[time-nuts] Timing over low bandwidth channels

[Magnus Danielson]

On 12/09/2010 03:16 PM, jimlux wrote:
> Hal Murray wrote:
>>> If you can indeed track a 1W signal from ~ Colorado, there might
>>> indeed be
>>> some timing use for the system.
>>
>> I have a start at understanding how much data you can get through a
>> channel. There is a tradeoff between data rate and error rate and it
>> depends on the signal/noise ratio.
>
> That's the Shannon bound.. (or Shannon-Hartley)..
> C = B*log2(1+S/N)
>
> You can get pretty darn close (hundredths of a dB) to this limit with
> coding.
>
>>
>> Is there a similar sort of high level picture about sending timing
>> info? I'm not even sure what the units are.
>>
>
> That's a bit trickier to conceptualize... In the data bit case, you can
> work at the "one bit" scale.. and say something about the probability
> that the bit is wrong. ANd, you can combine multiple bits and drive the
> probability of an error over all those bits combined down.
>
> But for "time" or "frequency" it's a bit trickier. You have to specify
> the time scale over which you're interested (I suppose that relates to
> the bandwidth in the Shannon formula). But more to the point, in digital
> communications there's a clear "two-state" thing..either the bit is
> correct or it's not. Time/Frequency has "degrees of wrongness"

Which is the reason you look a bit wider on Shannon's work and not use 
the oversimplified model of above. Shannon's article(s) cover both 
analog and digital transmissions. The bandwidth you use for your signal 
will be the bandwidth you toss into the formula, where spread spectrum 
helps to confuse the issue. The time and frequency reception is not all 
that strange. The analysis is done fairly deeply for GPS, where a 40 W 
transmission provides timing for 1/3 of the earth surface area some 
26000 km away or so.

Cheers,
Magnus