# How to get the expected value of the transmitted signal?

Started by April 6, 2007
```Hi,all

I would like to find the expected value of my OFDM transmitted signal.

As

Y= H*X + N

Y= Received Signal , H = Channel , X= transmitted signal ,N=noise

Since i need to generate a MMSE equalizer, i need to find the Expected
value of X , in order to do the simulation.

The algorithm of MMSE equalizer is

Gmmse= Ru * Transpose(H) * inv(Rn+ H * Ru * Transpose(H))

Where Ru = E[ x(i) * transpose(x(i)] and Rn=E [ n(i) * transpose(n(i))]

Actually, I have try to use the exact transmitted signal to generate the
mmse equalizer and the simulation, but i have noticed that the Error of my
signal is unacceptable large. Even a ZF equalizer also has a better
performance than it...

Therefore i think the problem might really come from the expected value Ru
and Rn.
i really hope some one can help me...i am really  frustrated on it.

Thank you.

_____________________________________
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```
```On Apr 6, 9:41 am, "ericknightX" <wil...@gmail.com> wrote:
> Hi,all
>
> I would like to find the expected value of my OFDM transmitted signal.
>
> As
>
> Y= H*X + N
>
> Y= Received Signal , H = Channel , X= transmitted signal ,N=noise
>
> Since i need to generate a MMSE equalizer, i need to find the Expected
> value of X , in order to do the simulation.
>
> The algorithm of MMSE equalizer is
>
> Gmmse= Ru * Transpose(H) * inv(Rn+ H * Ru * Transpose(H))
>
> Where Ru = E[ x(i) * transpose(x(i)] and Rn=E [ n(i) * transpose(n(i))]
>
> Actually, I have try to use the exact transmitted signal to generate the
> mmse equalizer and the simulation, but i have noticed that the Error of my
> signal is unacceptable large. Even a ZF equalizer also has a better
> performance than it...
>
> Therefore i think the problem might really come from the expected value Ru
> and Rn.
> i really hope some one can help me...i am really  frustrated on it.

Ru and Rn are not the expected values of X and N, they are the
covariance matrices.  In fact, the MMSE equation you have above
presupposes that E(X) and E(N) are both zero.  In an OFDM scenario, it
is quite likely that Ru and Rn are both diagonal matrices (and
possibly with all diagonal entries the same).

--
Oli

```