In this work, the problem of optimum and near-optimum identification of the parameters of the Middleton Class A impulsive interference model is considered. In particular, under the assumption of the availability of a set of independent samples from the Class A envelope distribution, the problems of basic batch estimation of the Class A parameters, recursive identification of the parameters, and efficient estimation of the parameters for small sample sizes, are investigated. Within the context of basic batch estimation, several estimators of the parameters are proposed and their asymptotic performances 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 moderate sample sizes reveals poor performance under these conditions. To overcome this lack of moderate-sample-size efficiency, a similar estimator that initiates likelihood iteration with physically motivated (but nonoptimal) estimates is also proposed. Simulation of this latter estimator for moderate sample sizes indicates that near-optimal performance is obtained by this technique. Within the context of recursive estimation, a recursive decision-directed estimator for on-line 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 either an impulsive sample or as a background sample. The performance characteristics of this algorithm are investigated, and an appropriately modified version is found to yield a global, recursive estimator of the parameters that performs very well for all parameter vectors in the parameter set of interest. Within the context of efficient estimation for small sample sizes, an algorithm that has the potential of providing efficient estimates of the Class A parameters for small sample sizes is proposed. For the single-parameter estimation problem, it is shown that the sequence of estimates obtained via this algorithm converges, and a characterization of the point to which the sequence converges is given. For both the single-parameter and two-parameter estimation problems, it is also seen, via an extensive simulation study, that the proposed estimator yields excellent estimates of the parameters for small sample sizes. It is anticipated that the results of this research will have widespread impact in the areas of communication, radar, and sonar due to the common occurrence of impulsive noise channels in these systems.
