[time-nuts] Fundamental limits on performance

Hal Murray hmurray at megapathdsl.net
Sun Sep 13 20:45:11 UTC 2009

james.p.lux at jpl.nasa.gov said:
>> Do you want time or frequency?
> Both, of course <grin>.. Frequency is probably a better place to
> start, but time is important too. 

Heisenberg gets involved.

The Radar guys call it range-velocity ambiguity.  To get accurate range you 
need good Doppler which means a narrow bandwidth on the filter which means 
you don't know when the pulse returned.  You can't get rid of it.  The 
schemes that claim to so only push some of the ambiguity to some place where 
you can reject it by other means.

> That's more of a practical detail.. The more basic question is, if I
> transmit a signal through a channel with some SNR, what is the best
> one can possibly do for frequency transfer (or time knowledge). 

I still think the Allan intercept is a critical idea.

Suppose you send 10 bits of information through your channel.  If you know 
the local clock within 1 Hz, then 10 bits will give you the frequency to 
within 0.001 Hz.  If you know the local clock to within 1E-6 then 10 bits 
will get you to 1E-9.

If you collect data for twice as long, you get 20 bits.  If you know your 
local clock within 1E-6, 20 bits should get you to 1E-12.  Somewhere in there 
that stops making sense.  You don't know "the" frequency but rather the 
average over the measurement period, or something like that.

The math or way-of-thinking about undersampling A/Ds may be helpful.

These are my opinions, not necessarily my employer's.  I hate spam.

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