optimization problem for exponential coefficients

Question

fima v 2024-3-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2098286-optimization-problem-for-exponential-coefficients

评论： fima v 2024-3-29

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.

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Catalytic 2024-3-25

What??

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Answer 1

Morgan 2024-3-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2098286-optimization-problem-for-exponential-coefficients#answer_1430801

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.

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Morgan 2024-3-26

编辑：Morgan 2024-3-26

在 MATLAB Online 中打开

% 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