98 lines
3 KiB
Mathematica
98 lines
3 KiB
Mathematica
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clear;
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close all;
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Fe = 24000; % fréquence d'échantillonage (Hz)
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Te = 1/Fe; % période d'échantillonage (s)
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N = 10000; % nombre de bits envoyés
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Rb = 3000; % débit binaire
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M = 2^1; % signal BPSK
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Ts = log2(M)/Rb; % période symbole
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Ns = floor(Ts/Te);
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T = (0:N*Ns/log2(M)-1) * Te; % échelle temporelle
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alpha0 = 1;
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alpha1 = 0.5;
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n0 = Ns;
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%% deux rectangles
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figure;
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LOS = ones(1, Ns);
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multipath = ones(1, Ns)/2;
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stairs(0:2*Ns-1, [LOS, multipath]);
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ylim([0 1.1]);
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xlim([0 2*Ns]);
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title("h_e");
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%% construction du signal avec les g
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alpha0 = 1;
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alpha1 = 0.5;
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h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
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h_c = [ alpha0 zeros(1, Ns-1) alpha1 ]; % propagation: sélectif
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%h_c = [ 1 zeros(1, Ns-1) ]; % propagation: dirac
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h_r = h; % réception: réponse impulsionnelle rectangulaire
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g = conv(conv(h, h_c), h_r); % réponse impulsionnelle globale
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bits = [ 1 1 1 0 0 1 0 ]; % bits envoyés
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X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
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X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
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X_f = filter(h, 1, X_k); % signal émis
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X_c = filter(h_c, 1, X_f); % signal transmis
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X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
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figure;
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hold;
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somme = zeros(1, length(g)+Ns*(length(bits)-1));
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for i=0:length(bits)-1
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somme = somme + [zeros(1, i*Ns) g*sign(X_m(i+1)) zeros(1, (length(bits)-i-1)*Ns) ];
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plot( [zeros(1, i*Ns) g*sign(X_m(i+1)) zeros(1, (length(bits)-i-1)*Ns) ], '--');
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text(Ns*(i+1) + 0, X_m(i+1), num2str(bits(i+1)), 'Color', '#7E2F8E');
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end
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plot(somme, 'LineWidth', 2);
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legend('g(t - 0*Ns)', 'g(t - 1*Ns)', 'g(t - 2*Ns)', 'g(t - 3*Ns)', 'g(t - 4*Ns)', 'g(t - 5*Ns)', 'g(t - 6*Ns)', 'somme');
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%% construction de z
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alpha0 = 1;
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alpha1 = 0.5;
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h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
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h_c = [ alpha0 zeros(1, Ns-1) alpha1 ]; % propagation: sélectif
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%h_c = [ 1 zeros(1, Ns-1) ]; % propagation: dirac
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h_r = h; % réception: réponse impulsionnelle rectangulaire
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g = conv(conv(h, h_c), h_r); % réponse impulsionnelle globale
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bits = [ 1 0 0 0 0 0 0 ]; % bits envoyés
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X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
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X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
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X_f = filter(h, 1, X_k); % signal émis
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X_c = filter(h_c, 1, X_f); % signal transmis
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X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
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figure;
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hold;
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somme = zeros(1, length(g)+Ns*(length(bits)-1));
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for i=0:length(bits)-1
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somme = somme + [zeros(1, i*Ns) g*sign(X_m(i+1)) zeros(1, (length(bits)-i-1)*Ns) ];
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plot( [zeros(1, i*Ns) g*sign(X_m(i+1)) zeros(1, (length(bits)-i-1)*Ns) ], '--');
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text(Ns*(i+1) + 0, X_m(i+1), num2str(bits(i+1)), 'Color', '#7E2F8E');
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end
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plot(somme);
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%% quatres gaussiennes
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T = -20:0.1:20;
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sigma_w = sqrt(Ns);
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g1 = gaussmf(T, [sigma_w -3*Ns/2]);
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g2 = gaussmf(T, [sigma_w -Ns/2]);
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g3 = gaussmf(T, [sigma_w Ns/2]);
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g4 = gaussmf(T, [sigma_w 3*Ns/2]);
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hold on;
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plot(T, g1);
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plot(T, g2);
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plot(T, g3);
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plot(T, g4);
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legend("$$-\alpha_0-\alpha_1$$", "$$-\alpha_0+\alpha_1$$", "$$+\alpha_0-\alpha_1$$", "$$+\alpha_0+\alpha_1$$", 'interpreter','latex');
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