srjm72499@frontiernet.net wrote:
> I've got a question regarding weight calculation in a beamformer...
>
> In previous work, I was able to ADAPTIVELY determine weights using
> something like LMS, but I needed to generate an actual inbound signal,
> noise, reference, interferers and what-not...  What I'd like to do now
> is pick a few directions in which to intentionally form beams, and
> other directions to intentionally form nulls.  That is, the directions
> are pre-determined, and not determined (adaptively) on the fly.
> Trouble is, I am not getting this to work.
...
> How can I pick my weights to, say, put a beam at theta_a0, theta_e0,
> and nulls in 2 other directions?.

With the caveat that I might have misunderstood your question, I am
pretty sure I have seen a method for doing this somewhere.
Unfortunately,
I don't have any of my books available, so I can't give the exact
references.

First, look for Capon's 1968 paper, you ought to find a reference to it
in
any book on statistical signal processing or array processing. I am not
sure
if this is the paper you look for, but it is a good starting point.

Next, see if you can find a paper by Henrik Schmidt from the mid 80s in

the Journal of the Acoustical Society of America. Schmidt has written
lots of articles, so you might have to look around for a bit to find
the
right one.

Apart from that, try to search for articles on "interference
cancelling".
As far as I can see, your problem is one of canceling interfernce
sources
in known directions.

Rune

Stan Pawlukiewicz wrote:
> Mark wrote:
> > I'm not an expert and I don't even play one on TV but....
> >
> > don't you change the DIRECTION of the nulls and lobes by chaning the
> > PHASE of the drive elements, not the weighting...
>
>
> Assume you have a ideal linear array with the ideal elements spaced at
> half a wavelength, a narrow band signal at the design frequency, and M
> elements. Also assume a reasonable weight function.  The beam pattern
> will have a main lobe and M-1 nulls.  If you fatten up the main lobe,
> the nulls will shift out a bit in the vicinity of the main lobe.  If you
> narrow the main lobe, they pull in a bit.  In general, you need to use
> complex weights, (shifts) to arbitrarily shift, as your question asks
> but the weights without phase shifts do have an effect on null position.
> There is also a difference in null location between the cases of a
> continuous aperture and discrete elements with the same weighting
> function.
> >
> > I'm thinking about the so called broadside and endfire arrays, in both
> > cases, all the elements are fed with equal power, but the phases are
> > changed to re-direct the pattern...
> >
> > I know so called taperd drive (various weighting of the elements) can
> > be used to modify the shape of the main lobe and reduce sidelobes etc,
> > but still I thought that changing DIRECTION of the lobes is done by
> > changing phase,  not weighting.... am I wrong?
> >
> > Mark
> >

OK thanks

I see now that the OP used the term "weights" to mean "complex weights"
 so phase is being changed.

thanks.

Mark

I think this is relevent, to anyone who is interested (and I actually
know the author).  Thanks to all for your help...

http://ieeexplore.ieee.org/iel1/53/43/00000665.pdf?tp=&arnumber=665&isnumber=43
Buckley's 1988 paper on Beamforming

Peter K. wrote:


>>It seems apparent that in a 10-element case, I would have 9 degrees of
>>freedom to play around with, and the overall performance will depend on
>>the geometry of the array.  
> 
> 
> Sounds sensible.
> 

Not quite.

Consider the simplest one dimensional case: 3-tap FIR filter. There are 
two degrees of freedom. It is trivial to set one zero at any frequency, 
however you can only have certain configurations with the two zeroes or 
a zero and a max. The situation with the antenna array is exactly the same.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Steve wrote:

> Vladimir, if possible, could you list any applicable references...

The beamforming with the phased arrays is the vast topic discussed in 
the many books on antennas and electrodynamics.

> It seems apparent that in a 10-element case, I would have 9 degrees of
> freedom to play around with, and the overall performance will depend on
> the geometry of the array.  I guess I'm just suprised that this is a
> difficult question.  Placing either a single beam or a single null in a
> given direction is trivial, and there would still appear to be 8 DOFs
> left.

Nevertheless the exact solution exists only for the certain beam/null 
configurations. There are also important technical difficulties like 
the dramatic drop in the efficiency of antenna system for some 
amplitude/phase distributions.


