fig7_34.rar_Almost Zero_www.34see.com

%%%%%%%%%%%%%%%%%%% DETECTION AND ESTIMATION THEORY %%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% SANA SYED %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURE 7.3 AND 7.4 %%%%%%%%%%%%%%%%%%%%%%%%% clc clear all close all N=50; m=1000; A=1; sigma_sq=0.05; f0=0.08; phi=pi/4; k=1; SNR = -20:5:10; % Define SNR for plotting the figure for k=1:length(SNR) Pdf=[]; phi_hat=[]; x=zeros(m,N); for M=1:m n=0:1:N-1; noise=sqrt(sigma_sq)*awgn(zeros(1,N),SNR(k)); % changing SNR x(M,:)=A*cos(2*pi*f0*n+phi)+noise; %x(M,:)=awgn((A*cos(2*pi*f0*n+phi)),SNR(k)); Pdf(M,:)=(1/(2*pi*sigma_sq)^(1/2))*(exp((-1/(2*sigma_sq))*(x(M,:)-A.*cos(2*pi*f0*n+phi)).^2)); Num=sum(x(M,:).*sin(2*pi*f0*n)); Den=sum(x(M,:).*cos(2*pi*f0*n)); phi_hat(M,:)=-atan(Num/Den); end phi_est(k)=(1/M)*sum(phi_hat); phi_var(k)=N*(1/M)*sum((phi_hat-phi_est(k)).^2); % eq 7.10 end % Compare actual mean with asymptotic mean against SNR figure; asymp_mean = pi/4*ones(1,length(SNR)); % Asymptotic mean plot(SNR,asymp_mean,'r--','LineWidth',2); hold on; plot(SNR,phi_est,'LineWidth',2) xlabel('SNR (dB)','FontWeight','bold','fontsize',12); ylabel('Mean','FontWeight','bold','fontsize',12); title('Actual vs. asymptotic mean for phase estimator','FontWeight','bold','fontsize',12); legend('Asymptotic mean','actual mean'); % Compare actual variance with asymptotic variance against SNR lg_asymp_var = -10*log10(N) - SNR; % Asymptotic variance lg_var = 10*log10(phi_var); figure; plot(SNR,lg_asymp_var,'r--','LineWidth',3); hold on; plot(SNR,lg_var,'LineWidth',3) xlabel('SNR (dB)','FontWeight','bold','fontsize',12); ylabel('10log_1_0 variance','FontWeight','bold','fontsize',12); title('Actual vs. asymptotic variance for phase estimator','FontWeight','bold','fontsize',12) legend('Asymptotic variance','actual variance'); %