2d array pattern

Hi,

I've been trying lately to plot an 2D array beamforming diagram, pointing in a direction ele and az as a function of the incident angle. From the textbooks I've managed to understand that to plot the array pattern as a function of the incidence angle then the array pattern value depends on the difference of the sines rather than the difference of the angles themselves. At least for an D array.
I've been trying to expand this to an 2D array using u=sin()*cos() and
v=sin()*sin() and taking the difference between that and the pointing
angle, however, it simply does not seem to work out.

The matlab code looks something like this:

 ele=0; az=0;   % array pointing direction
 lambda=2; w=[1 1 1 1 1];   % lambda / array weights
 xpos=[1 1 1 1 1]; ypos=[1 2 3 4 5]; % position of elements
 step=0.01;

 pattern=[];
 pu=xpos*cos(ele);
 pv=ypos*cos(az);
 c1=1; fx=-j*2*pi/lambda;
 for phi=-1:step:1
  c2=1;
   for the=-1:step:1
   af=0;
   k=[sin(0.5*pi*phi)*cos(0.5*pi*the)-sin(ele)*cos(az) sin(0.5*pi*phi*sin(0.5*pi*the)-sin(ele)*sin(az) 0];
   for m=1:length(w)
     af=af+w(m)*exp(fx*k*[pu(m); pv(m); 0]);
   end;
   pattern(c1,c2)=af;
  c2=c2+1;
  end;
  c1=c1+1;
end;
imagesc(abs(pattern))

I guess I'm simply doing an incorrect rotation or adding up something
incorrectly in the k=[] line. Could anyone please shed more light and helpe me fix this ? I think if i just replace in the following  k=[u-2*ele/pi v-2*az/pi 0]; then I get the plot in the wavenumber domain which seem to be OK, but in a real life situation I want to plot it as
a function of the incidence angle.

Thank you.

On Tuesday, January 28, 2014 2:37:24 AM UTC-6, mra...@gmail.com wrote:
> Hi,
> 
> 
> 
> I've been trying lately to plot an 2D array beamforming diagram, pointing in a direction ele and az as a function of the incident angle. From the textbooks I've managed to understand that to plot the array pattern as a function of the incidence angle then the array pattern value depends on the difference of the sines rather than the difference of the angles themselves. At least for an D array.
> 
> I've been trying to expand this to an 2D array using u=sin()*cos() and
> 
> v=sin()*sin() and taking the difference between that and the pointing
> 
> angle, however, it simply does not seem to work out.
> 
> 
> 
> The matlab code looks something like this:
> 
> 
> 
>  ele=0; az=0;   % array pointing direction
> 
>  lambda=2; w=[1 1 1 1 1];   % lambda / array weights
> 
>  xpos=[1 1 1 1 1]; ypos=[1 2 3 4 5]; % position of elements
> 
>  step=0.01;
> 
> 
> 
>  pattern=[];
> 
>  pu=xpos*cos(ele);
> 
>  pv=ypos*cos(az);
> 
>  c1=1; fx=-j*2*pi/lambda;
> 
>  for phi=-1:step:1
> 
>   c2=1;
> 
>    for the=-1:step:1
> 
>    af=0;
> 
>    k=[sin(0.5*pi*phi)*cos(0.5*pi*the)-sin(ele)*cos(az) sin(0.5*pi*phi*sin(0.5*pi*the)-sin(ele)*sin(az) 0];
> 
>    for m=1:length(w)
> 
>      af=af+w(m)*exp(fx*k*[pu(m); pv(m); 0]);
> 
>    end;
> 
>    pattern(c1,c2)=af;
> 
>   c2=c2+1;
> 
>   end;
> 
>   c1=c1+1;
> 
> end;
> 
> imagesc(abs(pattern))
> 
> 
> 
> I guess I'm simply doing an incorrect rotation or adding up something
> 
> incorrectly in the k=[] line. Could anyone please shed more light and helpe me fix this ? I think if i just replace in the following  k=[u-2*ele/pi v-2*az/pi 0]; then I get the plot in the wavenumber domain which seem to be OK, but in a real life situation I want to plot it as
> 
> a function of the incidence angle.
> 
> 
> 
> Thank you.