> I guess perhaps a better way to look at this is to assume the following
> (not the actual application at all!):
> 
> Lets say I have an array with k-elements already in place.  All I can
> do is vary the complex weights (which allow me to play with both the
> relative phases and amplitudes).  I know the relative locations of the
> elements (and thus their relative phases for any azimuth and elevation
> angle if I know what frequency I'm working with).  The task is to pick
> the weights given this phase relationship that provide a beam in
> directions A and B, and nulls in directions C, D, and E.  Let's assume
> that I'm transmitting, and I want to have high gain in the two
> directions because I klnow that's where my buddies are, and also assume
> that I have some devices that I don't want to disturb in the other
> specified directions.  Adaptive techniques can get me there (finding
> good weights, that is) if I "receive" desired signals from the beam
> directions and if I see interfering signals from the other specified
> directions, but if it's given that I am only transmitting, I don't have
> that info available.  Given only the desired beam/null locations and
> the element phase relationships (in all directions), I still think that
> I should be able to determine an optimal weight vector
> (non-adaptively).

What are you trying to do is to find the best approximation of the 
desired ideal beam/null pattern. There may be the closed form analytical 
solution depending on what is your criteria for the "best". Generally 
this is a classical multivariable minimization problem.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

"Steve" <srjm72499@frontiernet.net> writes:

> Vladimir, if possible, could you list any applicable references...
> It seems apparent that in a 10-element case, I would have 9 degrees of
> freedom to play around with, and the overall performance will depend on
> the geometry of the array.  

Sounds sensible.

> I guess I'm just suprised that this is a difficult question.

It's easy to ask; harder to answer.

> Placing either a single beam or a single null in a given direction
> is trivial, and there would still appear to be 8 DOFs left. 

Yup, depending no your array geometry. I can think of cases where you
might not get all the DOFs you're after (e.g. trivial example of
coincident elements).

> I guess perhaps a better way to look at this is to assume the
> following (not the actual application at all!):
> 
> Lets say I have an array with k-elements already in place.  All I can
> do is vary the complex weights (which allow me to play with both the
> relative phases and amplitudes).  I know the relative locations of the
> elements (and thus their relative phases for any azimuth and elevation
> angle if I know what frequency I'm working with).  The task is to pick
> the weights given this phase relationship that provide a beam in
> directions A and B, and nulls in directions C, D, and E.  Let's assume
> that I'm transmitting, and I want to have high gain in the two
> directions because I klnow that's where my buddies are, and also assume
> that I have some devices that I don't want to disturb in the other
> specified directions.  Adaptive techniques can get me there (finding
> good weights, that is) if I "receive" desired signals from the beam
> directions and if I see interfering signals from the other specified
> directions, but if it's given that I am only transmitting, I don't have
> that info available.  Given only the desired beam/null locations and
> the element phase relationships (in all directions), I still think that
> I should be able to determine an optimal weight vector
> (non-adaptively).

Yes, see the paper I referenced previously.  The "multiple frequency
nulling" part will impose nulls in the required directions at the
required operating frequencies.

What we found was that imposing nulls in a given direction worked, but
the beam pattern was very "steep" near the null.  So that any mistake
in direction meant you still had significant gain when you were trying
to null.  Our "solution" was to null in directions either side of the
required direction, that gave a pattern that was less deep (not
exactly zero) in the null direction, but broader to give some
robustness to directional uncertainties.

There are other ways of formulating the problem, too.

Ciao,

Peter K.

Mark wrote:
> I'm not an expert and I don't even play one on TV but....
> 
> don't you change the DIRECTION of the nulls and lobes by chaning the
> PHASE of the drive elements, not the weighting...


Assume you have a ideal linear array with the ideal elements spaced at 
half a wavelength, a narrow band signal at the design frequency, and M 
elements. Also assume a reasonable weight function.  The beam pattern 
will have a main lobe and M-1 nulls.  If you fatten up the main lobe, 
the nulls will shift out a bit in the vicinity of the main lobe.  If you 
narrow the main lobe, they pull in a bit.  In general, you need to use 
complex weights, (shifts) to arbitrarily shift, as your question asks 
but the weights without phase shifts do have an effect on null position. 
There is also a difference in null location between the cases of a 
continuous aperture and discrete elements with the same weighting 
function.
> 
> I'm thinking about the so called broadside and endfire arrays, in both
> cases, all the elements are fed with equal power, but the phases are
> changed to re-direct the pattern...
> 
> I know so called taperd drive (various weighting of the elements) can
> be used to modify the shape of the main lobe and reduce sidelobes etc,
> but still I thought that changing DIRECTION of the lobes is done by
> changing phase,  not weighting.... am I wrong?
> 
> Mark
> 

