1、Team Control NumberFor office use only For office use onlyT1 F1T2 0000 F2T3 Problem Chosen F3T4 F4A2014 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
2、 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
3、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
4、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 fi
5、gured 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 feature
6、s.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
7、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 wil
8、l 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
9、. 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 accommod
10、ate 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 relations
11、hip between radio attenuation x caused by obstacles and the eligible coverage radius d for repeater is 249.35710xd, 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 repeat
12、ers 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
13、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, MatlabRepeaters coordination and distributionContent1 Restatement of the Problem11.1 Introduction.
14、11.2 The Problem 12 Simplifying Assumption 13 Phrase explain 14 Model.14.1 Model I 14.1.1 Analysis of the Problem.14.1.2 Model Design.25 Sensitivity analysis .26 Model extension27 Evaluating our model 27.1 The strengths of model .27.2 The weaknesses of model2References3Team #9449 Page 1 of 41 Restat
15、ement 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 mobil
16、e 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: Design a scheme that
17、 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 freq
18、uency, 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 Simplifying Assumption3 Phrase explain4 Model4.1 Model I4.1.1
19、 Analysis of the ProblemTeam #9449 Page 2 of 44.1.2 Model Design5 Sensitivity analysis Symbol N: the number of total repeaters in the circle area Q: the number of the users in the circle area k: the number of the red circle in figure 2最前面最好有一个 Symbol List6 Model extension7 Evaluating our model7.1 The strengths of model 7.2 The weaknesses of model Team #9449 Page 3 of 4References参考文献不要引用非常差的期刊的论文，要引用比较厉害的英文期刊，证明你有足够的阅读文献量。
