M receiver antennas receive M signals each represented as:

rm = αms + ηm,

where ηm is a white Gaussian noise sample added to the mth copy of the signal. A maximum-likelihood (ML) decoder combines these M received signals to find the most likely transmitted signal.We consider a coherent detection scheme where the receiver knows the channel path gains, αm. 

Owing to its array gain, MRC typically achieves a few dB better SNR than does SC.