% ray1.m 
% Rayleigh fading simulator
% Uses the method of filtering complex Gaussians with approximate doppler spread.
%
% These variables may be defined before the program runs:
%   ftype   type of shaping filter used (default =0 gives predefined bathtub curve)
%           otherwise ftype = >0 to 0.5 is the normalised LPF cutoff
%
% Richard Wyrwas, 2 February 1995,  with additions by Bill Cowley 4/97 

disp('ray1: Rayleigh signal simulation by filtering random I and Q signals.');
disp('(press space to continue)');

if exist('ftype')~=1,    ftype =0;  end;	% check if filter type is defined
if ftype==0 
    disp('Using predefined bathtub shape')
    %  define a frequency vector and a magnitude vector to simulate the classic 'bathtub' shape
    f=(0.0:0.05:1.0);
    m=[1.0,1.2,1.5,1.9,2.8,4.0,6.0,9.0,15.0,25.0,1.00,0.05,0.03,0.02,0.01,0.005,0.005,0.005,0.005,0.005,0.005];
    plot(f,m);
    title('Desired magnitude response of I and Q shaping filters');
    xlabel(' Frequency normalised by Fs/2');
    pause;
    B=fir2(16,f,m);		% design an FIR filter based on the shape above. 
else 
    B = fir1(60, ftype*2);	% design LPF using ftype as Fcutoff/Fs 
    disp('Using flat LPF Fc/Fs given by ftype');
    freqz(B, 1);		% plot response 
    title('Response of shaping filter');
    pause;
end

x=randn(2048,1);	% make 2048 normally distributed random number for I and Q
y=randn(2048,1);
% z=sqrt(x.*x + y.*y);
x1=filter(B,1,x);	% filter the I and Q signals 
y1=filter(B,1,y);
R=x1+j.*y1;		% generate the complex baseband Rayleigh signal 

Mag=abs(R);		% find magnitude of the signal 
hist(Mag,20);
title('Histogram of simulated Rayleigh complex baseband signal')
xlabel(' Signal magnitude ');
pause;

plot(Mag);
title('Magnitude of the simulated Rayleigh signal')
xlabel(' Sample Number');
pause;
axis([100,300,0,max(Mag)]);
title('Magnitude of the simulated Rayleigh signal over 200 samples');
pause;

psd(R);
[Pxx,fr]=psd(R);
%pause;
plot(fr-1.0,fftshift(Pxx));
title('Power Spectral Estimate (2 sided) of the Simulated Rayleigh Signal')
xlabel('Normalised frequency');

%pause;
%plot(abs(fft(R)));