beamforming /steering vector for planar array

Hi All,
I am doing beamforming in MATLAB and I am not familiar in both very much.
I hope someone can help me out by giving link of paper or MATLAB work.
I have a planar array antenna (rectangular shape) with 16 elements. The RF
signal will be incident on those array. I am trying to find the
DOA(direction-of-arrival)on the antenna array. 
I am now trying to use a conventional beamformer algorithm which calculate
the power of the beam(DOA) at each angle.

My attempted algorithm is 

weight = W
steering_vector = a(theta)

(1) calculate  the steering vector in function of theta
(2) calculate the weight using steering vector
(3) calculate the power spectrum at each angle theta (0 to 180 deg)

My azimuth angle is theta
My elevation angle is phi

I found out ,to find the steering vector in theta, it is related with the
angle phi in such a way of 

steering_vector = [1 exp(j*phi).......exp(j*(L-1)*phi]'; 

L = antenna elements


My main question is I don't know how to find steering vector matrix for
2by2 planar array antenna.

I hope someone could please answer about it.
Thanks a lot in advance.

On 27 Feb, 02:44, "hsquared" <hnin...@yahoo.com> wrote:
> Hi All,
> I am doing beamforming in MATLAB and I am not familiar in both very much.
> I hope someone can help me out by giving link of paper or MATLAB work.
> I have a planar array antenna (rectangular shape) with 16 elements. The RF
> signal will be incident on those array. I am trying to find the
> DOA(direction-of-arrival)on the antenna array.
> I am now trying to use a conventional beamformer algorithm which calculate
> the power of the beam(DOA) at each angle.
>
> My attempted algorithm is
>
> weight = W
> steering_vector = a(theta)
>
> (1) calculate &#4294967295;the steering vector in function of theta
> (2) calculate the weight using steering vector
> (3) calculate the power spectrum at each angle theta (0 to 180 deg)
>
> My azimuth angle is theta
> My elevation angle is phi
>
> I found out ,to find the steering vector in theta, it is related with the
> angle phi in such a way of
>
> steering_vector = [1 exp(j*phi).......exp(j*(L-1)*phi]';
>
> L = antenna elements
>
> My main question is I don't know how to find steering vector matrix for
> 2by2 planar array antenna.

There used to be a book by Ziomek that addressed those soerts
of questions. I don't know if it is still available, though.

Rune

>On 27 Feb, 02:44, "hsquared" <hnin...@yahoo.com> wrote:
>> Hi All,
>> I am doing beamforming in MATLAB and I am not familiar in both very
much.
>> I hope someone can help me out by giving link of paper or MATLAB work.
>> I have a planar array antenna (rectangular shape) with 16 elements. The
RF=
>
>> signal will be incident on those array. I am trying to find the
>> DOA(direction-of-arrival)on the antenna array.
>> I am now trying to use a conventional beamformer algorithm which
calculate=
>
>> the power of the beam(DOA) at each angle.
>>
>> My attempted algorithm is
>>
>> weight =3D W
>> steering_vector =3D a(theta)
>>
>> (1) calculate =A0the steering vector in function of theta
>> (2) calculate the weight using steering vector
>> (3) calculate the power spectrum at each angle theta (0 to 180 deg)
>>
>> My azimuth angle is theta
>> My elevation angle is phi
>>
>> I found out ,to find the steering vector in theta, it is related with
the
>> angle phi in such a way of
>>
>> steering_vector =3D [1 exp(j*phi).......exp(j*(L-1)*phi]';
>>
>> L =3D antenna elements
>>
>> My main question is I don't know how to find steering vector matrix
for
>> 2by2 planar array antenna.
>
>There used to be a book by Ziomek that addressed those soerts
>of questions. I don't know if it is still available, though.
>
>Rune
>

On Feb 27, 6:44 am, "hsquared" <hnin...@yahoo.com> wrote:
> Hi All,
> I am doing beamforming in MATLAB and I am not familiar in both very much.
> I hope someone can help me out by giving link of paper or MATLAB work.

I have worked on this sometime back. Here are a few links to my
papers:

http://bdsatish.googlepages.com/VIT.pdf

http://bdsatish.googlepages.com/6by16by2.pdf

http://bdsatish.googlepages.com/NCET_1.pdf

If you really want the ready-made MATLAB program, contact me
personally.

> I have a planar array antenna (rectangular shape) with 16 elements. The RF
> signal will be incident on those array. I am trying to find the
> DOA(direction-of-arrival)on the antenna array.
> I am now trying to use a conventional beamformer algorithm which calculate
> the power of the beam(DOA) at each angle.
>
> My attempted algorithm is
>
> weight = W
> steering_vector = a(theta)
>
> (1) calculate  the steering vector in function of theta
> (2) calculate the weight using steering vector
> (3) calculate the power spectrum at each angle theta (0 to 180 deg)
>
> My azimuth angle is theta
> My elevation angle is phi
>
> I found out ,to find the steering vector in theta, it is related with the
> angle phi in such a way of
>
> steering_vector = [1 exp(j*phi).......exp(j*(L-1)*phi]';
>
> L = antenna elements
>
> My main question is I don't know how to find steering vector matrix for
> 2by2 planar array antenna.
>
> I hope someone could please answer about it.
> Thanks a lot in advance.

