Horus Binary Telemetry and FreeDV

Since our last post on Testing HAB Telemetry Protocols, Mark and I have been working steadily on making the Horus Binary protocol easier to use for High Altitude Balloon (HAB) telemetry.

The objectives for this work are:

  1. Test our 4FSK Binary open source balloon telemetry over the air on a real HAB mission.
  2. Develop a GUI version of the decoder to make it usable by a wider audience. Now anyone with a SSB radio (or SDR) and Windows machine can crowd source telemetry using the new protocol.
  3. Move the art of open source, high performance telemetry forward. We now have a C API suitable for integrating telemetry protocols into other projects, and a cross platform GUI for end users. In our use case, we are outperforming Lora by a factor of 10.
  4. It’s a cool AREG club project. Now we’ve moved it off the Linux command line, club members who prefer Windows and SSB radios can get involved, along with people who like Linux and SDRs.
  5. Show how we develop open source protocols, by blogging on our work, sharing our design and test techniques and most importantly the source code.

RS41 Transmitter

Mark has been collecting RS41 Radiosondes. Conveniently, our local Bureau of Meterology launches two every day. They can be tracked, and many of them eventually fall from the sky into the hands of eager South Australian Radio Amateurs. Batteries are even included in the deal.

Mark has built a nice system to help track and recover them. Turns out they are rather hackable so he reprogrammed one to be a Horus Binary transmitter using this source code:

FreeDV GUI changes

FreeDV GUI is a cross platform (Linux/OSX/Windows) GUI program for digital voice. It’s designed to demodulate modem signals from sound cards, and I’m its maintainer so we decided to press it into service as a HAB telemetry decoder.

I spent a few hours each day for a week refactoring the code to handle 48 kHz sample rate we use for the Horus API. This code needed some maintenance so it was a useful step for my digital voice work as well. I post experimental Windows versions here. Or you can just build it from the source code.

Here is a weak (-7db SNR) Horus Binary mode test signal. You may be able to hear some tinkling sounds buried in the noise – that’s the 4FSK:

You can download this weak test signal to test FreeDV GUI using the Tool-Start/Stop Play File from Radio menu option.

Now FreeDV GUI is not for everyone. The good news is you can use the Horus API to roll your own GUI front end if that’s the itch you’d like to scratch. I have limited time, and my main focus is Digital Voice over HF radio. So I would really appreciate other people from the HAB community stepping up to help with further HAB features. If you can’t code, please consider supporting this work via Pateron or PayPal.

Bench Testing MDS

On Sat 23 June Mark and I performed some Minimum Detectable signal (MDS) tests on the telemetry stack. We used a RS41 as the Tx (13 dBm output power), many dBs of attenuators, and careful experimental design to attenuate the signal down to very low levels.

This post also describes how we do MDS tests, and includes some video.

For these tests we used my FT817 SSB radio and a RTL-SDR, both with a LNA. There was up to 160dB of fixed and switched attenuators. The Tx was placed in a metal box, and we added 100dB of attenuation directly at the output. We then routed the signal to the Rx in another room using good quality coax (so it wouldn’t leak RF). A switched attenuator was placed in front of the Rx so we could adjust the attenuation in 1dB steps.

It’s important to make sure the Rx signal is coming from the desired path. You can test this using a spectrum analyser or in our case the calibrated SNR meter in FreeDV GUI. Insert more attenuation and note how far the signal level drops. If you insert 10dB more attenuation and it drops just 1dB, well you have some RF feeding through another path!

Our calculated MDS (50% packet loss) was:

  MDS = EbNo + 10log10(Rb) + NF - 174
      = 4.5  + 10log10(200) + 1 - 174
      = -145.45 dBm

Note the baud (symbol) rate is 100 symbols/s, but 4FSK sends 2 bits/symbol, so our bit rate is 200 bits/s. Our experiments on HAB protocols gave us the Eb/No figure. The Noise Figure (NF) of our preamp is an estimate from previous work and the pre-amp data sheet.

We obtained consistent results down to about -143dBm, but from there on it was difficult to get repeatable results. The signal is so weak, and the RF finds other paths. But hey – that lets us know we are close and we can conclude there are no obvious problems in the integrated system.

The comparable Lora mode 10 with a similar (1 second) packet duration has a MDS of -132dBm. Our mode requires at least 10dB less power, which gives it four times the range using the same transmit power (every 6dB doubles the line of sight range). Or we can transmit the same distance on 10% of the power of Lora. Our solution is based on good engineering, open source software, and commodity hardware rather than a chipset. The chipset form-factor has some advantages, and we hope to develop a similar form factor solution in the future. You can help if you like.

Test Flight

On Sunday 8 July the 4FSK Binary Horus system had a work out on a real Horus HAB flight. A lot of things can go wrong on a real flight but it worked well. Many people set up receive stations for the binary protocol, and crowd sourced the uploading of packets.

Callsign Packets Rx-ed % of Flight
VK5AKH 1511 82.4%
VK5APR 1541 84.0%
VK5FJGM 1234 67.3%
VK5FLJG 1577 86.0%
VK5FTAZ 832 45.4%
VK5IX 1491 81.3%
VK5KJP 1471 80.2%
VK5RR 288 15.7%
VK5ST 1663 90.7%
VK5TRM 1719 93.7%
VK5QI-9 (Mobile Station) 1560 85.1%
VK5WTF (Mobile Station) 1039 56.7%

Here is a plot of the telemetry collated by HabHub. Note on the far right hand side that the telemetry is still being received on the ground, as the recovery team tracked through the bush to collect the various payloads – fortunately Mark’s car was nearby so the signal was strong enough to be picked up even after landing.

Next Steps

The current system requires both FreeDV GUI and a Python script to to upload packets to HabHub. An obvious next step is to put some C++ code into FreeDV GUI to create a single application. Would anyone like to help us with this task?

I’d like to see more Open source telemetry, and encourage people to build their own protocols using open source components. We have demonstrated that we can outperform closed source systems like Lora. A great next step would be our own radio hardware, such as a simple FSK transmitter that can be easily integrated with a microcontroller.

Reading Further

FreeDV GUI for Windows with Horus Binary support.
Horus binary set up instructions with FreeDV.
AREG post on the flight.
RS41 source code to make it a Horus Binary telemetry transmitter.
Wenet – 115 kbit/s system for HD images that uses the same FSK modem.
All Your Modem are Belong To Us – the start of our open source modem development for HAB.
Binary Telemetry Protocol – first flight of a similar binary protocol in 2016, using 2FSK.
Testing HAB Telemetry Protocols – bench testing the 4FSK binary protocol against various RTTY demodulators.
High Speed Balloon Data Link – start of the Wenet work, and a nice example of MDS testing @ home.

Bench Testing HF Radios with a HackRF

This post describes how we implemented a HF channel simulator to bench test a digital HF radio using modern SDRs.

Yesterday Mark and I bench tested a HF radio with calibrated SNR over simulated AWGN and HF channels. We recorded the radios transmit signal with an AirSpy HF and GQRX, added calibrated noise and “CCIR Poor” fading, and replayed the signal using a HackRF.

For the FreeDV 700C and 700D work I have developed a utility called cohpsk_ch, that takes a real modem signal, adds channel impairments like noise and fading, and outputs another real signal. It has a built in Hilbert Transformer so it can do complex math cleverness like small frequency shifts and ITUT/CCIR HF fading channel models.

