The best explanation of the Discrete Fourier Transform (DFT) I have ever seen from Bill Cowley on his Low SNR blog.
There’s a lot of discussion about ADC resolution and SDRs. I’m trying to develop a simple HF data system that uses RTL-SDRs in “Direct Sample” mode. This blog post describes how I measured the Minimum Detectable Signal (MDS) of my 100 bit/s 2FSK receiver, and a spreadsheet model of the receiver that explains my results.
Noise in a receiver comes from all sorts of places. There are two sources of concern for this project – HF band noise and ADC quantisation noise. On lower HF frequencies (7MHz and below) I’m guess-timating signals weaker than -100dBm will be swamped by HF band noise. So I’d like a receiver that has a MDS anywhere under that. The big question is, can we build such a receiver using a low cost SDR?
Experimental Set Up
So I hooked up the experimental setup in the figure below:
The photo shows the actual hardware. It was spaced apart a bit further for the actual test:
Rpitx is sending 2FSK at 100 bit/s and about 14dBm Tx power. It then gets attenuated by some fixed and variable attenuators to beneath -100dBm. I fed the signal into a RTL-SDR plugged into my laptop, demodulated the 2FSK signal, and measured the Bit Error Rate (BER).
I tried a command line receiver:
rtl_sdr -s 1200000 -f 7000000 -D 2 - | csdr convert_u8_f | csdr shift_addition_cc `python -c "print float(7000000-7177000)/1200000"` | csdr fir_decimate_cc 25 0.05 HAMMING | csdr bandpass_fir_fft_cc 0 0.1 0.05 | csdr realpart_cf | csdr convert_f_s16 | ~/codec2-dev/build_linux/src/fsk_demod 2 48000 100 - - | ~/codec2-dev/build_linux/src/fsk_put_test_bits -
and also gqrx, using this configuration:
with the very handy UDP output option sending samples to the FSK demodulator:
$ nc -ul 7355 | ./fsk_demod 2 48000 100 - - | ./fsk_put_test_bits -
Both versions demodulate the FSK signal and print the bit error rate in real time. I really love the csdr tools, and gqrx is also great for a more visual look at the signal and the ability to monitor the audio.
For these tests the gqrx receiver worked best. It attenuated nearby interferers better (i.e. better sideband rejection) and worked at lower Rx signal levels. It also has a “hardware AGC” option that I haven’t worked out how to enable in the command line tools. However for my target use case I’ll eventually need a command line version, so I’ll have to improve the command line version some time.
The RF Gods are smiling on me today. This experimental set up actually works better than previous bench tests where we needed to put the Tx in another room to get enough isolation. I can still get 10dB steps from the attenuator at -120dBm (ish) with the Tx a few feet from the Rx. It might be the ferrites on the cable to the switched attenuator.
I tested the ability to get solid 10dB steps using a CW (continuous sine wave) signal using the “test” utility in rpitx. FSK bounces about too much, especially with the narrow spec an settings I need to measure weak signals. The configuration of the Rigol DSA815 I used to see the weak signals is described at the end of this post on the SM2000.
The switched attenuator just has 10dB steps. I am getting zero bit errors at -115dBm, and the modem fell over on the next step (-125dBm). So the MDS is somewhere in between.
This spreadsheet (click for the file) models the receiver:
By poking the RTL-SDR with my signal generator, and plotting the output waveforms, I worked out that it clips at around -30dBm (a respectable S9+40dB). So that’s the strongest signal it can handle, at least using the rtl_sdr command line options I can find. Even though it’s an 8 bit ADC I figure there are 7 magnitude bits (the samples are unsigned chars). So we get 6dB per bit or 42dB dynamic range.
This lets us work out the the power of the quantisation noise (42dB beneath -30dBm). This noise power is effectively spread across the entire bandwidth of the ADC, a little bit of noise power for each Hz of bandwidth. The bandwidth is set by the sample rate of the RTL-SDRs internal ADC (28.8 MHz). So now we can work out No (N-nought), the power/unit Hz of bandwidth. It’s like a normalised version of the receiver “noise floor”. An ADC with more bits would have less quantisation noise.
