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

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. >