feat: add files
This commit is contained in:
Laureηt
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ac17c38479
165
TEB_test.m
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165
TEB_test.m
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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 = 100000; % nombre de bits envoyés
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Rb = 3000; % débit binaire
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Fp = 2000; % fréquence porteuse
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bits = [ 1 1 1 0 0 1 0 ];
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% bits = randi([0, 1], 1, N); % bits envoyés
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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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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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n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou 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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axis square;
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%% chaine de transmission
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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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%% tracé de x_e
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figure;
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stairs(X_c);
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axis(axis*1.1);
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title("Signal transmis");
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ylabel("Amplitude");
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for i=1:length(bits)
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index = n0/2 + (i-1)*Ns;
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text(index + 0.8, X_c(index), num2str(bits(i)), 'Color', '#7E2F8E');
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end
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%% diagramme de l'oeil
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figure;
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X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
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oeil = reshape(X_r(Ns+1:end), Ns, length(X_r(Ns+1:end))/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");
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ylabel("Amplitude");
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axis square;
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%% tracé de x_r
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figure;
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plot(X_r);
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axis(axis*1.1);
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title("Signal reçu");
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ylabel("Amplitude");
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%% réception
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X_e = X_r( n0:Ns:length(bits)*Ns ); % échantillonage du signal reçu
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recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
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erreur = mean((recu - bits).^2) % on calcule l'erreur
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%% tracé des constellations
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figure;
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plot(complex(X_e(2:end)), "*");
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hold;
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plot(complex(X_m), ".", 'MarkerSize', 20);
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axis(axis*1.1);
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axis square;
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title("Constellations");
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legend("canal sélectif", "canal dirac");
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xlabel("Re");
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ylabel("Im");
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%% tracé de TEB = f(E_b/N_0)
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bits = randi([0, 1], 1, N); % 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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P_x = mean(abs(X_c).^2); % puissance du signal en entrée de la reception
