├── End-to-end_channel_generator ├── Coupling_Dipoles.m ├── DMA_admittance.m ├── GenChannel.m ├── Topologies_DMA.m └── main.m ├── Figures_from_paper ├── DMAmodelPaperPlots.m └── simulationData │ ├── TangentialFieldsFinal.txt │ ├── farfieldPattern.txt │ └── farfieldPatternRotated.txt └── LICENSE /End-to-end_channel_generator/Coupling_Dipoles.m: -------------------------------------------------------------------------------- 1 | function [Y_rr] = Coupling_Dipoles(f, l, xyz_user, mu, epsilon) 2 | 3 | %% Physical constants - Dont edit 4 | k = 2*pi*f*sqrt(epsilon*mu); 5 | 6 | %% Y_rr calculation 7 | Ga_e2 = @(r,rhat) ((norm(r-rhat)^2 - (r(3)-rhat(3))^2)/norm(r-rhat)^2 - ... 8 | 1i*(norm(r-rhat)^2 - 3*(r(3)-rhat(3))^2)/(norm(r-rhat)^3*k)... 9 | - (norm(r-rhat)^2 - 3*(r(3)-rhat(3))^2)/(norm(r-rhat)^4*k^2))... 10 | *exp(-1i*k*norm(r-rhat))/(4*pi*norm(r-rhat)); 11 | 12 | Y_rr = zeros(size(xyz_user,1),size(xyz_user,1)); 13 | 14 | for row = 1:size(xyz_user,1) 15 | for col = 1:size(xyz_user,1) 16 | % If diagonal element -> self-admittance 17 | if(row == col) 18 | Y_rr(row,col) = l^2*k*2*pi*f*epsilon/(6*pi); 19 | else 20 | Y_rr(row,col) = l^2*1i*2*pi*f*epsilon*... 21 | Ga_e2(xyz_user(row,:),xyz_user(col,:)); 22 | end 23 | end 24 | end 25 | 26 | end 27 | 28 | -------------------------------------------------------------------------------- /End-to-end_channel_generator/DMA_admittance.m: -------------------------------------------------------------------------------- 1 | function [Y_tt, Y_st, Y_ss] =... 2 | DMA_admittance(f, a, b, l, S_mu, xyz_dma, xyz_rf, mu, epsilon) 3 | % Computes the mutual admittances in the DMA topology where all actors are 4 | % modelled as magnetic dipoles 5 | 6 | 7 | %% Physical constants 8 | k = 2*pi*f*sqrt(epsilon*mu); 9 | 10 | kx = sqrt(k^2 - (pi/a)^2); % only for TE_10 11 | 12 | %% Y_tt calculation 13 | % Position of RF chain in the width of the waveguide (0 <= z_rf <= a) 14 | z_rf = a/2; 15 | 16 | y_tt = -l^2 * 2i*kx*sin(pi/a*z_rf)^2*cos(kx*S_mu) / (a*b*2*pi*f*mu*sin(kx*S_mu)); 17 | 18 | Y_tt = diag(y_tt * ones(size(xyz_rf,1),1)); 19 | 20 | %% Y_st calculation 21 | Y_st = zeros(size(xyz_dma,1),size(xyz_rf,1)); 22 | 23 | % r, rhat are vectors such that 0 <= x, xhat <= S_mu 24 | % 0 <= y, yhat <= b 25 | % 0 <= z, zhat <= a 26 | Gw_e2 = @(r,rhat) -kx*sin(pi/a*rhat(3))*sin(pi/a*r(3))*... 27 | (cos(kx*(rhat(1) + r(1)-S_mu)) + ... 28 | cos(kx*(S_mu-abs(rhat(1) - r(1))))) / (a*b*k^2*sin(kx*S_mu)); 29 | 30 | % We compute the normalized x coordinate of the antennas wrt their RF chain 31 | N_ant_wg = size(xyz_dma,1)/size(xyz_rf,1); 32 | temp = zeros(size(xyz_dma,1),1); 33 | temp(1:N_ant_wg:end) = xyz_rf(:,1); 34 | x_ant_norm = xyz_dma(:,1) - ... 