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[转载]2018美国数学建模MCM A题(连续型)翻译 多跳HF无线电传播

已有 5791 次阅读 2018-2-9 09:51 |系统分类:博客资讯|文章来源:转载

PROBLEM A: Multi-hop HF Radio Propagation

Background: On high frequencies (HF, defined to be 3 – 30 mHz), radio waves can travel long

distances (from one point on the earth’s surface to another distant point on the earth’s surface) by

multiple reflections off the ionosphere and off the earth. For frequencies below the maximum

usable frequency (MUF), HF radio waves from a ground source reflect off the ionosphere back

to the earth, where they may reflect again back to the ionosphere, where they may reflect again

back to the earth, and so on, travelling further with each successive hop. Among other factors,

the characteristics of the reflecting surface determine the strength of the reflected wave and how

far the signal will ultimately travel while maintaining useful signal integrity. Also, the MUF

varies with the season, time of day, and solar conditions. Frequencies above the MUF are not

reflected/refracted, but pass through the ionosphere into space. In this problem, the focus is

particularly on reflections off the ocean surface. It has been found empirically that reflections off

a turbulent ocean are attenuated more than reflections off a calm ocean. Ocean turbulence will

affect the electromagnetic gradient of seawater, altering the local permittivity and permeability

of the ocean, and changing the height and angle of the reflection surface. A turbulent ocean is

one in which wave heights, shapes, and frequencies change rapidly, and the direction of wave

travel may also change.

Problem:

Part I: Develop a mathematical model for this signal reflection off the ocean. For a 100-watt HF

constant-carrier signal, below the MUF, from a point source on land, determine the strength of

the first reflection off a turbulent ocean and compare it with the strength of a first reflection off a

calm ocean. (Note that this means that there has been one reflection of this signal off the

ionosphere.) If additional reflections (2 through n) take place off calm oceans, what is the

maximum number of hops the signal can take before its strength falls below a usable signal-tonoise

ratio (SNR) threshold of 10 dB?

Part II: How do your findings from Part I compare with HF reflections off mountainous or

rugged terrain versus smooth terrain?

Part III: A ship travelling across the ocean will use HF for communications and to receive

weather and traffic reports. How does your model change to accommodate a shipboard receiver

moving on a turbulent ocean? How long can the ship remain in communication using the same

multi-hop path?

Part IV: Prepare a short (1 to 2 pages) synopsis of your results suitable for publication as a short

note in IEEE Communications Magazine.

Your submission should consist of:

 One-page Summary Sheet,

 Two-page synopsis,

 Your solution of no more than 20 pages, for a maximum of 23 pages with your summary

and synopsis.

 Note: Reference list and any appendices do not count toward the 23-page limit and

should appear after your completed solution.



A题中文翻译:

问题A:多跳HF无线电传播

在高频(HF,定义为3-30 mHz)区域,通过电离层和地球外的多重

反射,无线电波可以传输较远距离(从地球表面上的一个点到地球表

面上另一个遥远的点)。对于低于最大值(MUF)的可用频率,来自

地面源的HF 无线电波通过电离层反射到地球,在那里他们可能再次

反射回电离层,或许也可能会再次反映回到地球上,等等,每一个连

续的跳跃都会使得电波传输的更远。除其他因素外,反射面的特性决

定反射波的强度以及在保证有用信号完整性的同时如何最大程度的

传输信号。另外,MUF(最大可用频率)随季节、一天中的时间及太

阳能条件而变化。高于MUF 的频率不会反射/折射,而是穿过电离层

进入太空。在本问题上,重点关注在海洋表面的电波反射。根据经验

性发现,在动荡海域表面电波的反射衰减程度会比平静海域大很多。

海洋湍流会影响海水的电磁梯度,改变海洋的局部介电常数和渗透率,

并改变反射面的高度和角度。动荡海洋表面的波高、形状和频率迅速

变化,且波浪的运动方向也可能改变。

问题:

第一部分:为通过海洋表层反射的信号建立一个数学模型。 对于一

个100 瓦的HF 恒定载波信号,其值低于MUF,从陆地上的一个点

源,确定在动荡海域的首次反射强度,并将其与在平静海域的第一次

反射强度相比较。(请注意,这意味着这个信号的有一个反射会从电

离层进行。)如果从平静的海洋发生附加的反射(2 到n),在其强度

低于可用信噪比(SNR)阈值10 dB 之前该信号所能采取的最大跳数

为多少?

第二部分:第一部分的研究结果如何与通过山区的HF 反射进行比较?

或者崎岖的地形与光滑的地形之间如何比较呢?

第三部分:在海上旅行的船舶将使用HF 进行通信、接收天气及交通

报告。你的模型如何改变,以适应在动荡的海洋上移动的船上接收器?

当使用多跳路径时,船还能保持联系多久?

第四部分:准备一份简短的(1 到2 页)结果摘要以方便在IEEE 通

信杂志上出版。


您的MCM提交应包括三个要素:标准的1页MCM摘要表,1-2页简要评估报告(要求1)和您的主要MCM解决方案(要求2)不超过20页,最多提交23页面。注意:您加入的任何附录或参考页面不会计入23页的上限。


© 2018 COMAP, The Consortium for Mathematics and Its Applications
May be reproduced for academic/research purposes
For More information on COMAP and this project visit
http://www.comap.com


更多美赛赛题资料、参考文献见

数学建模与统计建模论坛http://www.mathsccnu.com/forum.php

Mathematical Modelling and Statistical Modelling Forum

美赛板块
http://www.mathsccnu.com/forum.php?mod=forumdisplay&fid=41




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