Maximum Ratio Combining (MRC) is an optimization technique for combining signals that are carrying the same information.  Maximum ratio combining is most often applied to MIMO or SIMO wireless communications systems.  MRC is similar to classical beamforming.  The goal of classical beamforming solutions is to maximize the signal level from a specified direction by aligning the phases of the signals.  MRC includes phase alignment, but the phase alignment may not correspond to a particular direction.  The ultimate goal is to maximize the SNR of the received signal.

The image below shows the diagram and equations of a SIMO system, and the equations for maximum ratio combining.

maximum ratio combining block diagram

The transmitted symbol, s[n], can be transmitted out in all directions.  The path for which the symbols took to arrive at each receiver are not equal. A MRC receiver applies a weight to each receive symbol, x[n]. In order to determine the optimal combination, the characteristics of the channels need to be estimated blindly or through a pilot signal.  Once the channel information has been estimated more weight is given to the receiver that has the higher SNR.  This weighted receiver combination along with phase alignment mitigates the effects of channel fading and lowers the bit error rate of the communication channel.