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.

在本文中，研究了对于一般非线性系统，在Neyman–Pearson（NP）准则下，随机共振对最优检测的影响。为此，提出了一种噪声增强的检测优化问题，用于在错误警报的概率受到恒定约束的情况下使检测的概率最大化，其中将附加噪声添加到非线性系统输入中，并根据噪声来做出最终决策。根据NP标准输出系统。首先，推导了经噪声修正的NP决策规则。由于一个加性噪声对应于一个噪声修改的NP决策规则，因此可以将噪声修改后的NP决策规则视为加性噪声的函数。然后，简单讨论了通过提出的噪声修正决策方法在NP准则下最优检测性能的可改进性。最佳加性噪声被推导为不超过两个常数向量的随机信号，并且还确定了相应的经噪声修改的NP决策规则。最后，对正弦变换系统和幅值极限系统的原始和经过噪声修改的最优NP决策解决方案之间的性能进行了比较，以说明理论结果。