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
Convergence of Linear Equalizer
Started by ●September 15, 2009
Reply by ●September 15, 20092009-09-15
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. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●September 15, 20092009-09-15
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 > > ChintanYou're screwing up? (Sorry, I had nothing positive to add so I made a smart-ass comment. 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
Reply by ●September 16, 20092009-09-16
> > >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 isproblem>> specific i.e. tracking of system identification is different problemthan>> 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 problemwhere>> he models the time varying environment as first order Markov processi.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 dentificationin>> 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 amnot>> getting the desired response. Does anybody know what could be thereason?> >No wonder. The system identification and the SG LMS generally give you >the different results. > > >Vladimir Vassilevsky >DSP and Mixed Signal Design Consultant >http://www.abvolt.com >%%%% HI Vlad Wassup??? Thanks for your reply. I have already done MLSE viterbi and all that stuff when I know the channel at receiver. 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
Reply by ●September 17, 20092009-09-17
On Sep 16, 3:51�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? �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. > > >Vladimir Vassilevsky > >DSP and Mixed Signal Design Consultant > >http://www.abvolt.com > > %%%% > > HI Vlad > > Wassup??? Thanks for your reply. > > I have already done MLSE viterbi and all that stuff when I know the > channel at receiver. > > 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. > > ChintanCan you actually do equalization without (explicitly or implicitly) estimating the channel?
Reply by ●September 18, 20092009-09-18
>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
Reply by ●September 20, 20092009-09-20