There follows some modem working which gives us an estimate of the MDS for the modem. The MDS of -117.6dBm is between my two measurements above, so we have a good agreement between this model and the experimental results. Cool!
Falling through the Noise Floor
The “noise floor” depends on what you are trying to receive. If you are listening to wide 10kHz wide AM signal, you will be slurping up 10kHz of noise, and get a noise power of:
-146.6+10*log10(10000) = -106.6 dBm
So if you want that AM signal to have a SNR of 20dB, you need a received signal level of -86.6dB to get over the quantisation noise of the receiver.
I’m trying to receive low bit rate FSK which can handle a lot more noise before it falls over, as indicated in the spreadsheet above. So it’s more robust to the quantisation noise and we can have a much lower MDS.
The “noise floor” is not some impenetrable barrier. It’s just a convention, and needs to be considered relative to the bandwidth and type of the signal you want to receive.
One area I get confused about is noise bandwidth. In the model above I assume the noise band width is the same as the ADC sample rate. Please feel free to correct me if that assumption is wrong! With IQ signals we have to consider negative frequencies, complex to real conversions, which all affects noise power. I muddle through this when I play with modems but if anyone has a straight forward explanation of the noise bandwidth I’d love to hear it!
At the suggestion of Mark, I repeated the MDS tests with a strong CW interferer from my signal generator. I adjusted the Sig Gen and Rx levels until I could just detect the FSK signal. Here are the results, all in dBm:
|Sig Gen||2FSK Rx MDS||Difference|
The FSK signal was at 7.177MHz. I tried the interferer at 7MHz (177 kHz away) and 7.170MHz (just 7 kHz away) with the same blocking results. I’m pretty impressed that the system can continue to work with a 65dB stronger signal just 7kHz away.
So the interferer desensitises the receiver somewhat. When listening to the signal on gqrx, I can hear the FSK signal get much weaker when I switch the Sig Gen on. However it often keeps demodulating just fine – FSK is not sensitive to amplitude.
I can also hear spurious tones appearing; the quantisation noise isn’t really white noise any more when a strong signal is present. Makes me feel like I still have a lot to learn about this SDR caper, especially direct sampling receivers!
As with the MDS results – my blocking results are likely to depend on the nature of the signal I am trying to receive. For example a SSB signal or higher data rate might have different blocking results.
Still, 65dB rejection on a $27 radio (at least for my test modem signal) is not too shabby. I can get away with a S9+40dB (-30dBm) interferer just 7kHz away with my rx signal near the limits of where I want to detect (-96dBm).
So I figure for the lower HF bands this receivers performance is OK – the ADC quantisation noise isn’t likely to impact performance and the strong signal performance is good enough. An overload of -30dBm (S9+40dB) is also acceptable given the use case is remote communications where there is unlikely to be any nearby transmitters in the input filter passband.
The 100 bit/s signal is just a starting point. I can use that as a reference to help me understand how different modems and bit rates will perform. For example I can increase the bit rate to say 1000 bit/s 2FSK, increasing the MDS by 10dB, and still be well beneath my -100dBm MDS target. Good.
If it does falls over in the real world due to MDS performance, overload or blocking, I now have a good understanding of how it works so it will be possible to engineer a solution.
For example a pre-amp with X dB gain would lower the quantisation noise power by X dB and allow us to detect weaker signals but then the Rx would overload at -30-X dB. If we have strong signal problems but our target signal is also pretty strong we can insert an attenuator. If we drop in another SDR I can recompute the quantisation noise from it’s specs, and estimate how well it will perform.
This post describes tests to evaluate the use of rpitx as a 2FSK transmitter.
About 10 years ago I worked on the Village Telco – a system for community telephone networks based on WiFi. At the time we used WiFi SoCs which were open source at the OS level, but the deeper layers were completely opaque which led (at least for me) to significant frustration.
Since then I’ve done a lot of work on the physical layer, in particular building my skills in modem implementation. Low cost SDR has also become a thing, and CPU power has dropped in price. The physical layer is busy migrating from hardware to software. Software can, and should, be free.
