广义相关检测器中噪声增强条件的研究

为了检测在噪声存在的情况下弱信号是否出现,本文对噪声增强广义相关检测器性能的条件进行了研究.通过观测数据,给定虚警概率,证明了一类广义相关检测器中随机共振现象的存在性,并给出了噪声增强广义相关检测器性能的必要条件及求解最优尺度噪声强度的解析方程.研究结果表明,当观测数据足够大时,广义相关检测器的检测概率是检测功效的单调函数;噪声与检测器结构参数都可以视为一种增强检测器性能的调谐因素.该方法作为一种新的信号检测技术,对非线性信号处理的发展具有重要意义.

Study of Noise-Enhanced Conditions for the Generalized Correlation Detector

In order to detect the weak signal in additive white noise, this paper studies the noise-enhanced detection condition for a generalized correlation detector. Given the false probability, the occurrence of sto- chastic resonance effect is demonstrated in the considered generalized correlation detector, and the positive derivative of the efficacy with respect to the noise level is the necessary condition of the detector perform- ance enhancement. The optimal scaled-noise level that maximizes the detector efficacy can be analytically solved. The obtained results show that, with a large number of observations, the detection probability of a generalized correlation detector is a monotonically function of the detection efficacy for detecting the weak signal in additive white noise. Noise, as the same as the detector parameters, is a tunable factor of enhan- cing the detector performance. The noise-enhancement method becomes a novel signal detection technique, which is meaningful for the field of nonlinear signal processing.