# Convergence of Linear Equalizer

Started by September 15, 2009
```Hi All

In Haykin book of adaptive filter, he has explained tracking of LMS in
non-stationary environment. In that he says that the tracking is problem
specific i.e. tracking of system identification is different problem than
equalizing. I get what he is saying.

And then he derives all the math for system identification problem where
he models the time varying environment as first order Markov process i.e.

W(n)=alpha*W(n-1)+v(n), where alpha is close to unity to get low pass
process.

All these is fine. So I thought to implement this system dentification in
Matlab. It works fine. I compared the output with the time varying
environment and it is exactly same. The MSE also shows convergence.

My problem is that when I try to equalize the same environment, I am not
getting the desired response. Does anybody know what could be the reason?

Thanks

Chintan

```
```
cpshah99 wrote:

> Hi All
>
> In Haykin book of adaptive filter, he has explained tracking of LMS in
> non-stationary environment. In that he says that the tracking is problem
> specific i.e. tracking of system identification is different problem than
> equalizing.

Of course. System identification corresponds to the zero forcing
equalization, i.e. inverting the channel. This is generally not what you
want if your goal is receiving the data symbol-by-symbol with minimum
error.

> I get what he is saying.
> And then he derives all the math for system identification problem where
> he models the time varying environment as first order Markov process i.e.
>
> W(n)=alpha*W(n-1)+v(n), where alpha is close to unity to get low pass
> process.
> All these is fine. So I thought to implement this system dentification in
> Matlab.

Matlabi

> It works fine. I compared the output with the time varying
> environment and it is exactly same.

Now, instead of trying to invert the channel, make the MLSE Viterbi
receiver using the identified system model.

> The MSE also shows convergence.

What do you call MSE?  Stochastic gradient LMS algorithm?

> My problem is that when I try to equalize the same environment, I am not
> getting the desired response. Does anybody know what could be the reason?

No wonder. The system identification and the SG LMS generally give you
the different results.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com
```
```On Tue, 15 Sep 2009 06:06:36 -0500, cpshah99 wrote:

> Hi All
>
> In Haykin book of adaptive filter, he has explained tracking of LMS in
> non-stationary environment. In that he says that the tracking is problem
> specific i.e. tracking of system identification is different problem
> than equalizing. I get what he is saying.
>
> And then he derives all the math for system identification problem where
> he models the time varying environment as first order Markov process
> i.e.
>
> W(n)=alpha*W(n-1)+v(n), where alpha is close to unity to get low pass
> process.
>
> All these is fine. So I thought to implement this system dentification
> in Matlab. It works fine. I compared the output with the time varying
> environment and it is exactly same. The MSE also shows convergence.
>
> My problem is that when I try to equalize the same environment, I am not
> getting the desired response. Does anybody know what could be the
> reason?
>
> Your opinion matters a lot.
>
> Thanks
>
> Chintan

You're screwing up?

Please ask a control systems question, or one pertaining to some corner
of comms that I'm familiar with, so I can feel like I'm helping.)

( ( Vladimir's comment seemed to make sense -- equalizing a channel and
pulling the best guess of what was transmitted _through_ that channel
cannot, in general, be the same thing ) ).

--
www.wescottdesign.com
```
```>
>
>cpshah99 wrote:
>
>> Hi All
>>
>> In Haykin book of adaptive filter, he has explained tracking of LMS in
>> non-stationary environment. In that he says that the tracking is
problem
>> specific i.e. tracking of system identification is different problem
than
>> equalizing.
>
>Of course. System identification corresponds to the zero forcing
>equalization, i.e. inverting the channel. This is generally not what you

>want if your goal is receiving the data symbol-by-symbol with minimum
>error.
>
>> I get what he is saying.
>> And then he derives all the math for system identification problem
where
>> he models the time varying environment as first order Markov process
i.e.
>>
>> W(n)=alpha*W(n-1)+v(n), where alpha is close to unity to get low pass
>> process.
>> All these is fine. So I thought to implement this system dentification
in
>> Matlab.
>
>Matlabi
>
>> It works fine. I compared the output with the time varying
>> environment and it is exactly same.
