Optimum classifier for M-ary PSK signals

An optimum classifier is designed to classify the general M -ary phase-shift keyed (MPSK) signal buried in additive white Gaussian noise. The classification problem is treated as an N-ary (N=1+log₂ M) hypothesis testing problem, and the performance of this optimum classifier is expressed in terms of the probability of misclassification. One case illustrates the capability of this classifier, and this optimum classifier and several other algorithms are compared. The structure of this classifier is flexible and is easy to expand. Theoretical analysis shows that for a finite observation interval the performance of this proposed classifier is reasonable even in a noisy environment. Further improvement in performance can be obtained by increasing the length of the observation interval