This research aims at developing a unified statistical framework for nonlinear signal processing for communications by using a recent extension of maximum likelihood estimation, the maximum partial likelihood (MPL) estimation theory, which allows for dependent and missing observations, and sequential processing of data using only the information that is available at the time of processing. Previous research has established the theoretical foundation for the statistical analysis of MPL estimation with a general nonlinear probability model and provided a very useful information theoretic connection. The inclusion of the dependent data in the framework allows addressing of problems in coding and modulation in the presence of sources and channels with memory. This research includes development of a new class of realtime adaptive signal processing algorithms based on MPL estimation by using gradient optimization and information theoretic alternating projections, and the study of their statistical and dynamic properties and implementations in specific communications applications such as equalization in long distance optical fiber communications and voiced/unvoiced/transition classification in variable rate speech coding. Another important part of the effort is the investigation of the choices for the conditional probability model within the MPL framework, for which, along with other nonlinear models, such as polynomials, finite normal mixtures, and neural networks, piecewise linear models are used to provide a highly desirable compromise between the approximation ability of nonlinear structures and the efficiency and theoretical accessibility of the linear domain to develop new adaptive algorithms. The techniques which result from this work are very likely to lead to breakthroughs in realtime signal processing for communications via new algorithms with superior performances and in the general theory of nonlinear techniques in communications via rigorous treatment of t he underlying dependent time series problems.
