the difference two MIMO systems

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medototy

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what is the difference between this systems(y=HX+w) and (y=H*P^1/2*X+w) in sense of detection process of MIMO systems? where y is the receive symbols, H is the channel matrix, X is the transmit symbols, P is the trasmit power for each antenna, w: noise .
 


P is diagonal?
 

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