35 | filter(ones(N_ant_wg,1), 1, temp); 36 | 37 | % We assume all the waveguides are equal, i.e., same position for the 38 | % elements and RF chain, so that Y_st is a block matrix with same elements 39 | % within each block 40 | for row = 1:N_ant_wg 41 | y_val = l^2 * 1i*2*pi*f*epsilon*Gw_e2([x_ant_norm(row), 0, z_rf], [0, 0, z_rf]); 42 | for k_rf = 1:size(xyz_rf,1) 43 | Y_st(row + (k_rf-1)*N_ant_wg,k_rf) = y_val; 44 | end 45 | end 46 | 47 | %% Y_ss calculation 48 | Ga_e2 = @(r,rhat) ((norm(r-rhat)^2 - (r(3)-rhat(3))^2)/norm(r-rhat)^2 - ... 49 | 1i*(norm(r-rhat)^2 - 3*(r(3)-rhat(3))^2)/(norm(r-rhat)^3*k)... 50 | - (norm(r-rhat)^2 - 3*(r(3)-rhat(3))^2)/(norm(r-rhat)^4*k^2))... 51 | *exp(-1i*k*norm(r-rhat))/(4*pi*norm(r-rhat)); 52 | 53 | Y_ss = zeros(size(xyz_dma,1),size(xyz_dma,1)); 54 | 55 | for row = 1:size(xyz_dma,1) 56 | for col = 1:size(xyz_dma,1) 57 | % If diagonal element -> self-admittance 58 | if(row == col) 59 | Y_ss(row,col) = l^2 * k*2*pi*f*epsilon/(3*pi) + ... 60 | 1i*2*pi*f*epsilon*Gw_e2([xyz_dma(row,1), 0, z_rf], [xyz_dma(col,1), 0, z_rf]); 61 | 62 | % If different waveguide 63 | elseif (abs(xyz_dma(row,1) - xyz_dma(col,1))>= S_mu || ... 64 | abs(xyz_dma(row,3) - xyz_dma(col,3))>= b/2) 65 | 66 | Y_ss(row,col) = l^2 * 1i*2*pi*f*epsilon*... 67 | 2*Ga_e2(xyz_dma(row,:),xyz_dma(col,:)); 68 | 69 | else 70 | Y_ss(row,col) = l^2 * 1i*2*pi*f*epsilon*... 71 | (2*Ga_e2(xyz_dma(row,:),xyz_dma(col,:)) + ... 72 | Gw_e2([xyz_dma(row,1), 0, z_rf], [xyz_dma(col,1), 0, z_rf])); 73 | end 74 | end 75 | end 76 | 77 | end -------------------------------------------------------------------------------- /End-to-end_channel_generator/GenChannel.m: -------------------------------------------------------------------------------- 1 | function [Y_rs] = GenChannel(channel_type, lambda, ant_xyz, user_xyz) 2 | 3 | L = size(ant_xyz,1); % Number of DMA elements 4 | M = size(user_xyz,1); % Number of users 5 | 6 | k = 2*pi/lambda; 7 | 8 | % Rayleigh fading 9 | if channel_type 10 | 11 | % Distances between users and DMA elements 12 | D = zeros(M,L); 13 | for idn = 1:L 14 | for idm = 1:M 15 | D(idm,idn) = norm(ant_xyz(idn,:) - user_xyz(idm,:),2); 16 | end 17 | end 18 | % Pathloss 19 | PL = (lambda ./ (4*pi*D)).^2; 20 | 21 | % Uncorrelated Complex Gaussian realizations 22 | Yrs_uncorr = (randn(M, L) + 1i * randn(M, L)) .* sqrt(PL/2); 23 | 24 | % Compute correlation coefficient. 25 | dZ = squareform(pdist(ant_xyz(:,3))); 26 | dR = squareform(pdist(ant_xyz)); 27 | Sigma = 3./2.*((1 + (-k.^2.*dZ.^2 - 1)./(dR.^2.*k.^2) + ... 28 | 3.*dZ.^2./(dR.^4.*k.^2)).*sin(k.*dR)./(k.*dR) +... 29 | cos(k.*dR).*(1./(k.*dR) - 3.*dZ.^2./(dR.^3.*k))./(k.