Array-PSO-main.zip

close all set(groot, 'DefaultAxesTickLabelInterpreter', 'latex') %% c = physconst('LightSpeed'); Nx = 5; %# of elements in x-direction Ny = 5; %# of elements in y-direction I = ones(Ny,Nx); % Matri of element excitation amplitudes Ai = ones(Ny,Nx); %Feeding Coefficient % Constants associated with material Dk = 1; %substrate relative permittivity/dielectric constant freq0 = 27e9; %Operating frequency of 28 GHz lambda = c/freq0/sqrt(Dk); k = 2*pi/lambda; %phase constant % Angle domain; covers top hemisphere theta = linspace(0,pi/2,500); phi = linspace(0,2*pi,500); [Theta, Phi] = meshgrid(theta, phi); % spacing matrices % Dx: size = [Nx Ny]; The value in the ith row, jth column % is the distance in x from the y-axis of the element % in the corresponding row & column % Dy: size = [Nx Ny]; The value in the ith row, jth column % is the distance in y from the x-axis of the element % in the corresponding row & column d = 1/2*lambda; %uniform element spacing in meters D = (0:1:Nx-1)*d; %array of element positions [Dx, Dy] = meshgrid(D); % scanning angle scan_theta_deg = 20; scan_phi_deg = 0; scan_theta = deg2rad(scan_theta_deg); %scan angle of phased array scan_phi = deg2rad(scan_phi_deg); %scan angle of phased array %Cartesian axes x_cart = sin(Theta).*cos(Phi); y_cart = sin(Theta).*sin(Phi); % Per elment scanning angle phase shifts Beta_x = -k*Dx*sin(scan_theta)*cos(scan_phi); Beta_y = -k*Dy*sin(scan_theta)*sin(scan_phi); Beta = Beta_x + Beta_y; %smallest dB value shown on rad patter; used to remove extreme nulls from data rlim_low_db = -40; % name of svg svg_cart_name = sprintf("Figs/%dx%d_%.2f_theta%.1f_phi%.1f.svg",Nx,Ny, d/lambda, rad2deg(scan_theta), rad2deg(scan_phi)); svg_sph_name = sprintf("Figs/sph%dx%d_%.2f_theta%.1f_phi%.1f.svg",Nx,Ny, d/lambda, rad2deg(scan_theta), rad2deg(scan_phi)); %% Calculate AF AF = zeros(size(x_cart)); % iterate over each of the Nx*Ny elements, calculating % and adding the 2D array factor contributions for i = 1:Nx % iterate in x-direction (i.e. cols or dim 2) for j = 1:Ny %iterate in y-direction (i.e. rows or dim 1) dx = Dx(j,i); % x location of current antenna element dy = Dy(j,i); % y location of current antenna element a = Ai(j,i); % feed amplitude of current antenna element beta = Beta(j,i); % total phase of current antenna element AF = AF + a*exp(1i*(k*(dx*x_cart + dy*y_cart) + beta)); end end AF_max = max(AF,[],'all'); AF_norm = AF./AF_max; AF2 = abs(AF).^2; [AF2_max] = max(AF2,[],'all'); AF2_norm = AF2./AF2_max; %% Peak Detection input = abs(AF_norm); % select which array factor form to process % obtaining all peaks and their indices TF = imregionalmax(input); TF_1 = islocalmax(input,1); % local maxima along dimension 1 TF_2 = islocalmax(input,2); % local maxima along dimension 2 TF_intersect = TF_1 & TF_2; % Maxima that exist in both dimensions % vector subset of just the detected local maxima amplitudes and their % linear indices relative to input mag_local_maxima = input(TF_intersect); idx_local_maxima = find(TF_intersect); % searches subset of local maxima for the global maxima and its linear % index RELATIVE TO SUBSET. Use this to index idx_local_maxima to obtain % the linear index of the global max relative to input [glob_max, tempidx_glob_max] = max(mag_local_maxima); idx_glob_max = idx_local_maxima(tempidx_glob_max); % Remove global max index from idx_local_maxima. % Largest of remaining peaks is SLL. idx_side_maxima = idx_local_maxima(idx_local_maxima ~= idx_glob_max); [SLL, tempidx_SLL] = max(input(idx_side_maxima)); idx_SLL = idx_local_maxima(tempidx_SLL); %% Plots against angle in rectangular figure(); patternCustom(input, rad2deg(theta), rad2deg(phi), 'CoordinateSystem', 'rectangular') % s0 = surf(Theta, Phi, input); % s0.EdgeColor = 'none'; xlabel('Theta', 'Interpreter', 'latex') ylabel('Phi', 'Interpreter', 'latex') hold on % plot points at all detected maxima plot3(rad2deg(Theta(TF_1)),... rad2deg(Phi(TF_1)),... input(TF_1), 'y.', 'MarkerSize', 15); % plot points at all detected maxima plot3(rad2deg(Theta(TF_2)),... rad2deg(Phi(TF_2)),... input(TF_2), 'y.', 'MarkerSize', 15); % plot points at all detected maxima plot3(rad2deg(Theta(TF_intersect)),... rad2deg(Phi(TF_intersect)),... input(TF_intersect), 'y.', 'MarkerSize', 15); % points at the global max plot3(rad2deg(Theta(idx_glob_max)),... rad2deg(Phi(idx_glob_max)),... input(idx_glob_max), 'g.','MarkerSize', 20); % points at detected SLL plot3(rad2deg(Theta(idx_SLL)),... rad2deg(Phi(idx_SLL)),... input(idx_SLL), 'rd','MarkerSize', 25); hold off %% Figure plots spatially wihtin unit circle figure() z_cart = input; s1 = surf(x_cart, y_cart,z_cart); s1.EdgeColor = 'none'; xlabel("X"); ylabel("Y"); hold on % local maxima in dimension 1 plot3(x_cart(TF_1),... y_cart(TF_1),... z_cart(TF_1), 'k.', 'MarkerSize', 15); % local maxima in dimension 2 plot3(x_cart(TF_2),... y_cart(TF_2),... z_cart(TF_2), 'b.', 'MarkerSize', 15); % points at intersection plot3(x_cart(TF_intersect),... y_cart(TF_intersect),... z_cart(TF_intersect), 'r.', 'MarkerSize', 50); % points at the global max plot3(x_cart(idx_glob_max),... y_cart(idx_glob_max),... z_cart(idx_glob_max), 'g.','MarkerSize', 20); % points at detected SLL plot3(x_cart(idx_SLL),... y_cart(idx_SLL),... z_cart(idx_SLL), 'rd','MarkerSize', 15); % plot3(x_cart(TF_intersect), y_cart(TF_intersect), z_cart(TF_intersect), 'r.','MarkerSize', 25); hold off %% Plots in cylindrical coordinates % Radius maps to elevation scanning angle % Azimuthal angle maps to aimuthal scanning angle % Height (z) maps to abs(AF) x_cyl = cos(Phi).*Theta; y_cyl = sin(Phi).*Theta; z_cyl = input; cyl_ax_limits = [-1*pi/2 1*pi/2]; figure() % Figure 2 s2 = surf(x_cyl, y_cyl,z_cyl); s2.EdgeColor = 'none'; xlim(cyl_ax_limits) ylim(cyl_ax_limits) xlabel('Phi=0 Plane', 'Interpreter', 'latex') ylabel('Phi=$\pi/2$ Plane', 'Interpreter', 'latex') %% Converting to Spherical % sph_ax_lims = [-1 1]; % [x, y, z] = sph2cart(Phi,Theta,input); % figure() % Figure 3 % s3 = surf(x,y,z); % xlim(sph_ax_lims) % ylim(sph_ax_lims) % % zlim([0 1]) % s3.EdgeColor = 'none'; figure3 = figure(); title("|AF|^2") patternCustom(input, rad2deg(theta), rad2deg(phi), 'CoordinateSystem', 'polar'); % adding textbox w/ user parameters annotation(figure3,'textbox',... [0.0350629342862732 0.1013015873015876 0.151785714285714 0.137301587301593],... 'String',{array_str, lambda_str, theta_str, phi_str},... 'FontSize',10,... 'FitBoxToText','off',... 'EdgeColor','none'); %saveas(figure3, svg_sph_name);