# Modeling of Rayleigh Fading Channel

Started by January 4, 2008
```Hello Dear,

I'm looking for a accurate and simple way to model Rayleigh distributed
sequences for modeling a wireless communication channel. I've already made
a model by filtering white noise sequence but it doesn't work well and it
is not accurate.

Thanks.
```
```Rayleigh distribution can be generated from uniform distribution
using the following formula.

Z   = a + sqrt(b*log[1 - U]); % log is natural log.

where U is uniformly distributed random number in the range
[0 <= U < 1]; In matlab rand function can be used to generate
pseudo random numbers. In hardware we use LFSR to generate
pseudo random numbers.

mean of generated rayleigh distribution is given by

m   = a + sqrt(pi*b/4);        ...... eq 2

and variance is given by

var = b*(4-pi)/4;              ...... eq 3

you can reverse calculate parameters a and b using eq 2 and 3,
based on the desired mean and variance of rayleigh distribution.

Regards
Bharat Pathak
Founder and CEO
Arithos Designs
www.arithos.com

>Hello Dear,
>
>I'm looking for a accurate and simple way to model Rayleigh distributed
>sequences for modeling a wireless communication channel. I've already
>a model by filtering white noise sequence but it doesn't work well and
it
>is not accurate.
>
>Thanks.
>
```
```On Jan 4, 4:32 pm, "zohreh" <zand2...@gmail.com> wrote:
> Hello Dear,
>
> I'm looking for a accurate and simple way to model Rayleigh distributed
> sequences for modeling a wireless communication channel. I've already made
> a model by filtering white noise sequence but it doesn't work well and it
> is not accurate.
>
> Thanks.

If you have Matlab's Communications Toolbox, you can use its Rayleigh
channel function.

Darol Klawetter
```
```Thanks a lot. Now I have another problem. How the Doppler spread can affect
the mean and variance of that? I mean how I can generate Rayleigh sequence
by given Doppler spread and the variance (from Jakes's model)?

>Rayleigh distribution can be generated from uniform distribution
>using the following formula.
>
>Z   = a + sqrt(b*log[1 - U]); % log is natural log.
>
>where U is uniformly distributed random number in the range
>[0 <= U < 1]; In matlab rand function can be used to generate
>pseudo random numbers. In hardware we use LFSR to generate
>pseudo random numbers.
>
>mean of generated rayleigh distribution is given by
>
>m   = a + sqrt(pi*b/4);        ...... eq 2
>
>and variance is given by
>
>var = b*(4-pi)/4;              ...... eq 3
>
>you can reverse calculate parameters a and b using eq 2 and 3,
>based on the desired mean and variance of rayleigh distribution.
>
>Regards
>Bharat Pathak
>Founder and CEO
>Arithos Designs
>www.arithos.com
>
>
>>Hello Dear,
>>
>>I'm looking for a accurate and simple way to model Rayleigh distributed
>>sequences for modeling a wireless communication channel. I've already