Optimal detection of digitally modulated signals

In this paper optimal detectors are derived and analyzed for the general class of digitally modulated signals in which the sequence of symbols is unknown a priori and information data are not of interest. The detectors test the signal present condition in background white Gaussian noise versus the null condition of noise alone. Particular attention is focused upon cases in which the SNR per symbol is low compared to unity. The models employed herein are sufficiently general to include most forms of spread-spectrum signals as well as other digital type communication signals.