# Is there a relationship between Average energy of transmission and power saving

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

Second, you don't transmit $$\log_2(M)$$ bits per second, but rather $$\log_2(M)$$ bits per channel use, which is roughly $$T_s$$ seconds, where $$T_s$$ is the symbol time. So, the bit rate is $$\frac{\log_2(M)}{T_s}$$.
If you adjust your wording to the above by saying 8 bits/channel use, then, yes, you are right, you save energy by using MIMO, but the saving is $$170/20$$ not the reciprocal.
• Thank you .. Yes I totally agree with you. However I supposed that $T_s$ equals one second for simplification. But that means we have power saving almost 90% !! is that right? – Gze Jan 13 '19 at 6:19