Set Up

The basic idea is to upconvert a 8 kHz real sample file to HF in real time. I have some utilities to help with this in codec2-dev:

$ svn co https://svn.code.sf.net/p/freetel/code/codec2-dev codec2-dev
$ cd codec2-dev/octave
$ octave --no-gui
octave:1> cohpsk_ch_fading("../raw/fast_fading_samples.float", 8000, 1.0, 8000*60)
octave:2> cohpsk_ch_fading("../raw/slow_fading_samples.float", 8000, 0.1, 8000*60)
$ exit
$ cd ..
$ cd codec2-dev && mkdir build_linux && cd build_linux
$ cmake -DCMAKE_BUILD_TYPE=Debug ..
$ make
$ cd unittest 

You also need GNU Octave to generate the HF fading files for cohpsk_ch, and you need to install the very useful CSDR tools.

Connect the HackRF to your SSB receiver, we put a 30dB attenuator in line. Tune the radio to 7.177 MHz LSB. First generate a carrier with your HackRF, offset so we get a 500Hz tone in the SSB radio in LSB mode:

$ hackrf_transfer -f 7176500 -s 8000000 -c 127

Now lets try some DSB audio:

$ cat ../../wav/ve9qrp.wav | csdr mono2stereo_s16 | ./tsrc - - 10 -c |
./tlininterp - - 100 -df | hackrf_transfer -f 5177000 -s 8000000  -t - 2>/dev/null

Don’t change the frequency, but try switching the mode between USB and LSB. Should sound about the same, with a slight frequency offset due to the HackRF. Note that HackRF is tuned to Fs/4 = 2MHz beneath 7.177MHz. “tlininterp” has a simple Fs/4 mixer that we use to shift the signal away from the HackRF DC spike. We up-sample from 8 kHz to 8 MHz in two steps to save MIPs.

The “csdr mono2stereo_s16” just repeats the real output samples, so we get a DSB signal at HF. A bit lazy I know, a better approach would be to modify cohpsk_ch to have a complex output option. Let me know if you want to modify cohpsk_ch – I can tell you how.

Checking Calibration

Now I’m pretty confident that cohpsk_ch works well at baseband on digital signals as I have used it extensively in my HF DV work. However I wanted to make sure the off air signal had the correct SNR.

To check the calibration, we generated a 1000 Hz sine wave Signal + Noise signal:

$ ./mksine - 1000 30  | ./../src/cohpsk_ch - - -30 --Fs 8000 --ssbfilt 0 | csdr mono2stereo_s16 | ./tsrc - - 10 -c | ./tlininterp - - 100 -df | hackrf_transfer -f 12177000 -s 8000000  -t - 2>/dev/null 

Then just a noise signal:

cat /dev/zero | ./../src/cohpsk_ch - - -30 --Fs 8000 --ssbfilt 0 | csdr mono2stereo_s16 | ./tsrc - - 10 -c | ./tlininterp - - 100 -df | hackrf_transfer -f 5177000 -s 8000000  -t - 2>/dev/null

With moderate SNRs (say 10dB), Signal + Noise power is roughly Signal power. So I measured the off air power of the above signals using my FT817 connected to a USB sound card, and an Octave script:

$ rec -t raw -r 8000 -s -2 -c 1 - -q | octave --no-gui -qf power_from_stdio.m

I used alsamixer and the plots from the script to make sure I wasn’t overloading the ADC. You need to turn your receiver AGC OFF, and adjust RF/AF gain to get the levels right.

However from the FT817 I was getting results a few dB off due to the crystal filter bandwidth and non-rectangular shape factor. Mark hooked up his AirSpy HF and GQRX, and we piped the received audio over the LAN to the script:

nc -ul 7355 | octave --no-gui -qf power_from_stdio.m

GQRX had a nice flat response from a few 100 Hz to 3kHz, the same bandwidth cohpsk_ch uses for SNR measurement. OK, so now we had sensible numbers, within 0.2dB of the SNR reported by cohpsk_ch. We moved the levels up and down 3dB, made sure everything was repeatable and linear. We went down to 0dB, where signal and noise power is the same, and Signal+Noise power should be 3dB more than Noise alone. Check.


Then we could play the HF tx signal at a variety of SNRS, by tweaking third (No) argument. In this case we set No to -100dB, so no noise:

cat tx_file_from_radio.wav | ./../src/cohpsk_ch - - -100 --Fs 8000 --ssbfilt 0 | csdr mono2stereo_s16 | ./tsrc - - 10 -c | ./tlininterp - - 100 -df | hackrf_transfer -f 5177000 -s 8000000  -t - 2>/dev/null

At the end of the cohpsk_ch run, it will print the SNR is has measured. So you read that and tweak No as required to get the SNR you need. In our case around -30 was 8dB SNR. You can also add fast (–fast) or slow (–slow) fading, here is a fast fading run at about 2dB SNR:

cat tx_file_from_radio.wav | ./../src/cohpsk_ch - - -24 --Fs 8000 --ssbfilt 0 --fast | csdr mono2stereo_s16 | ./tsrc - - 10 -c | ./tlininterp - - 100 -df | hackrf_transfer -f 5177000 -s 8000000  -t - 2>/dev/null

The “–ssbfilt 0” option switches off the 300-2600 Hz filter inside cohpsk_ch, that is used to simulate a SSB radio crystal filter. For out tests, the modem waveform was too wide for that filter.


I guess we could also have used the HackRF to sample the signal. The nice thing about SDRs is the frequency response is ‘flat”, no crystal filters messing things up.

The only thing we weren’t sure about was the sample rate and frequency offset accuracy of the HackRF, for example if the sample clock was a bit off that might upset modems.

The radio we tested delivered performance pretty much on it’s data sheet at the SNRs tested, giving us extra confidence in the bench testing system described here.

Reading Further

Measuring SDR Noise Figure in Real Time
High Speed Balloon Data Link, here we bench test a UHF FSK data radios
README_ofdm.txt, Lots of examples of using cohpsk_ch to test the latest and greatest OFDM modem.
PathSim is a very nice Windows GUI HF path simulator, that runs well on Linux using Wine.

FreeDV 700D Released

Here is a sample of Mark, VK5QI, sending a FreeDV 700D signals from Adelaide, South Australia, to a Kiwi SDR at the Bay of Islands, New Zealand. It was a rather poor channel with a path length of 3200km (2000 miles). First SSB, then FreeDV 700D, then SSB again:

Here is FreeDV 700D on the waterfall of Mark’s IC7610. That little narrow signal at 7.176 MHz is 700D, note the “overweight” SSB signals to the right! This is a very bandwidth efficient mode.

Last weekend FreeDV GUI 1.3 was released, which includes the new 700D mode. I’ve been working hard for the last few months to get 700D out of the lab and onto the air. Overall, I estimate about 1000 hours were required to develop FreeDV 700D over the last 12 months.

For the last few weeks teams of beta testers dotted around the world have been running FreeDV 1.3 in the wild. FreeDV 700D is fussy about lost samples so I had to do some work with care and feeding of the sound drivers, espcially on the Windows build. Special thanks to Steve K5OKC, Richard KF5OIM, Mark VK5QI, Bill VK5DSP; Hans PA0HWB and the Dutch team; Eric GW8LJJ, Kieth GW8TRO and the UK team; Mel K0PFX, Walt K5WH and the US team, Peter VK5APR, Peter VK2TPM, Bruce K6BP, Gerhard OE3GBB, John VK5DM/VK3IC, Peter VK3RV and the Sunbury team, and my local AREG club. I apologise if I have missed anyone, all input is greatly appreciated.

