%Minimum MSE beamforming
% Example 8.3
d=.5;
N=5;
sig2=.001;        % noise variance
theta=-pi/2:.01:pi/2;
ang=theta*180/pi;
th0=20*pi/180;      % receive angle
th1=-20*pi/180;          % first interferer angle
th2=40*pi/180;           % second interferer angle
n=1:N;
s=1;                %signal amplitude
  
a=exp(1j*2*pi*d*(n-3)*sin(th0)).';   % received angle steering vector
Rss=a*a';
n1=exp(1j*2*pi*d*(n-3)*sin(th1)).';     % interferer 1 steering vector
n2=exp(1j*2*pi*d*(n-3)*sin(th2)).';      % interferer 2 steering vector
R11=n1*n1';
R22=n2*n2';
A=[n1 n2];
Rnn=sig2*eye(N);        % noise correlation matrix       
Rii=A*A';               % interferer correlation matrix
%Rii=R11+R22;
Ruu=Rii+Rnn; % total undesired signal correlation matrix
Rxx=Ruu+Rss;

w=inv(Rxx)*a;        % normalize weight vector
for j=1:length(theta)
    th=theta(j);
    aa=exp(1j*2*pi*d*(n-3)*sin(th)).';
    y(j)=w'*aa;
end
figure;
plot(ang,abs(y)/max(abs(y)),'k')
axis([-90 90 0 1])
xlabel('\theta')
ylabel('|AF(\theta)|')

figure;
polarpattern(theta,log10(abs(y)/max(abs(y))))