Achievable Rates for Tomlinson–Harashima Precoding

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1、824IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.44,NO.2,MARCH1998valueofjC()jfor1n01[13]±[15].OurcurrenteffortsAchievableRatesforTomlinson±HarashimaPrecodingaredirectedtowarddiscoveringsystematicmethodsofconstructingsuchsequences.RichardD.Wesel,Member,IEEE,andJohnM.Cioffi,Fellow,

2、IEEEACKNOWLEDGMENTAbstractÐThiscorrespondenceexaminesTomlinson±Harashimapre-coding(THP)ondiscrete-timechannelshavingintersymbolinterferenceTheauthorswishtothankP.Gaal,agraduatestudentattheandadditivewhiteGaussiannoise.AnexactexpressionforthemaximumUniversityofSouthernCalifornia

3、,forhelpfuldiscussionsandaachievableinformationrateofzero-forcing(ZF)THPisderivedasacarefulreviewofthemanuscript.functionofthechannelimpulseresponse,theinputpowerconstraint,andtheadditivewhiteGaussiannoisevariance.Informationrateboundsareprovidedfortheminimummean-squareerror(MM

4、SE)THP.TheperformanceofZF-THPandMMSE-THPrelativetoeachotherandtoREFERENCESchannelcapacityisexploredingeneralandforsomeexamplechannels.TheimportanceofsymbolratetoZF-THPperformanceisdemonstrated.[1]S.W.GolombandR.A.Scholtz,ªGeneralizedBarkersequences,ºIEEETrans.Inform.Theory,vol.

5、IT-11,pp.533±537,Oct.1965.IndexTermsÐAdditivewhiteGaussiannoise,capacity,intersymbol[2]R.H.Barker,ªGroupsynchronizationofbinarydigitalsystems,ºininterference,peakconstraint,Tomlinson±Harashimaprecoding.CommunicationTheory,W.Jackson,Ed.London,U.K.:Butterworths,1953,pp.273±287.(P

6、apersreadataSymposiumonªApplicationsofCommunicationTheoryºheldattheInstitutionofElectricalEngineers,I.INTRODUCTIONLondon,Sept.22±26,1952.)[3]R.TurynandJ.Storer,ªOnbinarysequences,ºProc.Amer.Math.Soc.,Tomlinson[1]andHarashima[2],[3]independentlyintroducedvol.12,pp.394±399,June19

7、61.precodingasatechniqueforintersymbolinterferencemitigation.[4]R.L.Frank,ªPolyphasecodeswithgoodnonperiodiccorrelationThestructurethattheypresentedisreferredtoastheTomlin-properties,ºIEEETrans.Inform.Theory,vol.IT-9,pp.43±45,Jan.1963.son±HarashimaPrecoder(THP).Thereareotherpre

8、codingstructures[5]R.Turyn,ªThecorrelationfunctionofas