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TeamControlNumberForofficeuseonly0000ForofficeuseonlyT1F1T2F2T3ProblemChosenF3T4AF42014MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoeachcopyofyoursolutionpaper.)RepeatersCoordinationAndDistributionFebruary6,2015AbstractInthispaper,itaimstocomputingproblemonRelayStrategy(repeaterscoordinationanddistribution).Accordingtoadvancedradiocellularcoveragetechnology,usageoffrequencyattenuationandgeometricmappingmethods,Hatamodel，cellularcoveragesolutionandFDM(FrequencyDivisionMultiplexing)modelwereestablished.ThealgorithmsusedMATLABtosimulate,withthefinalmodelingresultsofsensitivityanalysisandimprovement&promotiononmodels.Questionone:Foracircularflatareaofradius40milesradius,determinetheminimumnumberofrepeatersnecessarytoaccommodate1,000simultaneoususers.Assumethatthespectrumavailableis145to148MHz,thetransmitterfrequencyinarepeateriseither600kHzaboveor600kHzbelowthereceiverfrequency,andthereare54differentPLtonesavailable.Answer:1.BasedonFrequencyattenuationexpressionandcalculationwithMATLAB,itfiguredouttheeligiblecoverageradiuses,whichare30kmforBS(basestation),and14.9kmforrepeater.2.Assumingtheusersinagivenareaunderuniformdistribution,usingadvancedcellularcoveragesolution,wecancalculatethatminimumnumberofrequiredrepeateris36undercellularfeatures.3.BasedontheUSVHFspectrumallocationstandard,theminimumspacingforadjacentchannelsis30kHz.Andwithupto54differentPLtones,maximum4320channelscanbeallocatedtoprovide1000simultaneoususerstouseatthesametime.Conclusion:Theminimumnumberofrepeatersnecessarytoaccommodate1,000simultaneoususersis36.QuestionTwo:Howdoesyoursolutionchangeifthereare10,000users?Answer:1.Sincethegivenspectrumisinafixedrange,evenif54differentPLtonescannotbeallocatedenoughchannelsfor10,000simultaneoususers.Sothenumberofrepeaterswillbeincreased,meanwhile,thegivenareawillbedividedintodifferentparts.2.Ontheassumptionthatuniformdistributionofthepopulationinthegivenarea,itwillbedividedinto3sub-regionsequallybyanalyzingthebindingdomain,frequencyspectrumandPLtonesthreeindependentfactors.Andthenthenumberofrepeaterswithineachsub-regionwillbeclassifieddiscussion.3.TheFDM(FrequencyDivisionMultiplexing)modelisestablishedheretoimprovechannelefficiencytoaccommodateupto10,000simultaneoususersConclusion:Theminimumnumberofrepeatersnecessarytoaccommodate10,000simultaneoususersis126.QuestionThree:Discussthecasewheretheremightbedefectsinline-of-sightpropagationcausedbymountainousareas.Answer:Basically,underthesameconditionforquestion1&2,themountainousareawillbeanalyzedasfollowing:1.Thefunctionforrelationshipbetweenradioattenuationxcausedbyobstaclesandtheeligiblecoverageradiusdforrepeateris2249.354371.4110xd,whichistoanalyzetheimpactonthenumberofrepeatersunderfullsignalcoverage.2.Forthemountainbarrier,basedonthedifferentsituationofmountains,theadditionofrepeatersonthesuitablelocationwillbediscussedtoachievefullcoverage.Thispaperdescribesmodelestablishedbyusingofcellularcoveragetechnologyandfrequencyattenuationexpression,toachievesimple,fast,accuratealgorithm.Andalsoillustratedtheeffecttakestheentirearticle.Intheend,thesensitivityanalysisanderrorcalculationareappliedformodeling,makingthemodelpractically.Keywords:CellularCoveragetechnology,frequencyattenuationexpression,channelallocation,MatlabRepeaterscoordinationanddistributionContent1RestatementoftheProblem.................................................................................................11.1Introduction.....................................................................................................................................11.2TheProblem.....................................................................................................................................12SimplifyingAssumption........................................................................................................13Phraseexplain........................................................................................................................14Model......................................................................................................................................14.1ModelI..........................................................................................................................................14.1.1AnalysisoftheProblem......................................................................................14.1.2ModelDesign......................................................................................................25Sensitivityanalysis.................................................................................................................26Modelextension.....................................................................................................................27Evaluatingourmodel............................................................................................................27.1Thestrengthsofmodel........................................................................................