Tim Lee

Radio Propagation and Frequency

I’m finally reading Cato’s 2006 Policy Analysis on spectrum property rights. It’s got a lot of good information, but this sentence made me do a double-take:

In free space, radio waves steadily weaken in a very uniform, predictable way and at a rate that depends on frequency. In particular, the higher the frequency, the faster the waves weaken. In the real world—on the earth and in its environs—the situation is much more complicated, and radio links are affected by the earth itself, the atmosphere, and the intervening topography and natural and manmade objects such as foliage and buildings.

It’s been a while since I took physics, but I seem to recall (and Wikipedia seems to agree) that the strength of an electromagnetic wave falls with the square of the distance from the source. Indeed, this result seems to be compelled by the geometry of the situation and the conservation of energy. What am I missing?

Assuming I’m not just confused, one possibility is that they’re talking about propagation in the atmosphere rather than free space. It appears to be true that lower-frequency radio waves travel further along the surface of the Earth because they are affected more by the Earth’s atmosphere.

July 31, 2008 | Comments |

Viewing 6 Comments

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    You're right. The effect of the inverse square law on radio waves, geometric spreading, is not dependent on frequency. In the atmosphere, however, there is an additional effect called "attenuation" that is frequency-dependent. See your favorite reference source for attenuation:

    Attenuation decreases the intensity of electromagnetic radiation due to absorption or scattering of photons. Attenuation does not include the decrease in intensity due to inverse-square law geometric spreading. Therefore, calculation of the total change in intensity involves both the inverse-square law and an estimation of attenuation over the path.

    The primary causes of attenuation in matter are the photoelectric effect, compton scattering and, for photon energies of above 1.022MeV, pair production.


    So what happens is this: in free space, radio waves spread in a uniform pattern over distance. In the atmosphere, this effect is compounded by the absorption of radio waves by water particles and the dispersion by dust and over teensy things in the air.

    The Cato passage is a bit ambiguous because the term "free space" has different meanings, which God's Encyclopedia also explains. The patent office defines it the way Cato does - an unobstructed path through the atmosphere - but physics defines it as the perfect vacuum that doesn't actually exist in nature.
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    It should also be said that, at low frequencies, the ionosphere can either absorb or reflect radio signals. This varies, with the ionosphere being more reflective at night (hence, FCC rules about AM stations and the traditional "clear channel" regulations).

    It also makes for nutty behavior during sun spots, which makes amateur radio operators get really excited because they can "DX" far-away stations. These spots follow a rough cycle. I can't wait until 2012!

    Also, "attenuation" in the broad sense of the word, does happen due to topography (lower frequencies pass more easily through trees and walls). That's why the 700 MHz frequencies were so highly valued.

    At least we can agree on science.
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    My radio experts tell me that millimeter wave is better for Internet access than the 700 MHz stuff. Millimeter wave is 30-300 GHz, highly directional, and doesn't propagate too far, so you can re-use the frequencies without interference. It also makes a cool weapon in the 94 GHz range.

    The trouble with 700 Meg is that it covers such large area you aren't going to get good throughput; too many users, not enough time.
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    The CATO report acknowledges "However, defining rights to use spectrum is far more difficult than ordinarily suggested." and I have been expressing this for the past two years when there have been discussions on spectrum privatization. While, one can establish on paper so-called property lines for the spectrum, the physical reality is that radio waves simply don't respect property lines. Creating paper property boundaries for the spectrum will mean that the lawyers will have a field day with filing "infringing" lawsuits.

    If the spectrum were privatized (given the complexity of managing the spectrum) I predict that we would see the owners of the spectrum joining together to form an industry association that would be functionally identical to the FCC. I also bet that this hypothetical association would be even more "abusive" than the existing FCC. Given the choice of a private FCC or a government FCC, I would take the government one. Privatization of the spectrum will be a major mistake.

    On less than 100 watts of power, as an amateur radio operator, I have been able on 20 meters using a dipole (a very simple antenna) to talk from North Carolina to stations as far away as the Galapagos Islands and Macedonia. Other amateur radio operators, who have more experience than I, have done much better.
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    Several factors other than the r-squared law come into play when you send a wireless signal. The two most important are as follows. Firstly, there's atmospheric attenuation; the air absorbs some of the signal. Secondly, there's interference. The farther you are from the transmitter, the more noise your antenna will pick up trying to receive the signal from it. These, plus some other technical factors, can be compensated for by using an exponent larger than 2. A good rule of thumb for microwave transmission is to use an exponent of 3.5.
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    I finally had the time to read "Toward Property Rights in Spectrum The Difficult Policy Choices Ahead"by Dale Hatfield and Phil Weiser. It was a good read and I am pleased that they had not taken the extreme privatization position that I feared. They also did a very good job explaining how it would be difficult to establish a property right anyway. Essentially, the article is promoting the concept that spectrum leaseholders should have greater "rights" in their leases and that we need to have the FCC guided by market forces.

    Though I may not totally agree with Hatfield and Weiser, I have no philosophical objection to what they are proposing.

    As an aside, from an absolutist private property viewpoint, the spectrum laying above a piece of private property would belong to the surface property owner. The selling of spectrum rights would actually be depriving the surface property owner of some of his property rights. In fact, the surface property owner should be entitled to compensation for any radio waves that trespass through his property. Obviously this would put a crimp in the telecommunications business.

    My point with the absurd statement above is that there are rationale limits to the concept of private property as some monolithic unalienable right and that at a certain, though undefined, point some property belongs in the public domain.

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