瑞利衰落是一種小尺度衰落效應，它總是疊加於大尺度衰落效應上如衰減、陰影等。發射端和接收端相對運動速度的大小決定了通道衰落的快慢。相對運對導致接收訊號存在多普勒頻移，即通道衰落的快慢與多普勒頻移的大小有關。

        基於頻率單調衰落的基帶等效Jakes模型搭建的多徑瑞利衰落通道，Jakes模擬模型用多個多普勒頻偏和一個最大多普勒頻偏模擬多徑瑞利衰落通道，其模擬器框圖如圖所示：

多徑瑞利衰落通道的matlab程式碼為：模擬了6條衰落通道，不同延時，不同衰落功率。直接自己編寫的程式碼，可以自己修改引數，沒有使用MATLAB的自帶函式，我覺得那個函式，嗯。。。。。，用起來不方便，而且有的時候衰落和延時加不進去。

function [xout]=MUL_RAYLEIGH(x,itau,dlvl,itn,n1,nsamp,tstp,fd,flat)
%****************** variables *************************
% x  input Ich baseband data     
% yout   output Qch baseband data
% itau   : Delay time for each multipath fading
% dlvl   : Attenuation level for each multipath fading
% itn    : Fading counter for each multipath fading
% n1     : Number of summation for direct and delayed waves 
% nsamp   : Total number od symbols
% tstp   : Mininum time resolution
% fd   : Maxmum doppler frequency
% flat     flat fading or not 
% (1->flat (only amplitude is fluctuated),0->nomal(phase and amplitude are fluctutated)   
%******************************************************
n0 = 25;      % n0     : Number of waves in order to generate each multipath fading
xout = zeros(1,nsamp);
total_attn = sum(10 .^(  dlvl ./ 20.0));

for k = 1 : n1 
    
	atts = 10.^ (dlvl(k)/20.0);

	if dlvl(k) >= 40.0 
	       atts = 0.0;
	end

	[xtmp] = delay ( x, nsamp , itau(k));
	[xtmp3] = siglfade (xtmp,nsamp,tstp,fd,n0,itn(k),flat);% single fade
	
  xout = xout + atts .* xtmp3 ./ sqrt(total_attn);

end
% ************************end of file***********************************
function [xout] = delay(x,nsamp,idel )
% Gives delay to input signal
%****************** variables *************************
% x      input Ich data     
% xout   output Qch data
% nsamp   Number of samples to be simulated 
% idel   Number of samples to be delayed
%******************************************************

xout=zeros(1,nsamp);
if idel ~= 0 
  xout(1:idel) = zeros(1,idel);
end

xout(idel+1:nsamp) = x(1:nsamp-idel);

% ************************end of file***********************************

function [xout]=siglfade(x,nsamp,tstp,fd,no,counter,flat)
% Generate Rayleigh fading
% %****************** variables *************************
% x  : input Ich data     
% xout   : output Qch data
% nsamp  : Number of samples to be simulated       
% tstp   : Minimum time resolution                    
% fd     : maximum doppler frequency               
% no     : number of waves in order to generate fading   
% counter  : fading counter                          
% flat     : flat fading or not 
% (1->flat (only amplitude is fluctuated),0->nomal(phase and amplitude are fluctutated)    
%******************************************************

if fd ~= 0.0  
    ac0 = sqrt(1.0 ./ (2.0.*(no + 1)));   % power normalized constant(ich)
    as0 = sqrt(1.0 ./ (2.0.*no));         % power normalized constant(qch)
    ic0 = counter;                        % fading counter
 
    pai = 3.14159265;   
    wm = 2.0.*pai.*fd;
    n = 4.*no + 2;
    ts = tstp;
    wmts = wm.*ts;
    paino = pai./no;                        

    xc=zeros(1,nsamp);
    xs=zeros(1,nsamp);
    ic=[1:nsamp]+ic0;

  for nn = 1: no
	  cwn = cos( cos(2.0.*pai.*nn./n).*ic.*wmts );
	  xc = xc + cos(paino.*nn).*cwn;
	  xs = xs + sin(paino.*nn).*cwn;
  end

  cwmt = sqrt(2.0).*cos(ic.*wmts);
  xc = (2.0.*xc + cwmt).*ac0;
  xs = 2.0.*xs.*as0;

  ramp=sqrt(xc.^2+xs.^2);   

  if flat ==1
    xout = sqrt(xc.^2+xs.^2).*x;    % output signal
  else
    xout = x .*(xc+1i*xs);
  end

else  
  xout = x;
end

% ************************end of file***********************************