gngauss.m

TCM的仿真 包括编码器

function[gsrv1,gsrv2]=gngauss(m,sgma) 
%  高斯随机变量1,高斯随机变量2,发生器generate 
%   I was asked to realize the gaussian distribution,which may be generated by the matlab function randn,normrnd......  
%   but it is still necessary to know how to realize it just by uniform random numbers in (0,1).  
%   here is a way.for simplicity I suppose sigma=1 and u=0,the standard normal distribution.  
 
%   we should know that we can not give the analystic equation of the probabilty distrbution function of  gaussian distribution.  
%   but we know that R(x)=1-exp(-x^2/(2*sigma^2)) when x>=0 and R(x)=0 when x<0.R(x) is the probability distribution function of relay distribution.  
 
%   and the gaussian distribution has the following relationship:  
%  c=x*cos(theta)  
%  d=x*sin(theta)  
%  where c,d are two gaussian variables,x is the variable in the former function.  
%  theta is the random variable in the uniform distribution of(0,2*pi).  
%  if we have R(x)=A,A is uniformly distributed in (0,1)  
%  then x= sqrt(2*sigma^2*ln(1/1-A)).  
%  and another variable B uniformly distributed in (0,1),suppose  
%  theta=2*pi*B  
%  then we have two statically independent gaussian random variables c ,d .  
%  if you want to have more variables,just to make A ,B vectors.  
%  the realization:  
 
%  m=0; sgma=1;  
%  N=1000;  
%  u=rand(1,N);  
%  %  z=sgma*(sqrt(2*log(1./(1-u))));  
%  u=rand(1,N);  
%  gsrv2=m+z.*sin(2*pi*u);  
%  gsrv1=m+z.*cos(2*pi*u);  
%  g=[gsrv1,gsrv2];  
%  hist(g);  
 
%  if the gaussian distribution is not standard, just to change m and sigma. 
 
 
 
if nargin==0, 
	m=0;sgma=1; 
elseif nargin==1, 
	sgma=m;m=0; 
end; 
 
u=rand; 
z=sgma*(sqrt(2*log(1/(1-u)))); 
u=rand; 
gsrv1=m+z*cos(2*pi*u); 
gsrv2=m+z*sin(2*pi*u);