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Wiener Hopf Equalizer delay

Started by porterboy 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
news:c4b57fd0.0407060630.7b67827c@posting.google.com...
> 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.