modelo_jakes.m

Jakes model to RAleigh Fading

%modelo de jakes para Rayleigh Fading
%suma de senoidales 
% Ivan Gabriel Ayala Esquivel MAT: 884608

clc
clear all
close all

k=12;             % numero de rayos del scattering
fd=0.02;          % doppler shift m醲imo
M=50;             % numero de senoidales
suma1=0;          % variable de la sumatioria Parte real he imaginaria
N=1024            % tama駉 de la secuencia en el simbolo
ds=0.1            % duracion del simbolo
T=(N-1)*ds;
t=0:ds:T;

for n=1:M
betan= (pi*n)/(M+1);
%betan=  (pi*n)/M;
thetan=betan+(2*pi*(k-1)/(M+1));
alphan=pi*(n-0.5)/(2*M);
fn=fd*cos(betan);
suma1= suma1+ (cos(betan)+j*sin(betan))*cos(2*pi*fn*t+thetan);    
end
alpha=0
R=2*sqrt(2)*(suma1+ 1/sqrt(2)*(cos(alpha)+j*sin(alpha))*cos(2*pi*fd*t));

[corr,m]=xcorr(R,'coeff'); 
m1=find(m>=0); 

plot (abs(R))
title('suma de sinoidales')
grid on
figure
plot(10*log10((abs(fft(R))).^2))
title('Densidad de potencia espectral')
grid on
figure
plot(m(m1),corr(m1));  %correlacion 
title('Correlacion')
grid on
figure
plot(10*log10((abs(xcorr(R))).^2))% magnitud en decibeles de potencia
title('Magnitud')
grid on
figure
plot(abs(ifft(fft(R)))); % salida del sistema
title('Respuesta al impulso')
grid on
figure
hist(abs(R))
title('Distribuci髇 Rayleigh')