So now we can build open source radios. No more chip sets and closed source.
Sadly, some other aspects haven’t changed. In many parts of the world it’s still very difficult (and expensive) to move an IP packet over the “last 100 miles”. So, armed with some new skills and technology, I feel it’s time for another look at developing world and humanitarian communications.
I’m exploring the use rpitx as the heart of HF and UHF data terminals. This clever piece of software turns a Raspberry Pi into a radio transmitter. Evariste (F5OEO) the author of rpitx, has recently developed the v2beta branch that has improved performance, and includes some support for FreeDV waveforms.
I have some utilities for the Codec 2 FSK modem that generate frames of test bits. I modified the fsk_mod_ext_vco utility to drive a utility Evariste kindly wrote for FreeDV experiments with rpitx. So here are the command lines that generate 600 seconds (10 minutes) of 100 bit/s 2FSK test frames, and transmit them out of rpitx, using a 7.177 MHz carrier frequency:
$ ./fsk_get_test_bits - 60000 | ./fsk_mod_ext_vco - ~/rpitx/2fsk_100.f 2 --rpitx 800 100
~/rpitx $ sudo ./freedv 2fsk_100.f 7177000
On the receive side I used my FT-817 connected to FreeDV to sample the signal as a wave file, then fed the signal into C and Octave versions of the demodulator. The RPi is top left at rear, the HackRF in the foreground was used initially as a reference transmitter:
It works really well! One of the most important tests for any modem is adding calibrated noise and measuring the Bit Error Rate (BER). I tried Eb/No = 9dB (-5.7dB SNR), and obtained 1% BER, right on theory for a 2FSK modem:
$ ./cohpsk_ch ~/Desktop/2fsk_100_rx_rpi.wav - -26 | ./fsk_demod 2 8000 100 - - | ./fsk_put_test_bits - FSK BER 0.009076, bits tested 11900, bit errors 108 SNR3k(dB): -5.62
This line takes the sample wave file from the FT-817, adds some noise using the cohpsk_ch utility, then pipes the signal to the FSK demodulator, before counting the bit errors in the test frames. I adjusted the 3rd “No” parameter in cohpsk_ch by hand until I obtained about 1% BER, then checked the SNR against the theoretical SNR for an Eb/No of 9dB.
Here are some plots from the Octave version of the demodulator, with no channel noise applied. The first plot shows the time and frequency domain signal at the input of the demodulator. I set the shift at 800 Hz, so you can see one tone at 800 Hz,the other at 1600 Hz:
Here is the output the of the FSK demodulator filters (red and blue for the two filter outputs). We can see a nice separation, but the red “high” level is a bit lower than blue. Red is probably the 1600 Hz tone, the FT-817 has a gentle low pass filter in it’s output, reducing higher frequency tones by a few dB.
There is some modulation on the filter outputs, which I think is explained by the timing offset below:
The sharp jump at 160 samples is expected, that’s normal behaviour for modem timing estimators, where a sawtooth shape is expected. However note the undulation of the timing estimate as it ramps up, indicating the modem sample clock has a little jitter. I guess this is an artefact of rpitx. However the BER results are fine and the average sample clock offset (not shown) is about 50ppm which is better than many sound cards I have seen in use with FreeDV. Many of our previous modem transmitters (e.g. the first pass at Wenet) started with much larger sample clock offsets.
A common question about rpitx is “how clean is the spectrum”. Here is a sample from my Rigol DSA815, with a span of 1MHz around the 7.177 MHz tx frequency. The Tx power is actually 11dBm, but the marker was bouncing around due to FSK modulation. On a wider span all I can see are the harmonics one would expect of a square wave signal. Just like any other transmitter, these would be removed by a simple low pass filter.
So at 7.177 MHz it’s clean to the limits of my spec analyser, and exceeds spectral purity requirements (-43dBc + 10log(Pwatts)) for Amateur (and I presume other service) communications.
In the previous post on Codec 2 2200 I described a prototype speech codec for a new, higher quality FreeDV mode. In this post I describe the modem development and initial over the air tests.
