Channel Estimation of OFDM using kalman filter

[shams_313]

I need channel estimation of OFDM using kalman filter mathlab code. Does any body can help me with that? Plz ... Its urgent.

 

[tabraiz]

Did you get the code, plz reply thru message

 

[shams_313]

Not Yet Buddy........ I m working on it...

 

[almoudamer1]

if you have the code plz send it to me to this mail : lacmach@yahoo.com

 

[chano]

I think.......

"Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (v. 1) by Steven M. Kay "

This book would help for your question. One of the chapter deals with kalman filter ans its application to the channel estimation. (there's so long time to review this book. however I remember that the author give us to a intuitive principle of kalman filter and channel model.) I think.. you can simply extended the kalman filter channel estimation with ofdm systems.

 

[chano]

Dear shams_313

Here's my codes for single-carrier channel estimation using kalman filter. This codes is basically and based on a Kay's book.
I think... you can easily extend this code with multi-carrier system.

% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
%
% File Name : main_Kalman_CE.m
% Description: Time varying channel estimation using Kalman filter
%
% Date : 2009.8.3. (by chano.)
%
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %


clear all;
close all;


% % % % % % % % % % % % Parameter Define % % % % % % % % % % % %
N = 101; % number of observation
p = 2; % number of multipath
A = [0.99 0; 0 0.999];
sigma_u = 0.01;
Q = [sigma_u^2 0; 0 sigma_u^2];
sigma = sqrt(0.1); % observation noise S.D

H = [1; .9]; % h[-1]
h_hat_1 = [0; 0]; % initial channel state, h_hat[-1|-1]
M_1 = 100*eye(p); % initial MMSE val, M[-1|-1]

w = sigma*randn;
v = [zeros(5,1); ones(5,1);zeros(5,1); ones(5,1)];
v = [v;v;v;v;v;v]; % channel input, v[n]
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %


h_mat_True = zeros(p,N);
h_mat_Est= zeros(p,N);
K_mat= zeros(p,N);
M_mat= zeros(p,N);
x_free_vec = zeros(1,N);
x_vec= zeros(1,N);


for n = 1 : N-1

U = sigma_u*randn(p,1);
H = A*H+U; % unknown channel update
V = [ v(n+1);v ]; % known input
w = sigma*randn; % wgn
x_free = V'*H ; % Noiseless channel output
x = x_free + w; % Channel Output

h_hat_2 = A*h_hat_1;
M_2 = A*M_1*A'+Q;
K = ( M_2*V )./ ( sigma^2 + V'*M_2*V );
h_hat_1 = h_hat_2 + K*(x -V'*h_hat_2 );
M_1 = ( eye(p) - K*V' )*M_2;

% % % for plotting % % %
x_vec = x;
x_free_vec = x_free;

h_mat_True,n) = H;
h_mat_Est,n) = h_hat_2;

K_mat,n) = K;

M_mat,n) = [ M_1(1,1); M_1(2,2) ];

end

figure(1); %title('Realization of TDL coefficients');
subplot(2,1,1);
plot(h_mat_True(1,1:100), '--', 'LineWidth', 2);
hold on; grid on;
plot(h_mat_Est(1,1:100),'r', 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Tap weight, h_n[0]');
legend('True','Estimate');
ylim( [0 2] )

subplot(2,1,2);
plot(h_mat_True(2,1:100), '--', 'LineWidth', 2);
hold on; grid on;
plot(h_mat_Est(2,1:100), 'r', 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Tap weight, h_n[1]');
legend('True','Estimate');
ylim( [0 2] )


figure(2);
subplot(3,1,1);
plot(v(1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Channel input, v[n]');
ylim( [-1 2.5] )

subplot(3,1,2);
plot(x_free_vec(1,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Noiseless channel, y[n]');
ylim( [-1 2.5] )

subplot(3,1,3);
plot(x_vec(1,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Channel input, v[n]');
ylim( [-1 2.5] )


figure(3);
subplot(2,1,1);
plot(K_mat(1,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Kalman gain, K_1[n]');
ylim( [-.6 1.1] )

subplot(2,1,2);
plot(K_mat(2,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Kalman gain, K_2[n]');
ylim( [-.6 1.1] )


figure(4)
subplot(2,1,1);
plot(M_mat(1,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Min. MSE, M_11[n]');
ylim( [0 0.2] )

subplot(2,1,2);
plot(M_mat(2,1:100), 'LineWidth', 2);
xlabel('Sample number, n');
ylabel('Min. MSE, M_22[n]');
ylim( [0 0.2] )

 

[Lekshmi B S]

Dear chano,,
can u plz giv any explanations for the notations used in your code..