Sign in

Not a member? | Forgot your Password?

Search compdsp

Search tips

Find us on Facebook!





Free PDF Downloads

A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction

Discussion Groups

FIR Filter Design Software

Free Online Books

See Also

Embedded SystemsFPGA

Discussion Groups | Comp.DSP | Adaptive Algorithm for Zero Forcing Equalizer


There are 8 messages in this thread.

You are currently looking at messages 1 to .


Is this discussion worth a thumbs up?

0

Adaptive Algorithm for Zero Forcing Equalizer - despite - 2008-05-03 12:13:00

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
distortion creteria adaptive?
Thanks in advance.


Re: Adaptive Algorithm for Zero Forcing Equalizer - Manolis C. Tsakiris - 2008-05-03 15:04:00

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


Re: Adaptive Algorithm for Zero Forcing Equalizer - despite - 2008-05-03 17:00:00

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
>


Re: Adaptive Algorithm for Zero Forcing Equalizer - Vladimir Vassilevsky - 2008-05-03 17:32:00

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
> distortion creteria adaptive?
> Thanks in advance.

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


Re: Adaptive Algorithm for Zero Forcing Equalizer - despite - 2008-05-03 18:13:00

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. 

From your answer I understood that regardless of coefficient update
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
>> distortion creteria adaptive?
>> Thanks in advance.
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>
>


Re: Adaptive Algorithm for Zero Forcing Equalizer - Manolis C. Tsakiris - 2008-05-04 02:22:00

>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. 
>
>From your answer I understood that regardless of coefficient update
>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


Re: Adaptive Algorithm for Zero Forcing Equalizer - 2008-05-04 23:24:00

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.
>
> From your answer I understood that regardless of coefficient update
> 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


Re: Adaptive Algorithm for Zero Forcing Equalizer - despite - 2008-05-08 08:41:00

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
>