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EbN0_db = linspace(0, 10, 200);
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EbN0 = 10.^(EbN0_db./10);
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TEBs = [];
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for e=EbN0
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sigma2_x = P_x * Ns / (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:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
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recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
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TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
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TEBs = [ TEBs TEB ];
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end
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TEB_theorique = 1/2*qfunc(3/2*sqrt(4/5*EbN0)) + 1/2*qfunc(1/2*sqrt(4/5*EbN0));
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% TEB_theorique = qfunc(sqrt(EbN0));
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close all;
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figure;
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semilogy(EbN0_db, TEBs, '+');
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hold;
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plot(EbN0_db, TEB_theorique);
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title("TEB $$= f(E_b/N_0)$$", 'interpreter','latex');
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xlabel("$$E_b/N_0$$ (dB)", 'interpreter','latex');
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ylabel("TEB", 'interpreter','latex');
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legend("TEB numérique", "TEB théorique (canal selectif)");
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%% tracé de constellations bruitées
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EbN0_db = linspace(0, 12, 4);
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EbN0 = 10.^(EbN0_db./10);
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for e=EbN0
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sigma2_x = P_x * Ns / (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:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
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recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
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TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
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close all;
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figure;
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sp1 = subplot(2, 1, 1);
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histogram(X_e, 100);
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xlim([-40 40]);
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xlabel("Re");
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title("Histogramme, $$E_b/N_0 =$$ " + num2str(10*log10(e)) +"dB", 'interpreter','latex');
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sp2 = subplot(2, 1, 2);
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plot(complex(X_e(2:10:end)), "*");
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hold;
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plot(complex(X_m), ".", 'MarkerSize', 20);
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xlim([-40 40]);
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title("Constellations, $$E_b/N_0 =$$ " + num2str(10*log10(e)) +"dB", 'interpreter','latex');
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legend("symboles bruités", "symboles théoriques");
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xlabel("Re");
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ylabel("Im");
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sp2.Position(4) = 0.1;
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sp1.Position(2) = 0.28;
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sp1.Position(4) = 0.68;
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pause(1);
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print(gcf,"histcons_selectif_" + num2str(10*log10(e)) + "db.png", '-dpng', '-r300');
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end
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97
dessins.m
Normal file
97
dessins.m
Normal file
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@ -0,0 +1,97 @@
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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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222
