Possibility of using Power allocation with Maximum likelihood estimation I have a basic question about maximum likelihood (ML) estimator and its implementation with power allocation.
Suppose we are using $MIMO$ system with $4$x$4$ transmit and receive antennas, so the received signal which includes the signal + noise + ISI can be written :
$y = HX + n$
$H,X, n $ are the channel, transmitted signal and noise, respectively.
suppose that only first antennas is active and other antennas are not active, so the transmitted signal will be as below:

My question is about the possibility to use power allocation to detect the active antenna, which means the estimated signal will be as:

I am asking if we can detect the active antenna in that way, is that possible ? Is there another method we can use instead of that ? Is there any document explain that ?
Thank you.
What you mention could be right in low modulation order, such as QAM but in 16-QAM and 32-QAM, the amplitude is changed also, I mean you will have different amplitude levels, so you can't implement that detector.