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.

# Adaptive Algorithm for Zero Forcing Equalizer

Started by ●May 3, 2008

Reply by ●May 3, 20082008-05-03

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

Reply by ●May 3, 20082008-05-03

Hello, I have the possibility of training the equalizer. Thanks,>Hi, > >first of all, do you have the possibility of training the equalizerusing>a reference sequence(namely a desired signal)? Or will your equalizer be >blind? > >Manolis >

Reply by ●May 3, 20082008-05-03

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

Reply by ●May 3, 20082008-05-03

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 beused>> 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 betweenequalizer>> output and desired signal. Then no difference remains with the othertype>> of equalizer that uses mean square error criteria which tries tominimize>> 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 > >

Reply by ●May 4, 20082008-05-04

>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 minimizethe>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, theyconverge>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

Reply by ●May 5, 20082008-05-05

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

Reply by ●May 8, 20082008-05-08

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 >