Novel Nonlinearity Based on Gaussianization and Generalized Matching for Impulsive Noise Suppression

Abstract

This paper proposes a novel design of nonlinearity preprocessor for impulsive noise suppression. This design is developed based on Gaussianization of noise distribution and generalized matching of the desired signal. The Gaussianization and generalized matching (GGM) nonlinearity has two advantages. First, the GGM nonlinearity is robust and only slightly suboptimal in various models of impulsive noise. Contrarily, traditional nonlinearity is generally designed and limited to a specific noise model. Second, the GGM can be designed in a nonparametric way without noise models, but just based on noise samples and kernel density estimation. Thus, the GGM design is more robust and less sensitive to noise models than existing parametric nonlinearity approaches. Three widely-used models of impulsive noise, i.e., the $\alpha $ -stable distribution, the Middleton class-A model, and the Gaussian mixture model are employed for numerical demonstration. The simulation results show that the GGM nonlinearity is slightly suboptimal relative to the locally optimal detector, whereas traditional clipper and a blanker are not robust in different models. For the case when the noise distribution is unknown, the GGM design can outperform the locally optimal detectors which are based on incorrect parameters or models. Hence, the GGM nonlinearity is a promising choice in practice when neither the noise model nor the parameter is known a prior.