Lecture 12: Detection of Signals With Random Parameters

In the previous lecture the detection of deterministic signals was dealt with. In this lecture, the focus will be on deciding between signals that are known except for a set of unknown random parameters. For this situation the hypothesis testing problem can be conveniently written as, (1) where Θ is an unknown parameter taking values from a parameter set Λ. Density of Θ is ω j under the hypothesis H j , j ∈ {0, 1}. Moreover, N is random noise which is independent of the signal and hence independent of Θ. The likelihood ratio for (1) is given by,