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%                                                    %
%                 RLS Algorithm                      %
%                                                    %
% Written By: Sundar Sankaran and A. A. (Louis) Beex %
%             DSP Research Laboratory                %
%             Dept. of Electrical and Comp. Engg     %
%             Virginia Tech                          %
%             Blacksburg VA 24061-0111               %
%                                                    %
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randn('seed', 0) ;
rand('seed', 0) ;

NoOfData = 8000 ;	% Set no of data points used for training
Order = 32 ;		% Set the adaptive filter order

Lambda = 0.98 ;		% Set the forgetting factor
Delta = 0.001 ;		% R initialized to Delta*I

x = randn(NoOfData, 1) ;% Input assumed to be white
h = rand(Order, 1) ;	% System picked randomly
d = filter(h, 1, x) ;	% Generate output (desired signal)

% Initialize RLS

P = Delta * eye ( Order, Order ) ;
w = zeros ( Order, 1 ) ;

% RLS Adaptation

for n = Order : NoOfData ;
		
	u = x(n:-1:n-Order+1) ;
	pi_ = u' * P ;
	k = Lambda + pi_ * u ;
	K = pi_'/k;
	e(n) = d(n) - w' * u ;
	w = w + K * e(n) ;
	PPrime = K * pi_ ;
	P = ( P - PPrime ) / Lambda ;
	w_err(n) = norm(h - w) ;

end ;


% Plot results

figure ;
plot(20*log10(abs(e))) ;
title('Learning Curve') ;
xlabel('Iteration Number') ;
ylabel('Output Estimation Error in dB') ;

figure ;
semilogy(w_err) ;
title('Weight Estimation Error') ;
xlabel('Iteration Number') ;
ylabel('Weight Error in dB') ;