# Wiener Hopf Equalizer delay

Started by July 6, 2004
```CONTEXT:**********************

Transmit x(n) receive y(n). Wiener-Hopf (MMSE) FIR Equalizer is...
w = inv(Ryy)rxy
where Ryy is the received signal autocorrelation and rxy is the
channel input-output crosscorrelation: rxy(k) = E(x(n-D)y(n+k)). The D
is a delay parameter chosen to make sure the equalizer is causal. It
specifies the location of the impulse of the equalized channel.

QUESTION:*********************

Is it possible to impose a delay constraint on the actual equalizer?
Would it have to be linear phase for this to work? I was hoping to
specify the equalizer output as being a fixed delay relative to the
equalizer input.
```
```The delay of the equalizer is dependent on the length of the channel Impulse
Response.

"porterboy" <porterboy76@yahoo.com> wrote in message
> CONTEXT:**********************
>
> Transmit x(n) receive y(n). Wiener-Hopf (MMSE) FIR Equalizer is...
> w = inv(Ryy)rxy
> where Ryy is the received signal autocorrelation and rxy is the
> channel input-output crosscorrelation: rxy(k) = E(x(n-D)y(n+k)). The D
> is a delay parameter chosen to make sure the equalizer is causal. It
> specifies the location of the impulse of the equalized channel.
>
> QUESTION:*********************
>
> Is it possible to impose a delay constraint on the actual equalizer?
> Would it have to be linear phase for this to work? I was hoping to
> specify the equalizer output as being a fixed delay relative to the
> equalizer input.

```
```"trellis coder" <trellis_coder@earthlink.net> wrote in message news:<d%4Hc.8721\$R36.2109@newsread2.news.pas.earthlink.net>...
> The delay of the equalizer is dependent on the length of the channel Impulse
> Response.

I understand that is the case if an unconstrained Wiener-Hopf
equlaizer is used. I was wondering is there a constrained Wiener-Hopf
solution, which allows delay specification? Anyway, I found a
solution, whereby the equalizer is constrained to be linear phase, and
hence has a fixed delay equal to half its length. However, the
performance drop is significant compared to the unconstrained case.
```