脉冲噪声下基于改良Kendall’s Tau的随机信号检测

Random Signal Detection Based on Improved Kendall’s Tau under Impulsive Noise

摘要: 在双通道信号检测领域，肯德尔秩相关系数(Kendall’s Tau, KT)作为一种检测器，对含脉冲噪声的信号具有显著的鲁棒性。然而，当通道间的噪声存在相关性时，KT的检测性能仍有待提升。为此，本文提出一种改进的肯德尔秩相关系数(Improved Kendall’s Tau, IKT)检测器，在KT的基础上引入了阈值可调节的硬限幅函数。同时采用二元高斯混合模型(Gaussian Mixture Model, GMM)模拟两通道间噪声的相关性及脉冲特性，深入探讨了IKT在该模型下的统计性质，并建立了针对双通道高斯随机信号检测问题的虚警率和检测概率的解析式。通过蒙特卡罗实验与高斯噪声下性能最优的匹配滤波器(Matched Filter Detector, MFD)、脉冲噪声下具有鲁棒性的极性重合相关器(Polarity Coincidence Correlator, PCC)、KT的接收机工作特性(Receiver Operating Characteristic, ROC)曲线下面积(Area Under the Curve, AUC)进行比较，表明IKT在含相关性高斯噪声的信号检测中相较于PCC在AUC上表现出12.9%左右的提升，相较于KT的提升约为4.8%。在含相关性脉冲噪声的信号检测中相较于PCC的AUC提升约为8.3%，相较于KT的提升约为1.6%，从而验证了其优越性。

Abstract: In dual-channel signal detection, the Kendall’s Tau (KT) correlation coefficient is well-regarded for its robustness in handling signals affected by impulsive noise. However, its detection performance declines when there is noise correlation between channels. To address this limitation, this paper presents an Improved Kendall’s Tau (IKT) detector, which enhances the traditional KT by incorporating a threshold-adjustable hard limiting function. Furthermore, a bivariate Gaussian Mixture Model (GMM) is used to simulate the noise correlation and impulsive characteristics between the two channels. The statistical properties of IKT under this model are thoroughly analyzed, and analytical expressions for the false alarm rate and detection probability in dual-channel Gaussian random signal detection are derived. Monte Carlo simulations and comparisons with the matched filter detector (MFD), which is optimal for Gaussian noise, the polarity coincidence correlator (PCC), known for its robustness against impulsive noise, and the area under the curve (AUC) of the receiver operating characteristic (ROC) curve for KT, are performed. The results show that in the presence of correlated Gaussian noise, IKT achieves approximately a 12.9% improvement in AUC over PCC and a 4.8 % improvement over KT. In the presence of correlated impulsive noise, IKT shows about an 8.3% improvement in AUC over PCC and a 1.6% improvement over KT, thereby validating its superiority.