Implementing Beamforming...a question about algorithms!

Hi, please read this question, I'm really confused about what the
literature tells...

Some days ago, I asked about the possibilities of using DOA stimation
algorithms with adaptive algorithms for implementing beamforming. I found
diferent articles that told me this was a good idea. Howerver, I asked it
in this forum and someone (that I think is an expert about that) told me
that I've to stay away from DOA stimation algorithms...The problem is that
I'm finding a lot of articles that tell me to use these algorithms first of
the adaptive algortihm. A part of my conversation is written below:

My article told:

"A smart antenna system at the base station of a cellular mobile
> system is depicted in Fig. 1. It consists of a uniform linear
> antenna array for which the current amplitudes are adjusted
> by a set of complex weights using an adaptive beamforming
> algorithm. The adaptive beamforming algorithm optimizes
> the array output beam pattern such that maximum radiated
> power is produced in the directions of desired mobile users
> and deep nulls are generated in the directions of undesired
> signals representing co-channel interference from mobile users
> in adjacent cells. Prior to adaptive beamforming, the directions
> of users and interferes must be obtained using a direction-ofarrival
> (DOA) estimation algorithm"
>
> After this, as I had seen in other documents, it talks about MUSIC and
> LMS algorithms and specifies that LMS algorithm needs to know a
reference
> signal.

This person told me:

I would *guess* that they use MUSIC to obtain
the DoA of the source, and then use the LMS to extract
the actual signal. This is the sort of thing that might
look good on paper and even generate some funding, if
mentioned in an application.

However, using MUSIC or ESPRIT in an unsupervised setting
is a sure recipe for disaster. Your first task ought to
be to research the literature and find out how many
people have used MUSIC or ESPRIT successfully in "the
wild." Not how many say they *will*; how many who have
*actually* used these methods.

The reason why there are so few (any at all?) is that
both MUSIC and ESPRIT require that the antenna array
is tailored to the signals they will measure. If you
look closely at the equations, you will find that those
sorts of methods require that the dimension of certain
data covariance matrices are larger than the number
of signals present. The rank of the covariance matrices
depend in turn on the number of elements in the array.

For an N-element ULA you need to *guarantee* that there
will *never* be more than N/2-1 signals present. The whole
system will go down if there are N/2 or more signals.
(If you don't believe me, make sure to run simulations
before you engage in any large design projevts.)


---------------I really believed this person but I'm not sure about the
articles...could someone help me?

On 26 Nov, 14:06, "scc" <sandracorr...@gmail.com> wrote:
> Hi, please read this question, I'm really confused about what the
> literature tells...
>
> Some days ago, I asked about the possibilities of using DOA stimation
> algorithms with adaptive algorithms for implementing beamforming. I found
> diferent articles that told me this was a good idea. Howerver, I asked it
> in this forum and someone (that I think is an expert about that)

It was me who told you and I am no expert. I spent only 6 years
working with those sorts of things, so don't take my word for
anything.

> told me
> that I've to stay away from DOA stimation algorithms...The problem is that
> I'm finding a lot of articles that tell me to use these algorithms first of
> the adaptive algortihm. A part of my conversation is written below:
>
...
> This person told me:
...
> However, using MUSIC or ESPRIT in an unsupervised setting
> is a sure recipe for disaster. Your first task ought to
> be to research the literature and find out how many
> people have used MUSIC or ESPRIT successfully in "the
> wild." Not how many say they *will*; how many who have
> *actually* used these methods.
>
> The reason why there are so few (any at all?) is that
> both MUSIC and ESPRIT require that the antenna array
> is tailored to the signals they will measure. If you
> look closely at the equations, you will find that those
> sorts of methods require that the dimension of certain
> data covariance matrices are larger than the number
> of signals present. The rank of the covariance matrices
> depend in turn on the number of elements in the array.
>
> For an N-element ULA you need to *guarantee* that there
> will *never* be more than N/2-1 signals present. The whole
> system will go down if there are N/2 or more signals.
> (If you don't believe me, make sure to run simulations
> before you engage in any large design projevts.)
>
> ---------------I really believed this person but I'm not sure about the
> articles...could someone help me?

If you have been assigned to work with these sorts of things,
you should not believe any one person. You should implement
and test the algorithms yourself from scratch. That's what I did
(this was years before matlab included MUSIC in their signal
processing toolbox) and my *opinions* are based on that
experience.

As a first test (and you can use the Matlab version for this)
make a signal containing one sinusoidal at f = pi/8 with
16 samples and SNR > 50 dB. Compute the pseudospectrum
and compare it to where you expect to see a spectrum line.

Next, add one line at f=pi/4  (now the signal has two
sinusoidal components) and compare the pseudospectrum
to what you expect to see.

Continue by adding one line at n*pi/8 for n = 3,4,...,12.

