[Elecraft] dB Changes, Loudness, and Signal to Noise Ratio

[Kok Chen]

On Dec 15, 2009, at 9:52 AM, Jim Brown wrote:

> ...we are working on the signal to noise ratio, NOT LOUDNESS. It's apples and 
> oranges!  The only thing in common is that we're using a log ratio to 
> describe it. 

I couldn't agree more with Jim on this one.  In our "business," we are trying to get information across, instead of determining if one signal is louder than another.  This is demonstrated especially well with digital modes, where we can measure with objective detectors instead of using the subjective gray matter between our ears.

Take a look at this example for DominoEX 8:

http://homepage.mac.com/chen/Technical/DominoEX/AWGN/AWGN/dominoex8.html

The vertical axis is the percentage character error rate.  

Notice that for the primary DominoEX channel, a single dB of signal-to-noise ratio change, from a SNR of -13 dB to a SNR of -14 dB, moves the percentage character error from about 0.2% to almost 2%, a factor of almost 10 of errors.

(In case you wonder how deep the signal is within noise and yet be copied reliably, it is really not.  The noise in the above plot is measured within a 3 kHz bandwidth.  In a 500 Hz noise bandwidth for example, the -13 dB SNR would correspond to about -5 dB SNR; albeit, still not too shabby.  This is why you often see the SNR expressed as Eb/No in technical circles, but hams like to use SNR within 3 kHz noise bandwidth.)

Steep sensitivity curves like this is very typical for digital mode demodulators.  The curves do flatten out when you add multipath and Rayleigh fading.  It can be seen in the example here:

http://homepage.mac.com/chen/Technical/DominoEX/ITU/ITU/nvis.html

That being said, there are cases where even a 10 dB increase in power will still not get you anywhere. In extreme propagation cases, some modes don't get through no matter how much power you use, see the case of non-FEC DominoEX 4 (blue curve) here, while the FEC versions will get through:

http://homepage.mac.com/chen/Technical/DominoEX/ITU/ITU/highLatModerate.html

73
Chen, W7AY