Bandwidth, not SNR limited
Turns out I am RF bandwidth limited rather than SNR limited. My target bandwidth over the channel is 2000 Hz, as FreeDV needs to pass through the various crystal filters in Commercial Off the Shelf (COTS) SSB radios. Things get messy near the edge of those filters. I want to stick with QPSK for now as QAM means a 4dB hit in SNR at the same bit rate. By messing with my waveform design spreadsheet it turns out I can get between 2000 and 2400 bit/s of coded speech through the channel by reducing the FEC code rate. This is acceptable for high-ish SNR channels with light fading.
This gives us an AWGN channel operating point of 4dB SNR, so we have 6dB margin for fading if we design for an average channel SNR of 10dB. That feels about right.
For the speech quality target I wanted to used 20ms frame updates (the lower rate Codec 2 1300 and 700C modes use 40ms updates). However that was a bit of a squeeze. I messed about with Vector Quantisation for a while but the quality was slipping beneath the Codec 2 2400 bit/s target I had set for this project. Then I hit on the idea of 25ms updates, and that seems to work well. I can’t hear any difference between 20 and 25ms updates.
Note the interaction between the speech codec frame rate and the modem bandwidth. As the entire system is open source, I can adapt with the codec to help the modem. This is a very powerful engineering technique that is not available to teams using closed source codec or modem software.
FreeDV 2200, like FreeDV 1600 has some “unprotected bits”. The LDPC forward error correction only covers part of the frame. I’m not sure about this approach, and will talk to Bill, VK5DSP sometime about a lower rate code that protects the entire frame.
A digital voice system is complex. Building the real time C code for a new codec, FEC, modem stack can take a lot of time and effort. FreeDV 700D took around 1000 man-hours. So I tend to simulate the whole thing in GNU Octave first. This allows me to prototype the entire system with the least possible effort. If it works, I then port to C, and I have a working reference to test the C port against. The basic idea is find any bad news early.
I modified the Octave version of the modem to handle the different bit rate through changing the number of carriers, symbol rate, and FEC. I started by modifying the raw, uncoded OFDM modem simulations (ofdm_tx.m, ofdm_rx.m), then moved to the versions that include the LDPC FEC.
After a few days of careful programming, testing, and refactoring I was able to transmit and receive test frame using the prototype “FreeDV 2200” waveform. Such a surprise when something complex starts working! Engineers are not used to success, we spend most of our time chasing bugs.
Using the new waveform I ran some coded speech through simulated AWGN and HF channels at the calculated operating points. Ouch! That hurts. Some really high amplitude excursions in the decoded speech, especially when the frames are messed up by a fade or during initial synchronisation.
These sorts of noises used to be common in the early days of speech coding. In contrast, my recent codecs have a “softer” response to bit errors – the speech gets messed up, but not in a way that causes pain.
OK so my initial tests showed that even with 10dB average SNR, sometimes that nasty old HF channel wipes out the codec and it makes loud cracks. What to do? I don’t have any bandwidth left over for more FEC and don’t want to dramatically change the Codec design.
The first thing I did was change the variable bit rate allocation Huffman code to a fixed bit allocation, as explained in the Codec 2 2200 blog post. That helped. The next step was to spent a few days developing some “error masking” ideas. These don’t actually fix the problem, but make it sound more acceptable.
The LDPC decoder kindly tells us when it can’t successfully decode a frame. When that happens, the masking algorithm swings into action. We know some of the bits are rubbish, but not exactly which ones. An AGC algorithm adjusts the energy of the current frame to be similar to the last good one. This helps with the big spikes. If we get a burst of errors the level is smoothly reduced, effectively squelching the signal.
After a few days of tweaking I had this working OK. Here are some plots of the speech signal before and after masking:
Here are some plots that illustrate the masking algorithm. The top plot is the number of errors/frame, they appear in bursts with the channel fading. The lower plot is the energy of the decoded speech before and after masking. When there are no errors, the energy is the same. During an error burst we reduce the gain, exponentially dropping the level if an error burst continues.
