Posts – Page 12 – Daniel Estévez

Voyager 1 and Reed-Solomon

In one of my previous posts about Voyager 1, I stated that the Voyager probes used as forward error correction only the k=7, r=1/2 CCSDS convolutional code, and that Reed-Solomon wasn’t used. However, some days ago, Brett Gottula asked about this, citing several sources that stated that the Voyager probes used Reed-Solomon coding after their encounter with Saturn.

My source for stating that Reed-Solomon wasn’t used was some private communication with DSN operators. Since the XML files describing the configuration of the DSN receivers for Voyager 1 didn’t mention Reed-Solomon either, I had no reason to question this. However, the DSN only processes the spacecraft data up to some point (which usually includes all FEC decoding), and then passes the spacecraft frames to the mission project team without really looking at their contents. Therefore, it might be the case that it’s the project team the one who handles the Reed-Solomon code for the Voyagers. This would make sense specially if the code was something custom, rather than the CCSDS code (recall that Voyager predates the CCSDS standards). If this were true, the DSN wouldn’t really care if there is Reed-Solomon or not, and they might have just forgotten about it.

After looking at the frames I had decoded from Voyager 1 in more detail, I remarked that Brett might be right. Doing some more analysis, I have managed to check that in fact the Voyager 1 frames used Reed-Solomon as described in the references that Brett mentioned. In this post I give a detailed look at the Reed-Solomon code used by the Voyager probes, compare it with the CCSDS code, and show how to perform Reed-Solomon decoding in the frames I decoded in the last post. The middle section of this post is rather math heavy, so readers might want to skip it and go directly to the section where Reed-Solomon codewords in the Voyager 1 frames are decoded.

Reed-Solomon bug in Queqiao

Queqiao is the communications relay satellite for the Chang’e 4 Chinese lunar lander mission to the far side of the Moon. It is in a halo orbit around the Earth-Moon Largrange L2 point and provides communications to the lander in Von Kármán crater.

Queqiao transmits telemetry in S-band, using the frequency 2234.5 MHz. The modulation and coding is similar to other recent Chinese probes, such as Chang’e 5 and Tianwen-1. Here I report an interesting bug that I found in the Reed-Solomon encoding performed by Queqiao.

More data from Voyager 1

Back in September, I showed how to decode the telemetry signal from Voyager 1 using a recording made with the Green Bank Telescope in 2015 by the Breakthrough Listen project. The recording was only 22.57 seconds long, so it didn’t even contain a complete telemetry frame. To study the contents of the telemetry, more data would be needed. Often we can learn things about the structure of the telemetry frames by comparing several consecutive frames. Fields whose contents don’t change, counters, and other features become apparent.

Some time after writing that post, Steve Croft, from BSRC, pointed me to another set of recordings of Voyager 1 from 16 July 2020 (MJD 59046.8). They were also made by Breakthrough Listen with the Green Bank Telescope, but they are longer. This post is an analysis of this set of recordings.

Computing the symbol error rate of m-FSK

How to compute the symbol error rate rate of an m-FSK modulation is something that comes up in a variety of situations, since the math is the same in any setting in which the symbols are orthogonal (so it also applies to some spread spectrum modulations). I guess this must appear somewhere in the literature, but I can never find this result when I need it, so I have decided to write this post explaining the math.

Here I show an approach that I first learned from Wei Mingchuan BG2BHC two years ago during the Longjiang-2 lunar orbiter mission. While writing our paper about the mission, we wanted to compute a closed expression for the BER of the LRTC modulation used in the uplink (which is related to \(m\)-FSK). Using a clever idea, Wei was able to find a formula that involved an integral of CDFs and PDFs of chi-squared distributions. Even though this wasn’t really a closed formula, evaluating the integral numerically was much faster than doing simulations, specially for high \(E_b/N_0\).

Recently, I came again to the same idea independently. I was trying to compute the symbol error rate of \(m\)-FSK and even though I remembered that the problem about LRTC was related, I had forgotten about Wei’s formula and the trick used to obtain it. So I thought of something on my own. Later, digging through my emails I found the messages Wei and I exchanged about this and saw that I had arrived to the same idea and formula. Maybe the trick was in the back of my mind all the time.

Due to space constraints, the BER formula for LRTC and its mathematical derivation didn’t make it into the Longjiang-2 paper. Therefore, I include a small section below with the details.

