[opendtv] Re: The "real" problem with OFDM in the U.S.
- From: Henry Baker <hbaker1@xxxxxxxxxxxx>
- To: Tom Barry <trbarry@xxxxxxxxxxx>
- Date: Mon, 21 Mar 2005 15:57:28 -0800
Tom:
The answer is that the boundaries are not only not sharp, they are the
worst possible configuration from a mathematical point of view -- they're
almost fractal. The other problem is that the boundary is time-varying,
and can change dramatically with the fall of a leaf, a drop of rain, a
passing car, an updraft of warm air, etc. If you are on the edge between
two cells, even a few millimeters of movement can change you back and forth
between two cells, even though you are moving at a constant speed in the
same direction. Depending upon the environment, you can also get varying
polarizations, so the signals can cancel out or reinforce.
Those beautiful hexagonal cells that the cellular companies used to
show to Congress and others are a figment of someone's imagination --
actual measurements are infinitely more complex.
For these reasons, frequency "reuse" is much more complex than a map-coloring
problem.
(For the record, the 4-color theorem only works for "simply-connected" regions,
which the edges of frequency regions are _not_.)
At 06:03 AM 3/21/2005, Tom Barry wrote:
>When we cannot share the same channel across the country (usually) then
>we must have boundaries. And if we can't have very sharp boundaries
>then I guess we have to assume adjacent market areas can't use the same
>channel.
>
>This sounds sort of like a map coloring problem. I think it has finally
>been proven that any arbitrary map can be colored with only 4 different
>colors. A simplified view of equal sized market areas with no political
>gerrymandering would then suggest that 3/4 of the spectrum then would be
>unusable because of adjacent areas, which seems like a waste. I suppose
>that a carefully layed out grid of hexagons across the country could do
>it wasting only 2/3 of the spectrum but that still doesn't seem very
>good. And of course I'm ignoring all those subtleties of population
>density, terrain, etc.
>
>It's a thorny problem I hadn't really thought about much before. Seems
>like there should be a better way.
>
>How sharp can these boundaries be anyway?
>
>- Tom
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