Signal Detection Methods Based On Rank Correlation In Non-Gaussian Noise

Signal detection under noise background is a research hotspot in the field of signal processing and has a wide range of important applications in wireless systems such as mobile communications,radar,and sonar.Affected by the central limit theorem,traditional signal detection usually assumes that the background noise obeys a Gaussian distribution.However,this assumption is not always valid in real-world scenarios.Theoretical studies and experimental measurement results have shown that the background noise has large outliers,showing impulse characteristics in the time domain,and non-Gaussian behavior in the distribution with heavy tails.Due to the impulsive and non-Gaussian character of real noisy data,the Gaussian distribution is no longer suitable for modeling noisy data.As a result,detectors designed under the assumption of Gaussian noise will suffer significant performance loss in practical applications due to the mismatch between the assumed distribution and the distribution of the actual noise data.To obtain better detection performance in practical applications,the research on signal detection under impulse noise is particularly important.In terms of model selection for noise,it has been shown that the Middleton Class-A distribution(MCA)and the Gaussian mixture model(CGM)can model impulse noise well.However,the design and implementation of the optimal signal detector under the above-mentioned impulse noise distribution is complicated and has no practical engineering value.Therefore,it is necessary to study a simple and achievable sub-optimal detection scheme to reduce the complexity while ensuring the detection performance and meeting the requirements of fast real-time detection.In this thesis,we investigate the rank-based signal detection method in non-Gaussian noise environment.Firstly,in the first two chapters,the background of signal detection and the challenges and technical difficulties encountered so far are introduced,leading to the significance of studying new detectors.This is followed by a summary of the current state of research on signal detection methods and an introduction to the basic principles of signal detection,commonly used mathematical models for non-Gaussian noise and existing established signal detection techniques.Chapter 3 introduces the concept,definition and properties of the rank correlation statistic to provide a basis for its use as a signal detection method.Subsequently,from the perspective of addressing the limitations of existing methods,we propose stable suboptimal signal detection methods based on the rank statistic that can be adapted to a variety of scenarios,and provide a comprehensive analysis of their signal detection performance from both theoretical and simulation perspectives.The main findings of the thesis are summarised as follows.1.In view of the shortcomings of the existing detectors under non-Gaussian noise,such as complex design,high computational complexity and noise sensitivity,this thesis proposes a signal detection method based on Spearman correlation(SR)and Kendall correlation(KT).The method uses the ranking information of the received signal and the transmitted signal to construct the statistics,which are simple to calculate and easy to implement and meet the basic engineering requirements.In addition,we derive the analytical expressions for the mean and variance of SR and KT under two non-Gaussian noise models,MCA and CGM respectively.Based on these theoretical results,the expression of false alarm probability,detection probability,asymptotic efficiency,and ROC curve are given.These theoretical expressions of detection performance evaluation indicators provide a theoretical basis for the quantitative analysis of detection performance.Theoretical and simulation results show that 1)The null hypothesis distribution of SR and KT is noise-free,only relate to the length of the signal.This noise distribution-independent feature can simplify the solution process of the detection threshold and achieve constant false alarm detection;2)SR and KT are equivalent in terms of asymptotic relative efficiency,which means their detection performance is consistent;3)SR and KT can effectively detect signals in noise,they can achieve comparable detection performance to that of matched filters under Gaussian noise,and fill the gap between existing detectors and state-of-the-art detectors under non-Gaussian noise.To further reduce the computational complexity of the rank detection method,this thesis designs a parallel computing framework of SR based on the generalized correlation coefficient by taking advantage of the fact that each part of the generalized correlation coefficient is independent of the other.First,some parameters of the generalized correlation coefficient are replaced to obtain the equivalent expression of SR,and then a suitable parallel operation circuit implementation architecture is proposed based on the equivalent expression.The improved expression can effectively simplify the operation circuit,improve operation efficiency,and promote the engineering application of SR.2.To solve the problem of detection performance degradation caused by SR and KT not fully utilizing the useful amplitude information of the transmitted signal,this thesis proposes a method based on Gini correlation and Pearson rank variable correlation that utilizes the amplitude information of the transmitted signal and the rank information of the received signal.Under the MCA model and the CGM model,we established analytical expression of the mean and variance of the GC detector under the null and alternative hypotheses,which lay a theoretical foundation for subsequent research.Then,according to the results of the null hypothesis mean and variance,combined with the central limit theorem,it is proved that the null hypothesis distribution of GC is independent of the noise distribution and has the characteristics of constant false alarm detection.Secondly,a detection performance evaluation indicator system of GC is established based on the theoretical results of the alternative hypothesis.The detection performance of GC is systematically analyzed from a theoretical perspective,and the differences from the performance of the parametric best detector are explored.Theoretical results show that GC can achieve 93% efficiency to the optimal detector under the assumption of very low SNR in Gaussian noise,and at least 75% to the optimal detector under the assumption of extremely low SNR in non-Gaussian noise.Finally,the three rank correlation detectors are compared with the current mainstream detectors through a typical delay estimation application,which proves the effectiveness of the rank correlation statistic in practical applications.