How to set the parameter value for Rayleigh fading Simulation

When calcualate BER for certain modulation scheme, under Rayleigh fading,
exact theoretical valuse is available from books and publications.

But how to do set Rayleigh parameters in the simulation?

For example, received signal is  r(t) = Alpha * exp(-j*Phi) * s(t) + z(t)     
( By Proakis 's book) 

And 
        s(t) transmitted signal
        z(t)  Gaussian noise ~ N ( 0, Sigma)
       
Alpha is a Rayleigh distributed random variable descrbing the attenuation in
transmission.

To generat Alpha, how to set the sigma of Rayleigh distribution 
   p(a) =  z / (sigma2)  * exp ( - z2 / 2 sigma2 )

sigma2 = sigma^2, 
of course this sigma is the different with the one used in z(t), so how to set
the value ?

My question is :

When calcualte BER versus differenet Eb/No  value,  z(t) is calculated with
different sigma, which get from Eb/No.

But how about  the sigma2 of Alpha,  is it kept as constant ? or calculated
from Eb/No too, and how ?

Thanks !

Hi,

Usually, on a fading channel the average probability of error is
plotted against the average received signal-to-noise ratio. If Eb is
the transmitted bit energy, N0 the noise PSD, and alpha the fading
random variable, then the average received SNR is given by (Eb/N0)
*E(alpha^2), where E(alpha^2) is the statistical average value of the
fading random variable. Now, it should then be clear that the value of
sigma^2 for the fading is immaterial. One can choose any value.
Usually one chooses 2*sigma^2=1, so that on the average the fading
gain is unity.

Hope that helps
Ramesh

tangqinghui@163.net (Tang) wrote in message news:<63b2eb02.0406131644.6a310293@posting.google.com>...
> When calcualate BER for certain modulation scheme, under Rayleigh fading,
> exact theoretical valuse is available from books and publications.
> 
> But how to do set Rayleigh parameters in the simulation?
> 
> For example, received signal is  r(t) = Alpha * exp(-j*Phi) * s(t) + z(t)     
> ( By Proakis 's book) 
> 
> And 
>         s(t) transmitted signal
>         z(t)  Gaussian noise ~ N ( 0, Sigma)
>        
> Alpha is a Rayleigh distributed random variable descrbing the attenuation in
> transmission.
> 
> To generat Alpha, how to set the sigma of Rayleigh distribution 
>    p(a) =  z / (sigma2)  * exp ( - z2 / 2 sigma2 )
> 
> sigma2 = sigma^2, 
> of course this sigma is the different with the one used in z(t), so how to set
> the value ?
> 
> My question is :
> 
> When calcualte BER versus differenet Eb/No  value,  z(t) is calculated with
> different sigma, which get from Eb/No.
> 
> But how about  the sigma2 of Alpha,  is it kept as constant ? or calculated
> from Eb/No too, and how ?
> 
> Thanks !