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.

This paper is concerned withm-ary communication channels(m \geq 2)having intersymbol interference betweenLtime periods(L \geq 2). Receiver structures are developed for making jointly optimum (minimum probability of error) decisions aboutLconsecutive symbols on the basis of the complete message received. The decision statistics are computed by a sequential procedure, and the number of computations increases only linearly with the message length. The method can be applied to the general problem of making decisions about the states of a discrete-state Markov information source which is observable only through a channel with additive Gaussian or non-Gaussian noise.

A Bayes approach to nonsupervised pattern recognition is given wheren l-dimensional vector samplesX_{1}, X_{2}, \cdots , X_{n}are received unclassified, i.e., any one ofMpattern sources\omega_{1}, \omega_{2}, \cdots, \omega_{M}, with corresponding probabilities of occurrenceQ_{1_{o}}, Q_{2_{o}} , \cdots , Q_{M_{o}}, caused each sampleX_{s}, s=1,2, \cdots , n. The approach utilizes the fact that the cumulative distribution function (c.d.f.) ofX_{s}is a mixture c.d.f.,F(X_{s})= \sum_{i=1}^{M} F(X_{s}|\omega_{i}) Q_{i_{o}}. It is assumed that available a priori knowledge includes knowledge ofMand the family\{F(X_{s}|\omega_{i})\}, whereF(X_{s}|\omega_{i})is characterized by a vectorB_{i_{o}}. In general,B_{i_{o}}andQ_{i_{o}}, i = 1,2, \cdots , Mare considered fixed but unknown, and conditional probability of error in deciding which source causedX_{n}is minimized. When the functional form ofF(X_{s}|\omega_{i})in terms ofB_{i_{o}}is unknown, the family\{F(X_{s}|\omega_{i})\}is taken to be the family of multinomial c.d.f.'s--an application of the histogram concept to the nonsupervisory problem. Additional nonparameteric a priori knowledge about the family--such asF(X_{s}|\omega_{i})is symmetrical, and/orF(X_{s}|\omega_{i})differs fromF(X_{s}|\omega_{j})only by a translational vector--can be utilized in the Bayes solution.

In this paper, coincidence detection procedures with invariant or distribution-free false alarm rates are proposed and investigated. The only information concerning the channel statistics required by these coincidence procedures is the median of the noise under no-signal conditions. The coincidence procedures are subsequently modified so that the detectors constitute learning systems with respect to time-varying and/or unknown medians. It is shown that their false alarm rates remain distribution free for wide classes of detection problems. The distribution-free coincidence detectors are then applied to various detection problems of practical importance, and their performance evaluated and compared to the performance of comparable likelihood detectors. It is shown that the distribution-free detectors are reasonably efficient, though suboptimal, for channels with Gaussian statistics, and highly efficient for channels with a combination of Gaussian and impulse noise.

This paper considers the problem of intersymbol interference in a binary communication system and the optimization of a class of linear receivers to minimize the effects of this interference. The class of correlation receivers is chosen for investigation, and maximizing the probability of correct reception is used as the performance criterion. The optimum decision level as well as optimum impulse response is determined for receivers with and without memory where a priori knowledge of the channel characteristics are available. The performances of these receivers are evaluated and compared with nonoptimum linear receivers.