%Modelo Jacks con Rayleigh

clc;
clear all;
close all;

k = 12;             % Rayos del "Scattering"
fd = 0.02;          % N鷐ero m醲imo para el Doppler Shifting
M = 50;             % Senoidales
sumatoria = 0;      % Sumatioria
N = 1024;           % Tama馻no de la secuencia
ds = 0.1;           % Duraci髇
T = (N-1)*ds;
t = 0:ds:T;

for n=1:M
betan = (pi*n)/(M+1);
thetan = betan + (2*pi*(k-1)/(M+1));
alphan = pi * (n-0.5)/(2*M);
fn = fd * cos(betan);
sumatoria = sumatoria + (cos(betan) + j*sin(betan)) * cos(2*pi*fn*t+thetan);    
end

alpha = 0;
R = 2*sqrt(2)*(sumatoria+ 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 del espectro')
grid on

figure
plot(m(m1),corr(m1));
title('Correlaci髇')
grid on

figure
plot(10*log10((abs(xcorr(R))).^2))
title('Magnitud de potencia (dB)')
grid on

figure
plot(abs(ifft(fft(R))));
title('Respuesta al impulso')
grid on

figure
hist(abs(R))
title('Distribuci髇 Rayleigh')