Statistische Nachrichtentheorie: Erster Teil Signalerkennung Und Parameterschätzung
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1. Aufgaben der statistischen Nachrichtentheorie.- 1.1 Detektion.- 1.2 Estimation.- 1.3 Entwurfsansätze.- 2. Grundbegriffe der statistischen Systemtheorie.- 2.1 Begriffe der Statistik.- 2.2 Transformationen von Zufallsvariablen und Prozessen.- 3. Signaldarstellung durch Vektoren.- 3.1 Darstellung von Prozessen durch Vektoren.- 3.2 Vektordarstellung von M Signalen.- 3.2.1 Gram-Schmidt-Verfahren.- 3.3 Irrelevante Information.- 3.4 Vektorkanäle.- 3.5 Zusammenfassung.- 4. Signalerkennung (Detektion).- 4.1 Binäre Detektion.- 4.1.1 Bayes-Kriterium.- 4.1.2 Maximum-a-posteriori-Kriterium (MAP).- 4.1.3 Neyman-Pearson-Kriterium.- 4.1.4 Empfängerarbeitscharakteristik (ROC).- 4.2 Multiple Detektion.- 4.2.1 MAP-Prinzip für multiple Detektion.- 4.2.2 Entscheidungsregel bei Gau prozessen.- 4.2.3 Wahl der Signalvektoren.- 4.2.3.1 Signalvektorkonfiguration mit rechtwinkligen Entscheidungsräumen.- 4.2.3.2 Orthogonale und damit verwandte Signalvektorkonfigurationen.- 4.2.4 Abschätzung der Fehlerwahrscheinlichkeit.- 4.2.5 Vergleich der Signalvektorkonfiguration.- 4.3 Realisierung der Empfänger für die Detektion.- 4.4 Anwendung von Detektionsprinzipien bei der Datenübertragung.- 4.4.1 Vergleich von digitalen Modulationsverfahren.- 4.4.2 Daten-Modem zur Übertragung von Datenblöcken.- 4.4.2.1 Berechnung der Fehlerwahrscheinlichkeit P (F).- 4.5 Zusammenfassung.- 5. Parameterschätzung (Estimation).- 5.1 Schätzung von Parametern mit bekannter Dichtefunktion (Bayes-Kriterium).- 5.1.1 Kostenfunktion des quadratischen Fehlers.- 5.1.2 Kostenfunktion des absoluten Fehlers.- 5.1.3 Kostenfunktion mit konstanter Bewertung gro er Fehler.- 5.1.4 Invarianz des optimalen Schätzwertes bezüglich einer Klasse von Kostenfunktionen.- 5.2 Schätzung von Parametern ohne jede A-priori-Information (Maximum-Likelihood-Schätzung).- 5.3 Der minimale mittlere quadratische Schätzfehler.- 5.3.1 Minimale Fehlervarianz bei unbekannter A-priori-Dichte.- 5.3.2 Minimaler mittlerer quadratischer Fehler bei bekannter A-priori-Dichte.- 5.4 Multiple Parameterestimation.- 5.4.1 Schätzverfahren.- 5.4.1.1 Parametervektor mit bekannter A-prioriDichte.- 5.4.1.2 Parametervektor ohne A-priori-Information.- 5.4.2 Schätzfehler.- 5.4.2.1 Minimale Fehlervarianz. Parametervektor ohne A-priori-Information.- 5.4.2.2 Mittlerer quadratischer Fehler. Parametervektor mit bekannter A-priori-Dichte.- 5.5 Lineare Schätzeinrichtungen.- 5.5.1 Gau -Markoff-Theorem.- 5.5.2 Geometrische Interpretation des Gau -Markoff-Theorems.- 5.5.3 Additive unkorrelierte Störungen.- 5.5.4 Parametervektor ohne A-priori-Information.- 5.5.5 Verbesserung der Schätzwerte.- 5.5.6 Verbesserte Schätzwerte: Kalman Formel.- 5.6 Anwendung der Parameterschätzung bei der Datenübertragung.- 5.6.1 Automatische Verstärkungsregelung (AGC).- 5.6.2 Entzerrung von linearen Übertragungskanälen.- 5.6.2.1 Impulsantwort des Entzerrers.- 5.6.2.2 Schätzung der Kanalparameter.- 5.7 Zusammenfassung.- Aufgaben.- Namen- und Sachverzeichnis.
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