Can someone please help me(provide me) with Bilinear LMS algo along with MATLAB code?

I am working on the estimation of 3 phase symmetrical components using Bilinear LMS algorithm. The equation is expanded in bilinear form and components are to be estimated using LMS algo. What I need help is with the code of Bilinear LMS, my code should give the output for 500 samples, however, after only 10 samples the output tends to infinite( NaN).

Answer 1

[Abraham Boayue]

There are different formulations of the bilinear lms algorithm on the Internet. Perhaps you can post the one you are working with. The lms algorithm and its variants are usually not difficult to code.

[Anuj Jena]

I am following the algorithm shown in the screenshot I have attached.

Answer 2

[Abraham Boayue]

Hey Anuj; I wrote a function based on your algorithm and tested it on a channel estimation problem. The image below is a sample average of the cost function, however, I still have some questions that I need your response to before making any conclusion. I assumed that x and y are the input signals, with input vectors, XA, XB and XC. In addition, I took N1 = N2 for the forward and recursive coefficient vectors, A, B and C. Are there assumptions realistic concerning your problem?

[Anuj Jena]

X is the input signal, Y is the required output. I have given an arbitrary value of Y for recursive algorithm initially.

Please share the code if possible, and you can send it to me personally.

Thanks.

Answer 3

[Abraham Boayue]

 Here is the code. 

function [e,A,B,C,Wa,Wb,Wc,ya,yb,yc] = BilinearLMS(x,y,d,mua,mub,muc,M1,M2)

            % Define length of signal vectors
            N1 = length(x);  
            N  = length(y);

          % Initialize coefficient vectors
          A = zeros(M1,1); Wa = zeros(M1,N);
          B = zeros(M1,1); Wb = zeros(M1,N);
          C = zeros(M2,1); Wc = zeros(M2,N);

          % Initialize the regressors for input signals
          ua  = zeros(1,M1);
          ub  = ua;
          uc  = zeros(1,M2);

          % Initialize the output signal vectors
          ya = zeros(1,N1);
          yb = ya;
          yc = zeros(1,N);
          e = zeros(1,N);
          delay = 1;

         % Perform the bilinear lms
       for k  = 1:N
           ua = [x(k),ua(1:M1-1)];
           y  = [zeros(1,delay) y(1,1:N-delay)];
           uc = [y(k),uc(1:M2-1)];            
           ub = [x(k)*y(k),ub(1:M2-1)];

           ya(k) = ua*A;
           yb(k) = ub*B; 
           yc(k) = uc*C;
           e(k)  = d(k)-(ya(k)+ yb(k)+ yc(k));

           A = A + mua*ua'*e(k);   Wa(:,k) = A;
           B = B + mub*ub'*e(k);   Wb(:,k) = B;
           C = C + muc*uc'*e(k);   Wc(:,k) = C;

       end
  end
clear 
close all

% Parameters
N = 1000;   % number of iterations
L = 500;    % number of runs
M1 = 4;
M2 = 4;
mua = 0.01;
mub = 0.03;
muc = 0.06;
sigman = sqrt(0.01);
h = [1 0.5 -1 2]'; % Channel
% Initialization
J_ave  = zeros(1,N);
w1 = zeros(1,N);
w2 = zeros(1,N);
w3 = zeros(1,N);
w4 = zeros(1,N);
for k = 1:L
          v = sigman*randn(1,N);  % adiditive noise at channel output
          x = randn(1,N);         % input signals x and y,
          y = x;
          d = filter(h,1,x)+v;
          [e,A,B,C,Wa,Wb,Wc,ya,yb,yc]=BilinearLMS(x,y,d,mua,mub,muc,M1,M2); 
          J_ave = J_ave + abs(e).^2; 
          w1 = w1 + Wa(1,:);
          w2 = w2 + Wa(2,:);
          w3 = w3 + Wa(3,:);
          w4 = w4 + Wa(4,:);
end

ind = 0:N-1;
J_ave = J_ave/L;     
J_ave = 10*log10(J_ave);
          w1 = w1/L;
          w2 = w2/L;
          w3 = w3/L;
          w4 = w4/L;

% Color codes
s = distinguishable_colors(60);

%figure  : Average MSE ,J(ei)
figure
plot(ind,J_ave,'linewidth',3,'color', s(38,:)); 
grid
a =title('Using Bilinear LMS J_{average} = |e(i)|^2 over N = 500');
set(a,'fontsize',14);
a = xlabel('NO. OF ITERATIONS');
set(a,'fontsize',14);
a = ylabel('MSE dB');
set(a,'fontsize',14);

% figure  : Average estimated coefficient vector 
%           A = [1.0011    0.4906   -1.0011    2.0066] ,w1 to w4
figure
indw = 0:N-1;
plot(indw,w1,'linewidth',2,'color', s(1,:));
hold on
plot(indw,w2,'linewidth',2,'color', s(2,:));
plot(indw,w3,'linewidth',2,'color', s(7,:));
plot(indw,w4,'linewidth',2,'color', s(26,:));
a = title('Estimated coefficients');
set(a,'fontsize',14);
a = xlabel('NO. OF ITERATIONS');
set(a,'fontsize',14);
a = ylabel('coef. trajectories'); 
set(a,'fontsize',14);
grid
% %%
%   figure
%   image(reshape(s,[1 size(s)]))
%