Stochastic Resonance Effect in Optimal Decision Solution Under Neyman–Pearson Criterion

Abstract

In this paper, stochastic resonance effect on the optimal detection under Neyman–Pearson (NP) criterion is investigated for a general nonlinear system. To this end, a noise enhanced detection optimization problem for maximizing the probability of detection under a constant constraint on the probability of false-alarm is formulated, where an additive noise is added to the nonlinear system input and the final decision is made based on the system output according to the NP criterion. Firstly, the noise modified NP decision rule is derived. Since one additive noise corresponds to one noise modified NP decision rule, the noise-modified NP decision rule can be viewed as a function of the additive noise. Then, the improvability of the optimal detection performance under NP criterion via the proposed noise-modified decision solution is simply discussed. The optimal additive noise is deduced as a random signal of no more than two constant vectors and the corresponding noise-modified NP decision rule is also determined. Finally, the performance comparisons between the original and the noise-modified optimal NP decision solutions for the sine transform system and the Amplitude limit system are made to illustrate the theoretical results.