Least Lp-norm impulsive noise cancellation with polynomial filters

Abstract

It is a common experience in signal processing that impulsive noise observed in various natural environments cannot be described with the Gaussian distribution. Recently, a heavy tailed distribution namely the α- stable distribution has become a popular model for impulsive noise since it agrees very well with empirical data and is also theoretically justified with the generalised central limit theorem. Although, it is a generalisation of the Gaussian distribution and shares important properties with it, the non-Gaussian α-stable distribution differs from the Gaussian distribution in many ways, the most notable of which is the lack of finite second-order statistics. Therefore, the classical techniques based on linear least-squares estimation perform very poorly in impulsive noise elimination. In this paper, motivated by some properties of the α-stable distribution, new techniques based on linear and nonlinear least l p -norm estimation are introduced and several simulation results are presented which show that least l p -norm estimation with a Volterra-type prediction filter performs significantly better than the conventional linear techniques such as linear least-squares estimation and than nonlinear least-squares estimation. A new measure for signal distortion in impulsive noise, namely fractional order signal-to-noise ratio (FSNR) is also introduced to quantify the performance of various impulsive noise cancellation algorithms.