%SFRLS3 Problem 2.3
%
%   'ifile.mat' - input file containing:
%      K - iterations
%      H - FIR channel
%      Neq - equalizer order
%      sigman - standard deviation of measurement noise
%      epsilon - small auxiliary constant
%      kappa1, kappa2, kappa3 - auxiliary parameters
%      lambda - forgetting factor
% 
%   'ofile.mat' - output file containing:
%      ind - sample indexes 
%      Weq - coefficient vector of equalizer

clear all	% clear memory
load ifile;	% read input variables
LH=length(H);		% channel length
NH=LH-1;		% channel order
Leq=Neq+1;		% equalizer length
Leq1=Leq+1;		% auxiliary constant
ND=round((Neq+NH)/2);	% delayer order
LD=ND+1;		% delayer length (>LH by hipothesis)
D=zeros(LD,1);		% initial delayer memory
Xe=zeros(Leq1,1);	% extended initial memory
t=sign(randn(K,1));	% training signal
n=randn(K,1)*sigman;	% noise at channel output
%
% initial coefficient vectors
Wbeq=zeros(Leq,1);	
Wfeq=Wbeq;	
Weq=Wbeq;	
%
% initialization
phih=zeros(Leq,1);
gamma=1;
xibmin=epsilon;
ixifmin=1/epsilon;

for k=1:K,		% iterations
   D=[t(k)
      D(1:ND)];		% new delay vector
   d=D(LD);		% desired signal sample
   x=H'*D(1:LH)+n(k);	% input sample   
   Xe=[x
       Xe(1:Leq)];	% new extended input vector
   %
   % predictions
   efp=Xe'*[1 
            -Wfeq];
   ef=efp*gamma;
   phihe=[0
          phih]+ixifmin/lambda*[1
                                -Wfeq]*efp;
   gamma=1/(1/gamma+phihe(1)*efp);		% gamma1
   ixifmin=ixifmin/lambda-gamma*(phihe(1))^2;
   Wfeq=Wfeq+phih*ef;
   ebp1=lambda*xibmin*phihe(Leq1);    
   ebp2=[-Wbeq' 1]*Xe;     
   ebp=[1-kappa1 kappa1
        1-kappa2 kappa2
        1-kappa3 kappa3]*[ebp1 
                          ebp2];
   gamma=1/(1/gamma-phihe(Leq1)*ebp(3));	% gamma2
   eb=gamma*ebp;
   xibmin=lambda*xibmin+eb(2)*ebp(2);
   phih=phihe(1:Leq)+phihe(Leq1)*Wbeq;
   Wbeq=Wbeq+phih*eb(1);
   gamma=1/(1+phih'*Xe(1:Leq));			% gamma3
   %
   % joint-process estimation
   ep=d-Weq'*Xe(1:Leq);
   e=ep*gamma;		% error sample
   Weq=Weq+phih*e;	% new coefficient vector
end

ind=0:Neq;		% sample indexes
save ofile ind Weq;	% write output variables