ABSTRACT
This chapter deals with a finite number of samples. The samples are also called data or observations. The data is used to decide which hypothesis, that is, which signal or symbol is true and hence was transmitted. Initially, the Bayes’ detector is derived and then its structure is used as the basic building block to motivate other detection schemes. These other detection schemes are based on the maximum a priori, the maximum likelihood, and the minimum probability of error, the Min-Max, or the Neyman-Pearson criterion. This detection criterion is used in binary communication problems, where the cost of making an error that is calling a true zero a one or calling a true one a zero is the same and the cost of making a correct decision is zero. The basic receiver operating characteristic curve is a two-dimensional graph of probability of detection (PD) versus the probability of false alarm (PFA).