Anyone who writes software should be sentenced to use it. So I’ve poked a few antennas up into the air and, conditions permitting have made 700D contacts, getting annoyed with things that don’t work, then tweaking and improving. Much to my surprise it really does handle some nasty fading, and it really does work better than SSB in many cases. Engineers aren’t used to things working, so this is a bit of an adjustment for me personally.


Here’a demo video of FreeDV 1.3 decoding a low SNR Transatlantic contact between Gerhard OE3GBB and Walt, K5WH:

You can see the fast fading on the signal. The speech quality is not great, but you get used to it after a little while and it supports conversations just fine. Remember at this stage we are targeting low SNR communications, as that has been the major challenge to date.

Here’s a screen shot of the FreeDV QSO Finder (thanks John K7VE) chat log, when the team tried SSB shortly afterwards:

FreeDV 700D also has some robustness to urban HF Noise. I’m not sure why, this still needs to be explored. Here is the off-air signal I received from Peter, VK2TPM. It’s full of nasty buzzing switching power supply noises, and is way down in the noise, but I obtained an 80% decode:

It’s hard to hear the modem signal in there!

FreeDV 700D Tips

Lots of information of FreeDV, and the latest software, at freedv.org. Here are some tips on using 700D:

  1. The 700 bit/s codec is’s sensitive to your microphone and the FreeDV microphone equaliser settings (Tools-Filter). Suggest you set up a local loopback to hear your own voice and tune the quality using the Tools-Filter Mic equaliser. You can play pre-recorded wave files of your own voice using Tools-Play File to Mic in or with the “voice keyer” feature.
  2. The current 700D modem is sensitive to tuning, you need to be within +/- 20Hz for it to acquire. This is not a practical problem with modern radios that are accurate to +/- 1Hz. One you have acquired sync it can track drift of 0.2Hz/s. I’ll get around to improving the sync range one day.
  3. Notes on the new features in FreeDV 1.3 User Guide.
  4. Look for people to talk to on the FreeDV QSO Finder (thanks John K7VE)
  5. Adjust the transmit drive to your radio so it’s just moving the ALC. Don’t hammer your PA! Less is more with DV. Aim for about 20W average power output on a 100W PEP radio.
  6. If you get stuck reach out for help on the Digital Voice mailing list (digitalvoice at googlegroups.com)


The last time a new HF voice mode was introduced was the 1950’s and it was called Single Side Band (SSB). It’s lasted so long because it works well.

So a new voice mode that competes with SSB is something rare and special. We don’t want the next HF Voice mode to be locked down by codec vendors. We want it to be open source.

I feel 700D is a turning point for FreeDV and open source digital voice. After 10 years of working on Codec 2 and FreeDV, we are now competitive with SSB on HF multipath channels at low SNRs. The 700 bits/ codec isn’t great. It’s fussy about microphones, EQ settings, and background noise. But it’s a start, and we can improve from here.

It takes some getting used to, but our growing experience has shown 700D is quite usable for conversations. Bear in mind SSB isn’t pretty at low SNRs either (see sample at the top), indeed untrained listeners struggle with SSB even at high SNRs.

Quite remarkably, the 700 bit/s codec outperforms locked down, proprietary, expensive, no you can’t look at my source or modify me, codecs like MELP and TWELP at around the same bit rate.

The FreeDV 700D waveform (the combined speech codec, FEC, modem, protocol) is competitive at low SNRs (-2dB AWGN, +2dB CCIR Poor channel), with several closed source commercial HF DV systems that we have explored.

FreeDV 700D requires about 1000 Hz of RF bandwidth, half of SSB.

Most importantly FreeDV and Codec 2 are open source. It’s freely available to not just Radio Amateurs, but emergency services, the military, humanitarian organisations, and commercial companies.

Now that we have some traction with low SNR HF fading channels, the next step is to improve the speech quality. We can further improve HF performance with experience, and I’d like to look at VHF/UHF again, and push down to 300 bit/s. The Lower SNR limit of Digital Voice is around -8dB SNR.

This is experimental radio. DV over HF is a very tough problem. Unlike other almost all other voice services (mobile phones, VHF/UHF radio), HF is still dominatted by analog SSB modulation. I’m doing much of the development by myself, so I’m taking one careful, 1000 man-hour, step at a time. Unlike other digital voice modes (I’m looking at you DStar/C4FM/DMR/P25) – we get to set the standard (especially the codec), rather than following it and being told “this is how it is”.

Get Involved

Here is how you can get involved:

  1. Support this work via Patreon or PayPal
  2. Refactor and maintain the FreeDV GUI source code. This will help free me to push forward the DSP code where my skills are unique. See bottom of FreeDV GUI README.
  3. Experienced or not, if you want to play DSP, I have some work for you too. You will learn a lot. Like Steve Did.
  4. Find corner cases where 700D breaks. Then help me fix it.
  5. Work with me to port 700D to the SM1000.
  6. Make freedv.org look great and maintain it.
  7. Help me use Deep Learning to make Codec 2 even better.
  8. Start a FreeDV Net.
  9. Set up a FreeDV beacon.
  10. Help me get some UHF/VHF FreeDV modes on the air. Some coding and messing with radios required.
  11. Help others get set up on FreeDV, 700D voice quality depends on the right microphone and equaliser settings, and noobs tend to over drive their PA.
  12. Create and Post Demo/instructional Videos.

Like the good people above, you have the opportunity to participate in the evolution of HF radio. This has happened once in the last 60 years. Lets get started.

If you are interested in development, please subscribe to the Codec 2 Mailing List.

Reading Further

Peter VK2TPM, blogs on 700D.
AREG Blog Post on FreeDV 700D
Steve Ports an OFDM modem from Octave to C. This is the sort of support I really need – thanks Steve for stepping up and helping!
Windows Installers for development versions of FreeDV.
Codec 2 700C
AMBE+2 and MELPe 600 Compared to Codec 2
Lower SNR limit of Digital Voice
700D OFDM modem README and specs
FreeDV User Guide, including new 700D features.
Bill, VK5DSP designed the LDPC code used in 700D and has helped with its care and feeding. He also encouraged me to carefully minimise the synchronisation (pilot symbol) overhead for the OFDM modem used in 700D.

FreeDV 700D Part 4 – Acquisition

Since 2012 I have built a series of modems (FDMDV, COHPSK, OFDM) for HF Digital voice. I always get stuck on “acquisition” – demodulator algorithms that acquire and lock onto the received signal. The demod needs to rapidly estimate the frequency offset and “coarse” timing – the position where the modem frame starts in the sequence of received samples.

For my application (Digital Voice over HF), it’s complicated by the low SNR and fading HF channels, and the requirement for fast sync (a few hundred ms). For Digital Voice (DV) we need something fast enough to emulate Push To Talk (PTT) operation. In comparison HF data modems have it easy – they can take many lazy seconds to synchronise.

The latest OFDM modem has been no exception. I’ve spent several weeks messing about with acquisition algorithms to get half decent performance. Still some tuning to do but for my own sanity I think I’ll stop development here for now, write up the results, and push FreeDV 700D out for general consumption.