egalisation.m
Normal file
222
egalisation.m
Normal file
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@ -0,0 +1,222 @@
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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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zero_pad = 2^12;
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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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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_r = h; % réception: réponse impulsionnelle rectangulaire
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n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou g
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%% création de Z et C
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ordre = 10;
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K = ordre;
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bits = [ 1 zeros(1, ordre-1) ]; % dirac
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X_k = kron(bits, [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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X_e = X_r( n0 : Ns : length(bits)*Ns ); % échantillonage du signal reçu
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Z = zeros(K, ordre);
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for i=1:ordre
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Z(i:end, i) = X_e(1:K-i+1);
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end
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Y_0 = [ 1 zeros(1, ordre-1) ]';
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C = Z \ Y_0;
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%% tracés réponses en fréquence
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X_eg = filter(C, 1, X_e);
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g = conv(conv(h, h_c), h_r); % chaine globale
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figure;
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plot(abs(fft(C, zero_pad)));
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title("C");
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figure;
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plot(abs(fft(g, zero_pad)));
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title("G");
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figure;
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plot(abs(fft(g, zero_pad).*fft(C', zero_pad)));
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title("G \times C");
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figure;
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plot( ifft( abs(fft(g, zero_pad).*fft(C', zero_pad)) ));
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title("g * c");
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%% tracés réponses impulsionnelles
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bits = [ 1 zeros(1, N-1) ];
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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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X_e = X_r( n0 : Ns : length(bits)*Ns ); % échantillonage du signal reçu
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X_eg = filter(C, 1, X_e); % égaliseur ZFE
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figure;
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tiledlayout(3,1);
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ax1 = nexttile;
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stairs(bits);
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legend("Dirac");
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ax2 = nexttile;
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plot(X_e);
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legend("Réponse impulsionnel non égalisée");
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ax3 = nexttile;
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plot(X_eg);
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legend("Réponse impulsionnel égalisée");
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linkaxes([ax1 ax2 ax3], 'xy');
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axis( axis + [-1 1 -1 1]/5 );
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axis
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%% constellations
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bits = randi([0, 1], 1, N); % 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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X_e = X_r( n0 : Ns : length(bits)*Ns ); % échantillonage du signal reçu
