[log_LF_CP]=compute_LF_CP(received_signal,n,l)

function [log_LF_CP]=compute_LF_CP(received_signal,n,l)

%HELP compute_LF_CP
%Compute the Information criteria for a STBC of code length l using n
%number of symbols per block (CP
%Classifier).
%
%Input:   - received_signal
%           - n: number of symbols per block
%           - l: code length
%
%Output:    - LF: Fonction de vraisemblance
%         
%reference: [1] V. Choqueuse, M. Marazin, L. Collin, K.C. Yao, K and G. Burel
%"Blind Recognition of Linear SpaceTime Block Codes: A Likelihood-Based
%Approach" IEEE Transactions on Signal Processing, Vol 58 (3), p 1290-1299,
%2010

N=size(received_signal,2);
nr=size(received_signal,1);

%% Compute the estimated covariance matrice R (equation 26)
Nb=N/l;
received_signal_block1=[real(received_signal);imag(received_signal)];
received_signal_block=reshape(received_signal_block1,2*nr*l,Nb);
R=(received_signal_block*received_signal_block.')/Nb;

%% Compute the eigenvalue rho of the covariance matrix R
[Ue,rho]=eig(R);
[rho,index]=sort(diag(rho),'descend');
rho_signal=rho(1:2*n);
rho_noise=rho(2*n+1:end);

%% Compute log LF (remove the last term since it does not depend on the STBC)
log_LF=-(Nb/2)*sum(log(rho_signal))...
       -(N*nr-Nb*n)*log(mean(rho_noise));
   
%% Compute the Number of free parameter z   (equation 37)
z=n*(4*nr*l-2*n+1)+1;

%% Compute the Cost function  
log_LF_CP=log_LF-z;