>On Feb 27, 6:44 am, "hsquared" <hnin...@yahoo.com> wrote:
>> Hi All,
>> I am doing beamforming in MATLAB and I am not familiar in both very
much.
>> I hope someone can help me out by giving link of paper or MATLAB work.
>
>I have worked on this sometime back. Here are a few links to my
>papers:
>
>http://bdsatish.googlepages.com/VIT.pdf
>
>http://bdsatish.googlepages.com/6by16by2.pdf
>
>http://bdsatish.googlepages.com/NCET_1.pdf
>
>If you really want the ready-made MATLAB program, contact me
>personally.
>
>> I have a planar array antenna (rectangular shape) with 16 elements. The
RF
>> signal will be incident on those array. I am trying to find the
>> DOA(direction-of-arrival)on the antenna array.
>> I am now trying to use a conventional beamformer algorithm which
calculate
>> the power of the beam(DOA) at each angle.
>>
>> My attempted algorithm is
>>
>> weight = W
>> steering_vector = a(theta)
>>
>> (1) calculate  the steering vector in function of theta
>> (2) calculate the weight using steering vector
>> (3) calculate the power spectrum at each angle theta (0 to 180 deg)
>>
>> My azimuth angle is theta
>> My elevation angle is phi
>>
>> I found out ,to find the steering vector in theta, it is related with
the
>> angle phi in such a way of
>>
>> steering_vector = [1 exp(j*phi).......exp(j*(L-1)*phi]';
>>
>> L = antenna elements
>>
>> My main question is I don't know how to find steering vector matrix
for
>> 2by2 planar array antenna.
>>
>> I hope someone could please answer about it.
>> Thanks a lot in advance.
>
>

Hi BDstish,

Thanks a lot for pointing out the papers which are very helpful to
understand  the DOA and the beamforming step by step. 

I sent out emails to you for MATLAB codes help. 
Now I am implementing the DOA and beam forming in MATLAB, if you could
help me with MATLAB, this would be very great. If you can, please let me
look at your MATLAB implementation. 

Even though I am doing a bit different, I do believe that they will be
very helpful to me.

Thanks a lot for your help and time.

hsquared.

I have done beamforming using genetic algorithm as I could not figure out
spatial filtering. 

1)What are the differences between using covariance matrix and using
genetic algorithm to find the weights to have a null or minimum power?

For a rectangular array of 3 x 2. I went thru CA Balanis antenna theory
but its array factor formulation is assumed using progressive phase
difference. 
I am required to use individual phase excitations of each element so 
2)how can i use pattern multiplication of the horizontal dx arrays and dy
arrays to formulate my array factor?

3) How can i justify my claim for using GA as somehow I feel that spatial
processing i better.. haha.. the more i read. -->versatility?

Would be great if there are simpler paper references to read.. 

On 7 Apr, 11:35, "terrp" <te...@hotmail.com> wrote:
> I have done beamforming using genetic algorithm as I could not figure out
> spatial filtering.
>
> 1)What are the differences between using covariance matrix and using
> genetic algorithm to find the weights to have a null or minimum power?

What kind of beamforming is this? What problem do you try
to solve? Interference cancellation? DoA estimation?
Phased-array antenna?

...
> 3) How can i justify my claim for using GA as somehow I feel that spatial
> processing i better.. haha.. the more i read. -->versatility?

One pre-requisite to defend such a claim is that you can
find arguments to support it. Now, you don't seem to be
in a very good position since you started your post by
stating that  "I could not figure out spatial filtering."
If you don't know the alternatives it is very hard to
argue in favour of one particular approach.

So depending on exactly what your goal is and the
context of your work (somehow I suspect that this might
be a term project which is due in a few days or weeks),
I would start by carefully sanitizing every hint of who
made the claim about the GAs from all texts and reports.
'A' claim has been made, without refernce to who made it.
Form there on you have to investigates the claim about the
GAs in detail:

- What are the appealing aspects of GAs?
- What are the downsides of GAs?
- What are the practical aspects with working
  with GAs?

Once you set up a structured account of your expectations
and experiences, you might find a conclusion emerging
from your report. I don't know what the conclusion will
be, but the fact that you state the question whether
GAs is worth their while is a very good seign in my book.

Remember: The fact that somebody had an idea does *not*
mean that the idea is good or worth investigating in any
depth!

Very few people have the discipline to discard ideas based
on investigations and analysis. Even fewer are able to do
that with their own ideas.

If this indeed is a term project, you might be a bit
depressed right now because that idea you wanted to
investigate did not work. Just be aware that you have
learned something far more valuable: To criticize
the idea and question whether it is worth prusuing
at all.

Rune

Thanks Rune, I have a better idea how should i shape my report.. 
I underestimated my time, as I have no background in antenna array, GA and
spatial processing and did not expect the scope to be so wide.

Any idea for formulation of a rectangular array? I cant find any papers on
a 4x2 rectangular array with individual phase weights. Only able to find
using progressive phase on the textbook.

Progressive phase on txtbook
Array factor = Sxm*Sym 
Sxm = e*w1 + e*w2 + e*w3
Sym = e*w1 + e*w4 (assume progressive phase so w5 and w6 are similar to w2
and w3 respectively.

My formulation:
Array factor = e*w1 + e*w2 + e*w3 +.... + e*w6
w is my weights for each element..
which i think is not complete due to elements on x axis and y axis.

Should it be : array factor = e*(w1+w4)+e*(w2+w5)+e*(w3+w6)
Any good references on the web?

Its an adaptive nulling algorithm. Given phi, theta of jamming signal.

Objective is to find the optimum weights and form a null. 

Yep, i chose GA. Basically, I have successfully optimise for a circular
array.

Phase 2 was to use a rectangular array..which i also could use the same
algorithm to find the null but just couldn't verify my fitness
function(array factor) is correct.

Well if i were to find 2 nulls. my approach:
fitnessfunction = Arrayfactor of angle1 + array factor of angle2
But my null turn out to be low and miss the angle by 10 degrees...

Any idea on how to use GA for 2 nulls?