefuladviceandencouragementforthispaper.

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LionelHussonwasborninParis,France,onJuly29,1970.HereceivedthetheEcole´Sup´erieured’Electricit´´engineerdiplomae(SUPELEC),´from

Gif-sur-Yvette,France,in1993andthePh.D.degreefromtheUniversit´eParisXI,Orsay,France,in1998.

Since1993,hehasbeenworkinginanalogelec-tronicsanddigitalcommunications.Heiscurrently

anAssociateProfessoratSUPELEC´andteaches

modulations,spacecommunications,andsystemsoftelecommunications.Hismainresearchinterestsare

intheareasofequalization,diversity,andperformanceevaluationinmobileradiosystems.

Jean-ClaudeDanywasborninFranceonJune12,1946.HereceivedtheengineerdiplomafromtheEcole´Sup´erieured’Electricit´´e(SUPELEC),´Gif-sur-Yvette,France,in1969.

Sincethisyear,hehasbeenworkingatSUPELEC

´inanaloganddigitalelectronics.HeisnowaProfessorofinformationtheory,coding,anddigitalcommunications,andhisresearchactivitiesareintheseareas.