Nonparametric density estimation and detection in impulsive interference channels. I. Estimators

Discusses the development of effective nonparametric probability density estimators and detectors for impulsive noise channels, In the present paper, nonparametric probability density estimators are developed for both the instantaneous amplitude and envelope densities of impulsive interference waveforms. These kernel-based density estimators use the known properties of the impulsive noise densities to be estimated in their construction and, in so doing, yield estimates that closely approximate the true densities for small sample sizes. In fact, from an extensive small-sample-size simulation study, it is seen that the proposed nonparametric schemes significantly outperform the standard estimators, A method for comparing the L₁-performance of nonparametric and parametric-based density estimators is also derived in the paper. Use of this method shows that the performance of the proposed nonparametric estimators is near that of their optimum (efficient) parametric counterparts for a wide variety of impulsive noise models (including the class A model, the Johnson S_u model, and the Gaussian-Laplacian mixture)