Mathews

 FUNCTION mathews() implements the Mathews's variable step size CLMS algorithm 

 Based on the paper "A stochastic gradient adaptive filter with gradient adaptive step size",
 IEEE Trans. Signal Processing, vol. 41, pp. 2075-2087, 1993.

 INPUT:
 x: input signal
 N: filter length
 mu: step-size
 rho: step-size of adaptation of mu

 OUTPUT:
 y: filter output


 Complex Valued Nonlinear Adaptive Filtering toolbox for MATLAB
 Supplementary to the book:
 
 "Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models"
 by Danilo P. Mandic and Vanessa Su Lee Goh
 
 (c) Copyright Danilo P. Mandic 2009
 http://www.commsp.ee.ic.ac.uk/~mandic
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You can obtain a copy of the GNU General Public License from
    http://www.gnu.org/copyleft/gpl.html or by writing to
    Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 ...........................................

0001 % FUNCTION mathews() implements the Mathews's variable step size CLMS algorithm
0002 %
0003 % Based on the paper "A stochastic gradient adaptive filter with gradient adaptive step size",
0004 % IEEE Trans. Signal Processing, vol. 41, pp. 2075-2087, 1993.
0005 %
0006 % INPUT:
0007 % x: input signal
0008 % N: filter length
0009 % mu: step-size
0010 % rho: step-size of adaptation of mu
0011 %
0012 % OUTPUT:
0013 % y: filter output
0014 %
0015 %
0016 % Complex Valued Nonlinear Adaptive Filtering toolbox for MATLAB
0017 % Supplementary to the book:
0018 %
0019 % "Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models"
0020 % by Danilo P. Mandic and Vanessa Su Lee Goh
0021 %
0022 % (c) Copyright Danilo P. Mandic 2009
0023 % http://www.commsp.ee.ic.ac.uk/~mandic
0024 %
0025 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0026 %    This program is free software; you can redistribute it and/or modify
0027 %    it under the terms of the GNU General Public License as published by
0028 %    the Free Software Foundation; either version 2 of the License, or
0029 %    (at your option) any later version.
0030 %
0031 %    This program is distributed in the hope that it will be useful,
0032 %    but WITHOUT ANY WARRANTY; without even the implied warranty of
0033 %    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0034 %    GNU General Public License for more details.
0035 %
0036 %    You can obtain a copy of the GNU General Public License from
0037 %    http://www.gnu.org/copyleft/gpl.html or by writing to
0038 %    Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0039 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0040 % ...........................................
0041 function y = Mathews(x,N,mu,rho)
0042 
0043 M = 1;% prediction horizon
0044 L = length(x)-M; % length of simulation
0045 filterinput = zeros(N,L);%input of FIR
0046 filteroutput = zeros(1,L);%output of FIR
0047 learning = zeros(1,L);% the adaptive learning rate;
0048 Phi = zeros(N,1);
0049 WVSLMS = zeros(N,1);% weight
0050 eVSLMS = zeros(1,L);% error
0051 EVSLMS = zeros(1,L);% mean square error
0052 filteroutput = zeros(1,L);% output
0053 
0054 
0055 
0056 for i = 1:L
0057     for m = 1:N
0058         if (i-m+1)>0
0059             filterinput(m,i) = x(1,i-m+1);
0060         else
0061             filterinput(m,i) = 0;
0062         end
0063     end % inputing FIR
0064     filteroutput(i) = transpose(filterinput(:,i)) * WVSLMS;%
0065     eVSLMS(i) = x(i+M) - filteroutput(i);%
0066     EVSLMS(i) = 10 * log10(1/2 * eVSLMS(i)' * eVSLMS(i));
0067     if i == 1
0068         learning(1) = mu;
0069         Phi = zeros(N,1);
0070     else
0071         Phi = eVSLMS(i-1) * conj(filterinput(:,i-1));
0072         learning(i) = learning(i-1) + rho * real(eVSLMS(i) * filterinput(:,i)'* conj(Phi));
0073     end
0074     WVSLMS = WVSLMS + learning(i) * eVSLMS(i) * conj(filterinput(:,i));
0075 end
0076 y = filteroutput;
0077 
0078 
0079 
0080 
0081