*dR)); 30 | 31 | Sigma(isnan(Sigma)) = 1; 32 | sq_Sigma = real(Sigma^(1/2)); % Real operator due to imaginary part 33 | % being a product of quantization 34 | 35 | Y_rs = Yrs_uncorr * sq_Sigma; 36 | 37 | % LoS channel 38 | else 39 | 40 | % Distances between users and DMA elements 41 | D = zeros(M, L); 42 | dz = zeros(M, L); 43 | for idn = 1:L 44 | for idm = 1:M 45 | D(idm,idn) = norm(ant_xyz(idn,:) - user_xyz(idm,:),2); 46 | dz(idm,idn) = abs(ant_xyz(idn,3) - ant_xyz(idm,3)); 47 | end 48 | end 49 | % Polar angle 50 | theta = pi/2 - asin(dz./D); 51 | 52 | % Pathloss 53 | PL = (lambda ./ (4*pi*D)).^2.* (3/2 * sin(theta).^2) .* ... 54 | (6/2 * sin(theta).^2); 55 | Y_rs = sqrt(PL) .* exp(-1i*k*D); 56 | 57 | end 58 | 59 | end 60 | 61 | -------------------------------------------------------------------------------- /End-to-end_channel_generator/Topologies_DMA.m: -------------------------------------------------------------------------------- 1 | function [ant_xyz, rf_xyz] = Topologies_DMA(site_xyz,... 2 | N, Lmu, wvg_spacing, elem_spacing, S_mu, a, b, Plot_topology) 3 | 4 | % Total number of antennas 5 | L = Lmu*N; 6 | 7 | % Pre-allocating 8 | ant_xyz = zeros(L*size(site_xyz,1),3); 9 | rf_xyz = zeros(N*size(site_xyz,1),3); 10 | 11 | % The sites are generated according to a local coordinate system, and 12 | % then shifted according to site_xyz 13 | for ksite = 1:size(site_xyz,1) 14 | % Coordinates of RF chains 15 | z_rf = (0:N-1)*wvg_spacing + a/2; 16 | y_rf = b/2; 17 | x_rf = 0; 18 | 19 | % Coordinates of DMA elements 20 | z_dma = z_rf; 21 | y_dma = b; 22 | x_dma = (1:Lmu) * elem_spacing; 23 | x_dma = x_dma - mean(x_dma) + S_mu/2; 24 | 25 | % Store coordinates for antennas in site ksite 26 | [Xant,Yant,Zant] = ndgrid(x_dma+site_xyz(ksite,1),... 27 | y_dma+site_xyz(ksite,2),... 28 | z_dma+site_xyz(ksite,3)); 29 | 30 | ant_xyz((L*(ksite-1))+1:(L*ksite),:) = ... 31 | [Xant(:), Yant(:), Zant(:)]; 32 | 33 | % Store coordinates for RF chains in site ksite 34 | [Xrf,Yrf,Zrf] = ndgrid(x_rf+site_xyz(ksite,1),... 35 | y_rf+site_xyz(ksite,2),... 36 | z_rf+site_xyz(ksite,3)); 37 | rf_xyz((N*(ksite-1))+1:(N*ksite),:) = ... 38 | [Xrf(:), Yrf(:), Zrf(:)]; 39 | 40 | end 41 | 42 | %----------------------------------------------------------------- 43 | % Plotting deployment 44 | %----------------------------------------------------------------- 45 | if (~Plot_topology) 46 | return 47 | end 48 | 49 | figure(); hold on; grid on; 50 | xlabel('x'); ylabel('y'); zlabel('z'); 51 | antplt = scatter3(ant_xyz(:,1),ant_xyz(:,2),ant_xyz(:,3)); 52 | rfplt = scatter3(rf_xyz(:,1),rf_xyz(:,2),rf_xyz(:,3)); 53 | 54 | % Loop to plot the waveguides 55 | xtot = zeros(4*N,4); 56 | ytot = zeros(0,4); 57 | ztot = zeros(0,4); 58 | xyz_aux = rf_xyz; 59 | 60 | for idn = 1:N 61 | zt = [0, a, a, 0; ... 62 | 0, a, a, 0; ... 63 | 0, 0, 0, 0; ... 64 | a, a, a ,a] + (xyz_aux(2,3)-xyz_aux(1,3))*(idn-1); 65 | yt = [0, 0, 0, 0; ... 66 | b, b, b, b; ... 67 | 0, b, b, 0; ... 68 | 0, b, b, 0]; 69 | xt = [0, 0, S_mu, S_mu; ... 70 | 0, 0, S_mu, S_mu;... 71 | 0, 0, S_mu, S_mu;... 