Communication

Maximum Likelihood Decoding Algorithm for Multiple Input Multiple Output Communications

If a multiple i/p and multiple o/p system is there as shown in below fig...   
The above system contains 'm' transmit antennas and 'm' receive antennas. The data is transmitted from transmitter to receiver through the fading channel. The channel matrix(H) is given by.....

H= h_ij

Here ‘i’ stands for receiver index and ‘j’ stands for transmitter index…..

The general channel matrix ‘H’ is given by….

 

This channel parameters changes after some interval of time for fading channel, the length of channel matrix is now (n*m). If channel parameters are complex and if we separate real and imaginary part by writing them as a separate entity then the length of channel matrix become (2n*2m).....
For this fading channel if we transmitted some data over the channel by adding channel noise, and decoded the same data using Maximum Likelihood Decoding algorithm the graph of Probability of error v/s SNR will be as shown below......
The following calculations are made for 'n=m'....

for n=m=2....

For n=m=4

The Matlab code for the above simulation is available on following link...........