[time-nuts] Pre-averaging Phase Data

[Simon Lewis]

@Bob and @Poul-Henning Thanks for the input guys! This was my understanding
too, which was the confusion.

@Anders Wallin <anders.e.e.wallin at gmail.com> Thank you, this is exactly
what I was looking for. You're actually the one that introduced me to these
SDR measurements.
So in essence we are reducing the sampled bandwidth (similar to MDEV
without the LPF), under the assumption that the noise is predominantly
white below ~1s.
Based on the phase spectrum of the dual channel measurements in the paper,
the 1/f noise starts at about ~100Hz. Wouldn't the limit of averaging be up
to the flicker corner (~10ms averages)? Granted that the flicker noise is
quite low due to the common-mode channel cancellation.

Thanks again,
Simon

On Tue, May 5, 2020 at 7:29 AM Anders Wallin <anders.e.e.wallin at gmail.com>
wrote:

> Hi Simon, you can play around with different averaging ideas with e.g.
> allantools (or some other adev-library). The script for the attached image
> is here: https://gist.github.com/aewallin/a10966ac50846e264ca3ee97f2e0d832
> (the script also plots time-series, PSDs, and histograms, which might
> illustrate things)
>
> For an SDR-based phase-meter the key point is not that the individual
> sampled I/Q measurements would be superbly good (at femtosecond level) but
> that there are lots and lots of samples sampled quickly with some
> reasonable noise.
> If you just compute ADEV/MDEV from the raw high-bandwidth data it will
> average down, but not as far as we want.
> For white phase-noise downsampling (and reducing the bandwidth) by two
> decades reduces the 1-sample ADEV by one decade.
> The 'process gain' for an SDR thus comes from bandwidth-reduction by e.g.
> 6-decades and gives an ADEV-reduction of 3-decades. This is shown in the
> image below where at tau=1s the raw simulated data is at 2e-12, and after
> 6-decades of downsampling we are at 2e-15.
>
> In practice the challenge is to find an SDR that truly has white
> phase-noise also at low (1Hz) offset from the carrier. Usually there is an
> 1/f shape towards zero frequency. The averaging trick stops working at some
> point, and with the mentioned N210 radio we have not seen 1s ADEVs below
> 1e-14 (IIRC). The 2e-12/tau level for 1MS/s should be roughly right for an
> N210 fed with two 10MHz signals (again, IIRC).
>
> hope this helps,
> Anders
>
> [image: SDR_phasenoise_Figure_2.png]
>
> On Sat, May 2, 2020 at 4:22 PM Simon Lewis <siaclewis at gmail.com> wrote:
>
> > Hi all,
> >
> > I have a fairly newbie question on averaging of phase data, prior to
> ADEV.
> >
> > In a paper by Sherman and Jordens (https://arxiv.org/pdf/1605.03505.pdf)
> > on
> > oscillator metrology using SDR (Ettus N210), for long term measurements
> (1
> > tau up) the group estimates an average phase to reduce the data volume.
> > They use both a novel lower-bound variance estimate, and what I assume
> was
> > a rectangular average of N samples per second (original data rate was
> > 1Msamples/s). Both apparently provided similar results.
> >
> > From what I've read/tried to understand, pre-averaging phase isn't
> > practically a good idea, considering the ADEV natively does this, and you
> > end up with a lower estimate than reality. They state that time interval
> > counters effectively do this for frequency measurements.
> >
> > I know that one can do this with caveats, and in essence this is what
> MDEV
> > does (I believe?), but is it not more 'real' to just downsample the phase
> > data? That is, drop N-1 samples per second (not decimating which would
> > filter the higher order components), and then ADEV the downsampled data.
> > I'm sure I'm missing some understanding here!
> >
> > Thanks,
> > Simon
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