Colored Noise in Noise cancellation

Hello,

I can't seem to find references on the performance of noise cancellation
algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored
noise.  

I have read somewhere that these algorithms do not perform very well when
the noise spectrum isn't flat but I can't seem to find a reference to that
claim.  

Can somebody explain this behavior to me and why?  Is this even true?  Can
you point to a good reference?

The noise I am trying to cancel out is not flat and there are very large
differences in amplitudes across the frequency band.  I am doing this for
RF.

Thank you

JT

On 12/10/2010 12:33 PM, pacman101 wrote:
> Hello,
>
> I can't seem to find references on the performance of noise cancellation
> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored
> noise.
>
> I have read somewhere that these algorithms do not perform very well when
> the noise spectrum isn't flat but I can't seem to find a reference to that
> claim.
>
> Can somebody explain this behavior to me and why?  Is this even true?  Can
> you point to a good reference?
>
> The noise I am trying to cancel out is not flat and there are very large
> differences in amplitudes across the frequency band.  I am doing this for
> RF.

I don't know anything about this application specifically, but I would 
think that -- if you structured your algorithm right -- you could do 
better with colored noise than with white, as you'd have more 
predictability.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

pacman101 wrote:
> Hello,
> 
> I can't seem to find references on the performance of noise cancellation
> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored
> noise.  

Those algoritms do not suppress noise. They minimize mean square error.

> I have read somewhere that these algorithms do not perform very well when
> the noise spectrum isn't flat but I can't seem to find a reference to that
> claim.  

There is nothing special about colored interference spectrum; colored 
signal spectrum could be the problem though.

> Can somebody explain this behavior to me and why?  Is this even true?  Can
> you point to a good reference?
> 
> The noise I am trying to cancel out is not flat and there are very large
> differences in amplitudes across the frequency band.  I am doing this for
> RF.

Are you sure there isn't a trivial bug somewhere?


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>
>
>pacman101 wrote:
>> Hello,
>> 
>> I can't seem to find references on the performance of noise
cancellation
>> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing
colored
>> noise.  
>
>Those algoritms do not suppress noise. They minimize mean square error.
>
>> I have read somewhere that these algorithms do not perform very well
when
>> the noise spectrum isn't flat but I can't seem to find a reference to
that
>> claim.  
>
>There is nothing special about colored interference spectrum; colored 
>signal spectrum could be the problem though.
>
>> Can somebody explain this behavior to me and why?  Is this even true? 
Can
>> you point to a good reference?
>> 
>> The noise I am trying to cancel out is not flat and there are very
large
>> differences in amplitudes across the frequency band.  I am doing this
for
>> RF.
>
>Are you sure there isn't a trivial bug somewhere?
>
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

From what I have read from some IEEE paper is that when the noise spectrum
is not white, these algorithms converge slower, but I do not know if it
gives the same amount of noise suppression.  It makes sense when the noise
isn't constantly on, in that case the noise is nonstationary.  These
algorithms do perform very well when the signals are highly non-stationary
since they have to keep reconverging.

On Dec 10, 2:33=A0pm, "pacman101" <janpac01@n_o_s_p_a_m.yahoo.com>
wrote:
> Hello,
>
> I can't seem to find references on the performance of noise cancellation
> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colore=
d
> noise. =A0
>
> I have read somewhere that these algorithms do not perform very well when
> the noise spectrum isn't flat but I can't seem to find a reference to tha=
t
> claim. =A0
>
> Can somebody explain this behavior to me and why? =A0Is this even true? =
=A0Can
> you point to a good reference?
>
> The noise I am trying to cancel out is not flat and there are very large
> differences in amplitudes across the frequency band. =A0I am doing this f=
or
> RF.
>
> Thank you
>
> JT

These algorithms attempt to estimate the Wiener filter which relys on
the input autocorrelation and the input/desired cross correlation. The
only constraint on the signal is that the desired response and the
interference be uncorrelated. The fastest convergence ususally will
result when a single-frequency sinusoid is the desired. The slowest
convergence usually will result when the desired is guassian and
white. The worst overall convergence will occur when the desired is a
single-frequency sinusoid. The best overall convergence will occur
when the desired is gaussian and white.

Vlad is correct when he says these algorithms can only minimize the
mean-squared error.

If your model is exact, and if the interference is not correlated with
the desired, you should have no problem.

Maurice Givens

On Dec 11, 9:33=A0am, "pacman101" <janpac01@n_o_s_p_a_m.yahoo.com>
wrote:
> Hello,
>
> I can't seem to find references on the performance of noise cancellation
> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colore=
d
> noise. =A0
>
> I have read somewhere that these algorithms do not perform very well when
> the noise spectrum isn't flat but I can't seem to find a reference to tha=
t
> claim. =A0
>
> Can somebody explain this behavior to me and why? =A0Is this even true? =
=A0Can
> you point to a good reference?
>
> The noise I am trying to cancel out is not flat and there are very large
> differences in amplitudes across the frequency band. =A0I am doing this f=
or
> RF.
>
> Thank you
>
> JT

You don't define your problem very well. First of all you miss-spell
Colour - that's important.
Are you are using LMS, RLS etc to identify an FIR unknown system or
are you filtering random coloured signal from random coloured noise?
How many sensors are available and where?  If the eigenvalues of the
correlation matrix is ill-conditioned then the convergence may be a
bit slow.

Hardy

On 12/10/2010 12:33 PM, pacman101 wrote:
> Hello,
>
> I can't seem to find references on the performance of noise cancellation
> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored
> noise.
>
> I have read somewhere that these algorithms do not perform very well when
> the noise spectrum isn't flat but I can't seem to find a reference to that
> claim.
>
> Can somebody explain this behavior to me and why?  Is this even true?  Can
> you point to a good reference?
>
> The noise I am trying to cancel out is not flat and there are very large
> differences in amplitudes across the frequency band.  I am doing this for
> RF.
>
> Thank you
>
> JT

I agree that the objectives could be clearer.
The only "noise canceller" I know about attempts to remove correlated 
interference - the output of a repeating sweep generator for example.
The adapted filter adjusts frequency magnitude and phase in order to 
deliver a signal that can optimally subtract from the signal channel. 
Where you get the input for that filter depends on the application and 
what's available for that purpose.

In the end, the adapted filter has to "shut off" at frequencies where 
its input is random / uncorrelated.  And, the filter ends up looking 
like a set of bandpasses that deliver the signal to be subtracted out. 
So, I'd say that it doesn't matter what the noise amplitudes are with 
frequency (the "color") because the filter is going to shut off (i.e. 
attenuate) anyway.  The color may affect convergence and dynamic change 
rates but I'd think that would be a secondary effect.

Sounds like there's pretty good consensus here.

Fred