Noise benefits in joint detection and estimation problems

• We investigate noise benefits for joint detection and estimation systems.
• We obtain the optimal additive noise in Bayesian and NP detection frameworks.
• We formulate a linear programming (LP) problem to obtain the optimal additive noise.
• We specify cases in which additive noise can or cannot improve system performance.

Adding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In the literature, noise benefits have been studied for detection and estimation systems separately. In this study, noise benefits are investigated for joint detection and estimation systems. The analysis is performed under the Neyman–Pearson (NP) and Bayesian detection frameworks and according to the Bayesian estimation criterion. The maximization of the system performance is formulated as an optimization problem. The optimal additive noise is shown to have a specific form, which is derived under both NP and Bayesian detection frameworks. In addition, the proposed optimization problem is approximated as a linear programming (LP) problem, and conditions under which the performance of the system can or cannot be improved via additive noise are obtained. With an illustrative numerical example, performance comparison between the noise enhanced system and the original system is presented to support the theoretical analysis.