Planar Array DOA Beamforming

Hi,

I am trying to implement the Bartlett's algorithm (conventional
beamforming) to find the DOA for a planar array geometry which has a
2x2 array structure. I generate a input signal and then find the
steering vector for the antenna array as
A = [1                                         exp(-
j*k*d*sin(theta)*cos(phi)
       exp(-j*k*d*sin(theta)*sin(phi)   exp(-j*k*d*(sin(theta)*cos(phi)
+sin(theta)*sin(phi) ]
I then found the power at each value of theta and phi (the elevation
and azimuth angles being sweeped from 0 to 30 degrees) and then the
value of theta and phi which has the maximum power was to have been
the desired DOA.I generated a test input signal in the same form as
the steering vector (transposed) to test the algorithm and put in some
value of theta and phi. The problem was that I could get the correct
value of theta when I ran the program, but not for phi. I have no idea
what is wrong with the program. Could someone guide me as to where I
am going wrong in the formulas or in the code?

Thanks, Farah.

Here is my MATLAB code:

c = 3e8; % speed of light in m/s
f = 3.432e9; % carrier signal frequency
lambda = c/f; % lambda = c/f
d = lambda/2; %distance between array elements
k = (2*pi)/lambda; % delay between each element signal
theta_range=30;
phi_range=30;

%% Generate Input Signal
angle_t=10; angle_p=20;
input = [1; exp( -( j*k*d*sin(pi*angle_t/180)*sin(pi*angle_p/
180)) ); ...
    exp( -( j*k*d*sin(pi*angle_t/180)*cos(pi*angle_p/180)) );...
    exp( -( j*k*d*( sin(pi*angle_t/180)*cos(pi*angle_p/180)+
sin(pi*angle_t/180)*sin(pi*angle_p/180)) ))];
R=input*ctranspose(input)/length(input);

%% Compute steering vector by sweeping theta and phi angles
index_row=1;
% calculate 'a' for each value of theta and phi
for theta=1:theta_range % sweep elevation angle from 0 to 180 degrees
    for phi = 1:phi_range % sweep azimuth angle from 0 to 180 degrees
        A(index_row,:)= [1,exp( -( j*k*d*sin(pi*theta/180)*cos(pi*phi/
180)) ),exp( -( j*k*d*sin(pi*theta/180)*sin(pi*phi/180)) ),exp( -
( j*k*d*( sin(pi*theta/180)*cos(pi*phi/180)+ sin(pi*theta/
180)*sin(pi*phi/180)) ))];
        index_row=index_row+1;
        steering_vector(:,:)=[A(theta*phi,1);A(theta*phi,
3);A(theta*phi,2);A(theta*phi,4)];
        temp1=(ctranspose(steering_vector)*R*steering_vector);
        temp2=(ctranspose(steering_vector)*steering_vector);
        temp=temp1/temp2;
        power(theta,phi)=temp;
    end
end