72 | 0, 0, S_mu, S_mu] + (xyz_aux(2,1)-xyz_aux(1,1))*(idn-1); 73 | 74 | xtot(4*(idn-1)+1 : 4*idn, :) = xt + site_xyz(1,1); 75 | ytot(4*(idn-1)+1 : 4*idn, :) = yt + site_xyz(1,2); 76 | ztot(4*(idn-1)+1 : 4*idn, :) = zt + site_xyz(1,3); 77 | 78 | end 79 | h1 = patch('XData',xtot','YData',ytot','ZData',ztot'); 80 | h1.FaceAlpha = 0.2; 81 | 82 | axis([0 2*S_mu 0 0.2 site_xyz(1,3) site_xyz(1,3)+(N+1)*wvg_spacing]) 83 | legend([antplt, rfplt, h1],{'DMA elements', 'RF chains', 'Waveguides'}) 84 | title('Deployment DMA') 85 | view([135,37]); 86 | end -------------------------------------------------------------------------------- /End-to-end_channel_generator/main.m: -------------------------------------------------------------------------------- 1 | %% Parameters 2 | f = 10e9; % Frequency of operation 3 | c = 299792458; % Light speed in vacuum 4 | mu = 4*pi*1E-7; % Vacuum permeability 5 | epsilon = 1/ (c^2 * mu); % Vacuum permittivity 6 | lambda = c/f; % Wavelength 7 | k = 2*pi/lambda; % Wavenumber 8 | a = 0.73*lambda; % Width of waveguides (only TE_10 mode) 9 | b = 0.17*lambda; % Height of waveguides (only TE_10 mode) 10 | channel_type = 1; % Type of channel: 11 | % 0 -> LoS 12 | % 1 -> Rayleigh 13 | N = 4; % Number of RF chains / waveguides 14 | Lmu = 8; % Number of elements per waveguide 15 | wvg_spacing = lambda; % Spacing between waveguides 16 | elem_spacing = lambda/2; % Spacing between the elements 17 | l = 1; % Length of dipoles -> just normalization 18 | M = 3; % Number of static users 19 | Plot_topology = 1; % Boolean to plot the chosen setup 20 | 21 | Y_s = diag(1i*randn(N*Lmu,1)); % Load admittances of DMA element 22 | % Has to be a diagonal matrix of 23 | % N*Lmu x N*Lmu (total number of elements) 24 | 25 | Y_intrinsic_source = 35.3387; % Intrinsic impedance of source 26 | % matched to waveguide of width a = 27 | % 0.73*lambda and height b = 0.17*lambda 28 | 29 | 30 | %% DMA and users coordinates 31 | site_xyz = [0 0 10]; % [x y z] coordinates of bottom right 32 | % corner of DMA 33 | S_mu = (Lmu+1)*elem_spacing; % Length of waveguides 34 | 35 | % Coordinates of DMA elements and RF chains 36 | [ant_xyz, rf_xyz] = Topologies_DMA(site_xyz,N, Lmu, wvg_spacing,... 37 | elem_spacing, S_mu, a, b, Plot_topology); 38 | 39 | % Users positions (In this example, they are set randomly) 40 | x_lim = [-20 20]; 41 | y_lim = [20 60]; 42 | user_xyz = [x_lim(1)+(x_lim(2)-x_lim(1))*rand(M,1) ... 43 | y_lim(1)+(y_lim(2)-y_lim(1))*rand(M,1) 1.5*ones(M,1)]; 44 | 45 | %% Calculation of Admittances 46 | 47 | % Calculating Y_tt, Y_st and Y_ss according to Eqs. (35)-(42) 48 | [Y_tt, Y_st, Y_ss] = DMA_admittance(f, a, b, l, S_mu, ant_xyz, ... 49 | rf_xyz, mu, epsilon); 50 | 51 | % Calculating Y_rr according to Eqs. (44)-(46) 52 | Y_rr = Coupling_Dipoles(f, l, user_xyz, mu, epsilon); 53 | 54 | % Choosing Y_r (load admittance of users) as conjugate of self-admittance 55 | Y_r = Y_rr'.