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 L/sub 1/-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/sub u/ model, and the Gaussian-Laplacian mixture).>

For pt. I see ibid., vol.42, no.2-4, p.1684-1697 (1994). Nonlinear processing significantly enhances detector performance in nongaussian noise relative to that of linear detectors. Several nonparametric detection schemes for impulsive noise channels are formulated using the nonparametric probability density estimators developed in Part I. The likelihood ratio test and the small-signal (locally optimum) nonlinearity provide the basis for the formulation of these nonparametric detection schemes. Several modifications to these basic strategies are used to compensate for inaccuracies in the density estimates. In particular, for the problem of detecting a known signal in impulsive noise, two modifications to the standard likelihood ratio test are considered: the first is adapted from robust statistics, whereas the second, the "L/sub 1/-error-based" detector is specifically formulated for use with density estimates. Both schemes are found to perform close to the optimum likelihood ratio detector for a wide variety of impulsive noise densities. From the merits of these two tests, a new detection scheme that approximates the locally optimum nonlinearity is then developed. This detector, which uses the nonparametric density estimators developed in Part I, is shown to perform very well for the wide variety of impulsive and heavy tailed densities considered in the study. This nonparametric-density-estimate-based detector is also shown to outperform more conventional nonparametric detectors in impulsive noise.>

A kernel-based density estimator for positive random variables is proposed and analyzed. In particular, a nonparametric estimator is developed which takes advantage of the fact that positive random variables can be represented as the norms of random vectors. By appropriately choosing the dimension of the assumed vector space, the estimator can be structured to exploit a priori knowledge about the density to be estimated. The asymptotic properties (e.g., pointwise and L/sub 1/-consistency) of this density estimator are investigated and found to be similar to the desirable features of the standard kernel estimator. An upper bound on the expected value of the L/sub 1/ error is also derived which provides insight into the behavior of the estimator. Upon using this upper bound, the optimal form for the estimator (i.e., the kernel function, the smoothing factor, etc.) is selected via a minimax strategy. In addition, this upper bound is used to compare the asymptotic performance of the proposed estimator to that of the standard kernel estimator and to boundary-corrected kernel estimators. Numerical examples illustrate that the proposed scheme outperforms the standard and boundary-corrected estimators for a variety of density types.>