Editing Maximal-ratio combining

In [[telecommunications]], '''maximum-ratio combining''' ('''MRC''') is a method of [[diversity combining]] in which:
#the signals from each [[Communication channel|channel]] are added together,
#the [[Gain (electronics)|gain]] of each channel is made [[Proportionality (mathematics)|proportional]] to the rms [[signal level]] and inversely proportional to the mean square [[Noise (electronics)|noise level]] in that channel.
#different proportionality constants are used for each channel. 
It is also known as '''ratio-squared combining''' and '''predetection combining'''.  Maximum-ratio combining is the optimum combiner for independent [[additive white Gaussian noise]] channels.

MRC can restore a signal to its original shape. The technique was invented by American engineer [[Leonard R. Kahn]]<ref name="MRC">{{cite journal|last1=Kahn|first1=Leonard|title=Ratio Squarer|journal=Proc. IRE (Corresp.)|date=November 1954|volume=42|issue=11|page=1704|doi=10.1109/JRPROC.1954.274666}}</ref> in 1954.

MRC has also been found in the field of neuroscience, where it has been shown that neurons in the retina scale their dependence on two sources of input in proportion to the signal-to-noise ratio of the inputs.<ref>{{Cite journal|last1=Homann|first1=Jan|last2=Freed|first2=Michael A.|date=2016-12-30|title=A mammalian retinal ganglion cell implements a neuronal computation that maximizes the SNR of its postsynaptic currents|journal=Journal of Neuroscience|volume=37|issue=6|language=en|pages=2814–16|doi=10.1523/JNEUROSCI.2814-16.2016|issn=0270-6474|pmid=28039376|pmc=5299566}}</ref>

This has the advantage of producing an output with acceptable SNR even when none of the individual signals are themselves acceptable.

== Example: Least Squares estimate in the case of Rx diversity ==

We consider an example of which the receiver is endowed with N antennas. In this case, the received vector <math>y</math> is
{{NumBlk|:|<math>y=hs+\rho n \,</math>|{{EquationRef|1}}}}
where <math>n</math> is noise vector <math>n \sim CN(0, I_{N \times N})</math>. Following the ML detection criterion the detection procedure may be written as
{{NumBlk|:|<math>\tilde{s}=argmin_{s \in \mathcal{M}}|\hat{s}-s|^2,</math>|{{EquationRef|2}}}}
where <math>\mathcal{M}</math> is the considered constellation of <math>s</math> and <math>\hat{s}</math> is the least square solution to the above model.
{{NumBlk|:|<math>\hat{s}=(h^*h)^{-1}h^*y.</math>|{{EquationRef|3}}}}
The least square solution in this case is also known as maximum-ratio-combining (MRC). In the case of N antennas the LS can be written as
{{NumBlk|:|<math>\hat{s}=\frac{h_0^*y_0+h_1^*y_1+...+h_{N-1}^*y_{N-1}}{|h_0|^2+|h_1|^2+...+|h_{N-1}|^2},</math>|{{EquationRef|4}}}}
which means that the signal from each antenna is rotated and weighted according to the phase and strength of the channel, such that the signals from all antennas are combined to yield the maximum ratio between signal and noise terms.

==References==
{{reflist}}
{{refbegin}}
*{{FS1037C MS188}}
{{refend}}

==External links==
* [http://www.google.com.na/patents/EP2015468A1?cl=sv Siae Microelettronica patent]

{{DEFAULTSORT:Maximum-Ratio Combining}}
[[Category:Telecommunications techniques]]
[[Category:Radio resource management]]