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X_eg = filter(C, 1, X_e); % égaliseur ZFE
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figure;
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tiledlayout(3,1);
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ax1 = nexttile;
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plot(complex(X_m), ".", 'MarkerSize', 20);
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symbols = unique(X_m(2:end));
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for i=1:length(symbols)
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text(symbols(i), 0.1, num2str(bits(find(X_m == symbols(i), 1))), 'Color', '#7E2F8E');
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end
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xlabel("Re");
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ylabel("Im");
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legend("Symboles théoriques");
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grid;
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ax2 = nexttile;
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plot(complex(X_e(2:end)), ".", 'MarkerSize', 20);
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symbols = unique(X_e(2:end));
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for i=1:length(symbols)
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text(symbols(i), 0.1, num2str(bits(find(X_e == symbols(i), 1))), 'Color', '#7E2F8E');
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end
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xlabel("Re");
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ylabel("Im");
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legend("Symboles reçus");
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grid;
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ax3 = nexttile;
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plot(complex(X_eg(2:end)), ".", 'MarkerSize', 20);
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symbols = unique(X_eg(2:end));
|
||||
for i=1:length(symbols)
|
||||
text(symbols(i), 0.1, num2str(bits(find(X_eg == symbols(i), 1))), 'Color', '#7E2F8E');
|
||||
end
|
||||
xlabel("Re");
|
||||
ylabel("Im");
|
||||
legend("Symboles égalisés");
|
||||
grid;
|
||||
|
||||
linkaxes([ax1 ax2 ax3], 'xy');
|
||||
|
||||
%% tracé de constellations bruitées
|
||||
|
||||
P_x = mean(abs(X_c).^2); % puissance du signal en entrée de la reception
|
||||
EbN0_db = linspace(0, 12, 4);
|
||||
EbN0 = 10.^(EbN0_db./10);
|
||||
for e=EbN0
|
||||
sigma2_x = P_x * Ns / (log2(M) * e); % calcul de sigma^2
|
||||
X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
|
||||
X_r = filter(h_r, 1, X_b); % signal reçu
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
|
||||
|
||||
X_eg = filter(C, 1, X_e); % égaliseur ZFE
|
||||
recu = double( X_eg > 0 ); % on récupère les bits, décision + "démapping"
|
||||
|
||||
close all;
|
||||
figure;
|
||||
|
||||
sp1 = subplot(2, 1, 1);
|
||||
histogram(X_eg, 100);
|
||||
xlim([-4 4]);
|
||||
xlabel("Re");
|
||||
title("Histogramme, $$E_b/N_0 =$$ " + num2str(10*log10(e)) +"dB", 'interpreter','latex');
|
||||
|
||||
sp2 = subplot(2, 1, 2);
|
||||
plot(complex(X_eg(2:10:end)), "*");
|
||||
hold;
|
||||
plot(complex(X_m), ".", 'MarkerSize', 20);
|
||||
xlim([-4 4]);
|
||||
title("Constellations, $$E_b/N_0 =$$ " + num2str(10*log10(e)) +"dB", 'interpreter','latex');
|
||||
legend("symboles bruités", "symboles théoriques");
|
||||
xlabel("Re");
|
||||
ylabel("Im");
|
||||
|
||||
sp2.Position(4) = 0.1;
|
||||
sp1.Position(2) = 0.28;
|
||||
sp1.Position(4) = 0.68;
|
||||
|
||||
pause(1);
|
||||
print(gcf,"histcons_egalise_" + num2str(10*log10(e)) + "db.png", '-dpng', '-r300');
|
||||
|
||||
end
|
||||
|
||||
%% tracé de TEB = f(E_b/N_0)
|
||||
N = 100000; % nombre de bits envoyés
|
||||
bits = randi([0, 1], 1, N); % bits envoyés
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
|
||||
P_x = mean(abs(X_c).^2); % puissance du signal en entrée de la reception
|
||||
EbN0_db = linspace(0, 10, 200);
|
||||
EbN0 = 10.^(EbN0_db./10);
|
||||
TEBs = [];
|
||||
for e=EbN0
|
||||
sigma2_x = P_x * Ns / (log2(M) * e); % calcul de sigma^2
|
||||
X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
|
||||
X_r = filter(h_r, 1, X_b); % signal reçu
|
||||
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
|
||||
X_eg = filter(C, 1, X_e); % égaliseur ZFE
|
||||
|
||||
recu = double( X_eg > 0 ); % on récupère les bits, décision + "démapping"
|
||||
TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
|
||||
|
||||
TEBs = [ TEBs TEB ];
|
||||
end
|
||||
|
||||
TEB_theorique = qfunc(sqrt(EbN0));
|
||||
|
||||
close all;
|
||||
|
||||
figure;
|
||||
semilogy(EbN0_db, TEBs, '+');
|
||||
hold;
|
||||
plot(EbN0_db, TEB_theorique);
|
||||
title("TEB $$= f(E_b/N_0)$$", 'interpreter','latex');
|
||||
xlabel("$$E_b/N_0$$ (dB)", 'interpreter','latex');
|
||||
ylabel("TEB", 'interpreter','latex');
|
||||
legend("TEB numérique", "TEB théorique (canal dirac)");
|
||||
84
oeil_g_trace_constellation.m
Normal file
84
oeil_g_trace_constellation.m
Normal file
|
|
@ -0,0 +1,84 @@
|
|||
clear;
|
||||
close all;
|
||||
|
||||
Fe = 24000; % fréquence d'échantillonage (Hz)
|
||||
Te = 1/Fe; % période d'échantillonage (s)
|
||||
N = 10000; % nombre de bits envoyés
|
||||
Rb = 3000; % débit binaire
|
||||
Fp = 2000; % fréquence porteuse
|
||||
|
||||
bits = [ 1 1 1 0 0 1 0 ];
|
||||
% bits = randi([0, 1], 1, N); % bits envoyés
|
||||
|
||||
M = 2^1; % signal BPSK
|
||||
Ts = log2(M)/Rb; % période symbole
|
||||
Ns = floor(Ts/Te);
|
||||
T = (0:N*Ns/log2(M)-1) * Te; % échelle temporelle
|
||||
|
||||
alpha0 = 1;
|
||||
alpha1 = 0.5;
|
||||
|
||||
h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
|
||||
h_c = [ alpha0 zeros(1, Ns-1) alpha1 ]; % propagation: sélectif
|
||||
% h_c = [ 1 zeros(1, Ns-1) ]; % propagation: dirac
|
||||
h_r = h; % réception: réponse impulsionnelle rectangulaire
|
||||
|
||||
n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou g
|
||||
|
||||
%% tracé de g
|
||||
g = conv(conv(h, h_c), h_r); % réponse impulsionnelle globale
|
||||
|
||||
figure;
|
||||
plot(g);
|
||||
title("Tracé de g");
|
||||
ylabel("Amplitude");
|
||||
axis square;
|
||||
|
||||
%% chaine de transmission
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
|
||||
%% tracé de x_e
|
||||
figure;
|
||||
stairs(X_c);
|
||||
axis(axis*1.1);
|
||||
title("Signal transmis");
|
||||
ylabel("Amplitude");
|
||||
for i=1:length(bits)
|
||||
index = n0/2 + (i-1)*Ns;
|
||||
text(index + 0.8, X_c(index), num2str(bits(i)), 'Color', '#7E2F8E');
|
||||
end
|
||||
|
||||
%% diagramme de l'oeil
|
||||
figure;
|
||||
X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
|
||||
oeil = reshape(X_r(Ns+1:end), Ns, length(X_r(Ns+1:end))/Ns); % permet de tracer le diagramme de l'oeil, on retrouve n0 = 8
|
||||
plot(oeil);
|
||||
title("Diagramme de l'oeil");
|
||||
ylabel("Amplitude");
|
||||
axis square;
|
||||
|
||||
%% tracé de x_r
|
||||
figure;
|
||||
plot(X_r);
|
||||
axis(axis*1.1);
|
||||
title("Signal reçu");
|
||||
ylabel("Amplitude");
|
||||
|
||||
%% réception
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns ); % échantillonage du signal reçu
|
||||
recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
|
||||
erreur = mean((recu - bits).^2) % on calcule l'erreur
|
||||
|
||||
%% tracé des constellations
|
||||
figure;
|
||||
plot(complex(X_m), ".", 'MarkerSize', 20);
|
||||
hold;
|
||||
plot(complex(X_e(2:end)), "*");
|
||||
axis(axis*1.1);
|
||||
title("Constellations");
|
||||
legend("canal dirac", "canal sélectif");
|
||||
xlabel("Re");
|
||||
ylabel("Im");
|
||||
85
q2_2_4.m
Normal file
85
q2_2_4.m
Normal file
|
|
@ -0,0 +1,85 @@
|
|||
clear;
|
||||
close all;
|
||||
|
||||
Fe = 24000; % fréquence d'échantillonage (Hz)
|
||||
Te = 1/Fe; % période d'échantillonage (s)
|
||||
N = 50000; % nombre de bits envoyés
|
||||
Rb = 3000; % débit binaire
|
||||
Fp = 2000; % fréquence porteuse
|
||||
|
||||
% bits = [ 1 1 1 0 0 1 0 ];
|
||||
bits = randi([0, 1], 1, N); % bits envoyés
|
||||
|
||||
M = 2^1; % signal BPSK
|
||||
Ts = log2(M)/Rb; % période symbole
|
||||
Ns = floor(Ts/Te);
|
||||
T = (0:N*Ns/log2(M)-1) * Te; % échelle temporelle
|
||||
|
||||
alpha0 = 1;
|
||||
alpha1 = 0.5;
|
||||
|
||||
h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
|
||||
h_c = [ alpha0 zeros(1, Ns-1) alpha1 ]; % propagation: sélectif
|
||||
% h_c = [ 1 zeros(1, Ns-1) ]; % propagation: dirac
|
||||
h_r = h; % réception: réponse impulsionnelle rectangulaire
|
||||
|
||||
n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou g
|
||||
|
||||
%% tracé de g
|
||||
g = conv(conv(h, h_c), h_r); % réponse impulsionnelle globale
|
||||
|
||||
% figure;
|
||||
% plot(g);
|
||||
% title("Tracé de g");
|
||||
% ylabel("Amplitude");
|
||||
|
||||
%% chaine de transmission
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
|
||||
%% tracé de X_c
|
||||
% figure;
|
||||
% stairs(X_c);
|
||||
% axis(axis*1.1);
|
||||
|
||||
%% diagramme de l'oeil
|
||||
figure;
|
||||
X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
|
||||
