%Smart Antennas  example 8.8
% Use SMI and RLS to find the correlation matrix estimate for block length K

alpha=1;
d=.5;
N=4;
K=200;
th0=45*pi/180;
n=1:N;
a0=exp(1j*(n-1)*2*pi*d*sin(th0));
S=cos(2*pi*(0:K-1)/(K-1));
vS=a0.'*S(1:K);

Rxx2=vS*vS'/K   %SMI correlation matrix for block length K

vs=a0.'*S(1);
Rxx=vs*vs';     % first correlation matrix for RLS
Rxxtr=real(trace(Rxx2))*ones(1,K);      % calculate trace
Rtrace(1)=real(trace(vs*vs'));
for k=2:K
   vs=a0.'*S(k);
   Rxx=alpha*(k-1)*Rxx/k+vs*vs'/k;
   Rtrace(k)=real(trace(Rxx));
end
figure;plot(1:K,Rtrace,'k',1:K,Rxxtr,'k--')
xlabel('Iteration no.')
ylabel('trace(R_x_x)')
axis([1 200 0 4])
legend('RLS','SMI for block K')