Ultimately, the time-bandwidth-power product of a communications protocol must exceed noise by a suitable margin in order for the signal to be detected reliably.
By design, the antenna signal input level of a GPS receiver is 54 dB below the noise floor of the receiver front end. With a liberal application of time and BW, the receiver achieves over 60 dB processing gain. I should note that is not 20-30 dB below the noise, merely 6 dB or so.
The human ear is not phase sensitive. We do no hear zero mean white noise as silence. We perceive the absolute amplitude. So the noise we perceive is the average of that.
The sole difference between integrating over a dit frame and the mean value is dividing by N. Neither has any processing gain in the sense of raising the signal above the noise. It does allow constructing a non-linear filter which appears to recover signals below the noise level. In fact it is a 2 dimensional filter. A frequency and time domain operator. The main advantage is the ability to set a detection threshold which is below human hearing discrimination.
The big gain in clocked Morse is being able to null the noise without predicting it at signal levels below human audio discrimination.
The virtue of clocked Morse is every jurisdiction that allows amateur radio allows Morse. Thus the gain from optimizing Morse by clock synchronization. Statistically, being a few standard deviations above the mean noise over a 1-10 second dit frame is a very sensitive discriminator. One only need to look at the QRSS distance records to confirm this.
Have Fun!
Reg
