# [SOLVED]Average energy of square M-QAM constellation

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#### andre_teprom

##### Super Moderator
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I´m not sure, but take a look on ML property stated on page 17 and its resulted equation (1.32). I guess could be due to the dismemberment of the two-dimensional sum into 2 separated sums. I think.

##### Junior Member level 2

I think I understand what's happening.

He adds the $\sqrt{M}$ terms, because he associates MQAM with MPAM modulation, considering also all symbols equally likely to be transmitted, as you suggested.

Specifically, he views the M-QAM system as two separate M-PAM systems with signal constellations of size L=$\sqrt{M}$, one transmitted over the in phase component and the other transmitted over the quadrature component.

Therefore, the square MQAM constellation equals $\sqrt{M}$ $\times$ $\sqrt{M}$.

In order to calculate the average energy of the MQAM system, you calculate the energy of the separate MPAM systems.

So, for each component we add $\sqrt{M}$ points, multiplying the sum by $\sqrt{M}$,
because each dimension has $\sqrt{M }$ series of points.

Finally, each component is divided by M, so as to find the average energy of the MQAM system.

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