## Update on the QO-100 local oscillator wiggles

This post is a follow up to my study of the “wiggles” observed in the local oscillator of the QO-100 NB transponder. After writing that post, I have continued measuring the frequency of the BPSK beacon with my station almost without interruptions. Now I have some 44 days of measurements, spanning from April 9 to May 23. This data can be interesting to look at, so I’m doing this short post to share the data and look at it briefly.

The Jupyter notebook with all the data can be found here. The data is also linked in my jupyter_notebooks Github repository, which now uses git-annex to store the data in my home server. See the README for instructions on how to download some or all of the data files in the repository.

The whole time series can be seen in the figure below. We note that the typical Doppler sinusoidal curve varies slowly due to orbit perturbations and sometimes suddenly as a consequence of a station-keeping manoeuvre. I tweeted about one of the manoeuvres a while back.

There are now too many days in order to see things clearly when the frequency curves for each day are overlaid, but hopefully the figure below gives a good idea. We can see that the wiggles still happen approximately between 21:00 and 06:00 UTC, and between 11:00 and 17:00 UTC.

If we add an artificial offset of -15 Hz per day to the curves to prevent them from overlapping, we obtain the figure below. We see that the pattern of the wiggles keeps changing slightly, but also remains quite similar.

In my last post about this topic I said that it seemed that the wiggles repeated with a period of a sidereal day. Now it is clear that it is not the case. The wiggles seem to repeat roughly with a period of a solar day (24 hours). In fact, in 44 days sidereal time “advances” 2.88 hours with respect to solar time. However, it is clear that the wiggles haven’t shifted that much in time.

## Wiggles in the QO-100 local oscillator

Some days ago, Hans Hartfuss DL2MDQ sent me an email about some frequency measurements of the QO-100 NB transponder BPSK beacon that he had been doing. The BPSK beacon is uplinked from Bochum (Germany) through the transponder, and as the beacon is generated using a very good Z3081A GPSDO as a reference, the frequency drift observed on the beacon downlink is caused by Doppler and the drift of the local oscillator of the transponder.

In his measurements, Hans observed some small oscillations or “wiggles” that didn’t seem to be caused by Doppler. Decided to investigate this, I started to do some measurements of my own. This post is an account of my measurements and findings so far.

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## Coherence and QO-100

My tweet about the AMSAT-BR QO-100 FT8 QRPp experiment has spawned a very interesting discussion with Phil Karn KA9Q, Marcus Müller and others about weak signal modes specifically designed for the QO-100 communications channel, which is AWGN albeit with some frequency drift (mainly due to the imperfect reference clocks used in the typical groundstations).

Roughly speaking, the conversation shifted from noting that FT8 is not so efficient in terms of EbN0 to the idea of using something like coherent BPSK with $$r=1/6$$ CCSDS Turbo code, then to observing that maybe there was not enough SNR for a Costas loop to work, so a residual carrier should be used, and eventually to asking whether a residual carrier would work at all.

There are several different problems that can be framed in this context. For me, the most interesting and difficult one is how to transmit some data with the least CN0 possible. In an ideal world, you can always manage to transmit a weaker signal just by transmitting slower (thus maintaining the Eb/N0 constant). In the real world, however, there are some time-varying physical parameters of the signal that the receiver needs to track (be it phase, frequency, clock synchronization, etc.). In order to detect and track these parameters, some minimum signal power is needed at the receiver.

This means that, in practice, depending on the physical channel in question, there is a lower CN0 limit at which communication on that channel can be achieved. In many situations, designing a system that tries to approach to that limit is a hard and interesting question.

Another problem that can be posed is how to transmit some data with the least Eb/N0 possible, thus approaching the Shannon capacity of the channel. However, the people doing DVB-S2 over the wideband transponder are not doing it so bad at all in this respect. Indeed, by transmitting faster (and increasing power, to keep the Eb/N0 reasonable), the frequency drift problems become completely manageable.

In any case, if we’re going to discuss about these questions, it is important to characterize the typical frequency drift of signals through the QO-100 transponder. This post contains some brief experiments about this.

## Oscillations and relativistic effects in Galileo broadcast clocks

A few days ago, Bert Hubert, the creator of galmon.eu, discovered a sinusoidal oscillation in the clock drift $$a_{f1}$$ parameter of the broadcast ephemerides of Galileo satellites. This variation has a frequency that matches the orbital period of 14 hours and 7 minutes. At first, I suggested that it might be caused by relativistic effects, which are given by$-\frac{\sqrt{\mu}}{c^2}e\sqrt{A}\sin E,$where $$\mu$$ is the Earth’s gravitational parameter, $$c$$ is the speed of light, $$e$$ is the eccentricity, $$A$$ is the semi-major axis, and $$E$$ is the eccentric anomaly. In fact, the order of magnitude of the oscillations that Bert was seeing seemed to agree with this formula.

