数学建模美赛论文.docx

数学建模美赛论文.docx

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数学建模美赛论文

RepeaterCoordination:

Achievingcommunications

withthefewestrepeaters

Summery

LimitedbythetransmissioncharacteristicsofVHFradiospectrum,usersfarawayfromeachothercannotcommunicatewithoneanother.Ingeneral,itisthroughrepeatersthatthecommunicationdistancecanbeincreased.However,withtheincreaseofrepeaters,mutualinterferenceappearsintheoverlappingareaofrepeatersusingthesamefrequency.SolutiontothisproblemistousedifferentfrequenciesoradoptCTCSStechnology.ButduetothebandwidthlimitationsandtherestrictiononthenumberofPLs,theresourcesallocatedtorepeatersarelimited,whichisachallengetotherepeater’sconfigurationandtoresourceallocation.Therefore,withtheaimtosolvethisproblem,weestablishedmathematicalmodelswiththeaimthefinishthefollowingthreetasks.

Forthegivenregion,weestablishedtheoptimalcoveragemodeltoguaranteethatallusershaveenoughcommunicationchannelsandtominimizethenumberofcellsthatareneededtocoverthegivenregioncompletely.Inthecaseofcellradiusdetermination,weproposedtwoschemesrespectively,basedonthedistanceofuser-to-usercommunicationandbetweenuser-to-repeatercommunication,andobtainedtwokindsofresults:

225repeatersand37repeaters.Theformerusesmorerepeaters,buttherearemorechannelsinonecell.Thisschemeissuitableforthecasethatusersaredenseinasub-cell.Whilethelatterusesasmallernumberofrepeaters,butbecausethenumberofrepeatersissmaller,PLscannotbefullyutilized,leadingtofewercommunicationchannelsineachsub-cell.Thiscommunicationsystemcannotservealargenumberofusers.

Toensurethatoverlappingrepeatersdonotinterferewitheachother,weestablishedthefrequencyandPLallocationmodel.ByfrequencyandPLreuse,weincreasethenumberofavailableremotecommunicationchannelsasmanyaspossible.WhensolvingthePLreuseproblem,weproposedtwoschemes:

allocatingonePLtodifferentrepeaterswhohavenooverlappingareaorusedifferentfrequencies,andproposedtheresourceallocationmodelbasedonminimuminterferencedistance.Then,weusethesemodelstosetrepeatersandtoallocateresources,respectively,inthetwocasewith1,000and10,000users.Ourresultsshowthat37repeatersareneededwhenthereare1,000users,while225repeatersareneededwhen10,000users.Intheformerconditions,eachpairofusershave7.3channelsinaveragewhentheycommunicatedirectly;27usersshareachannelinaveragewhenusersinonesub-cellcommunicateviatherepeater;37channelscanbeusedintotalforcell-to-cellcommunications.Inthelattercondition,eachpairofusershas4.3channelsinaveragefordirectcommunications;225channelscanbeuseintotalforcell-to-cellcommunications.

Forthemountainousregion,weneedtoadjustthedistributionofrepeaters:

transferringrepeatersonthefootofmountaintothetop.Thisschemecangreatlyincreasethecommunicationdistance,expandtherepeaters’coverage,andreducethenumberofrepeaters.

Contents

1.Introduction...................................................................................................................................................3

2.ProblemOverviews...................................................................................................................................32.1Ourunderstandingoftheproblem.................................................................................................3

2.2AvailableResourcesandOurTasks.............................................................................................4

3.Analysis…………….........................................................................................................................................4

3.1Thecoverageproblem..........................................................................................................................5

3.2.Resourceassignsmentstorepeaters..............................................................................................5

4.Assumptions.................................................................................................................................................5

5.Establishmentofmodel.........................................................................................................................6

5.1Coveragemodel...................................................................................................................................6

5.1.1Smallcellcoverage....................................................................................................................8

5.1.2Largeregioncoveragemodel.............................................................................................12

5.2.resourceallocationmodel.............................................................................................................13

6.Discussion......................................................................................................................................................17

6.1Thecomparisonoftwodivisionmethods..............................................................................17

6.2InfluencesofMountainsinthecommunicationregion..................................................17

6.3Optimizationof frequencyreuse.............................................................................................19

7.Conclusion...................................................................................................................................................19

7.1Question1.............................................................................................................................................19

7.2Question2..............................................................................................................................................20

7.3Question3..............................................................................................................................................20

8.Evaluation....................................................................................................................................................21

7.1Advantages..........................................................................................................................................21

7.2Limitations............................................................................................................................................21

9.References......................................................................................................................................................21

I.Introduction

Withtherapiddevelopmentofscienceandtechnologies,wirelesscommunicationsplaymoreandmoreimportantroleinhumanbeingdailylife.Becauseofthis,allthecountriesinworld,whethertheyaredevelopedordevelopingnations,havebeendevotedgreatamountsofattentionstotheconstructionofefficientandeconomicalcommunicationmanners.However,therearemanychallengesinachievingmoreeffectivecommunicationwithlimitedresources,sincemoderncommunicationsystemsarequitemoney-consuming.Thus,tradeoffsmustbemadeamonglimitedresourcestogetanoptimalsolution.Especially,therehavebeenquitefewfrequencyresourceleftforustouse.Inadditiontothenarrowfrequencyband,theseparationbetweenoperatingfrequenciesoftwodevicesmustbelargeenough,whichfurtherincreasesthedifficultyweareconfrontedwith.Inordertoachieveeffectivecommunicationswithinnarrowfrequencyband,othertechnologieshavetobeintroduced.

Ofthesechallenges,extendingtheeffectivecommunicationextentisoneofthemostimportantones.Inpractice,theuser’stransmittingpowerisquitelow,whichmeansshortworkingradiusoftheuser.Toextendtheeffectiveworkingradius,astraightforwardmethodistoamplifytheweaksignalstransmittedbyusersbyhigh-powerdevicesandthenretransmittedthem.Thisistheverytaskthatarepeaterdoes.Tobespecific,arepeaterpicksupweaksignals,amplifiesthemandthenretransmitsthemonadifferentfrequency.So,repeatersplayimportantrolesinrealizingefficientandeconomicalwirelesscommunications.However,repeatersalonearefarfromenoughtosolveourproblem.Duetolimitedavailablefrequencyresource,repeatersarepronetointerferewithoneanother.Tofurtherovercomethisproblem,theprivateline（PL）technologyisproposedbyassigningaspecificsub-audibletonetoeachrepeater.Inthisway,twophysicallycloserepeaterscanworkeffectivelyunderthesamefrequencypair,withoutinter-repeaterinterferences.

Byproperlyassigningthenarrow-bandfrequencyresourceplusalimitednumberofprivatelines,anoptimalcommunicationsystem,whichusesminimalresourcestoservemaximaluser,canbeachievedtosavethecost.Inthispaper,wearetryingourbest,withourlimitedknowledge,toinvestigatetheconstructionofanoptimizedcommunicationnetworkinagivenareabyproperlyassigningavailableresources.

II.ProblemOverviews

2.1ourunderstandingoftheproblem

User-to-usercommunicationdistanceislimitedbyusers’transmitterpower.Communicationcannotgoonoveralongdistance.Fortunately,repeaters,withmuchhigherpower,areintroducedtohelpremoteuserscommunicatewitheachotherbyamplifyingandretransmittingsignals.Repeatersareneededtoenlargethesignalcoveragearea.But,mutualinterferencemaybecausedbecausetherewillberepeatercoveragesuperpositionand/orretransmittedsignalsonthesamefrequencyasthenumberofrepeaterincreases.Ones