sa_ex8_2.m

Smart antennas for wireless communication - With MATLAB (Gross F.B. - 2005 - McGraw-Hill)

%Maximum SIR beamforming
% example 8.2
d=.5;
N=3;
sig2=.001;        % noise variance
theta=-pi/2:.01:pi/2;
ang=theta*180/pi;
th0=pi/6;      % receive angle
th1=-pi/6;          % first interferer angle
th2=pi/4;           % second interferer angle

s=1;                %signal amplitude
n=1:N;
a=exp(1j*2*pi*(n-2)*d*sin(th0)).';      % received angle steering vector
Rss=a*a';
 
n1=exp(1j*2*pi*(n-2)*d*sin(th1)).';      % interferer 1 steering vector
n2=exp(1j*2*pi*(n-2)*d*sin(th2)).';     % interferer 2 steering vector

A=[n1 n2];
Rnn=sig2*eye(N);        % noise correlation matrix       
Rii=A*A';               % interferer correlation matrix
Ruu=Rii+Rnn;           % total undesired signal correlation matrix
R=inv(Ruu)*Rss;
[Ev,v]=eig(R);          % calculate eigenvalues and eigenvectors
[Y,Index]=sort(diag(v));   % sorts the eigenvalues from least to greatest
SIRmax=max(Y);             % find maximum SIR
w=inv(Ruu)*a/SIRmax;        % normalize weight vector   or we can find w by
%w=Ev(:,Index(N));
for j=1:length(theta)
    th=theta(j);
    aa=exp(1j*2*pi*(n-2)*d*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)|')