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Multi-Amplitude Signaling (MAS) Concept
IF your circuits could go as fast as you wanted, and
IF complexity were free, and
IF your SNR slope is at least -40 dB/decade or worse,
THEN try multi-level signaling
B = number of informational bits carried per baud
f/B = new signaling rate (where f is the old rate)
N = 2B number of levels
1/(N-1) = 1/(2B-1) = reduction in spacing between levels
. . . . . .simplistic model - things might not be this bad
What you GAIN by reduction in baud rate:
log(B)*(SNR slope)
Sometimes exceeds what you LOSE by reduced level-spacing:
20*log(2B-1)
With a large enough SNR slope you always GAIN more than you LOSE
Those of you familiar with communications theory will recognize that a circuit afflicted with
merely 20 or even 30 dB/decade of SNR deterioration is optimally filled with a binary signal,
operating at the highest cycle frequency possible. That's what we've always done to date, and
in a world dominated by skin-effect losses, where the SNR deterioration isn't too fast, binary
signaling is the way to go.
On the other hand, when you are faced with a brick-wall communications channel, one with a
finite bandwidth above which the SNR deteriorates miserably (like an analog telephone channel),
the best this to do, to the extent that you have any excess SNR to work with, is to use
multi-level signaling.
In the PCB world, the -40 dB/decade SNR slope produced by dielectric loss forms, in effect, a
brick wall. The best way to increase bandwidth on long, dielectric-loss-afflicted channels is
to use multilevel signaling.
In it's most simplistic form, the multilevel argument goes like this: start with a binary system,
then chop the signaling rate by a factor of B and try using 2B levels. You gain
SNR at a rate of log(B)*40 (because of the 40 dB/decade SNR slope), but lose SNR
proportional to 20*log(2B-1) due to the number of levels.
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