Binary Composite-hypothesis Testing

Abstract

The communication detection systems discussed thus far have been describable in terms of deciding between a simple hypothesis and a simple alternative. In this section we shall consider binary decision rules which are describable in terms of a composite hypothesis versus a composite alternative. More precisely, by simple hypothesis is meant that under the assumed hypothesis the probability distribution of the test data is completely specified. When the assumed hypothesis does not specify completely the probability distribution of the obtained data, the hypothesis is called composite. Composite-hypothesis testing for binary systems results in a generality in that the signal space is partitioned into two disjoint subsets Ω ₀ and Ω ₁, each of which may contain an arbitrarily large number of signals. For examples, Ω ₀ may consist of a class of time waveforms characterized by an unknown parameter, say s ₀(t;m, where m is an unknown random variable or vector; the same is true for Ω ₁.