Live~NRGY

Quadrature amplitude modulation

http://en.wikipedia.org/wiki/Quadrature_amplitude_modulation

…”Non-rectangular QAM

Constellation diagram for circular 8-QAM.

Constellation diagram for circular 16-QAM.
It is the nature of QAM that most orders of constellations can be constructed in many different ways and it is neither possible nor instructive to cover them all here. This article instead presents two, lower-order constellations.

Two diagrams of circular QAM constellation are shown, for 8-QAM and 16-QAM. The circular 8-QAM constellation is known to be the optimal 8-QAM constellation in the sense of requiring the least mean power for a given minimum Euclidean distance. The 16-QAM constellation is suboptimal although the optimal one may be constructed along the same lines as the 8-QAM constellation. The circular constellation highlights the relationship between QAM and PSK. Other orders of constellation may be constructed along similar (or very different) lines. It is consequently hard to establish expressions for the error rates of non-rectangular QAM since it necessarily depends on the constellation. Nevertheless, an obvious upper bound to the rate is related to the minimum Euclidean distance of the constellation (the shortest straight-line distance between two points):

Again, the bit-error rate will depend on the assignment of bits to symbols.

Although, in general, there is a non-rectangular constellation that is optimal for a particular , they are not often used since the rectangular QAMs are much easier to modulate and demodulate.”…

The Big Dipper – for all you geniuses out there, let’s see if you can figure it out without me having to put it in print. Then I would like someone to explain it to me in plain English language and see if we can come up with a common and precise definition of the conclusion that can be drawn from 8-QAM.

Hint – use the mirror principle if at a loss for ideas.

And this is very important – if that mathematical formula is right, then we’ve all hit the Jack POT and unlimited Pot of Gold here.

This is really important – so focus here. I’ll explain later.