Do all lines in all tests fall where you expect to see them?
Exactly where does the change take place? What is the
ratio of the max number of correct lines and the number of
samples in the sequence (16)?

If you do this simple test and document it, you have a very
good basis for emailing not me, but the authors of the
articles you found and ask them what is going on.
If they are correct in that using MUSIC or ESPRIT as
a pre-processing step is a good idea, then I have
misunderstood something and the test outlined above
is fundamentally flawed. Just do the test and ask the
authors what I (Rune) has misunderstood about these
methods.

I am sure the answers will be very informative.

Rune

On 26 Nov, 14:35, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 26 Nov, 14:06, "scc" <sandracorr...@gmail.com> wrote:
>
> > Hi, please read this question, I'm really confused about what the
> > literature tells...
>
> > Some days ago, I asked about the possibilities of using DOA stimation
> > algorithms with adaptive algorithms for implementing beamforming. I found
> > diferent articles that told me this was a good idea. Howerver, I asked it
> > in this forum and someone (that I think is an expert about that)
>
> It was me who told you and I am no expert. I spent only 6 years
> working with those sorts of things, so don't take my word for
> anything.

> > told me
> > that I've to stay away from DOA stimation algorithms...The problem is that
> > I'm finding a lot of articles that tell me to use these algorithms first of
> > the adaptive algortihm. A part of my conversation is written below:
>
> ...
> > This person told me:
> ...
> > However, using MUSIC or ESPRIT in an unsupervised setting
> > is a sure recipe for disaster. Your first task ought to
> > be to research the literature and find out how many
> > people have used MUSIC or ESPRIT successfully in "the
> > wild." Not how many say they *will*; how many who have
> > *actually* used these methods.
>
> > The reason why there are so few (any at all?) is that
> > both MUSIC and ESPRIT require that the antenna array
> > is tailored to the signals they will measure. If you
> > look closely at the equations, you will find that those
> > sorts of methods require that the dimension of certain
> > data covariance matrices are larger than the number
> > of signals present. The rank of the covariance matrices
> > depend in turn on the number of elements in the array.
>
> > For an N-element ULA you need to *guarantee* that there
> > will *never* be more than N/2-1 signals present. The whole
> > system will go down if there are N/2 or more signals.
> > (If you don't believe me, make sure to run simulations
> > before you engage in any large design projevts.)
>
> > ---------------I really believed this person but I'm not sure about the
> > articles...could someone help me?
>
> If you have been assigned to work with these sorts of things,
> you should not believe any one person. You should implement
> and test the algorithms yourself from scratch. That's what I did
> (this was years before matlab included MUSIC in their signal
> processing toolbox) and my *opinions* are based on that
> experience.
>
> As a first test (and you can use the Matlab version for this)
> make a signal containing one sinusoidal at f = pi/8 with
> 16 samples and SNR > 50 dB. Compute the pseudospectrum
> and compare it to where you expect to see a spectrum line.
>
> Next, add one line at f=pi/4  (now the signal has two
> sinusoidal components) and compare the pseudospectrum
> to what you expect to see.
>
> Continue by adding one line at n*pi/8 for n = 3,4,...,12.

Just one correction: Use 12 signals but locate them at

f = n*pi/13, n = 1,2,...,12

instead.

Rune

> Do all lines in all tests fall where you expect to see them?
> Exactly where does the change take place? What is the
> ratio of the max number of correct lines and the number of
> samples in the sequence (16)?
>
> If you do this simple test and document it, you have a very
> good basis for emailing not me, but the authors of the
> articles you found and ask them what is going on.
> If they are correct in that using MUSIC or ESPRIT as
> a pre-processing step is a good idea, then I have
> misunderstood something and the test outlined above
> is fundamentally flawed. Just do the test and ask the
> authors what I (Rune) has misunderstood about these
> methods.
>
> I am sure the answers will be very informative.
>
> Rune- Skjul sitert tekst -
>
> - Vis sitert tekst -

