Experiments – Page 13 – Daniel Estévez

Testing LDPC code erasure decoding performance

In my previous post I talked about the RFC5170 LDPC codes used in Outernet. There I explained in some detail the pseudorandom construction of the LDPC codes and the simple erasure decoding algorithm used both in free-outernet and in the official closed-source receiver.

The Outernet LDPC codes follow what I call the “identity scheme”. This is different from the staircase and triangle schemes introduced in the RFC. The identity scheme already appeared in the literature, but it did not make it into the RFC. See, for instance, the report by Roca and Neumann Design, Evaluation and Comparison of Four Large Block FEC Codecs, LDPC, LDGM, LDGM Staircase and LDGM Triangle, plus a Reed-Solomon Small Block FEC Codec, especially Section 2, where it is called “LDGM”.

I also commented that erasure decoding for an LDPC code (or any other linear code) amounts to solving a linear system. This can be done using any algebraic method, such as Gaussian elimination. However, the simple decoding algorithm used in Outernet is as follows: try to find an equation with only one unknown, solve for that unknown, and repeat until the system is solved. Clearly this algorithm can fail even if the system can be solved (see my previous post for some examples and formal results). I will refer to this algorithm as iterative decoding, as it is done in the RFC.

With these two things in mind, I wondered about the performance of the LDPC codes used in Outernet and the iterative decoding algorithm. I’ve done some simulations and here I present my results.

Studying IONEX files

Many Amateur radio operators are familiar with the effects of the ionosphere at HF frequencies. However, the effects of the ionosphere are also noticeable at much higher frequencies. In particular, at L band, which is used by most satellite navigation systems. Thus, GNSS receivers can be used to measure ionospheric parameters. These measurements are usually distributed as TEC maps in IONEX files.

Here I describe some basic ionospheric physics, how a GNSS receiver can measure the ionosphere, and give some Python code to study TEC maps in IONEX files. Then I use TEC maps to study the CODAR ionospheric observations I did in December last year.

Mystery 9k6 BPSK satellite

On January 28th, Tetsu JA0CAW reported on Twitter his reception of an unknown satellite. The time of reception was 2018-01-28 12:15 UTC and the frequency was around 435.525MHz. The time and frequency coincided with a PicSat pass over JA0CAW’s station in Japan. He provided an IQ recording of the signal. So far, the satellite that originated the signal has not been identified. Several people have tried to listen to this satellite again, but I haven’t seen any other reports. Doppler identification has not been attempted and it is perhaps unfeasible with the few packets in JA0CAW’s recording.

I have looked at the recording to try to identify the satellite. The modulation is easily seen to be BPSK at 9600baud. The signal presents a lot of fading, so demodulation without bit errors is difficult. There seems to be a scrambler in use. I’ve tried descrambling with G3RUH and CCSDS without any luck. I’ve also failed to identify a preamble or frame sync marker.

To look at the packets in more detail, I’ve resorted to do demodulation as postprocessing in a Jupyter Python notebook. The resulting notebook is here. It is written with detailed comments, so it can be of interest to anyone who wants to learn these techniques.

The only interesting piece of information that I’ve been able to extract from my analysis is that the bits in the packets present strong self-correlations at lags of 1920 bits (and multiples). This is 240 bytes, but I have no clue of what to make of this.

As always, I would be grateful if anyone can provide any additional information about this unknown satellite.

Analysis of my Hermes-Lite 2 bandscope recording

A few weeks ago I posted how I make wideband recordings of bandscope data with my Hermes-Lite 2. In that post, I sort of promised to do a small analysis of the waterfall I showed. After being busy with other things (PicSat’s launch among them), I’ve finally had time to write something up.

A first look at TY-2

TY-2 is a 6U Chinese cubesat that was launched on January 19th in a CZ-11 rocket from Jiuquan, together with several other small satellites, including TY-6. According to the IARU Satcoord, TY-2 and TY-6 transmit 9k6 GMSK telemetry in the 70cm Amateur satellite band (435.350MHz for TY-2 and 436.100MHz for TY-6).

Several Amateurs such as K4KDR and PD0OXW have tried to decode the packets from TY-2 and TY-6 without success. I have taken a look to an IQ recording of TY-2 that Scott K4KDR has sent me and at least I’ve managed to do something (though not much) with it. Here I describe my findings.

A CODAR advent

Over the last few days, I have been recording CODAR on 4463kHz to produce images of the ionosphere. I started on Friday 15th and the plan was to leave the recording running until Christmas Day, thus producing some kind of “CODAR advent” images. Unfortunately, there seems to be a problem when the receiver runs for several days that results in the sudden loss of the CODAR signal. This problem can be seen at the bottom of the image below. Thus, I have finished the recording on the morning of the 24th. The equipment and software used is the same that I detailed in a previous post.

Using CODAR for ionospheric sounding

CODAR is an HF radar used to measure surface ocean currents in coastal areas. Usually, it consists of a chirp which repeats every second. The chirp rate is usually on the order of 10kHz/s, and the signal is gated in small pulses so that the CODAR receiver can listen between pulses. The gating frequency can be on the order of 1kHz.

CODAR can be received by skywave many kilometers inland. Being a chirped signal, it is easy to extract the multipath information from the received signal. In this way, one can see the signal bouncing off the different layers of the ionosphere, and magnificent pictures showing the changes in the ionosphere (especially at dawn and dusk) can be obtained. For instance, see these images by Pieter Ibelings N4IP, or the image at the top of this post, which contains 48 hours worth of CODAR data.