However, then I realised that this relativistic effect is not included in the broadcast clock model. It needs to be included back by the receivers. Therefore, it shouldn’t appear at all in the broadcast clock. Something didn’t seem quite right. This post is an in-depth look at this problem.

## QO-100 BPSK beacon frequency measured at Bochum

The experiments about measuring the frequency stability of the local oscillator of the QO-100 NB transponder with a Vectron MD-011 GPSDO I made a few days ago indicated that the Allan deviation of the local oscillator was probably better than $$10^{-11}$$ for $$\tau$$ between 1 and 100 seconds. The next step in trying to characterize the stability of the local oscillator is to use a reference clock which is more stable than the Vectron.

I contacted Achim Vollhardt DH2VA asking him if it was possible to record the downlink of the BPSK beacon at Bochum, so as to have a recording referenced to the Z3801A GPSDO in Bochum, which is much more stable than the Vectron. He and Mario Lorenz DL5MLO have been very kind and they have taken the effort to make a recording for me. This post is an analysis of this recording made at Bochum.

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## More frequency measurements of the QO-100 NB transponder

This post is a follow up to my experiments about measuring the stability of the QO-100 NB transponder local oscillator. I am now using the Vectron MD-011 GPSDO that Carlos Cabezas EB4FBZ has lent me to reference all my QO-100 groundstation (see more information about the Vectron GPSDO in this post).

The Vectron MD-011 has an Allan deviation of $$10^{-11}$$ at $$\tau = 1\,\mathrm{s}$$ and $$2\cdot10^{-11}$$ at $$\tau = 10\,\mathrm{s}$$ according to the datasheet, so it is an improvement of an order of magnitude compared to my DF9NP TCXO-based GPSDO. I have made more measurements with the Vectron MD-011 as in my previous experiments, measuring the phase of the BPSK beacon transmitted from Bochum and a CW tone transmitted with my station. This post summarizes my results and conclusions.

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## Measuring the Allan deviation of a GPSDO with an SDR

A few days ago I tried to measure the QO-100 NB transponder LO stability using my DF9NP 10MHz GPSDO. It turned out that my GPSDO was less stable than the LO, so my measurements showed nothing about the QO-100 LO. Carlos Cabezas EB4FBZ has been kind enough to lend me a Vectron MD-011 GPSDO, which is much better than my DF9NP GPSDO and should allow me to measure the QO-100 LO.

Before starting the measurements with QO-100, I have taken the time to use the Vectron GPSDO to measure the Allan deviation of my DF9NP GPSDO over several days. This post is an account of the methods and results.

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## Can my station measure the QO-100 NB transponder LO stability?

Following a long discussion with Bernd Zoelgert DL2BZ about the frequency stability of the local oscillator of the QO-100 narrowband transponder, I have decided to try to measure the Allan deviation of the transponder. The focus here is on short-term stability, so we are concerned with observation intervals around $$\tau = 1 \mathrm{s}$$.

Of course, as with any measurement problem, the performance of the measurement equipment should be better than the “device under test”. In this case, to measure the QO-100 LO it is necessary to compare it against a reference clock which is more stable (ideally an order of magnitude better).

My whole station is locked to a DF9NP GPSDO, which is a 10MHz VCTCXO disciplined by a uBlox LEA-4S GPS receiver. That’s great to measure long-term stability, but for short-term measurements you are essentially relying on the stability of the VCTCXO, which is not so great. Therefore, the whole purpose of this experiment is first to determine whether my station is actually able to measure the QO-100 LO or not. Spoiler: it turns out the answer is “no”, as in most articles whose title is phrased as a question.

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## Using an external reference with the LimeSDR Mini

A while ago I spoke about feeding an external reference to the LimeSDR USB. Now I wanted to use an external reference with the LimeSDR Mini that I have in my QO-100 groundstation to lock all the system to GPS. Preferably I wanted to use 27MHz as the reference, since this is what I am using in my LNB, so this would save me from having to run 10MHz or another frequency to the groundstation.

I wasn’t so sure how well this would work, since there are a few threads with questions in the MiriadRF forums, but I haven’t seen any explaining things in a clear way. There are different anecdotes of things that worked or didn’t work for several people, but not that many definitive answers. Among all the threads, this one seems mostly helpful.

Somewhat surprisingly, everything has worked well on the first try. I am now using a 27MHz external reference with my LimeSDR Mini. Hopefully this post will be of help to other people.

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