For the last two months I have been beavering away at FreeDV 700D, as part my eternal quest to show SSB who’s house it is.
This work was inspired by Bill, VK5DSP, who kindly developed some short LDPC codes for me; and suggested I could improve on the synchronisation overhead of the cohpsk modem. As an aside – Bill is part if the communications payload team for the QB50 SUSat Cubesat – currently parked at the ISS awaiting launch! Very Kerbal.
Anyhoo – I’ve developed a new OFDM modem that has less syncronisation overhead, works better, and occupies less RF bandwidth (1000 Hz) than the cohpsk modem used for 700C. I have wrapped my head around such arcane mysteries as coding gain and now have LDPC codes playing nicely over that nasty old HF channel.
It looks like FreeDV 700D has a gain of 4dB over 700C. This means error free operation at -2dB SNR for AWGN, and 2dB SNR over a challenging fast fading HF channel (two paths, 1Hz Doppler, 1ms delay).
- An OFDM modem with with low overhead (small Eb/No penalty) synchronisation, even on fading channels.
- Use of LDPC codes.
- Long (several seconds) interleaver.
- Ruthlessly hunting down any dB’s leaking out of my performance curves.
One nasty surprise was that after a closer look at the short (224,112) LDPC codes, I discovered they don’t give any real improvement over the simple diversity scheme used for FreeDV 700C. However with long interleaving (several seconds) of the short codes, or a long (few thousand bit/several seconds) LDPC code we get an additional 3dB gain. The interleaver allows us to ride over the ups and downs of the fast fading channel.
Interleaving has a few downsides. One is delay, the other is when they fail you lose a big chunk of data.
I’ve avoided delay until now, using the argument that low delay is essential for PTT radio. However I’d like to test long delays and see what the trade off/end user experience is. Once someone is speaking – i.e in the middle of an “over” – I suspect we won’t notice the delay. However it could get confusing in fast handovers. This is experimental radio, designed for very low SNRs, so lets give it a try.
We could send the uncoded data without interleaving – allowing low delay decoding when the SNR is high. A switch could control LDPC decoding, allowing a user selection of coded-high-delay or uncoded-low-delay, like a noise banker. Mark, VK5QI, has suggested interleaver depth also be adjustable which I think is a good idea. The decoder could automagically determine interleaver depth by attempting decoding over a range of depths (1,2,4,8,16 frames etc) and noting when the LDPC code converges.
Or maybe we could use a small, low delay, interleaver, and just live with the fades (like we do on SSB) and get the vocoder to mute or interpolate over them, and enjoy low or modest latency.
I’m also interested to see how the LDPC code mops up errors like static bursts and other real-world HF rubbish that SSB subjects us to even on high SNR channels.
So, lots of room for experimentation. At this stage it’s all in GNU Octave simulation form, no C implementation or FreeDV GUI mode exists yet.
Lots more I could write about the engineering behind the modem, but lets leave it there for now and take a look at some results.
Here is a rather busy set of BER versus SNR curves (click for larger version, and here is an EPS file version):
The 10-2 line is where the codec gets easy to listen to.
Observe far-right green (700C) to black (700D candidate with lots of interleaving) HF curves, which are about 4dB apart. Also the far-left cyan shows 700D working at -3dB SNR on AWGN channels. One dB later (-2dB) LDPC magic stomps all errors.
Here are some speech/modem tone samples on simulated channels:
|AWGN -2dB SNR||Analog SSB||700D modem||700D DV|
|HF +0.8dB SNR||Analog SSB||700D modem||700D DV|
The analog samples have a 300 to 2600 Hz BPF applied at the tx and rx side, to model an analog SSB radio. The analog SSB and 700D modem signals have exactly the same RMS power and channel models applied to them. In the AWGN channel, it’s difficult to hear the 700D modem signal, however the SSB is audible as it has peaks 9dB above the average.
OK so the 700 bit/s vocoder (Codec 2 700C) speech quality is not great even with no errors, but we have found it supports conversations just fine, and there is plenty of room for improvement. The same techniques (OFDM modem, LDPC interleaving) can also be applied to high quality/high bit rate/high SNR voice modes. But first – I want to push this low SNR DV work through to completion.
This list summarises the GNU Octave code I’ve developed, as I’ll probably forget the details when I move onto the next project. Feel free to try any of these scripts and let me know what I’ve forgotten to check in. It’s all checked into codec2-dev/octave.
|ldpc.m||Wrapper functions for using the CML library LDPC functions with Octave|
|ldpcut.m||Unit test/demo for ldpc.m|
|ldpc_qpsk.m||Runs simulations for a bunch of codes for AWGN and HF channels using a simulated QPSK OFDM modem. Runs at the Rs (the symbol rate), assumes ideal modem|
|ldpc_short.m||Simulation used for initial short LDPC code investigation using an ideal rate Rs BPSK modem. Bunch of codes and interleaving schemes tested|
|ofdm_lib.m||Library of OFDM modem functions|
|ofdm_rs.m||Rate Rs OFDM modem simulation used to develop low overhead pilot symbol phase estimation scheme|
|ofmd_dev.m||Rate Fs OFDM modem simulation. This is the real deal, with timing and frequency offset estimation, LDPC integration, and tests for coarse timing and frequency offset estimation|
|ofdm_tx.m||Generates test frames of OFDM raw file samples to play over your HF radio|
|ofdm_rx.m||Receives raw file samples from your HF radio and 700D-demodulates-decodes, and measures BER and PER|
Just this morning I tried to radiate some FreeDV 700D from my home to some interstate SDRs on 40M, but alas conditions were against me. I did manage to radiate across my bench so I know the waveform does make it through real HF radios OK.
Please try sending these files through your radio:
|ssb_otx_224_32.wav||32 frame (5.12 second) interleaver|
|ssb_otx_224_4.wav||4 frame (0.64 second) interleaver|
Get someone (or a websdr) to sample the received signal (8000Hz sample rate, 16 bit mono), and email me the received file.
Or you can decode it yourself using:
The rx side is still a bit rough, I’ll refine it as I try the system with real off-air signals and flush out the bugs.
QB50 SUSat cubesat – Bill and team’s Cubesat currently parked at the ISS!
Codec 2 700C and Short LDPC Codes
Testing FreeDV 700C
Modems for HF Digital Voice Part 1
Modems for HF Digital Voice Part 2
FreeDV 700D – First Over The Air Tests