optimization problem for exponential coefficients

Hello , i have the attached code which produces certain radiation pattern shown below.

basicly in matlab view its AF,theta plot.

In in code the coeeficients of real_voltage phases are known, however i want to create a code which given AF,theta it whould return me the best optimized real_voltage phases coefficients.

Thanks.

theta=linspace(-pi/2,pi/2,1000);
f=5.6;
N=6;
lambda=300/f;
d=0.8*lambda;
theta_0=pi*((0)/180);
amplitude_norm_V=[0.05,0.3,0.75,1,0.75,0.3,0.05];
k=(2*pi)/lambda;
delta=k*d*cos(theta_0);
x=sqrt(1/(sum(amplitude_norm_V.^2)));
real_voltage=amplitude_norm_V.*x;
real_power=(real_voltage.^2);
sum(real_power);
phases=[0,0,0,0,0,0,0];
total=0;
tot=0;
for z=1:6
    AF=real_voltage(z)*exp(1i*(phases(z)/180*pi))*exp(-1i*(z-1)*k*d*cos(theta)+1i*(z-1)*delta);
    total=total+AF;
end
plot((theta/pi)*180,20*log10(total)), grid on

Warning: Imaginary parts of complex X and/or Y arguments ignored.

[Catalytic]

What??

Answer 1

[Morgan]

This sounds like a non-linear regression problem if I'm understanding your question correctly.

The function you're fitting to looks like:

Use fitnlm() and how to use fitnlm() to solve for the best fit coefficients in your case.

[fima v]

Hello Morgan, how do I use my exponential expression with fitnml? Could you please elaborate. Thanks .

[Morgan]

% NUMBER OF FIT PARAMETERS
N = 6;

% THETA ARRAY
theta = linspace(-pi/2,+pi/2,1000);

% V DATA
V = ... % Your data for V that has length of N

% AF DATA
AF = ... % Your data for AF the same size as theta

% COEFFICIENT GUESS
beta0 = zeros(1,N);

% SOLVE NONLINEAR REGRESSION MODEL
mdl = fitnlm(theta,AF,@(b,theta) modelfun(b,theta,V),beta0)

% FUNCTION MODEL
function y = modelfun(b,theta,V)
    y = 0;
    for n = 1 : length(V)
        y = y + V(n)*exp(1i*b(n))*exp(1i*(n-1)*(delta - k*d*cos(theta)));
    end
end

[fima v]

Hello, what is my expression has not jus V but also phases.How does the code will change then?

Thanks.