[time-nuts] Pre-averaging Phase Data

[Anders Wallin]

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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