基于最小均方 (LMS) 算法的系统识别附matlab代码.zip

%% System Identification Using Least Mean Square (LMS) algorithm % Plant identification simulation %% Start clc; clear all; close all; %% LMS parameter runs = 10; % Monte Carlos Simulations (number of independent simulations) etas = 1e-2; % Learning rate for LMS N = 1000; % Number of samples SNR = 10; % Noise level (signal to noise ratio) NWD_lms=0; MSE_lms=0; for run=1:runs h = randn(1,5); % Plant impulse response x = sqrt(1)*randn(1,N)+0; % random signal from zero mean gaussian distribution of variance one r = filter(h,1,x); % Input passed trought system(h) d = awgn(r, SNR); % Addition of white Gaussian noise of SNR value defined above Wlms = randn(size(h)); % Initial weights of LMS Us = zeros(1,length(h)); % Input frame length of LMS for n = 1 : N %% LMS % Convolution Us(1,2:end) = Us(1,1:end-1); % Shifting of frame window Us(1,1) = x(n); % Input of LMS ys = (Wlms)*Us'; % Output of LMS es = d(n) - ys; % Instantaneous error of LMS Wlms = Wlms + etas * es * Us; % Weight update rule of LMS %% Normalized weight difference (NWD) temp_NWD_lms(n) = norm(Wlms-h)./norm(h); % Normalized weight difference of LMS temp_MSE_lms(n) = es*es; end NWD_lms=NWD_lms+temp_NWD_lms; MSE_lms=MSE_lms+temp_MSE_lms; end % Mean values NWD_lms=NWD_lms./runs; MSE_lms=MSE_lms./runs; % %% Cost function plots figure fsize=14; % plot text font size subplot(2,1,1) plot(10*log10(NWD_lms),'r','linewidth',2) lgh=legend(horzcat('Least mean square (LMS)', int2str(SNR),' (dB)'),'Location','NorthEast'); grid minor xlabel('Iterations','FontName','Times New Roman','FontSize',fsize); ylabel('NWD in (dB)','FontName','Times New Roman','FontSize',fsize); title('NWD vs iterations)','FontName','Times New Roman','FontSize',6*fsize/5); set(lgh,'FontName','Times New Roman','FontSize',fsize) set(gca,'FontName','Times New Roman','FontSize',fsize) subplot(2,1,2) plot(10*log10(MSE_lms),'','linewidth',2) lgh=legend(horzcat('Least mean square (LMS)', int2str(SNR),' (dB)'),'Location','NorthEast'); grid minor xlabel('Iterations','FontName','Times New Roman','FontSize',fsize); ylabel('MSE in (dB)','FontName','Times New Roman','FontSize',fsize); title('MSE vs iterations','FontName','Times New Roman','FontSize',6*fsize/5); set(lgh,'FontName','Times New Roman','FontSize',fsize) set(gca,'FontName','Times New Roman','FontSize',fsize) saveas(gcf,strcat('LMS_Results.png'),'png') actual_plant=h; obtained_model=Wlms; fprintf('\nactual_plant \t=\t') fprintf('%2.2f\t',actual_plant) fprintf('\nobtained_model \t=\t') fprintf('%2.2f\t',obtained_model) fprintf('\n\n')