Non-Gaussian mixtures are commonly used as parametric models for impulsive interference superimposed on a Gaussian background. In this study, the problem of efficient batch and recursive estimation of the parameters of such mixtures via minimization of the Kullback-Leibler distance is considered. The maximum-likelihood estimator (MLE) provides the starting point for the development of these estimators. First, it is shown that the MLE yields consistent estimates of the parameters, despite the existence of multiple roots in the Kullback-Leibler distance function. Since direct implementation of the MLE is difficult, an alternative estimator, designed with the objective of maximizing the likelihood function, is proposed. A simulation study of the proposed estimator reveals that it performs very well in terms of attaining the Cramer-Rao lower bound. Stochastic approximation is also considered in this study. A "complete data" modification to the standard recursion is presented, which greatly facilitates its implementation. Three initiating estimators are developed for these recursions: an iterative likelihood-based scheme, a batch estimator that uses a histogram of the data, and an iterative scheme that integrates the concept of complete data into the method-of-moments estimator. Upon initiating the modified stochastic approximation recursion with these estimators, it is seen that excellent estimates of the parameters can be obtained.

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.>

The Class A Middleton noise model is a commonly used, statistical-physical parametric model for impulsive interference superimposed on a Gaussian background. An optimum and practically efficient batch estimator of the Class A parameters is proposed, In particular, this estimator is shown to yield strongly consistent and asymptotically efficient estimates of the Class A parameters. Moreover, via an extensive simulation study, it is seen that the proposed estimator yields excellent estimates of the Class A parameters for moderate sample sizes.>

The Class A Middleton noise model is a commonly used statistical-physical, parametric model for non-Gaussian interference superimposed on a Gaussian background. In this study, the problem of efficient estimation of the Class A parameters for small sample sizes is considered. The proposed estimator is based on the EM algorithm, a two-step iterative estimation technique that is ideally suited for the Class A estimation problem since the observations can be readily treated as incomplete data. For the single-parameter estimation problem, a closed-form expression for the estimator is obtained. Furthermore, for the single-parameter estimation problem, it is shown that the sequence of estimates obtained via the EM algorithm converges, and a characterization of the point to which the sequence converges is given. In particular, it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest, then it must be a stationary point of the traditional likelihood function. In addition, for both the single-parameter and two-parameter estimation problems, the small-sample-size performance of the proposed EM algorithm is examined via an extensive simulation study.>

The Class A Middleton model is a widely accepted statistical-physical parameteric model for impulsive interference superimposed on a Gaussian background. In the present work, a recursive decision-directed estimator for online identification of the parameters of the Class A model is proposed. This estimator is based on an adaptive Bayesian classification of each of a sequence of Class A envelope samples as an impulsive sample or as a background sample. As each sample is so classified, recursive updates of the estimates of the second moment of the background component of the interference envelope density, the second moment of the impulsive component of the interference envelope density, and the probability with which the impulsive component occurs, are readily obtained. From these estimates, estimates of the parameters of the Class A model follow straightforwardly, since closed-form expressions for the parameters exist in terms of these quantities. The performance characteristics of this algorithm are investigated and an appropriately modified version is found to yield a recursive algorithm with excellent global performance.>

The problem of estimating the parameters of the Middleton Class A interference model is considered. On the assumption of the availability of a set of independent samples from Class A envelope distribution, the asymptotic performances of several estimation procedures are explored. From this analysis, estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient, whereas more efficient likelihood-based estimators are seen to be computationally unwieldy. However, an estimator that initiates likelihood iteration with the method-of-moments estimates is seen to overcome these difficulties in its asymptotic performance. Unfortunately, simulation of this third estimator for practical sample sizes reveals poor performance under these conditions. To overcome this lack of small-sample efficiency, a similar estimator that initiates likelihood iteration with physically motivated (but nonoptimal) estimates is also proposed. Simulation of this latter estimator for practical sample sizes indicates that near-optimal performance is attained by this technique.>