In the a posteriori theory of reception, a posteriori probabilities and probability densities provide a complete description of the results of the receiving process. An ideal receiver, by definition, calculates and presents the a posteriori distribution of a desired quantity or quantities to an observer. Owing to the dependence of the a posteriori distribution on a priori information, which may not always be available, the concept of a sufficient receiver was introduced. A sufficient receiver calculates and presents to the observer a sufficient statistic; this statistic contains the essential information in the received waveform and permits the a posteriori distribution to be computed when the a priori statistics are known. When reception occurs in additive Gaussian noise, the a posteriori theory leads to sufficient receivers that employ matched filters. However, the theory has been found to be useful in many situations where the optimum receiver structure is not obvious.

Chapter Contents:

• 7.1 Introduction
• 7.2 Information Measure - Discrete Case
• 7.3 Information Measure - Continuous Case
• 7.4 Ideal Receiver
• 7.5 The A Posteriori Distribution in the Presence of White Gaussian Noise
• 7.6 Sufficient Receiver (Correlation Receiver)
• 7.7 Estimating Radar Range of a Stationary Target with Known Cross Section
• 7.8 A Posteriori Detection
• 7.9 Band-Limited Signals in Colored Noise
• 7.10 Arbitrary Signals in Colored Noise
• 7.11 Signals Perturbed by a Random Channel
• 7.12 Summary
• Problems
• References

Inspec keywords: matched filters; probability; Gaussian noise; radar receivers

Other keywords: probability densities; posteriori distribution; priori statistics; optimum receiver structure; posteriori probabilities; matched filters; additive Gaussian noise; reception posteriori theory; receiving process

Subjects: Filtering methods in signal processing; Other topics in statistics; Radar equipment, systems and applications