rayleigh.m

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Property of Freescale
%  Freescale Confidential Proprietary
%  Freescale Copyright (C) 2005 All rights reserved
%  ------------------------------------------------------------------------
%  $RCSfile: rayleigh.m.rca $
%  $Date: Tue Oct 31 16:35:09 2006 $
%  Target: Matlab
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 802.16-2004 OFDMA PHY - Rayleigh Fading Waveform Generator
%
%   Description: Z=rayleigh(Ts,fd,OutLen,ChanNum,samp_index,M) generates 
%                samples of a rayleigh fading channel according to the 
%                modified Jakes  model described in "Improved Models for the 
%                Generation of Multiple Uncorrelated Rayleigh Fading Waveforms", 
%                IEEE Comm Letters, Vol. 6, No. 6, June 2002. The channel is 
%                generated at a sample rate which is at least 40X the maximum 
%                doppler frequency, then interpolated to the desired sample rate 
%                using a 2nd order curve fit. 
% 
%   Output:      Z => Each column of Z contains OutLen complex samples of a 
%                complex fading channel.  The output channels are mutually 
%                uncorrelated. The adjacent columns cannot be made to be 
%                continuous. 
%
%   Inputs:
%            Ts => Sample period in seconds.
%            fd => Doppler frequency in Hz.
%            OutLen => Number of output samples in each channel.
%            ChanNum => Number of channels to output (one per column).
%                       This argument is optional. Default is 1.
%            samp_index => sample index. Useful for simulating non-
%                          contiguous bursts of data (i.e. GSM). This
%                          argument is optional. Default is 0;
%            M => Number of sinusiods to mix together in the Jakes model.
%                 This argument is optional and defaults to 8.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Zout=rayleigh(TsIn,fd,OutLenIn,ChanNum,samp_index,M)

if nargin==3
    samp_index=0;
    ChanNum=1;
    M=8;
end

if nargin==4
    samp_index=0;
    M=8;
end

if nargin==5
    M=8;
end

% The following variables only need to be recalculated on the first 
% function call in a simulation. They are retained in memory within the
% scope of the function.

persistent theta cos_alpha sin_alpha psi phi IntRate Ts h OutLen Z0

% Initialize the persistent variables if they have not been initialized or
% if the sample index is set to zero. 

if samp_index==0 | (fd~=0 & isempty(theta)) | (fd==0 & isempty(Z0)) ,
    if fd==0
        for k=1:ChanNum,
            Z0(1:OutLenIn,k)=(1/sqrt(2))*(randn+sqrt(-1)*randn)*ones(OutLenIn,1);
        end
    else
    
% Internal sample rate is normally chosen to be 40X the doppler frequency.
% A higher sampling rate is chosen in some cases to ensure at least 20 fading 
% samples are calculated.

        IntRate=min([floor(1/(40*TsIn*fd)) floor(OutLenIn/min([OutLenIn 20]))]);

        Ts=TsIn*IntRate;
        OutLen=ceil(OutLenIn/IntRate)+6;
       
% A 2nd order curve fit is implemented by using a polyphase filter with a parabolic
% impulse response.

        h=conv(conv(boxcar(IntRate),boxcar(IntRate)),boxcar(IntRate));
        h=IntRate*h/sum(h);
    
% Three phase matrices from IEEE paper.
    
        for k=1:ChanNum
            theta=2*pi*(rand-0.5);
            cos_alpha(k,:)=cos(0.25*(2*pi*(1:M)-pi+theta)/M);
            sin_alpha(k,:)=sin(0.25*(2*pi*(1:M)-pi+theta)/M);
            psi(k,:)=2*pi*(rand(1,M)-0.5);
            phi(k,:)=2*pi*(rand(1,M)-0.5);
        end 
    end
end

if fd==0
    Zout=Z0;
else
    
% Convert the first sample index to the proper sampling rate. Start a few samples early to
% eliminate transient on the begining.

    samp_index=round(samp_index/IntRate)-3;

% Model from IEEE paper.

    wdt=2*pi*fd*Ts*(samp_index:1:samp_index+OutLen-1)';
    Z=zeros(OutLen,ChanNum);
    for k=1:ChanNum,
        Z(:,k)=sum(cos(wdt*cos_alpha(k,:)+ones(OutLen,1)*phi(k,:)),2)+sqrt(-1)*sum(cos(wdt*sin_alpha(k,:)+ones(OutLen,1)*psi(k,:)),2);
    end

% Interpolate to the desired sample rate using a polyphase filter.

%     for k=1:ChanNum
%         temp = zeros(OutLen*IntRate,1);
%         temp(1:IntRate:end) = sqrt(1/M)*Z(:,k);
%         temp = [temp;zeros(ceil(length(h)/2),1)];
%         Zout(:,k) = filter(h,1,temp);
%     end

    Zout=upfirdn(sqrt(1/M)*Z,h,IntRate,1);

% Remove transients from the begining and end of the waveform.

    [Zlen c]=size(Zout);
    StartTail=floor((Zlen-OutLenIn)/2);
    Zout=Zout(StartTail+1:StartTail+OutLenIn,:);
end