Stochastic resonance benefits in signal detection under MAP criterion

In this paper, a noise enhanced hypothesis testing framework for a general nonlinear sys-tem is established under the Maximum A Posteriori (MAP) criterion, where an additive noise is added to the nonlinear system input and then the optimal MAP test for the dis-crimination between two hypotheses is made based on the noise modified nonlinear sys-tem output. The improvability of the noise modified MAP detection system is presented first, and then the noise enhanced decision solutions for the performance optimization are explored under three kinds of different cases. In opt SR case, the minimization of the av-erage error probability is studied, and the optimal additive noise is proved as a constant vector, i.e. its probability distribution function is expressed by Dirac type delta(n-n(o)). Further-more, constraints on detection and false-alarm probabilities are considered in the mini-mization problem in UCSR and CSR cases. The difference is that no randomization between different detectors is allowed in UCSR case, while the randomization between detectors is feasible in CSR case. Finally, numerical results for sine transform and amplitude limit sys-tems are given to confirm the theoretical results. The performance comparisons of no SR (i.e., in the absence of additive noise), opt SR, CSR and UCSR cases demonstrate that the SR phenomenon could occur to improve the optimal MAP decision under certain conditions. (C) 2021 Elsevier B.V. All rights reserved.