Noise enhancement in joint detection and estimation systems

Adding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In this study, a noise enhanced joint detection and estimation system is investigated. Maximization of the system performance is defined as an optimization problem. Statistical characterization of the optimal additive noise distribution is determined. A condition under which performance of the system cannot be improved is obtained. The proposed optimization problem is approximated as a linear programming (LP) problem. With an illustrative numerical example, a performance comparison between the noise enhanced system and the original system is performed to support the theoretical analysis.