107 lines
3.1 KiB
Mathematica
107 lines
3.1 KiB
Mathematica
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clear;
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close all;
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Fe = 24000; % Hz
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Te = 1/Fe; % s
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N = 5000; % nombre de bits envoyés
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Rb = 6000; % débit binaire
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bits = randi([0, 1], 1, N); % bits envoyés
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M = 2^2; % signal 4-aire
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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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h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
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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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n0 = 8; % déterminé en traçant g
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%% tracé de g
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g = conv(conv(h, h_c), h_r); % réponse impulsionnelle globale
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figure;
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plot(g);
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title("Tracé de g");
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ylabel("Amplitude");
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%% chaine de transmission
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X_re = reshape(bits, 2, N/2).'; % on regroupe pour avoir un symbole 4-aire
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X_d = bi2de(X_re); % conversion en décimaux
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X_m = X_d*2 - 3; % mapping 4-aire 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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%% tracé du diagramme de l'oeil du signal non bruité
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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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oeil = reshape(X_r, Ns, length(X_r)/Ns); % permet de tracer le diagramme de l'oeil, on retrouve n0 = 8
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plot(oeil);
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title("Diagramme de l'oeil, signal non bruité");
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xlabel("Temps (s)");
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ylabel("Amplitude");
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%% tracé de TEB = f(E_b/N_0)
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P_x = mean(abs(X_c).^2);
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EbN0_db = linspace(0, 8, 200);
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EbN0 = 10.^(EbN0_db./10);
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TEBs = [];
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TESs = [];
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for e=EbN0
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sigma2_x = P_x * Ns / (2 * log2(M) * e); % calcul de sigma^2
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X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
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X_r = filter(h_r, 1, X_b); % signal reçu
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X_e = X_r( n0:Ns:N*Ns/log2(M) ); % échantillonage du signal reçu
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decision = 3*( X_e >= 16 ) + 1*( X_e >= 0 & X_e < 16 ) + -1*( X_e < 0 & X_e > -16 ) + -3*( X_e <= -16 ); % decision
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TES = mean(((decision+3)/2 - (X_m'+3)/2).^2); % on calcule l'erreur symbole
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recu = reshape(de2bi((decision + 3)/2).', 1, N); % demapping + conversion en binaire
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TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
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TESs = [ TESs TES ];
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TEBs = [ TEBs TEB ];
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end
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TEB_Gray = TESs / log2(M);
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TES_theorique = 3/2*qfunc(sqrt(4/5*EbN0));
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TEB_theorique = 3/4*qfunc(sqrt(4/5*EbN0));
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TEB_theorique_ref = qfunc(sqrt(2*EbN0));
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figure;
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semilogy(EbN0_db, TESs, '+');
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hold;
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semilogy(EbN0_db, TEBs, '+');
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%semilogy(EbN0_db, TEB_Gray, '+');
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plot(EbN0_db, TES_theorique);
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plot(EbN0_db, TEB_theorique);
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plot(EbN0_db, TEB_theorique_ref);
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title("TEB = f(E_b/N_0)");
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xlabel("E_b/N_0 (dB)");
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ylabel("erreur (dB)");
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legend("TES numérique", "TEB numérique", "TES théorique", "TEB théorique", "TEB référence");
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%% tracé de plusieurs diagrammes de l'oeil
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EbN0_db = linspace(0, 12, 4);
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for e=EbN0_db
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sigma2_x = P_x * Ns / (2 * log2(M) * 10^(e/10)); % calcul de sigma^2
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X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
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X_r = filter(h_r, 1, X_b); % signal reçu
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figure;
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oeil = reshape(X_r, Ns, length(X_r)/Ns); % permet de tracer le diagramme de l'oeil
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plot(oeil);
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title("Diagramme de l'oeil, E_b/N_0 = " + num2str(e) + " dB");
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xlabel("Temps (s)");
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ylabel("Amplitude");
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end
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