美赛论文模板1.doc

PAGE Team Control Number For office use only 0000 For office use only T1 F1 T2 F2 T3 Problem Chosen F3 T4 A F4 2014 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Repeaters Coordination And Distribution February 6,2015 Abstract 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. 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,