Here are some speech samples so you can hear the effect of bit errors:
|HF Channel Masking||Listen|
|HF Channel SSB||Listen|
|HF Channel FreeDV 1600||Listen|
The FreeDV 1600 sample takes a while to sync, perhaps due to that deep fade at the start of the sample. The 2200 modem was derived from 700D, which can sync up at very low SNRs. Much to my annoyance the SSB sample doesn’t seem very bothered by the fading – a testament to robustness of SSB and why it’s so hard to beat. The first few seconds of the SSB sample are “down in the mud” and would probably be lost to untrained listeners.
Over the Air Testing with the Peters
So now I had simulations of every part of FreeDV 2200 ready to roll. The modem simulations work on wave files, which can be played over the air through real HF radios. This is a very important test, as real radios have crystal filters, power amplifiers, and audio filtering that can affect the passage of bits through them.
My first test was across the bench. I played the OFDM signal at low power through my IC-7200 tuned to 7.177MHz, and connected to an external dipole. I received the signal on my FT-817 without an antenna, while recording the signal using FreeDV. I took special care to make sure the IC-7200 wasn’t being over driven, adjusting the transmit drive so the ALC wasn’t moving at all.
The scatter diagram was a bit messed up, and SNR about 13dB, which is pretty typical of tests through real radios, even with no noise. I measure SNR from the scatter diagram, so any distortion in the signal will lower the SNR reported by FreeDV. An important figure of merit is the effect on Bit Error Rate (BER), which can be measured in dB. So I generated a transmit signal with additive noise that had an Eb/No of 3dB. When passed directly to the Rx script I measured a BER of 3%. When the same signal was passed through the radios, then to the Rx script, I measured a BER of 5%.
Looking at the PSK BER versus Eb/No curves, this is a difference of 1.2dB. The distortion of the path through the radios is equivalent to 1.2dB more noise in the system. That’s quite acceptable to me; given the wide bandwidth of the signal compared to the crystal filter skirts, PA distortion, likely rx overload as the radios are so close, and other real world factors.
The next step was some ground wave and DX tests. Peter, VK2PTM, happened to be staying with me. So we hopped in his van and set up a receive station about 4km away, where Peter, VK5APR joined us for the tests. We received a very nice signal on Peter’s (2TPM Peter that is) KX3, in fact a nicer scatter diagram than with my FT-817. Zero BER, despite just a few watts Tx power.
Peter has documented our FreeDV experiments on his blog.
For the final test, we radiated the same test signal from Adelaide about 700km to Peter, VK3RV, about 700km away in Sunbury, near Melbourne. Once again we were on 40M, and this time I was using a few 10’s or watts. Hard to tell exactly with these waveforms. Peter kindly recorded the FreeDV 2200 signal, and emailed it back to me.
You don’t have to be called Peter to be a FreeDV early adopter. But it helps.
This time there was some significant fading, and bursts of bit errors. The SNR averaged about 8dB over our 60 second sample but being a real HF channel the SNR wandered all over the place:
Note the deep fade at the start of the sample, which is also evident in the second plot of uncoded and coded errors above. The Scatter diagram is the classic cross shape, as the amplitudes of the QPSK symbols fade in and out. The channel noise is evident in the width of the cross.
When played back through the speech codec it worked OK (Listen), and sounds similar to the simulated HF channel samples above. The deep fades are gently muted and the overall effect was not unpleasant. Long distance HF conditions are poor here at the moment, so I didn’t get a chance to test the system on more benign HF channels.
I’m very pleased with these tests. It’s a very complicated system and so many things can go wrong when it hits the real world. The careful work I put into test and simulation has paid off. I am particularly happy with the 2000 Hz wide modem waveform making it through real radios and real channels as I felt that was a major risk.
These two posts have described the development to date of a new FreeDV mode. It’s a work in progress, and I feel another iteration on the speech codec quality and FEC would be useful. I’m quite pleased with the higher bit rate version of the OFDM modem. It would also be nice to get the current work into real time, so we can test it on air – using the open source principle of “release early and often”.
The development process for a new FreeDV waveform is not linear. I started with the codec, got a feel for the bit rate, played with the modem waveforms design spreadsheet, then headed back to the codec design. When I put the waveform through a simulated channels I found bit errors made the speech codec fall over so it was back to the codec for some rework.
