[time-nuts] Fundamental limits on performance

Lux, Jim (337C) james.p.lux at jpl.nasa.gov
Sun Sep 13 16:14:52 UTC 2009

On 9/12/09 10:49 PM, "Hal Murray" <hmurray at megapathdsl.net> wrote:

>> In the deep space exploration biz, we've been talking about time and
>> frequency transfer between spacecraft. It's pretty easy to figure out
>> what the "Shannon limit" for the link between the spacecraft is (given
>> power transmitted, antenna gain, etc... And with coding, we get within
>> tenths, if not hundredths of a dB of the limit)...
>> So, if I have a clock of some performance on Spacecraft A, is there a
>> "simple" way to say how well I can do transfering that to Spacecraft
>> B?
> Do you want time or frequency?

Both, of course <grin>.. Frequency is probably a better place to start, but
time is important too.

> I don't think it's going to be simple.

That's for sure

> As part of demodulating the data stream, you end up with a receive clock.
> That's got noise from the communication channel added to the (probably tiny)
> noise from the transmit clock.  You can filter out the channel noise.  The
> longer you filter (narrower bandwidth) the better the recovered clock will be.

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 suppose one could just consider it as an incremental addition of noise, as
if it were an amplifier in a distribution chain, with the added complexities
of things like doppler, relativity, etc.

It's true that doppler, relativitistic effects, etc, can be modeled-out  to
a certain extent; however, it's deviations from the model that, sometimes,
is the science observation you're trying to make. (e.g. Measuring gravity
waves by looking at propagation of Ka-band signals through interplanetary

> I think what you are looking for is the Allan intercept: the crossover point
> between the noise from your (filtered) received clock and the long term drift
> of the local clock.

Or, what are the noise properties of that received clock...

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