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精品文档 1欢迎下载1欢迎下载1欢迎下载1欢迎下载 Team Control Number For office use onlyFor office use only T1F1 T2 00000000 F2 T3Problem ChosenF3 T4F4 A A 20142014 MathematicalMathematical ContestContest inin ModelingModeling MCM MCM SummarySummary SheetSheet Attach a copy of this page to each copy of your solution paper RepeatersRepeaters CoordinationCoordination AndAnd DistributionDistribution FebruaryFebruary 6 20156 2015 AbstractAbstract In this paper it aims to computing problem on Relay Strategy repeaters coordination and distribution According to advanced radio cellular coverage technology usage of frequency attenuation and geometric mapping methods Hata model cellular coverage solution and FDM Frequency Division Multiplexing model were established The algorithms used MATLAB to simulate with the final modeling results of sensitivity analysis and improvement promotion on models QuestionQuestion oneone For a circular flat area of radius 40 miles radius determine the minimum number of repeaters necessary to accommodate 1 000 simultaneous users Assume that the spectrum available is 145 to 148 MHz the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency and there are 54 different PL tones available Answer Answer 1 Based on Frequency attenuation expression and calculation with MATLAB it figured out the eligible coverage radiuses which are 30km for BS base station and 14 9km for repeater 2 Assuming the users in a given area under uniform distribution using advanced cellular coverage solution we can calculate that minimum number of required repeater is 36 under cellular features 3 Based on the US VHF spectrum allocation standard the minimum spacing for adjacent channels is 30kHz And with up to 54 different PL tones maximum 4320 channels can be allocated to provide 1000 simultaneous users to use at the same time Conclusion Conclusion The minimum number of repeaters necessary to accommodate 1 000 simultaneous users is 36 QuestionQuestion TwoTwo How does your solution change if there are 10 000 users Answer Answer 精品文档 2欢迎下载2欢迎下载2欢迎下载2欢迎下载 1 Since the given spectrum is in a fixed range even if 54 different PL tones can not be allocated enough channels for 10 000 simultaneous users So the number of repeaters will be increased meanwhile the given area will be divided into different parts 2 On the assumption that uniform distribution of the population in the given area it will be divided into 3 sub regions equally by analyzing the binding domain frequency spectrum and PL tones three independent factors And then the number of repeaters within each sub region will be classified discussion 3 The FDM Frequency Division Multiplexing model is established here to improve channel efficiency to accommodate up to 10 000 simultaneous users Conclusion Conclusion The minimum number of repeaters necessary to accommodate 10 000 simultaneous users is 126 QuestionQuestion ThreeThree Discuss the case where there might be defects in line of sight propagation caused by mountainous areas Answer Answer Basically under the same condition for question 1 2 the mountainous area will be analyzed as following 1 The function for relationship between radio attenuation x caused by obstacles and the eligible coverage radius d for repeater is 2249 35 4371 41 10 x d which is to analyze the impact on the number of repeaters under full signal coverage 2 For the mountain barrier based on the different situation of mountains the addition of repeaters on the suitable location will be discussed to achieve full coverage This paper describes model established by using of cellular coverage technology and frequency attenuation expression to achieve simple fast accurate algorithm And also illustrated the effect takes the entire article In the end the sensitivity analysis and error calculation are applied for modeling making the model practically KeyKey words words Cellular Coverage technology frequency attenuation expression channel allocation Matlab 精品文档 3欢迎下载3欢迎下载3欢迎下载3欢迎下载 RepeatersRepeaters coordinationcoordination andand distributiondistribution ContentContent 1 1 RestatementRestatement ofof thethe ProblemProblem 1 1 11 1 IntroductionIntroduction 1 1 21 2 TheThe ProblemProblem 1 2 2 SimplifyingSimplifying AssumptionAssumption 1 3 3 PhrasePhrase explainexplain 1 4 4 ModelModel 1 4 14 1 ModelModel I I 1 4 1 1 Analysis of the Problem 1 4 1 2 Model Design 2 5 5 SensitivitySensitivity analysisanalysis 2 6 6 ModelModel extensionextension 2 7 7 EvaluatingEvaluating ourour modelmodel 2 7 17 1 TheThe strengthsstrengths ofof modelmodel 2 7 27 2 TheThe weaknessesweaknesses ofof modelmodel 2 ReferencesReferences 3 精品文档 1欢迎下载1欢迎下载1欢迎下载1欢迎下载 1 1 RestatementRestatement ofof thethe ProblemProblem 1 11 1 IntroductionIntroduction The VHF radio spectrum involves line of sight transmission and reception This limitation can be overcome by repeaters which pick up weak signals amplify them and retransmit them on a different frequency Thus using a repeater low power users such as mobile stations can communicate with one another in situations where direct user to user contact would not be possible However repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies 1 21 2 TheThe ProblemProblem Your job is to Design a scheme that determines the minimum number of repeaters necessary to accommodate 1 000 simultaneous users in a circular flat area of radius 40 miles radius And assume that the spectrum available is 145 to 148 MHz the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency and there are 54 different PL tones available Change your scheme to accommodate 1 0000 simultaneous users base on your model Discuss the case where there might be defects in line of sight propagation caused by mountainous areas 2 2 SimplifyingSimplifying AssumptionAssumption 3 3 PhrasePhrase explainexplain 精品文档 2欢迎下载2欢迎下载2欢迎下载2欢迎下载 4 4 ModelModel 4 14 1 ModelModel I I 4 1 14 1