% Pisarenko (PHD) AOA estimation for a M = 6 element array with noise variance = .1


M=6;
sig2=.1;
th1=-5*pi/180;
th2=5*pi/180;
a1=[1];
a2=[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 .1;.1 1];

Rrr=A*Rss*A'+sig2*eye(M);

 [V,Dia]=eig(Rrr);
[Y,Index]=sort(diag(Dia));   % sorts the eigenvalues from least to greatest
 e1=V(:,Index(1));      % calculate the first noise eigenvector
                           

for k=1:360;
   th(k)=-pi/6+pi*k/(3*360);
clear a
   a=[1];
   for jj=2:M
      a = [a exp(-1j*jj*pi*sin(th(k)))];
   end
  P(k)=1./abs(conj(a)*e1).^2; 
end
figure;
plot(th*180/pi,10*log10(P/max(P)),'k')
grid on
xlabel('Angle')
ylabel('|P(\theta)|')
axis([-30 30 -30 10])

%num2str(A,2)