Hermes-Lite 2 external 10 MHz reference

Interested by the forthcoming HamSci December 2021 eclipse festival of frequency measurement, I have decided to enable and test the external 10 MHz input of my Hermes-Lite 2 DDC/DUC HF transceiver. This will allow me to use a GPSDO (the Vectron MD-011 which has appeared in other posts) to reference the Hermes-Lite 2 in order to measure frequency accurately.

Decoding DART

DART, the Double Asteroid Redirection Test, is a NASA mission that launched last Wednesday from Vandenberg. The goal of this mission is to crash the spacecraft into the small asteroid Dimorphos, allowing us to measure the small change in the orbit of the asteroid caused by the impact.

From the communications perspective, this spacecraft is the first to use a Spiral Radial Line Slot Array (RLSA) as high-gain antenna. Details about the antenna design can be seen in this paper. The paper shows that antenna polarization is LHCP. Most DSN communications use RHCP, although there are a few notable exceptions (for instance Emirates Mars Mission), and the DSN stations are equipped to handle both polarizations. I’m not sure if DART is indeed using LHCP or if this is just a matter of the convention in the definition of the polarization used in the paper (there are actually two opposite conventions to define the sense of circular polarization).

A few hours after launch, as the spacecraft passed over Europe, Miguel CT1BYM and Iban EB3FRN recorded the X-band telemetry signal from DART at 8421.79 MHz. This post is a first analysis of the signal.

Tianwen-1 remote sensing orbit

On November 8, the Tianwen-1 orbiter made a manoeuvre to move itself to the remote sensing orbit, as reported by Chinese media. This orbit is the final orbit in the mission, as depicted in this figure from Wikipedia. The main goal of this orbit is to study the geophysical properties of Mars with all the orbiter instruments (see this paper) and to continue acting as a communications relay for the rover Zhurong.

As usual, AMSAT-DL has been collecting telemetry from Tianwen-1 with the 20 metre antenna at Bochum observatory, including spacecraft state vectors. This allows us to study the orbit change manoeuvre and the properties of the remote sensing orbit. This post is a first look at the state vector data.

An update about Lucy’s telemetry

In my previous post I presented a description of the X-band telemetry of Lucy, including a GNU Radio decoder, some recordings from the Allen Telecope Array, and an analysis of some of the telemetry received in the two days following the launch. This is a short post with some updates about the telemetry analysis of the Lucy mission.

Decoding Lucy

Lucy is a spacecraft that will study the Trojan asteroids, during a twelve year mission. It was launched last Saturday at 9:34 UTC from Cape Canaveral on an Atlas V rocket. Its telemetry downlink is on X-band, at a frequency of 8445.768 MHz.

Iban Cardona EB3FRN made a 30 minute recording of the telemetry downlink at 19:00 UTC on Saturday, as the spacecraft first appeared over Europe after launch. r00t.cz did a brief analysis of this recording overnight, and then published some more details about the telemetry data. On Sunday, at 8:52 UTC, I did a long recording with one of the dishes in the Allen Telescope Array. This recording lasts 3 hours 26 minutes, and ends when the spacecraft set below the 16 degree elevation mask of the ATA. In this post I give a first analysis of the telemetry data in both recordings.

The recording done at ATA can be downloaded from the following datasets in Zenodo:

GNU Radio 3.9 in Buildroot

Recently I’ve had to cross-compile GNU Radio for an ARM embedded system. I have decided to use Buildroot to build GNU Radio and its dependencies, since I’m fairly familiar with using Buildroot to generate embedded Linux images. Earlier this year, Jean-Michel Friedt and
Gwenhaël Goavec-Merou presented in FOSDEM their work about adding a GNU Radio package in buildroot. They gave a talk called “Never compile on the target!“.

Unfortunately, the version they used was GNU Radio 3.8, and the package hasn’t been updated to GNU Radio 3.9 yet. I wanted to use GNU Radio 3.9, so I decided to try to update the Buildroot package. After some assorted problems, I have managed to get GNU Radio 3.9 running on my ARM target. The fixes I’ve done are really horrible, so I’ve been quite tempted not to share my changes. I’ve finally decide to share this even though it’s far from perfect, because it might save someone from having to replicate this work, and because if anyone wants to do this properly and update the upstream package, this could be useful as a starting point.