Optimal Noise Benefit in Composite Hypothesis Testing under Different Criteria

被引：0

作者：

Liu, Shujun ^{[1
]}

Yang, Ting ^{[1
]}

Tang, Mingchun ^{[1
]}

Liu, Hongqing ^{[2
]}

Zhang, Kui ^{[1
]}

Zhang, Xinzheng ^{[1
]}

机构：

[1] Chongqing Univ, Coll Commun Engn, Chongqing 400044, Peoples R China

[2] Chongqing Univ Posts & Telecommun, Chongqing Key Lab Mobile Commun Technol, Chongqing 400065, Peoples R China

来源：

ENTROPY | 2016年 / 18卷 / 08期

基金：

中国国家自然科学基金;

关键词：

additive noise; composite hypothesis testing; restricted Neyman-Pearson (NP); QUANTUM STOCHASTIC RESONANCE; SIGNAL-DETECTION; RATIO GAIN; INFORMATION; SYSTEMS; NEURONS;

D O I：

10.3390/e18080400

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The detectability for a noise-enhanced composite hypothesis testing problem according to different criteria is studied. In this work, the noise-enhanced detection problem is formulated as a noise-enhanced classical Neyman-Pearson (NP), Max-min, or restricted NP problem when the prior information is completely known, completely unknown, or partially known, respectively. Next, the detection performances are compared and the feasible range of the constraint on the minimum detection probability is discussed. Under certain conditions, the noise-enhanced restricted NP problem is equivalent to a noise-enhanced classical NP problem with modified prior distribution. Furthermore, the corresponding theorems and algorithms are given to search the optimal additive noise in the restricted NP framework. In addition, the relationship between the optimal noise-enhanced average detection probability and the constraint on the minimum detection probability is explored. Finally, numerical examples and simulations are provided to illustrate the theoretical results.

引用

页数：18

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