# Rectangular Antenna Array Model

Started by August 12, 2015
```Hi guys, i'm trying to simulate the MUSIC algorithm on rectangular array.

Here i post an example found in book "Digital signal and image processing"
but there is a little problem.
The array is on XY plane, then i confirmed the exact conversion from
cartesian to polar, as written here:

function A = array2D(dzeta,phi,loc_array)
A=(zeros(M,K));
for kk=1:K
beta = [cos(pk)*sin(tk);sin(pk)*sin(tk);cos(tk)];  %xOy   [x,y,z]
A(:,kk) = exp(2*pi*2j*(loc_array.')*beta);
end

From the polar model,now i have 0&deg;<dzeta (elevation) <90&deg; right, and
-180&deg;<phi(azimuth)<180&deg; because x is weighted by cos(pk), ok.

Below there is MUSIC script( only row is wrong)

clear all
N=100;
K=3;M=25; sigma=0.3;
dzeta = [10 30 70]; phi=[19 -40 -30]; %dzeta=elevation phi=azimuth
loc_array = zeros(3,M);

% array = phased.URA('Size',[5 5],'ElementSpacing',[0.05 0.05]);
% loc_array = getElementPosition(array);
% loc_array(1:2,:) = loc_array(2:3,:);
% loc_array(1,:) = 0;
for xx=1:5
for yy=1:5
loc_array(1:2,(xx-1)*5+yy)=[xx-1,yy-1]'/2-1;
end
end

Aalpha = array2D(dzeta,phi,loc_array);
sn = rand(K,N);
bn=sigma*(randn(M,N)+i*randn(M,N));
xn = Aalpha*sn + bn;

R=zeros(M);
R = (xn*xn')/N;
[U, D, V] = svd(R);
vnoise = V(:,(K+1):M);
PIest = vnoise*vnoise';
plage_theta=(0:0.5:90);         0<elevation<90
ltheta=length(plage_theta);

plage_phi=(0:0.5:90); %   PROBLEM!!!!  DOA is done if   0<phi<90 !!!
<--------------
lphi=length(plage_phi);

music2d = zeros(ltheta,lphi);

for iphi=1:lphi
ph =plage_phi(iphi);
for itheta=1:ltheta
th=plage_theta(itheta);
aij = array2D(th,ph,loc_array);
music2d(itheta,iphi) = -log10(abs(aij'*PIest*aij));
end
end

imagesc(plage_phi,plage_theta,music2d);
grid on;

The problem is the row : plage_phi=(0:0.5:90);   if i change the interval
between -180:180, or 0:360 the spectrum has some peaks that i don't want.
I don't understand...Why?? I want -180 to 180, not 0:90.

I'm very grateful if you look this post.

Thanks
Stefano

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