As mentioned in many books, the average energy of transmitted symbol is given by:
$E_s = (2/3)(M - 1) $
where $M$ indicated the modulation order. Suppose that we are using in the first scenario $SISO$ system, and we need to transmit 8bit/channel use, so the needed modulation is $256QAM$ which is equivalent to $E_s = 170$. now suppose that we are using $MIMO$ system with two transmitters antennas and two receiver antennas, so to transmit the data rate of 8bit/channel use, we need to transmit 4bit/channel use in each antenna, we will need to use $16QAM$, so the needed $E_s = 10$ in each antennas, which is in total 20.
can we say, the power saving for transmitting 8bit/s/Hz in case of using MIMO system is 170/20 ?
Is that right? thank you