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vahidkh6222
Joined: 11 Oct 2005
Posts: 183
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 04 Aug 2008 9:31 an equalization problem. |
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Hi friends
I'm trying to simulate some equalization related paper, but i am totally confused with it's notation.
specifically, here is a small part of paper. as you see there is a equation for approximating yi(k) (the ith channel output) from itself to form some cost function d(k); d(k)=yi(k)-y`i(k))
[img][/img]
I dont understand what kind of approximation it is (we already have yi(k) then why do we have to approximate it again, and what would happen in convergence condition so that d(k) becomes zero?)
in practice, the matrix inversion operation becomes divergent since Y'*Y is singular. so...
any ideas, hints, suggestions or truly welcomed.
Thanks in advance
PS : we may see inv(Yi'*Yi)Yi' as pseudoinverse of Yi but what does it suggest?!! when we multiply Yi from the left, we'll get the same yi(k) !!!! any ideas?
Last edited by vahidkh6222 on 08 Aug 2008 7:54; edited 1 time in total |
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bulx
Joined: 07 Aug 2004
Posts: 170
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| 04 Aug 2008 15:43 Re: an equalization problem. |
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Does this make sense:
you have outputs y(k-1) to y(k-L) (past samples). Now you want to predict whats the next sample ie; y(k) going to be, [called y'(k) ]. For that you use a(k). Later after you get the real y(k), you use the difference to improve your prediction for the next time, somehow.
key point is estimate at the _moment_k_
How?
-b
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vahidkh6222
Joined: 11 Oct 2005
Posts: 183
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| 05 Aug 2008 8:44 an equalization problem. |
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| yeah it make sense, but what about the convergence condition. what would happen so that d(k) become zero?!!
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senaydud
Joined: 23 Jun 2008
Posts: 151
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| 09 Aug 2008 1:36 an equalization problem. |
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Your questions are;
1. we already have yi(k) then why do we have to approximate it again?
Answer: Yes we have "yi(k)" but we dont have "Yi". The aim is to approximate "Yi", not yi(k). Does it make sense?
2. what would happen in convergence condition so that d(k) becomes zero?
Answ: It is an iterative loop that approximates Yi, so when Yi converges to the correct value, "d" will be equal to zero and the loop gets terminated, and you are done.
Added after 57 minutes:
Wait a minute,
I have taken a look at the issue again and I am sorry I think I am wrong. "Yi" is also known, because it is made up of yi(k).
bulx is exactly right, thats right, the aim seems to be to find the recent output by looking at previous observations, sorry for that.
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premkiran
Joined: 16 Mar 2007
Posts: 8
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| 09 Aug 2008 12:33 Re: an equalization problem. |
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I am trying to make an interpretation ...
When d(k) converges, then your estimate of y(k) and detected y(k) , are the same . when you know the transmitted x , it means that , you have computed the H , channel from your estimate. And can use this channel for equalization.
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pancho12a
Joined: 19 Oct 2008
Posts: 14
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| 19 Oct 2008 5:48 Re: an equalization problem. |
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| eii,, try to use the LMS algorithm
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