系统识别采用递归最小二乘法和最小二乘法Matlab代码.rar

%% System Identification Using Recursive Least Square (RLS) and Least Mean Square (LMS) algorithm % Plant identification simulation % Author: SHUJAAT KHAN ([email protected]) %% Start clc; clear all; close all; N = 100000; % Number of samples Bits = 2; % For PSK modulation SNR = 10; % Noise level h = [0.9 0.2 0.5 -0.7]; % Plant impulse response data = randint(1,N); % Random index for input data x = real(pskmod(data,Bits)); % Phase shit keying (PSK) modulation r = filter(h,1,x); % Input passed trought system(h) d = awgn(r, SNR); % Addition of white gaussian noise of decined SNR %% LMS parameter etac = 1e-3; % Learning rate for LMS Wlms = zeros(size(h)); % Initial weights of LMS V = zeros(1,length(h)); % Input frame length of LMS %% RLS Parameters p=3; lamda=1; sigma=1; Wrls = Wlms'; % Initial weights of RLS P=(sigma^-1)*eye(p+1); U = zeros(size(Wrls)); % Input frame length of RLS for n = 1 : N %% LMS V(1,2:end) = V(1,1:end-1); % Shifting of frame window V(1,1) = x(n); % Input of LMS yc = (Wlms)*V'; % Output of LMS ec = d(n) - yc; % Instantaneous error of LMS Wlms = Wlms + etac * ec * V; % Weight update rule of LMS %% RLS U(2:end,1) = U(1:end-1,1); % Shifting of frame window U(1,1) = x(n); % Input of RLS y(n) = U'*Wrls; % Output of RLS alpha(n) = d(n) - y(n); % Instantaneous error of RLS g(:,n)=P*U*((lamda + U'*P*U).^-1); % Gain vector P=(lamda^-1)*P - g(:,n)*U'*(lamda^-1)*P; % RLS intermediate term Wrls = Wrls + alpha(n)*g(:,n); % Weight update rule of RLS %% Normalized weight difference (NWD) NWDc(n) = norm(Wlms-h)./norm(h); % Normalized weight difference of LMS NWD(n) = norm(Wrls'-h)./norm(h); % Normalized weight difference of RLS end % %% Cost function plots figure fsize=14; % plot text font size plot(10*log10(NWDc),'','linewidth',4) hold on plot(10*log10(NWD),'r','linewidth',4) lgh=legend(strcat('Least mean square (LMS):', int2str(SNR),' (dB)'),strcat('Recursive least square (RLS):', int2str(SNR),' (dB)'),'Location','NorthEast'); grid minor xlabel('Iterations','FontName','Times New Roman','FontSize',fsize); ylabel('Normalized weight difference (NWD) in (dB)','FontName','Times New Roman','FontSize',fsize); title('Cost function (NWD vs epochs iteration)','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_RLS_Comparision.png'),'png') [h;Wrls';Wlms]