Vladimir, if possible, could you list any applicable references...
It seems apparent that in a 10-element case, I would have 9 degrees of
freedom to play around with, and the overall performance will depend on
the geometry of the array.  I guess I'm just suprised that this is a
difficult question.  Placing either a single beam or a single null in a
given direction is trivial, and there would still appear to be 8 DOFs
left.
I guess perhaps a better way to look at this is to assume the following
(not the actual application at all!):

Lets say I have an array with k-elements already in place.  All I can
do is vary the complex weights (which allow me to play with both the
relative phases and amplitudes).  I know the relative locations of the
elements (and thus their relative phases for any azimuth and elevation
angle if I know what frequency I'm working with).  The task is to pick
the weights given this phase relationship that provide a beam in
directions A and B, and nulls in directions C, D, and E.  Let's assume
that I'm transmitting, and I want to have high gain in the two
directions because I klnow that's where my buddies are, and also assume
that I have some devices that I don't want to disturb in the other
specified directions.  Adaptive techniques can get me there (finding
good weights, that is) if I "receive" desired signals from the beam
directions and if I see interfering signals from the other specified
directions, but if it's given that I am only transmitting, I don't have
that info available.  Given only the desired beam/null locations and
the element phase relationships (in all directions), I still think that
I should be able to determine an optimal weight vector
(non-adaptively).

Peter K. wrote:
> "Mark" <makolber@yahoo.com> writes:
>
> > I'm not an expert and I don't even play one on TV but....
> >
> > don't you change the DIRECTION of the nulls and lobes by chaning the
> > PHASE of the drive elements, not the weighting...
>
> Er, that's what his equations are doing.
>
> Ciao,
>
> Peter K.

OK I guess I took the OPs words too literally.

thanks

>>>How can I pick my weights to, say, put a beam at theta_a0, theta_e0,
>>>and nulls in 2 other directions?.  

Mark

srjm72499@frontiernet.net wrote:

> I've got a question regarding weight calculation in a beamformer...
> 
> In previous work, I was able to ADAPTIVELY determine weights using
> something like LMS, but I needed to generate an actual inbound signal,
> noise, reference, interferers and what-not...  What I'd like to do now
> is pick a few directions in which to intentionally form beams, and
> other directions to intentionally form nulls.  That is, the directions
> are pre-determined, and not determined (adaptively) on the fly.
> Trouble is, I am not getting this to work.
> 
> For a 4 element example (where the first element is at the origin, and
> the others may be anywhere in x,y,z space), my code looks like:
> 
> diff_dist2=p2x.*cos(theta_a).*cos(theta_e)+p2y.*sin(theta_a).*cos(theta_e)+p2z.*sin(theta_e);
> diff_dist3=p3x.*cos(theta_a).*cos(theta_e)+p3y.*sin(theta_a).*cos(theta_e)+p3z.*sin(theta_e);
> diff_dist4=p4x.*cos(theta_a).*cos(theta_e)+p4y.*sin(theta_a).*cos(theta_e)+p4z.*sin(theta_e);
> phi2=diff_dist2.*2.*pi./lambda;
> phi3=diff_dist3.*2.*pi./lambda;
> phi4=diff_dist4.*2.*pi./lambda;
> 
> mag_pattern=abs(w1.*rcart1+w2.*exp(j.*phi2).*rcart2+w3.*exp(j.*phi3).*rcart3+w4.*exp(j.*phi4).*rcart4);
> [x,y,z]=sph2cart(theta_a,theta_e,mag_pattern);
> 
> How can I pick my weights to, say, put a beam at theta_a0, theta_e0,
> and nulls in 2 other directions?.  How about additional beams/nulls, if
> I add elements?

The task requires the solution of the system of equations. The problem 
is you can't set the directions for nulls and beams as the arbitrary - 
the exact solution exists only for the certain cases. Instead of setting 
nulls and beams you can optimize the null/beam ratios in the directions 
of interest. This is a task of multi variable minimization and there are
some good algorithms to do that.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com