part2c.m

In this program, several statistical fading channel simulators using the Sum-of-Sinusoids (SoS)has b

clc;
close all;
clear all;
echo off;

fd=100;
wd=2*pi*fd;
M=8;
N=4*M+2;
Ts=1e-2;
Ns=100;
maxlags=200;
i=5;
% Zc=zeros(M,);
% Zs=zeros(M,);
% Z=zeros(M,);

for i=1:50   
 rand('state',sum(100*clock));
 s = rand('state');
 a= rand(1,M);
 thetan=a*(2*pi)-pi;
 b=rand(1,M);
 phin=b*(2*pi)-pi;

 t=-5:Ts:5;
    suma=0;
    sumb=0;    
    for n=1:M         
        alphan(n)=((2*pi*n)+thetan(n))/M;        
        suma=suma+(cos((wd*t*cos(alphan(n)))+phin(n)));
        sumb=sumb+(sin((wd*t*cos(alphan(n)))+phin(n)));
    end
    Zc(i,:)= sqrt(1/M)*suma;
    Zs(i,:)= sqrt(1/M)*sumb;
    Z(i,:)= Zc(i,:)+(j*Zs(i,:));
    Zz2(i,:)=abs(Z(i,:)).^2;
    Rcc(i,:)=xcorr(Zc(i,:),maxlags);
    Rcc_norm(i,:)=Rcc(i,:)/max(Rcc(i,:));
    Rss(i,:)=xcorr(Zs(i,:),maxlags);
    Rss_norm(i,:)=Rss(i,:)/max(Rss(i,:));
    Rcs(i,:)=xcorr(Zc(i,:),Zs(i,:),maxlags);
    Rcs_norm(i,:)=Rcs(i,:)/max(Rcs(i,:));
    Rsc(i,:)=xcorr(Zs(i,:),Zc(i,:),maxlags);
    Rsc_norm(i,:)=Rsc(i,:)/max(Rsc(i,:));
    Rzz(i,:)=xcorr(Z(i,:),Z(i,:),maxlags);
    Rzz_norm(i,:)=Rzz(i,:)/max(Rzz(i,:));
    Rz2(i,:)=xcorr(Zz2(i,:),maxlags);
    Rz2_norm(i,:)=Rz2(i,:)/max(Rz2(i,:));
    %Rz2_norm(i,:)=Rz2(i,:)/max(Rz2(i,:));    
    
end
 
Zcc=mean(Rcc_norm);
Zss=mean(Rss_norm);
Zcs=mean(Rcs_norm);
Zsc=mean(Rsc_norm);
Zzz=mean(Rzz_norm);
Zz2=mean(Rz2_norm);
plot([0:maxlags]*fd*Ts,abs(Zcc(maxlags:2*maxlags)),'m','LineWidth',2);
 title('Theoretical and Simulated Rcc');
 xlabel('time lag sec');
 ylabel('Normalised Autocorrelation Rcc');

hold on;
J = besselj(0,([0:maxlags]*fd*Ts));
J=J./2;
plot([0:maxlags]*fd*Ts,J,'k');
figure;
plot([0:maxlags]*fd*Ts,(Zss(maxlags:2*maxlags)),'m','LineWidth',2);
title('Theoretical and Simulated Rss');
xlabel('time lag sec');
ylabel('Normalised Autocorrelation Rss');
hold on;
plot([0:maxlags]*fd*Ts,J,'k');
figure;
plot([0:maxlags]*fd*Ts,(Zcs(maxlags:2*maxlags)),'m','LineWidth',2);
title('Theoretical and Simulated Rcs');
xlabel('time lag sec');
ylabel('Normalised Autocorrelation Rcs');
hold on;
J1=zeros(1,maxlags+1);
plot([0:maxlags]*fd*Ts,J1,'k');
figure;
plot([0:maxlags]*fd*Ts,(Zsc(maxlags:2*maxlags)),'LineWidth',2);
title('Theoretical and Simulated Rsc');
xlabel('time lag sec');
ylabel('Normalised Autocorrelation Rsc');
hold on;
plot([0:maxlags]*fd*Ts,J1,'k');
figure;
plot([0:maxlags]*fd*Ts,(Zzz(maxlags:2*maxlags)),'m','LineWidth',2);
title('Theoretical and Simulated Rzz');
xlabel('time lag sec');
ylabel('Normalised Autocorrelation Rzz');
hold on;
J = besselj(0,([0:maxlags]*fd*Ts));
plot([0:maxlags],J,'k'); 
figure;

plot([0:maxlags]*fd*Ts,abs(2*Zz2(maxlags:maxlags*2)),'m','LineWidth',2);
title('Theoretical and Simulated Rz2z2');
xlabel('time lag sec');
ylabel('Normalised Autocorrelation Rz2z2');
hold on;
J2=ones(1,length(J))+(abs(J).^2);
plot([0:maxlags]*fd*Ts,J2,'k');    


% [m,n]=hist(Zc,100);
% su=sum(m);
% m=m/su/(n(2)-n(1));
% figure;
% % subplot(3,1,1),
% plot(n,m,'m');
% title('PDF of Zc(t)-Gaussian');
% xlabel('Bins');
% ylabel('Normalised Probability');
% [m,n]=hist(Zs,100);
% su=sum(m);
% m=m/su/(n(2)-n(1));
% figure;
% % subplot(3,1,2),
% plot(n,m,'m');
% title('PDF of Zs(t)-Gaussian');
% xlabel('Bins');
% ylabel('Normalised Probability');
% [m,n]=hist(abs(Z),100);
% su=sum(m);
% m=m/su/(n(2)-n(1));
% figure;
% % subplot(3,1,3),
% plot(n,m,'m');
% hold on;
% title('PDF of Z(t)-Rayleigh');
% xlabel('Bin values');
% ylabel('Normalised Probability');

% [Nx,bins]=hist(abs(Z),100);
% m=bins(3)-bins(2);
% pdf=(Nx)/(m*length(Z));
% figure;
% plot(bins,pdf);
% hold on; 

% pdf_theory=n./(Variance_G).*exp(-(n).^2/2/Variance_G);
% plot(n,pdf_theory);


%  pdf_theory=(bins./(Variance_G)).*exp(-(bins).^2/(2*Variance_G));
%  plot(bins,pdf_theory,'m','LineWidth',1);

% %c=length(u)
% y=xcorr(u,50);
% figure;
% plot([0:0.1:10],real(y));