Acquisition and Sync Requirements

  1. Sync up quickly (a few 100ms) with high SNR signals.
  2. Sync up eventually (a few is seconds OK) for low SNR signals over poor channels. Sync eventually is better than none on channels where even SSB is struggling.
  3. Detect false sync and get out of it quickly. Don’t stay stuck in a false sync state forever.
  4. Hang onto sync through fades of a few seconds.
  5. Assume the operator can tune to within +/- 20Hz of a given frequency.
  6. Assume the radio drifts no more than +/- 0.2Hz/s (12 Hz a minute).
  7. Assume the sample clock offset (difference in ADC/DAC sample rates) is no more than 500ppm.

Actually the last three aren’t really requirements, it’s just what fell out of the OFDM modem design when I optimised it for low SNR performance on HF channels! The frequency stability of modern radios is really good; sound card sample clock offset less so but perhaps we can measure that and tell the operator if there is a problem.

Testing Acquisition

The OFDM modem sends pilot (known) symbols every frame. The demodulator correlates (compares) the incoming signal with the pilot symbol sequence. When it finds a close match it has a coarse timing candidate. It can then try to estimate the frequency offset. So we get a coarse timing estimate, a metric (called mx1) that says how close the match is, and a frequency offset estimate.

Estimating frequency offsets is particularly tricky, I’ve experienced “much wailing and gnashing of teeth” with these nasty little algorithms in past (stop laughing Matt). The coarse timing estimator is more reliable. The problem is that if you get an incorrect coarse timing or frequency estimate the modem can lock up incorrectly and may take several seconds, or operator intervention, before it realises its mistake and tries again.

I ended up writing a lot of GNU Octave functions to help develop and test the acquisition algorithms in ofdm_dev.

For example the function below runs 100 tests, measures the timing and frequency error, and plots some histograms. The core demodulator can cope with about +/ 1.5Hz of residual frequency offset and a few samples of timing error. So we can generate probability estimates from the test results. For example if we do 100 tests of the frequency offset estimator and 50 are within 1.5Hz of being correct, then we can say we have a 50% (0.5) probability of getting the correct frequency estimate.

octave:1> ofdm_dev
octave:2> acquisition_histograms(fin_en=0, foff_hz=-15, EbNoAWGN=-1, EbNoHF=3)
AWGN P(time offset acq) = 0.96
AWGN P(freq offset acq) = 0.60
HF P(time offset acq) = 0.87
HF P(freq offset acq) = 0.59

Here are the histograms of the timing and frequency estimation errors. These were generated using simulations of noisy HF channels (about 2dB SNR):

The x axis of timing is in samples, x axis of freq in Hz. They are both a bit biased towards positive errors. Not sure why. This particular test was with a frequency offset of -15Hz.

Turns out that as the SNR improves, the estimators do a better job. The next function runs a bunch of tests at different SNRs and frequency offsets, and plots the acquisition probabilities:

octave:3> acquisition_curves

The timing estimator also gives us a metric (called mx1) that indicates how strong the match was between the incoming signal and the expected pilot sequence. Here is a busy little plot of mx1 against frequency offset for various Eb/No (effectively SNR):

So as Eb/No increases, the mx1 metric tends to gets bigger. It also falls off as the frequency offset increases. This means sync is tougher at low Eb/No and larger frequency offsets. The -10dB value was thrown in to see what happens with pure noise and no signal at the input. We’d prefer not to sync up to that. Using this plot I set the threshold for a valid signal at 0.25.

Once we have a candidate time and freq estimate, we can test sync by measuring the number of bit errors a set of 10 Unique Word (UW) bits spread over the modem frame. Unlike the payload data in the modem frame, these bits are fixed, and known to the transmitter and receiver. In my initial approach I placed the UW bits right at the start of the modem frame. However I discovered a problem – with certain frequency offsets (e.g. multiples of the modem frame rate like +/- 6Hz) – it was possible to get a false sync with no UW errors. So I messed about with the placement of the UW bits until I had a UW that would not give any false syncs at any incorrect frequency offset. To test the UW I wrote another script:

octave:4> debug_false_sync

Which outputs a plot of UW errors against the residual frequency offset:

Note how at any residual frequency offset other than -1.5 to +1.5 Hz there are at least two bit errors. This allows us to reliably detect a false sync due to an incorrect frequency offset estimate.

State Machine

The estimators are wrapped up in a state machine to control the entire sync process:

  1. SEARCHING: look at a buffer of incoming samples and estimate timing, freq, and the mx1 metric.
  2. If mx1 is big enough, lets jump to TRIAL.
  3. TRIAL: measure the number of Unique Word bit errors for a few frames. If they are bad this is probably a false sync so jump back to SEARCHING.
  4. If we get a low number of Unique Word errors for a few frames it’s high fives all round and we jump to SYNCED.
  5. SYNCED: We put up with up two seconds of high Unique Word errors, as this is life on a HF channel. More than two seconds, and we figure the signal is gone for good so we jump back to SEARCHING.

Reading Further

HF Modem Frequency Offset Estimation, an earlier look at freq offset estimation for HF modems
COHPSK and OFDM waveform design spreadsheet
Modems for HF Digital Voice Part 1
Modems for HF Digital Voice Part 2
README_ofdm.txt, including specifications of the OFDM modem.

FreeDV 700D and SSB Comparison

Mark, VK5QI has just performed a SSB versus FreeDV 700D comparison between his home in Adelaide and the Manly Warringah Radio Society WebSDR SDR in Sydney, about 1200km away. The band was 40m, and the channel very poor, with some slow fading. Mark used SVN revision 3581, built himself on Ubuntu, with an interleaver setting (Tools-Options menu) of 1 frame. Transmit power for SSB and FreeDV 700D was about the same.

I’m still finishing off FreeDV 700D integration and tuning the mode – but this is a very encouraging start. Thanks Mark!

FreeDV 1600 Sample Clock Offset Bug

So I’m busy integrating FreeDV 700D into the FreeDV GUI program. The 700D modem works on larger frames (160ms) than the previous modes (e.g. 20ms for FreeDV 1600) so I need to adjust FIFO sizes.

As a reference I tried FreeDV 1600 between two laptops (one tx, one rx) and noticed it was occasionally losing frame sync, generating bit errors, and producing the occasional bloop in the audio. After a little head scratching I discovered a bug in the FreeDV 1600 FDMDV modem! Boy, is my face red.

The FMDMV modem was struggling with sample clock differences between the mod and demod. I think the bug was introduced when I did some (too) clever refactoring to reduce FDMDV memory consumption while developing the SM1000 back in 2014!

Fortunately I have a trail of unit test programs, leading back from FreeDV GUI, to the FreeDV API (freedv_tx and freedv_rx), then individual unit tests for each modem (fdmdv_mod/fdmdv_demod), and finally Octave simulation code (fdmdv.m, fdmdv_demod.m and friends) for the modem.

Octave (or an equivalent vector based scripting language like Python/numpy) is much easier to work with than C for complex DSP problems. So after a little work I reproduced the problem using the Octave version of the FDMDV modem – bit errors happening every time there was a timing jump.

The modulator sends parallel streams of symbols at about 50 baud. These symbols are output at a sample rate of 8000 Hz. Part of the demodulators job is to estimate the best place to sample each received modem symbol, this is called timing estimation. When the tx and rx are separate, the two sample clocks are slightly different – your 8000 Hz clock will be a few Hz different to mine. This means the timing estimate is a moving target, and occasionally we need to compenstate by talking a few more or few less samples from the 8000 Hz sample stream.