However the cool thing about open source is that we can consider all these factors at the same time. If you are stuck with a closed source codec or modem you have far more limited options and will end up with poorer performance. Ok, I also have the skills to work on both, but that’s why I’m publishing these posts and the source code! It’s a great starting point for anyone else who wants to learn, or build on this work. Yayyy open source!
An important next step is to put FreeDV 2200 into real time, so we can test with real over the air conversations. This means porting some code from Octave to C, unit tests, and a bunch of integration with the FreeDV API and FreeDV GUI program. Please contact me if you have C programming skills and would like to help. I’ll help you with the Octave side, and you’ll learn a lot!
Appendix – Command Lines for testing the new Waveform
Here are the command lines I used to test the new FreeDV waveform over the air. I tend to prototype in Octave, to minimise the amount of time it takes to get something over the air that I can listen to. A wrong turn can mean months of work, so an efficient process matters.
Use c2sim to generate files of Codec 2 model parameters from an input speech file:
$ ./c2sim ../../raw/vk5qi.raw --framelength_s 0.0125 --dump vk5qi_l --phase0 --lpc 10 --dump_pitch_e vk5qi_l_pitche.txt
Run an Octave script to encode model parameters to a 2200 (ish) bit/s second bit stream:
octave:40> newamp2_batch("../build_linux/src/vk5qi_l","no_output","mode", "enc", "bitstream", "vk5qi_2200_enc.c2");
Run an Octave script to generate OFDM modem transmitter audio. The payload data is known test frames at 2200 bit/s:
Three hundred seconds are generated in this example, about 5 minutes.
This raw file can be “played” over the air through a HF SSB radio, then recorded as a wave file by a HF radio receiver. The received wave (or raw) file, is run through the OFDM modem receiver. Using the known test frame data, it measures the Bit Error rate (BER) and plots various statistics. It also generates a file of errors, that shows each bit that was received in error:
This C utility “corrupts” the Codec 2 bit stream using the file of errors, simulating the path of real Codec 2 bits through the channel:
$ ../build_linux/src/insert_errors vk5qi_2200_enc.c2 vk5qi_2200_sunbury001_dec.c2 subury001_error.bin
Now decode the bit stream to a set of Codec 2 model parameters:
octave:43> newamp2_batch("../build_linux/src/vk5qi_l","output_prefix","../build_linux/src/vk5qi_l_dec_sunbury001", "mode", "dec", "bitstream", "vk5qi_2200_sunbury001_dec.c2", "mask", "subury001_error.bin");
The “mask” parameter uses the error file to implement an error masking algorithm. In a real world system, the LDPC decoder would tell use which frames were bad, so this is a mild cheat to expedite development.
Finally, run C part of Codec 2 decoder to listen to the results:
$ ./c2sim ../../raw/vk5qi.raw --framelength_s 0.0125 --pahw vk5qi_l_dec_sunbury001 --hand_voicing vk5qi_l_dec_sunbury001_v.txt -o - | aplay -f S16
FreeDV 700D has shown digital voice can outperform SSB at low SNRs over HF multipath channels. With practice the speech quality is quite usable, but it’s not high quality and is sensitive to different speakers and microphones.
However at times it’s like magic! The modem signal is buried in all sorts of HF noise, getting hammered by fading – then one of my friends 800km away breaks the FreeDV squelch (at -2dB!) and it’s like they are in the room. No more hunched-over-the-radio listening to my neighbours plasma TV power supply.
There is a lot of promise in FreeDV, and it’s starting to come together.
So now I’d like to see what we can do at a higher SNR, where SSB is an armchair copy. What sort of quality can we develop at 10dB SNR with light fading?
The OFDM modem and LDPC Forward Error Correction (FEC) used for 700D are working well, so the idea is to develop a high bit rate/high(er) quality speech codec, and adapt the OFDM modem and LPDC code.
So over the last few months I have been jointly designed a new speech codec, OFDM modem, and LDPC forward error correction scheme called “FreeDV 2200”. The speech codec mode is called “Codec 2 2200”.
