# [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

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：

© 2018 COMAP, The Consortium for Mathematics and Its Applications
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Mathematical Modelling and Statistical Modelling Forum

http://blog.sciencenet.cn/blog-752541-1099097.html

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