>
>Now, instead of trying to invert the channel, make the MLSE Viterbi
>receiver using the identified system model.
>
>> The MSE also shows convergence.
>
>What do you call MSE?  Stochastic gradient LMS algorithm?
>
>> My problem is that when I try to equalize the same environment, I am
not
>> getting the desired response. Does anybody know what could be the
reason?
>
>No wonder. The system identification and the SG LMS generally give you
>the different results.
>
>
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

%%%%

I have already done MLSE viterbi and all that stuff when I know the

What I wanted is: When the channel is time varying, I can estimate the
channel using least mean square algorithm (LMS) and the mean square error
(MSE) also shows convergence. This is like what you said earlier, estimate
the channel and then use either MLSE, ZF or MMSE to equalize the channel.

My que was: Instead of doing estimation and then equalization, when I did
direct implementation of equalizer (I dont see what is wrong in that) I do
not get proper result. Even at high SNR.

So I believe there is something which I am missing and I do not know what
is that.

It will be really great if u can please give some more details.

>
>Matlabi
>

lol......To be honest, I am really not...

Thanks.

Chintan
```
```On Sep 16, 3:51&#2013266080;am, "cpshah99" <cpsha...@rediffmail.com> wrote:
> >cpshah99 wrote:
>
> >> Hi All
>
> >> In Haykin book of adaptive filter, he has explained tracking of LMS in
> >> non-stationary environment. In that he says that the tracking is
> problem
> >> specific i.e. tracking of system identification is different problem
> than
> >> equalizing.
>
> >Of course. System identification corresponds to the zero forcing
> >equalization, i.e. inverting the channel. This is generally not what you
> >want if your goal is receiving the data symbol-by-symbol with minimum
> >error.
>
> >> I get what he is saying.
> >> And then he derives all the math for system identification problem
> where
> >> he models the time varying environment as first order Markov process
> i.e.
>
> >> W(n)=alpha*W(n-1)+v(n), where alpha is close to unity to get low pass
> >> process.
> >> All these is fine. So I thought to implement this system dentification
> in
> >> Matlab.
>
> >Matlabi
>
> >> It works fine. I compared the output with the time varying
> >> environment and it is exactly same.
>
> >Now, instead of trying to invert the channel, make the MLSE Viterbi
> >receiver using the identified system model.
>
> >> The MSE also shows convergence.
>
> >What do you call MSE? &#2013266080;Stochastic gradient LMS algorithm?
>
> >> My problem is that when I try to equalize the same environment, I am
> not
> >> getting the desired response. Does anybody know what could be the
> reason?
>
> >No wonder. The system identification and the SG LMS generally give you
> >the different results.
>
> >DSP and Mixed Signal Design Consultant
> >http://www.abvolt.com
>
> %%%%
>
>
>
> I have already done MLSE viterbi and all that stuff when I know the
>
> What I wanted is: When the channel is time varying, I can estimate the
> channel using least mean square algorithm (LMS) and the mean square error
> (MSE) also shows convergence. This is like what you said earlier, estimate
> the channel and then use either MLSE, ZF or MMSE to equalize the channel.
>
> My que was: Instead of doing estimation and then equalization, when I did
> direct implementation of equalizer (I dont see what is wrong in that) I do
> not get proper result. Even at high SNR.
>
> So I believe there is something which I am missing and I do not know what
> is that.
>
> It will be really great if u can please give some more details.
>
>
>
> >Matlabi
>
> lol......To be honest, I am really not...
>
> Thanks.
>
> Chintan

Can you actually do equalization without (explicitly or implicitly)
estimating the channel?
```
```>Can you actually do equalization without (explicitly or implicitly)
>estimating the channel?
>

Why not????? Chapter 11 of Proakis.

Now if u see this chapter, I sure u must have seen that before, he is
doing adaptive linear equalization without separate channel estimation.

So what is wrong in that?

Chintan
```
```Hello Guys

Found the ans....it is given in Ali Sayed's book.

On his personal web, there are video lectures and 'Matlabi' code as well
:-)

Chintan
```