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### examen_final_2004

Course: GEL 10280, Fall 2009
School: Northwestern State...
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Laval Universit Professeur: Leslie A. Rusch Dpartement de gnie lectrique et de gnie informatique GEL10280: Communications numriques 2004 Examen final Mercredi le 28 avril 2004; Dure: 08h30 10h20 Deux feuilles de documentation permises; une calculatrice permise Problme 1 (25 points sur 100) Voici un graphique d'un PLL de Costas pour le QPSK. A. (10 points) Compltez les boites vides pour un PLL d'ordre un. B....

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Laval Universit Professeur: Leslie A. Rusch Dpartement de gnie lectrique et de gnie informatique GEL10280: Communications numriques 2004 Examen final Mercredi le 28 avril 2004; Dure: 08h30 10h20 Deux feuilles de documentation permises; une calculatrice permise Problme 1 (25 points sur 100) Voici un graphique d'un PLL de Costas pour le QPSK. A. (10 points) Compltez les boites vides pour un PLL d'ordre un. B. (10 points) Indiquez dans le graphique fourni o nous trouvons les lments suivants : a. signal d'entre b. signal d'erreur c. signal de control d. estim des donnes e. estim de la phase C. (5 points) Comment pouvons nous changer le PLL pour assurer une erreur nulle asymptotiquement pour une phase qui varie linairement (une rampe)? GEL10280: Communications numriques 2004 Examen final Problme 2 (25 points sur 100) Voici la matrice de parit pour un code en bloc (7,4) : 1 1 P= 0 1 A. (5 points) B. (5 points) D. (5 points) 1 0 1 1 0 1 1 1 Combien d'erreurs de bit peuvent tre corriges? Donnez la matrice gnratrice pour un code systmatique. Quelle est la sortie (4 bits de message) du dcodeur pour C. (10 points) Donnez la table des syndromes. [0 1 0 0 0 11] Page 2 GEL10280: Communications numriques 2004 Examen final Problme 3 (20 points sur 100) L'usager dsir dans un systme DS-CDMA est situ l'extrmit d'une cellule, donc le contrle de puissance ne peut pas assurer que les signaux des interfrents arrivent avec la mme nergie que le signal de l'usager dsir. En effet, chaque interfrent est reu avec une nergie qui est le double de l'nergie de l'usager dsir. Pour un rapport signal--AWGN de 15 dB et un gain d'talement de 127, combien usagers peuvent tre supports et garantir un taux d'erreur de 10-3 pour l'usager dsir? Note : Q ( 3.1) = 10-3 Page 3 GEL10280: Communications numriques 2004 Examen final Problme 4 (30 points sur 100) Voici l'encoder et treillis d'encodage pour un systme TCM avec taux de code 2/3. Supposons que l'tat original des registres est zro. Voici l'espace du signal et le rcepteur pour la modulation 8PSK TCM (=.5) 011 (=.75) 001 010 (=.25) (=) 100 8PSK TCM 000 (=0) (=-.75) 110 111 (=-.5) 101 (=-.25) Correspondance des mots de codes symboles et (phase) Vous devez trouver la sortie du dcodeur TCM exploitant des dcisions souples dans un canal Gaussien. La squence des estims de la phase qui sort du rcepteur 8PSK est Page 4 GEL10280: Communications numriques 2004 Examen final [ -1.4 1.2 3 .8] Il faut trouver le chemin le plus probable dans le diagramme en treillis en utilisant des distances Euclidiennes. Il faut indiquer tous les rsultats de calcul dans la feuille des treillis vides qui vous est fournie. Indice : Distance locale dist ( u1,v1 ) = (u 1, x - v 1,x ) + ( u1,y - v 1,y ) = 2sin 2 2 ^ - 2 Page 5 Nom Matricule Partie A calculer les distances locales = a=00 -1.4 (1.3,1.6) (2 .0 , .1 7 ) 1.2 (____,____) (_ __ ,_ _ _) (_ __ ,_ __ 3 (____,____) (_ _ _ ,_ __ ) __ ) .8 (____,____) (_ __ ,_ _ _) ,__ _) __ Exemple: 0 + 1.4 2sin = 1.3 2 + 1.4 2sin = 1.6 2 2 + 1.4 2sin = 2.0 2 __ b=10 (_ ) (_ (_ (_ _ _ _ ,_ _) _, __(_ ( __ (_ __ ,_ _ _ __ ) ,_ ,_ _ (_ __ c=01 _) __ ,__ d=11 __ (_ (___,___) _ ,_ _) __ (_ (___,___) _ ,_ _) - 2 + 1.4 2sin = .17 2 Partie B liminer les distances locales plus grandes ,_ __ ) _) _) = a=00 -1.4 (1.3,--) (-, .1 7) 1.2 (____,____) (_ __ ,_ _ _) (_ __ ,_ __ 3 (____,____) (_ _ _ ,_ __ ) __ ) .8 (____,____) (_ __ ,_ _ _) __ (...

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