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Hi,

A signal received from an antenna has two stochastic sources that
appear in the signal model: one is from the environment (for example,
solar flares can produce freq in the bw of many communication
signals), and one is from the electrical circuitry itself ("random
channel" or "thermal" noise).

The problem is that these components can be different statistically.
(If you're not sure what this means, see footnote below) As a
consequence, they can affect beamforming techniques differently too.
(This is *usually* not the case, but I am working with a new
beamforming algorithm where this does happen). The problem here is
that the electrical engineers who work on this problem assume the
major component of noise is *from* the environment, but they they
statistically model the single stochastic component in the signal *as
if* it came from thermal noise. In the signal processing lit, however,
people model the noise as if it was *from* thermal noise and their
models reflect this (i.e. they don't seem to consider the component
that engineers thing is the dominant noise contribution). My question
is : does anyone know of any studies that have been done to separately
examine these two noise components? (Of course, the environmental
noise has a large degree of variation in its properties, but I want to
begin to consider this problem and get a handle on how it can affect
beamforming). This of course would not be easy to do but there are
anechoic chambers (for RF radiation) where this problem, in principle,
should be amenable to study.

If you would be so kind as to respond to my e-mail address rather than
post on the ng, I'd be most appreciative.

Thank you,

Matt Brenneman

Footnote:
Suppose you have a discrete time signal from an M antenna array that
contains only these two stochastic components where:
 X_i,j = environmental noise from ith channel at the jth time point
then you *can* have <X_i,j*X_i,k> = 0 for j ne k but will defintely
not have <X_i,m*X_i,j> = 0 for any j,m
In other words, the environmental noise may be uncorrelated in an
inter-element sense but will not be uncorrelated in a intra-element
sense. This of course is not typically true for thermal noise which
*is* always uncorrelated in both of these scenarios.

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On Mon, 18 Jun 2007 06:48:03 +0000 (UTC), junoexpress
<M...@gmail.com> wrote:

>Hi,
>
>A signal received from an antenna has two stochastic sources that
>appear in the signal model:
>...........
Antenna specialists are lurking here:
rec.radio.amateur.antenna

Don't be confused by the "amateur" in the newsgroup name.

w.

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On Jun 18, 1:48 am, junoexpress <MTBrenne...@gmail.com> wrote:
[snip]
> The problem here is
> that the electrical engineers who work on this problem assume the
> major component of noise is *from* the environment, but they they
> statistically model the single stochastic component in the signal *as
> if* it came from thermal noise. In the signal processing lit, however,
> people model the noise as if it was *from* thermal noise and their
> models reflect this (i.e. they don't seem to consider the component
> that engineers thing is the dominant noise contribution). My question
> is : does anyone know of any studies that have been done to separately
> examine these two noise components? (Of course, the environmental
> noise has a large degree of variation in its properties, but I want to
> begin to consider this problem and get a handle on how it can affect
> beamforming). This of course would not be easy to do but there are
> anechoic chambers (for RF radiation) where this problem, in principle,
> should be amenable to study.

Matt, are you looking for references of work on (1) characterizing
the noise terms or (2) how to deal with such noise?

For (1), I don't think what you are saying is correct.  There's
already
a lot of work that consider noise terms that are parametric.  This
also applies to signal reconstruction in lieu of quantization and
sampling (i.e. using an analog-to-digital converter).

Now for (2) I know only the case of uniform, linear antenna arrays.
In that case, when the signal is narrowband it becomes the equivalent
of line spectra estimation (except that now you are in "space" rather
than in "time").  The parameters that you want are mapped into
parameters of complex exponentials.  From here you can use
whatever is available in that problem area.  And those studies
include
colored noise terms, other forms of parametric disturbances, etc.

Hope that helps,
Julius

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junoexpress <M...@gmail.com> in
<1...@n60g2000hse.googlegroups.com> wrote:

>The problem here is
>that the electrical engineers who work on this problem assume the
>major component of noise is *from* the environment, but they they
>statistically model the single stochastic component in the signal *as
>if* it came from thermal noise. 

I'm not sure that I fully understand what the problem is. If I hear that 
something is modeled as a thermal noise, I understand that it is modeled
by the Gaussian white noise. Are you saying that the environmental noise
is not white, or even not Gaussian? Then the only thing to do is to actually
measure the noise, fit it to some non-(Gaussian and white) model and include 
it in the final model of your array, but this can be very demanding both 
analytically and numerically.

>Suppose you have a discrete time signal from an M antenna array that
>contains only these two stochastic components where:
> X_i,j = environmental noise from ith channel at the jth time point
>then you *can* have <X_i,j*X_i,k> = 0 for j ne k but will defintely
>not have <X_i,m*X_i,j> = 0 for any j,m
>In other words, the environmental noise may be uncorrelated in an
>inter-element sense but will not be uncorrelated in a intra-element
>sense. This of course is not typically true for thermal noise which
>*is* always uncorrelated in both of these scenarios.

This is not true. While the thermal noise is usually considered to be the
equilibrium (or white, or time-uncorrelated) noise, it can be correlated 
between different sites. In the stochastic resonance community the thermal 
noise  is frequently termed "internal" and is supposed to be identical 
on all sites. The spatially uncorrelated environmental (or "external") noise,
with a different intensity (or temperature) is added on top of that; the
external noise can be time-uncorrelated (white) or time-correlated (colored).
If the two noises just add to, or disturb, the signal, the situation is fairly
simple: you have a correlated array of noises, and the correlations result
from the internal (thermal) part. If the internal noise acts parametrically
(multiplicatively), modifying the parameters of your antenna, the situation
is much more complicated. In the most general situation, you have two
different arrays of correlated noises: the internal (thermal) noise, acting 
parametrically, and the external (environmental) noise that adds to the 
signal. I don't think that this most general situation has been solved yet,
even in the simplest linear case. 

In any case, do the web search for the "spatially correlated noise"
or perhaps for the "array enhanced stochastic resonance"; I'm not sure
you will see the stochastic resonance in your antenna, but at least you
will see what other people have done in this area.

>If you would be so kind as to respond to my e-mail address rather than
>post on the ng, I'd be most appreciative.

This is not very polite as it means "use your time to prepare an answer to my
question, but I won't be bothered to check whether an answer has appeared."

Best regards,

Pawel Gora
Krakow, Poland

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