oeil = reshape(X_r(Ns+1:end), Ns, length(X_r(Ns+1:end))/Ns); % permet de tracer le diagramme de l'oeil, on retrouve n0 = 8
|
||||
plot(oeil);
|
||||
title("Diagramme de l'oeil");
|
||||
xlabel("Temps (s)");
|
||||
ylabel("Amplitude");
|
||||
|
||||
%% tracé de TEB = f(E_b/N_0)
|
||||
P_x = mean(abs(X_c).^2);
|
||||
EbN0_db = linspace(0, 10, 200);
|
||||
EbN0 = 10.^(EbN0_db./10);
|
||||
TEBs = [];
|
||||
for e=EbN0
|
||||
|
||||
sigma2_x = P_x * Ns / (2 * log2(M) * e); % calcul de sigma^2
|
||||
X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
|
||||
X_r = filter(h_r, 1, X_b); % signal reçu
|
||||
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
|
||||
|
||||
recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
|
||||
TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
|
||||
|
||||
TEBs = [ TEBs TEB ];
|
||||
|
||||
end
|
||||
|
||||
bidule = sqrt ( EbN0 / 2 );
|
||||
TEB_theorique = 1/2*qfunc(3 * bidule) + 1/2*qfunc(bidule);
|
||||
|
||||
figure;
|
||||
semilogy(EbN0_db, TEBs, '+');
|
||||
hold;
|
||||
plot(EbN0_db, TEB_theorique);
|
||||
title("TEB $$= f(E_b/N_0)$$", 'interpreter','latex');
|
||||
xlabel("$$E_b/N_0$$ (dB)", 'interpreter','latex');
|
||||
ylabel("TEB", 'interpreter','latex');
|
||||
123
q3_2_2_a.m
Normal file
123
q3_2_2_a.m
Normal file
|
|
@ -0,0 +1,123 @@
|
|||
clear;
|
||||
close all;
|
||||
|
||||
Fe = 24000; % fréquence d'échantillonage (Hz)
|
||||
Te = 1/Fe; % période d'échantillonage (s)
|
||||
N = 50000; % nombre de bits envoyés (bit)
|
||||
Rb = 3000; % débit binaire (bit/s)
|
||||
|
||||
% bits = [ 1 1 1 0 0 1 0 ];
|
||||
|
||||
M = 2^1; % signal BPSK
|
||||
Ts = log2(M)/Rb; % période symbole
|
||||
Ns = floor(Ts/Te);
|
||||
T = (0:N*Ns/log2(M)-1) * Te; % échelle temporelle
|
||||
|
||||
h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
|
||||
h_c = [ 1 zeros(1, Ns-1) 0.5 ]; % propagation: sélectif
|
||||
h_r = h; % réception: réponse impulsionnelle rectangulaire
|
||||
|
||||
n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou g
|
||||
|
||||
%% création de Z et C
|
||||
|
||||
ordre = 10;
|
||||
K = ordre;
|
||||
|
||||
bits = [ 1 zeros(1, ordre-1) ]; % dirac
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns ); % échantillonage du signal reçu
|
||||
|
||||
Z = zeros(K, ordre);
|
||||
for i=1:ordre
|
||||
Z(i:end, i) = X_e(1:K-i+1);
|
||||
end
|
||||
|
||||
Y_0 = [ 1 zeros(1, ordre-1) ]';
|
||||
C = Z \ Y_0;
|
||||
|
||||
%% tracé de X_c
|
||||
% figure;
|
||||
% plot(X_e);
|
||||
% axis(axis*1.1);
|
||||
% title("non égalisé");
|
||||
|
||||
%% tracé de X_egal
|
||||
|
||||
% X_egal = filter(C, 1, X_e);
|
||||
|
||||
% figure;
|
||||
% plot(X_egal);
|
||||
% axis(axis*1.1);
|
||||
% title("égalisé");
|
||||
|
||||
%% tracé de g et g_eg
|
||||
|
||||
g = conv(conv(h, h_c), h_r);
|
||||
g_eg = conv(g, C);
|
||||
|
||||
figure;
|
||||
plot(abs(fft(g, 4096)));
|
||||
figure;
|
||||
plot(abs(fft(g_eg, 4096)));
|
||||
|
||||
%% tracé de g et g_eg
|
||||
|
||||
% figure;
|
||||
% plot(g);
|
||||
% figure;
|
||||
% plot(g_eg);
|
||||
|
||||
%% tracé de TEB = f(E_b/N_0)
|
||||
|
||||
bits = randi([0, 1], 1, N); % bits envoyés
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
|
||||
P_x = mean(abs(X_c).^2);
|
||||
EbN0_db = linspace(0, 10, 200);
|
||||
EbN0 = 10.^(EbN0_db./10);
|
||||
TEBs = [];
|
||||
for e=EbN0
|
||||
|
||||
sigma2_x = P_x * Ns / (2 * log2(M) * e); % calcul de sigma^2
|
||||
X_b = X_c + sqrt(sigma2_x) * randn(1, length(X_c)); % signal bruité
|
||||
|
||||
X_eg = filter(C, 1, X_b); % égalisation ZFE
|
||||
X_r = filter(h_r, 1, X_eg); % signal reçu
|
||||
|
||||
X_e = X_r( n0:Ns:length(bits)*Ns/log2(M) ); % échantillonage du signal reçu
|
||||
|
||||
recu = double( X_e > 0 ); % on récupère les bits, décision + "démapping"
|
||||
TEB = mean((recu - bits).^2); % on calcule l'erreur binaire
|
||||
|
||||
TEBs = [ TEBs TEB ];
|
||||
|
||||
end
|
||||
|
||||
bidule = sqrt ( EbN0 / 2 );
|
||||
TEB_theorique = 1/2*qfunc(3 * bidule) + 1/2*qfunc(bidule);
|
||||
|
||||
figure;
|
||||
semilogy(EbN0_db, TEBs, '+');
|
||||
hold;
|
||||
plot(EbN0_db, TEB_theorique);
|
||||
title("TEB $$= f(E_b/N_0)$$", 'interpreter','latex');
|
||||
xlabel("$$E_b/N_0$$ (dB)", 'interpreter','latex');
|
||||
ylabel("TEB", 'interpreter','latex');
|
||||
|
||||
%% tracé des constellations
|
||||
|
||||
figure;
|
||||
plot(complex(X_m), '.', 'MarkerSize', 25);
|
||||
hold;
|
||||
plot(complex(X_e), '+');
|
||||
plot(complex(X_eg), '*');
|
||||
axis([-2 2 -1 1]);
|
||||
legend("symboles", "non égalisé", "égalisé");
|
||||
BIN
rapport.pdf
Normal file
BIN
rapport.pdf
Normal file
Binary file not shown.
