# Where is the matched filtering operation in this?

Started by November 6, 2008
```Hi...
I am struggling to understand the following:

If r(t) = sum_i{s(t)*h_i(t-tau_i)} + n(t) is the received signal where
h_i(t) is the overall channel impulse response, the MLSE Viterbi algorithm
is simply done by calculating branch metrics of the form
|r(t)-noiseless_r(t)|, where noiseless_r(t) is a reconstructed version of
r(t) using the estimated channel impulse response taps h_est_i(t).

Since these branch metrics direcly use r(t), without any matched filtering
with h*(t) (the impulse response matched to the overall channel response
h(t), where is the matched filtering done that is supposed to be required
by the MLSE equalizer??

Thanks for helping me understand this !

Cheers.

Guy

```
```There is no matched filtering here if we use "euclidean metric". But
we don't usually use "euclidean metric" in MLSE equalizer due to the
complexity. What we usually use is the "matched filter metric" or
"ungerboeck metric".  Then r(t) is indeed convolved with h_est_i(t).

Regards
Piyush

On Nov 6, 6:22&#2013266080;pm, "zolguy" <zol...@hotmail.com> wrote:
> Hi...
> I am struggling to understand the following:
>
> If r(t) = sum_i{s(t)*h_i(t-tau_i)} + n(t) is the received signal where
> h_i(t) is the overall channel impulse response, the MLSE Viterbi algorithm
> is simply done by calculating branch metrics of the form
> |r(t)-noiseless_r(t)|, where noiseless_r(t) is a reconstructed version of
> r(t) using the estimated channel impulse response taps h_est_i(t).
>
> Since these branch metrics direcly use r(t), without any matched filtering
> with h*(t) (the impulse response matched to the overall channel response
> h(t), where is the matched filtering done that is supposed to be required
> by the MLSE equalizer??
>
> Thanks for helping me understand this !
>
> Cheers.
>
> Guy

```