What is _the_ in the line beginning with

k=[sin(0.5*pi*phi)*cos(0.5*pi*the)-sin(ele)*cos(az)

On Tuesday, January 28, 2014 11:32:14 PM UTC+1, maury wrote:
> On Tuesday, January 28, 2014 2:37:24 AM UTC-6, mra...@gmail.com wrote: > Hi, > > > > I've been trying lately to plot an 2D array beamforming diagram, pointing in a direction ele and az as a function of the incident angle. From the textbooks I've managed to understand that to plot the array pattern as a function of the incidence angle then the array pattern value depends on the difference of the sines rather than the difference of the angles themselves. At least for an D array. > > I've been trying to expand this to an 2D array using u=sin()*cos() and > > v=sin()*sin() and taking the difference between that and the pointing > > angle, however, it simply does not seem to work out. > > > > The matlab code looks something like this: > > > > ele=0; az=0; % array pointing direction > > lambda=2; w=[1 1 1 1 1]; % lambda / array weights > > xpos=[1 1 1 1 1]; ypos=[1 2 3 4 5]; % position of elements > > step=0.01; > > > > pattern=[]; > > pu=xpos*cos(ele); > > pv=ypos*cos(az); > > c1=1; fx=-j*2*pi/lambda; > > for phi=-1:step:1 > > c2=1; > > for the=-1:step:1 > > af=0; > > k=[sin(0.5*pi*phi)*cos(0.5*pi*the)-sin(ele)*cos(az) sin(0.5*pi*phi*sin(0.5*pi*the)-sin(ele)*sin(az) 0]; > > for m=1:length(w) > > af=af+w(m)*exp(fx*k*[pu(m); pv(m); 0]); > > end; > > pattern(c1,c2)=af; > > c2=c2+1; > > end; > > c1=c1+1; > > end; > > imagesc(abs(pattern)) > > > > I guess I'm simply doing an incorrect rotation or adding up something > > incorrectly in the k=[] line. Could anyone please shed more light and helpe me fix this ? I think if i just replace in the following k=[u-2*ele/pi v-2*az/pi 0]; then I get the plot in the wavenumber domain which seem to be OK, but in a real life situation I want to plot it as > > a function of the incidence angle. > > > > Thank you. What is _the_ in the line beginning with k=[sin(0.5*pi*phi)*cos(0.5*pi*the)-sin(ele)*cos(az)

Well, the (theta) and phi are the angles I run the algorithm over. So the goal is to cover all phi/theta angles from -1 to 1 (scaled with pi/2).

Well, the (theta) and phi are the angles I run the algorithm over. So the goal is to cover all phi/theta angles from -1 to 1 (scaled with pi/2) and then plot them.

On Wednesday, January 29, 2014 2:11:43 AM UTC-6, mra...@gmail.com wrote:
> Well, the (theta) and phi are the angles I run the algorithm over. So the goal is to cover all phi/theta angles from -1 to 1 (scaled with pi/2) and then plot them.

Sorry for the delay, I'm giving exams this week, and am a bit busy. I'm trying to determine what you're trying to do. For example, I use the following Matlab code to plot array patterns. It gives me array gain as a function of azimuth for a linear array. For a 2-dimensional array, the general display is still array gain as a function of azimuth, but the array structure must be accounted for.
function [x,y,r,a] = PolarPlot(N,D,S)

%   Function to plot an phased-array antenna pattern
%   Gives normalized field pattern in polar and rectangular coordinates
%   
%   plot(x,y) gives plot using rectangular coordinates
%   polar(a,r) gives plot using polar coordinates
%
%   N = number of sources
%   D = spacing, in wavelengths, of the sources
%   S = phasing of the sources, in radians (e.g., 90 degree = 1.57)

y = [];
x = [];
cd = 6.28*D;
j = 1;
a = .01:.01:6.27;
ca = cos(a);
pf = cd*ca + S;
r = sin(N*pf/2)./sin(pf/2);
r = abs(r);
y = r.*ca;
x = r.*sin(a);
end

From your code, it appears that you are trying to plot 3-dimensional data on a 2-dimensional surface, much like the information displayed in a spectrogram. What do you think the display should look like?