NONPARAMETRIC DENSITY-ESTIMATION AND DETECTION IN IMPULSIVE INTERFERENCE CHANNELS .1. ESTIMATORS

This study is concerned with the development of effective nonparametri c probability density estimators and detectors for impulsive noise cha nnels. In this part (Part I) of this two-part study, nonparametric pro bability density estimators are developed for both the instantaneous a mplitude and envelope densities of impulsive interference waveforms. T hese kernel-based density estimators use the known properties (e.g., s ymmetry, heavy tails, etc.) of the impulsive noise densities to be est imated in their construction and, in so doing, yield estimates that cl osely 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 standa rd estimators. A method for comparing the L1-performance of nonparamet ric and parametric-based density estimators is also derived in this pa per (Part I). Use of this method shows that the performance of the pro posed nonparametric estimators is near that of their optimum (efficien t) parametric counterparts for a wide variety of impulsive noise model s (including the Class A model, the Johnson S. model, and the Gaussian -Laplacian mixture). (The utility of the proposed estimators in variou s detection problems is investigated in Part II of this study.)