% Written by Chandra Athaudage 12/10/2001, CUBIN
function ralf = jakes_ralfunc(fm,fs,M,N_0,index)
% Jakes Model of a Rayleigh fading channel
%
% jakes_ralfunc(fm,fs,M,N_0,index)
%
% fm Doppler frequency 
% fs sampling frequency
% M  number of samples
% N_0 number of sinusoids
% index (1-N_0) uncorrelated Rayleigh fading functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N = 2*(2*N_0+1);
nn = 1 : N_0;
f = fm*cos(2*pi*nn/N);        %frequency vector
Ts = 1/fs;                                         %sampling interval (discrete signals)
onset = N_0*(1/fm);                %onset before steady model output
Te = 2*onset + M*Ts;         %evaluation period
t = 0 : Ts : Te;                        %time vector
%%%%%%%%%%%%%%%   
%Initial phases
phi_N = 0;
phi_n = pi*(nn + 2*(index-1))/(N_0+1);         %phase vector
%%%%%%%%%%%
%simulation
%%%%%%%%%%%
%real part
Xc0 = sqrt(2)*cos(phi_N)*cos(2*pi*fm*t);
Xc = Xc0 + 2*cos(phi_n)*cos(2*pi*f'*t);
%imaginary part
Xs0 = sqrt(2)*sin(phi_N)*cos(2*pi*fm*t);
Xs = Xs0 + 2*sin(phi_n)*cos(2*pi*f'*t);
%%%%%%%%%%%%%%%%%%%%%%%%
%complex fading function
T  = (1/sqrt(2*N_0+1))*(Xc+sqrt(-1)*Xs);
%%%%%%%%%
Tstart = onset + 0.9*rand(1)*onset; %avoid onset and random start 
Mstart = round(Tstart/Ts);
Mend = Mstart + M -1;
ralf = T(Mstart:Mend);
% -------- End ---------------------