gngd

 FUNCTION gngd() implements the GNGD algorithm 

 Based on the paper "A generalized normalized gradient descent algorithm",
 IEEE Signal Processing Letter, vol. 11, no. 2, 2004.

 INPUT:
 x: input signal which should be scaled according to the dynamic range of nonlinearity 
 N: filter length
 mu: step-size
 C: regularization parameter
 rho: step-size of adaptation of regularization parameter

 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 gngd() implements the GNGD algorithm
0002 %
0003 % Based on the paper "A generalized normalized gradient descent algorithm",
0004 % IEEE Signal Processing Letter, vol. 11, no. 2, 2004.
0005 %
0006 % INPUT:
0007 % x: input signal which should be scaled according to the dynamic range of nonlinearity
0008 % N: filter length
0009 % mu: step-size
0010 % C: regularization parameter
0011 % rho: step-size of adaptation of regularization parameter
0012 %
0013 % OUTPUT:
0014 % y: filter output
0015 %
0016 %
0017 % Complex Valued Nonlinear Adaptive Filtering toolbox for MATLAB
0018 % Supplementary to the book:
0019 %
0020 % "Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models"
0021 % by Danilo P. Mandic and Vanessa Su Lee Goh
0022 %
0023 % (c) Copyright Danilo P. Mandic 2009
0024 % http://www.commsp.ee.ic.ac.uk/~mandic
0025 %
0026 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %    This program is free software; you can redistribute it and/or modify
0028 %    it under the terms of the GNU General Public License as published by
0029 %    the Free Software Foundation; either version 2 of the License, or
0030 %    (at your option) any later version.
0031 %
0032 %    This program is distributed in the hope that it will be useful,
0033 %    but WITHOUT ANY WARRANTY; without even the implied warranty of
0034 %    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0035 %    GNU General Public License for more details.
0036 %
0037 %    You can obtain a copy of the GNU General Public License from
0038 %    http://www.gnu.org/copyleft/gpl.html or by writing to
0039 %    Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0040 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0041 % ...........................................
0042 function y = gngd(x,N,mu,C,rho)
0043 
0044 M = 1;% prediction horizon
0045 L = length(x)-M; % length of simulation
0046 filterinput = zeros(N,L);%input of FIR
0047 filteroutput = zeros(1,L);%output of FIR
0048 learning = zeros(1,L);% the adaptive learning rate;
0049 Phi = zeros(N,1);
0050 WGNGD = zeros(N,1);% weight
0051 eGNGD = zeros(1,L);% error
0052 EGNGD = zeros(1,L);% mean square error
0053 filteroutput = zeros(1,L);% output
0054 
0055 for i = 1:L
0056     for m = 1:N
0057         if (i-m+1)>0
0058             filterinput(m,i) = x(1,i-m+1);
0059         else
0060             filterinput(m,i) = 0;
0061         end
0062     end 
0063     filteroutput(i) = transpose(filterinput(:,i)) * WGNGD;%
0064     eGNGD(i) = x(i+M) - filteroutput(i);%
0065     EGNGD(i) = 10 * log10(1/2 * eGNGD(i)' * eGNGD(i));
0066     if i == 1
0067         C = C;
0068     else
0069         Phi =  -1 * mu * eGNGD(i-1) * filterinput(:,i-1) / ((norm(filterinput(:,i-1)).^2 + C).^2);
0070         C= C + rho * eGNGD(i) * transpose(filterinput(:,i)) * Phi;
0071     end
0072     learning(i) = mu /(norm(filterinput(:,i))^2 + C);
0073     WGNGD = WGNGD + learning(i) * eGNGD(i) * filterinput(:,i);
0074 end
0075 y = filteroutput;
0076 
0077 
0078