# Lower SNR limit of Digital Voice

I’m currently working on a Digital Voice (DV) mode that will work at negative SNRs. So I started thinking about where the theoretical limits are:

1. Lets assume we have a really good rate 0.5 FEC code that approaches the Shannon Limit of perfectly correcting random bit errors up to a channel BER of 12%
2. A real-world code this good requires a FEC frame size of 1000’s of bits which will mean long latency (seconds). Lets assume that’s OK.
3. A large frame size with perfect error correction means we can use a really low bit rate speech codec that can analyse seconds of speech at a time and remove all sorts of redundant information (like silence). This will allow us to code more efficiently and lower the bit rate. Also, we only want speech quality just on the limits of intelligibility. So lets assume a 300 bit/s speech codec.
4. Using rate 0.5 FEC that’s a bit rate over the channel of 600 bit/s.
5. Lets assume QPSK on a AWGN channel. It’s possible to make a fading channel behave like a AWGN channel if we use diversity, e.g. a long code with interleaving (time diversity), or spread spectrum (frequency diversity).
6. QPSK at around 12% BER requires an Eb/No of -1dB or an Es/No of Eb/No + 3 = 2dB. If the bit rate is 600 bit/s the QPSK symbol rate is 300 symbols/s

So we have SNR = Es/No – 10*log10(NoiseBW/SymbolRate) = 2 – 10*log10(3000/300) = -8dB. Untrained operators find SSB very hard to use beneath 6dB, however I imagine many Ham contacts (especially brief exchanges of callsigns and signal reports) are made well beneath that. DV at -8dB would be completely noise free, but of low quality (e.g. a little robotic) and high latency.

For VHF applications C/No is a more suitable measurement, this is a C/No = SNR – 10*log10(3000) = 26.7dBHz (FM is a very scratchy readability 5 at around 43dBHz). That’s roughly a 20dB (100 x) power improvement over FM!

## 2 thoughts on “Lower SNR limit of Digital Voice”

1. John says:

Hi David,

From what I see on HF, SNR changes rapidly due to both propogation and QRM. So it seems to me that a CAN type of protocol might make the most sense.

Us ham radio folks like to push the transmit button and just talk, but it seems to me that interrupting the forward channel to give real-time feedback of received

SNR and then adjusting the forward rate and coding to match the current channel conditions would be something well worthwhile designing in.

So the real issue becomes how slow and robust is the ‘slow’ rate? Certainly some Olivia type signal make the most sense to me.

I regularly run Linrad and feed that into FLDIGI. So I can see various types of fading real-time on the Linrad HF screen. So simple FSK seems to NOT be a good

choice for the slow rate. Maybe some sweep sort of thing. I am not sure of what sorts of ‘good’ simple decoding routines are available to look for low SNR

swept bits. But i bet some of the gurus hanging around here have some real suggestions!

Anyways, I think we could very soon have a robust low-SNR worldwide communications system for voice and data.

Pretty neat :).

John

2. Bill Cowley says:

Hi David,

With some big assumptions and quick sums I think we can go even lower!
Shannon tells us that the Eb/No limit is -1.6 dB. So C/No is then
just -1.6dB + 10*log10(300) = ~23 dBHz if you assume 300 information
bits per second. To translate that to an SNR, let’s assume 4kHz. (The
-1.6dB limit assumes infinite BW, but 4000 is still a fairly large BW
expansion for 300 bit/s.) So now SNR is 23 – 10*log10(4000) = -13dB.

Of course these numbers are unrealistic for various reasons. Apart from
all the sync issues at low SNRs, huge latency and ideal channel coding
requirement, HF is time varying and fading which makes life even more
difficult!

Regards, Bill