*eye(M); 56 | 57 | % Calculation of Y_rs (Wireless channel) 58 | Y_rs = GenChannel(channel_type, lambda, ant_xyz, user_xyz); 59 | 60 | %% Equivalent channel according to Eq. (60) 61 | Heq = eye(M)/(Y_r + Y_rr) * (Y_rs/(Y_s + Y_ss)*Y_st); 62 | 63 | %% Computing received, transmitted and supplied power: 64 | 65 | % Computing approximate reflection coefficient assuming no cross-waveguide 66 | % coupling 67 | Y_p = Y_tt - (Y_st.' / (Y_s + Y_ss)) * Y_st; 68 | Y_in = eye(N) .* Y_p; 69 | Gamma = (Y_in - eye(N)*Y_intrinsic_source) / (Y_in + eye(N)*Y_intrinsic_source); 70 | 71 | % Choosing random beam 72 | B = randn(N,M) + 1i*randn(N,M); 73 | 74 | % Computing received, transmit, and supplied power 75 | x = randn(M,1); 76 | y = Heq * B * x; 77 | 78 | P_r = 1/2 * real(Y_r) * abs(y).^2 79 | P_t = 1/2 * real(x' * B' * Y_p * B * x) 80 | P_s = 1/2 * real(x' * B' * ((eye(N) - Gamma' * Gamma) \ Y_p) * B * x) 81 | -------------------------------------------------------------------------------- /Figures_from_paper/DMAmodelPaperPlots.m: -------------------------------------------------------------------------------- 1 | %% Script to generate figures for the paper. 2 | % 3 | % NOTE here that the coordinate system is rotated 90 degrees in the 4 | % xz-plane to align with the CST simulation used for comparison. 5 | % 6 | % To clarify, the DMA is positioned in the xz-plane such that: 7 | % Waveguide width is along the x-coordinate 8 | % Waveguide height is along the y-coordinate 9 | % Waveguide length is along the z-coordinate 10 | 11 | plot_stuff = true; 12 | remove_spherical_guides = 1; 13 | remove_cartesian_guides = 0; 14 | 15 | addpath('simulationData'); 16 | setFigOptions; 17 | colours = [ 0 0 1.0000 ; 18 | 1.0000 0 0; 19 | 0 1.0000 0; 20 | 0 0 0.1724]; 21 | colourIndx = 0; 22 | lineSpec = {'--','-',':','-.'}; 23 | markerSpec = {'+','','o','*','x','s','d','^','v','>','<','p','h'}; 24 | right = 1; left = 0; 25 | 26 | linewidth = 262*0.03514; 27 | 28 | Y_intrinsic_source = 35.3387; 29 | 30 | orderM = 1; 31 | orderN = 0; 32 | 33 | 34 | %% Physical constants 35 | f = 10E9; 36 | mu = 1.25663706212*1E-6; 37 | eps = 8.8541878128*1E-12; 38 | lambda = 1/sqrt(mu*eps) / f; 39 | k = 2*pi*f*sqrt(eps*mu); 40 | omega = 2*pi*f; 41 | c = 1/sqrt(mu*eps); 42 | eta = sqrt(mu/eps); 43 | 44 | l_m = 1; % Magnetic length of dipoles. This is just a normalization constant. 45 | 46 | 47 | %% Grab constants and data from CST simulation 48 | CST_data = cst_data_reader('TangentialFieldsFinal.txt'); 49 | H_cst = CST_data(1).h_field_center_1_Re + 1i* CST_data(1).h_field_center_1_Im; 50 | H_cst_top = CST_data(3).h_field_top_1_Re + 1i* CST_data(3).h_field_top_1_Im; 51 | waveguide_length = CST_data(1).Par('l_wg') * 1E-3; 52 | waveguide_width = CST_data(1).Par('w_wg') * 1E-3; 53 | waveguide_height = CST_data(1).Par('h_wg') * 1E-3; 54 | waveguide_spacing = CST_data(1).Par('distance_wg') * lambda ; 55 | element_spacing = CST_data(1).Par('distance_slot') * lambda ; 56 | n_elem = 5; % Number of elements per waveguide. 