[outputVector,...

function    [outputVector,...
             errorVector,...
             coefficientVector] =   Affine_projectionCM(input,S)

%   Affine_projectionCM.m
%       Implements the Complex Affine-Projection Constant-Modulus algorithm for COMPLEX valued data.
%       (Algorithm 13.4 - book: Adaptive Filtering: Algorithms and Practical
%                                                        Implementation, Diniz)
%
%   Syntax:
%       [outputVector,errorVector,coefficientVector] = Affine_projectionCM(input,S)
%
%   Input Arguments:
%       . input     : Signal fed into the adaptive filter.          (ROW vector)
%       . S         : Structure with the following fields
%           - step                  : Convergence (relaxation) factor.
%           - filterOrderNo         : Order of the FIR filter.
%           - initialCoefficients   : Initial filter coefficients.  (COLUMN vector)
%           - gamma                 : Regularization factor.
%                                     (small positive constant to avoid singularity)
%           - memoryLength          : Reuse data factor.
%                                     (referred as L in the textbook)
%
%   Output Arguments:
%       . outputVector      :   Store the estimated output of each iteration.   (COLUMN vector)
%       . errorVector       :   Store the error for each iteration.             (COLUMN vector)
%       . coefficientVector :   Store the estimated coefficients for each iteration.
%                               (Coefficients at one iteration are COLUMN vector)
%
%   Authors:
%       . Guilherme de Oliveira Pinto   - [e-mail] & [e-mail]
%       . Markus Vinícius Santos Lima   - mvsl20@gmailcom           & [e-mail]
%       . Wallace Alves Martins         - [e-mail]     & [e-mail]
%       . Luiz Wagner Pereira Biscainho - [e-mail]          & [e-mail]
%       . Paulo Sergio Ramirez Diniz    -                             [e-mail]
%


%   Some Variables and Definitions:
%       . prefixedInput         :   Input is prefixed by nCoefficients -1 zeros.
%                                   (The prefix led to a more regular source code)
%
%       . regressor             :   Auxiliar variable. Store the piece of the
%                                   prefixedInput that will be multiplied by the
%                                   current set of coefficients.
%                                   (regressor is a COLUMN vector)
%
%       . nCoefficients         :   FIR filter number of coefficients.
%
%       . nIterations           :   Number of iterations.


%   Initialization Procedure
nCoefficients       =   S.filterOrderNo+1;
nIterations         =   length(input);

%   Pre Allocations
errorVectorApConj       =   zeros((S.memoryLength+1)    ,nIterations);
outputVectorApConj      =   zeros((S.memoryLength+1)    ,nIterations);
coefficientVector       =   zeros(nCoefficients         ,(nIterations+1));
regressor               =   zeros(nCoefficients         ,(S.memoryLength+1));

%   Initial State Weight Vector
coefficientVector(:,1)  =   S.initialCoefficients;

%   Improve source code regularity
prefixedInput           =   [zeros((nCoefficients-1),1)
                             transpose(input)];

%   Body
for it = 1:nIterations,

    regressor(:,2:S.memoryLength+1) =   regressor(:,1:S.memoryLength);

    regressor(:,1)                  =   prefixedInput(it+(nCoefficients-1):-1:it);

    outputVectorApConj(:,it)        =   (regressor')*coefficientVector(:,it);
    
    desiredLevelConj                =   sign(outputVectorApConj(:,it));

    errorVectorApConj(:,it)         =   desiredLevelConj...
                                        -outputVectorApConj(:,it);

    coefficientVector(:,it+1)       =   coefficientVector(:,it)+(S.step*regressor*...
                                        inv(regressor'*regressor+S.gamma*...
                                        eye(S.memoryLength+1))*errorVectorApConj(:,it));

end

outputVector            =   outputVectorApConj(1,:)';
errorVector             =   errorVectorApConj(1,:)';

%   EOF