Coarse Quantisation of Spectral Magnitudes
I started with the design used for Codec 2 700C. The resampling step is the key, it converts the time varying number of harmonic amplitudes to fixed number (K=20) of samples covering 100 to 4000 Hz. They are sampled using the “mel” scale, which means we take more finely spaced samples at low frequencies, with coarser steps at high frequencies. This matches the log frequency response of the ear. I arrived at K=20 by experiment.
This Mel-resampling is not perfect. Some samples, like hts1a, have narrow formants at higher frequencies that get undersampled by the Mel resampling, leading to some distortion. Linear Predictive Coding (LPC) (as used in many Codec 2 modes) does a better job for some of these samples. More work required here.
In Codec 2 700C, we vector quantise the K=20 Mel sample vectors. For this new Codec 2 mode, I experimented with directly quantising each sample. To my surprise, I found very little difference in speech quality with coarsely quantised 6dB steps. Furthermore, I found we can limit the rate of change between samples to a maximum of +/-12 dB. This allows each sample to be delta-coded in frequency using a step of 0, -6, +6, -12, or +12dB. Using a 2 or 3 bit Huffman coding approach it turns out we need 45-ish bit/s frame for good quality speech.
After some experimentation with bit errors, I ended up using a fixed bit allocation rather than Huffman coding. Huffman coding uses variable length symbols (in my case 2 and 3 bits). After a bit error you don’t know where the next variable length symbol in the string starts and ends. So a single bit error early in the bits describing the spectrum can corrupt the entire spectrum.
|Parameter||Bits Per Frame|
At a 25ms frame update rate this is 56/0.025 = 2240 bits/s.
Here are some samples that show the effect of the processing stages. During development it’s useful to listen to the effect each stage has on the codec speech quality, for example to diagnose problems with a sample that codes poorly.
|Codec 2 Unquantised 12.5ms frames||Listen|
|Quantised to 6dB steps||Listen|
|Fully Quantised with 44 bits/25ms frame||Listen|
Here is a plot of 50 frames of coarsely quantised amplitude samples, the 6dB steps are quite apparent:
To test the prototype 2200 mode I performed listening tests using 15 samples. I have collected these samples over time as examples that tend to challenge speech codecs and in particular code poorly using FreeDV 1600 (i.e. Codec 2 1300). During my listening tests I use a small set of powered speakers and for each sample chose which codec algorithm I prefer, then average the results over the 15 samples.
Over the 15 samples I felt 2200 was just in front of 2400 (on average), and well in front to 1300. There were some exceptions of course – it would useful to explore them some time. I was hoping that I could make 2200 significantly better than 2400, but ran out of time. However I am pleased that I have developed a new method of spectral quantisation for Codec 2 and come up with a fully quantised speech codec based on it at such an early stage.
Here are a few samples processed with various speech codecs. On some of them 2200 isn’t as good as 2400 or even 1300. I’m presenting some of the poorer samples on purpose – the poorly coded samples are the interesting ones worth investigating. Remember the aims of this work are significant improvements over (i) Codec 2 1300, and (ii) SSB at around 10dB SNR. See what you think.
I feel the coarse quantisation trick is a neat way to reduce the information in the speech spectrum and is worth exploring further. There must be more efficient, and higher quality ways to encode this information. I did try some vector quantisation but wasn’t happy with the results (I always seem to struggle with VQ). However I just don’t have the time to explore every R&D path this work presents.
Quantisers can be stored very efficiently, as the dynamic range of the spectral sample is low (a few bits/sample) compared to floating point numbers. This simplifies storage requirements, even for large VQs.
Machine learning techniques could also be applied, using some of the ideas in this post as “pre-processing” steps. However that’s a medium term project which I haven’t found time for yet.
In the next post, I’ll talk about the modem and LDPC codec required to build FreeDV 2200.
Peter, VK2TPM, visited my home this week and has written nice blog post showing FreeDV development in action. Really enjoyed your visit Peter!
The objectives for this work are:
- Test our 4FSK Binary open source balloon telemetry over the air on a real HAB mission.
- 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.
