TO DISPLAY HISTOGRAM PLOT OF RAYLEIGH ENVELOPE AND UNIFORM PHASE AND CALCULATING LCR AND AFD

clc;
clear all;
close all;

% description of the values

N=100;
d=input('enter the velocity in km/hr ');
fc=input('enter the carrier frequency in hz');

% finding doppler frequency

v=d*5/18;
lambda=(3*(10^8))/fc;
vmax=v/lambda;

% definig 8000 samples

s= 8000;
Ts=1/s;
t=0:2*Ts:2;

% rayleigh pdf for comparison

r=0:0.01:3.5;
q=raylpdf(r,0.7);

% uniform pdf for comparison

l= -3.5:0.1:3.5;

% envelope of inphase and qudrature

a=length(t);
r_I=zeros(1,a);
r_Q=zeros(1,a);
b=sqrt(N);

for k=1:N
theta=rand*360;
phi=rand*360;
r_I=r_I+(randn*cos(2*pi*vmax*cos(theta)*t+phi)*(1/b));
r_Q=r_Q+(randn*sin(2*pi*vmax*cos(theta)*t+phi)*(1/b));
end
z=(r_I+1i*r_Q);
x=abs(z);
y=10*log(x);

% phase

psi=atan(r_Q./r_I);

% LCR and ADF

w=10^-0.3;
rms=sqrt(mean(x.^2));
wh=w/(sqrt(2)*rms);
df=(vmax*2);
T=1/df;
c1=0;
c2=0;


for j=1:length(x)
if x(j) > w
c1=c1+1;
end

if x(j) < w
c2=c2+1;
end
end

LCR_n =((c1/2)/(T*s))+1/2;
AFD_n=((c2*Ts)/2)/LCR_n;

% LCR and AFD theoretical

LCR_t=sqrt(2*pi)*vmax*wh*exp(-(wh^2));
AFD_t=(exp(wh^2)-1)/(wh*vmax*sqrt(2*pi));



% DISPLAY

display(lambda);
display(LCR_n);
display(LCR_t);
display(AFD_n);
display(AFD_t);


% plotting of fading envelope in dB

figure(1);
plot(t,y);
title('ENVELOPE IN dB vs TIME');
xlabel('TIME IN SECONDS');
ylabel('ENVELOPE IN dB');

% plotting of fading envelope and comparing it with Rayleigh

figure(2);
[f,c]=hist(x,50);
bar(c,f/trapz(c,f),'g');
hold on
plot(r,q,'b');
hold off
title('ENVELOPE HISTOGRAM COMPARISON WITH RAYLEIGH');
ylabel('ENVELOPE AND RAYLEIGH');

% plotting of phase and comparing it with uniform

figure(3);
[g,p]=hist(psi,20);
bar(p,g/trapz(p,g),'g');
hold on
plot(l, unifpdf(l, -1.5,1.5),'r');
hold off
title('PHASE HISTOGRAM COMPARISON WITH UNIFORM');
ylabel('PHASE AND UNIFROM');