MSE lower bounds conditioned by the energy detector

A wide variety of processing incorporates a binary detection test that restricts the set of observations for parameter estimation. This statistical conditioning must be taken into account to compute the Cramér-Rao bound [1] (CRB) and more generally, lower bounds on the Mean Square Error (MSE) [2]. Therefore, we propose a derivation of some lower bounds — including the CRB — for the deterministic signal model conditioned by the energy detector [3] widely used in signal processing applications.