57 | 58 | a = waveguide_width; 59 | b = waveguide_height; 60 | l = waveguide_length; 61 | 62 | nTx = 2; % number of waveguides 63 | sTx = waveguide_spacing; % spaceing of waveguides 64 | nDMA = n_elem; % per waveguide (does not have to be the same for all waveguides in general). 65 | sDMA = element_spacing; % DMA element spacing along waveguide 66 | 67 | %% Variables and functions 68 | syms x y z X Y Z ... % cartesian coordinates 69 | m n ... % Mode indexes 70 | delta_0 dirac ... % a dirac function 71 | 72 | assume(x,'real'); assume(y,'real'); assume(z,'real'); 73 | assume(X,'real'); assume(Y,'real'); assume(Z,'real'); 74 | assume(m,{'real','integer'}); assume(n,{'real','integer'}); 75 | 76 | omega=2*pi*f; 77 | 78 | % To insert values, use 'subs(fun, {var1, var2}, {val1, val2})' 79 | %global Rot rot 80 | r = [x;y;z]; 81 | ri = [-x;y;-z]; 82 | R = [X;Y;Z]; 83 | d = norm(r-R,2); 84 | lr = norm(r,2); 85 | rot = @(V) curl(V,r); 86 | Rot = @(V) curl(V,R); 87 | 88 | %% half-space propagation / image theory: 89 | G_air=symZeros(3,3); 90 | G_air(1,1) = 2*exp(-1i*k*sqrt(x^2 + y^2 + z^2))*((((y^2 + z^2)*(x^2 + y^2 + z^2)*k^2)/2 + x^2 - y^2/2 - z^2/2)*sqrt(x^2 + y^2 + z^2) + (x^2 + y^2 + z^2)*(x^2 - y^2/2 - z^2/2)*k*1i)/(2*(x^2 + y^2 + z^2)^3*k^2*pi); 91 | 92 | G_airFull=symZeros(3,3); 93 | G_airFull(1,1) = 2*exp(-1i*k*sqrt(x^2 + y^2 + z^2))*(((x^2 + y^2 + z^2)*(y^2 + z^2)*k^2)/2 + sqrt(x^2 + y^2 + z^2)*(2*x^2 - y^2 - z^2)*k*1i/2 - y^2/2 - z^2/2 + x^2)/(2*(x^2 + y^2 + z^2)^(5/2)*pi*k^2); 94 | G_airFull(2,1) = 2*3*(k*sqrt(x^2 + y^2 + z^2)*1i + 1 + (-x^2/3 - y^2/3 - z^2/3)*k^2)*exp(-1i*k*sqrt(x^2 + y^2 + z^2))*x*y/(4*(x^2 + y^2 + z^2)^(5/2)*pi*k^2); 95 | G_airFull(3,1) = 2*(3*exp(-1i*k*sqrt(x^2 + y^2 + z^2))*(k*sqrt(x^2 + y^2 + z^2)*1i + 1 + (-x^2/3 - y^2/3 - z^2/3)*k^2)*x*z)/(4*(x^2 + y^2 + z^2)^(5/2)*pi*k^2); 96 | 97 | H_air = matlabFunction(-1i*omega*eps*G_air*[l_m;0;0]); % Function of distance vector in (dx, dy, dz) 98 | H_airFull = matlabFunction(-1i*omega*eps*G_airFull*[l_m;0;0]); % Function of distance vector in (dx, dy, dz) 99 | 100 | Y_0 = 2*l_m^2*k*omega*eps/(6*pi); % Free space above ground real part self-impedance 101 | 102 | %% wavenumbers 103 | k_x = m * pi / a; k_y = n * pi / b; 104 | k_c = sqrt(k_x^2 + k_y^2); 105 | k_z = sqrt(k^2 - k_c^2); 106 | 107 | % If higher order modes are considered, we must remember to take negative 108 | % imaginary part. 109 | if (orderM > 1) || (orderN > 0) 110 | k_z = real(sqrt(k^2 - k_c^2)) - 1i*imag(sqrt(k^2 - k_c^2)); 111 | end 112 | 113 | x_hat = [1; 0; 0]; y_hat = [0; 1; 0]; z_hat = [0; 0; 1]; 114 | 115 | %% Cartesian vector wave functions 116 | 117 | psi_e = @(h) cos(m*pi*x/a)*cos(n*pi*y/b)*exp(1i*h*z); 118 | psi_o = @(h) sin(m*pi*x/a)*sin(n*pi*y/b)*exp(1i*h*z); 119 | 120 | N_e = @(h) rot(rot(psi_e(h) * z_hat)) / sqrt(k_c^2 + h^2); N_ex = @(h) subs(N_e(h), {x,y,z},{X,Y,Z}); 121 | M_o = @(h) rot(psi_o(h) * z_hat); M_ox = @(h) subs(M_o(h), {x,y,z},{X,Y,Z}); 122 | 123 | genFunE2Pos = -1i/(a*b) * (2-delta_0)/(k_c^2 * k_z) * ... 124 | (M_o(-k_z)*M_ox(k_z).' + N_e(-k_z)*N_ex(k_z).'); 125 | genFunE2Neg = -1i/(a*b) * (2-delta_0)/(k_c^2 * k_z) * ... 126 | (M_o(k_z)*M_ox(-k_z).' + N_e(k_z)*N_ex(-k_z).'); 127 | 128 | pl = exp(-1i*k_z*l)/(2*1i*sin(k_z*l)); 129 | plB = exp(1i*k_z*l)/(2*1i*sin(k_z*l)); 130 | genFunE2s = -1i/(a*b) * (2-delta_0)/(k_c^2 * k_z) * (... 131 | M_o(k_z) * (pl*M_ox(k_z).' + pl*M_ox(-k_z).') + ... 132 | N_e(k_z) * (-pl*N_ex(k_z).' + pl*N_ex(-k_z).') + ... 133 | M_o(-k_z) * (pl*M_ox(k_z).' + plB*M_ox(-k_z).') + ... 134 | N_e(-k_z) * (pl*N_ex(k_z).' + (-plB)*N_ex(-k_z).') ); 135 | 136 | % Here we for simplicity only account for the TE_10 mode. 137 | if orderM == 1 && orderN == 0 138 | G_e2_positive = simplify(subs(gen_Ge2(orderM,orderN,1, genFunE2Pos, genFunE2Neg, genFunE2s),{x, X},{a/2, a/2})); 139 | G_e2_negative = simplify(subs(gen_Ge2(orderM,orderN,0, genFunE2Pos, genFunE2Neg, genFunE2s),{x, X},{a/2, a/2})); 140 | else 141 | G_e2_positive = (subs(gen_Ge2(orderM,orderN,1, genFunE2Pos, genFunE2Neg, genFunE2s),{x, X},{a/2, a/2})); 142 | G_e2_negative = (subs(gen_Ge2(orderM,orderN,0, genFunE2Pos, genFunE2Neg, genFunE2s),{x, X},{a/2, a/2})); 143 | end 144 | H_wgPos = matlabFunction(-1i*omega*eps*G_e2_positive*[l_m;0;0]); 145 | H_wgNeg = matlabFunction(-1i*omega*eps*G_e2_negative*[l_m;0;0]); 146 | 147 | 148 | 149 | %% Define system 150 | x_dma = (0:(nTx-1)) * sTx + a/2; 151 | y_dma = b; 152 | z_dma = (1:nDMA) * sDMA; z_dma = z_dma - mean(z_dma) + l/2; 153 | 154 | [Xt,Yt,Zt] = ndgrid(x_dma, y_dma, z_dma); 155 | xyz_dma = [Xt(:), Yt(:), Zt(:)]; 156 | 157 | x_tx = (0:(nTx-1)) * sTx + a/2; 158 | y_tx = b/2; 159 | z_tx = 0; 160 | [Xt,Yt,Zt] = ndgrid(x_tx, y_tx, z_tx); 161 | xyz_tx = [Xt(:), Yt(:), Zt(:)]; 162 | 163 | %% Compute Y_tt 164 | % we assume that there's only a single input per waveguide. 165 | if orderM == 1 && orderN == 0 166 | Y_tt = eye(size(xyz_tx,1)) * (-[l_m,0,0] * H_wgPos(0,0)); 167 | else 168 | Y_tt = eye(size(xyz_tx,1)) * -[l_m,0,0] * H_wgPos(b/2,0,b/2,0); 169 | end 170 | 171 | %% Compute Y_st 172 | Y_st = zeros(size(xyz_dma,1),size(xyz_tx,1)); 173 | 174 | if orderM == 1 && orderN == 0 175 | yst = @(z,Z) -[l_m,0,0] * H_wgPos(Z,z); 176 | else 177 | yst = @(z,Z) -[l_m,0,0] * H_wgPos(b/2,Z,b,z); 178 | end 179 | 180 | for idn = 1:size(xyz_dma,1) 181 | for idm = 1:size(xyz_tx,1) 182 | if