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%% LMS Algorithm example 8.6 %%
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%----- Givens -----%

d = .5;  % element spacing in terms of wavelength d = lambda/2
%N = input('   How many element do you want in uniform linear array?   ');   % number of elements in array
N=5;
thetaS = input('   What is the desired users AOA (in degrees)?   ');
thetaI = input('   What is the interferers AOA(in degrees)?   ');
%----- Desired Signal & Interferer -----%
T=1E-3;
t=(1:100)*T/100;
it=1:100;
S=cos(2*pi*t/T);
thetaS = thetaS*pi/180;                  % desired user AOA
I = randn(1,100);  
thetaI = thetaI*pi/180;                    % interferer AOA
  
%----- Create Array Factors for each user's signal for linear array -----%

vS = []; vI = [];
i=1:N;
vS=exp(1j*(i-1)*2*pi*d*sin(thetaS)).';
vI=exp(1j*(i-1)*2*pi*d*sin(thetaI)).';

%----- Solve for Weights using LMS -----%

w = zeros(N,1);     snr = 10;  % signal to noise ratio
 X=(vS+vI);
Rx=X*X';
mu=1/(4*real(trace(Rx)))
%mu = input('What is step size?')
wi=zeros(N,max(it));
for n = 1:length(S)
    x = S(n)*vS + I(n)*vI;
    %y = w*x.';
    y=w'*x;
    
    e = conj(S(n)) - y;      esave(n) = abs(e)^2;
%    w = w +mu*e*conj(x);
    w=w+mu*conj(e)*x;
    wi(:,n)=w;
    yy(n)=y;
end
w = (w./w(1));    % normalize results to first weight

%----- Plot Results -----%

theta = -pi/2:.01:pi/2;
AF = zeros(1,length(theta));

% Determine the array factor for linear array

for i = 1:N
    AF = AF + w(i)'.*exp(1j*(i-1)*2*pi*d*sin(theta));
end

figure
plot(theta*180/pi,abs(AF)/max(abs(AF)),'k')
xlabel('AOA (deg)')
ylabel('|AF_n|')
axis([-90 90 0 1.1])
set(gca,'xtick',[-90 -60 -30 0 30 60 90])
grid on

figure;
plot(it,S,'k',it,yy,'k--')
xlabel('No. of Iterations')
ylabel('Signals')
legend('Desired signal','Array output')

disp('%------------------------------------------------------------------------%')
disp(' ')
disp(['   The weights for the N = ',num2str(N),' ULA are:'])
disp(' ')
for m = 1:length(w)
    disp(['   w',num2str(m),' = ',num2str(w(m))])
end
disp(' ')

figure;plot(it,abs(wi(1,:)),'kx',it,abs(wi(2,:)),'ko',it,abs(wi(3,:)),'ks',it,abs(wi(4,:)),'k+',it,abs(wi(5,:)),'kd','markersize',2)
xlabel('Iteration no.')
ylabel('|weights|')
figure;plot(it,esave,'k')
xlabel('Iteration no.')
ylabel('Mean square error')