- 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.
- 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.
- Show how we develop open source protocols, by blogging on our work, sharing our design and test techniques and most importantly the source code.
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.
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.
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|
|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.
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.
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.
Thomas Kurin is a Masters student at the Institute of Electronics Engineering, part of the Friedrich-Alexander University Erlangen-Nuremberg. Thomas and his supervisor Stefan Erhardt recently contacted me with some exciting news – a version of Codec 2 running at 450 bit/s, including a 16 kHz mode!
I’m very happy that Codec 2 can be used as a starting point for academic research, and thrilled about the progress Thomas has made. It’s also great for me to have a contribution to Codec 2 on such a deep technical level. Thomas has done a lot of work in vector quantisation, an area that I struggle in, and has developed an innovative 16 kHz mode.
Any speech codec running as low at 450 bit/s is pretty special, and this work is also a great starting point for further innovation and quality improvements.
Thomas has sent me some samples, and is working with me to merge his new mode into codec2-dev, and has kindly offered to tell us his story below. Well done Thomas
Here are Thomas (left) and Stefan (right) working together on their innovative 450 bit/s Codec 2 mode at the University of Erlangen:
Now this is bleeding edge, very low bit rate speech coding. Don’t expect Hi-Fi. The use case is channels where no other speech signal can get through. Ham radio operators will know what I mean.
If integrated with FreeDV, a 450 bit/s codec translates to a 2dB improvement in SNR over FreeDV 700D. This would support digital speech over HF radio at lower than -4dB SNR. Weak signal or FreeDV EME anyone?
Listen to the samples, and please add your comments. How does it compare to Codec 2 at 1300 and 700 bit/s? Could you communicate using this mode?
|Sample||1300||700C||450 8kHz||450 16kHz|
The samples I use are deliberately chosen to give codecs a hard time. mmt1 is the worst, it has high level truck background noise added to it.
As a masters student at FAU Erlangen-Nürnberg I have been working on and with Codec 2 and especially with 700C for the last few months. I experimented with the source code and the Vector Quantisation. This lead to the 450 bit/s Codec which shall be shown in the following post.
The 450 Codec builds on the 700C Codec. It consists of 3 major changes:
- The training data used for Vector Quantisation (VQ) was changed to include multiple languages, as for other languages the VQ sometimes performed poorly because certain vectors were missing. The used dataset consisted of approximately 30 minutes English, 30 minutes German, 15 minutes Russian, 15 minutes Chinese and 15 minutes Spanish. This Codebook allowed a switch from the two stage VQ with 9 * 2 = 18 bit per frame to a one stage VQ with just 9 bit per frame for VQ. The audio quality is of course somewhat changed, but still understandable.
- The energy quantisation was changed from 4 bit to 3 bit as no change in quality for the one stage VQ was detectable. This leads to a reduction of 9 + 1 = 10 bit, from a 28 bit frame to a 18 bit frame. This means a 450 bit/s Codec.
- The biggest change was the inclusion of a 16k mode. This means the 8kHz sampled and encoded signal can be converted to a 16kHz sampled signal at the decoder. To achieve this, the codebook was trained with data sampled at 16kHz. Then only the vectors for the 0-4 kHz frequencies (= 8kHz sample rate) are used for encoding. The decoder uses the indices to look up the 16kHz sampled and trained vectors. This works because a vector that is similar between 0-4 kHz mostly also looks similar in 4-8 kHz. This results in a pseudo-wideband format without any additional bits. For some speakers this improves quality, but for some speakers it just creates noise. But that’s the beauty of the system, as the same data can both be decoded to a 8kHz sampled signal, and to a 16kHz sampled signal. Therefore the transmitted signal stays the same and the receiver can choose dependent on quality which mode he wants to listen on.The 16k mode still needs some refinement but its fascinating that it works at all.
Over the next week or so I will patch the changes with David against codec2-dev. As it is a new codec, it shouldn’t change any of the other codecs when patching, as most of the patching will be to include new files.
I’ve written so many blog posts in the last 12 years I can’t find them when I need them again. So here is an Archive page…
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.
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.
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.
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.