abs(xyz_dma(idn,1) - xyz_tx(idm,1)) <= (a/2) 183 | Y_st(idn,idm) = yst(xyz_dma(idn,3), xyz_tx(idm,3)); 184 | end 185 | end 186 | end 187 | 188 | %% Compute Y_ss 189 | Y_ss = zeros(size(xyz_dma,1),size(xyz_dma,1)); 190 | 191 | yssAir = @(x,y,z) -[l_m,0,0] * H_air(x,y,z); 192 | if orderM == 1 && orderN == 0 193 | yssPos = @(z,Z) -[l_m,0,0] * H_wgPos(Z,z); 194 | yssNeg = @(z,Z) -[l_m,0,0] * H_wgNeg(Z,z); 195 | else 196 | yssPos = @(z,Z) -[l_m,0,0] * H_wgPos(b,Z,b,z); 197 | yssNeg = @(z,Z) -[l_m,0,0] * H_wgNeg(b,Z,b,z); 198 | end 199 | 200 | for idn = 1:size(xyz_dma,1) % to 201 | for idm = 1:size(xyz_dma,1) % from 202 | if idm == idn 203 | ent = Y_0 + yssPos(xyz_dma(idn,3),xyz_dma(idn,3)); 204 | elseif abs(xyz_dma(idn,1) - xyz_dma(idm,1)) <= (a/2) % Same waveguide 205 | if xyz_dma(idn,3) >= xyz_dma(idm,3) % Positive 206 | ent = yssPos(xyz_dma(idn,3), xyz_dma(idm,3)) + ... 207 | yssAir(xyz_dma(idn,1)-xyz_dma(idm,1),xyz_dma(idn,2)-xyz_dma(idm,2),xyz_dma(idn,3)-xyz_dma(idm,3)); 208 | else % Negative 209 | ent = yssNeg(xyz_dma(idn,3), xyz_dma(idm,3)) + ... 210 | yssAir(xyz_dma(idn,1)-xyz_dma(idm,1),xyz_dma(idn,2)-xyz_dma(idm,2),xyz_dma(idn,3)-xyz_dma(idm,3)); 211 | end 212 | else % other waveguide 213 | ent = yssAir(xyz_dma(idn,1)-xyz_dma(idm,1),xyz_dma(idn,2)-xyz_dma(idm,2),xyz_dma(idn,3)-xyz_dma(idm,3)); 214 | end 215 | Y_ss(idn,idm) = ent; 216 | end 217 | end 218 | 219 | %% Compute currents and fields: 220 | zm = (CST_data(1).Z_mm -CST_data(1).Z_mm(1)) * 1E-3; % Measurement points 221 | 222 | Y_s0 = eye(size(xyz_dma,1))*(2-15.7934i) * l_m^2; 223 | 224 | Yp = Y_tt- Y_st.' * inv(Y_ss+Y_s0) * Y_st; 225 | Y0 = ones(nTx,1) * Y_intrinsic_source*l_m^2; 226 | 227 | j = [1;1]; 228 | Yin = sum(Yp * j,2) ./ j; 229 | Gamma = diag( -(Yin - Y0) ./ (Yin + Y0) ); 230 | j_t = (eye(nTx) + Gamma) * j; 231 | 232 | % normalize power: 233 | Ps = real(j_t' * inv((eye(nTx) - Gamma' * Gamma)) * Yp * j_t) / 2; 234 | 235 | j = j / sqrt(Ps); 236 | j_t = (eye(nTx)+Gamma) * j ; 237 | j_s = -(Y_ss+Y_s0)^(-1)* Y_st * j_t; % DMA element currents 238 | 239 | Ps = real(j_t' * inv((eye(nTx) - Gamma' * Gamma)) * Yp * j_t) / 2; % Power supplied 240 | Pt = real(j_t' * Yp * j_t) / 2; % Power radiated 241 | 242 | if plot_stuff 243 | H = zeros(length(zm),1); 244 | H_top = zeros(length(zm),1); 245 | x0 = a/2; % The center of the waveguide of interest 246 | for n = 1:length(zm) 247 | 248 | H_field = zeros(3,1); 249 | H_field_top = zeros(3,1); 250 | 251 | for id_tx = 1:size(xyz_tx,1) 252 | if xyz_tx(id_tx,1) == x0 % If it's in the waveguide of interest 253 | H_field = H_field + j_t(id_tx) * ... 254 | (H_wgPos(xyz_tx(id_tx,3),zm(n))*(zm(n)>=xyz_tx(id_tx,3)) + H_wgNeg(xyz_tx(id_tx,3),zm(n))*((zm(n)=xyz_dma(id_dma,3)) + H_wgNeg(xyz_dma(id_dma,3),zm(n))*((zm(n) 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------