数学建模美赛论文.docx

1、数学建模美赛论文Repeater Coordination: Achieving communications with the fewest repeatersSummeryLimited by the transmission characteristics of VHF radio spectrum, users far away from each other cannot communicate with one another. In general, it is through repeaters that the communication distance can be in

2、creased. However, with the increase of repeaters, mutual interference appears in the overlapping area of repeaters using the same frequency. Solution to this problem is to use different frequencies or adopt CTCSS technology. But due to the bandwidth limitations and the restriction on the number of P

3、Ls, the resources allocated to repeaters are limited, which is a challenge to the repeaters configuration and to resource allocation. Therefore, with the aim to solve this problem, we established mathematical models with the aim the finish the following three tasks.For the given region, we establish

4、ed the optimal coverage model to guarantee that all users have enough communication channels and to minimize the number of cells that are needed to cover the given region completely. In the case of cell radius determination, we proposed two schemes respectively, based on the distance of user-to-user

5、 communication and between user-to-repeater communication, and obtained two kinds of results: 225 repeaters and 37 repeaters. The former uses more repeaters, but there are more channels in one cell. This scheme is suitable for the case that users are dense in a sub-cell. While the latter uses a smal

6、ler number of repeaters, but because the number of repeaters is smaller, PLs cannot be fully utilized, leading to fewer communication channels in each sub-cell. This communication system cannot serve a large number of users.To ensure that overlapping repeaters do not interfere with each other, we es

7、tablished the frequency and PL allocation model. By frequency and PL reuse, we increase the number of available remote communication channels as many as possible. When solving the PL reuse problem, we proposed two schemes: allocating one PL to different repeaters who have no overlapping area or use

8、different frequencies, and proposed the resource allocation model based on minimum interference distance. Then, we use these models to set repeaters and to allocate resources, respectively, in the two case with 1,000 and 10,000 users. Our results show that 37 repeaters are needed when there are 1,00

9、0 users, while 225 repeaters are needed when 10,000 users. In the former conditions, each pair of users have 7.3 channels in average when they communicate directly; 27 users share a channel in average when users in one sub-cell communicate via the repeater; 37 channels can be used in total for cell-

10、to-cell communications. In the latter condition, each pair of users has 4.3 channels in average for direct communications; 225 channels can be use in total for cell-to-cell communications.For the mountainous region, we need to adjust the distribution of repeaters: transferring repeaters on the foot

11、of mountain to the top. This scheme can greatly increase the communication distance, expand the repeaters coverage, and reduce the number of repeaters.Contents1. Introduction.3 2. Problem Overviews.3 2.1 Our understanding of the problem .32.2 Available Resources and Our Tasks.4 3. Analysis.43.1 The

12、coverage problem.53.2. Resource assignsments to repeaters.5 4. Assumptions.5 5. Establishment of model .6 5.1 Coverage model.65.1.1 Small cell coverage.85.1.2 Large region coverage model.12 5.2. resource allocation model.136. Discussion.176.1 The comparison of two division methods.17 6.2 Influences

13、of Mountains in the communication region.17 6.3 Optimization offrequency reuse. 197. Conclusion. 19 7.1 Question 1.19 7.2 Question 2.207.3 Question 3.208. Evaluation.217.1 Advantages.21 7.2 Limitations.219.References.21I. IntroductionWith the rapid development of science and technologies, wireless c

14、ommunications play more and more important role in human being daily life. Because of this, all the countries in world, whether they are developed or developing nations, have been devoted great amounts of attentions to the construction of efficient and economical communication manners. However, ther

15、e are many challenges in achieving more effective communication with limited resources, since modern communication systems are quite money-consuming. Thus, tradeoffs must be made among limited resources to get an optimal solution. Especially, there have been quite few frequency resource left for us

16、to use. In addition to the narrow frequency band, the separation between operating frequencies of two devices must be large enough, which further increases the difficulty we are confronted with. In order to achieve effective communications within narrow frequency band, other technologies have to be

17、introduced. Of these challenges, extending the effective communication extent is one of the most important ones. In practice, the users transmitting power is quite low, which means short working radius of the user. To extend the effective working radius, a straightforward method is to amplify the we

18、ak signals transmitted by users by high-power devices and then retransmitted them. This is the very task that a repeater does. To be specific, a repeater picks up weak signals, amplifies them and then retransmits them on a different frequency. So, repeaters play important roles in realizing efficien

19、t and economical wireless communications. However, repeaters alone are far from enough to solve our problem. Due to limited available frequency resource, repeaters are prone to interfere with one another. To further overcome this problem, the private line (PL) technology is proposed by assigning a s

20、pecific sub-audible tone to each repeater. In this way, two physically close repeaters can work effectively under the same frequency pair, without inter-repeater interferences. By properly assigning the narrow-band frequency resource plus a limited number of private lines, an optimal communication s

21、ystem, which uses minimal resources to serve maximal user, can be achieved to save the cost. In this paper, we are trying our best, with our limited knowledge, to investigate the construction of an optimized communication network in a given area by properly assigning available resources. II. Problem

22、 Overviews2.1 our understanding of the problemUser-to-user communication distance is limited by users transmitter power. Communication cannot go on over a long distance. Fortunately, repeaters, with much higher power, are introduced to help remote users communicate with each other by amplifying and retransmitting signals. Repeaters are needed to enlarge the signal coverage area. But, mutual interference may be caused because there will be repeater coverage superposition and/or retransmitted signals on the same frequency as the number of repeater increases. One s