In the plot below the Octave demodulator was fed with a signal that is transmitted at 8010 Hz instead of the nominal 8000 Hz. So the tx is sampling faster than the rx. The y axis is the timing estimate in samples, x axis time in seconds. For FreeDV 1600 there are 160 samples per symbol (50 baud at 8 kHz). The timing estimate at the rx drifts forwards until we hit a threshold, set at +/- 40 samples (quarter of a symbol). To avoid the timing estimate drifting too far, we take a one-off larger block of samples from the input, the timing takes a step backwards, then starts drifting up again.

Back to the bug. After some head scratching, messing with buffer shifts, and rolling back phases I eventually fixed the problem in the Octave code. Next step is to port the code to C. I used my test framework that automatically compares a bunch of vectors (states) in the Octave code to the equivalent C code:

octave:8> system("../build_linux/unittest/tfdmdv")
sizeof FDMDV states: 40032 bytes
ans = 0
octave:9> tfdmdv
tx_bits..................: OK
tx_symbols...............: OK
tx_fdm...................: OK
pilot_lut................: OK
pilot_coeff..............: OK
pilot lpf1...............: OK
pilot lpf2...............: OK
S1.......................: OK
S2.......................: OK
foff_coarse..............: OK
foff_fine................: OK
foff.....................: OK
rxdec filter.............: OK
rx filt..................: OK
env......................: OK
rx_timing................: OK
rx_symbols...............: OK
rx bits..................: OK
sync bit.................: OK
sync.....................: OK
nin......................: OK
sig_est..................: OK
noise_est................: OK

passes: 46 fails: 0

Great! This system really lets me move fast once the Octave code is written and tested. Next step is to test the C version of the FDMDV modem using the command line arguments. Note how I used sox to insert a sample rate offset by changing the same rate of the raw sample stream:

build_linux/src$ ./fdmdv_get_test_bits - 30000 | ./fdmdv_mod - - | sox -t raw -r 8000 -s -2 - -t raw -r 7990 - | ./fdmdv_demod - - 14 demod_dump.txt | ./fdmdv_put_test_bits -
bits 29568  errors 0  BER 0.0000

Zero errors, despite 10Hz sample clock offset. Yayyyyy. The C demodulator outputs a bunch of vectors that can be plotted with an Octave helper program:

octave:6> fdmdv_demod_c("../build_linux/src/demod_dump.txt",28000)

The FDMDV modem is integrated with Codec 2 in the FreeDV API. This can be tested using the freedv_tx/freedv_rx programs. For convenience, I generated some 60 second test files at different sample rates. Here is how I test using the freedv_rx program:

./freedv_rx 1600 ~/Desktop/ve9qrp_1600_8010.raw - | aplay -f S16

The ouput audio sounds good, no bloops, and by examining the freedv_rx_log.txt file I can see the demodulator didn’t loose sync. Cool.

Here is a table of the samples I used for testing:

No clock offset Simulates Tx sample rate 10Hz slower than Rx Simulates Tx sampling 10Hz faster than Rx

Finally, the FreeDV API is linked with the FreeDV GUI program. Here is a video of me testing different sample clock offsets using the raw files in the table above. Note there is no audio in this video as my screen recorder fights with FreeDV for use of sound cards. However the decoded FreeDV audio should be uninterrupted, there should be no re-syncs, and zero bit errors:

The fix has been checked into codec2-dev SVN rev 3556, and will make it’s way into FreeDV GUI 1.3, to be released in late May 2018.

Reading Further

FDMDV modem
Steve Ports an OFDM modem from Octave to C, some more on the Octave/C automated test framework and porting complex DSP algorithms.
Testing a FDMDV Modem. Early blog post on FDMDV modem with some more disucssion on sample clock offsets
Timing Estimation for PSK modems, talks a little about how we generate a timing estimate

FreeDV 700D Part 3

After a 1 year hiatus, I am back into FreeDV 700D development, working to get the OFDM modem, LDPC FEC, and interleaver algorithms developed last year into real time operation. The aim is to get improved performance on HF channels over FreeDV 700C.

I’ve been doing lots of refactoring, algorithm development, fixing bugs, tuning, and building up layers of C code so we can get 700D on the air.

Steve ported the OFDM modem to C – thanks Steve!

I’m building up the software in the form of command line utilities, some notes, examples and specifications in Codec 2 README_ofdm.txt.

Last week I stayed at the shack of Chris, VK5CP, in a quiet rural location at Younghusband on the river Murray. As well as testing my Solar Boat, Mark (VK5QI) helped me test FreeDV 700D. This was the first time the C code software has been tested over a real HF radio channel.

We transmitted signals from YoungHusband, and received them at a remote SDR in Sydney (about 1300km away), downloading wave files of the received signal for off-line analysis.

After some tweaking, it worked! The frequency offset was a bit off, so I used the cohpsk_ch utility to shift it within the +/- 25Hz acquisition range of the FreeDV 700D demodulator. I also found some level sensitivity issues with the LDPC decoder. After implementing a form of AGC, the number of bit errors dropped by a factor of 10.

The channel had nasty fading of around 1Hz, here is a video of the “sample #32” spectrum bouncing around. This rapid fading is a huge challenge for modems. Note also the spurious birdie off to the left, and the effect of receiver AGC – the noise level rises during fades.

Here is a spectrogram of the same sample 33. The x axis is time in seconds. It’s like a “waterfall” SDR plot on it’s side. Note the heavy “barber pole” fading, which corresponds to the fades sweeping across the spectrum in the video above.

Here is the smoothed SNR estimate. The SNR is moving target for real world HF channels, the SNR moves between 2 and 6dB.

FreeDV 700D was designed to work down to 2dB on HF fading channels so pat on the back for me! Hundreds of hours of careful development and testing meant this thing actually worked when it went on air….

Sample 32 is a longer file that contains test frames instead of coded voice. The QPSK scatter diagram is a messy cross, typical of fading channels, as the amplitude of the signal moves in and out:

The LDPC FEC does a good job. Here are plots of the uncoded (raw) bit errors, and the bit errors after LDPC decoding, with the SNR estimates below:

Here are some wave and raw (headerless) audio files. The off air audio is error free, albeit at the low quality of Codec 2 at 700 bits/s. The goal of this work is to get intelligible speech through HF channels at low SNRs. We’ll look at improving the speech quality as a future step.

Still, error free digital voice on a heavily faded HF channel at 2dB SNR is pretty cool.

See below for how to use the last two raw file samples.

sample 33 off air modem signal Sample 33 decoded voice Sample 32 off air test frames raw file Sample 33 off air voice raw file

SNR estimation

After I sampled the files I had a problem – I needed to know the SNR. You see in my development I use simulated channels where I know exactly what the SNR is. I need to compare the performance of the real world, off-air signals to my expected results at a given SNR.

Unfortunately SNR on a fading channel is a moving target. In simulation I measure the total power and noise over the entire run, and the simulated fading channel is consistent. Real world channels jump all over the place as the ionosphere bounces around. Oh well, knowing we are in the ball park is probably good enough. We just need to know if FreeDV 700D is hanging onto real world HF channels at roughly the SNRs it was designed for.

