function [Pe]=RayleighAWGN(snr_in_db)
E=1;    %Normalize energy
snr=10^(snr_in_db/10);
sgma=E/sqrt(2*snr);  %standard deviation of noise
Num=4000;  % The number of binary data
%generation of binary data
for i=1:Num
    u=rand;
    if(u<=0.5)
        data(i)=0;
    else
        data(i)=1;
    end;
end;
%Detection and calculation BER
error=0;
% The correlator outputs
for i=1:Num
        if (data(i)==0)
        r0=E+GnRayleigh(sgma);
        r1=GnRayleigh(sgma);
    else
        r1=E+GnRayleigh(sgma);
        r0=GnRayleigh(sgma);
    end
% Detection
   if(r0>r1)
        result=0;
   else
        result=1;
   end
   if(result~=data(i))  %error accumlator
    error=error+1;
   end
end
Pe=error/Num;   %Calculation BER