Classical Signal Detection Theory

Abstract

It can be said with confidence that classical signal detection theory has two avenues, with each differing in the investigative technique employed. The first avenue of investigation, which we will call the Gaussian approach to signal detection in noise, is based on the assumption that the signals, interference, and noise being studied are Gaussian processes with known statistical characteristics. The second avenue of investigation, which we will call the Markov approach to signal detection in noise, is based on the assumption that the signals, interference, and noise to be analyzed are Markov processes. It should be noted that the assumption about Gaussian signals, interference, and noise holds true for various applications of signal detection theory. Furthermore, since any continuous stochastic process may be approximated by a Markov process with a corresponding order within the given accuracy limits, the assumption about Gaussian and Markov processes for signals, interference, and noise simultaneously often holds good for various applications of signal detection theory. Under this assumption, the design and construction of optimal detectors or receivers can be performed using the techniques of the Gaussian and Markov approaches to signal detection theory. However, as it is out of the question to define which techniques are more convenient for problems of construction and analysis of optimal detectors from the viewpoint of noise immunity, Gaussian and Markov approaches to signal detection theory are of equal importance.