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function fa_comp= rayleigh(fd, fs, Ns) 
%************************************************************************************* 
%function fade= rayleigh(fd, fs, Ns) 
% Copyright 2002 The Mobile and Portable Radio Research Group 
% 
% function to generate Rayleigh faded waveform 
% The input to the function are 
%    Doppler frequency 
%    Sampling Frequency 
%    Number of samples needed 
% The output of the funtion is an array of complex number whose amplitude has Rayleigh  
% distribution and the phase is uniformly distributed from -pi to +pi. 
% ~~~~~~~~~~~~~~~~~~~~~~~~ 
 
% Written by James Hicks 
% Modified by Fakhrul Alam 
 
% ~~~~~~~~~~~~~~~~~~~~~~~~ 
 
%function fade= rayleigh(fd, fs, Ns) 
% constants: 
order= 3;  % order of polynomial extrapolation  
		   % along verticle assymptote of Doppler  
		   % Spectra, SEZ. 
 
% Create longer duration of fading envelope than needed in order 
% to have a spectrum that is a power of two. 
% Set the frequency spacing for the required sampling rate. 
% Adjust Doppler shift to assure that assymptote is sampled. 
 
N= 2^ceil(log2(Ns));  
delta_f= fs/N;   % (Hz) frequency spacing 
kd= ceil(fd/delta_f); 
 
% If Doppler shift is very small, envelope will be roughly constant: no 
% apparent fade. 
if(kd <= order) % assure at least one point outside interpolation keys 
   %fade= ones(Ns,1); 
   fa_comp=ones(Ns,1)*(1+j); 
else 
 
% compute actual adjusted Doppler Shift.  
fm= delta_f*kd; 
 
% Compute the Doppler Power Spectral Density  
SEZ= zeros(kd+1,1); 
f= (0:kd-1)*delta_f; 
SEZ(1:kd)= 1.5./(pi*fm*sqrt(1-(f/fm).^2)); 
% Use Polynomial fit to get the component at f= fm 
% replace infite value at f=fm with a polynomial extrapolation. 
p= polyfit( f(kd-order:kd), SEZ(kd-order:kd).', order);     
SEZ(kd+1)= polyval(p, fm); 
 
 
I_RAND= [sqrt(2)*randn(1); randn(kd-1,1)+j*randn(kd-1,1); sqrt(2)*randn(1)]; 
Q_RAND= [sqrt(2)*randn(1); randn(kd-1,1)+j*randn(kd-1,1); sqrt(2)*randn(1)]; 
Io= sqrt(SEZ).*I_RAND; 
Qo= sqrt(SEZ).*Q_RAND; 
 
pad = 2^(nextpow2(2*Ns-1)); 
 
If= [Io; zeros(pad-2*kd-1,1); conj(Io(kd+1:-1:2))]; 
Qf= [Qo; zeros(pad-2*kd-1,1); conj(Qo(kd+1:-1:2))]; 
Ienv= real(ifft(If)); 
Qenv= real(ifft(Qf)); 
 
fade= sqrt(Ienv(Ns:2*Ns-1).^2 + Qenv(Ns:2*Ns-1).^2); 
fa_comp=(Ienv(Ns:2*Ns-1)+j*Qenv(Ns:2*Ns-1))/ sqrt(mean(fade.^2)); 
%fade= fade/ sqrt(mean(fade.^2)); 
 
end;