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:
- 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%
- 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.
- 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.
- Using rate 0.5 FEC that’s a bit rate over the channel of 600 bit/s.
- 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).
- 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!