I came up with a way of measuring SNR, and tested it with a range of simulated AWGN (just noise) and fading channels. The fading bandwidth is the speed at which the fading channel evolves. Slow fading channels might change at 0.2Hz, faster channels, like samples #32 and #33, at about 1Hz.

The blue line is the ideal, and on AWGN and slowly fading channels my SNR estimator does OK. It reads a dB low as the fading bandwidth increases to 1Hz. We are interested in the -2 to 4dB SNR range.

Command Lines

With the samples in the table above and codec2-dev SVN rev 3465, you can repeat some of my decodes using Octave and C:

octave:42> ofdm_ldpc_rx("32.raw")
EsNo fixed at 3.000000 - need to est from channel
Coded BER: 0.0010 Tbits: 54992 Terrs:    55
Codec PER: 0.0097 Tpkts:  1964 Terrs:    19
Raw BER..: 0.0275 Tbits: 109984 Terrs:  3021

david@penetrator:~/codec2-dev/build_linux/src$ ./ofdm_demod ../../octave/32.raw /dev/null -t --ldpc
Warning EsNo: 3.000000 hard coded
BER......: 0.0246 Tbits: 116620 Terrs:  2866
Coded BER: 0.0009 Tbits: 54880 Terrs:    47

build_linux/src$ ./freedv_rx 700D ../../octave/32.raw /dev/null --testframes
BER......: 0.0246 Tbits: 116620 Terrs:  2866
Coded BER: 0.0009 Tbits: 54880 Terrs:    47

build_linux/src$ ./freedv_rx 700D ../../octave/33.raw  - | aplay -f S16

Next Steps

I’m working steadily towards integrating FreeDV 700D into the FreeDV GUI program so anyone can try it. This will be released in May 2018.

Reading Further

Towards FreeDV 700D
FreeDV 700D – First Over The Air Tests
Steve Ports an OFDM modem from Octave to C
Codec 2 README_ofdm.txt

Testing HAB Telemetry Protocols

On Saturday Mark and I had a pleasant day bench testing High Altitude Balloon (HAB) Telemetry protocols and demodulators.

Project Horus HAB flights use a low power transmitter to send regular updates of the balloons position and status. To date, this has been sent using RTTY, and demodulated using Fldigi, or a special version modified for HAB work called dl-Fldigi.

Lora is becoming common in HAB circles, however I am confident we can do better using a custom protocol and well engineered, and most importantly – open source – modems. While very well designed and conveniently packaged, Lora is not magic – modem performance is defined by physics.

A few year ago, Mark and I developed and flight tested a binary protocol (Horus Binary) for HAB flights. We have dusted this off, and I’ve written a C callable API (horus_api.c) to make Horus RTTY and Binary easy to use. The plan is to release a cross platform GUI application that supports Horus Binary, so anyone with a SSB receiver can join in the fun of tracking Horus flights using Horus Binary.

A good HAB telemetry protocol works at low SNRs, and has fast updates to allow accurate positioning of the payload during the final decent. A way of measuring the performance is Packet Error Rate (PER) – how many telemetry packets get through at a given Signal to Noise Ratio (SNR).

So we generated some synthetic Horus RTTY and Binary packets at calibrated SNRs using GNU Octave simulation code (fsk_horus.m), then played the wave files through several modems.

Here are the results (click for a larger version):

The X-axis is in Eb/No, which is proportional to SNR:

  SNR = EBNodB + 10log10(Rb/BW)

where Rb is the bit rate and BW is the noise bandwidth you want to measure SNR in. Eb/No is handy as it normalises for the effect of bit rate and noise bandwidth, making modem comparison easier.

Protocol dl-Fldigi
(50% PER)
13.0 12.0 11.5 4.5
Rb 100 100 100 200
SNR (3000Hz) -1.7 -2.7 -3.2 -7.2
6 6 6 1.6
Wave File Listen Listen Listen Listen


The older dl-Fldigi is a few dB behind the more modern Fldigi. Our Horus RTTY and especially Binary protocols are doing very well. At the same bit rate (Eb/No curve), Horus Binary is 9dB ahead of dl-Fldigi, which is a very useful gain; at least double the Line of Site (LOS) range, and equivalent to having nearly 10x the transmit power. The Binary packets are fast as well, allowing for rapid position updates in the final descent.

Trade offs are possible, for example if we slowed Horus Binary to 50 bits/s, it’s packet duration would be 6.4s (about the same as RTTY) however 50% PER would occur at a SNR of -13dB, a 15dB improvement over dl-Fldigi.

Reading Further

Project Horus
Binary Telemetry Protocol
All Your Modem are Belong To Us
SNR and Eb/No Worked Example

Measuring SDR Noise Figure in Real Time

I’m building a sensitive receiver for FreeDV 2400A signals. As a first step I tried a HackRF with an external Low Noise Amplifier (LNA), and attempted to measure the Noise Figure (NF) using the system Mark and I developed two years ago.

However I was getting results that didn’t make sense and were not repeatable. So over the course of a few early morning sessions I came up with a real time NF measurement system, and wrinkled several bugs out of it. I also purchased a few Airspy SDRs, and managed to measure NF on them as well as the HackRF.

It’s a GNU Octave script called nf_from_stdio.m that accepts a sample stream from stdio. It assumes the signal contains a sine wave test tone from a calibrated signal generator, and noise from the receiver under test. By sampling the test tone it can establish the gain of the receiver, and by sampling the noise spectrum an estimate of the noise power.

The script can be driven from command line utilities like hackrf_transfer or airspy_rx or via software receivers like gqrx that can send SSB-demodaulted samples over UDP. Instructions are at the top of the script.


I’m working from a home workbench, with rudimentary RF skills, a strong signal processing background and determination. I do have a good second hand signal generator (Marconi 2031), that cost AUD$1000 at a Hamfest, and a Rigol 815 Spec An (generously donated by Mel K0PFX, and Jim, N0OB) to support my FreeDV work. Both very useful and highly recommended. I cross-checked the sig-gen calibrated output using an oscilloscope and external attenuator (within 0.5dB). The Rigol is less accurate in amplitude (1.5dB on its specs), but useful for relative measurements, e.g. comparing cable attenuation.

For the NF test method I have used a calibrated signal source is required. I performed my tests at 435MHz using a -100dBm carrier generated from the Marconi 2031 sig-gen.

Usage and Results

The script accepts real samples from a SSB demod, or complex samples from an IQ source. Tune your receiver so that the sinusoidal test tone is in the 2000 to 4000 Hz range as displayed on Fig 2 of the script. In general for minimum NF turn all SDR gains up to maximum. Check Fig 1 to ensure the signal is not clipping, reduce the baseband gain if necessary.

Noise is measured between 5000 and 10000 Hz, so ensure the receiver passband is flat in that region. When using gqrx, I drag the filter bandwidth out to 12000 Hz.

The noise estimates are less stable than the tone power estimate, leading to some sample/sample variation in the NF estimate. I take the median of the last five estimates.

I tried supplying samples to nf_from_stdio using two methods:

  1. Using gqrx in UDP mode to supply samples over UDP. This allows easy tuning and the ability to adjust the SDR gains in real time, but requires a few steps to set up
  2. Using a “single” command line approach that consists of a chain of processing steps concatenated together. Once your signal is tuned you can start the NF measurements with a single step.

