# Maximal Ratio Combining

Maximal ratio combining is a method of combining the multiple received signal in a MIMO to produce a signal with improved quality.

The received signal are added together after multiplying each with a weight factor that is proportional to the amplitudes of the received signal. Each received signal is weighted according to the received strength and phase and then added together. This assures that the weak signals or the noise is attenuated and the strong signals are enhanced. The weighted addition provides higher signal to noise ratio, thus strengthening the required signal.

This technique was developed in 1954 by an American engineer L R Kahn.

The weight for each signal is directly proportional to the RMS amplitude of the signal and inversely proportional to the mean square noise. MRC is generally used to restore the shape of received signal, to the transmitted one.

Let’s consider a signal *x *transmitted to a receiver endowed with *N* antennas and *h* represent Gaussian variable,

*y = h * x + noise*

then the least squared signal or the maximal ratio combination given by *s’ *can be given by

*s’ = (h₀*y₀ +h₁*y₁…hₙ-₁*yₙ-₁)/(|h₀|²+|h₁|²+…+|hₙ-₁|²)*

This signifies that each signal is individually scaled and rotated according to its phase and strength of the channel. These are then combined to produce maximum ratio between signal and noise.

The MRC technique not only finds its application in field of 5G cellular data communication but is also used in neurology to obtain optimum signals from neurons.

# Conclusion

Thus, with the series of blogs we covered an overview of equalization, its need and different techniques incorporated to achieve improved wireless communication and high speed data transfer.

# References

[1]Jain, Aishwary, Pankaj Shukla, and Lokesh Tharani. “Comparison of various equalization techniques for MIMO system under different fading channels.” In *2017 2nd International Conference on Communication and Electronics Systems (ICCES)*, pp. 913–918. IEEE, 2017.

[2]Wireless Pi — Discover the Joy of Signals and Wireless

[3]Tanbourgi, Ralph, and Friedrich K. Jondral. “Downlink MIMO diversity with maximal-ratio combining in heterogeneous cellular networks.” In *2015 IEEE International Conference on Communications (ICC)*, pp. 1831–1837. IEEE, 2015.

[4] Maximal-ratio combining- wikipedia.com