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Greetings everyone,

I have a channel with impulse response h, with size h_r x h_c and for
computational reasons I will need to reduce the support size, i.e.
"compress" the signal and represent an equivalent channel of smaller
support. I tried an approach using the Weiner Filter, where I use it
as a "pre-processor" to obtain a "residual" channel, such that the
composite channel and Wiener filter compresses the energy into fewer
samples.

Using the Wiener formulation in the frequency domain (Sn(w) and Sf(w)
are the noise and signal PSDs respectively and the '*' means
conjugate):

Heq(w) = [ H(w).H(w)* ]/ [ |H(w)|^2 + Sn(w)/Sf(w) ]

When the noise is small, I was able to get a small size support (the
limiting case of no noise would give me an impulse response as is the
case with a perfectly matched filter). However, I find that for
smaller values of SNR, the support size seems to increase or remain
the same or even increases. I am confident in my estimation of Sf(w).

1. Is their anything that I can do to reduce this effect? However,
from the Wiener filter equation, I dont see a whole lot of parameters
that I can play with.

2. Maybe I am not thinking far enough, but is there any other way I
can compress this energy optimally?

I appreciate any pointers/literature references in this regard.

Thanks so much for your time!

Sincerely,
Palani

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Hi,

as matrix elements, channel co-efficients are quite hightly
correlated. so they could be dealt with with common decorrelating
procedures like the weiner filter option you have tried. wavelets
could be another good option. but there are also  wavelet bases
specifically available for wireless channel modelling. I am not really
sure how compact a support they offer.

amar

p...@gmail.com (Palani) wrote in message news:<1...@posting.google.com>...
> Greetings everyone,
> 
> I have a channel with impulse response h, with size h_r x h_c and for
> computational reasons I will need to reduce the support size, i.e.
> "compress" the signal and represent an equivalent channel of smaller
> support. I tried an approach using the Weiner Filter, where I use it
> as a "pre-processor" to obtain a "residual" channel, such that the
> composite channel and Wiener filter compresses the energy into fewer
> samples.
> 
> Using the Wiener formulation in the frequency domain (Sn(w) and Sf(w)
> are the noise and signal PSDs respectively and the '*' means
> conjugate):
> 
> Heq(w) = [ H(w).H(w)* ]/ [ |H(w)|^2 + Sn(w)/Sf(w) ]
> 
> When the noise is small, I was able to get a small size support (the
> limiting case of no noise would give me an impulse response as is the
> case with a perfectly matched filter). However, I find that for
> smaller values of SNR, the support size seems to increase or remain
> the same or even increases. I am confident in my estimation of Sf(w).
> 
> 1. Is their anything that I can do to reduce this effect? However,
> from the Wiener filter equation, I dont see a whole lot of parameters
> that I can play with.
> 
> 2. Maybe I am not thinking far enough, but is there any other way I
> can compress this energy optimally?
> 
> I appreciate any pointers/literature references in this regard.
> 
> Thanks so much for your time!
> 
> Sincerely,
> Palani

______________________________
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a...@yahoo.com (amara vati) wrote in message news:<f...@posting.google.com>...
> Hi,
> 
> as matrix elements, channel co-efficients are quite hightly
> correlated. so they could be dealt with with common decorrelating
> procedures like the weiner filter option you have tried. wavelets
> could be another good option. but there are also  wavelet bases
> specifically available for wireless channel modelling. I am not really
> sure how compact a support they offer.
> 
> amar
> 
Hi Amar,

Thanks for the follow-up. 
Is the decorrelation procedure specific to wireless channels? 
I'd be glad if you can point to some of the specific references in
this regard so that I can see if this procedure can be extended to
channels of a different nature.

Thanks!
Palani

> p...@gmail.com (Palani) wrote in message news:<1...@posting.google.com>...
> > Greetings everyone,
> > 
> > I have a channel with impulse response h, with size h_r x h_c and for
> > computational reasons I will need to reduce the support size, i.e.
> > "compress" the signal and represent an equivalent channel of smaller
> > support. I tried an approach using the Weiner Filter, where I use it
> > as a "pre-processor" to obtain a "residual" channel, such that the
> > composite channel and Wiener filter compresses the energy into fewer
> > samples.
> > 
> > Using the Wiener formulation in the frequency domain (Sn(w) and Sf(w)
> > are the noise and signal PSDs respectively and the '*' means
> > conjugate):
> > 
> > Heq(w) = [ H(w).H(w)* ]/ [ |H(w)|^2 + Sn(w)/Sf(w) ]
> > 
> > When the noise is small, I was able to get a small size support (the
> > limiting case of no noise would give me an impulse response as is the
> > case with a perfectly matched filter). However, I find that for
> > smaller values of SNR, the support size seems to increase or remain
> > the same or even increases. I am confident in my estimation of Sf(w).
> > 
> > 1. Is their anything that I can do to reduce this effect? However,
> > from the Wiener filter equation, I dont see a whole lot of parameters
> > that I can play with.
> > 
> > 2. Maybe I am not thinking far enough, but is there any other way I
> > can compress this energy optimally?
> > 
> > I appreciate any pointers/literature references in this regard.
> > 
> > Thanks so much for your time!
> > 
> > Sincerely,
> > Palani

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