87
reponse_impsulsionnelle.m
Normal file
87
reponse_impsulsionnelle.m
Normal file
|
|
@ -0,0 +1,87 @@
|
|||
clear;
|
||||
close all;
|
||||
|
||||
Fe = 24000; % fréquence d'échantillonage (Hz)
|
||||
Te = 1/Fe; % période d'échantillonage (s)
|
||||
N = 10; % nombre de bits envoyés
|
||||
Rb = 3000; % débit binaire
|
||||
|
||||
M = 2^1; % signal BPSK
|
||||
Ts = log2(M)/Rb; % période symbole
|
||||
Ns = floor(Ts/Te);
|
||||
T = (0:N*Ns/log2(M)-1) * Te; % échelle temporelle
|
||||
|
||||
alpha0 = 1;
|
||||
alpha1 = 0.5;
|
||||
|
||||
h = ones(1, Ns); % mise en forme: réponse impulsionnelle rectangulaire
|
||||
h_c = [ alpha0 zeros(1, Ns-1) alpha1 ]; % propagation: sélectif
|
||||
h_r = h; % réception: réponse impulsionnelle rectangulaire
|
||||
|
||||
n0 = Ns; % déterminé en traçant le diagramme de l'oeil ou g
|
||||
|
||||
%% création de Z et C
|
||||
|
||||
ordre = 10;
|
||||
K = ordre;
|
||||
|
||||
bits = [ 1 zeros(1, ordre-1) ]; % dirac
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
|
||||
X_e = X_r( n0 : Ns : length(bits)*Ns ); % échantillonage du signal reçu
|
||||
|
||||
Z = zeros(K, ordre);
|
||||
for i=1:ordre
|
||||
Z(i:end, i) = X_e(1:K-i+1);
|
||||
end
|
||||
|
||||
Y_0 = [ 1 zeros(1, ordre-1) ]';
|
||||
C = Z \ Y_0;
|
||||
|
||||
X_eg = filter(C, 1, X_e);
|
||||
|
||||
g = conv(conv(h, h_c), h_r); % chaine globale
|
||||
|
||||
% figure;
|
||||
% plot(g);
|
||||
% hold;
|
||||
% plot(g_eg);
|
||||
|
||||
% figure;
|
||||
% plot(abs(fft(C, 2^10)));
|
||||
% title("C");
|
||||
% figure;
|
||||
% plot(abs(fft(g, 2^10)));
|
||||
% title("g");
|
||||
% figure;
|
||||
% plot(abs(fft(g, 2^10).*fft(C', 2^10)));
|
||||
% title("g \times C");
|
||||
|
||||
%% tracé d'une réponse impulsionnelle
|
||||
|
||||
bits = [ 1 zeros(1, N-1) ];
|
||||
X_m = 2 * bits - 1; % mapping binaire à moyenne nulle
|
||||
X_k = kron(X_m, [1 zeros(1, Ns-1)]); % Suréchantillonnage
|
||||
X_f = filter(h, 1, X_k); % signal émis
|
||||
X_c = filter(h_c, 1, X_f); % signal transmis
|
||||
X_r = filter(h_r, 1, X_c); % signal reçu, sans bruit
|
||||
X_e = X_r( n0 : Ns : length(bits)*Ns ); % échantillonage du signal reçu
|
||||
X_eg = filter(C, 1, X_e); % égaliseur ZFE
|
||||
|
||||
figure;
|
||||
stairs(X_m);
|
||||
title("X_m");
|
||||
axis([1 10 -1.1 1.1]);
|
||||
|
||||
figure;
|
||||
plot(X_e);
|
||||
title("X_e");
|
||||
saveaxis = axis;
|
||||
figure;
|
||||
|
||||
plot(X_eg);
|
||||
title("X_{eg}");
|
||||
axis(saveaxis);
|
||||
Loading…
Reference in a new issue