FRLS 优化算法（Matlab代码实现）

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randn('seed',0);
rand('seed',0);
%%%%%%%%%%%%%% Input parameters %%%%%%%%%%%%%%%%
N = 50;                 % Length of the adaptive filter
M_set = 61:20:201;      % Set of window lengths
Nmc = 50;               % number of simulation trials
Nit = 13000;            % signal length (number of samples)
sigma = sqrt(10^(2.5)); % sqrt(noise variance)
% - DCD parameters: -
dcd.Mb = 16;            % number of bits for representation of taps in the adaptive filter
dcd.H = 1;              % initial step-size
dcd.Nu = 8;             % number of updates
% -------------------------------------------
% - Channel model parameters: -
fs = 1000;              % sampling frequency (Hz)
max_f = 1;              % maximum frequency of the channel variation (Hz)
Nfft = 100e4;           % FFT size in the channel model
delta_f = fs/Nfft;      % FFT bin step (Hz)
power_delay_profile = 2;
Np = 2*round(max_f/delta_f) + 1;
% --------------------------------------------
MSD_dB = zeros(length(M_set),Nmc);
for trial = 1 : Nmc
   disp(['trial number: ', num2str(trial)])
   % -- Channel model: --
   h_t = zeros(N,Nit);
   for i = 1 : N
      H1 = zeros(Nfft, 1);
      H1(1) = randn(1,1) + 1i*randn(1,1);
      if max_f > 0
         H1(2:(Np-1)/2+1) = randn((Np-1)/2,1) + 1i*randn((Np-1)/2,1);
         H1(Nfft-(Np-1)/2+1:Nfft) = randn((Np-1)/2,1) + 1i*randn((Np-1)/2,1);
      elseif max_f == 0
         H1(2:(Np-1)/2+1) = 0;
         H1(Nfft-(Np-1)/2+1:Nfft) = 0;
      end
      h = ifft(H1);
      h_t(i,:) = h(1:Nit);
   end
   E_h = 0;
   for i = 1 : Nit
      E_h = E_h + h_t(:,i)'*h_t(:,i);
   end
   coeff = sqrt(1/(E_h/Nit));
   h_t = coeff.*h_t;
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   % Initialization
   x_new = randn(Nit,1) + 1i*randn(Nit,1);
   Eh = 0;
   y_true = zeros(Nit,1);
   for sample = 1 : Nit
      if sample == 1
         x = zeros(N,1);
      else
         x = [x_new(sample);x(1:end-1)];
      end
      h_et = h_t(:, sample);
      y_true(sample) = h_et'*x;
      Eh = Eh + sum(abs(h_et).^2);
   end
   E_y = y_true'*y_true;
   noise = randn(Nit,1) + 1i*randn(Nit,1);
   E_n = noise'*noise;
   sigma_n = sqrt(E_y/(E_n*sigma^2));
   noise = sigma_n*noise;
   E_n = noise'*noise;
   print_SNR = 10*log10(E_y/E_n);
   disp(['SNR = ', num2str(print_SNR), ' dB'])
   z = y_true + noise;
   for idx_M = 1:length(M_set)
      M = M_set(idx_M);
      Delay = (M-1)/2;
      MSD = zeros(Nit,1);
      %- window function
      window = hanning(M);
      h_est = FRLS(x_new, z, dcd, N, Delay, window);
      % -
      for sample = 1 : length(h_est(1,:))
         MSD(sample) = sum(abs((h_est(:,sample) - h_t(:,sample))).^2);
      end
      Eh1 = Eh / Nit;
      MSD = MSD/Eh1;
      print_MSD = mean(MSD(1501:end-1500),1);
      MSD_dB(idx_M, trial) = 10*log10(print_MSD);
      disp(['M = ', num2str(M_set(idx_M)), ', MSD = ', num2str(MSD_dB(idx_M, trial)), 'dB'])
   end
end
MSD = reshape(MSD_dB, length(M_set), Nmc);
mean_MSD = mean(MSD, 2);
figure(1)
plot(M_set, mean_MSD,  ':ro', 'LineWidth', 1.5, 'MarkerSize', 10)
xlabel('M')
ylabel('MSD, dB')
grid on
box on
axis([50 201 -24 -8])
legend('FRLS')
saveas(gcf,'MSD_results.png')
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