# Adaptive Algorithm for Zero Forcing Equalizer

Started by May 3, 2008
```Hello,
Could you please give me an example of adaptive algorithm that can be used
for a zero forcing equalizer.
I am a bit confused. If I would like to use peak distortion as cost
function, could I use LMS algorithm to make my equalizer adaptive??.
-If yes, how?
(Because the error fed to LMS algorithm is difference between equalizer
output and desired signal. Then no difference remains with the other type
of equalizer that uses mean square error criteria which tries to minimize
the error between the same.)
-If no, which algorithm is used to make an equalizer based on peak

```
```Hi,

first of all, do you have the possibility of training the equalizer using
a reference sequence(namely a desired signal)? Or will your equalizer be
blind?

Manolis
```
```Hello,
I have the possibility of training the equalizer.
Thanks,

>Hi,
>
>first of all, do you have the possibility of training the equalizer
using
>a reference sequence(namely a desired signal)? Or will your equalizer be
>blind?
>
>Manolis
>
```
```
despite wrote:

> Hello,
> Could you please give me an example of adaptive algorithm that can be used
> for a zero forcing equalizer.

If there is no noise in the channel, any adaptive algorithm will
converge to the zero forcing equalizer.

> I am a bit confused.

No, you are not confused. You simply don't have a clue, do you?

If I would like to use peak distortion as cost
> function, could I use LMS algorithm to make my equalizer adaptive??.
> -If yes, how?
> (Because the error fed to LMS algorithm is difference between equalizer
> output and desired signal. Then no difference remains with the other type
> of equalizer that uses mean square error criteria which tries to minimize
> the error between the same.)
> -If no, which algorithm is used to make an equalizer based on peak

DSP and Mixed Signal Design Consultant
http://www.abvolt.com

```
```Hi,
Maybe I could not put what I wanted to ask into correct words.

ZF equalizer tries to minimize ISI and MS equalizer tries to minimize the
difference btw desired signal and equalizer output.

Where I am confused or lacking clue is the adaptive algorithm part.

implementation, the adaptive algorithms try to minimize difference btw
desired signal and equalizer output but if there is no noise, they converge
to ZF equalizer because this difference will only be due to ISI.Is this
correct?

Thanks.

>
>despite wrote:
>
>> Hello,
>> Could you please give me an example of adaptive algorithm that can be
used
>> for a zero forcing equalizer.
>
>If there is no noise in the channel, any adaptive algorithm will
>converge to the zero forcing equalizer.
>
>> I am a bit confused.
>
>No, you are not confused. You simply don't have a clue, do you?
>
>  If I would like to use peak distortion as cost
>> function, could I use LMS algorithm to make my equalizer adaptive??.
>> -If yes, how?
>> (Because the error fed to LMS algorithm is difference between
equalizer
>> output and desired signal. Then no difference remains with the other
type
>> of equalizer that uses mean square error criteria which tries to
minimize
>> the error between the same.)
>> -If no, which algorithm is used to make an equalizer based on peak
>
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>
>
```
```>Hi,
>Maybe I could not put what I wanted to ask into correct words.
>
>ZF equalizer tries to minimize ISI and MS equalizer tries to minimize
the
>difference btw desired signal and equalizer output.
>
>Where I am confused or lacking clue is the adaptive algorithm part.
>
>implementation, the adaptive algorithms try to minimize difference btw
>desired signal and equalizer output but if there is no noise, they
converge
>to ZF equalizer because this difference will only be due to ISI.Is this
>correct?
>
>Thanks.
>

Hi,

yes this is correct. Actually, by minimizing the differene between the
desired signal and equalizer output, the adaptive filter models the inverse
transfer function of the channel! This is equivalent to removing the ISI.

Manolis
```
```On May 3, 6:13 pm, "despite" <han...@gmail.com> wrote:
> Hi,
> Maybe I could not put what I wanted to ask into correct words.
>
> ZF equalizer tries to minimize ISI and MS equalizer tries to minimize the
> difference btw desired signal and equalizer output.
>
> Where I am confused or lacking clue is the adaptive algorithm part.
>
> implementation, the adaptive algorithms try to minimize difference btw
> desired signal and equalizer output but if there is no noise, they converge
> to ZF equalizer because this difference will only be due to ISI.Is this
> correct?
>

As Manolis pointed out, this is correct. The frequency response of a
zero-forcing equalizer is equivalent to that of a linear minimum mean-
squared error (LMMSE) equalizer when the signal-to-noise ratio is
infinite (i.e. there is only ISI, and no noise). The LMS algorithm
iterates toward these solutions by attempting to minimize the mean-
squared error between the filter output and the desired signal. This
is inherent in the development of the LMS algorithm, as it is a
stochastic gradient technique that "searches" for the coefficients of
the Wiener filter (i.e. the one that is optimal and actually minimizes
the MSE). So, I don't think your peak-distortion criterion is directly
applicable to an LMS implementation.

Jason
```
```Hi,
Thank you all for your detailed explanations. I can understand better
now.
Regards.

>
>As Manolis pointed out, this is correct. The frequency response of a
>zero-forcing equalizer is equivalent to that of a linear minimum mean-
>squared error (LMMSE) equalizer when the signal-to-noise ratio is
>infinite (i.e. there is only ISI, and no noise). The LMS algorithm
>iterates toward these solutions by attempting to minimize the mean-
>squared error between the filter output and the desired signal. This
>is inherent in the development of the LMS algorithm, as it is a
>stochastic gradient technique that "searches" for the coefficients of
>the Wiener filter (i.e. the one that is optimal and actually minimizes
>the MSE). So, I don't think your peak-distortion criterion is directly
>applicable to an LMS implementation.
>
>Jason
>
```