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1、TeamControlNumberForofficeuseonly0000ForofficeuseonlyT1F1T2F2T3ProblemChosenF3T4AF42014MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoeachcopyofyoursolutionpaper.)RepeatersCoordinationAndDistributionFebruary6,2015AbstractInthispa
2、per,itaimstocomputingproblemonRelayStrategy(repeaterscoordinationanddistribution).Accordingtoadvancedradiocellularcoveragetechnology,usageoffrequencyattenuationandgeometricmappingmethods,Hatamodel,cellularcoveragesolutionandFDM(FrequencyDivisionMultipl
3、exing)modelwereestablished.ThealgorithmsusedMATLABtosimulate,withthefinalmodelingresultsofsensitivityanalysisandimprovement&promotiononmodels.Questionone:Foracircularflatareaofradius40milesradius,determinetheminimumnumberofrepeatersnecessarytoaccommoda
4、te1,000simultaneoususers.Assumethatthespectrumavailableis145to148MHz,thetransmitterfrequencyinarepeateriseither600kHzaboveor600kHzbelowthereceiverfrequency,andthereare54differentPLtonesavailable.Answer:1.BasedonFrequencyattenuationexpressionandcalculat
5、ionwithMATLAB,itfiguredouttheeligiblecoverageradiuses,whichare30kmforBS(basestation),and14.9kmforrepeater.2.Assumingtheusersinagivenareaunderuniformdistribution,usingadvancedcellularcoveragesolution,wecancalculatethatminimumnumberofrequiredrepeateris36
6、undercellularfeatures.3.BasedontheUSVHFspectrumallocationstandard,theminimumspacingforadjacentchannelsis30kHz.Andwithupto54differentPLtones,maximum4320channelscanbeallocatedtoprovide1000simultaneoususerstouseatthesametime.Conclusion:Theminimumnumberofr
7、epeatersnecessarytoaccommodate1,000simultaneoususersis36.QuestionTwo:Howdoesyoursolutionchangeifthereare10,000users?Answer:1.Sincethegivenspectrumisinafixedrange,evenif54differentPLtonescannotbeallocatedenoughchannelsfor10,000simultaneoususers.Sothenum
8、berofrepeaterswillbeincreased,meanwhile,thegivenareawillbedividedintodifferentparts.2.Ontheassumptionthatuniformdistributionofthepopulationinthegivenarea,itwillbedividedinto3sub-regionsequallybyanalyzingthebindingdomain,frequencyspectru