Adaptive Signal Processing for Communications by Maximum Partial Likelihood Estimation

本研究旨在通过使用最大似然估计的最新扩展，最大部分似然（MPL）估计理论，开发用于通信非线性信号处理的统一统计框架，该理论允许依赖和缺失观测，以及仅使用处理时可用的信息对数据进行顺序处理。前人的研究为广义非线性概率模型的MPL估计的统计分析奠定了理论基础，并提供了非常有用的信息论联系。在框架中包含相关数据允许在存在内存源和信道的情况下解决编码和调制中的问题。本研究包括基于梯度优化和信息论交替投影的MPL估计的一种新型实时自适应信号处理算法的开发，并研究其统计和动态特性及其在特定通信应用中的实现，如长距离光纤通信中的均衡和可变速率语音编码中的浊音/浊音/过渡分类。研究的另一个重要部分是研究MPL框架内条件概率模型的选择，为此，分段线性模型与其他非线性模型（如多项式、有限正态混合和神经网络）一起，在非线性结构的近似能力与线性域的效率和理论可及性之间提供了一个非常理想的折衷方案，以开发新的自适应算法。从这项工作中产生的技术很可能通过具有优异性能的新算法在通信实时信号处理方面取得突破，并且通过严格处理潜在的相关时间序列问题，在通信非线性技术的一般理论中取得突破。

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.