Instructions on how to use both methods are at the top of nf_from_stdio.m

Here are some results using both gqrx and command line methods, with and without an external (20dB gain/1dB NF) LNA. They were consistent across two laptops.

SDR Gqrx LNA Cmd Line LNA Cmd Line no LNA
AirSpy Mini 2.0 2.2 7.9
AirSpy R2 1.7 1.7 7.0
HackRF One 2.6 3.4 11.1

The results with LNA are what we would expect for system noise figures with a good LNA at the front end.

The “no LNA” Airspy NF results are curious – the Airspy specs state a NF of just 3.5dB. So we contacted Airspy via Twitter and email to see how they measured their stated NF. We haven’t received a response to date. I posted to the Airspy mailing list and one gentleman (Dave – WØLEV) kindly replied and has measured noise figures of 4dB using calibrated noise sources and attenuators.

Looking into the data sheets for the Airspy, it appears the R820T tuner at the front end of the Airspy has a NF of 3.5dB. However a system NF will always be worse than the first device, as other devices (e.g. the ADC) also inject noise.

Other possibilities for my figures are measurement error, ambient noise sources at my site, frequency dependent NF, or variations in individual R820T samples.

In our past work we have used Bit Error Rate (BER) results as an independent method of confirming system noise figure. We found a close match between theoretical and measured BER when testing with and without a LNA. I’ll be repeating similar low level BER tests with FreeDV 2400A soon.

Real Time Noise Figure

It’s really nice to read the system noise figure in real time. For example you can start it running, then experiment with grounding, tightening connectors, or moving the SDR away from the laptop, or connect/disconnect a LNA in real time and watch the results. Really helps catch little issues in these difficult to perform tests. After all – we are measuring thermal noise, a very weak signal.

Some of the NF problems I could find and remove with a real time measurement:

  • The Airspy mini is nearly 1dB worse on the front left USB port than the rear left USB port on my X220 Thinkpad!
  • The Airspy mini really likes USB extension cables with ferrite clamps – without the ferrite I found the LNA was ineffective in reducing the NF – being swamped by conducted laptop noise I guess.
  • Loose connectors can make the noise figure a few dB worse. Wiggle and tighten them all.
  • Position of SDR/LNA near the radio and other bench equipment.
  • My magic touch can decrease noise figure! Grounding effect I guess?

Development Bugs

I had to work through several problems before I started getting sensible numbers. This was quite discouraging for a while as the numbers were jumping all over the place. However its fair to say measuring NF is a tough problem. From what I can Google its an uncommon measurement for people in home workshops.

These bugs are worth mentioning as traps for anyone else attempting home NF measurements:

  1. Cable loss: I found a 1.5dB loss is some cable I was using between the sig gen and the SDR under test. I Measured the loss by comparing a few cables connected between my sig gen and spec an. While the 815 is not accurate in terms of absolute calibration (rated at 1.5dB), it can still be used for comparative measurements. The cable loss can be added to the calculations or just choose a low loss cable.
  2. Filter shape: I had initially placed the test tone under 1000Hz. However I noticed that the gqrx signal had a few dB of high pass filtering in this region (Fig 2 below). Not an issue for regular USB demodulation, but a few dB really matters for NF! So I moved the test tone to the 2-4kHz region where the gqrx output was nice and flat.
  3. A noisy USB port, especially without a clamp, on the Airspy Mini (photo below). Found by trying different SDRs and USB ports, and finally a clamp. Oh Boy, never expected that one. I was connecting the LNA and the NF was stuck at 4dB – swamped by noise from the USB Port I guess.
  4. Compression: Worth checking the SDR output is not clipped or in compression. I adjusted the sig gen output up and down 3dB, and checked the power estimate from the script changed by 3dB. Also worth monitoring Fig 1 from the script, make sure it’s not hitting the limits. The HackRF needed it’s baseband gain reduced, but the Airspys were OK.
  5. I used latest Airspy tools built from source (rather than Ubuntu 17 package) to get stdout piping working properly and not have other status information from printfs injected into the sample stream!


Thanks Mark, for the use of your RF hardware, and I’d also like to mention the awesome CSDR tools and fantastic gqrx software – both very handy for SDR work.

Steve Ports an OFDM modem from Octave to C

Earlier this year I asked for some help. Steve Sampson K5OKC stepped up, and has done some fine work in porting the OFDM modem from Octave to C. I was so happy with his work I asked him to write a guest post on my blog on his experience and here it is!

On a personal level working with Steve was a great experience for me. I always enjoy and appreciate other people working on FreeDV with me, however it is quite rare to have people help out with programming. As you will see, Steve enjoyed the process and learned a great deal in the process.

The Problem with Porting

But first some background on the process involved. In signal processing it is common to develop algorithms in a convenient domain-specific scripting language such as GNU Octave. These languages can do a lot with one line of code and have powerul visualisation tools.

Usually, the algorithm then needs to be ported to a language suitable for real time implementation. For most of my career that has been C. For high speed operation on FPGAs it might be VHDL. It is also common to port algorithms from floating point to fixed point so they can run on low cost hardware.

We don’t develop algorithms directly in the target real-time language as signal processing is hard. Bugs are difficult to find and correct. They may be 10x or 100x times harder (in terms of person-hours) to find in C or VHDL than say GNU Octave.

So a common task in my industry is porting an algorithm from one language to another. Generally the process involves taking a working simulation and injecting a bunch of hard to find bugs into the real time implementation. It’s an excellent way for engineering companies to go bankrupt and upset customers. I have seen and indeed participated in this process (screwing up real time implementations) many times.

The other problem is algorithm development is hard, and not many people can do it. They are hard to find, cost a lot of money to employ, and can be very nerdy (like me). So if you can find a way to get people with C, but not high level DSP skills, to work on these ports – then it’s a huge win from a resourcing perspective. The person doing the C port learns a lot, and managers are happy as there is some predictability in the engineering process and schedule.

The process I have developed allows people with C coding (but not DSP) skills to port complex signal processing algorithms from one language to another. In this case its from GNU Octave to floating point C. The figures below shows how it all fits together.

Here is a sample output plot, in this case a buffer of received samples in the demodulator. This signal is plotted in green, and the difference between C and Octave in red. The red line is all zeros, as it should be.

This particular test generates 12 plots. Running is easy:

$ cd codec2-dev/octave
$ ../build_linux/unittest/tofdm
$ octave
>> tofdm
W........................: OK
tx_bits..................: OK
tx.......................: OK
rx.......................: OK
rxbuf in.................: OK
rxbuf....................: OK
rx_sym...................: FAIL (0.002037)
phase_est_pilot..........: FAIL (0.001318)
rx_amp...................: OK
timing_est...............: OK
sample_point.............: OK
foff_est_hz..............: OK
rx_bits..................: OK

This shows a fail case – two vectors just failed so some further inspection required.

Key points are:

  1. We make sure the C and Octave versions are identical. Near enough is not good enough. For floating point I set a tolerance like 1 part in 1000. For fixed point ports it can be bit exact – zero difference.
  2. We dump a lot of internal states, not just the inputs and outputs. This helps point us at exactly where the problem is.
  3. There is an automatic checklist to give us pass/fail reports of each stage.
  4. This process is not particularly original. It’s not rocket science, but getting people (especially managers) to support and follow such a process is. This part – the human factor – is really hard to get right.
  5. The same process can be used between any two versions of an algorithm. Fixed and float point, fixed point C and VHDL, or a reference implementation and another one that has memory or CPU optimisations. The same basic idea: take a reference version and use software to compare it.
  6. It makes porting fun and strangely satisfying. You get constant forward progress and no hard to find bugs. Things work when they hit real time. After months of tough, brain hurting, algorithm development, I find myself looking forward to the productivity the porting phase.

