A Signal-to-Noise Property of Binary Decisions

Abstract

THE statistical theory of Neyman and Pearson¹, which uses the likelihood ratio in making binary decisions, has proved very valuable when applied to the physical problem of detecting a signal in noise². This theory uses error probabilities as the basic criterion of performance in detection and tends to suggest that the attention given to the signal-to-noise ratio in older approaches is now outmoded. The purpose of this communication is to point out that, while a maximum signal-to-noise property is not any longer to be considered necessary in an optimum receiver for detection, a suitably formulated signal-to-noise requirement is sufficient to lead to a likelihood ratio receiver. This conclusion rests on a fully general property of the Neyman–Pearson binary decision theory which seems to have escaped previous notice.