% Min-Norm AOA estimation for a M = 6 element array with noise variance = .1

figure;
M=6;
D = 2;  % number of signals
sig2=.1;
th1=-5*pi/180;
th2=5*pi/180;

a1=[1];
a2=[1];
temp=eye(M);
u1=temp(:,1);
for i=2:M
    a1=[a1 exp(-1j*i*pi*sin(th1))];
    a2=[a2 exp(-1j*i*pi*sin(th2))];
end
A=[a1.' a2.'];
Rss=[1 0;0 1];      % source correlation matrix with uncorrelated signals
Rrr=A*Rss*A'+sig2*eye(M);

[V,D]=eig(Rrr);
[Y,Index]=sort(diag(D));   % sorts the eigenvalues from least to greatest
 EN=V(:,Index(1:4));      % calculate the noise subspace matrix of eigenvectors
                           % using the sorting done in the previous line
for k=1:180;
   th(k)=-pi/6+pi*k/(3*180);
   clear a
a=[1];
   for jj=2:M
      a = [a exp(-1j*jj*pi*sin(th(k)))];
   end
a=a.';  
P(k)=1/abs(a.'*EN*EN'*u1); 
end

plot(th*180/pi,10*log10(P/max(P)),'k')
grid on
xlabel('Angle')
ylabel('|P(\theta)|')
axis([-30 30 -30 10])