In this case Steve was the man doing the C port. Here is his story…..

Initial Code Construction

I’m a big fan of the Integrated Debugging Environment (IDE). I’ve used various versions over the years, but mostly only use Netbeans IDE. This is my current favorite, as it works well with C and Java.

When I take on a new programming project I just create a new IDE project and paste in whatever I want to translate, and start filling-in the Java or C code. In the OFDM modem case, it was the Octave source code ofdm_lib.m.

Obviously this code won’t do anything or compile, but it allows me to write C functions for each of the Octave code blocks. Sooner or later, all the Octave code is gone, and only C code remains.

I have very little experience with Octave, but I did use some Matlab in college. It was a new system just being introduced when I was near graduation. I spent a little time trying to make the program as dynamic as the Octave code. But it became mired in memory allocation.

Once David approved the decision for me to go with fixed configuration values (Symbol rate, Sample rate, etc), I was able to quickly create the header files. We could adjust these header files as we went along.

One thing about Octave, is you don’t have to specify the array sizes. So for the C port, one of my tasks was to figure out the array sizes for all the data structures. In some cases I just typed the array name in Octave, and it printed out its value, and then presto I now knew the size. Inspector Clouseau wins again!

The include files were pretty much patterned the same as FDMDV and COHPSK modems.

Code Starting Point

When it comes to modems, the easiest thing to create first is the modulator. It proved true in this case as well. I did have some trouble early on, because of a bug I created in my testing code. My spectrum looked different than Davids. Once this bug was ironed out the spectrums looked similar. David recommended I create a test program, like he had done for other modems.

The output may look similar, but who knows really? I’m certainly not going to go line by line through comma-separated values, and anyway Octave floating point values aren’t the same as C values past some number of decimal points.

This testing program was a little over my head, and since David has written many of these before, he decided to just crank it out and save me the learning curve.

We made a few data structure changes to the C program, but generally it was straight forward. Basically we had the outputs of the C and Octave modulators, and the difference is shown by their different colors. Luckily we finally got no differences.

OFDM Design

As I was writing the modulator, I also had to try and understand this particular OFDM design. I deduced that it was basically eighteen (18) carriers that were grouped into eight (8) rows. The first row was the complex “pilot” symbols (BPSK), and the remaining 7 rows were the 112 complex “data” symbols (QPSK).

But there was a little magic going on, in that the pilots were 18 columns, but the data was only using 16. So in the 7 rows of data, the first and last columns were set to a fixed complex “zero.”

This produces the 16 x 7 or 112 complex data symbols. Each QPSK symbol is two-bits, so each OFDM frame represents 224 bits of data. It wasn’t until I began working on the receiver code that all of this started to make sense.

With this information, I was able to drive the modulator with the correct number of bits, and collect the output and convert it to PCM for testing with Audacity.

DFT Versus FFT

This OFDM modem uses a DFT and IDFT. This greatly simplifies things. All I have to do is a multiply and summation. With only 18 carriers, this is easily fast enough for the task. We just zip through the 18 carriers, and return the frequency or time domain. Obviously this code can be optimized for firmware later on.

The final part of the modulator, is the need for a guard period called the Cyclic Prefix (CP). So by making a copy of the last 16 of the 144 complex time-domain samples, and putting them at the head, we produce 160 complex samples for each row, giving us 160 x 8 rows, or 1280 complex samples every OFDM frame. We send this to the transmitter.

There will probably need to be some filtering, and a function of adjusting gain in the API.

OFDM Modulator

That left the Demodulator which looked much more complex. It took me quite a long time just to get the Octave into some semblance of C. One problem was that Octave arrays start at 1 and C starts at 0. In my initial translation, I just ignored this. I told myself we would find the right numbers when we started pushing data through it.

I won’t kid anyone, I had no idea what was going on, but it didn’t matter. Slowly, after the basic code was doing something, I began to figure out the function of various parts. Again though, we have no idea if the C code is producing the same data as the Octave code. We needed some testing functions, and these were added to tofdm.m and tofdm.c. David wrote this part of the code, and I massaged the C modem code until one day the data were the same. This was pretty exciting to see it passing tests.

One thing I found, was that you can reach an underflow with single precision. Whenever I was really stumped, I would change the single precision to a double, and then see where the problem was. I was trying to stay completely within single precision floating point, because this modem is going to be embedded firmware someday.

Testing Process

There was no way that I could have reached a successful conclusion without the testing code. As a matter of fact, a lot of programming errors were found. You would be surprised at how much damage a miss placed parenthesis can do to a math equation! I’ve had enough math to know how to do the basic operations involved in DSP. I’m sure that as this code is ported to firmware, it can be simplified, optimized, and unrolled a bit for added speed. At this point, we just want valid waveforms.

C99 and Complex Math

Working with David was pretty easy, even though we are almost 16 time-zones apart. We don’t need an answer right now, and we aren’t working on a deadline. Sometimes I would send an email, and then four hours later I would find the problem myself, and the morning was still hours away in his time zone. So he sometimes got some strange emails from me that didn’t require an answer.

David was hands-off on this project, and doesn’t seem to be a control freak, so he just let me go at it, and then teamed-up when we had to merge things in giving us comparable output. Sometimes a simple answer was all I needed to blow through an Octave brain teaser.

I’ve been working in C99 for the past year. For those who haven’t kept up (1999 was a long time ago), but still, we tend to program C in the same way. In working with complex numbers though, the C library has been greatly expanded. For example, to multiply two complex numbers, you type” “A * B”. That’s it. No need to worry about a simulated complex number using a structure. You need a complex exponent, you type “cexp(I * W)” where “I” is the sqrt(-1). But all of this is hidden away inside the compiler.

For me, this became useful when translating Octave to C. Most of the complex functions have the same name. The only thing I had to do, was create a matrix multiply, and a summation function for the DFT. The rest was straight forward. Still a lot of work, but it was enjoyable work.

Where we might have problems interfacing to legacy code, there are functions in the library to extract the real and imaginary parts. We can easily interface to the old structure method. You can see examples of this in the testing code.

Looking back, I don’t think I would do anything different. Translating code is tedious no matter how you go. In this case Octave is 10 times easier than translating Fortran to C, or C to Java.

The best course is where you can start seeing some output early on. This keeps you motivated. I was a happy camper when I could look and listen to the modem using Audacity. Once you see progress, you can’t give up, and want to press on.


Reading Further

The Bit Exact Fairy Tale is a story of fixed point porting. Writing this helped me vent a lot of steam at the time – I’d just left a company that was really good at messing up these sorts of projects.

Modems for HF Digital Voice Part 1 and Part 2.

The cohpsk_frame_design spreadsheet includes some design calculations on the OFDM modem and a map of where the data and pilot symbols go in time and frequency.

Reducing FDMDV Modem Memory is an example of using automated testing to port an earlier HF modem to the SM1000. In this case the goal was to reduce memory consumption without breaking anything.

Fixed Point Scaling – Low Pass Filter example – is consistently one of the most popular posts on this blog. It’s a worked example of a fixed point port of a low pass filter.