Signal Detection Algorithm Based On Spearman's Footrule Correlation Coefficient In Impulsive Noise

Target signal extraction in the background of noise is a research hotspot in the field of information processing.It has a wide and important application in the fields of radar communication systems,underwater sonar,voice,medical diagnosis and so on.When designing the signal detector at the receiving end of the wireless system,the mathematical model of the noise background data should be established first.Due to the non-Gaussian and impulsive nature of real noisy data,Gaussian distributed noise is no longer suitable for modeling noisy data.In order to obtain better detection performance in practical applications,it is particularly important to study the impulsive noise.However,after consulting relevant literature,it is found that the current signal detector based on impulsive noise has shortcomings such as poor detection effect and complicated operation in its design and implementation method,so it has low practical value in engineering practice.In order to solve the above problems,this thesis adopts symmetric ?-stable distribution,Middleton standard A noise distribution,contaminated Gaussian model distribution to model the actual impulsive noise,and proposes a new detector based on Spearman's simple correlation coefficient(Spearman's Footrule,SF).and the analytical form of the mean and variance under the null hypothesis are derived in the scenario of practical impulsive noise.In order to further understand its properties,Monte Carlo experimental simulations not only validate our theoretical findings but also demonstrate the advantages of SF in the aspect of: 1)Without the prior knowledge of noise distribution,the false alarm probability can be accurately controlled.2)It has better performance than some classical detectors under impulsive noise.3)The theoretical and experimental results show that SF performs comparably in the presence of impulsive noise.This thesis studies the signal detection technology under impulse noise,and explores the signal detection performance of SF under impulsive noise interference.First of all,the theoretical analysis gives the theoretical expressions of the mean and variance under the null hypothesis of Spearman's Footrule(SF),Spearman(SR)and Kendall's correlation coefficient(KT)under the mixed Gaussian model,and in the simulation experiment and results chapter of the paper,the Monte Carlo experiment is used to verify the accuracy of the theoretical derivation results.Secondly,on the basis of the above theory,we further give the exact detection threshold expression of the SF method and the theoretical expression of the commonly used indicators for detection performance evaluation,including detection probability,false alarm probability,and receiver operating characteristics.At the same time,the results of the null hypothesis distribution of SF show that SF has a constant false alarm probability,that is,the null hypothesis distribution of SF has nothing to do with the noise distribution.Distribution independence is a significant feature of this method.Using this property,the solution process of the detection threshold can be simplified.When applying this detection method,only the sample size needs to be determined to obtain an accurate detection threshold without considering the real received signal data.What distribution does it follow.Finally,in the experimental results section,Monte Carlo experiments are used to verify the feasibility and effectiveness of the detection method proposed in this paper.The detection performance of the detection method under different noise types is analyzed through simulation experiments,and several sets of comparison experiments are carried out with other classical detectors.The experimental results show that SF has better performance and better robustness than some classical detectors under impulse noise.