Here I describe my approach to receiving CODAR. It uses GNU Radio for most of the signal processing, and Python with NumPy, SciPy and Matplotlib for plotting.

A brief study of TLE variation

During my research and experiments about using WSJT-X modes through linear transponder satellites, one of the questions I had is by how much do TLEs of different epochs for the same satellite vary. This was glimpsed in part II, where I plotted the “best delay” parameter for TLEs of different age.

The topic of accuracy in TLE computation and propagation is rather complex. A NORAD TLE is the result of an orbit determination after several radar measurements at different epochs, so the elements are in some sense “averaged” over time. Also, the SGP4 propagator is simple and doesn’t model many orbit perturbations. However, NORAD TLEs are specially crafted to give improved results when used with SGP4.

Nevertheless, here I present a simple way of studying the rate of change of NORAD TLEs at different epochs. This procedure might not be very meaningful or sophisticate, but still seems to yield some interesting results.

Waterfall from the FT8 test through FO-29

In the previous post, I detailed my experiments transmitting FT8 through the FO-29 linear transponder. I recorded a complete pass of the FO-29 satellite while I transmitted an FT8 signal trough the transponder on even periods. As I promised in that post, I have now made a waterfall with the recording to show the activity through the linear transponder, and the strength of my FT8 signal in comparison with the SSB and CW signals of other users.

The watefall can be seen below. You can click on the image to view it in full size. A higher resolution version is available here (24MB). The horizontal axis represents frequency and the vertical axis represents time, with the beginning of the pass at the top of the image. The waterfall has been corrected for the downlink Doppler and the DC spike of the FUNcube Dongle Pro+ has been removed.

From left to right, the following signals can be seen: The CW beacon can be seen as a faint vertical signal. Next, there is some interference coming through the transponder in the form of terrestrial FM signals. Then we can see my FT8 signal, being transmitted only on even periods. Finally, around the centre of the image, we have a few SSB and CW signals through the transponder. Note that most of these signals increase in frequency as the pass progresses. This is because many people keep a fixed uplink and only tune the downlink by hand to correct for Doppler. Unfortunately, full computer Doppler correction is not very popular. I also used a fixed uplink frequency for my FT8 signal, but only to simplify the experiment. The best procedure is to correct for the uplink Doppler to keep a constant frequency at the satellite.

Waterfall of FO-29 downlink (Doppler corrected)

We can see that the SSB and CW signals are much stronger than my FT8 signal. Indeed, some of the CW signals are particularly strong at times, perhaps putting too much pressure on the linear transponder.

The waterfalls in this post have been created using this Jupyter notebook.

First FT8 test through FO-29

Continuing with my research on using WSJT-X modes through linear transponder satellites in low Earth orbit (see part I and part II), a few days ago I transmitted and recorded an FT8 signal through the V/U linear transponder on FO-29 during a complete pass. The recording started at 2017/10/23 20:26:00 UTC and ended at 20:42:30 UTC. It was made with a FUNcube Dongle Pro+ set to a centre frequency of 435.850MHz and connected to a handheld Arrow satellite yagi through a duplexer. Here the duplexer was used to avoid desense on transmit.

An FT8 signal was transmitted on every even period during the recording, at a fixed frequency of 145.990MHz, using a Yaesu FT-817ND and the Arrow antenna. The signal was transmitted using lower sideband (i.e., inverted in the frequency domain) to get a correct FT8 signal through the inverting transponder. The transmit power was adjusted often to get a reasonable signal through the transponder and avoid using excessive power. There have been reports and complaints of people using too much power with digital modes through linear satellites. In this post, a study of the power is included to show that it is possible to use digital modes effectively without putting any pressure on the satellite’s transponder.

Out of the 33 even periods, a total of 24 can be decoded by WSJT-X using the best TLEs from Space-Track. No measures were taken to correct for the time offset \(\delta\) that has been studied in the previous posts, as the TLEs already provided a good Doppler correction. Regarding the choice of TLEs, there are still some remarks to make. First, the epoch of the TLEs used was 2017/10/23 21:39:16 UTC, so these TLEs were actually taken after the pass. The previous TLEs were taken a few hours before the pass, and it is likely that they also provided a good correction, perhaps by using a time offset \(\delta\) if necessary. However, I do not know if these previous TLEs were also available from CelesTrak before the start of the pass, as it seems that TLEs take a while to propagate from Space-Track to Celestrack. To explain why the TLEs with no time offset correction are enough, it will be interesting to study the rate of change of TLE parameters for FO-29. This will be done in a future post.

The results of this test look very promising. Even though this wasn’t an overhead pass (the maximum elevation was 40º), the maximum rate of change of the Doppler was over 20Hz/s for the self-Doppler seen on the FT8 signal and 35Hz/s for the downlink Doppler seen on the CW beacon. Most of the periods which couldn’t be decoded were near the start or end of the pass. This is the only test that I know of that has decoded FT8 signals in the presence of high rates of change of Doppler. The previous tests by other people were made at low elevations, where the rate of change of Doppler is small. This test has shown that it is possible to get many decodes with high rates of change of Doppler, even using no corrections to the TLEs. Here I continue with a detailed analysis of the recording.