美赛论文模板.doc

.Team Control NumberFor office use only0000For office use onlyT1F1T2F2T3Problem ChosenF3T4AF42014 Mathematical Contest in Modeling (MCM) Summary Sheet(Attach a copy of this page to each copy of your solution paper.)Repeaters Coordination And DistributionFebruary 6,2015AbstractIn 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.Question one : 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: 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:The minimum number of repeaters necessary to accommodate 1,000 simultaneous users is 36. Question Two : How does your solution change if there are 10,000 users?Answer: 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 usersConclusion:The minimum number of repeaters necessary to accommodate 10,000 simultaneous users is 126. Question Three : Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.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 caused by obstacles and the eligible coverage radius for repeater is , 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. Key words: Cellular Coverage technology, frequency attenuation expression, channel allocation, Matlab;.Repeaters coordination and distributionContent1 Restatement of the Problem11.1 Introduction11.2 The Problem12 Simplifying Assumption13 Phrase explain14 Model14.1 Model I14.1.1 Analysis of the Problem14.1.2 Model Design25 Sensitivity analysis26 Model extension27 Evaluating our model27.1 The strengths of model27.2 The weaknesses of model2References3.1 Restatement of the Problem1.1 IntroductionThe 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.1.2 The ProblemYour job is to:u 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.u Change your scheme to accommodate 1,0000 simultaneous users base on your model.u Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.2 Simplifying Assumption3 Phrase explain4 Model4.1 Model I4.1.1 Analysis of the Problem4.1.2 Model Design5 Sensitivity analysis Symbolu : the number of total