Stochastic Resonance Effect in Optimal Decision Solution Under Neyman–Pearson Criterion
Stochastic Resonance Effect in Optimal Decision Solution Under Neyman–Pearson Criterion
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DOI：
10.1007/s00034-020-01644-y
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Ting Yang;Yu Li;Shiju Yang;Shujun Liu
中科院分区：
文献类型：
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作者：
Ting Yang;Yu Li;Shiju Yang;Shujun Liu
研究了一般非线性系统在Neyman-Pearson（NP）准则下随机共振对最优检测的影响。为此，噪声增强的检测优化问题，最大限度地提高检测概率下的虚警概率的恒定约束制定，其中添加剂噪声被添加到非线性系统的输入和最终的决定是根据NP标准的系统输出的基础上。首先推导了噪声修正的NP判决规则。由于一个加性噪声对应于一个噪声修改的NP判定规则，因此噪声修改的NP判定规则可以被视为加性噪声的函数。然后，在NP准则下的最佳检测性能的改善，通过建议的噪声修改的决策解决方案进行了简单的讨论。最佳加性噪声被推导为不超过两个常向量的随机信号，并确定了相应的噪声修正NP判决规则。最后，对正弦变换系统和幅值限制系统进行了噪声修正后的最优NP判决解与原NP判决解的性能比较，以说明理论结果。
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.