Fast estimation of the parameters of alpha-stable impulsive interference

We address the problem of estimation of the parameters of the recently proposed symmetric, alpha-stable model for impulsive interference. We propose new estimators based on asymptotic extreme value theory, order statistics, and fractional lower order moments, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms. The performance of the new estimators is theoretically evaluated, verified via Monte Carlo simulation, and compared with the performance of maximum-likelihood estimators.

[1]  David Middleton,et al.  Statistical-Physical Models of Electromagnetic Interference , 1977, IEEE Transactions on Electromagnetic Compatibility.

[2]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .

[3]  David Middleton,et al.  Statistical-Physical Models of Man-Made Radio Noise, Part I. First-Order Probability Models of the Instantaneous Amplitude , 1974 .

[4]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[5]  D. Middleton.  Procedures for Determining the Parameters of the First-Order Canonical Models of Class A and Class B Electromagnetic Interference [10] , 1979, IEEE Transactions on Electromagnetic Compatibility.

[6]  Edward J. Wegman,et al.  Topics in Non-Gaussian Signal Processing , 2011 .

[7]  P. Mertz.  Model of Impulsive Noise for Data Transmission , 1961 .

[8]  John B. Thomas,et al.  Detectors for discrete-time signals in non-Gaussian noise , 1972, IEEE Trans. Inf. Theory.

[9]  Pierre Zakarauskas.  Detection and Localization of Nondeterministic Transients in Time Series and Application to Ice-Cracking Sound , 1993 .

[10]  C. L. Nikias,et al.  Signal processing with fractional lower order moments: stable processes and their applications , 1993, Proc. IEEE.

[11]  Pierre Zakarauskas,et al.  Automatic extraction of spring‐time Arctic ambient noise transients , 1991 .

[12]  H. Bergström,et al.  On some expansions of stable distribution functions , 1952 .

[13]  Ioannis A. Koutrouvelis,et al.  Regression-Type Estimation of the Parameters of Stable Laws , 1980 .

[14]  E. Fama,et al.  Parameter Estimates for Symmetric Stable Distributions , 1971 .

[15]  W. DuMouchel.  On the Asymptotic Normality of the Maximum-Likelihood Estimate when Sampling from a Stable Distribution , 1973 .

[16]  David Middleton.  Canonical Non-Gaussian Noise Models: Their Implications for Measurement and for Prediction of Receiver Performance , 1979, IEEE Transactions on Electromagnetic Compatibility.

[17]  Chrysostomos L. Nikias,et al.  Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process , 1995, IEEE Trans. Commun..

[18]  David Middleton,et al.  Threshold Detection in Non-Gaussian Interference Environments: Exposition and Interpretation of New Results for EMC Applications , 1984, IEEE Transactions on Electromagnetic Compatibility.

[19]  S. James Press,et al.  Estimation in Univariate and Multivariate Stable Distributions , 1972 .

[20]  W. DuMouchel.  Estimating the Stable Index $\alpha$ in Order to Measure Tail Thickness: A Critique , 1983 .

[21]  A. Paulson,et al.  The estimation of the parameters of the stable laws , 1975 .

[22]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[23]  B. Stuck,et al.  A statistical analysis of telephone noise , 1974 .

[24]  Chrysostomos L. Nikias,et al.  Detection of impulsive stochastic transients over background noise , 1995, Signal Process..

[25]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[26]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[27]  Edward C. Field,et al.  Amplitude-Probability Distribution Model for VLF/ELF Atmospheric Noise , 1978, IEEE Trans. Commun..

[28]  Brian H. Maranda,et al.  The optimal power law for the detection of a Gaussian burst in a background of Gaussian noise , 1991, IEEE Trans. Inf. Theory.

[29]  B. Mandelbrot.  The Variation of Some Other Speculative Prices , 1967 .

[30]  L. Kurz,et al.  An Optimal Nonlinear Detector for Digital Data Transmission Through Non-Gaussian Channels , 1966 .

[31]  Ronald I. Verrall,et al.  Extraction of the seabed reflectivity function using ice cracking noise as a signal source , 1993 .

[32]  B. Brorsen,et al.  Maximum likelihood estimates of sym-metric stable distribution parameters , 1990 .

[33]  I. A. Koutrouvelis.  An iterative procedure for the estimation of the parameters of stable laws , 1981 .

[34]  L. Berry.  Understanding Middleton's Canonical Formula for Class a Noise , 1981, IEEE Transactions on Electromagnetic Compatibility.