An optimum decision-directed scheme for Gaussian mixtures

The problem of making measurements upon some available signal mixture in order to extract or estimate certain parametric data for subsequent signal detection using the measurement data is considered. The development is carried out for a formal binary signal observation mixture (no a priori classification of the observations into isolated category or class ensembles is assumed), with the parameters of the noise and pulse waveforms unknown. Two categories of multidimensional mixture-resolving estimators are treated: an optimized decision-directed category and a moment method category. In the former, the optimization is formulated to minimize a measure of distance and dispersion with a constraint adjustment to "maximize" a measure of convergence rate. An eigenvalue theory approach is applied to illustrate the relationship of the measurement data to the detector structure. An experimental case study is carried out via digital computer simulation, and a comparison of error probability performance characteristics with the conventional decision-directed and Bayes matched-filter techniques is made. Results of the simulation are presented which indicate quantitatively the superiority of the estimators over conventional decision-directed techniques, in terms of convergence rates and asymptotic performance characteristics.