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1、OnQuasi-OrthogonalSignaturesforCDMASystemsRobertW.HeathJr.ThomasStrohmerDept.ofElect.andComp.Engr.Dept.ofMathematicsTheUniversityofTexasatAustinUniversityofCalifornia,DavisAustin,TX78712-1084USADavis,CA95616USAPhone:(512)232-2014Phone:(530)752-1071Fax:(512)471-1856Fax:(530)752-6
2、635rheath@ece.utexas.edustrohmer@math.ucdavis.eduArogyaswamiJ.Paulraj∗InformationSystemsLaboratoryStanfordUniversityStanford,CA94305USAPhone:(650)725-8307Fax:(650)723-8473apaulraj@stanford.eduSeptember15,2002AbstractCodebooksconstructedfromWelchboundequalitysequencesareoptimalin
3、termsofsumcapacityinsynchronousCDMAsystems.Theseoptimalcodebooksdependonboththese-quencelengthaswellasthenumberofactivesequences.Thustomaintainoptimalityatyp-icallydifferentcodebookisneededforeverypossiblenumberofactiveusers.Further,allthesequencesneedtobereassignedasthenumberof
4、activeuserschanges.Thispaperde-scribesandanalyzestwopromisingsubclassesofWelchboundequalitysequencesthathavegoodpropertieswhenonlyasubsetofsequencesisactive.Onesubclass,basedonmaximumWelchboundequalitysequencesets,hasequiangularsequencesthuseachuserexperiencesthesameamountofinte
5、rference.Theinterferencepowerdependsonlyonthetotalnumberofac-tiveusers.Anothersubclass,constructedbyconcatenatingmultipleorthonormalbasis,comesclosertotheWelchboundwhennotallsignaturesareactive.Optimalunionsoforthonormalbasisarederived.Performancewhensubsetsofsequencesareactivei
6、scharacterizedintermsofsum-squaredcorrelation,averageinterference,andconditionnumberoftheGrammatrix.Discussions,codeconstructions,andillustrationsareforbothsubclassesarepresented.Keyword:Code-divisionmultiple-accesssystems,Walshsequences∗AportionoftheseresultswillappearintheProc
7、eedingsofthe2002AllertonConferenceonCommunication,Control,andComputerstheProceedingsofthe2002AsilomarConferenceonCircuits,Signals,andSystems1IntroductionDirectspreadCDMAsystemsusesignaturesequencestodistinguishbetweenthesignalsofdiffer-entusers.Insingle-cellsynchronoussystems,th
8、euseoforthogonalsignaturesequenceseliminatesthe