On Nov 26, 8:06 am, "scc" <sandracorr...@gmail.com> wrote:
> Hi, please read this question, I'm really confused about what the
> literature tells...
>
> Some days ago, I asked about the possibilities of using DOA stimation
> algorithms with adaptive algorithms for implementing beamforming. I found
> diferent articles that told me this was a good idea. Howerver, I asked it
> in this forum and someone (that I think is an expert about that) told me
> that I've to stay away from DOA stimation algorithms...The problem is that
> I'm finding a lot of articles that tell me to use these algorithms first of
> the adaptive algortihm. A part of my conversation is written below:
>
> My article told:
>
> "A smart antenna system at the base station of a cellular mobile
>
>
>
> > system is depicted in Fig. 1. It consists of a uniform linear
> > antenna array for which the current amplitudes are adjusted
> > by a set of complex weights using an adaptive beamforming
> > algorithm. The adaptive beamforming algorithm optimizes
> > the array output beam pattern such that maximum radiated
> > power is produced in the directions of desired mobile users
> > and deep nulls are generated in the directions of undesired
> > signals representing co-channel interference from mobile users
> > in adjacent cells. Prior to adaptive beamforming, the directions
> > of users and interferes must be obtained using a direction-ofarrival
> > (DOA) estimation algorithm"
>
> > After this, as I had seen in other documents, it talks about MUSIC and
> > LMS algorithms and specifies that LMS algorithm needs to know a
> reference
> > signal.
>
> This person told me:
>
> I would *guess* that they use MUSIC to obtain
> the DoA of the source, and then use the LMS to extract
> the actual signal. This is the sort of thing that might
> look good on paper and even generate some funding, if
> mentioned in an application.
>
> However, using MUSIC or ESPRIT in an unsupervised setting
> is a sure recipe for disaster. Your first task ought to
> be to research the literature and find out how many
> people have used MUSIC or ESPRIT successfully in "the
> wild." Not how many say they *will*; how many who have
> *actually* used these methods.
>
> The reason why there are so few (any at all?) is that
> both MUSIC and ESPRIT require that the antenna array
> is tailored to the signals they will measure. If you
> look closely at the equations, you will find that those
> sorts of methods require that the dimension of certain
> data covariance matrices are larger than the number
> of signals present. The rank of the covariance matrices
> depend in turn on the number of elements in the array.
>
> For an N-element ULA you need to *guarantee* that there
> will *never* be more than N/2-1 signals present. The whole
> system will go down if there are N/2 or more signals.
> (If you don't believe me, make sure to run simulations
> before you engage in any large design projevts.)
>
> ---------------I really believed this person but I'm not sure about the
> articles...could someone help me?

Combining DOA and beam forming is in theory a good idea, but there are
some problems that depend on the application.

DOA algorithms typically assume that the spatial noise background is
isotropic and all the signals present are distinct point sources in
the far field and as discussed, you have narrow-band limitations on
the number of signals you can resolve that depend on the number of
appropriately spaced sensors.

You really can't make those kinds of assumption in underwater
acoustics, noise can be spatially distributed (not isotropic) so you
have to play with spatial pre-whitening which has its own set of
problems.

The assumptions in terrestrial RF tend to be different.  My
understanding is that the complication to DOA in terrestrial RF is
multi-path and most DOA algorithms don't handle that out of the box
either.

On 26 Nov, 14:39, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 26 Nov, 14:35, Rune Allnor <all...@tele.ntnu.no> wrote:

> > As a first test (and you can use the Matlab version for this)
> > make a signal containing one sinusoidal at f = pi/8 with
> > 16 samples and SNR > 50 dB. Compute the pseudospectrum
> > and compare it to where you expect to see a spectrum line.
>
> > Next, add one line at f=pi/4  (now the signal has two
> > sinusoidal components) and compare the pseudospectrum
> > to what you expect to see.
>
> > Continue by adding one line at n*pi/8 for n = 3,4,...,12.
>
> Just one correction: Use 12 signals but locate them at
>
> f = n*pi/13, n = 1,2,...,12
>
> instead.

I am 99.99% certain this test will expose the problem when
you add the 8th sinusoidal. The remaining uncertainty is related
to what estimator is used for the spatial covariance matrix.
I would use the unbiased estimator, and if that is indeed
the estimator which is used, then the breakdown happens at
n=8.

However, there is a chance that the biased covariance
estimator is used. If you don't see a breakdown happening
after having added the 8th sinusoidal, use these parameters
instead:

f = n*pi/21,   n = 1,2,...,20.

In this case the breakdown happens for n = 16.

Rune

Sorry if I haven't rispond early...

I'll do it, I hadn't done it because I was still looking for information
(I think I was losing my time).

Thanks your for help! I'll tell u about my results but I'm quite sure
you're right.

San
>

On 27 Nov, 17:35, "scc" <sandracorr...@gmail.com> wrote:
> Thanks your for help! I'll tell u about my results but I'm quite sure
> you're right.

Just be aware that when I said "sinusoidals" I meant
*complex-valued* sinusoidals on the form exp(jkx).
If you try my test with real-valued sines and cosines
the breakdown will occur at either n = 4 or n = 8, since
a real-valued sine or cosine comprises two complex
exponentials:

sin(kx) = 1/(2j)(exp(jkx)-exp(-jkx))
cos(kx) = 1/2(exp(jkx)+exp(-kx))

Rune

Wow, very interesting stuff.

Was wondering if MUSIC or ESPRIT algorithm can work if i used a circular
array or rectangular planar array?

How do u formulate rectangular planar array E field with phase excitations
only.